-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '801763542309649929880158046638', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -4, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.52054303693677, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '1568.1', 'coefficient_field': '1.1.1.1', 'conductor': 1568, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1, 4, 5], [1], [1, 0, 11], [1, -4, 13], [1, 8, 17], [1, 0, 19], [1, 0, 23], [1, -10, 29], [1, 0, 31], [1, -2, 37], [1, 8, 41], [1, 0, 43], [1, 0, 47], [1, -14, 53], [1, 0, 59], [1, -12, 61], [1, 0, 67], [1, 0, 71], [1, -16, 73], [1, 0, 79], [1, 0, 83], [1, -16, 89], [1, -8, 97], [1, 20, 101], [1, 0, 103], [1, 0, 107], [1, 6, 109], [1, 14, 113]], 'euler_factors_factorization': [[1], [[[1, 0, 3], 1]], [[[1, 4, 5], 1]], [1], [[[1, 0, 11], 1]], [[[1, -4, 13], 1]], [[[1, 8, 17], 1]], [[[1, 0, 19], 1]], [[[1, 0, 23], 1]], [[[1, -10, 29], 1]], [[[1, 0, 31], 1]], [[[1, -2, 37], 1]], [[[1, 8, 41], 1]], [[[1, 0, 43], 1]], [[[1, 0, 47], 1]], [[[1, -14, 53], 1]], [[[1, 0, 59], 1]], [[[1, -12, 61], 1]], [[[1, 0, 67], 1]], [[[1, 0, 71], 1]], [[[1, -16, 73], 1]], [[[1, 0, 79], 1]], [[[1, 0, 83], 1]], [[[1, -16, 89], 1]], [[[1, -8, 97], 1]], [[[1, 20, 101], 1]], [[[1, 0, 103], 1]], [[[1, 0, 107], 1]], [[[1, 6, 109], 1]], [[[1, 14, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-1568-1.1-c1-0-4', 'leading_term': '0.861655546781656334953705253017040000000000000000000000000000000000000000000000000000000000', '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/1568/2/a/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.8616555467816563, 0.8549700510470567, 0.8348094979667626, 0.8008709161576352, 0.7526794173924257, 0.6896309849771219, 0.6110481181498442, 0.5162448035247834, 0.40459710146879746, 0.2756157794135405, 0.12901777691939464, -0.035206272661861805, -0.21673080673911804, -0.41484235793115626, -0.6283965238392708, -0.8557863498405504, -1.0949234191873554, -1.343232784078788, -1.5976626940300418, -1.8547098604176226, -2.1104607229220966, -2.3606488470413147, -2.6007281814801106, -2.8259614459107194, -3.031522414516682, -3.2126103244233004, -3.3645740896273324, -3.4830434621046606, -3.564063776010902, -3.604230462941519, -3.6008191608627618, -3.551906980512959, -3.4564803629156144, -3.3145249793672695, -3.1270933061614548, -2.8963458607502504, -2.6255626185428564, -2.3191218379817626, -1.9824443965826233, -1.6219027653494784, -1.2446948987896898, -0.858684560620748, -0.47221090227951634, -0.09387141765396825, 0.2677163364910965, 0.6041676917731936, 0.9075909021153338, 1.1708458445843184, 1.3877923940293984, 1.553519194471265, 1.6645435957505634, 1.7189739247935683, 1.716626030480979, 1.659087179009266, 1.549721867074535, 1.3936159315296412, 1.1974574187414562, 0.9693549717638469, 0.7185969217664753, 0.4553567432346217, 0.19035295262323645, -0.06552620573701232, -0.30162093922792627, -0.5079069635986021, -0.6753962633263497, -0.7965157351929938, -0.8654478498568317, -0.8784180673315304, -0.8339150080351648, -0.7328313027845801, -0.5785155850074136, -0.37672917914068554, -0.1355045845042929, 0.1350932688823848, 0.42329795278282856, 0.7160555361745434, 0.999508586111364, 1.2595335182569034, 1.4823115543924008, 1.6549111345085108, 1.7658580447478083, 1.8056688776971879, 1.767323821367173, 1.646656219314597, 1.4426388524595037, 1.1575504101636687, 0.797010041648047, 0.36987305870934156, -0.11201339678044343, -0.6341898328457004, -1.180088000527045, -1.7316416242920074, -2.2699818405557557, -2.77619022581985, -3.2320786254367055, -3.6209625626589252, -3.928393988730851, -4.142819643535081, -4.256133381009245, -4.264094449515419, -4.166588804133114, -3.9677168900716677, -3.675698728336328, -3.3025952487612518, -2.863853293888594, -2.3776901674471502, -1.864341613815423, -1.3452042828081483, -0.8419096734094054, -0.3753709201907561, 0.03515369058804084, 0.37293610955725776, 0.6245501217736362, 0.780500276316141, 0.8356751306059228, 0.7895994762229452, 0.6464694035303086, 0.41496435110968216, 0.10784119147079152, -0.25867360603919065, -0.6656671793794828, -1.0924628055227916, -1.517637792483759, -1.9200868570337055, -2.28007760310097, -2.5802438677652555, -2.8064646509284907, -2.9485810832325976, -3.000911258162443, -2.962532455854995, -2.837311879331495, -2.6336799522971295, -2.364153842542559, -2.044632466738191, -1.6934970668876053, -1.3305628063891666, -0.9759360497235249, -0.6488384928326518, -0.3664626584572407, -0.14292317728170736, 0.011635363148238579, 0.09172031635036833, 0.09691920777444744, 0.03204386178448219, -0.09302496593095595, -0.26379150008462665, -0.4618796882370959, -0.6660148021194369, -0.8532031012510334, -1.000048250412351, -1.084133760921373, -1.0853950218494441, -0.987402937820204, -0.77848400861626, -0.4526088434050189, -0.00999232038385648, 0.5426366395694346, 1.19212015977034, 1.9193163989085449, 2.6998892478516967, 3.505407620873111, 4.304700804669336, 5.065400495509158, 5.755587901244396, 6.345456417555225, 6.808897480113876, 7.124919545126469, 7.278817757917583, 7.263024420873624, 7.07758725537498, 6.73024278124015, 6.236074797137033, 5.6167716534590095, 4.899519386170479, 4.115589431027705, 3.298698235165, 2.4832304502185765, 1.702426576628338, 0.9866392711243895, 0.3617597055291148, -0.1520935810260549, -0.5415455440295729, -0.8005369932513025, -0.9304636385162729, -0.9398728849970803, -0.8437362446069705, -0.6623413268289099, -0.4198711350547199, -0.14275830448244764, 0.1420833371715645, 0.4090389420622362, 0.6354718749106175, 0.8031946741408438, 0.8996366142051531, 0.9186311647506178, 0.8607702288739064, 0.733299386294468, 0.5495577903475832, 0.3279960228048357, 0.0908331947981702, -0.13756094155285747, -0.33245378898857464, -0.4705897223356002, -0.5319587112053595, -0.5013731740599905, -0.3697430920721638, -0.13495744390465622, 0.19769554277644627, 0.6156074610963509, 1.0994337836278263, 1.624155074851362, 2.160555174413533, 2.677027134764239, 3.1415939674689515, 3.5240145108958476, 3.7978362366740805, 3.942257303266069, 3.943669801982824, 3.796774479050819, 3.5051832230520428, 3.081457712473831, 2.5465688140263456, 1.9287992824943077, 1.2621495424697724, 0.5843403319583843, -0.06546557853280031, -0.6490795219957978, -1.1316861230507738, -1.4840690865758346, -1.6845158741699668, -1.720272290495303, -1.5884456571436736, -1.2962901287908464, -0.8608475836679782, -0.3079597949417394, 0.3292905530551567, 1.012613837693577, 1.7008936147588596, 2.352759588311777, 2.929185719631547, 3.3959424922652754, 3.7257406216289315, 3.89992290783639, 3.90959030361476, 3.756085722299426, 3.45080217175767, 3.0143275686661664, 2.4749839307744153, 1.8668604113645968, 1.2274748811160436, 0.5952249419378326, 0.006804437463627669, -0.5052354863885308, -0.9146112699497942, -1.2029698388508325, -1.3609737568558222, -1.388733512931337], 'positive_zeros': ['0.63247991375959544191760657110602', '2.53443050487252517839586499540835', '3.55887344410299009293086169964340', '4.24873327227852142886149189755590', '5.14312271521888697700030317913562', '6.43989265358166028466611552196070', '6.93218317388480289991978591057117', '8.197509550250461170763039761777588', '8.396621168864933987238022281799840', '9.083201307753543769979419428054272'], 'prelabel': '2-1568-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.538437937414866, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 789133953512083276, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63247991375959544191760657111', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.53443050487252517839586499541', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.55887344410299009293086169964', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 12.52054303693677, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 1568, 'conductor_radical': 14, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -4, 0, 0, 0, -3, 0, 0, 0, 4, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -8, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 32, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -4, 13], 'euler17': [1, 8, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -10, 29], 'euler3': [1, 0, 3], 'euler31': [1, 0, 31], 'euler37': [1, -2, 37], 'euler41': [1, 8, 41], 'euler43': [1, 0, 43], 'euler47': [1, 0, 47], 'euler5': [1, 4, 5], 'euler53': [1, -14, 53], 'euler59': [1, 0, 59], 'euler61': [1, -12, 61], 'euler67': [1, 0, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, -16, 73], 'euler79': [1, 0, 79], 'euler83': [1, 0, 83], 'euler89': [1, -16, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, 4, 5], [1, 0, 0], [1, 0, 11], [1, -4, 13], [1, 8, 17], [1, 0, 19], [1, 0, 23], [1, -10, 29], [1, 0, 31], [1, -2, 37], [1, 8, 41], [1, 0, 43], [1, 0, 47], [1, -14, 53], [1, 0, 59], [1, -12, 61], [1, 0, 67], [1, 0, 71], [1, -16, 73], [1, 0, 79], [1, 0, 83], [1, -16, 89], [1, -8, 97]], 'index': 4, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1568/d', 'ModularForm/GL2/Q/holomorphic/1568/2/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/1568/2/a/d'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-1568-1.1-c1-0-4', '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': '2-1568-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.538437937414866, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 789133953512083276, 'z1': {'__RealLiteral__': 0, 'data': '0.63247991375959544191760657111', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20741748
{'Lhash': '801763542309649929880158046638', 'Lhash_array': ['801763542309649929880158046638'], 'factors': ['2-1568-1.1-c1-0-4'], 'label': '2-1568-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1568/2/a/d'}
-
id: 24553634
{'Lhash': '801763542309649929880158046638', 'Lhash_array': ['801763542309649929880158046638'], 'factors': ['2-1568-1.1-c1-0-4'], 'label': '2-1568-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1568/2/a/d/1/1'}
-
id: 31875
{'Lhash': '789133953512083276', 'Lhash_array': ['789133953512083276'], 'factors': ['2-1568-1.1-c1-0-4'], 'label': '2-1568-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1568/d'}