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lfunc_lfunctions • Show schema
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{'Lhash': '1452639659376981346871396221724', 'a10': [-5.99923766719141, -1.906664133832276e-60], 'a2': [2.104376450992684, 1.528918986579174], 'a3': [-0.30901699437494745, 0.9510565162951535], 'a4': [1.4727729912203802, 4.532729189075318], 'a5': [-1.8658981039118208, 1.3556543254165037], 'a6': [-2.104376450992684, 1.528918986579174], 'a7': [-0.6469592814218484, -1.9911359296547546], 'a8': [-2.2233063595079976, 6.84263338075481], 'a9': [-0.8090169943749475, -0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.42558224671293, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.30901699437494745, -0.9510565162951535]]], [11, [[1.0, 0], [-2.9637657792510463, -1.4886545622609824]]], [13, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]]], 'bad_primes': [3, 11, 13], 'central_character': '429.235', 'coefficient_field': 'CDF', 'conductor': 429, 'conductor_radical': 429, 'conjugate': 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50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14593063665606775519267360783', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.63622323360698819264049029720', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.77912238509531046116375049909', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.42558224671293, 'bad_primes': [3, 11, 13], 'central_character': '11.4', 'conductor': 429, 'conductor_radical': 429, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/429/2/n/c/235/7'], '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': '2-429-11.4-c1-0-8', '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': '2-429-11.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8508328521811281, 'root_angle': -0.4297012818564616, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14593063665606775519267360783', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1452639659376981346871396221724', 'Lhash_array': ['1452639659376981346871396221724'], 'label': '2-429-11.4-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/429/2/n/c/235/7'}