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lfunc_lfunctions • Show schema
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{'Lhash': '3751593395382590929352248296164', 'a10': [0.1272144022282078, -0.14681324646918337], 'a2': [0.8412535328311812, -0.5406408174555976], 'a3': [0.14231483827328514, -0.9898214418809327], 'a4': [0.41541501300188644, -0.9096319953545183], 'a5': [0.1863927988858961, -0.05472986384583198], 'a6': [-0.41541501300188644, -0.9096319953545183], 'a7': [-1.2781894029499592, -1.4751092058976094], 'a8': [-0.14231483827328514, -0.9898214418809327], 'a9': [-0.9594929736144974, -0.28173255684142967], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1019355478936699, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8412535328311812, 0.5406408174555976]]], [3, [[1.0, 0], [-0.14231483827328514, 0.9898214418809327]]], [23, [[1.0, 0], [-3.3778215714551107, -3.404456113891399]]]], 'bad_primes': [2, 3, 23], 'central_character': '138.127', 'coefficient_field': 'CDF', 'conductor': 138, 'conductor_radical': 138, 'conjugate': '2292107066783216995229563329607', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8412535328311812, 0.5406408174555976]], [[1.0, 0], [-0.14231483827328514, 0.9898214418809327]], [[1.0, 0], [-0.1863927988858961, 0.05472986384583198], [4.206267664155906, -2.703204087277988]], [[1.0, 0], [1.2781894029499592, 1.4751092058976094], [-0.996203867912996, 6.92875009316653]], [[1.0, 0], [-5.301537702439814, -3.4070914003447195], [4.569565143020751, 10.005951948899702]], [[1.0, 0], [3.1517661967158865, -3.6373320893464762], [-1.850092897552707, -12.867678744452126]], [[1.0, 0], [1.332593370382715, 2.9179724578031254], [-11.132632477069846, 12.84774276402239]], [[1.0, 0], [-0.35702781233833336, 0.7817818595133488], [-12.442353944960416, -14.359241912730907]], [[1.0, 0], [-3.3778215714551107, -3.404456113891399]], [[1.0, 0], [-2.2504733226211493, -4.927849198696853], [-18.990961284413267, 21.91673765627349]], [[1.0, 0], [-0.1442652837960204, -1.0033870884645781], [-29.744282182049417, 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[-11.242872223589526, -78.19589390859369]], [[1.0, 0], [3.8448244670582894, 1.1289423242259504], [69.82404322498803, 44.8731878488146]], [[1.0, 0], [-1.3593311535735966, 9.454355840535433], [-85.39487465169027, -25.074197558887242]], [[1.0, 0], [-1.0755369184903856, 0.3158061334020699], [81.60159268462458, -52.442159293192965]], [[1.0, 0], [12.062180472434862, 3.5417757493107], [84.9666068159493, 54.60472256301536]], [[1.0, 0], [-16.317212035489863, -10.486435431390769], [42.7877463391943, 93.6920955215154]], [[1.0, 0], [0.43775256925542183, 3.044635995407807], [-102.66574817675122, 30.145383582032977]], [[1.0, 0], [-0.8097657133597942, -1.7731395798394018], [-71.37982000003608, 82.37670360461415]], [[1.0, 0], [14.42684590461451, -9.271570886516496], [46.94189646921317, -102.78841547506057]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-138-23.12-c1-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/138/2/e/b/127/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.478195742960085, 1.5482485127011512, 1.6377410050471375, 1.746578237815288, 1.8728329072349978, 2.0129867538966586, 2.162202958774514, 2.314565484159093, 2.463278179767013, 2.6008508841043536, 2.7193083992684612, 2.810451365141343, 2.8661853938198636, 2.878921450928882, 2.8420381245605113, 2.750385404760321, 2.600799941265319, 2.392593685546044, 2.127971861737221, 1.812333053570877, 1.4544046107696753, 1.0661712604013416, 0.662564228610195, 0.2608924577316368, -0.11998369511813647, -0.4607134438541074, -0.7427037552980382, -0.9494823561230816, -1.0680804999182691, -1.0903226110467505, -1.013899697922347, -0.8431032561897994, -0.5891081329310043, -0.2697174542855498, 0.09148001254255483, 0.466541437823092, 0.825135728655947, 1.1369294588197432, 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'root_analytic_conductor': 1.0497311788708907, 'root_angle': 0.35504564016627765, 'root_number': '0.4398104036158372 + 0.8980906462441719*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.177522820083', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.95948536190267993125782890777', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.21918002703971402997536291996', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.69747638130967357176740035943', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1019355478936699, 'bad_primes': [2, 3, 23], 'central_character': '23.12', 'conductor': 138, 'conductor_radical': 138, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/138/2/e/b/127/1'], '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': '2-138-23.12-c1-0-3', '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': '2-138-23.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0497311788708907, 'root_angle': 0.17752282008313883, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.95948536190267993125782890777', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3751593395382590929352248296164', 'Lhash_array': ['3751593395382590929352248296164'], 'label': '2-138-23.12-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/138/2/e/b/127/1'}