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lfunc_lfunctions • Show schema
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{'Lhash': '1647461135422186752339757489585', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -3.622582728609198], 'a4': [0, 0], 'a5': [4.968365771400742, 0.5615528128088303], 'a6': [0, 0], 'a7': [6.451009853355388, 0], 'a8': [0, 0], 'a9': [-4.123105625617661, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.438736919059004, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-4.968365771400742, -0.5615528128088303]]]], 'bad_primes': [2, 5], 'central_character': '640.319', 'coefficient_field': 'CDF', 'conductor': 640, 'conductor_radical': 10, 'conjugate': '1677240521480423386611387893382', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.622582728609198], [-9.0, 0]], [[1.0, 0], [-4.968365771400742, -0.5615528128088303]], [[1.0, 0], [-6.451009853355388, 0], [49.0, 0]], [[1.0, 0], [3.9456555193990543, 0], [121.0, 0]], [[1.0, 0], [-15.516731090787886, 0], [169.0, 0]], [[1.0, 0], [0, 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'positive_zeros': ['1.29961768260558215841506570154278', '2.80782463375935951558936869353229', '4.03213200365735979198045127307245', '5.14785679519744224110050748235779', '5.50125085241546627932468108392393', '6.89688835769636064494629076951388', '8.070498646315403968396342434069254', '8.995235472822060929496752753202528', '9.745409799594894365619195185908475', '10.28327024045613521265087294725257'], 'prelabel': '2-640-40.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.1759713743102935, 'root_angle': 0.28582514769613776, 'root_number': '0.6232174652882186182302339152284824097278759599778355412 + 0.7820485860608201506771425857201312938091142308533483147*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.14291257384806888', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29961768260558215841506570154', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80782463375935951558936869353', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.03213200365735979198045127307', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.438736919059004, 'bad_primes': [2, 5], 'central_character': '40.19', 'conductor': 640, 'conductor_radical': 10, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/640/3/e/i/319/4'], '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': '2-640-40.19-c2-0-30', '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': '2-640-40.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.1759713743102935, 'root_angle': 0.14291257384806888, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29961768260558215841506570154', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1647461135422186752339757489585', 'Lhash_array': ['1647461135422186752339757489585'], 'label': '2-640-40.19-c2-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/640/3/e/i/319/4'}