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lfunc_lfunctions • Show schema
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{'Lhash': '853980072568006147248453159213', 'a10': [0.8446766925498786, 0.0], 'a2': [0.8446766925498786, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.286521285062998, 0.0], 'a5': [1.0, 0.0], 'a6': [0.8446766925498786, 0.0], 'a7': [-2.4979108580848552, 0.0], 'a8': [-2.77604792906179, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.26956802186402, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]], [31, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 13, 31], 'central_character': '6045.1', 'coefficient_field': 'CDF', 'conductor': 6045, 'conductor_radical': 6045, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8446766925498786, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.4979108580848552, 0], [7.0, 0]], [[1.0, 0], [-0.5891022944167615, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [7.594039874609166, 0], 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'2.93867186609679851433421230689061', '3.60309159209119984402560669591031', '4.48990550817532543821172375979456', '4.98975023612981346543563961985547', '5.97118254530348036720549047722296', '6.60098007340504554052784386348984', '7.15440299953102752072765326805043', '8.265569351672139450648530731445904'], 'prelabel': '2-6045-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.947630388978966, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67367149308670268098787203294', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.16940819340698134323681328100', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.93867186609679851433421230689', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.26956802186402, 'bad_primes': [3, 5, 13, 31], 'central_character': '1.1', 'conductor': 6045, 'conductor_radical': 6045, 'degree': 2, 'index': 53, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6045/2/a/bi/1/10'], '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': '2-6045-1.1-c1-0-53', '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': '2-6045-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.947630388978966, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67367149308670268098787203294', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '853980072568006147248453159213', 'Lhash_array': ['853980072568006147248453159213'], 'label': '2-6045-1.1-c1-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6045/2/a/bi/1/10'}