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lfunc_lfunctions • Show schema
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{'Lhash': '1795000160534343621978115762162', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.9054888528699114, 0.0], 'a4': [0.0, 0.0], 'a5': [6.528551467039319, 0.0], 'a6': [0.0, 0.0], 'a7': [5.2270614252849334, 0.0], 'a8': [0.0, 0.0], 'a9': [-23.36911223158851, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 109.50754497065464, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [-29.0, 0]]]], 'bad_primes': [2, 29], 'central_character': '1856.1', 'coefficient_field': 'CDF', 'conductor': 1856, 'conductor_radical': 58, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.9054888528699114, 0], [27.0, 0]], [[1.0, 0], [-6.528551467039319, 0], [125.0, 0]], [[1.0, 0], [-5.2270614252849334, 0], [343.0, 0]], [[1.0, 0], [-21.129879954934705, 0], [1331.0, 0]], [[1.0, 0], [83.46151488752119, 0], [2197.0, 0]], [[1.0, 0], [-11.32727179636059, 0], [4913.0, 0]], [[1.0, 0], 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'4.53369169869112976909313680943484', '5.15489385806100733276816374516271', '6.10858128274664950271612941829480', '6.90322144254475724542664223182204', '7.81383669880812795802907851896418', '8.466387938717131168857234566619366'], 'prelabel': '2-1856-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.464585274661134, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41600545151098381940867217950', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52629396243925500829846400147', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.13394496298783334510622350428', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 109.50754497065464, 'bad_primes': [2, 29], 'central_character': '1.1', 'conductor': 1856, 'conductor_radical': 58, 'degree': 2, 'index': 137, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1856/4/a/y/1/4'], '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': '2-1856-1.1-c3-0-137', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1856-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.464585274661134, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41600545151098381940867217950', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1795000160534343621978115762162', 'Lhash_array': ['1795000160534343621978115762162'], 'label': '2-1856-1.1-c3-0-137', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1856/4/a/y/1/4'}