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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -3, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 0, 'Lhash': '1059297204122493313', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-1.3416407864998738, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1825.9551131010237, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [397, [1, 1]]], 'bad_primes': [2, 3, 397], 'central_character': '228672.1', 'coefficient_field': '1.1.1.1', 'conductor': 228672, 'conductor_radical': 2382, 'degree': 2, 'euler_factors': [[1], [1], [1, 3, 5], [1, -1, 7], [1, -3, 11], [1, -4, 13], [1, -6, 17], [1, -2, 19], [1, 3, 23], [1, 0, 29], [1, -2, 31], [1, -9, 37], [1, -9, 41], [1, 2, 43], [1, 7, 47], [1, 1, 53], [1, -10, 59], [1, 4, 61], [1, 0, 67], [1, 0, 71], [1, -17, 73], [1, -8, 79], [1, -3, 83], [1, -18, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 42, 'label': '2-228672-1.1-c1-0-42', 'leading_term': '3.28291038536', 'load_key': 'Cremona', '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': 'EllipticCurve/Q/228672/n', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.282910385357366, 2.528528943314652, 0.837547850184084, -0.3375264994386869, 0.1468510835314085, 1.529667382338863, 1.42662678852329, -1.259761107792311, -4.121129235450295, -3.52672265565334, 0.5407314858275843, 3.797488812759703, 3.03792243525839, 0.2972479357554665, -0.6133120277909027, 0.06113664000583462, -0.6848489602706863, -2.529044260489811, -2.096109257358686, 0.2520739187163646, -0.1746932464482058, -4.126001366251205, -5.896073285817306, -2.660864363383907, 0.3203923699748952, -1.123868220270329, -2.648932108785957, 0.3021575649636182, 3.751780683381238, 2.557467674996829, -0.3401225312005448, -0.3676310298805172, 0.2500080613465622, -1.077424283993799, -0.7860719193689794, 2.538086655392769, 3.125912535669203, -0.6773094371310081, -1.747884680936532, 1.854746105740686, 2.190870391848946, -2.758037053091351, -4.489166808247276, -0.4819134566816262, 1.748725539375639, 0.05488957926648577, -0.3456006580248069, 0.3384329741569251, -1.249470613287093, -1.711370680549486, 1.138672852120254, 0.966449690069885, -3.361717006362333, -2.874854201787409, 3.097664238218142, 4.26869458981636, -0.02144104544915679, -0.8071007120840651, 1.218829355297089, -0.130710127940492, -1.236216652656479, 1.760746416455236, 2.780885899941675, -0.1334349850186875, -0.5092967289523657, 1.067056212939258, -0.1491069053659772, 0.3536871545247459, 4.881213700285205, 4.375965354329224, -2.158296081193172, -3.477956131053668, 0.4443485502338718, 0.04819129119166733, -1.966785730598796, 0.79184594190315, 2.561235551163413, 0.03944675515011239, -0.4165298835419123, 0.4291557394278887, -2.191220650194233, -2.981171611996361, 0.4044301259453228, 0.2226408345649161, -2.112580586782601, 0.8485259877801326, 2.625652334537029, -2.560742536620229, -4.145218383557741, 1.414919140758753, 2.952417706818369, -0.1041345787242521, 0.01364207375056396, 0.224712659862498, -1.843845073206612, -0.5876788223337794, 1.263530409157893, -0.8367636306577538, 0.1870008336840502, 4.74923817033604, 3.069070349849701, -0.7029116550603484, 1.980955975311633, 2.908787020839951, -1.789540893316425, -1.395601277884092, 2.691147773117142, 0.7637541711723012, -1.914168634725007, -0.01423570203892929, 0.4201014084190512, -0.112849059417809, 1.356813335356382, -0.3280888052175778, -1.975629621775865, 2.846918179272774, 3.265154094683851, -5.909727624821228, -8.761181637151681, -2.213711505877947, 0.144459390508102], 'positive_zeros': ['0.6430533510430642', '0.9690603716943631', '1.653902212279633', '2.470361853323075', '3.285886183559951', '3.717176083951412', '3.865596772689409', '4.717127827760021', '4.983345676735415', '5.941310049069143', '6.132387608466929', '6.732883165511703', '7.457677629323952', '7.831527474700462', '8.073042481711839', '8.569663475401202', '9.207746747078662', '9.632823814680888', '10.12212706085596', '10.77805972190450', '11.25775134397376', '11.58319954918440', '11.84105387283099', '12.40693004390350', '12.81229499852568', '13.37354741538928', '13.99855563949282', '14.33768869206819', '14.73727127415473', '15.12618300300857', '15.73755097931630', '16.06680120144247', '16.47892796986627', '16.72075203853221', '17.41653353692358', '17.96476377848350', '18.25418677804357', '18.69913884379156', '19.25401588140992', '19.56964042689584', '19.82031774495612'], 'prelabel': '2-228672-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.7311960176757, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1059297204122493313, 'z1': {'__RealLiteral__': 0, 'data': '0.6430533510430642', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.9690603716943631', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.653902212279633', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1825.9551131010237, 'bad_primes': [2, 3, 397], 'central_character': '1.1', 'conductor': 228672, 'conductor_radical': 2382, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -3, 0, 1, 0, 0, 0, 3, 0, 4, 0, 0, 0, 6, 0, 2, 0, 0, 0, -3, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, -3, 0, 9, 0, 0, 0, 9, 0, -2, 0, 0, 0, -7, 0, -6, 0, 0, 0, -1, 0, -9, 0, 0, 0, 10, 0, -4, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 3, 0, 8, 0, 0, 0, 3, 0, -18, 0, 0, 0, 18, 0, 4, 0, 0, 0, -6, 0, 10, 0, 0, 0], 'euler11': [1, -3, 11], 'euler13': [1, -4, 13], 'euler17': [1, -6, 17], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 3, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, -2, 31], 'euler37': [1, -9, 37], 'euler41': [1, -9, 41], 'euler43': [1, 2, 43], 'euler47': [1, 7, 47], 'euler5': [1, 3, 5], 'euler53': [1, 1, 53], 'euler59': [1, -10, 59], 'euler61': [1, 4, 61], 'euler67': [1, 0, 67], 'euler7': [1, -1, 7], 'euler71': [1, 0, 71], 'euler73': [1, -17, 73], 'euler79': [1, -8, 79], 'euler83': [1, -3, 83], 'euler89': [1, -18, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 3, 5], [1, -1, 7], [1, -3, 11], [1, -4, 13], [1, -6, 17], [1, -2, 19], [1, 3, 23], [1, 0, 29], [1, -2, 31], [1, -9, 37], [1, -9, 41], [1, 2, 43], [1, 7, 47], [1, 1, 53], [1, -10, 59], [1, 4, 61], [1, 0, 67], [1, 0, 71], [1, -17, 73], [1, -8, 79], [1, -3, 83], [1, -18, 89], [1, -10, 97]], 'index': 42, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/228672/n'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-228672-1.1-c1-0-42', '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': '2-228672-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.7311960176757, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1059297204122493313, 'z1': {'__RealLiteral__': 0, 'data': '0.6430533510430642', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1059297204122493313', 'Lhash_array': ['1059297204122493313'], 'factors': ['2-228672-1.1-c1-0-42'], 'label': '2-228672-1.1-c1-0-42', 'type': 'ECQ', 'url': 'EllipticCurve/Q/228672/n'}