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lfunc_lfunctions • Show schema
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{'Lhash': '1099126515203226456991129660298', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-2.224744871391589, 0.22474487139158905], 'a6': [0, 0], 'a7': [0, -1.0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.623843418298286, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.224744871391589, -0.22474487139158905]]]], 'bad_primes': [2, 3, 5], 'central_character': '1080.649', 'coefficient_field': 'CDF', 'conductor': 1080, 'conductor_radical': 30, 'conjugate': '1177603954558666583225037564532', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.224744871391589, -0.22474487139158905]], [[1.0, 0], [0, 1.0], [-7.0, 0]], [[1.0, 0], [0.4494897427831781, 0], [11.0, 0]], [[1.0, 0], [0, -3.898979485566356], [-13.0, 0]], [[1.0, 0], [0, 4.898979485566356], [-17.0, 0]], [[1.0, 0], 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'4.61215967172612307793336079583578', '5.55751772577954270718501211801313', '6.48701999791385397793303490251955', '7.63672542566775209068636803104939', '8.100066048369795637886686014650347', '8.889457253960636705652971547551057', '9.939764983358776603369532663247057'], 'prelabel': '2-1080-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.936638114970635, 'root_angle': -0.03204710842448747, 'root_number': '0.99493615300512405273880451654705738104086836692028839908 - 0.100508962005208174175135049054546886864621023075678110*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.016023554212243735', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.867057937735633417282932925047', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.66163040182725667415818103655', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.59073139995616428503221657645', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.623843418298286, 'bad_primes': [2, 3, 5], 'central_character': '5.4', 'conductor': 1080, 'conductor_radical': 30, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1080/2/f/e/649/2'], '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': '2-1080-5.4-c1-0-8', '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': '2-1080-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.936638114970635, 'root_angle': -0.016023554212243735, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.867057937735633417282932925047', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1099126515203226456991129660298', 'Lhash_array': ['1099126515203226456991129660298'], 'label': '2-1080-5.4-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1080/2/f/e/649/2'}