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lfunc_lfunctions • Show schema
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{'Lhash': '1158997363045717021413972640955', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 1.9318516525781366], 'a6': [0, 0], 'a7': [0, -0.7320508075688773], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.394448407831774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '5184.5183', 'coefficient_field': 'CDF', 'conductor': 5184, 'conductor_radical': 6, 'conjugate': '221122090717340156393477586548', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.9318516525781366], [-5.0, 0]], [[1.0, 0], [0, 0.7320508075688773], [-7.0, 0]], [[1.0, 0], [5.277916867529369, 0], [11.0, 0]], [[1.0, 0], [4.464101615137754, 0], [13.0, 0]], [[1.0, 0], [0, -0.8965754721680536], [-17.0, 0]], [[1.0, 0], [0, -1.2679491924311228], [-19.0, 0]], [[1.0, 0], [-1.4142135623730951, 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'4.83683963724771038217674325881492', '5.33841456129718193089704854223721', '6.08098176143403896796170238908668', '7.11312823872764077924665940238249', '7.86461758074977829476975954577629', '8.172894433610833888986703155934999'], 'prelabel': '2-72e2-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.5, 'root_number': '0.e-55 + 1.0000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.914287708961009985560697375064', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.43542479076989545663079567764', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.69620839392640509349813127375', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.394448407831774, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'index': 52, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5184/2/c/i/5183/7'], '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': '2-72e2-12.11-c1-0-52', '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': '2-72e2-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.25, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.914287708961009985560697375064', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1158997363045717021413972640955', 'Lhash_array': ['1158997363045717021413972640955'], 'label': '2-72e2-12.11-c1-0-52', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/c/i/5183/7'}