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lfunc_lfunctions • Show schema
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{'Lhash': '2738764214698280114366605952432', 'a10': [-1.655554627684725, -2.86750472985572], 'a2': [0.0, 1.0577265673762128], 'a3': [1.564679474767375, -0.7428177039097089], 'a4': [0.881214508666534, 0.0], 'a5': [-2.711007568779167, 1.5652009496097647], 'a6': [0.7856980201426964, 1.655003049889711], 'a7': [0.7848909493637692, -0.4531570008996731], 'a8': [0.0, 3.0475371321263944], 'a9': [1.896443717516616, -2.3245432296027015], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.934249703648981, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.564679474767375, 0.7428177039097089]]], [13, [[1.0, 0], [1.5695123188397353, -3.2460177265397547]]]], 'bad_primes': [3, 13], 'central_character': '117.88', 'coefficient_field': 'CDF', 'conductor': 117, 'conductor_radical': 39, 'conjugate': '3356773527856478877813762157261', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0577265673762128], [-2.0, 0]], [[1.0, 0], 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'9.309868510897379909817003103606163', '10.27940452415350089727269388872998', '11.37974781963674735968510718565243', '12.47520102063534029444987621780562', '12.90853968642894547874544965883951'], 'prelabel': '2-117-117.88-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9665659334204681, 'root_angle': -0.12292173156210985, 'root_number': '0.7162797368039917 - 0.6978132548497517*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.122921731562', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.16050401759379877665024615265', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.75647396566953185895902876684', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.77966893049327107643648922591', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.934249703648981, 'bad_primes': [3, 13], 'central_character': '117.88', 'conductor': 117, 'conductor_radical': 39, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/117/2/l/b/88/8'], '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': '2-117-117.88-c1-0-6', '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': '2-117-117.88-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9665659334204681, 'root_angle': -0.12292173156210985, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.16050401759379877665024615265', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2738764214698280114366605952432', 'Lhash_array': ['2738764214698280114366605952432'], 'factors': ['2-117-117.88-c1-0-6'], 'label': '2-117-117.88-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/117/2/l/b/88/8'}