-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '854024788724619317037591061323,1652632530375692876638906709742', 'a10': 3, 'a2': -1, 'a3': -3, 'a4': -2, 'a5': -3, 'a6': 3, 'a7': 3, 'a8': 3, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2062.1519848844796, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [1]], [47, [1, -2, 1]]], 'bad_primes': [11, 47], 'central_character': '5687.1', 'coefficient_field': '1.1.1.1', 'conductor': 32341969, 'conductor_radical': 517, 'degree': 4, 'euler_factors': [[1, 1, 3, 2, 4], [1, 3, 7, 9, 9], [1, 3, 11, 15, 25], [1, -3, 5, -21, 49], [1], [1, -1, 25, -13, 169], [1, 4, 33, 68, 289], [1, -2, 19, -38, 361], [1, -4, 45, -92, 529], [1, 18, 139, 522, 841], [1, 0, 62, 0, 961], [1, 7, 75, 259, 1369], [1, -9, 71, -369, 1681], [1, 5, 91, 215, 1849], [1, -2, 1], [1, -11, 135, -583, 2809], [1, 5, 123, 295, 3481], [1, 12, 113, 732, 3721], [1, -12, 125, -804, 4489], [1, 12, 173, 852, 5041], [1, 20, 246, 1460, 5329], [1, 0, -22, 0, 6241], [1, 22, 282, 1826, 6889], [1, -18, 239, -1602, 7921], [1, 0, 149, 0, 9409], [1, -30, 422, -3030, 10201], [1, -12, 242, -1236, 10609], [1, -3, -65, -321, 11449], [1, -27, 389, -2943, 11881], [1, 12, 257, 1356, 12769]], 'euler_factors_factorization': [[[[1, 1, 3, 2, 4], 1]], [[[1, 3, 7, 9, 9], 1]], [[[1, 3, 11, 15, 25], 1]], [[[1, -3, 5, -21, 49], 1]], [1], [[[1, -1, 25, -13, 169], 1]], [[[1, 4, 33, 68, 289], 1]], [[[1, -2, 19, -38, 361], 1]], [[[1, -4, 45, -92, 529], 1]], [[[1, 9, 29], 2]], [[[1, 0, 31], 2]], [[[1, 7, 75, 259, 1369], 1]], [[[1, -9, 71, -369, 1681], 1]], [[[1, 5, 91, 215, 1849], 1]], [[[1, -1], 2]], [[[1, -11, 135, -583, 2809], 1]], [[[1, 5, 123, 295, 3481], 1]], [[[1, 12, 113, 732, 3721], 1]], [[[1, -12, 125, -804, 4489], 1]], [[[1, 12, 173, 852, 5041], 1]], [[[1, 10, 73], 2]], [[[1, 0, -22, 0, 6241], 1]], [[[1, 22, 282, 1826, 6889], 1]], [[[1, -18, 239, -1602, 7921], 1]], [[[1, 0, 149, 0, 9409], 1]], [[[1, -30, 422, -3030, 10201], 1]], [[[1, -6, 103], 2]], [[[1, -3, -65, -321, 11449], 1]], [[[1, -27, 389, -2943, 11881], 1]], [[[1, 12, 257, 1356, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 2, 'label': '4-5687e2-1.1-c1e2-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/5687/2/a/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0234375', 'prec': 30}, 'plot_values': [-3.4808329389052224e-121, 0.00166162192704844, 0.00661796135598464, 0.014783519817240848, 0.02601582981900926, 0.04011590396986197, 0.05682823922347055, 0.07584204225260505, 0.09679140758942947, 0.11925775497254741, 0.14277062673890065, 0.16681170203422696, 0.19081690755094796, 0.21418221022018366, 0.23626791813152032, 0.25640621255860946, 0.2739085946656404, 0.2880748209608316, 0.29820439714506675, 0.3036062546762694, 0.3036149896659759, 0.297600292054506, 0.28498827424703527, 0.26526937086499447, 0.23802461532534633, 0.2029305011560793, 0.15978947860124693, 0.10853014199345881, 0.04924058225340923, -0.01783772942803244, -0.09227572080697342, -0.1734706036750843, -0.2606133110523082, -0.3527112746500177, -0.44856042415728964, -0.5467774572027649, -0.6457794488143782, -0.7438255198076583, -0.8390069520228821, -0.9292973268989969, -1.0125555494506573, -1.0865826063885407, -1.1491390521365055, -1.198005597487449, -1.2310154212772493, -1.2461149360346468, -1.2414098149767774, -1.2152215921306975, -1.1661446324105151, -1.0930938155449093, -0.9953679618529743, -0.872683820293953, -0.7252398605471135, -0.5537322147975067, -0.3594114443359278, -0.14407701987321328, 0.08988114128137742, 0.339511626179645, 0.6012835691919998, 0.8711390964111771, 1.1445066427868196, 1.416374687727854, 1.6813425010250165, 1.9337105087664685, 2.167572199146046, 2.3769140178416786, 2.5557489480575244, 2.6982166627559523, 2.7987554729262194, 2.85219182629505, 2.8539431791935725, 2.8000850836832822, 2.6875734484328406, 2.514277615382868, 2.2792068567634196, 1.9824991555256253, 1.6256340822237245, 1.2113695097504364, 0.7439216446262076, 0.22884555573825066, -0.32683655333571565, -0.9148105420310705, -1.525410512882175, -2.1478440989647356, -2.770213598275995, -3.3797803889766933, -3.9630734865787915, -4.506177185844536, -4.994925971600359, -5.415195506648894, -5.753174323407094, -5.99563581375273, -6.1302683686050585, -6.145905553730598, -6.032888175589169, -5.783231677331991, -5.390986864825146, -4.852327857968803, -4.165873741787483, -3.332687043856711, -2.3565170766994616, -1.2437075011653829, -0.00332406658923527, 1.3530202782007685, 2.8111849956254478, 4.354740488019849, 5.965157846705345, 7.622082427609403, 9.303704708645462, 10.987032194674377, 12.648438589479161, 14.263891879145557, 15.809664511127002, 17.262473632241367, 18.600321083134357, 19.802504040598585, 20.850541810663394, 21.728021751395495, 22.4215614086123, 22.92046533767211, 23.217667141076323, 23.309186964794847, 23.19499913730896, 22.87829655284027, 22.366236042436075, 21.669033087992087, 20.800548381397075, 19.777252636570697, 18.618633057235634, 17.346081679253945, 15.983118226273485, 14.554264816566127, 13.08510013598369, 11.601187215906528, 10.127991019007133, 8.689923580986823, 7.310171056708322, 6.009911696941574, 4.808107485201503, 3.7209357679155737, 2.7616036564591724, 1.9400149027051614, 1.2626617292205833, 0.7325265831671548, 0.3490962227054641, 0.10847553990882118, 0.003553565448013587, 0.024286045843335692, 0.15802420066887451, 0.38990648812589496, 0.7033406325143361, 1.0804349482943003, 1.5026047812943297, 1.950971183672886, 2.4070468759953827, 2.853035448355229, 3.2725413084709776, 3.650715480013334, 3.974930194931478, 4.234736410126626, 4.422447344687365, 4.532895897263683, 4.563882195978484, 4.515743476039577, 4.391637343445585, 4.196959433535197, 3.939454527428044, 3.6285356498917425, 3.275236798512591, 2.891498733282184, 2.4899970329847965, 2.0834631624610247, 1.6844371573762378, 1.304687139426451, 0.9549449704717142, 0.644473858305753, 0.3808464753404683, 0.1696903728424354, 0.014561044512103286, -0.08312885824357324, -0.12410337307660466, -0.11112858974373478, -0.0488550188918473, 0.056402366770339774, 0.19696917101897918, 0.3641006783807531, 0.5484082442923949, 0.7401531976870479, 0.9297502087739564, 1.1080025719625721, 1.26662627239474, 1.398373186456612, 1.4975159599137278, 1.5598232777514733, 1.582951067101998, 1.566256761860615, 1.5110561459735443, 1.420288168591594, 1.2986170652352014, 1.1519821216794441, 0.9875486294192151, 0.8131945933707483, 0.6373380338958468, 0.4684222352388044, 0.3146672184860085, 0.18361512873150448, 0.08186712820998106, 0.014740739181914923, -0.013942347109691665, -0.002053398986725019, 0.05074169650448068, 0.14294036849084338, 0.27125644220436596, 0.4307164968663434, 0.6148890641323729, 0.8160785686626313, 1.0257251328058006, 1.2346369803197268, 1.433528502209959, 1.6132227977565334, 1.7652731526884387, 1.8820690893900196, 1.9574719785041472, 1.9867707375260337, 1.9672585380000558, 1.8980065317867338, 1.7803165106438712, 1.6173095708137448, 1.4142082654898567, 1.1777676130659251, 0.9163670987448924, 0.639339056910287, 0.3568817231161107, 0.07936019137376053, -0.1829183576932944, -0.4203467970971866, -0.6243155481656848, -0.7877173757777572, -0.9052387663729717, -0.9736637873331034, -0.9920798098152241, -0.9619445157777682, -0.8871395459825058, -0.7737992427711589, -0.6301712570836487, -0.4662416729419945, -0.29339577204575534, -0.12390603606894356, 0.02957614059307251, 0.15458075790970374, 0.23943090439404602, 0.27375377510102344, 0.2491040895078113, 0.1593349179103987, 0.0011289021968468455, -0.22584034805003494, -0.5185685816347447, -0.8708045566026283, -1.2729794587320886, -1.7125307619484749, -2.1741416217728236, -2.6402593159174503, -3.091638913996088, -3.5079763884093373, -3.868701203056761, -4.153622498296883, -4.343870234522322, -4.422448028673263, -4.375189541046262, -4.191125223620831, -3.8633056197886684, -3.388920105484111, -2.7698449887090453, -2.012495972046641, -1.1279864839021072, -0.13174538899262356, 0.9567834230821504, 2.114678648882468, 3.3163123187225283, 4.5339254281437515, 5.738819797124124, 6.901833467767665, 7.994849362338264, 8.99103258358065, 9.866510730156183, 10.600258091011534, 11.17578239881099, 11.580583710449382, 11.807686390701441, 11.854657318670842, 11.724849553921395, 11.426026959391388, 10.97123306927031, 10.377127577297204, 9.664452970042808, 8.856233202686807, 7.977872227691403, 7.0553890398145995, 6.1152363700289785, 5.182744770226271, 4.281787668998505, 3.4335799172214996, 2.6563309886220186, 1.9644942197394142, 1.3685407951581152, 0.8746922354159327, 0.4849157470499112, 0.19710428190894042, 0.005344619766008275, -0.09955262515267338, -0.12951841048602403, -0.09848867685985781, -0.021665126831570073, 0.08526237564199098, 0.2069540843403879, 0.32907818910909065, 0.43911889435726364, 0.5267843439161898, 0.5846560814799865, 0.6082680810199608, 0.5964947252218376, 0.551284489784747, 0.4777295585626917, 0.3835007197285743, 0.2786000857148644, 0.17459615933532144, 0.08412137996732706, 0.02003889712553603, -0.005202198376322969, 0.019670206099633478, 0.1041094500840586, 0.25517650829000016, 0.47705379256756525, 0.7707373974748761, 1.1338394049548173, 1.560564963942647, 2.0418921661315816, 2.565791211324832, 3.1178103504594583, 3.6814400897394024, 4.239066972095285, 4.772349375703843, 5.263439929860818, 5.695228246040064, 6.052688599065731, 6.322861585848826, 6.496164508579171, 6.566026006993366, 6.5300060516214415, 6.389057740111269, 6.148340402062397, 5.816150130527942, 5.404366623134982, 4.92715617396018, 4.40106002558973, 3.8436187071219226, 3.2731743355063774, 2.7075845051899923, 2.1638609548915393, 1.6571304949925725, 1.2002581807461172, 0.8031733510364553, 0.4726218608116782, 0.21191396091614637, 0.020917749441527255, -0.10378663237850541, -0.1686152689762301, -0.18250536153047475, -0.15633531960169933, -0.10226856103727641, -0.03296152626134125, 0.03910521563254765, 0.10250341648627713, 0.14737325314632002, 0.16623040844851558, 0.15419802927381698, 0.10959580498613133, 0.033815491348221344, -0.06841993351039125, -0.1895366540233966, -0.31923060945752674, -0.44523076834606046, -0.5537731907300776, -0.6305162721562055, -0.6612664402607262, -0.6328828543074715, -0.5340928969830327, -0.35622533335676165, -0.09392185342140891, 0.25442723274203644, 0.6862654029715831, 1.194795160877947, 1.76900409202599, 2.3939364292123386, 3.0512417260133033, 3.7196996428088127, 4.376281292236616, 4.996770954553372, 5.557239231423883, 6.034570743851694, 6.408172445152985, 6.660218239830707, 6.777369974775681, 6.750589420909936, 6.576643171451827, 6.257403271102802, 5.800942863633815, 5.220336306738701, 4.534224411439713, 3.765216445376225, 2.939899647719714, 2.087021473921777, 1.2370204040502815, 0.4202119795745911, -0.33399219351149095, -0.9986662497984506, -1.5502354866288055, -1.9696353071382138, -2.243014302587824, -2.362353727083148, -2.3257872838988596, -2.137661852310828, -1.8083196418272047, -1.353683473652383, -0.7944422623474017, -0.1553326362521329, 0.5362249670170476, 1.2509191846699537, 1.9593161864358608, 2.632482962426031, 3.2439449149352853, 3.7699262672422518, 4.191250778479684, 4.493057153227536, 4.666411623571324, 4.707454515756931, 4.6185501762487515, 4.40692768532465, 4.085280893501709, 3.6700613500408137, 3.181541855694065, 2.6419848850511007, 2.075277474844877, 1.5052214142196645, 0.954917418208581, 0.4454000031250123, -0.005018214791234914, -0.38160884081746793, -0.6737221014420586, -0.8750814974815292, -0.9839646277078956, -1.0029685374619521, -0.9388016658737381, -0.8016511941841616, -0.6045992303410489, -0.3627881316493195, -0.09255530092247666, 0.1893832287526036, 0.4669275674324458, 0.7251916623278828, 0.9514534541880925, 1.1353921394765518, 1.269835781100662, 1.3505810223092931, 1.3768302819766525, 1.3506290984123723, 1.276956837285072, 1.1628974554353655, 1.0174245855958608, 0.8504739016716785, 0.672528062973337, 0.4937728121757815, 0.32362512749722383, 0.17012890610659856, 0.03957258957034723, -0.06377926888470364, -0.1378647823436271, -0.18273970520698796, -0.20049766832526614, -0.19489390194244818, -0.17102382323899948, -0.13478045276805928, -0.09237529102806118, -0.04978603943702814, -0.01224939969867836, 0.01615051459557173, 0.03287520848301253, 0.0370944647505385, 0.02984748763452751, 0.013916116831319882, -0.0063067407917419445, -0.025196997838810645, -0.03630804709342881, -0.03290012254536157, -0.008532569492128576, 0.04240180375374627, 0.12405484276384958, 0.23873169145045217, 0.38641695425239325, 0.5646414235320092, 0.7683306196247264, 0.9899608611384755, 1.2197852781429983, 1.4463151341334648, 1.6571550024355342, 1.839339544219806, 1.9798182169833343, 2.067022374223681, 2.0941893269356058, 2.055533489603315, 1.9399417239120962, 1.7469468548983265], 'positive_zeros': ['0.67370676791448655064115416782904', '1.30369719390986037188790653672050', '1.86140459426729765786698715559093', '2.39068489842424337610336784061664', '3.42435789328946906373866063058970', '3.43462598153875759772487613601892', '4.17464832663752781873318726688985', '4.27759773965262635427123819436386', '4.85988956032325708922026743062902', '4.89986582765225426165279787445459', '5.46784837018212606625218687678717', '5.80769016271127479096417125839288', '5.95326208547498890982616152123298', '6.44824850245512109269483857828044', '7.21961423699867321786264827194025', '7.31769741387222476595669474727448', '7.67756283257147285951129414601791', '7.69889952025520372874330286260776'], 'prelabel': '4-5687e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.738762766970075, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 9201853091982160, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67370676791448655064115416783', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.30369719390986037188790653672', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.86140459426729765786698715559', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2062.1519848844796, 'bad_primes': [11, 47], 'central_character': '1.1', 'conductor': 32341969, 'conductor_radical': 517, 'degree': 4, 'dirichlet_coefficients': [1, -1, -3, -2, -3, 3, 3, 3, 2, 3, 0, 6, 1, -3, 9, 1, -4, -2, 2, 6, -9, 0, 4, -9, -2, -1, 6, -6, -18, -9, 0, -2, 0, 4, -9, -4, -7, -2, -3, -9, 9, 9, -5, 0, -6, -4, 2, -3, 4, 2, 12, -2, 11, -6, 0, 9, -6, 18, -5, -18, -12, 0, 6, 1, -3, 0, 12, 8, -12, 9, -12, 6, -20, 7, 6, -4, 0, 3, 0, -3, -14, -9, -22, 18, 12, 5, 54, 0, 18, 6, 3, -8, 0, -2, -6, 6, 0, -4, 0, 4], 'euler11': [1, 0, 0, 0, 0], 'euler13': [1, -1, 25, -13, 169], 'euler17': [1, 4, 33, 68, 289], 'euler19': [1, -2, 19, -38, 361], 'euler2': [1, 1, 3, 2, 4], 'euler23': [1, -4, 45, -92, 529], 'euler29': [1, 18, 139, 522, 841], 'euler3': [1, 3, 7, 9, 9], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, 7, 75, 259, 1369], 'euler41': [1, -9, 71, -369, 1681], 'euler43': [1, 5, 91, 215, 1849], 'euler47': [1, -2, 1, 0, 0], 'euler5': [1, 3, 11, 15, 25], 'euler53': [1, -11, 135, -583, 2809], 'euler59': [1, 5, 123, 295, 3481], 'euler61': [1, 12, 113, 732, 3721], 'euler67': [1, -12, 125, -804, 4489], 'euler7': [1, -3, 5, -21, 49], 'euler71': [1, 12, 173, 852, 5041], 'euler73': [1, 20, 246, 1460, 5329], 'euler79': [1, 0, -22, 0, 6241], 'euler83': [1, 22, 282, 1826, 6889], 'euler89': [1, -18, 239, -1602, 7921], 'euler97': [1, 0, 149, 0, 9409], 'euler_factors': [[1, 1, 3, 2, 4], [1, 3, 7, 9, 9], [1, 3, 11, 15, 25], [1, -3, 5, -21, 49], [1, 0, 0, 0, 0], [1, -1, 25, -13, 169], [1, 4, 33, 68, 289], [1, -2, 19, -38, 361], [1, -4, 45, -92, 529], [1, 18, 139, 522, 841], [1, 0, 62, 0, 961], [1, 7, 75, 259, 1369], [1, -9, 71, -369, 1681], [1, 5, 91, 215, 1849], [1, -2, 1, 0, 0], [1, -11, 135, -583, 2809], [1, 5, 123, 295, 3481], [1, 12, 113, 732, 3721], [1, -12, 125, -804, 4489], [1, 12, 173, 852, 5041], [1, 20, 246, 1460, 5329], [1, 0, -22, 0, 6241], [1, 22, 282, 1826, 6889], [1, -18, 239, -1602, 7921], [1, 0, 149, 0, 9409]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5687/2/a/h'], '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': '4-5687e2-1.1-c1e2-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-5687e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.738762766970075, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 9201853091982160, 'z1': {'__RealLiteral__': 0, 'data': '0.67370676791448655064115416783', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '854024788724619317037591061323,1652632530375692876638906709742', 'Lhash_array': ['854024788724619317037591061323', '1652632530375692876638906709742'], 'label': '4-5687e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5687/2/a/h'}