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lfunc_lfunctions • Show schema
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{'Lhash': '1695295117802237472742033731132', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -5.0], 'a6': [0, 0], 'a7': [0, -20.784609690826528], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 127.44412561239979, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 5.0]]]], 'bad_primes': [2, 3, 5], 'central_character': '2160.431', 'coefficient_field': 'CDF', 'conductor': 2160, 'conductor_radical': 30, 'conjugate': '234670179320962443984180552286', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 5.0]], [[1.0, 0], [0, 20.784609690826528], [-343.0, 0]], [[1.0, 0], [-36.373066958946424, 0], [1331.0, 0]], [[1.0, 0], [47.0, 0], [2197.0, 0]], [[1.0, 0], [0, -21.0], [-4913.0, 0]], [[1.0, 0], [0, -62.353829072479584], [-6859.0, 0]], [[1.0, 0], [-36.373066958946424, 0], [12167.0, 0]], [[1.0, 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'6.82074837197660996824644662398501', '7.40629457137832818037287898564131', '8.496245740881756200056824224533825', '9.148701862920846544285939254152156'], 'prelabel': '2-2160-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.289115360044816, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33735204124623489846335512415', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.50049631462422821294937239586', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.10462251469429307071810747416', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 127.44412561239979, 'bad_primes': [2, 3, 5], 'central_character': '12.11', 'conductor': 2160, 'conductor_radical': 30, 'degree': 2, 'index': 87, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2160/4/h/a/431/1'], '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': '2-2160-12.11-c3-0-87', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-2160-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.289115360044816, 'root_angle': 0.5, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33735204124623489846335512415', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1695295117802237472742033731132', 'Lhash_array': ['1695295117802237472742033731132'], 'factors': ['2-2160-12.11-c3-0-87'], 'label': '2-2160-12.11-c3-0-87', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2160/4/h/a/431/1'}