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lfunc_lfunctions • Show schema
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{'Lhash': '1957184917146195187304398473547', 'a10': [0, 0], 'a2': [0, 0], 'a3': [16.641230757808692, -16.641230757808692], 'a4': [0, 0], 'a5': [53.07000175294961, 17.56630051951535], 'a6': [0, 0], 'a7': [76.65209491676956, 76.65209491676956], 'a8': [0, 0], 'a9': [0, -310.8611222692761], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.661411170076907, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-53.07000175294961, -17.56630051951535]]]], 'bad_primes': [2, 5], 'central_character': '160.63', 'coefficient_field': 'CDF', 'conductor': 160, 'conductor_radical': 10, 'conjugate': '1636511567411292364927057884167', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-16.641230757808692, 16.641230757808692], [0, -243.0]], [[1.0, 0], [-53.07000175294961, -17.56630051951535]], [[1.0, 0], [-76.65209491676956, -76.65209491676956], [0, 16807.0]], [[1.0, 0], [0, 711.9608342302632], 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'0.6423577376676674422782497056512537021137100406963426517 + 0.7664049431328559326343621176249140226193307861006072492*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.138978178956828', 'prec': 57}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54394666542485852482667727548', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.93371364103482511303464513516', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.39073917382511909462508105025', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.661411170076907, 'bad_primes': [2, 5], 'central_character': '20.3', 'conductor': 160, 'conductor_radical': 10, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/160/6/n/d/63/7'], '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': '2-160-20.3-c5-0-25', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-160-20.3-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.06570934520299, 'root_angle': 0.138978178956828, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54394666542485852482667727548', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1957184917146195187304398473547', 'Lhash_array': ['1957184917146195187304398473547'], 'label': '2-160-20.3-c5-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/160/6/n/d/63/7'}