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lfunc_lfunctions • Show schema
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{'Lhash': '1403101191620482084518949462722', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.1731708902647706, -4.860418712645585], 'a6': [0, 0], 'a7': [-5.873670062235365, -3.391164991562634], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.1418028263681, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.1731708902647706, 4.860418712645585]]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.269', 'coefficient_field': 'CDF', 'conductor': 1620, 'conductor_radical': 30, 'conjugate': '813783735792632808474863345420', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.1731708902647706, 4.860418712645585]], [[1.0, 0], [5.873670062235365, 3.391164991562634], [24.5, 42.4352447854375]], [[1.0, 0], [-8.573214099741124, -4.949747468305833], [60.5, 104.78907385791707]], [[1.0, 0], 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'root_angle': 0.4801663343858031, 'root_number': '0.0622689872383654295993453453784047945867838168778276767 + 0.9980594036570710470213852892774074809243805783661901202*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.24008316719290157', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10685167613841384126529542385', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.53619467986412609031087062997', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53812925462567466032525516457', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.1418028263681, 'bad_primes': [2, 3, 5], 'central_character': '45.29', 'conductor': 1620, 'conductor_radical': 30, 'degree': 2, 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/3/t/c/269/2'], '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': '2-1620-45.29-c2-0-35', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1620-45.29-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.643929772835358, 'root_angle': 0.24008316719290154, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10685167613841384126529542385', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1403101191620482084518949462722', 'Lhash_array': ['1403101191620482084518949462722'], 'label': '2-1620-45.29-c2-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/3/t/c/269/2'}