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lfunc_lfunctions • Show schema
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{'Lhash': '2975656388003110707148533400255', 'a10': [0.8322724611250469, -1.4415381884089746], 'a2': [0.8322724611250469, 1.4415381884089746], 'a3': [0.5798778776151141, 1.004377946214585], 'a4': [-0.38535489909428544, 0.6674542641768804], 'a5': [-0.5, -0.8660254037844386], 'a6': [-0.9652327767093997, 1.6718322103914653], 'a7': [-2.4352547204386648, 0.0], 'a8': [2.0462087633970074, 0.0], 'a9': [0.8274832941051814, -1.4332431078046342], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.758578819202164, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.5, 0.8660254037844386]]], [19, [[1.0, 0], [-0.14941232419631492, 4.356337447601856]]]], 'bad_primes': [5, 19], 'central_character': '95.26', 'coefficient_field': 'CDF', 'conductor': 95, 'conductor_radical': 95, 'conjugate': '4349888465930733050417100959598', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8322724611250469, -1.4415381884089746], [-1.0, 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'7.942396577047318941995325308265290', '9.879168573822033094588934840320780', '10.66642836378644564513874016978079', '11.85561052462833769707490500789771', '12.86768598469082587225251727402310', '13.37415616752082970205865156647766'], 'prelabel': '2-95-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8709643042066443, 'root_angle': -0.42133369496405504, 'root_number': '0.2446294240450636 - 0.9696166484190443*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.210666847482', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.34737899186682024585389260596', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.46472210352320493045315886827', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.24124426899623972660220834703', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.758578819202164, 'bad_primes': [5, 19], 'central_character': '19.7', 'conductor': 95, 'conductor_radical': 95, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/95/2/e/c/26/4'], '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': '2-95-19.7-c1-0-3', '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': '2-95-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8709643042066443, 'root_angle': -0.21066684748202752, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.34737899186682024585389260596', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2975656388003110707148533400255', 'Lhash_array': ['2975656388003110707148533400255'], 'label': '2-95-19.7-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/95/2/e/c/26/4'}