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lfunc_lfunctions • Show schema
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{'Lhash': '2225349981315817775389386645471', 'a10': [2.5089575521077054, -0.7366964069566151], 'a2': [-1.7123812567604537, -1.976193316909195], 'a3': [0.8412535328311812, 0.5406408174555976], 'a4': [-0.6884607807454848, 4.788349907459288], 'a5': [-0.41541501300188644, 0.9096319953545183], 'a6': [-0.3721360114995536, -2.5882628118578457], 'a7': [-3.2219126282295116, -0.9460389055808672], 'a8': [6.242060863113862, -4.011528933832951], 'a9': [0.41541501300188644, 0.9096319953545183], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.754838869734175, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.8412535328311812, -0.5406408174555976]]], [5, [[1.0, 0], [0.41541501300188644, -0.9096319953545183]]], [23, [[1.0, 0], [3.08437936577372, 3.67241118721601]]]], 'bad_primes': [3, 5, 23], 'central_character': '345.151', 'coefficient_field': 'CDF', 'conductor': 345, 'conductor_radical': 345, 'conjugate': '524090872777395630391465562322', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.7123812567604537, 1.976193316909195], [-0.2846296765465703, 1.9796428837618654]], [[1.0, 0], [-0.8412535328311812, -0.5406408174555976]], [[1.0, 0], [0.41541501300188644, -0.9096319953545183]], [[1.0, 0], [3.2219126282295116, 0.9460389055808672], [5.888774729818268, 3.784485722189183]], [[1.0, 0], [-2.9753641514434257, 3.4337532767542074], [-1.5654632210061366, -10.88803586069026]], [[1.0, 0], [4.2493349972731815, -1.2477173325695885], [10.936295926805355, -7.028330626922768]], [[1.0, 0], [0.9238687265233477, 6.4256481340336915], [-16.311380551446454, 4.7894534663043045]], [[1.0, 0], [-1.0787105591302726, 7.502596735276229], [-18.23036649867545, -5.352918579987164]], [[1.0, 0], [3.08437936577372, 3.67241118721601]], [[1.0, 0], [-0.10332604439318857, -0.7186484240576744], [-27.825296234820424, 8.170244148401462]], [[1.0, 0], [2.897569544715664, -1.8621548750201649], [12.877865403058479, -28.19859185599007]], 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'root_analytic_conductor': 1.6597707280628173, 'root_angle': 0.9557019642439815, 'root_number': '-0.9903319775556281 + 0.13871760605906908*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.477850982122', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.75549160069435771815232359319', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.99088318837844890227330552603', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.68449605764464331072491244759', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.754838869734175, 'bad_primes': [3, 5, 23], 'central_character': '23.13', 'conductor': 345, 'conductor_radical': 345, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/345/2/m/c/151/1'], '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': '2-345-23.13-c1-0-11', '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': '2-345-23.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6597707280628173, 'root_angle': 0.47785098212199073, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.75549160069435771815232359319', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2225349981315817775389386645471', 'Lhash_array': ['2225349981315817775389386645471'], 'label': '2-345-23.13-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/345/2/m/c/151/1'}