Formats: - HTML - YAML - JSON - 2026-09-15T04:01:44.237387
  • lfunc_lfunctions • Show schema
    {'Lhash': '5218830375373169758831650295217', 'a10': [2.137054624375387, 2.3308791329530094], 'a2': [-0.541196100146197, -1.3065629648763766], 'a3': [-1.3065629648763766, -1.137054624375387], 'a4': [-1.4142135623730951, 1.4142135623730951], 'a5': [-2.1010029896154587, 0.7653668647301796], 'a6': [-0.7785266800637528, 2.322476309551706], 'a7': [-2.274109248750774, 0.0], 'a8': [2.613125929752753, 1.082392200292394], 'a9': [0.41421356237309503, 2.9712669225006008], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0.541196100146197, 1.3065629648763766]]], [3, [[1.0, 0], [1.3065629648763766, 1.137054624375387]]], [5, [[1.0, 0], [2.1010029896154587, -0.7653668647301796]]]], 'bad_primes': [2, 3, 5], 'central_character': '120.59', 'coefficient_field': 'CDF', 'conductor': 120, 'conductor_radical': 30, 'conjugate': '248726031412606142814775465623', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.541196100146197, 1.3065629648763766]], [[1.0, 0], [1.3065629648763766, 1.137054624375387]], [[1.0, 0], [2.1010029896154587, -0.7653668647301796]], [[1.0, 0], [2.274109248750774, 0], [7.0, 0]], [[1.0, 0], [0, 4.2020059792309175], [-11.0, 0]], [[1.0, 0], [3.216076141901435, 0], [13.0, 0]], [[1.0, 0], [1.5307337294603591, 0], [17.0, 0]], [[1.0, 0], [4.82842712474619, 0], [19.0, 0]], [[1.0, 0], [0, 1.082392200292394], [-23.0, 0]], [[1.0, 0], [1.7405278657702838, 0], [29.0, 0]], [[1.0, 0], [0, 6.82842712474619], [-31.0, 0]], [[1.0, 0], [-7.7642946394029835, 0], [37.0, 0]], [[1.0, 0], [0, -2.4614781134606334], [-41.0, 0]], [[1.0, 0], [0, -8.706261532553643], [-43.0, 0]], [[1.0, 0], [0, -1.082392200292394], [-47.0, 0]], [[1.0, 0], [0, 11.086554390135442], [-53.0, 0]], [[1.0, 0], [0, -4.2020059792309175], [-59.0, 0]], [[1.0, 0], [0, -8.48528137423857], [-61.0, 0]], [[1.0, 0], [0, -2.274109248750774], [-67.0, 0]], [[1.0, 0], [11.885067690002403, 0], [71.0, 0]], [[1.0, 0], [0, 4.548218497501548], [-73.0, 0]], [[1.0, 0], [0, 0.4852813742385703], [-79.0, 0]], [[1.0, 0], [6.942694730922329, 0], [83.0, 0]], [[1.0, 0], [0, 8.404011958461835], [-89.0, 0]], [[1.0, 0], [0, 10.98037078130442], [-97.0, 0]], [[1.0, 0], [-13.625595555772687, 0], [101.0, 0]], [[1.0, 0], [8.706261532553643, 0], [103.0, 0]], [[1.0, 0], [5.674593388673471, 0], [107.0, 0]], [[1.0, 0], [0, 16.48528137423857], [-109.0, 0]], [[1.0, 0], [-0.6340506711244288, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-120-120.59-c1-0-19', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/120/2/m/b/59/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [0.15160256966700497, 0.25582323773905247, 0.3717623540022715, 0.504251405989139, 0.6577125730690032, 0.8358981366435735, 1.041700957653844, 1.276999106836435, 1.542503146944035, 1.8375929080057865, 2.1601484376915616, 2.5063918665919407, 2.8707633046249463, 3.2458562099714765, 3.6224372338430224, 3.9895729450025597, 4.334881217572569, 4.644918392704167, 4.905704607293367, 5.103379097613525, 5.2249652463387815, 5.259212325875529, 5.197468233376565, 5.034526163421922, 4.769379416593507, 4.405813729230714, 3.9527668738421604, 3.4243918228094152, 2.8397730949020716, 2.2222660744355363, 1.5984555004800571, 0.9967606222164682, 0.445748611342485, -0.02774805895105261, -0.400583705364734, -0.6551703998185481, -0.781103491054175, -0.7763769975823231, -0.648039355046903, -0.41217163360284903, -0.0931177925910255, 0.27804261212115894, 0.6657188448115419, 1.0325968243992538, 1.342787261776387, 1.5650732661130173, 1.675958263952251, 1.662202853596033, 1.5225578774531823, 1.268452549816485, 0.9234795241547208, 0.5216281619162136, 0.10434411319017549, -0.28337440892672366, -0.5975098385813993, -0.7997545903480557, -0.8619416967319131, -0.7696700221622835, -0.5246619536772992, -0.14549370501537107, 0.3335075299767658, 0.8652120991052322, 1.3942812259591912, 1.8629944204535813, 2.2177197902559853, 2.415310233432561, 2.4286583462016695, 2.2506822854157784, 1.8961477565398086, 1.4009501934009043, 0.8187666370112278, 0.21530874956053037, -0.33927109155653795, -0.7789911719136112, -1.0506454583601352, -1.1213002616794476, -0.9836394934995056, -0.6583160949367974, -0.1927954780131705, 0.34339991461602104, 0.8666661641100236, 1.2896781583824137, 1.5329187352151328, 1.5359147715134414, 1.2666515894519292, 0.7277735806736747, -0.04148365621756871, -0.9681768522729981, -1.9532810963992027, -2.8833299115417574, -3.6447400465876933, -4.139033804953927, -4.2969321210040015, -4.089319903557398, -3.5333962377903045, -2.6928909290563268, -1.6719914025777591, -0.6034831828362138, 0.3675547650293508, 1.1024643479158058, 1.4876560790171103, 1.450605823907896, 0.9708751642894319, 0.08443808962768726, -1.1195176113206349, -2.5091001143872087, -3.9262626473702116, -5.207208425410412, -6.203846174651455, -6.8032655172093826, -6.942422679295331, -6.615878071446802, -5.875423524163171, -4.821635597406275, -3.5886116415961227, -2.3241956500508394, -1.1687097017236683, -0.235451011640649, 0.404057464594412, 0.7278321240519455, 0.7631085919567607, 0.5781595007230647, 0.26777453562053666, -0.0650146890066992, -0.3277530715115294, -0.45462955037280844, -0.4169908205536433, -0.22649057927418154, 0.06960692532660818, 0.4000129376816481, 0.6856451331218799, 0.8573578409536858, 0.8716898944653512, 0.7214576766219665, 0.4389399732238504, 0.09078000601114536, -0.23467379046906592, -0.44534682280440585, -0.4653450584696498, -0.2528524057275216, 0.18772392319877693, 0.8021700521758243, 1.4927248143886815, 2.1336001142004277, 2.5933261149989466, 2.759996997308398, 2.5646788979680846, 1.9982966817869834, 1.1182794461292287, 0.04298269863079658, -1.065871932872626, -2.030190209636584, -2.68742703834587, -2.921723076031584, -2.688354351086729, -2.02651618248648, -1.0573803707468947, 0.03303707006668578, 1.0238420962746082, 1.697194759297923, 1.877625383251172, 1.4656001846072082, 0.45896650672086925, -1.0420997078065721, -2.8481310758612772, -4.70960466425178, -6.3575452074920875, -7.548434364047477, -8.105402052901272, -7.948201901390299, -7.106427131304061, -5.713465835899906, -3.9822637162272074, -2.1673782594725606, -0.5204046646084656, 0.75288965448777, 1.525734651686197, 1.767751785080723, 1.5435994546201464, 0.9935945528073642, 0.3005887364679868, -0.34993064713509403, -0.8082690647558252, -0.9896465565553866, -0.888198383599962, -0.5732650178702398, -0.16914434473649728, 0.17700796528082596, 0.3319248855349054, 0.20943495116794697, -0.20727688073062348, -0.85937127767853, -1.623536861691498, -2.3383089090923432, -2.8397958184275693, -2.9989247679148625, -2.75187512195225, -2.1167657415438277, -1.192619760965281, -0.14051639505508864, 0.849195427484916, 1.5965856107724874, 1.970061134527671, 1.9141227117501372, 1.4607369950314684, 0.7217002963861938, -0.13639063940172413, -0.9290160901021767, -1.4941954119326146, -1.727403212818104, -1.6030246618167814, -1.1774884683247326, -0.5734330259754152, 0.05131801448315583, 0.5425991085155748, 0.7872841614086161, 0.7401876437182409, 0.43388860592152834, -0.031064021114296417, -0.513344960109747, -0.8688812498163289, -0.9902859798629161, -0.8376195606453202, -0.4522073428933232, 0.05084356286123879, 0.5106302750744995, 0.7629487875742971, 0.687325834184859, 0.24687890283958033, -0.4896749558022909, -1.3508561279883768, -2.0915128329438906, -2.443324520585121, -2.176424341198593, -1.1585207120675631, 0.6024109625700049, 2.9428698799087267, 5.561381632529394, 8.067097506263826, 10.050614317877976, 11.162829531005354, 11.185286419382708, 10.076742968815429, 7.985434773054199, 5.223711667456919, 2.20983013132269, -0.611143091305306, -2.8507596964970987, -4.2474437946277765, -4.709014104072828, -4.319118633335583, -3.307269983952653, -1.9902100712303374, -0.6985188823778088, 0.29470670351179207, 0.827289050037013, 0.872358296274626], 'positive_zeros': ['4.11693125411179153206936073440582', '5.03258589969553009185304166927154', '6.53214444788118060689317435763635', '7.41527878555189654546206572994321', '8.921409501696274229198855449339720', '9.795875636476771573357109276644686', '10.74396157971173393110827098010080', '12.19998986721175847357127509675249', '12.88480415649350000331614306675304', '14.66442085357218251923875634171317'], 'prelabel': '2-120-120.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.3791225561987731, 'root_number': '-0.7251835627632383 - 0.6885555898386249*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.379122556199', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.11693125411179153206936073441', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '5.03258589969553009185304166927', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '6.53214444788118060689317435764', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'bad_primes': [2, 3, 5], 'central_character': '120.59', 'conductor': 120, 'conductor_radical': 30, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/120/2/m/b/59/5'], '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': '2-120-120.59-c1-0-19', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-120-120.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.3791225561987731, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '4.11693125411179153206936073441', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '5218830375373169758831650295217', 'Lhash_array': ['5218830375373169758831650295217'], 'factors': ['2-120-120.59-c1-0-19'], 'label': '2-120-120.59-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/120/2/m/b/59/5'}