-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '558051458397601784711678089248', 'a10': [0, 0], 'a2': [3.0377620261207485, 4.772001872658765], 'a3': [-23.609492155702142, 0], 'a4': [-13.54400374531753, 28.992412154679794], 'a5': [0, 0], 'a6': [-71.72001872658765, -112.66454077953306], 'a7': [0, -160.7040599250805], 'a8': [-179.49530535418953, 23.44003745317531], 'a9': [314.408119850161, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.07676396259613, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-3.0377620261207485, -4.772001872658765]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '200.149', 'coefficient_field': 'CDF', 'conductor': 200, 'conductor_radical': 10, 'conjugate': '1197197790497889238009184943313', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.0377620261207485, -4.772001872658765]], [[1.0, 0], [23.609492155702142, 0], [243.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 160.7040599250805], [-16807.0, 0]], [[1.0, 0], [0, -129.12912563073223], [-161051.0, 0]], [[1.0, 0], [-759.6593733020517, 0], [371293.0, 0]], [[1.0, 0], [0, 323.408119850161], [-1419857.0, 0]], [[1.0, 0], [0, -198.51143964657953], [-2476099.0, 0]], [[1.0, 0], [0, 1193.1527790260466], [-6436343.0, 0]], [[1.0, 0], [0, -5987.236459492113], [-20511149.0, 0]], [[1.0, 0], [4872.448719100966, 0], [28629151.0, 0]], [[1.0, 0], [-3698.5618828402644, 0], [69343957.0, 0]], [[1.0, 0], [10437.876074905475, 0], [115856201.0, 0]], [[1.0, 0], [9873.106208437273, 0], [147008443.0, 0]], [[1.0, 0], [0, -6297.980764045653], [-229345007.0, 0]], [[1.0, 0], [-21728.14645853646, 0], [418195493.0, 0]], [[1.0, 0], [0, -33513.43866855141], [-714924299.0, 0]], [[1.0, 0], [0, -48506.81791188421], [-844596301.0, 0]], [[1.0, 0], [33182.38465996914, 0], [1350125107.0, 0]], [[1.0, 0], [-59464.131415729586, 0], [1804229351.0, 0]], [[1.0, 0], [0, -51278.62609737431], [-2073071593.0, 0]], [[1.0, 0], [-73724.54915355692, 0], [3077056399.0, 0]], [[1.0, 0], [61627.9718549943, 0], [3939040643.0, 0]], [[1.0, 0], [-106734.7415131004, 0], [5584059449.0, 0]], [[1.0, 0], [0, 12562.912419472057], [-8587340257.0, 0]], [[1.0, 0], [0, -64962.80607856495], [-10510100501.0, 0]], [[1.0, 0], [0, 69035.89003744222], [-11592740743.0, 0]], [[1.0, 0], [-187321.62858322592, 0], [14025517307.0, 0]], [[1.0, 0], [0, -49350.46588717091], [-15386239549.0, 0]], [[1.0, 0], [0, -171100.02570785602], [-18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 22, 'label': '2-200-40.29-c5-0-22', 'leading_term': '1.057610142766924242148456843777619638878535998591155055', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/200/6/f/a/149/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [1.0576101427669242, 0.9221810881196633, 0.7690888268082112, 0.6017108554804961, 0.4235572922873484, 0.2382335179381482, 0.049401644912052976, -0.1392593270004909, -0.32409476824327915, -0.5015171237825524, -0.668050010624257, -0.8203735492494173, -0.9553706487806863, -1.0701738339765061, -1.1622120644211893, -1.2292568578480574, -1.2694668960614734, -1.2814301692927685, -1.2642026089849492, -1.217342075813129, -1.1409365148163517, -1.035625068013143, -0.9026109513531426, -0.7436649610743269, -0.5611185772567627, -0.3578457811909631, -0.13723289838045605, 0.09686398063728897, 0.34017416675190637, 0.5880799705541372, 0.8356962247537653, 1.0779608471796966, 1.3097351707972371, 1.525912374155727, 1.721531962035855, 1.8918978852273285, 2.0326975644469334, 2.1401188107921088, 2.2109614280089764, 2.2427401537160625, 2.2337755597788314, 2.1832695966504763, 2.0913626406476262, 1.9591691918273337, 1.7887897749319317, 1.5832971144490964, 1.3466952806651453, 1.0838512257241302, 0.8003989317188195, 0.5026172569282741, 0.19728346757398094, -0.10849464665378611, -0.40746428508043464, -0.692426151957763, -0.9564406022911865, -1.1930354164246455, -1.3964087284118776, -1.5616203431610005, -1.684764596990215, -1.7631180661177337, -1.7952558215979701, -1.7811305733478031, -1.7221099374293432, -1.6209681874195294, -1.4818301903583708, -1.3100667483486856, -1.1121422267218455, -0.8954170983171212, -0.6679098127644734, -0.43802414563111086, -0.21424982681658117, -0.00484572094108632, 0.18248393406802443, 0.34090879535614965, 0.46477519006120716, 0.549880242389272, 0.5937054923664115, 0.5955989089390704, 0.5568954369656516, 0.4809679142404531, 0.37320231766190853, 0.24089379410715717, 0.09306272970869989, -0.0598068781710552, -0.2061013632082317, -0.3334751528702446, -0.42930087949041595, -0.4811576490619292, -0.47734094470400906, -0.4073758143043967, -0.2625137758510219, -0.03619335796974901, 0.27555555722029823, 0.6737823683822222, 1.156378281153003, 1.71794499110184, 2.349780413552608, 3.0399883455000563, 3.773714437046619, 4.5335059953770065, 5.2997881239011475, 6.051443711509768, 6.766480041143201, 7.422760494424962, 7.998776194306683, 8.474429638458957, 8.831800594799342, 9.05586388496534, 9.135129257511577, 9.062175387549127, 8.834053118004286, 8.452537309009394, 7.924211960354025, 7.260379439056892, 6.476791454193789, 5.593206608605866, 4.6327866266717415, 3.621350395696915, 2.5865114478867732, 1.556730142417822, 0.5603162994564101, -0.3755788543555345, -1.2259410387043888, -1.9688013552941026, -2.5860365273064483, -3.0640263383652284, -3.3941389758924085, -3.5730217428177737, -3.602682551227398, -3.490356426420392, -3.248160551495281, -2.8925507552483456, -2.443601355341721, -1.9241384814861857, -1.3587640096666929, -0.7728126719255438, -0.19128846424309023, 0.3621720639192861, 0.8662628170445873, 1.3028536429111957, 1.6576796498116906, 1.9208428137110491, 2.087103105130754, 2.1559463888509516, 2.1314271568619825, 2.021795220750292, 1.8389262593969173, 1.5975860359173937, 1.314566636424676, 1.007739771152723, 0.695076627676027, 0.39368569498510797, 0.11891922989080915, -0.11640440460525188, -0.30262131037700674, -0.433652629287268, -0.5072224332737573, -0.5248518459430364, -0.49163070277464405, -0.4157805678604463, -0.30803486577355943, -0.18087257898023648, -0.04765077539446959, 0.078312374765182, 0.18464888051876713, 0.26079085973768085, 0.2987062485453744, 0.29347334882013687, 0.24365608524760773, 0.1514531109596971, 0.022607035402785417, -0.13392566470480285, -0.3065288551899576, -0.4816757467683036, -0.6448305827336421, -0.7814502781966458, -0.8780255023919777, -0.9230963282056405, -0.9081769861856883, -0.8285276160763922, -0.6837181411416356, -0.47794019999609294, -0.22003693415118433, 0.07676337745189113, 0.395406213147887, 0.7158405457207925, 1.0160803136846932, 1.273442811176385, 1.465896198129786, 1.5734389574384435, 1.5794290580314831, 1.4717802880915756, 1.243947896524452, 0.8956352262365961, 0.4331670450265257, -0.1305069009640765, -0.7761939048954013, -1.4792192802370185, -2.210536864351071, -2.9381377006922484, -3.628685937018706, -4.249294907876725, -4.76934494493374, -5.162238530333399, -5.406988524051062, -5.489541555799109, -5.4037511019290045, -5.151932718996345, -4.744956474136055, -4.201857582210701, -3.5489741670802606, -2.8186492793540596, -2.0475611243537886, -1.2747692117371197, -0.539583297774954, 0.12062474707209907, 0.6725396256984135, 1.0888264083057055, 1.349742653467261, 1.4443380209325194, 1.3711629763617592, 1.1384359086902676, 0.7636494185763765, 0.2726298502202799, -0.30190267833277085, -0.9221954911132036, -1.5476407118842395, -2.13714271944181, -2.651536058506017, -3.0559089139211246, -3.3216908583660554, -3.4283759976908814, -3.3647732643222064, -3.129703315238144, -2.7320946695179584, -2.190468380820232, -1.5318384269226673, -0.7900917302381308, -0.003944943175302008, 0.7853973389838617, 1.5367382939285665, 2.2113828457200677, 2.775473004707292, 3.2020165044666684, 3.4724791144993015, 3.577838032243337, 3.519027729606369, 3.3067484334917965, 2.9606485876967805, 2.507933507526958, 1.9814903053368789, 1.4176514947885452, 0.853744259056431, 0.32558745822447166, -0.13489707656078379, -0.5017989979610084, -0.756917024358687], 'positive_zeros': ['0.44022497863143795405037164598321', '1.86975325794326641026882816847267', '3.56089671973284099074275978842620', '4.99389689761302644042274935913768', '5.80837380629824899490847258730667', '6.40771621911847821791446893386309', '8.478920549827805365274689143823909', '9.586260465007933732388494846751632', '10.72135896235184130891089468380352', '11.41637206338824983896004801418612'], 'prelabel': '2-200-40.29-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.663635225064917, 'root_angle': -0.6889173535323236, 'root_number': '-0.5592670373515843945318381541531031868759388715608254709 - 0.8289875637981437811201726466114451128367009405846322913*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3444586767661618', 'prec': 64}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44022497863143795405037164598', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86975325794326641026882816847', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56089671973284099074275978843', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 32.07676396259613, 'bad_primes': [2, 5], 'central_character': '40.29', 'conductor': 200, 'conductor_radical': 10, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/200/6/f/a/149/6'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-200-40.29-c5-0-22', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-200-40.29-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.663635225064917, 'root_angle': -0.3444586767661618, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44022497863143795405037164598', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '558051458397601784711678089248', 'Lhash_array': ['558051458397601784711678089248'], 'label': '2-200-40.29-c5-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/200/6/f/a/149/6'}