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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 0, 'Lhash': '229600949506485134', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 695.656702409395, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]], [11, [1]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '87120.1', 'coefficient_field': '1.1.1.1', 'conductor': 87120, 'conductor_radical': 330, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, 4, 7], [1], [1, 4, 13], [1, 0, 17], [1, -4, 19], [1, 8, 23], [1, 4, 29], [1, 4, 31], [1, 2, 37], [1, -4, 41], [1, -12, 43], [1, 8, 47], [1, -10, 53], [1, 0, 59], [1, 0, 61], [1, -4, 67], [1, -4, 71], [1, -4, 73], [1, 12, 79], [1, 16, 83], [1, -6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 11, 'label': '2-87120-1.1-c1-0-11', 'leading_term': '0.738057531474', '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/87120/dd', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.7380575314741756, 0.1318784266490017, -1.314957529918631, -2.516023567589758, -2.183224399417492, -0.01443339809670851, 2.568674784803518, 3.437587574682493, 1.980961315766194, 0.03826186709228436, -0.06686554400737468, 1.574254622955792, 2.448229718385864, 1.032404548033966, -0.8149093785892957, -0.2919865772863054, 2.006713190502252, 2.36125672206828, -0.7656376126551809, -3.942041189297315, -3.274751286412786, -0.009707439709584126, 1.404797943367069, 0.06138549520192304, -0.501524387260304, 1.330646117343891, 2.37918744385623, 0.3883948410221046, -1.640813022859218, -0.6476514804859078, 0.6316731462576995, -1.717922188647757, -5.050968777259252, -3.609995201854848, 1.651117086405738, 3.991641327624988, 1.558954362785921, -0.5314549049224137, 0.3414881211402597, 0.9289663817348, -0.002334228755134319, 0.8930678476617511, 3.420126548266068, 2.249125634956237, -2.881594394770102, -4.763231514830496, -0.8259395384968045, 2.126343856887606, 0.00396415233013011, -2.094850142265717, -0.5600343041604602, 0.5014894010102273, -1.034216729444514, -0.7231139812499058, 2.366321500070545, 2.778886411490836, -0.07355220699589828, -0.3721973509010704, 1.664466228446645, -0.3851422214749251, -5.364493626666261, -5.470368383530836, -1.181360172234372, 0.06185998744048217, -1.591236526976138, -0.6078645135608032, 1.245625427980802, -0.3572058020529548, -1.534046073499696, 1.577510072786861, 3.382371794623966, 0.2254408850441115, -1.435399122986295, 1.373799162269896, 1.910209215734262, -1.392494246170578, -1.491698104812464, 1.863154866121615, 1.998904072091163, -0.0677195503109159, 0.5240812719490499, 0.091623797453097, -4.56673515339039, -6.179374032879234, -1.311056104520383, 1.324619676473395, -1.819348693148803, -2.981593801318555, -0.2408941580677392, 0.4142352755059309, -0.329205734699261, 0.9206704954140238, -0.4026319063427899, -5.566141035678919, -5.715398900589547, 0.3903163794723106, 2.56928926646038, -0.2990275593147265, -0.1807133555536517, 1.148754026935428, -2.229983848635184, -4.994135750148229, -2.122180838636838, 0.2872120820925032, -0.4496144338793967, 0.3711289810472895, 0.5077430171454165, -3.782510840895666, -5.110549981272875, 0.2577122255889639, 2.439123192521789, -1.223385360887039, -0.8097187810274981, 3.624806669650646, 3.13491043674857, 0.08462734678116055, 0.6443069190056497, 0.9496216148243395, -0.7043424901248893, 0.1971400822096383, 0.1566518370083397], 'positive_zeros': ['0.2774765693331784', '1.251316685925353', '2.257650733308267', '2.514952892390691', '3.368885443427463', '3.785814473630532', '4.451736432670748', '5.250814505153204', '5.759537499712075', '6.093553827655698', '6.784621999393206', '7.331436144903252', '7.617760624830063', '8.421802965523278', '9.140872346207686', '9.440677314836233', '9.999022788239830', '10.10993356055010', '10.86570164557083', '11.54378328729616', '12.00029731017844', '12.56705290553046', '12.85376235149211', '13.31595707495196', '13.99263075946505', '14.29501523070485', '14.72890193082454', '15.60874526348387', '15.76234862078268', '16.31033853218547', '16.71586741625025', '17.14892177556585', '17.76495731503820', '18.14552755340587', '18.64756829055063', '19.11159011753867', '19.73442868586571', '19.89824435811468'], 'prelabel': '2-87120-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 26.375304783251227, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 229600949506485134, 'z1': {'__RealLiteral__': 0, 'data': '0.2774765693331784', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.251316685925353', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.257650733308267', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 695.656702409395, 'bad_primes': [2, 3, 5, 11], 'central_character': '1.1', 'conductor': 87120, 'conductor_radical': 330, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, -8, 0, 1, 0, 0, 0, -4, 0, -4, 0, 0, 0, -4, 0, -2, 0, 0, 0, 4, 0, 12, 0, 0, 0, -8, 0, 9, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, -12, 0, 0, 0, -16, 0, 0, 0, 0, 0, 6, 0, 16, 0, 0, 0, 4, 0, -2, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 4, 13], 'euler17': [1, 0, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, 4, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, -4, 41], 'euler43': [1, -12, 43], 'euler47': [1, 8, 47], 'euler5': [1, -1, 0], 'euler53': [1, -10, 53], 'euler59': [1, 0, 59], 'euler61': [1, 0, 61], 'euler67': [1, -4, 67], 'euler7': [1, 4, 7], 'euler71': [1, -4, 71], 'euler73': [1, -4, 73], 'euler79': [1, 12, 79], 'euler83': [1, 16, 83], 'euler89': [1, -6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, 4, 7], [1, 0, 0], [1, 4, 13], [1, 0, 17], [1, -4, 19], [1, 8, 23], [1, 4, 29], [1, 4, 31], [1, 2, 37], [1, -4, 41], [1, -12, 43], [1, 8, 47], [1, -10, 53], [1, 0, 59], [1, 0, 61], [1, -4, 67], [1, -4, 71], [1, -4, 73], [1, 12, 79], [1, 16, 83], [1, -6, 89], [1, 2, 97]], 'index': 11, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/87120/dd'], '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': '2-87120-1.1-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': '2-87120-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 26.375304783251227, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 229600949506485134, 'z1': {'__RealLiteral__': 0, 'data': '0.2774765693331784', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '229600949506485134', 'Lhash_array': ['229600949506485134'], 'label': '2-87120-1.1-c1-0-11', 'type': 'ECQ', 'url': 'EllipticCurve/Q/87120/dd'}