Formats: - HTML - YAML - JSON - 2026-10-11T08:46:39.796082
  • lfunc_lfunctions • Show schema
    {'Lhash': '2865282383837379307103198552370', 'a10': [261958202.43638283, 0], 'a2': [670.61299823714, 0], 'a3': [0, 0], 'a4': [318649.79340460635, 0], 'a5': [390625.0, 0], 'a6': [0, 0], 'a7': [-27080419.853429858, 0], 'a8': [125792106.4377699, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 82.44993930505191, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '8.5', 'prec': 7}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-390625.0, 0]]]], 'bad_primes': [3, 5], 'central_character': '45.1', 'coefficient_field': 'CDF', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [-670.61299823714, 0], [131072.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-390625.0, 0]], [[1.0, 0], [27080419.853429858, 0], [232630513987207.0, 0]], [[1.0, 0], [1016437517.8280613, 0], [505447028499293760, 0]], [[1.0, 0], [1048341692.8712277, 0], [8650415919381338000, 0]], [[1.0, 0], [20009875690.736774, 0], [827240261886336800000, 0]], [[1.0, 0], [-16441670984.88548, 0], [5480386857784803000000, 0]], [[1.0, 0], [592720869745.1757, 0], [141050039560662970000000, 0]], [[1.0, 0], [483211743430.14746, 0], [7257147736730074000000000, 0]], [[1.0, 0], [5208020935203.368, 0], [22550116774162744000000000, 0]], [[1.0, 0], [-38236695078278.805, 0], [456487940826035130000000000, 0]], [[1.0, 0], [-65640229363379.6, 0], [2614120267500775300000000000, 0]], [[1.0, 0], [58380447168258.51, 0], [5874403106360420000000000000, 0]], [[1.0, 0], [7436577752042.163, 0], [26647936506962194000000000000, 0]], [[1.0, 0], [-301465724941656.5, 0], [205442259656281400000000000000, 0]], [[1.0, 0], [-344389469413177.3, 0], [1271991467017507700000000000000, 0]], [[1.0, 0], [2432367454408486.0, 0], [2241853325254885400000000000000, 0]], [[1.0, 0], [-1196317640949616.8, 0], [11047694236668359000000000000000, 0]], [[1.0, 0], [5422535244428516.0, 0], [29606831241262270000000000000000, 0]], [[1.0, 0], [5847322652392601.0, 0], [47477585226700100000000000000000, 0]], [[1.0, 0], [-2034550092039704.8, 0], [181827912146592060000000000000000, 0]], [[1.0, 0], [-11834332223491414, 0], [421044084813170700000000000000000, 0]], [[1.0, 0], [-24317044286694624, 0], [1379209096840925500000000000000000, 0]], [[1.0, 0], [106104506608950960, 0], [5958260438588052000000000000000000, 0]], [[1.0, 0], [63653356735222500, 0], [11843044313729356000000000000000000, 0]], [[1.0, 0], [37641357937627870, 0], [16528476322717512000000000000000000, 0]], [[1.0, 0], [197603029925705440, 0], [31588152109649857000000000000000000, 0]], [[1.0, 0], [-214471780520410940, 0], [43276334103547420000000000000000000, 0]], [[1.0, 0], [329313088679253440, 0], [79860778452816620000000000000000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-45-1.1-c17-0-28', 'leading_term': '10.57524761447564545918919915311190865119190', 'load_key': 'CMFs-workshop', 'motivic_weight': 17, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [17], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/45/18/a/e/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.07421875', 'prec': 24}, 'plot_values': [-5.546019279859451e-60, 0.7827145616233461, 1.5524821389461922, 2.296632351122594, 3.003041558137519, 3.6603902197825136, 4.2584014678700255, 4.788055330470482, 5.241773626937332, 5.613571251854978, 5.899170368543774, 6.096074919666325, 6.203603813030077, 6.2228821325059664, 6.1567907336142085, 6.009875586721147, 5.788219203867431, 5.4992774044472865, 5.151685517787532, 4.755038866238854, 4.319653001902686, 3.8563096673610557, 3.375994802534149, 2.8896351161940257, 2.407839775489254, 1.9406536377161254, 1.497328157123128, 1.086115651393157, 0.7140920172141011, 0.3870122554376519, 0.10920232071877833, -0.11651013156955083, -0.28882454393640783, -0.40795530745682856, -0.47557925608250295, -0.4947444742241946, -0.46974313003643614, -0.40595202620056514, -0.3096454489199312, -0.18778566909097988, 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9.612167209073775, 9.64135806599172, 9.455163237678692, 9.050231665082313, 8.43113155444926, 7.610373424607301, 6.608092486738676, 5.451397512771971, 4.173408983043128, 2.8120241718116006, 1.4084601901152778, 0.005637176999108449, -1.353527776096453, -2.627840229810101, -3.7794841904389456, -4.775538842339382, -5.589286707655023, -6.201252884531511, -6.599927200235711, -6.782135763304077, -6.753044815467078, -6.525797175689297], 'positive_zeros': ['2.26030925502777364569602277057722', '2.99270835962231112265918300102323', '4.19302310159541258492904928685059', '5.57716537593172213541321281468164', '6.28116383351354129468907676232896', '7.46718707117094221168533143582830', '9.695986084623531292024287146854931', '10.76479610593183395282742554330847', '12.24321485543385708424813749749291'], 'prelabel': '2-45-1.1-c17-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.080194893561035, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c17-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.26030925502777364569602277058', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.99270835962231112265918300102', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.19302310159541258492904928685', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 82.44993930505191, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/45/18/a/e/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': '2-45-1.1-c17-0-28', 'motivic_weight': 17, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [17], 'order_of_vanishing': 1, 'prelabel': '2-45-1.1-c17-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.080194893561035, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c17-0', 'z1': {'__RealLiteral__': 0, 'data': '2.26030925502777364569602277058', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2865282383837379307103198552370', 'Lhash_array': ['2865282383837379307103198552370'], 'factors': ['2-45-1.1-c17-0-28'], 'label': '2-45-1.1-c17-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/18/a/e/1/3'}