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lfunc_lfunctions • Show schema
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{'Lhash': '873632253433613471201599822130', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.7933533402912352, 0.6087614290087207], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9563348495213695, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.7933533402912352, -0.6087614290087207]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '3920.3743', 'coefficient_field': 'CDF', 'conductor': 3920, 'conductor_radical': 70, 'conjugate': '1696927453376973307997586121271', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0.7933533402912352, -0.6087614290087207]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.541196100146197, 0.541196100146197], [0, 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'z1': {'__RealLiteral__': 0, 'data': '0.68917433027391272190956518837', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.85631519466179718673316781499', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17721926390160841739470778842', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9563348495213695, 'bad_primes': [2, 5, 7], 'central_character': '140.103', 'conductor': 3920, 'conductor_radical': 70, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3920/1/cx/a/3743/1'], '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': '2-3920-140.103-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3920-140.103-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3986904051724132, 'root_angle': -0.20953857380993843, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68917433027391272190956518837', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '873632253433613471201599822130', 'Lhash_array': ['873632253433613471201599822130'], 'label': '2-3920-140.103-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3920/1/cx/a/3743/1'}