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lfunc_lfunctions • Show schema
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{'Lhash': '1949218057111351969557292007248', 'a10': [1.2222226756649321, 2.1169517724144398], 'a2': [0.9781476007338057, 0.20791169081775934], 'a3': [0.10452846326765347, -0.9945218953682733], 'a4': [0.9135454576426009, 0.4067366430758002], 'a5': [1.6356532001464443, 1.8165769140030599], 'a6': [0.30901699437494745, -0.9510565162951535], 'a7': [2.4904271732908114, 0.8931811095935348], 'a8': [0.8090169943749475, 0.5877852522924731], 'a9': [-0.9781476007338057, -0.20791169081775934], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9781476007338057, -0.20791169081775934]]], [3, [[1.0, 0], [-0.10452846326765347, 0.9945218953682733]]], [7, [[1.0, 0], [-2.4904271732908114, -0.8931811095935348]]], [11, [[1.0, 0], [2.6012830272118497, -2.0575049483147194]]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '462.247', 'coefficient_field': 'CDF', 'conductor': 462, 'conductor_radical': 462, 'conjugate': '2577413454015203745526144527857', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9781476007338057, -0.20791169081775934]], [[1.0, 0], [-0.10452846326765347, 0.9945218953682733]], [[1.0, 0], [-1.6356532001464443, -1.8165769140030599], [-0.5226423163382674, 4.972609476841367]], [[1.0, 0], [-2.4904271732908114, -0.8931811095935348]], [[1.0, 0], [2.6012830272118497, -2.0575049483147194]], [[1.0, 0], [0.13719909600438696, 0.42225539908802884], [-10.517220926874316, 7.641208279802151]], [[1.0, 0], [3.969512695574285, -0.8437459700767713], [15.530272779924216, -6.9145229322886035]], [[1.0, 0], [-1.053748397092681, 0.46915901348355177], [12.713481520818306, -14.11975168407049]], [[1.0, 0], [-3.3512943180030748, 5.804612029898216], [-11.5, -19.91858428704209]], [[1.0, 0], [-1.2462985969949723, 0.9054889333102615], [8.961492836873475, -27.580638972559452]], [[1.0, 0], [1.0004899784548118, -1.1111566910331037], [-3.2403823612972578, 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32.13219480298822]], [[1.0, 0], [5.438096833809458, -16.73674109898024], [-67.14841053312064, -48.78617594027527]], [[1.0, 0], [7.459964405541461, -12.921037373053167], [-44.5, -77.07626093681505]], [[1.0, 0], [2.899504428761531, 8.923757046366102], [-78.4746484543699, 57.01516947236989]], [[1.0, 0], [9.395122120289125, -10.434340205141684], [-10.557374790033, -100.44671143219561]], [[1.0, 0], [-0.12646375921615607, -1.203222295433559], [-100.74920287558199, 21.414904154229212]], [[1.0, 0], [-11.31605151128, 5.038230737250868], [71.59697488039782, -79.51649632608118]], [[1.0, 0], [-8.503891857868473, -14.72917275989949], [-54.5, 94.39676901250381]], [[1.0, 0], [11.865058112815703, 8.620469316215637], [34.91892036436906, 107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-462-77.16-c1-0-7', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 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1.9207000217064496, 'root_angle': -0.10900916611889667, 'root_number': '0.9419306311150462 - 0.3358075135657493*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0545045830594', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.53766192100600300242181956105', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.02085709670779245129661591685', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.45494704330470691254607817847', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'bad_primes': [2, 3, 7, 11], 'central_character': '77.16', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/462/2/y/a/247/3'], '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': '2-462-77.16-c1-0-7', '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': '2-462-77.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': -0.05450458305944834, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53766192100600300242181956105', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1949218057111351969557292007248', 'Lhash_array': ['1949218057111351969557292007248'], 'label': '2-462-77.16-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/2/y/a/247/3'}