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lfunc_lfunctions • Show schema
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{'Lhash': '1511790530109965884618721006353', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-28.922663788089924, 0.0], 'a4': [0.0, 0.0], 'a5': [63.53361693307637, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [593.5204805988883, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.87045736668842, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '392.1', 'coefficient_field': 'CDF', 'conductor': 392, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [28.922663788089924, 0], [243.0, 0]], [[1.0, 0], [-63.53361693307637, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [592.5204805988883, 0], [161051.0, 0]], [[1.0, 0], [433.35873981774154, 0], [371293.0, 0]], [[1.0, 0], [32.204868126949776, 0], [1419857.0, 0]], [[1.0, 0], [-2712.560889719949, 0], [2476099.0, 0]], [[1.0, 0], 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'4.59042451691373925301747166164557', '5.39876082273450150808812024996861', '5.89845560984097690607823344937861', '6.93334765370203421030927799996437', '7.917637665189491610709303256691490', '9.750071188729590688007505000541707', '10.06394873988487230423531707077669'], 'prelabel': '2-392-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.929089315090883, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19259244608710099172340758763', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.57631134028465108204872478711', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.59042451691373925301747166165', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.87045736668842, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 392, 'conductor_radical': 14, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/392/6/a/h/1/1'], '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': '2-392-1.1-c5-0-29', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-392-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.929089315090883, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19259244608710099172340758763', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1511790530109965884618721006353', 'Lhash_array': ['1511790530109965884618721006353'], 'label': '2-392-1.1-c5-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/392/6/a/h/1/1'}