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lfunc_lfunctions • Show schema
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{'Lhash': '2292107066783216995229563329607', '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': '138.25', 'coefficient_field': 'CDF', 'conductor': 138, 'conductor_radical': 138, 'conjugate': 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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': 1, 'label': '2-138-23.2-c1-0-1', '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/25/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.478195742960085, 1.425745496323678, 1.387265582357997, 1.3577086523174473, 1.3311358812467613, 1.3012481495575667, 1.2618327364216033, 1.207106685618039, 1.1319867535417392, 1.0323269165450057, 0.9051517763743204, 0.7488946611879858, 0.5636320498737293, 0.3512938850401592, 0.11582217865755742, -0.13675276139302567, -0.3983487076907382, -0.6590069642264619, -0.9072263539362805, -1.1304650135919145, -1.3158061611296157, -1.4507685476161398, -1.5242254302305764, -1.5273788906709604, -1.4547207782498992, -1.3048992991181936, -1.08140319186709, -0.7929752916524613, -0.4536755118432135, -0.0825307090248065, 0.2972644058037346, 0.6595961088317774, 0.9770896662917415, 1.2230912211321008, 1.3738443045194368, 1.4106931173079118, 1.3221164859365475, 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1.0497311788708907, 'root_angle': -0.35504564016627765, 'root_number': '0.4398104036158372 - 0.8980906462441719*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.177522820083', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.80815365556608671869491429685', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.65212002451216462848031331302', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.95529860332498646354984784881', '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': '23.2', 'conductor': 138, 'conductor_radical': 138, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/138/2/e/b/25/1'], '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': '2-138-23.2-c1-0-1', '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': '2-138-23.2-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': '1.80815365556608671869491429685', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2292107066783216995229563329607', 'Lhash_array': ['2292107066783216995229563329607'], 'label': '2-138-23.2-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/138/2/e/b/25/1'}