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lfunc_lfunctions • Show schema
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{'Lhash': '2947551737447991802129090921780', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -16.98251613332169], 'a4': [0, 0], 'a5': [-12.3893197919697, -54.511510299131395], 'a6': [0, 0], 'a7': [0, -211.69122025054784], 'a8': [0, 0], 'a9': [-45.405854218531445, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 51.32282234015381, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [12.3893197919697, 54.511510299131395]]]], 'bad_primes': [2, 5], 'central_character': '320.129', 'coefficient_field': 'CDF', 'conductor': 320, 'conductor_radical': 10, 'conjugate': '356709714719468236633323011131', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 16.98251613332169], [-243.0, 0]], [[1.0, 0], [12.3893197919697, 54.511510299131395]], [[1.0, 0], [0, 211.69122025054784], [-16807.0, 0]], [[1.0, 0], [520.7065463559792, 0], [161051.0, 0]], [[1.0, 0], [0, -732.1051185455394], [-371293.0, 0]], [[1.0, 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'2.32520833178898893449799360115', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.13540065974709898775412399671', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.42341173762134746929482278571', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 51.32282234015381, 'bad_primes': [2, 5], 'central_character': '5.4', 'conductor': 320, 'conductor_radical': 10, 'degree': 2, 'index': 56, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/320/6/c/l/129/3'], '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': '2-320-5.4-c5-0-56', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-320-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.163994859026199, 'root_angle': -0.28556835015829063, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.32520833178898893449799360115', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2947551737447991802129090921780', 'Lhash_array': ['2947551737447991802129090921780'], 'label': '2-320-5.4-c5-0-56', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/320/6/c/l/129/3'}