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lfunc_lfunctions • Show schema
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{'Lhash': '2427454355257071626224814379484', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.9058840008543132, -0.606305348226087], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.539001938166965, -3.8317383891906536], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.4021322673726955, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [103, [[1.0, 0], [-10.137053859805935, -0.4900398385780519]]]], 'bad_primes': [3, 103], 'central_character': '927.667', 'coefficient_field': 'CDF', 'conductor': 927, 'conductor_radical': 309, 'conjugate': '836067760563551477706832848872', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-1.9058840008543132, 0.606305348226087]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [4.405060971428923, 2.3654677841800504]], [[1.0, 0], [2.539001938166965, 3.8317383891906536], [-2.7285011130487558, 6.4463386256146755]], [[1.0, 0], [0, 0], 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[27.190039702368836, -54.6049607726588]], [[1.0, 0], [-13.642253791066361, -0.841425412487047], [66.4921741480197, 8.233515474535846]], [[1.0, 0], [0, 0], [-2.186449157488095, 70.96632609964898]], [[1.0, 0], [-4.424538937650465, 15.550641350253116], [-62.06585090826184, -38.429547890046976]], [[1.0, 0], [-4.555907726192828, -16.012354750005528], [-67.16715372263951, 41.58814086731111]], [[1.0, 0], [0, 0], [82.37090230277067, -10.199728125171273]], [[1.0, 0], [0, 0], [8.211883992233878, -88.62034169025807]], [[1.0, 0], [-0.5911880726692113, 19.188392928132682], [-96.81602288749328, -5.971407894992455]], [[1.0, 0], [0, 0], [-96.24714204314282, 30.618420085417394]], [[1.0, 0], [-10.137053859805935, -0.4900398385780519]], [[1.0, 0], [0, 0], [87.33306962211572, -61.82179996068287]], [[1.0, 0], [0.21156858363799466, -6.866953684916196], [-108.7932628323378, -6.710138768599769]], [[1.0, 0], [0, 0], [-111.0759602642809, -20.76369551327245]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 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'9.459382471933058881261777760836617', '10.29920381262394821778248056519790'], 'prelabel': '2-927-103.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.720685992056543, 'root_angle': 0.5688758176225058, 'root_number': '-0.21469522033500757 + 0.9766810955298063*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.284437908811', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91492384007078110032345774296', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.83894261626523623250544582614', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73331180060024612758092496357', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.4021322673726955, 'bad_primes': [3, 103], 'central_character': '103.49', 'conductor': 927, 'conductor_radical': 309, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/927/2/ba/a/667/1'], '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': '2-927-103.49-c1-0-38', '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': '2-927-103.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.720685992056543, 'root_angle': 0.2844379088112529, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91492384007078110032345774296', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2427454355257071626224814379484', 'Lhash_array': ['2427454355257071626224814379484'], 'label': '2-927-103.49-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/927/2/ba/a/667/1'}