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lfunc_lfunctions • Show schema
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{'Lhash': '1533129571324935497519629452368', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.701659167912, -0.3230419109976908], 'a4': [0, 0], 'a5': [0, -1.5548068384992908], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [2.79128784747792, 1.0994144589380659], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.780814555405154, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.701659167912, 0.3230419109976908]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '2352.2255', 'coefficient_field': 'CDF', 'conductor': 2352, 'conductor_radical': 42, 'conjugate': '444354001822609151382763142166', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.701659167912, 0.3230419109976908]], [[1.0, 0], [0, 1.5548068384992908], [-5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [2.5332635680173827, 0], [13.0, 0]], [[1.0, 0], [0, 4.339913433478635], [-17.0, 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'3.57629730634821820345350084206862', '4.72919472374402745914503222513037', '5.19862510894377594576658382921836', '6.27518700268741614861439763676076', '6.92381767257114072811621096232294', '7.34664916072588469092078344260842', '8.645357549483966616725269180235081', '9.284978816830397613448748811798649'], 'prelabel': '2-2352-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.33368371658629, 'root_angle': 0.7263838015991794, 'root_number': '-0.6527476448303392877018179657115713875337258289946387122 + 0.7575754168189760074684203210863705620561691627955988546*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3631919007995897', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.20942598145649040012859361967', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.62621740154058830251403806152', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57629730634821820345350084207', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.780814555405154, 'bad_primes': [2, 3, 7], 'central_character': '12.11', 'conductor': 2352, 'conductor_radical': 42, 'degree': 2, 'index': 56, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2352/2/h/p/2255/1'], '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': '2-2352-12.11-c1-0-56', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2352-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.33368371658629, 'root_angle': 0.3631919007995897, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20942598145649040012859361967', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1533129571324935497519629452368', 'Lhash_array': ['1533129571324935497519629452368'], 'label': '2-2352-12.11-c1-0-56', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2352/2/h/p/2255/1'}