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lfunc_lfunctions • Show schema
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{'Lhash': '529984155676241386437527597045', 'a10': [0, 0], 'a2': [0, 0], 'a3': [2.0, 0], 'a4': [0, 0], 'a5': [0, 1.0], 'a6': [0, 0], 'a7': [0, 1.0], 'a8': [0, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.97210096932068, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, -1.0]]], [11, [[1.0, 0], [0, 1.0]]], [13, [[1.0, 0], [-2.0, -3.0]]]], 'bad_primes': [2, 7, 11, 13], 'central_character': '4004.2157', 'coefficient_field': 'CDF', 'conductor': 4004, 'conductor_radical': 2002, 'conjugate': '2078792345972573445799993832783', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, 0], [3.0, 0]], [[1.0, 0], [0, -1.0], [-5.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-2.0, -3.0]], [[1.0, 0], [4.0, 0], [17.0, 0]], [[1.0, 0], [0, -5.0], [-19.0, 0]], [[1.0, 0], [9.0, 0], [23.0, 0]], [[1.0, 0], [-5.0, 0], [29.0, 0]], [[1.0, 0], [0, -7.0], 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'-0.5547001962252291220183417334569993763463533190531148020 - 0.8320502943378436830275126001854990645195299785796722030*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3435835209054994', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41808378079955342218917946664', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.80918778310023956417071817803', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.65203919939696281157628525320', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.97210096932068, 'bad_primes': [2, 7, 11, 13], 'central_character': '13.12', 'conductor': 4004, 'conductor_radical': 2002, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4004/2/m/a/2157/2'], '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': '2-4004-13.12-c1-0-15', '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': '2-4004-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.654387762554022, 'root_angle': -0.3435835209054994, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.41808378079955342218917946664', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '529984155676241386437527597045', 'Lhash_array': ['529984155676241386437527597045'], 'label': '2-4004-13.12-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4004/2/m/a/2157/2'}