-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '582199424273740973908041600090', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.944775186696442, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.11613287362019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '8280.1', 'coefficient_field': 'CDF', 'conductor': 8280, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.944775186696442, 0], [7.0, 0]], [[1.0, 0], [5.628163685563317, 0], [11.0, 0]], [[1.0, 0], [-4.424011347735828, 0], [13.0, 0]], [[1.0, 0], [3.414101888011005, 0], [17.0, 0]], [[1.0, 0], [2.358877074707447, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [8.57293887225976, 0], [29.0, 0]], [[1.0, 0], [8.996950219995588, 0], [31.0, 0]], [[1.0, 0], [-1.055224813303558, 0], [37.0, 0]], [[1.0, 0], [-9.355827294703033, 0], [41.0, 0]], [[1.0, 0], [-4.782888422443275, 0], [43.0, 0]], [[1.0, 0], [2.358877074707447, 0], [47.0, 0]], [[1.0, 0], [-11.46627692131015, 0], [53.0, 0]], [[1.0, 0], [13.245377668095918, 0], [59.0, 0]], [[1.0, 0], [-11.693297958591698, 0], [61.0, 0]], [[1.0, 0], [8.931815946967205, 0], [67.0, 0]], [[1.0, 0], [-4.683388498866876, 0], [71.0, 0]], [[1.0, 0], [-1.5306732986854372, 0], [73.0, 0]], [[1.0, 0], [-16.769929182714037, 0], [79.0, 0]], [[1.0, 0], [-5.414101888011005, 0], [83.0, 0]], [[1.0, 0], [18.835063455742418, 0], [89.0, 0]], [[1.0, 0], [-8.473438948683361, 0], [97.0, 0]], [[1.0, 0], [11.40114264828177, 0], [101.0, 0]], [[1.0, 0], [9.94172540669203, 0], [103.0, 0]], [[1.0, 0], [-10.559979632530524, 0], [107.0, 0]], [[1.0, 0], [-8.734825636512927, 0], [109.0, 0]], [[1.0, 0], [-14.449530005923407, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-8280-1.1-c1-0-11', 'leading_term': '0.95681236421590372388559793084979', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/8280/2/a/br/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [0.9568123642159038, 0.9466460236246569, 0.9161550937702762, 0.8653700481746649, 0.794361899992729, 0.7032710543607886, 0.5923448712393424, 0.46198140455389114, 0.3127764300663579, 0.14557072141706906, -0.03850543717688078, -0.23799333434581638, -0.45107505332624664, -0.6755530080478039, -0.9088415574952483, -1.1479720259325676, -1.3896120094012605, -1.6300993981132899, -1.8654910931726274, -2.091625946017111, -2.3042010018132033, -2.498859687004249, -2.6712901517819105, -2.8173315683469866, -2.933085805662684, -3.0150315630379354, -3.0601377615896896, -3.0659727781940544, -3.0308059744351485, -2.9536979357149735, -2.8345759036813307, -2.6742910665009125, -2.4746546711023147, -2.2384503404598965, -1.9694205142472345, -1.672225575271961, -1.3523749649377246, -1.0161304119324799, -0.670382278436792, -0.3225009424512092, 0.01983394494267437, 0.3488225933588485, 0.6567480262786676, 0.9361875351793891, 1.180226692859286, 1.3826695151858932, 1.5382380735068635, 1.6427547783190015, 1.6933006961858077, 1.6883436372959495, 1.6278303637700213, 1.513238113776306, 1.3475816998026062, 1.1353736981685125, 0.8825366693818867, 0.5962678953342032, 0.28485874234545155, -0.04252759461106831, -0.3761145993563868, -0.7058003095689394, -1.0214663142858462, -1.313298482392969, -1.5721091540753442, -1.789649968549285, -1.9589042999970028, -2.074348457768001, -2.1321713920433347, -2.1304436334376433, -2.0692275703468614, -1.9506229014710172, -1.7787431475901723, -1.5596214064005895, -1.3010460138485616, -1.0123293505996256, -0.7040156102308086, -0.38753582829933586, -0.07482075876604032, 0.2221158213611409, 0.4916091883508794, 0.7227757940001918, 0.9059294874779953, 1.0329658616897015, 1.0976993319899986, 1.0961387557948068, 1.026689202008003, 0.8902698360430635, 0.6903407319149788, 0.4328346666795851, 0.1259934831460779, -0.21988770399284197, -0.5928014765476557, -0.9794436973086336, -1.3656898562520936, -1.7371154539205267, -2.079541387417324, -2.379583672078891, -2.6251859717877926, -2.806113389861363, -2.914386825272476, -2.944638925422705, -2.8943752299661516, -2.7641274267057976, -2.557489621500313, -2.2810330183492464, -1.9440992446716523, -1.5584775499728698, -1.137976048993145, -0.6979018623347617, -0.25446922053079524, 0.17584185445411696, 0.5769509682229337, 0.9338398287323662, 1.2331841032887898, 1.4639275140102361, 1.617772733392201, 1.6895664886351407, 1.6775601868470202, 1.5835321983721642, 1.412763502063867, 1.1738644848291175, 0.8784570478233915, 0.5407225319861441, 0.17683205545112385, -0.19571862314101135, -0.5588429006133584, -0.8946353239742422, -1.1861489273983306, -1.418144053483369, -1.577775280085507, -1.6551850559903925, -1.6439760874793872, -1.5415392997147987, -1.3492201429374402, -1.0723128858543707, -0.7198800493964784, -0.3044019570393778, 0.1587308374790482, 0.6518620973334619, 1.1558246394907412, 1.6507729151487522, 2.1170568895440587, 2.536098072653128, 2.8912277043862544, 3.1684480907949166, 3.3570809214904376, 3.450270985613399, 3.445319871294653, 3.3438317285632575, 3.1516616747245845, 2.878666544137032, 2.538267010642985, 2.1468391991980686, 1.7229623117821917, 1.286556100978907, 0.8579478545228065, 0.4569125895146263, 0.10173215905296719, -0.19168119694315425, -0.41055371175691296, -0.5458727534785931, -0.5928311891318939, -0.551069560797904, -0.424701723064139, -0.2221200202028485, 0.04441309735059395, 0.35936943320203757, 0.7047277849747406, 1.0608786399587273, 1.40761722789898, 1.725176205842457, 1.99524647267823, 2.201934372870481, 2.33260591578357, 2.3785735442584777, 2.335588238440646, 2.204109019038564, 1.9893327882025658, 1.7009793945392573, 1.3528392428999778, 0.9621030626077519, 0.5485049658340271, 0.13332006262301216, -0.2617338999652635, -0.6156356028150327, -0.9091815933660373, -1.1260316685439618, -1.2536226985390222, -1.2839012473428872, -1.213833892538858, -1.0456649884781513, -0.7869042328687256, -0.45004016192336205, -0.0519899148428738, 0.38669046264802803, 0.8427980012904198, 1.2916287217385523, 1.7082202859263382, 2.068628213128635, 2.351169732012671, 2.537570015098541, 2.6139496745751893, 2.571599831227417, 2.4075014647278823, 2.124558611907744, 1.7315296562671614, 1.2426566933056362, 0.6770089369748203, 0.057571498921640867, -0.5898752123759752, -1.238028534589116, -1.8594232995964535, -2.427807164860585, -2.919458782194598, -3.314378341930647, -3.597286159398723, -3.758374669954464, -3.793771993627482, -3.7056904677206695, -3.502250426750276, -3.196987131145303, -2.808066150081473, -2.3572487265765636, -1.8686627807190332, -1.3674464269411357, -0.8783385291601374, -0.42429441708947424, -0.025204179962514322, 0.30321408114437165, 0.5502828035782024, 0.710944872078344, 0.7860202225878302, 0.7821223959176569, 0.7112373735740859, 0.58998620234919, 0.43861110186459284, 0.2797409053724566, 0.13700486302310652, 0.03357324743493023, -0.009291744823304646, 0.026409045763443526, 0.15423031678071542, 0.38234476772879, 0.712906611050091, 1.1417566468452744, 1.6584902374108637, 2.2468888685304798, 2.885695037044668, 3.5496901641901464, 4.21101727276258, 4.840675351615888, 5.410101564920811, 5.892751425537911, 6.2655861561398805, 6.510380828900286, 6.614776319617536, 6.573012150339071, 6.386295165083177], 'positive_zeros': ['0.45927436485173521828108752383521', '1.87224405904429818286111278499670', '2.66586559047192184633676977325910', '3.57400840190912942996989389609446', '4.14261257908554026966187488337162', '5.08993238855482861556521728513014', '5.74099635003379820536201752380478', '6.35936409030260970362588050183335', '7.32756715758634408626039786937020', '7.68031560341228996209230195269356'], 'prelabel': '2-8280-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.45927436485173521828108752384', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.87224405904429818286111278500', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.66586559047192184633676977326', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 66.11613287362019, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 8280, 'conductor_radical': 690, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8280/2/a/br/1/3'], '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': '2-8280-1.1-c1-0-11', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-8280-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.45927436485173521828108752384', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '582199424273740973908041600090', 'Lhash_array': ['582199424273740973908041600090'], 'label': '2-8280-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8280/2/a/br/1/3'}