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lfunc_lfunctions • Show schema
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{'Lhash': '2654913786470124389051059202894', 'a10': [0.0, 0.0], 'a2': [-2.0, 0.0], 'a3': [1.0, -2.8284271247461903], 'a4': [4.0, 0.0], 'a5': [0.0, 0.0], 'a6': [-2.0, 5.656854249492381], 'a7': [0.0, 0.0], 'a8': [-8.0, 0.0], 'a9': [-7.0, -5.656854249492381], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.193478979111839, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [2.0, 0]]], [3, [[1.0, 0], [-1.0, 2.8284271247461903]]], [11, [[1.0, 0], [7.0, 8.48528137423857]]]], 'bad_primes': [2, 3, 11], 'central_character': '264.131', 'coefficient_field': 'CDF', 'conductor': 264, 'conductor_radical': 66, 'conjugate': '524942527332531100958120127642', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0, 0]], [[1.0, 0], [-1.0, 2.8284271247461903]], [[1.0, 0], [0, 0], [25.0, 0]], [[1.0, 0], [0, 0], [49.0, 0]], [[1.0, 0], [7.0, 8.48528137423857]], [[1.0, 0], [0, 0], [169.0, 0]], [[1.0, 0], [2.0, 0], [289.0, 0]], [[1.0, 0], [0, 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True, 'rational': False, 'root_analytic_conductor': 2.682066177243179, 'root_angle': 0.44430562298846815, 'root_number': '-0.9393939393939394 + 0.3428396514843865*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.444305622988', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.09435769287856637016964126806', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.47699813429912053767108011948', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.98341732910305405642762075367', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.193478979111839, 'bad_primes': [2, 3, 11], 'central_character': '264.131', 'conductor': 264, 'conductor_radical': 66, 'degree': 2, 'index': 77, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/264/3/p/b/131/1'], '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': '2-264-264.131-c2-0-77', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-264-264.131-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.682066177243179, 'root_angle': 0.44430562298846815, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.09435769287856637016964126806', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2654913786470124389051059202894', 'Lhash_array': ['2654913786470124389051059202894'], 'factors': ['2-264-264.131-c2-0-77'], 'label': '2-264-264.131-c2-0-77', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/264/3/p/b/131/1'}