+
    ‰°³jm  ã                   óØ   € ^ RI 5 ^ RIHtHtHt R tR tR tR tR t	R t
R	 tR
 tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR t R t!R  t"R!# )"é    )Ú*)Úround_upÚ
from_floatÚmpf_zeta_intc                  ó>   € \        ^ ^
4      \        R4      8X  g   Q hR# )r   Nç      à¿)r   r   © ó    Ú\/home/luca/screen-checking/.venv/lib/python3.14/site-packages/mpmath/tests/test_gammazeta.pyÚtest_zeta_int_bugr      s   € Ü˜˜2Ó¤*¨TÓ"2Ô2Ð2Ò2r
   c                  ól  € \        ^ 4      R8X  g   Q h\        ^4      R8X  g   Q h\        ^4      R8X  g   Q h\        ^4      R8X  g   Q h\        ^4      R8X  g   Q h\        ^4      R8X  g   Q h\        ^4      R8X  g   Q h\        ^4      R8X  g   Q h\        ^
4      R8X  g   Q h\        ^4      R8X  g   Q h\        ^4      R8X  g   Q h\        ^ä4      w  rV R,          R8X  g   Q hVR8X  g   Q h\        R4      w  rV R,          R8X  g   Q hVR8X  g   Q h^\        n        \        ^ 4      ^8X  g   Q h\        ^4      R8X  g   Q h\        ^4      P	                  R4      '       g   Q h\        ^4      ^ 8X  g   Q h\        ^4      P	                  R4      '       g   Q h\        ^4      ^ 8X  g   Q h\        ^4      P	                  R4      '       g   Q h\        \        ^
4      4      R8X  g   Q h\        \        ^ê4      4      R8X  g   Q h\        \        R4      4      R8X  g   Q h\        \        R4      4      R	8X  g   Q h^2\        n        \        \        ^
4      4      R
8X  g   Q h\        \        ^ê4      4      R8X  g   Q h\        \        R4      4      R8X  g   Q h\        \        R4      4      R8X  g   Q hR\        n        \        ^
4      P	                  \        ^4      ^B,          4      '       g   Q hR\        n        \        ^
4      P	                  \        ^4      ^B,          4      '       g   Q h^\        n        R# ) r   i‘sÔ	iŠ	 éè  l   kLÃ3 iö¿qz0.0757575757575758z7.62772793964344e+267z-5.82229431461335e+376755z1.19570355039953e+676752584z50.075757575757575757575757575757575757575757575757576z87.6277279396434392486994969020496121553385863373331e+267z<-5.8222943146133508236497045360612887555320691004308e+376755z>1.1957035503995297272263047884604346914602088317782e+676752584iPÃ  N)é   r   )éÿÿÿÿé   )r   é   )r   r   )r   é   )r   é*   )é   éB   )iMýÿÿiª
  )i[«  i  ì    d(	 r   gUUUUUUÅ?g¡¿g†a†a˜?é † iáõ)ÚbernfracÚmpÚdpsÚ	bernoulliÚaeÚstrÚmpf)ÚpÚqs     r   Útest_bernoullir"      sÚ  € Ü�A‹;˜%ÔÐÐÜ�A‹;˜&Ô Ð Ð Ü�A‹;˜%ÔÐÐÜ�A‹;˜%ÔÐÐÜ�A‹;˜'Ô!Ð!Ð!Ü�A‹;˜%ÔÐÐÜ�A‹;˜&Ô Ð Ð Ü�A‹;˜'Ô!Ð!Ð!Ü�B‹<˜6Ô!Ð!Ð!Ü�B‹<˜;Ô&Ð&Ð&Ü�B‹<˜;Ô&Ð&Ð&Ü�C‹=�D€AØˆv�:˜Ô"Ð"Ð"Ø�Œ;Ðˆ;Ü�D‹>�D€AØˆv�:˜Ô#Ð#Ð#Ø�	Œ>Ðˆ>Ø„B„FÜ�Q‹<˜1ÔÐÐÜ�Q‹<˜4ÔÐÐÜ�Q‹<�?‰?˜4× Ò Ð Ð Ü�Q‹<˜1ÔÐÐÜ�Q‹<�?‰?˜6×"Ò"Ð"Ð"Ü�Q‹<˜1ÔÐÐÜ�Q‹<�?‰?˜5×!Ò!Ð!Ð!ÜŒy˜‹}ÓÐ!5Ô5Ð5Ð5ÜŒy˜‹~ÓÐ"9Ô9Ð9Ð9ÜŒy˜ÓÓ Ð$?Ô?Ð?Ð?ÜŒy˜Ó!Ó"Ð&CÔCÐCÐCà„B„FÜŒy˜‹}ÓÐ!XÔXÐXÐXÜŒy˜‹~ÓÐ"\Ô\Ð\Ð\ÜŒy˜ÓÓ Ð$bÔbÐbÐbÜŒy˜Ó!Ó"Ð&fÔfÐfÐfà„B„FÜ�R‹=×ÑœC ›F 2�I×&Ò&Ð&Ð&à„B„FÜ�R‹=×ÑœC ›F 2�I×&Ò&Ð&Ð&à„B†Fr
   c                  ó.  € ^\         n        \        ^ R*4      P                  ^4      '       g   Q h\        ^ ^ 4      P                  ^4      '       g   Q h\        ^ R4      P                  ^4      '       g   Q h\        ^ R4      P                  ^4      '       g   Q h\        ^ ^4      P                  ^4      '       g   Q h\        ^ ^4      P                  ^4      '       g   Q h\        ^R*4      P                  R4      '       g   Q h\        ^^ 4      P                  R4      '       g   Q h\        ^R4      P                  ^ 4      '       g   Q h\        ^R4      P                  R4      '       g   Q h\        ^^4      P                  R4      '       g   Q h\        ^^4      P                  R4      '       g   Q h\        ^R*4      P                  R4      '       g   Q h\        ^^ 4      P                  R4      '       g   Q h\        ^R4      P                  R	4      '       g   Q h\        ^R4      P                  R
4      '       g   Q h\        ^^4      P                  R4      '       g   Q h\        ^^4      P                  R4      '       g   Q h\        ^R*4      P                  R+4      '       g   Q h\        ^^ 4      P                  ^ 4      '       g   Q h\        ^R4      P                  ^ 4      '       g   Q h\        ^R4      P                  R4      '       g   Q h\        ^^4      P                  ^ 4      '       g   Q h\        ^^4      P                  ^4      '       g   Q h\        ^R*4      P                  R4      '       g   Q h\        ^^ 4      P                  R4      '       g   Q h\        ^R4      P                  R4      '       g   Q h\        ^R4      P                  R4      '       g   Q h\        ^^4      P                  R4      '       g   Q h\        ^^4      P                  R4      '       g   Q h\        ^R*4      P                  R,4      '       g   Q h\        ^^ 4      P                  ^ 4      '       g   Q h\        ^R4      P                  ^ 4      '       g   Q h\        ^R4      P                  R4      '       g   Q h\        ^^4      P                  ^ 4      '       g   Q h\        ^^4      P                  ^4      '       g   Q h\        ^
R*4      P                  R4      '       g   Q h\        ^
^ 4      P                  R4      '       g   Q h\        ^
R4      P                  R4      '       g   Q h\        ^
R4      P                  R4      '       g   Q h\        ^
^4      P                  R4      '       g   Q h\        ^
^4      P                  R4      '       g   Q h\        ^R*4      P                  R-4      '       g   Q h\        ^^ 4      P                  ^ 4      '       g   Q h\        ^R4      P                  ^ 4      '       g   Q h\        ^R4      P                  R4      '       g   Q h\        ^^4      P                  ^ 4      '       g   Q h\        ^^4      P                  ^4      '       g   Q h\	        ^ R*4      P                  ^4      '       g   Q h\	        ^ ^ 4      P                  ^4      '       g   Q h\	        ^ R4      P                  ^4      '       g   Q h\	        ^ R4      P                  ^4      '       g   Q h\	        ^ ^4      P                  ^4      '       g   Q h\	        ^ ^4      P                  ^4      '       g   Q h\	        ^R*4      P                  R4      '       g   Q h\	        ^^ 4      P                  R4      '       g   Q h\	        ^R4      P                  ^ 4      '       g   Q h\	        ^R4      P                  R4      '       g   Q h\	        ^^4      P                  R4      '       g   Q h\	        ^^4      P                  R4      '       g   Q h\	        ^R*4      P                  ^4      '       g   Q h\	        ^^ 4      P                  ^ 4      '       g   Q h\	        ^R4      P                  R4      '       g   Q h\	        ^R4      P                  R4      '       g   Q h\	        ^^4      P                  ^ 4      '       g   Q h\	        ^^4      P                  ^4      '       g   Q h\	        ^R*4      P                  R4      '       g   Q h\	        ^^ 4      P                  R4      '       g   Q h\	        ^R4      P                  ^ 4      '       g   Q h\	        ^R4      P                  R4      '       g   Q h\	        ^^4      P                  R4      '       g   Q h\	        ^^4      P                  R4      '       g   Q h\	        ^R*4      P                  ^4      '       g   Q h\	        ^^ 4      P                  ^ 4      '       g   Q h\	        ^R4      P                  R4      '       g   Q h\	        ^R4      P                  R4      '       g   Q h\	        ^^4      P                  ^ 4      '       g   Q h\	        ^^4      P                  ^4      '       g   Q h\	        ^R*4      P                  R4      '       g   Q h\	        ^^ 4      P                  R4      '       g   Q h\	        ^R4      P                  ^ 4      '       g   Q h\	        ^R4      P                  R4      '       g   Q h\	        ^^4      P                  R4      '       g   Q h\	        ^^4      P                  R4      '       g   Q h\	        ^
R*4      P                  ^4      '       g   Q h\	        ^
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R4      P                  R4      '       g   Q h\	        ^
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^4      P                  ^4      '       g   Q h\	        ^R*4      P                  R 4      '       g   Q h\	        ^^ 4      P                  R!4      '       g   Q h\	        ^R4      P                  ^ 4      '       g   Q h\	        ^R4      P                  R"4      '       g   Q h\	        ^^4      P                  R#4      '       g   Q h\	        ^^4      P                  R$4      '       g   Q h\        R%R%4      P                  R&4      '       g   Q h\        ^ÈR'4      P                  R(4      '       g   Q h\	        ^ÈR'4      P                  R.4      '       g   Q hR)# )/é   z1/2z3/4z-3/2z-1/2z1/4z3/2z13/6z1/6z-1/12z-1/48z-3/64z119/30z-1/30z7/240z7/3840z25/1024z665/66z5/66z-2555/33792z-2555/34603008z-555731/4194304z-1/4z-3/16z-9/4z-11/64z9/4z5/16z57/256z361/1024z-50521/1024z-36581523/1048576z-699/4z691/4z-512343611/4194304z-691/4z699/4é'  z5.8196915936323387117e+39999g     €1@g€ÙÂôJ¶rNr   éýÿÿÿéûÿÿÿéõÿÿÿg,ŸQr�%ù)r   r   Úbernpolyr   Ú	eulerpolyr	   r
   r   Útest_bernpoly_eulerpolyr+   4   sl  € Ø„B„FÜ�A�b‹>×Ñ˜Q×ÒÐÐÜ�A�a‹=×Ñ˜A×ÒÐÐÜ�A�eÓ×Ñ ×"Ò"Ð"Ð"Ü�A�eÓ×Ñ ×"Ò"Ð"Ð"Ü�A�a‹=×Ñ˜A×ÒÐÐÜ�A�a‹=×Ñ˜A×ÒÐÐÜ�A�b‹>×Ñ˜V×$Ò$Ð$Ð$Ü�A�a‹=×Ñ˜F×#Ò#Ð#Ð#Ü�A�eÓ×Ñ ×"Ò"Ð"Ð"Ü�A�eÓ×Ñ ×&Ò&Ð&Ð&Ü�A�a‹=×Ñ˜E×"Ò"Ð"Ð"Ü�A�a‹=×Ñ˜E×"Ò"Ð"Ð"Ü�A�b‹>×Ñ˜V×$Ò$Ð$Ð$Ü�A�a‹=×Ñ˜E×"Ò"Ð"Ð"Ü�A�eÓ×Ñ ×(Ò(Ð(Ð(Ü�A�eÓ×Ñ ×(Ò(Ð(Ð(Ü�A�a‹=×Ñ˜E×"Ò"Ð"Ð"Ü�A�a‹=×Ñ˜F×#Ò#Ð#Ð#Ü�A�b‹>×Ñ˜R× Ò Ð Ð Ü�A�a‹=×Ñ˜A×ÒÐÐÜ�A�eÓ×Ñ ×"Ò"Ð"Ð"Ü�A�eÓ×Ñ ×(Ò(Ð(Ð(Ü�A�a‹=×Ñ˜A×ÒÐÐÜ�A�a‹=×Ñ˜A×ÒÐÐÜ�A�b‹>×Ñ˜X×&Ò&Ð&Ð&Ü�A�a‹=×Ñ˜G×$Ò$Ð$Ð$Ü�A�eÓ×Ñ ×(Ò(Ð(Ð(Ü�A�eÓ×Ñ ×)Ò)Ð)Ð)Ü�A�a‹=×Ñ˜G×$Ò$Ð$Ð$Ü�A�a‹=×Ñ˜H×%Ò%Ð%Ð%Ü�A�b‹>×Ñ˜R× Ò Ð Ð Ü�A�a‹=×Ñ˜A×ÒÐÐÜ�A�eÓ×Ñ ×"Ò"Ð"Ð"Ü�A�eÓ×Ñ 	×*Ò*Ð*Ð*Ü�A�a‹=×Ñ˜A×ÒÐÐÜ�A�a‹=×Ñ˜A×ÒÐÐÜ�B�r‹?×Ñ˜h×'Ò'Ð'Ð'Ü�B�q‹>×Ñ˜V×$Ò$Ð$Ð$Ü�B�uÓ× Ñ  ×/Ò/Ð/Ð/Ü�B�uÓ× Ñ Ð!1×2Ò2Ð2Ð2Ü�B�q‹>×Ñ˜V×$Ò$Ð$Ð$Ü�B�q‹>×Ñ˜X×&Ò&Ð&Ð&Ü�B�r‹?×Ñ˜c×"Ò"Ð"Ð"Ü�B�q‹>×Ñ˜Q×ÒÐÐÜ�B�uÓ× Ñ  ×#Ò#Ð#Ð#Ü�B�uÓ× Ñ Ð!2×3Ò3Ð3Ð3Ü�B�q‹>×Ñ˜Q×ÒÐÐÜ�B�q‹>×Ñ˜R× Ò Ð Ð Ü�Q�r‹?×Ñ˜a× Ò Ð Ð Ü�Q�q‹>×Ñ˜Q×ÒÐÐÜ�Q�uÓ× Ñ  ×#Ò#Ð#Ð#Ü�Q�uÓ× Ñ  ×#Ò#Ð#Ð#Ü�Q�q‹>×Ñ˜Q×ÒÐÐÜ�Q�q‹>×Ñ˜Q×ÒÐÐÜ�Q�r‹?×Ñ˜f×%Ò%Ð%Ð%Ü�Q�q‹>×Ñ˜V×$Ò$Ð$Ð$Ü�Q�uÓ× Ñ  ×#Ò#Ð#Ð#Ü�Q�uÓ× Ñ  ×'Ò'Ð'Ð'Ü�Q�q‹>×Ñ˜U×#Ò#Ð#Ð#Ü�Q�q‹>×Ñ˜U×#Ò#Ð#Ð#Ü�Q�r‹?×Ñ˜a× Ò Ð Ð Ü�Q�q‹>×Ñ˜Q×ÒÐÐÜ�Q�uÓ× Ñ  ×(Ò(Ð(Ð(Ü�Q�uÓ× Ñ  ×)Ò)Ð)Ð)Ü�Q�q‹>×Ñ˜Q×ÒÐÐÜ�Q�q‹>×Ñ˜Q×ÒÐÐÜ�Q�r‹?×Ñ˜f×%Ò%Ð%Ð%Ü�Q�q‹>×Ñ˜U×#Ò#Ð#Ð#Ü�Q�uÓ× Ñ  ×#Ò#Ð#Ð#Ü�Q�uÓ× Ñ  ×*Ò*Ð*Ð*Ü�Q�q‹>×Ñ˜V×$Ò$Ð$Ð$Ü�Q�q‹>×Ñ˜U×#Ò#Ð#Ð#Ü�Q�r‹?×Ñ˜a× Ò Ð Ð Ü�Q�q‹>×Ñ˜Q×ÒÐÐÜ�Q�uÓ× Ñ  ×(Ò(Ð(Ð(Ü�Q�uÓ× Ñ  ×*Ò*Ð*Ð*Ü�Q�q‹>×Ñ˜Q×ÒÐÐÜ�Q�q‹>×Ñ˜Q×ÒÐÐÜ�Q�r‹?×Ñ˜f×%Ò%Ð%Ð%Ü�Q�q‹>×Ñ˜V×$Ò$Ð$Ð$Ü�Q�uÓ× Ñ  ×#Ò#Ð#Ð#Ü�Q�uÓ× Ñ  ×,Ò,Ð,Ð,Ü�Q�q‹>×Ñ˜U×#Ò#Ð#Ð#Ü�Q�q‹>×Ñ˜U×#Ò#Ð#Ð#Ü�R˜Ó×Ñ˜q×!Ò!Ð!Ð!Ü�R˜‹?×Ñ˜a× Ò Ð Ð Ü�R˜Ó×!Ñ! -×0Ò0Ð0Ð0Ü�R˜Ó×!Ñ!Ð"5×6Ò6Ð6Ð6Ü�R˜‹?×Ñ˜a× Ò Ð Ð Ü�R˜‹?×Ñ˜a× Ò Ð Ð Ü�R˜Ó×Ñ˜x×(Ò(Ð(Ð(Ü�R˜‹?×Ñ˜g×&Ò&Ð&Ð&Ü�R˜Ó×!Ñ! !×$Ò$Ð$Ð$Ü�R˜Ó×!Ñ!Ð"6×7Ò7Ð7Ð7Ü�R˜‹?×Ñ˜h×'Ò'Ð'Ð'Ü�R˜‹?×Ñ˜g×&Ò&Ð&Ð&ä�E˜%Ó ×#Ñ#Ð$B×CÒCÐCÐCÜ�C˜Ó× Ñ Ð!:×;Ò;Ð;Ð;Ü�S˜Ó×!Ñ!Ð"<×=Ò=Ð=Ò=r
   c                  ó  € ^\         n        \        R4      P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h^p \	        ^^4       F  p\        V4      V 8X  g   Q hW,          p K  	  R F=  p^p V\         n        \	        ^^i4       F  p\        V4      V 8X  g   Q hW,          p K  	  K?  	  ^d\         n        \        R4      P                  \        \        4      4      '       g   Q h^\         n        \        ^ 4      \        ^ 4      u;8X  d	   ^8X  g   Q h Q h\        ^4      ^8X  g   Q h\        \        \        4      4      '       g   Q h\        R	4      P                  R
4      '       g   Q h\        ^ 4      ^ 8X  g   Q h\        R4      ^ 8X  g   Q h\        ^4      R8X  g   Q h\        ^4      R8X  g   Q h\        R4      P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h\        R4      P                  \        RR4      4      '       g   Q hR# )r$   ç      Ð?gêî~Ä?@ç-Cëâ6?gí¨	!¶‡Ã@i,  z1.0201917073881354535e612ç      à?gf<9b1?éL  z4.8579168073569433667e2866g      ð?Ú1e10000z 2.302485092994045684017991e10004Ú1e10000jz!-1.570796326794896619231322e10000Nr   gkï´‘ø[Àg¸…ëQ¸Ày      ð?      ð?y±Ý}ßß?'Þ‰^eÕÃ¿r   y      ð¿{®Gáz„?yT})�Û¿Of[µÿX@y      4@      >@y<lãsªÕÁîfs¼uWÑA)éª   iX  y       @       @yaañJ�
!Àz…ÛÂ¶%@)r   r   Úgammar   ÚrangeÚsqrtÚpiÚ	factorialÚfacÚisnanÚnanÚrgammaÚloggammaÚmpc)ÚfactÚir   s      r   Ú
test_gammarA   ›   sƒ  € Ø„B„FÜ�‹;�>‰>Ð/×0Ò0Ð0Ð0Ü�‹=×ÑÐ1×2Ò2Ð2Ð2Ü�‹:�=‰=Ð4×5Ò5Ð5Ð5Ü�‹;�>‰>Ð0×1Ò1Ð1Ð1Ü�‹<�?‰?Ð4×5Ò5Ð5Ð5ô �‹;�>‰>ÐJ×KÒKÐKÐKÜ�‹?×ÑÐL×MÒMÐMÐMÜ�‹=×ÑÐE×FÒFÐFÐFð €DÜ�1�bŽ\ˆÜ�Q‹x˜4ÔÐÐØ�	Šñ ó ˆØˆØŒŒÜ�q˜#–ˆAÜ˜“8˜tÔ#Ð#Ð#Ø�IŠDó ñ ð „B„FÜ�‹:�=‰=œœb›×"Ò"Ð"Ð"Ø„B„FÜ�Q‹<œ3˜q›6Ö& QÔ&Ð&Ñ&Ð&Ð&Ü�Q‹<˜1ÔÐÐÜ””s“×ÒÐÐÜ�‹;�>‰>Ð6×7Ò7Ð7Ð7Ü�!‹9˜Œ>Ðˆ>Ü�"‹:˜Œ?Ðˆ?Ü�!‹9˜ÔÐÐÜ�!‹9˜ÔÐÐÜ�D‹>×ÑÐM×NÒNÐNÐNÜ�IÓ×!Ñ!Ð"D×EÒEÐEÐEÜ�JÓ×"Ñ"¤3Ð'JÐKmÓ#n×oÒoÐoÒor
   c                  ó  € ^\         n        \        ^
4       U u. uF  p \        V 4      NK  	  up . RO8X  g   Q h\        R4      P	                  R4      '       g   Q h\        R4      P	                  R4      '       g   Q h\        ^24      P	                  R4      '       g   Q h\        R4      P	                  R	4      '       g   Q h\        \
        4      \
        8X  g   Q h\        \        \
        ) 4      4      '       g   Q hR# u up i )
r$   g!a?Ã@©¹FN)
r   r   r   é   é   r$   é0   éi   i€  i±  r'   gUUUUUUÕ?r(   gg¼jVQ¿y      à?      è?yÓHŽ´Oê?j6¶¶.VÖ¿)r   r   r5   Úfac2r   Úinfr:   )Úns    r   Ú	test_fac2rJ   Â   sÅ   € Ø„B„FÜ" 2œYÓ'™Y˜ŒD�ŽG™YÑ'Ò+HÔHÐHÐHÜ�‹8�;‰;�t×ÒÐÐÜ�‹9�<‰<˜× Ò Ð Ð Ü�‹8�;‰;Ð-×.Ò.Ð.Ð.Ü�	‹?×ÑÐL×MÒMÐMÐMÜ”‹9œÔÐÐÜ””s�d“×ÒÐÒùò (s   ™C>c                  óP
  € ^\         n        Rp Rp\        p\        R.RR.4      ^ 8X  g   Q h\        R^ .R.4      \        8X  g   Q h\        \        R.R.4      V! RV ,           4      V! RV ,           4      ,          ,
          4      R8  g   Q h\        \        RR.R^ .4      V! RV ,           4      V! RV ,           4      ,          V! RV ,           4      ,          V! ^ V ,           4      ,          ,
          4      R8  g   Q h\        ^^ 4      ^8X  g   Q h\        R^4      R8X  g   Q h\        R^4      ^8X  g   Q h\        \        \        4      P                  \        ^\        ,          4      \        \        4      ,          4      '       g   Q h\        RR4      P                  R4      '       g   Q h\        R^ 4      ^8X  g   Q h\        R^4      R8X  g   Q h\        ^^4      ^8X  g   Q h\        ^^4      ^ 8X  g   Q h\        ^ ^ 4      ^8X  g   Q h\        ^^ 4      ^8X  g   Q h\        ^ R4      ^ 8X  g   Q h\        ^^4      ^8X  g   Q h\        ^^4      ^
8X  g   Q h\        ^^4      ^
8X  g   Q h\        ^^4      ^8X  g   Q h\        R^ 4      ^8X  g   Q h\        RR4      ^8X  g   Q h\        RR4      R	8X  g   Q h\        R
^4      R
8X  g   Q h\        R
^4      R8X  g   Q h\        ^^4      ^8X  g   Q h\        ^ ^ 4      \        8X  g   Q h\        ^^ 4      \        8X  g   Q h\        RR4      \        8X  g   Q h\        R^4      P                  R4      '       g   Q h\        RR4      P                  \        ^,          4      '       g   Q hR\        ^
^d4      ,          P                  R4      '       g   Q h\        \        \        4      ^ 8X  g   Q h\        \        \        ) \        4      4      '       g   Q h\        \        R\        4      4      '       g   Q h\        \        ^ \        4      4      '       g   Q h\        \        R4      \        R\        4      u;8X  d	   ^ 8X  g   Q h Q h\        \        R4      \        8X  g   Q h\        \        R4      \        ) 8X  g   Q h\        RR\        ^,          ,
          4      P                  R4      '       g   Q h\        RR4      ^ 8X  g   Q h\        R^4      P                  R4      '       g   Q h\        RR4      P                  R4      '       g   Q hR# )r$   g:Œ0âŽyE>r.   g      @z-255.5815971722918z-0.5119253100282322z-0.1952720278805729485g      @ç      ø?g     @@r0   i"9	 gr‰îP§Ã@r/   z18.157330562703710339Nr   r&   éüÿÿÿr'   éþÿÿÿgUUUUUUå?l     �Iú5 ç      ø¿r   ù      ð?       @yß+5šŸò?Œ\K�9Êµ?gUUUUUUÕ¿)r   r   r4   Ú	gammaprodrH   ÚabsÚrfÚjr   ÚffÚbinomialÚbetar7   r:   )ÚhÚepÚGs      r   Útest_gamma_quotientsr[   Ì   sh  € Ø„B„FØ€AØ	€BÜ€AÜ�b�T˜2˜b˜'Ó" aÔ'Ð'Ð'Ü�b˜�V˜R˜DÓ!¤SÔ(Ð(Ð(ÜŒy˜"˜˜r˜dÓ#¡a¨¨1­£g©a°°1µ«g¥oÕ5Ó6¸Ô=Ð=Ð=ÜŒy˜"˜R˜ " Q Ó(©1¨R°­T«7±1°R¸µT³7­?¹1¸RÀ½T»7Õ+BÁ1ÀQÀqÅSÃ6Õ+IÕIÓJÈTÔQÐQÐQÜˆa�‹7�aŒ<Ðˆ<Üˆc�!‹9˜ÔÐÐÜˆb�‹8�rŒ>Ðˆ>ÜŒa”‹7�:‰:”e˜Aœa�C“j¤¤q£Õ)×*Ò*Ð*Ð*ÜÐ"Ð#8Ó9×<Ñ<Ð=U×VÒVÐVÐVÜˆb�‹8�qŒ=Ðˆ=Üˆb�‹8�rŒ>Ðˆ>Üˆa�‹7�bŒ=Ðˆ=Üˆa�‹7�aŒ<Ðˆ<Ü�A�a‹=˜AÔÐÐÜ�A�a‹=˜AÔÐÐÜ�A�b‹>˜QÔÐÐÜ�A�a‹=˜AÔÐÐÜ�A�a‹=˜BÔÐÐÜ�A�a‹=˜BÔÐÐÜ�A�a‹=˜AÔÐÐÜ�B�q‹>˜QÔÐÐÜ�B�r‹?˜aÔÐÐÜ�C˜Ó Ô'Ð'Ð'Ü�D˜Ó˜tÔ#Ð#Ð#Ü�D˜Ó˜vÔ%Ð%Ð%Ü��!‹9˜Œ>Ðˆ>Ü��!‹9œÔÐÐÜ��!‹9œÔÐÐÜ��2‹;œ#ÔÐÐÜ��A‹;�>‰>˜$×ÒÐÐÜ��C‹=×ÑœB˜r�E×"Ò"Ð"Ð"Ø”4˜˜3“<Õ×#Ñ#Ð$9×:Ò:Ð:Ð:Ü””C‹=˜AÔÐÐÜ””s�dœ3“× Ò Ð Ð Ü”�bœ“×ÒÐÐÜ”�aœ“×ÒÐÐÜ”�C‹=œD ¤S›MÖ.¨QÔ.Ð.Ñ.Ð.Ð.Ü”�D‹>œSÔ Ð Ð Ü”�D‹>œc˜TÔ!Ð!Ð!Ü��Rœ˜!�•VÓ×ÑÐ N×OÒOÐOÐOÜ��S‹>˜QÔÐÐÜ��1‹:�=‰=˜×ÒÐÐÜÐ$Ð%:Ó;×>Ñ>Ð?V×WÒWÐWÒWr
   c                  ó¬  € ^\         n        \        ^4      P                  \        ^,          ^,          4      '       g   Q h\        R4      P                  \        ^,          ^,          4      '       g   Q h\        \        ^4      4      P                  \        ^,          ^,          4      '       g   Q h\        ^d4      P                  ^4      '       g   Q h\        ^ 4      P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h\        R4      P                  \        ^4      ) ^,          4      '       g   Q h\        R4      ^ 8X  g   Q h\        R4      P                  \        ^4      ^x,          4      '       g   Q h\        R4      ^ 8X  g   Q h\        R4      ^ 8X  g   Q h\        \        \        4      4      '       g   Q h\        R4      P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h\        \        RR4      4      P                  ^ 4      '       g   Q h\        \        RR4      4      P                  ^ 4      '       g   Q h\        \        RR4      4      P                  ^ 4      '       g   Q h\        \        RR4      4      P                  R4      '       g   Q h\        \        RR4      4      P                  R4      '       g   Q h^2\         n        Rp \        \        RV 4      4      P                  ^ R	4      '       g   Q h^\         n        \        R4      ^
^",          ,          P                  R4      '       g   Q h\        ^ R4      ^ 8X  g   Q h\        ^ ^ 4      R8X  g   Q h\        ^ R^4      P                  R4      '       g   Q h\        RR
4      P                  R4      '       g   Q hR# )r$   g       @r/   ç ÂëþKH´9g"f›±úD,@gO½Çc¤5@g²£÷�Ç9@çœWw'&l¡7z8236.5242296658162058024755079556629786895294952121891237gaU,$ÎDb6y              à?Nr   gÿs~°œ]÷¿r   rN   r&   rM   éœÿÿÿç ÂëþKH´¹y      NÀ      @y¾Ž9ŽA!@û²¤€¿¬.@gï9úþB.Ö¿rO   y³Nñ*ØÁ¿iÐÎˆ6½?)	r   r   Úzetar   r7   r>   r   r:   r;   )Úims    r   Ú	test_zetarc   ý   sè  € Ø„B„FÜ�‹7�:‰:”b˜!•e˜a•i× Ò Ð Ð Ü�‹9�<‰<œ˜A� �	×"Ò"Ð"Ð"Ü”�A“‹<�?‰?œ2˜q�5 1�9×%Ò%Ð%Ð%Ü�‹9�<‰<˜�?Š?Ðˆ?Ü�‹7�:‰:�d×ÒÐÐÜ�‹9�<‰<Ð,×-Ò-Ð-Ð-Ü�‹8�;‰;œ˜A›�w˜r•z×"Ò"Ð"Ð"Ü�‹8�qŒ=Ðˆ=Ü�‹8�;‰;”s˜1“v˜c•z×"Ò"Ð"Ð"Ü�‹8�qŒ=Ðˆ=Ü�‹:˜Œ?Ðˆ?Ü””c“×ÒÐÐÜ�‹;�>‰>˜$×ÒÐÐÜ�‹<�?‰?˜4× Ò Ð Ð ä”�CÐ/Ó0Ó1×4Ñ4°Q×7Ò7Ð7Ð7Ü”�CÐ/Ó0Ó1×4Ñ4°Q×7Ò7Ð7Ð7Ü”�CÐ/Ó0Ó1×4Ñ4°Q×7Ò7Ð7Ð7Ü”�E˜%Ó Ó!×$Ñ$ T×*Ò*Ð*Ð*Ü”�F˜5Ó!Ó"×%Ñ% d×+Ò+Ð+Ð+Ø„B„FØ	C€BÜ”�C˜“Ó× Ñ   E×*Ò*Ð*Ð*Ø„B„Fä�‹L˜2˜r�6Õ!×%Ñ%Ð&L×MÒMÐMÐMä��#‹;˜!ÔÐÐÜ��!‹9˜ÔÐÐÜ��#�a‹=×ÑÐ0×1Ò1Ð1Ð1ä��T‹?×ÑÐO×PÒPÐPÒPr
   c                  óN  € ^\         n        \        R4      ^ 8X  g   Q h\        R4      ^ 8X  g   Q h\        R4      ^ 8X  g   Q h\        ^ 4      R8X  g   Q h\        R4      R8X  g   Q h\        R4      R8X  g   Q h\        R4      R8X  g   Q h\        R4      R8X  g   Q h\        ^4      P                  \	        ^4      4      '       g   Q h\        ^4      P                  \
        ^,          ^,          4      '       g   Q h\        ^
4      P                  ^I\
        ^
,          ,          R,          4      '       g   Q h\        ^24      ^8  g   Q h\        ^<RR7      ^8  g   Q h\        ^<RR7      ^8X  g   Q h\        RRR7      ^8  g   Q h\        RRR7      ^8X  g   Q h\        R4      \        ^4      8X  g   Q hRp \        V 4      P                  ^^^V ,
          ,          ,
          \        V 4      ,          4      '       g   Q hRp \        V 4      P                  ^^^V ,
          ,          ,
          \        V 4      ,          4      '       g   Q h\        R4      P                  R	4      '       g   Q h\        R
4      P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h\        \        RR4      4      P                  R4      '       g   Q h\        \        RR4      4      P                  R4      '       g   Q hR# )r$   r/   r-   g  �z\—ÑAi jh Úd©ÚroundingÚur%   g¨@o“.>VgÍÌÌÌÌÌô?g^©sŸç?r]   r^   NrN   rM   r_   r   r&   g      À¿r'   iëÿÿÿù      @        ù      @      @y      À      @ç      YÀr`   )r   r   Úaltzetar   Úlogr7   ra   r>   )Úss    r   Útest_altzetaro      s�  € Ø„B„FÜ�2‹;˜!ÔÐÐÜ�2‹;˜!ÔÐÐÜ�4‹=˜AÔÐÐÜ�1‹:˜ÔÐÐÜ�2‹;˜$ÔÐÐÜ�2‹;˜&Ô Ð Ð Ü�2‹;˜$ÔÐÐÜ�3‹<˜=Ô(Ð(Ð(Ü�1‹:�=‰=œ˜Q›× Ò Ð Ð Ü�1‹:�=‰=œ˜Q�˜r�×"Ò"Ð"Ð"Ü�2‹;�>‰>˜"œR �V�) GÕ+×,Ò,Ð,Ð,Ü�2‹;˜Œ?Ðˆ?Ü�2 Ô$ qÔ(Ð(Ð(Ü�2 Ô$¨Ô)Ð)Ð)Ü�5 3Ô'¨!Ô+Ð+Ð+Ü�5 3Ô'¨1Ô,Ð,Ð,Ü�4‹=œG A›JÔ&Ð&Ð&Ø€AÜ�1‹:�=‰=˜!˜A  !¥�H�*¤d¨1£gÕ-×.Ò.Ð.Ð.Ø€AÜ�1‹:�=‰=˜!˜A  !¥�H�*¤d¨1£gÕ-×.Ò.Ð.Ð.Ü�6‹?×ÑÐ6×7Ò7Ð7Ð7Ü�3‹<�?‰?Ð.×/Ò/Ð/Ð/Ü�5‹>×Ñ˜S×!Ò!Ð!Ð!Ü�6‹?×Ñ˜c×"Ò"Ð"Ð"Ü”3�u˜UÓ#Ó$×'Ñ'¨×,Ò,Ð,Ð,Ü”3�v˜eÓ$Ó%×(Ñ(¨×-Ò-Ð-Ò-r
   c                  óD  € ^\         n        \        \        4      ^8X  g   Q h^2\         n        \        ^d4      P	                  R4      '       g   Q h\        ^(\
        ,          4      P	                  R4      '       g   Q hR\         n        \        R4      p ^\         n        \        V ^,
          4      R8X  g   Q h\        \
        R,          \        R7      ^8”  g   Q h\        R\        R7      ^8”  g   Q h\        \
        R,          4      ^8X  g   Q h\        R4      ^8X  g   Q hR	# )
r$   z61.0000000000000000000000000000007888609052210118073522z61.0000000000000000000000000000000000000148407238666182r%   iè€  z1.02363019598118e-9934r   rf   i¸  N)r   r   ra   rH   r   r7   r   r   )Úvs    r   Útest_zeta_hugerr   >  sÚ   € Ø„B„FÜ”‹9˜Œ>Ðˆ>Ø„B„FÜ�‹9�<‰<ÐP×QÒQÐQÐQÜ�”2•‹;�>‰>ÐR×SÒSÐSÐSØ„B„FÜˆU‹€AØ„B„FÜˆq��s‹8Ð/Ô/Ð/Ð/Ü”�4•¤(Ô+¨aÔ/Ð/Ð/Ü�œxÔ(¨1Ô,Ð,Ð,Ü”�4•‹=˜AÔÐÐÜ�‹:˜Œ?ÐŠ?r
   c                  óô   € ^–\         n        \        ) ^
^(,          ,          p ^\         n        \        \	        V 4      4      R8X  g   Q h^2\         n        \        \	        V 4      4      R8X  g   Q h^\         n        R# )é–   z=2.55880492708712e+1233536161668617575553892558646631323374078z`2.5588049270871154960875033337384432038436330847333e+1233536161668617575553892558646631323374078N)r   r   r7   r   ra   )Úas    r   Útest_zeta_negativerv   M  s[   € Ø„B„FÜ	ˆˆB��F�
€AØ„B„FÜŒt�A‹w‹<ÐZÔZÐZÐZØ„B„FÜŒt�A‹w‹<Ð}Ô}Ð}Ð}Ø„B†Fr
   c            	      ó  € ^\         n        R p R pV ! ^4      \        ^ ^4      u;8X  d   \        ^4      8X  g   Q h Q hV ! \        4      P                  R4      '       g   Q hV ! \        ) 4      P                  R4      '       g   Q hV ! \        ) ^,           4      P                  R4      '       g   Q hV ! \        \        ,           4      P                  R4      '       g   Q hV ! \        ) \        ,
          4      P                  R4      '       g   Q h\        V ^4      P                  R4      '       g   Q hV ! R4      P                  R4      '       g   Q hV ! R4      P                  R4      '       g   Q hV ! R4      P                  R4      '       g   Q hV ! R4      P                  R4      '       g   Q hV ! \        4      \        8X  g   Q hV! \        4      ^ 8X  g   Q h\        ^\        4      ^ 8X  g   Q hV! \        4      P                  R	4      '       g   Q hV! \        ) 4      P                  R
4      '       g   Q hV! \        \        ,           4      P                  R4      '       g   Q hV! \        ) \        ,
          4      P                  R4      '       g   Q hR\        ^^^
\        ,          \        ,          ,           4      ,          P                  R4      '       g   Q hV ! ^^
\        ,          \        ,          ,           4      P                  R4      '       g   Q h\        V ! \        4      4      '       g   Q h\        V ! \        ) 4      4      '       g   Q hV ! R4      P                  R4      '       g   Q hV ! R4      P                  V ! ^4      4      '       g   Q hV ! R4      P                  R4      '       g   Q h\        \        ^\        ^ \        4      4      4      '       g   Q h\        \        ^\        ^ \        4      4      4      '       g   Q h\        \        ^\        ^ \        ) 4      4      4      '       g   Q h\        \        ^\        ^\        4      4      4      '       g   Q h\        \        ^\        ^\        4      4      4      '       g   Q h\        \        ^\        ^\        ) 4      4      4      '       g   Q h\        \        ^\        \        \        4      4      4      '       g   Q h\        \        ^\        \        \        4      4      4      '       g   Q h\        \        ^\        \        ) \        ) 4      4      4      '       g   Q h^\         n        \        R 4      P                  \        RR4      4      '       g   Q h^\         n        R# )!r$   c                 ó   € \        ^ V 4      # ©r   ©Úpsi©Úzs   &r   Ú<lambda>Ú test_polygamma.<locals>.<lambda>X  ó
   € ”S˜˜1”Xr
   c                 ó   € \        ^V 4      # ©r   rz   r|   s   &r   r~   r   Y  r€   r
   gïuÚ×TEï?gì,$7‹@gd�GDE@g?¾VcØb÷?ç»½×Ùß|Û=r^   gaÙ#œó×?g^™¨jåƒJ@gÙ69ãu@z%0.46317279488182026118963809283042317z$2.4821070143037957102007677817351115Ny)\Z[­ð?Ã•Þ›DòÖ?ybabJrõ?ÌøëN<Àg&ž _ Âg¥\Ãñ)c=Èy»½×Ùß|Û=»½×Ùß|Û=yF<	 _ òÁ    _ òAyœWw'&l¡7œWw'&l¡7y¥\Ãñ)c-È¥\Ãñ)c-Hy·ÓYÑ/Õ?ä·ÙÖêI¿¿yÏ�ÙÙ=Ó¿{–’¿Œ‡?i@B yÕÀ­»Â˜ÀhÓVK¯Ù¿y_ä%F”@ý@K¹Êàø?rk   ri   y      YÀ      @y]výCq@‡’Ë¼Ýä@y      è¿      ð?)r   r   r{   Údigammar7   r   rT   ÚfindrootrH   r:   r;   r>   )Úpsi0Úpsi1s     r   Útest_polygammarˆ   V  s%  € Ø„B„FÙ€DÙ€DÙ�‹7”c˜!˜A“hÖ,¤'¨!£*Ô,Ð,Ñ,Ð,Ð,ñ ”‹8�;‰;Ð*×+Ò+Ð+Ð+Ù”�‹9�<‰<Ð*×+Ò+Ð+Ð+Ù”��A•‹;�>‰>Ð,×-Ò-Ð-Ð-Ù””1•‹:�=‰=ÐC×DÒDÐDÐDÙ”�”A•‹;�>‰>ÐB×CÒCÐCÐCÜ�D˜!Ó×ÑÐ 2×3Ò3Ð3Ð3Ù�‹;�>‰>Ð,×-Ò-Ð-Ð-Ù�‹;�>‰>Ð0×1Ò1Ð1Ð1Ù�Ó× Ñ Ð!H×IÒIÐIÐIÙ�Ó× Ñ Ð!P×QÒQÐQÐQÙ”‹9œÔÐÐÙ”‹9˜Œ>Ðˆ>Üˆq”‹:˜Œ?Ðˆ?Ù”‹8�;‰;Ð*×+Ò+Ð+Ð+Ù”�‹9�<‰<Ð*×+Ò+Ð+Ð+Ù””1•‹:�=‰=ÐC×DÒDÐDÐDÙ”�”A•‹;�>‰>ÐE×FÒFÐFÐFØ”#�a˜˜"œR�%¤�'�	Ó"Õ"×&Ñ&Ð'P×QÒQÐQÐQÙ��"”R•%œ•'•	‹?×ÑÐF×GÒGÐGÐGÜ‘”c“×ÒÐÐÜ‘”s�d“×ÒÐÐÙ�‹<�?‰?Ð,×-Ò-Ð-Ð-Ù�‹:�=‰=™˜a›×!Ò!Ð!Ð!Ù�‹=×ÑÐH×IÒIÐIÐIÜ”�Q”s˜1œS“zÓ"×#Ò#Ð#Ð#Ü”�Q”s˜1œS“zÓ"×#Ò#Ð#Ð#Ü”�Q”s˜1œc˜T“{Ó#×$Ò$Ð$Ð$Ü”�Q”s˜1œS“zÓ"×#Ò#Ð#Ð#Ü”�Q”s˜1œS“zÓ"×#Ò#Ð#Ð#Ü”�Q”s˜1œc˜T“{Ó#×$Ò$Ð$Ð$Ü”�Q”sœ3œs“|Ó$×%Ò%Ð%Ð%Ü”�Q”sœ3œs“|Ó$×%Ò%Ð%Ð%Ü”�Q”sœC˜4¤ “~Ó&×'Ò'Ð'Ð'Ø„B„Fä�8Ó×Ñ¤Ð$KÐMsÓ t×uÒuÐuÐuØ„B†Fr
   c                  óœ   € ^d\         n        \        \        ^ \        4      4      R8X  g   Q h\        \        ^
\        4      4      R8X  g   Q hR# )éd   zf0.9772133079420067332920694864061823436408346099943256380095232865318105924777141317302075654362928734zf-12.98876181434889529310283769414222588307175962213707170773803550518307617769657562747174101900659238N)r   r   r   r{   r7   r	   r
   r   Útest_polygamma_high_precr‹   ƒ  sS   € Ø„B„FÜŒs�1”R‹y‹>ð  Fô  Fð  Fð  FÜŒs�2”b‹z‹?ð  Gô  Gð  Gò  Gr
   c                  ó¶  € ^\         n        R p R pR pV ! R4      P                  \        ) ^\	        ^4      ,          ,
          4      '       g   Q hV ! ^4      P                  \        ) 4      '       g   Q hV! R4      P                  R\
        ^,          ,          4      '       g   Q hV! ^4      P                  \
        ^,          ^,          4      '       g   Q hV! R4      P                  \
        ^,          ^\        ,          ,           4      '       g   Q hV! ^4      P                  R\        ,          4      '       g   Q h^\         n        R\        ,          ^\        ^4      ,          \
        ^,          ,          ,           p^\         n        \        ^R	4      P                  V4      '       g   Q h\        ^R4      P                  \
        ^,          4      '       g   Q hR# )
r$   c                 ó   € \        ^ V 4      # ry   rz   r|   s   &r   r~   Ú+test_polygamma_identities.<locals>.<lambda>Š  r€   r
   c                 ó   € \        ^V 4      # r‚   rz   r|   s   &r   r~   rŽ   ‹  r€   r
   c                 ó   € \        ^V 4      # )r   rz   r|   s   &r   r~   rŽ   Œ  r€   r
   r/   r-   NrN   iJÿÿÿg«ªªªªªê?)
r   r   r   Úeulerrm   r7   ÚcatalanÚaperyr6   r{   )r†   r‡   Úpsi2rh   s       r   Útest_polygamma_identitiesr•   ˆ  sE  € Ø„B„FÙ€DÙ€DÙ€DÙ�‹9�<‰<œ˜˜q¤ Q£�x�×(Ò(Ð(Ð(Ù�‹7�:‰:”u�f×ÒÐÐÙ�‹9�<‰<˜œB �E�	×"Ò"Ð"Ð"Ù�‹7�:‰:”b˜!•e˜A•g×ÒÐÐÙ�‹:�=‰=œ˜Q� ¤7¥Õ*×+Ò+Ð+Ð+Ù�‹7�:‰:�bœ•h×ÒÐÐØ„B„FØŒU�
�1”T˜!“W•9œR �U•?Õ"€AØ„B„FÜˆq�‹;�>‰>˜!×ÒÐÐÜˆq�‹:�=‰=œ˜Q�×ÒÐÒr
   c                  óÚ  € R  p ^2\         n        R\        ^^4      ,          pR\        ^^4      ,          pV ! RV,          4      ) V ! RV,          4      ,
          V ! R^V,           ,          4      ,           V ! R^V,
          ,          4      ,           p^\        ,          \	        R\        ^4      ,          \        ,          4      ,          pVP                  V4      '       g   Q h^\         n        R# )c                 ó   € \        ^ V 4      # ry   rz   r|   s   &r   r~   Ú'test_foxtrot_identity.<locals>.<lambda>�  r€   r
   r/   Nr   r   )r   r   Úfractionr7   Úsechr6   r   )r†   ru   ÚbÚxÚys        r   Útest_foxtrot_identityrž   ™  s¥   € ñ €DØ„B„FØ	Œh�q˜‹mÕ€AØ	Œh�q˜‹mÕ€AÙ	ˆc�!�e‹ˆ‘t˜D �F“|Õ#¡d¨3°°!µ­9£oÕ5¹¸SÀ!ÀAÅ#½Y»ÕG€AØ	Œ"�ŒT�#”d˜1“g•+œb•.Ó!Õ!€AØ�4‰4��7Š7€Nˆ7Ø„B†Fr
   c                  ón  € ^d\         n        \        \        ^2\        4      4      R8X  g   Q h\        \        ^2\        ^\
        ,          ,           4      4      R8X  g   Q h\        \        ^2\        ^\
        ,          \        ,          ,           4      4      R8X  g   Q h^\         n        \        \        ^2\        4      4      R8X  g   Q h\        \        ^2\        ^\
        ,          ,           4      4      R8X  g   Q h\        \        ^2\        ^\
        ,          \        ,          ,           4      4      R8X  g   Q hR# )rŠ   zf-1344100348958402765749252447726432491812.641985273160531055707095989227897753035823152397679626136483zw-0.00000000000000000189793739550804321623512073101895801993019919886375952881053090844591920308111549337295143780341396zó(-0.00000000000000005225169411521692489752254721556835657523758895106315132447859377385233700094871256507814151956624433 - 0.00000000000000001813157041407010184702414110218205348527862196327980417757665282244728963891298080199341480881811613j)z-1.34410034895841e+39z-1.89793739550804e-18z.(-5.2251694115217e-17 - 1.81315704140701e-17j)N)r   r   r   r{   r7   ÚerT   r	   r
   r   Útest_polygamma_high_orderr¡   ¦  sþ   € Ø„B„FÜŒs�2”r‹{Óð   Hô  Hð  Hð  HÜŒs�2”r˜Bœq�D•yÓ!Ó"ð  '`ô  `ð  `ð  `ÜŒs�2”r˜Bœq�D¤�F•{Ó#Ó$ð *^ô _ð _ð _ð „B„FÜŒs�2”r‹{ÓÐ6Ô6Ð6Ð6ÜŒs�2”r˜Bœq�D•yÓ!Ó"Ð&=Ô=Ð=Ð=ÜŒs�2”r˜Bœq�D¤�F•{Ó#Ó$Ð(XÔXÐXÒXr
   c                  óp  € ^\         n        \        ^ 4      ^ 8X  g   Q h\        ^4      ^8X  g   Q h\        ^4      R8X  g   Q h\        ^4      P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h\        ^
R,          4      P                  R4      '       g   Q h\        R4      P                  ^^\	        ^4      ,          ,
          4      '       g   Q h\        \
        4      \
        8X  g   Q h\        R	4      R
8X  g   Q h\        R4      P                  R4      '       g   Q hR# )r$   rL   g_†’bš7@r   gÜSþ¡@r/   NgUUUUUUý?r   y       @        y      ø?        rP   ykŠ³4qÞ÷?†¾›Õ@wí?)r   r   Úharmonicr   rm   rH   r	   r
   r   Útest_harmonicr¤   ²  sþ   € Ø„B„FÜ�A‹;˜!ÔÐÐÜ�A‹;˜!ÔÐÐÜ�A‹;˜#ÔÐÐÜ�A‹;�>‰>Ð*×+Ò+Ð+Ð+Ü�FÓ×ÑÐ4×5Ò5Ð5Ð5Ü�B˜•HÓ× Ñ Ð!2×3Ò3Ð3Ð3Ü�C‹=×Ñ˜A˜a¤ A£�h�J×'Ò'Ð'Ð'Ü”C‹=œCÔÐÐÜ�D‹>˜VÔ#Ð#Ð#Ü�D‹>×ÑÐD×EÒEÐEÒEr
   c                  óî   € R \         n        \        R4      ^,          p ^\         n        \        \	        V 4      4      R8X  g   Q h^2\         n        \        \	        V 4      4      R8X  g   Q h^\         n        R# )éô  z6.26075321389519e+12458010678z@6.2607532138951929201303779291707455874010420783933e+12458010678Nr   ©r   r   r   r   r4   ©rœ   s    r   Útest_gamma_huge_1r©   ¿  sY   € Ø„B„FÜˆF‹�a�€AØ„B„FÜŒu�Q‹x‹=Ð;Ô;Ð;Ð;Ø„B„FÜŒu�Q‹x‹=Ð^Ô^Ð^Ð^Ø„B†Fr
   c                  óæ   € R \         n        \        ^
^d,          4      ^,          p ^\         n        \        \	        V 4      4      R8X  g   Q h^2\         n        \        \	        V 4      4      R8X  g   Q hR# )r¦   zw1.82341134776679e+51729974693233641689901335581750771368291828240422018860515119656908623426021308685461258226190190661z˜1.82341134776678875374414910350027596939980412984e+51729974693233641689901335581750771368291828240422018860515119656908623426021308685461258226190190661Nr§   r¨   s    r   Útest_gamma_huge_2r«   È  sm   € Ø„B„FÜˆB��G‹�rÕ€AØ„B„FÜŒu�Q‹x‹=ð	3ô4ð 4ð 4ð „B„FÜŒu�Q‹x‹=ð	TôUð Uò Ur
   c                  ó´  € R \         n        ^
^P,          ^,          ^
^F,          \        ,          ^,          ,           p ^\         n        \        V 4      p\	        VP
                  4      R8X  g   Q h\	        VP                  4      R8X  g   Q h^2\         n        \        V 4      p\	        VP
                  4      R8X  g   Q h\	        VP                  4      R8X  g   Q hR# )r¦   ze-6.82925203918106e+2636286142112569524501781477865238132302397236429627932441916056964386399485392600zd8.54647143678418e+2636286142112569524501781477865238132302397236429627932441916056964386399485392600zˆ-6.8292520391810548460682736226799637356016538421817e+2636286142112569524501781477865238132302397236429627932441916056964386399485392600z‡8.5464714367841748507479306948130687511711420234015e+2636286142112569524501781477865238132302397236429627932441916056964386399485392600N©r   r   rT   r4   r   ÚrealÚimag©rœ   r�   s     r   Útest_gamma_huge_3r±   Ô  sÑ   € Ø„B„FØ
ˆB��!��b˜"•fœQ•h •lÕ"€AØ„B„FÜˆa‹€AÜˆq�v‰v‹;ð	 ô!ð !ð !ô ˆq�v‰v‹;ð	ô ð  ð  ð „B„FÜˆa‹€AÜˆq�v‰v‹;ð	CôDð Dð Dô ˆq�v‰v‹;ð	BôCð Cò Cr
   c                  ó¸   € Rp ^\         n        \        \        V 4      4      R8X  g   Q h^2\         n        \        \        V 4      4      R8X  g   Q h^\         n        R# )i€  z2(8.95783268539713e+5164 - 1.94678798329735e+5164j)zx(8.9578326853971339570292952697675570822206567327092e+5164 - 1.9467879832973509568895402139429643650329524144794e+5164j)Ny      ©@     vÆ@)r   r   r   r4   r¨   s    r   Útest_gamma_huge_4r³   è  sZ   € Ø€AØ„B„FÜŒu�Q‹x‹=Ø<ô=ð =ð =à„B„FÜŒu�Q‹x‹=ð	ôð ð ð „B†Fr
   c                  ó   € R \         n        ^
^<,          \        ,          ^,          p ^\         n        \        V 4      p\	        VP
                  4      R8X  g   Q h\	        VP                  4      R8X  g   Q h^2\         n        \        V 4      p\	        VP
                  4      R8X  g   Q h\	        VP                  4      R8X  g   Q h^\         n        R# )r¦   zO-3.27753899634941e-227396058973640224580963937571892628368354580620654233316839zN-7.1519888950416e-227396058973640224580963937571892628368354580620654233316841zr-3.2775389963494132168950056995974690946983219123935e-227396058973640224580963937571892628368354580620654233316839zr-7.1519888950415979749736749222530209713136588885897e-227396058973640224580963937571892628368354580620654233316841Nr­   r°   s     r   Útest_gamma_huge_5rµ   ô  s±   € Ø„B„FØ
ˆB�”�
�Q�€AØ„B„FÜˆa‹€AÜˆq�v‰v‹;ÐkÔkÐkÐkÜˆq�v‰v‹;ÐjÔjÐjÐjØ„B„FÜˆa‹€AÜˆq�v‰v‹;ð	-ô.ð .ð .ô ˆq�v‰v‹;ð	-ô.ð .ð .ð „B†Fr
   c                  óœ  € ^d\         n        ^\        \        ^
4      R,          ,          ,           p ^\         n        \	        V 4      p\        VP                  4      R8X  g   Q h\        VP                  4      R8X  g   Q h^2\         n        \	        V 4      p\        VP                  4      R8X  g   Q h\        VP                  4      R8X  g   Q hR# )rŠ   r   z2.0z1.84556867019693e-1000z91.8455686701969342787869758198351951379156813281202e-1000N)r   r   rT   r   r4   r   r®   r¯   )ru   r�   s     r   Útest_gamma_huge_7r·     s›   € Ø„B„FØ	ŒAŒc�"‹g�t�m�OÕ€AØ„B„FÜˆa‹€AÜˆq�v‰v‹;˜%ÔÐÐô ˆq�v‰v‹;Ð2Ô2Ð2Ð2Ø„B„FÜˆa‹€AÜˆq�v‰v‹;˜%ÔÐÐäˆq�v‰v‹;ÐVÔVÐVÒVr
   c                  ó¶  € ^\         n        \        ^ 4      P                  \        54      '       g   Q h^\         n        \        ^4      P                  R4      '       g   Q h\        ^4      P                  R4      '       g   Q h\        ^4      P                  R4      '       g   Q h\        ^4      P                  R4      '       g   Q h^\         n        \        ^4      P                  R4      '       g   Q h\        ^4      P                  R	4      '       g   Q h\        ^4      P                  R4      '       g   Q h\        ^4      P                  R4      '       g   Q hR# )
r$   z -0.07281584548367672486058637587z!-0.009690363192872318484530386035z 0.002053834420303345866160046543z 0.002325370065467300057468170178g²ÍTõ3Ó`?g¢;Œ§c?Ng¢¤û*¤²¿gF|ÿ‡ŠØƒ¿)r   r   Ú	stieltjesr   r‘   r	   r
   r   Útest_stieltjesrº     s  € Ø„B„FÜ�Q‹<�?‰?œE˜6×"Ò"Ð"Ð"Ø„B„FÜ�Q‹<�?‰?Ð=×>Ò>Ð>Ð>Ü�Q‹<�?‰?Ð>×?Ò?Ð?Ð?Ü�Q‹<�?‰?Ð=×>Ò>Ð>Ð>Ü�Q‹<�?‰?Ð=×>Ò>Ð>Ð>Ø„B„FÜ�Q‹<�?‰?Ð;×<Ò<Ð<Ð<Ü�Q‹<�?‰?Ð<×=Ò=Ð=Ð=Ü�Q‹<�?‰?Ð;×<Ò<Ð<Ð<Ü�Q‹<�?‰?Ð<×=Ò=Ð=Ò=r
   c                  óœ  € ^\         n        \        ^ 4      \        R4      u;8X  d	   ^ 8X  g   Q h Q h\        ^4       U u. uF  p \	        V 4      NK  	  up . RO8X  g   Q h\        \	        R4      4      R8X  g   Q h\        \        \        4      4      '       g   Q h\        \	        \        4      4      '       g   Q h\        \        \        4      4      '       g   Q h\        \        4      \        8X  g   Q h\	        \        4      \        8X  g   Q h\        \        4      \        8X  g   Q h\        \	        \        ) 4      4      '       g   Q h\        R4      P                  R4      '       g   Q h\        R4      P                  R	4      '       g   Q h\        ^4       Uu. uF  p\        V4      NK  	  up. R
O8X  g   Q h\        ^ RR4       Uu. uF  p\        V4      NK  	  up. RO8X  g   Q h\        R4      pV^ 8X  d   \        V\        4      '       g   Q h\        R4      pVR8X  d   \        V\        4      '       g   Q hR# u up i u upi u upi )r$   r   z3.24570818422368e+1177245gffffffæ?gd£ÍåÑé?Nr   )r   r   r   é   i   i ‡  i °{l     2ft y       @      @y¨­gÌÆ¿µøì¸1§?)r   r   é   él   é l  i \&l     þªéùÿÿÿrM   )r   r   r   rM   r¾   r¿   i ¤Ùúy      À        )r   r   Úbarnesgr5   Úsuperfacr   r:   r;   ÚhyperfacrH   r   Ú
isinstancer>   )r@   rI   ru   s      r   Útest_barnesgrÅ   "  sÎ  € Ø„B„FÜ�1‹:œ ›Ö)¨Ô)Ð)Ñ)Ð)Ð)Ü!& q¤Ó*¡˜AŒH�QŽK¡Ñ*Ò._Ô_Ð_Ð_ÜŒx˜‹~ÓÐ"=Ô=Ð=Ð=Ü”œ“×ÒÐÐÜ”œ#“×ÒÐÐÜ”œ#“×ÒÐÐÜ”3‹<œ3ÔÐÐÜ”C‹=œCÔÐÐÜ”C‹=œCÔÐÐÜ”œ3˜$“× Ò Ð Ð Ü�3‹<�?‰?Ð-×.Ò.Ð.Ð.Ü�4‹=×ÑÐE×FÒFÐFÐFÜ!& q¤Ó*¡˜AŒH�QŽK¡Ñ*Ò.\Ô\Ð\Ð\Ü!& q¨¨B¤Ó0¡˜AŒH�QŽK¡Ñ0Ò4SÔSÐSÐSÜ�‹€AØ�Œ6”j ¤C×(Ò(Ð(Ð(Ü�‹€AØ�Œ7”z !¤S×)Ò)Ð)Ð)Ñ)ùò! +ùò +ùÚ0s   ¿H?ÆIÇ	I	c                  ó^	  € ^\         n        R U u. uF  p \        V 4      NK  	  pp V F7  p \        ^V 4      P	                  \        ^V ,
          4      ) 4      '       d   K7  Q h	  V F4  p \        ^ V 4      P	                  V ^V ,
          ,          4      '       d   K4  Q h	  V F;  p \        RV 4      P	                  V ^V ,
          ^,          ,          4      '       d   K;  Q h	  V FI  p \        RV 4      P	                  V ^V ,           ,          ^V ,
          ^,          ,          4      '       d   KI  Q h	  V F^  p \        RV 4      P	                  V ^^V ,          ,           V ^,          ,           ,          ^V ,
          ^,          ,          4      '       d   K^  Q h	  \        ^^4      P	                  R4      '       g   Q h\        ^R4      P	                  R4      '       g   Q h\        ^R4      P	                  R4      '       g   Q h\        ^R4      P	                  R4      '       g   Q h\        ^R4      P	                  R4      '       g   Q h\        ^R4      P	                  R4      '       g   Q h\        ^R4      P	                  R4      '       g   Q h\        ^R\        \        4      ,          4      P	                  R4      '       g   Q h\        RR4      P	                  R4      '       g   Q h\        RR4      P	                  R4      '       g   Q h\        ^R4      P	                  R4      '       g   Q h\        RR4      P	                  R4      '       g   Q h\        RR4      P	                  R4      '       g   Q h\        R\        ^,          ,           R\        ^,          ,           4      P	                  R4      '       g   Q h\        R^4      P	                  \        R4      4      '       g   Q h\        RR4      P	                  \        R4      ) 4      '       g   Q h\        R	R 4      P	                  R!4      '       g   Q h\        R	^È4      P	                  R"4      '       g   Q h\        R#R4      P	                  \        ^4      R
,          4      '       g   Q h\        R#R4      P	                  R$4      '       g   Q hR# u up i )%r$   r/   çÍÌÌÌÌÌì?gØùVª¡Ëô?y        ÍÌÌÌÌÌì?gš™™™™™ñ?i®  g=ð.gËð?i2¾  rL   g      +@g      ô?NrM   rj   )r   r/   g®Gáz®ï?r½   r   rM   y              ð?rj   r   rN   r&   y[-‘ëF@áUÞ´¬ÊÀrÀ   g÷!føGÀgÍÌÌÌÌÌì¿göÊÿƒ¸è¿y#á]ÞüÅ¿øö`�jÀê?y�8n+Ydÿ?¬^nªÊ)Ó¿gš™™™™™ñ¿g¨¤öá¾�ì¿y¨Èp/MÔâ?[©]Ó˜ñ?g „µjßŠ¿g-Cëâ6z¿y£¹B8$PÔ?½g Ãï?gÖåúí—tHÀgWÓcF‹Ày…Q‘Üÿ² ÀKÀ1…ÃQ Ày       À        iLÿÿÿ)r   r   Ú	mpmathifyÚpolylogr   rm   r6   rT   ra   rl   r   )r}   Úzss     r   Útest_polylogrË   7  s´  € Ø„B„FÙ EÓ	FÑ E˜1Œ)�AŽ,Ñ E€BÐ	FÛˆœ  1›×(Ñ(¬#¨a°­c«(¨×3Ô3Ð3Ð3‰RÛˆœ  1›×(Ñ(¨¨A¨a­C­×1Ô1Ð1Ð1‰RÛˆœ  A›×)Ñ)¨!¨Q¨q­S°1­H­*×5Ô5Ð5Ð5‰RÛˆœ  A›×)Ñ)¨!¨Q¨q­S­'°1°Qµ3¸µ(Õ*:×;Ô;Ð;Ð;‰RÛˆœ  A›×)Ñ)¨!¨Q¨q°­s­U°1°aµ4­Z­.¸!¸A½#À½Õ*A×BÔBÐBÐB‰RÜ�1�a‹=×ÑÐH×IÒIÐIÐIÜ�1�b‹>×ÑÐ3×4Ò4Ð4Ð4Ü�1�c‹?×ÑÐ3×4Ò4Ð4Ð4Ü�1�dÓ×ÑÐ6×7Ò7Ð7Ð7Ü�1�dÓ×ÑÐN×OÒOÐOÐOÜ�1�c‹?×ÑÐJ×KÒKÐKÐKÜ�1�dÓ×ÑÐ6×7Ò7Ð7Ð7Ü�1�cœ$œq›'•kÓ"×%Ñ%Ð&T×UÒUÐUÐUÜ�2�sÓ×Ñ˜t×$Ò$Ð$Ð$Ü�2�tÓ×Ñ 	×*Ò*Ð*Ð*Ü�1�c‹?×ÑÐ3×4Ò4Ð4Ð4Ü�2�sÓ×Ñ˜u×%Ò%Ð%Ð%Ü�2�r‹?×Ñ˜g×&Ò&Ð&Ð&Ü�3”q˜•s•7˜C¤ !¥�GÓ$×'Ñ'Ð(X×YÒYÐYÐYÜ�4˜‹?×Ñœd 4›j×)Ò)Ð)Ð)Ü�4˜Ó×Ñ¤¨£˜~×.Ò.Ð.Ð.ä�3Ð+Ó,×/Ñ/Ð0B×CÒCÐCÐCÜ�3˜Ó×ÑÐ M×NÒNÐNÐNÜ�5˜"Ó× Ñ ¤ Q£¨¥×-Ò-Ð-Ð-Ü�5˜$Ó×"Ñ" 4×(Ò(Ð(Ò(ùò5 
Gs   �R*c                  ó¸  € ^\         n        \        ^ R4      R,          P                  R4      '       g   Q h\        ^R4      R,          P                  R4      '       g   Q h\        ^R4      P                  R4      '       g   Q h\        RR4      P                  R4      '       g   Q h\	        ^ ^ 4      ^8X  g   Q h\	        ^ ^4      ^8X  g   Q h\	        ^ ^4      ^8X  g   Q h\	        ^ \
        4      ^8X  g   Q h\	        ^ \
        ) 4      ^8X  g   Q h\        \	        ^ \        4      4      '       g   Q h\	        ^^4      ^8X  g   Q h\	        ^^ 4      ^ 8X  g   Q h\	        ^\
        4      \
        8X  g   Q h\	        ^\
        ) 4      \
        ) 8X  g   Q h\        \	        ^\        4      4      '       g   Q h\	        ^R4      ^ 8X  g   Q h\	        ^^ 4      ^ 8X  g   Q h\	        ^
4      R8X  g   Q h\	        ^
^4      R8X  g   Q h\	        ^
R4      R8X  g   Q h\	        ^R4      R8X  g   Q h\	        ^2R4      P                  R	4      '       g   Q h^P\         n        \	        ^2R4      R
8X  g   Q h\	        ^(^24      R8X  g   Q h\	        ^J4      R8X  g   Q h^\         n        \	        ^
R4      R8X  g   Q h\	        R^ 4      P                  \        \        R,          4      4      '       g   Q hR# )r$   rƒ   gœo   ð?g8ß   ð?y              @g      @gã*
Õ0(@iÅ i¸«¨ z3.4746902914629720259e74l   ªv­Ýreh¥@3 ¥VBF²v'r….y	UR|s&‹TÄ l   .e0uï&Y:Õj+ØI<1÷ ´|6ÀávåJbë l   ôrw_3dtL#�m,§€`3	.v(¡*õA‘=V y              4@r/   Nr   y™·¢ý‚ÀÑ)fÉ³?€@r   iøÿÿÿiÎÿÿÿiÂ0êðy @j#M›B (3Vjw¬B)
r   r   Úpolyexpr   ÚbellrH   r:   r;   Úsincr7   r	   r
   r   Útest_bell_polyexprÐ   U  sz  € Ø„B„Fä�A�eÓ˜VÕ#×'Ñ'¨×6Ò6Ð6Ð6Ü�A�eÓ˜VÕ#×'Ñ'¨×5Ò5Ð5Ð5Ü�1�R‹=×ÑÐI×JÒJÐJÐJÜ�2�c‹?×ÑÐ2×3Ò3Ð3Ð3ä��!‹9˜Œ>Ðˆ>Ü��!‹9˜Œ>Ðˆ>Ü��!‹9˜Œ>Ðˆ>Ü�”#‹;˜!ÔÐÐÜ�”3�$‹<˜1ÔÐÐÜ”�aœ“×ÒÐÐä��!‹9˜Œ>Ðˆ>Ü��!‹9˜Œ>Ðˆ>Ü�”#‹;œ#ÔÐÐÜ�”3�$‹<œC˜4ÔÐÐÜ”�aœ“×ÒÐÐä��"‹:˜Œ?Ðˆ?Ü��!‹9˜Œ>Ðˆ>ä�‹8�vÔÐÐÜ��1‹:˜ÔÐÐÜ��B‹<˜8Ô#Ð#Ð#Ü��#‹;˜*Ô$Ð$Ð$Ü��3‹<�?‰?Ð5×6Ò6Ð6Ð6Ø„B„FÜ��3‹<ÐfÔfÐfÐfÜ��2‹;ÐcÔcÐcÐcÜ�‹8ÐfÔfÐfÐfØ„B„FÜ��3‹<Ð8Ô8Ð8Ð8ä��A‹;�>‰>œ$œr #�v›,×'Ò'Ð'Ò'r
   c                  ó<  € ^\         n        \        R4      P                  R4      '       g   Q h\        ^4      P                  R4      '       g   Q h\        ^4      \        8X  g   Q h\        \        4      ^ 8X  g   Q h\        \        \        4      4      '       g   Q hR# )r$   rÇ   gªÅM‰Òµ³?Nyùø2³Úký?-DTû!	@)r   r   Ú	primezetar   rH   r:   r;   r	   r
   r   Útest_primezetarÓ   {  sx   € Ø„B„FÜ�S‹>×ÑÐK×LÒLÐLÐLÜ�Q‹<�?‰?Ð2×3Ò3Ð3Ð3Ü�Q‹<œ3ÔÐÐÜ”S‹>˜QÔÐÐÜ”œ3“× Ò Ð Ò r
   c                  óæ  € ^\         n        \        R4      P                  R4      '       g   Q h\        R4      P                  R4      '       g   Q h\        R^R7      P                  R	4      '       g   Q h\        R
^R7      P                  R4      '       g   Q h\        R
^R7      P                  R4      '       g   Q h\        R^R7      P                  R4      '       g   Q hRR lp V ! \        P                  R4      R4      '       g   Q hV ! \        P                  R4      R4      '       g   Q hV ! \        P                  R4      R4      '       g   Q hV ! \        P                  R^R7      R4      '       g   Q hV ! \        P                  R
4      R4      '       g   Q hV ! \        P                  R
^R7      R4      '       g   Q hV ! \        P                  R^R7      R4      '       g   Q hV ! \        P                  R^R7      R4      '       g   Q hV ! \        P                  R^R7      R4      '       g   Q hV ! \        P                  R^R7      R4      '       g   Q hV ! \        P                  R^R7      R4      '       g   Q hV ! \        P                  R^R7      R4      '       g   Q hV ! \        P                  R^R7      R4      '       g   Q hV ! \        P                  R^R7      R4      '       g   Q hR# )r$   ©Ú
derivativec                 óJ   € \        W,
          4      V\        V4      ,          8  # )N)rR   )rœ   r�   Útols   &&&r   r   Útest_rs_zeta.<locals>.ae�  s   € Ü�1•3‹x˜#œc !›f�*Ñ$Ð$r
   Ny      à?     jø@y& 6ž#+ñ?Œ®ÄÂ–@y      è?     jø@y¾û5Ú×gý?7-m^Iûÿ?y      à?    €„.Ayš¥ÿ¿™@óV%‚<–Ày      ð?    €„.AyË‡ÐÉD@•åÆß-2ÀyVÖê¥!¯º¿V1‘Ìéç¿y      à?    €„.Áyžáº.F'@	p¹“ 1@)g�íµ ÷Æ°>y      à?     jøÀy& 6ž#+ñ?Œ®ÄÂ–Ày      è?     jøÀy¾û5Ú×gý?7-m^Iûÿ¿yôÖÂ’z³?ÛŒÎ^Ùp@yžáº.F'@	p¹“ 1Ày¦$¤ÿPî?•­¢¥Ùã?y,Ï‚?¯ˆ%@úlUSí>ÀyÛÔ‚îÙ]Àã5MÔº$k@yë!&§‘@\_ÝåUšÀy(1º•”SÄÀ¡gŠ²äèÊ@y-ž6û·Ú¿+~ÈÀy"è™ºm"À'±=U‰A@yÅÙ�œ@§[@MÇÚoœmÀy�ÐkLVy�À"DâÐ«§›@)r   r   ra   r   Úfp)r   s    r   Útest_rs_zetarÛ   ƒ  s�  € Ø„B„FÜ�Ó×ÑÐ N×OÒOÐOÐOÜ�Ó× Ñ Ð!N×OÒOÐOÐOÜ�¨Ô+×.Ñ.Ð/]×^Ò^Ð^Ð^Ü�
 qÔ)×,Ñ,Ð-[×\Ò\Ð\Ð\Ü�
 qÔ)×,Ñ,Ð-^×_Ò_Ð_Ð_Ü�¨Ô+×.Ñ.Ð/]×^Ò^Ð^Ð^ô%áŒb�g‰g�kÓ"Ð$R×SÒSÐSÐSÙŒb�g‰g�lÓ#Ð%R×SÒSÐSÐSÙŒb�g‰g�hÓÐ!Q×RÒRÐRÐRÙŒb�g‰g�h¨1ˆgÓ-Ð/]×^Ò^Ð^Ð^ÙŒb�g‰g�f‹oÐO×PÒPÐPÐPÙŒb�g‰g�f¨ˆgÓ+Ð-^×_Ò_Ð_Ð_ÙŒb�g‰g�k¨aˆgÓ0Ð2_×`Ò`Ð`Ð`ÙŒb�g‰g�k¨aˆgÓ0Ð2a×bÒbÐbÐbÙŒb�g‰g�k¨aˆgÓ0Ð2`×aÒaÐaÐaÙŒb�g‰g�k¨aˆgÓ0Ð2a×bÒbÐbÐbÙŒb�g‰g�l¨qˆgÓ1Ð3c×dÒdÐdÐdÙŒb�g‰g�l¨qˆgÓ1Ð3`×aÒaÐaÐaÙŒb�g‰g�l¨qˆgÓ1Ð3a×bÒbÐbÐbÙŒb�g‰g�l¨qˆgÓ1Ð3a×bÒbÐbÒbr
   c                  óN  € ^\         n        \        R4      P                  R4      '       g   Q h\        R^R7      P                  R4      '       g   Q h\        R^R7      P                  R4      '       g   Q h\        R\        ,           ^R7      P                  R4      '       g   Q hR# )r$   r   g1/[ã³„@rÕ   NgÀÎK½KÀgÙFh¯änqÀyÅþQ·1…@Öaûãß»wÀ)r   r   Úsiegelzr   rT   r	   r
   r   Útest_siegelzrÞ   ž  s†   € Ø„B„FÜ�6‹?×ÑÐ4×5Ò5Ð5Ð5Ü�6 aÔ(×+Ñ+Ð,C×DÒDÐDÐDÜ�6 aÔ(×+Ñ+Ð,C×DÒDÐDÐDÜ�6œ!•8 qÔ)×,Ñ,Ð-[×\Ò\Ð\Ò\r
   c                  ó.  € ^\         n        \        ^RRR7      p \        ^RRR7      p\        ^RRR7      p\        V 4      P	                  R4      '       g   Q h\        V4      P	                  R4      '       g   Q h\        V4      pVP
                  P	                  R4      '       g   Q hVP                  P	                  R4      '       g   Q h^\         n        \        ^RRR7      p \        ^R	RR7      p\        ^R
RR7      p\        V 4      P	                  R4      '       g   Q h\        V4      P	                  R4      '       g   Q h\        V4      pVP
                  P	                  R4      '       g   Q hVP                  P	                  R4      '       g   Q hR# )r$   z1e-10T)Úexactz-1e-10z1e-10jg#ž _ Bg¶oüŒxâ?z1e-50z-1e-50z1e-50jÚ1e50z-1e50z40.57721566490153286060651209008240243104215933593992NgÝaû_ Âg    _ Â)r   r   Úfaddra   r   r®   r¯   )Ús1Ús2Ús3r}   s       r   Útest_zeta_near_1ræ   §  sC  € à„B„FÜ	ˆa� Ô	%€BÜ	ˆa� Ô	&€BÜ	ˆa� Ô	&€BÜ�‹8�;‰;Ð7×8Ò8Ð8Ð8Ü�‹8�;‰;Ð6×7Ò7Ð7Ð7ÜˆR‹€AØ�6‰6�9‰9Ð+×,Ò,Ð,Ð,Ø�6‰6�9‰9Ð3×4Ò4Ð4Ð4Ø„B„FÜ	ˆa� Ô	%€BÜ	ˆa� Ô	&€BÜ	ˆa� Ô	&€BÜ�‹8�;‰;�v×ÒÐÐÜ�‹8�;‰;�w×ÒÐÐÜˆR‹€AØ�6‰6�9‰9ÐK×LÒLÐLÐLØ�6‰6�9‰9�W×ÒÐÒr
   N)#ÚmpmathÚmpmath.libmpr   r   r   r   r"   r+   rA   rJ   r[   rc   ro   rr   rv   rˆ   r‹   r•   rž   r¡   r¤   r©   r«   r±   r³   rµ   r·   rº   rÅ   rË   rÐ   rÓ   rÛ   rÞ   ræ   r	   r
   r   Ú<module>ré      s·   ðÜ ß ;Ñ ;ò3ò+òZe>òN%pòNò/Xòb!QòF.ò<òò+òZGò
 ò"ò
YòFòò
UòCò(
òò"Wò>ò*ò*)ò<$(òL!òcò6]ôr
   