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lfunc_lfunctions • Show schema
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{'Lhash': '1442434858355180797427436028993', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-3.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-10.156634174168413, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 69.386246166751, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [3.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1176.1', 'coefficient_field': 'CDF', 'conductor': 1176, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [10.156634174168413, 0], [125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [37.800452797084404, 0], [1331.0, 0]], [[1.0, 0], [-74.08809004291638, 0], [2197.0, 0]], [[1.0, 0], [-44.66944972542084, 0], [4913.0, 0]], [[1.0, 0], [139.36737811248582, 0], [6859.0, 0]], [[1.0, 0], [-57.81999870874874, 0], [12167.0, 0]], [[1.0, 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'5.69671048687724483648362094582924', '6.37006264386044612882830252110585', '7.39258881800031844839904949107830', '8.215107844107113752991814230693609', '8.721791548321619366463841877121585'], 'prelabel': '2-1176-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.329840704764466, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13788046808440986753111833155', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68419286622225052212091786806', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.85841823848544116395014416687', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 69.386246166751, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1176, 'conductor_radical': 42, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1176/4/a/x/1/1'], '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': '2-1176-1.1-c3-0-36', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1176-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.329840704764466, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13788046808440986753111833155', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1442434858355180797427436028993', 'Lhash_array': ['1442434858355180797427436028993'], 'label': '2-1176-1.1-c3-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1176/4/a/x/1/1'}