-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1275232741455080452166089431152,1424401351132986720372816649821', 'a10': 0, 'a2': 2, 'a3': 2, 'a4': 3, 'a5': 0, 'a6': 4, 'a7': 0, 'a8': 4, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 931.3985971344308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [3, [1, -2, 1]], [7, [1]], [13, [1, -2, 1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '3822.1', 'coefficient_field': '1.1.1.1', 'conductor': 14607684, 'conductor_radical': 546, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, -2, 1], [1, 0, 8, 0, 25], [1], [1, 2, 21, 22, 121], [1, -2, 1], [1, -2, 17, -34, 289], [1, -6, 47, -114, 361], [1, 4, 0, 92, 529], [1, -10, 83, -290, 841], [1, -8, 70, -248, 961], [1, -4, 28, -148, 1369], [1, -12, 116, -492, 1681], [1, -4, 82, -172, 1849], [1, -18, 175, -846, 2209], [1, -2, -21, -106, 2809], [1, -18, 197, -1062, 3481], [1, 2, 105, 122, 3721], [1, 18, 183, 1206, 4489], [1, 2, 143, 142, 5041], [1, -12, 132, -876, 5329], [1, -4, 34, -316, 6241], [1, 4, 138, 332, 6889], [1, 4, 164, 356, 7921], [1, 4, 100, 388, 9409], [1, 8, 210, 808, 10201], [1, 4, 138, 412, 10609], [1, -16, 246, -1712, 11449], [1, 8, 202, 872, 11881], [1, -2, 177, -226, 12769]], 'euler_factors_factorization': [[[[1, -1], 2]], [[[1, -1], 2]], [[[1, 0, 8, 0, 25], 1]], [1], [[[1, 2, 21, 22, 121], 1]], [[[1, -1], 2]], [[[1, -2, 17, -34, 289], 1]], [[[1, -3, 19], 2]], [[[1, 4, 0, 92, 529], 1]], [[[1, -5, 29], 2]], [[[1, -8, 70, -248, 961], 1]], [[[1, -4, 28, -148, 1369], 1]], [[[1, -12, 116, -492, 1681], 1]], [[[1, -4, 82, -172, 1849], 1]], [[[1, -9, 47], 2]], [[[1, -2, -21, -106, 2809], 1]], [[[1, -18, 197, -1062, 3481], 1]], [[[1, 2, 105, 122, 3721], 1]], [[[1, 18, 183, 1206, 4489], 1]], [[[1, 1, 71], 2]], [[[1, -12, 132, -876, 5329], 1]], [[[1, -4, 34, -316, 6241], 1]], [[[1, 4, 138, 332, 6889], 1]], [[[1, 4, 164, 356, 7921], 1]], [[[1, 4, 100, 388, 9409], 1]], [[[1, 8, 210, 808, 10201], 1]], [[[1, 4, 138, 412, 10609], 1]], [[[1, -16, 246, -1712, 11449], 1]], [[[1, 8, 202, 872, 11881], 1]], [[[1, -2, 177, -226, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 8, 'label': '4-3822e2-1.1-c1e2-0-8', 'leading_term': '15.7754151183549096177227218475618492155377526194577547660535000000000000000000000000000000', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3822/2/a/bs', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.025390625', 'prec': 37}, 'plot_values': [15.775415118354907, 15.75348972147171, 15.711153487177242, 15.63235517409236, 15.518196752792115, 15.372925193347175, 15.196163051362847, 14.986769464455204, 14.744849698350937, 14.470817594173715, 14.16484323319101, 13.827175163082337, 13.458294541081917, 13.05887589887872, 12.62978532816544, 12.17210513926165, 11.687198597428539, 11.176683075406414, 10.642497636035305, 10.086854029115349, 9.512316411724179, 8.921723500599692, 8.318269988972233, 7.705404472686567, 7.086907071784687, 6.466766558442215, 5.849248046093179, 5.238754603594387, 4.639880332507061, 4.057262571883423, 3.495617199925244, 2.9595882958479622, 2.453764454755629, 1.9825331457584108, 1.550078955144853, 1.1602498613602032, 0.8165404870076219, 0.5219770249632574, 0.27909059783698115, 0.08982658066063817, -0.044485145084077755, -0.1231922248485729, -0.14634471147109238, -0.11472617678748853, -0.0298652255208182, 0.10596423924934624, 0.2897531394065337, 0.5177851285141618, 0.7856755838428658, 1.0884223544361749, 1.4204790284559445, 1.7758206989875043, 2.148054404303332, 2.5304900011384177, 2.916287662607559, 3.298522507229559, 3.6703657728524623, 4.025131263962255, 4.3564836028790745, 4.658454983089693, 4.9256710604768505, 5.153328011857571, 5.337424492357906, 5.4746915718916185, 5.56281803103195, 5.600329249104106, 5.586793142834377, 5.522648262458065, 5.409378988122932, 5.249297610736951, 5.045679951407066, 4.802510644092325, 4.524573952260136, 4.217175376819616, 3.886186794973449, 3.537760445080744, 3.178332176155487, 2.8143454273255686, 2.4522208502878162, 2.0981078312868933, 1.7578325104821089, 1.4366925685421448, 1.1393982344370206, 0.869922539610502, 0.6314509005683545, 0.42629408839229677, 0.25586117550332255, 0.1206365179419281, 0.020188249061259215, -0.046795783130535715, -0.08245600471237478, -0.08967735747380165, -0.07199119689124785, -0.0334599409715359, 0.021463714794564357, 0.08806404047894958, 0.16153648950644234, 0.23710577350853657, 0.31021931720332957, 0.3766361300657687, 0.4326219538514422, 0.47499230308474877, 0.5012905512882287, 0.5097740035905162, 0.49955739808303923, 0.470537870971096, 0.4234900174874738, 0.35993330596691164, 0.28217061857194187, 0.19310911726454452, 0.09624142867613292, -0.004562813404490079, -0.10512614929883878, -0.20117972863412134, -0.28846849323303375, -0.362952874020937, -0.4209297318195738, -0.45919830158285424, -0.4751731765609312, -0.4669981815304466, -0.43362726470478347, -0.37487717810793847, -0.2914550276232671, -0.1849494629454555, -0.057789635781140415, 0.08681610262951286, 0.2449966236602978, 0.4123143489472542, 0.5839539692030878, 0.7548299506208365, 0.9198345120624305, 1.073929220728965, 1.2124305842583403, 1.3310591998692416, 1.4262353942956083, 1.49506389191128, 1.5356097204134698, 1.5468043937752949, 1.5286743405684262, 1.4821651890718384, 1.4093012135485177, 1.3129360478135959, 1.196831391253365, 1.0653536829707806, 0.9234722929764548, 0.7764306473085633, 0.6296766513524684, 0.48854197593458076, 0.3581286210423618, 0.24303052918844903, 0.14720818118596218, 0.07378202890111052, 0.024930372275600285, 0.0017746938259992431, 0.004333974740482742, 0.0315090197557812, 0.08111880911952572, 0.14997610938362374, 0.2340192737810554, 0.32845702696420925, 0.4279939650242908, 0.5270106516005358, 0.6198651754654584, 0.701067607161513, 0.7656258777992685, 0.8091726213121831, 0.8283137751999475, 0.8206714041846754, 0.7851897256264533, 0.7220691860532098, 0.6329881635975305, 0.5209198431515554, 0.3902386346681266, 0.24642991092538866, 0.09606701527411539, -0.053558195290267396, -0.19458126190010858, -0.31897157517342833, -0.4187733724636543, -0.48649894617507755, -0.5154182346893301, -0.49988849455898837, -0.4356332542313514, -0.31996665303413707, -0.15199821862011828, 0.06727368219542482, 0.3348893351635981, 0.6459688341684962, 0.9938149068169461, 1.370068205969514, 1.7650056745332419, 2.167766838329956, 2.566840380847733, 2.9503010752672396, 3.3064491701021756, 3.623989104247471, 3.892762206556148, 4.10380066134681, 4.250078049205454, 4.326385602508707, 4.330020337014268, 4.260454040625907, 4.119886579057944, 3.9127081332551295, 3.6458651091059067, 3.3281483753959074, 2.9703484237854374, 2.584431576628286, 2.183495253385622, 1.780915279924587, 1.3901458429723732, 1.0239301119533732, 0.6940169857579798, 0.4105219671008392, 0.18164913049398446, 0.013269564125446756, -0.09126125375736431, -0.1312716964201116, -0.10878488162826462, -0.02843677764395347, 0.1027330521256257, 0.2755701025883106, 0.47924492118879825, 0.7016703568533497, 0.9301412268825319, 1.1517787515211098, 1.3543004707611297, 1.5263832559544923, 1.658465979985745, 1.7429333417934834, 1.7748416019617363, 1.7518533317379128, 1.674783360414421, 1.5472554436841728, 1.3759914070907986, 1.1702081088115728, 0.941614222415424, 0.7036117457229296, 0.471015591882907, 0.2591601008110472, 0.08340821583655972, -0.0417169128147184, -0.10312294963365896, -0.089872861247087, 0.0062611973102380345, 0.1903130980458622, 0.46374836955289234, 0.8242731315770919, 1.2657624166330366, 1.7783628337721131, 2.3488052873566265, 2.9607442334350855, 3.5954787951235283, 4.232421351987966, 4.850186340754133, 5.4270472891357056, 5.942291824162988, 6.376516153888811, 6.713098781671604, 6.938198025699215, 7.0421743550933265, 7.019198346136336, 6.868457341558104, 6.593342163477702, 6.202308028024839, 5.707678473674724, 5.126088119234113, 4.4770095370617, 3.782777077415977, 3.066994626683286, 2.354212981923253, 1.6684035037440048, 1.0324232813154413, 0.46673559922676316, -0.01116414318990219, -0.3876361313449937, -0.6533285364196726, -0.803590966342203, -0.8386093968411088, -0.7633420714440595, -0.587255680442603, -0.3238623754108896, 0.009969543000063199, 0.3947287493487674, 0.8093212900676522, 1.231840053915132, 1.6408692566835865, 2.0161054919996673, 2.3397293545467392, 2.5966994654306954, 2.775997239735517, 2.8704748278293306, 2.8777992314163945, 2.7998179014656626, 2.643083157853453, 2.417790360339092, 2.13784339110053, 1.8195028767196773, 1.4810435865223943, 1.1413081748966036, 0.8190903439189974, 0.5318111698112357, 0.2948210451824548, 0.12039559456212529, 0.017171988686364516, -0.010397660727937687, 0.0377198732882454, 0.15709979877706612, 0.33909014351598515, 0.5712296703859081, 0.8379872089595743, 1.1214926112686703, 1.4027239830393703, 1.6623396616742285, 1.8821552879897823, 2.0458368093846886, 2.140438916033811, 2.1567382330084395, 2.090577054134784, 1.9426802190398427, 1.7195714099620323, 1.432815644516309, 1.0993480496878154, 0.7401980487641183, 0.38018097657041544, 0.04626750826870854, -0.23328295032000781, -0.43066536855059445, -0.519752692731024, -0.47767678620018206, -0.28611629273717776, 0.06753658595490336, 0.58915755893024, 1.2773134048714003, 2.122825618306087, 3.1088420439758693, 4.211213685359046, 5.399136510739891, 6.636441895722158, 7.88260031761246, 9.094869305335534, 10.229354131809876, 11.243803197197504, 12.098378852658447, 12.758768408929168, 13.196342383787558, 13.391184445739844, 13.331403646722142, 13.01569325616845, 12.451703953958633, 11.657821105856117, 10.66067269118913, 9.495954471453286, 8.205308461245309, 6.836200865649232, 5.438532500551103, 4.063752807779123, 2.7616268411633214, 1.578915969162785, 0.5567120080609282, -0.27089773112156607, -0.8786102322985517, -1.250831143481559, -1.3824040609948585, -1.2787713326079733, -0.9556781917525822, -0.4383595503401075, 0.23956599309482093, 1.0379084542085484, 1.9114545151041495, 2.812611295998862, 3.692942437153995, 4.506313342066317, 5.209960547979912, 5.767708808177026, 6.150205497676281, 6.337763562933033, 6.319551263631644, 6.095686274207383, 5.675372031156167, 5.07801396143873, 4.3304984534890245, 3.467293983823617, 2.527237138270151, 1.5527812429323797, 0.5867523112900611, -0.3289246068146514, -1.1560284297059888, -1.8614066890249963, -2.4189508559935096, -2.8106073797839506, -3.0272999318545, -3.069220246705021, -2.945678206394867, -2.6744600732841852, -2.2807976600932274, -1.7957808167232603, -1.2548088982624797, -0.6952478673937874, -0.15482590579569072, 0.33110914292639304, 0.730783208705336, 1.0186903568355123, 1.1759984816614752, 1.1927491335448124, 1.067265470123159, 0.8075075915790053, 0.4294820743484623, -0.04242443939126502, -0.5778262698196013, -1.1409898671423164, -1.693633333557504, -2.1963135937240437, -2.6111870808420137, -2.90371907249354, -3.044960285506586, -3.0130812991919727, -2.7948273073100425, -2.3863977871031516, -1.7939225565012196, -1.0333225509081956, -0.12986688307757263, 0.8831577296635007, 1.9655426774056224, 3.072622675518536, 4.156605545716682, 5.169895337937196, 6.0661721042475705, 6.8041303020358175, 7.347861176453059, 7.670486107359565, 7.753526492145805, 7.589937958824072, 7.182353752859435, 6.545150198857471, 5.701678028784255, 4.685185957288842, 3.5353625638573383, 2.2981722888432192, 1.022174812164638, -0.24246107276636733, -1.44734347320687, -2.547248746371371, -3.5027503482338886, -4.281537160338296, -4.859970401763639, -5.223890411931781, -5.368996780904468, -5.300835246369125, -5.034124213966841, -4.591804346103765, -4.003633188798626, -3.3043894888300227, -2.532185834661086, -1.7261023373833153, -0.9246995498853118, -0.1634731988646322, 0.5260185621333733, 1.118459800249004, 1.5947731058451122, 1.9438289394099217, 2.1615045709105964, 2.251584208004479, 2.224025673307638, 2.0950207102078973, 1.8847808422721604, 1.6169110702858163, 1.3161181944905007, 1.0071942169597932, 0.7130500911188424, 0.4536763926459391, 0.24481612611572837, 0.09725543910777543, 0.016293585967966557, 0.0016213277644370084, 0.04756144555521282, 0.14364093282423593, 0.2754041610802552, 0.42561342812277037, 0.5753174286291427, 0.7054634480088132, 0.7978617709341271, 0.8368966004742847, 0.810069619278696, 0.7094768989227691, 0.5317294940225721, 0.27892331155988986, -0.0421075540683169, -0.41947735033973127, -0.8375441283871247, -1.2772446204041548, -1.717690954466547, -2.136992511731231, -2.5138402626969345, -2.828540706970063, -3.0642863671500598, -3.2080800945160055, -3.2514724997631035, -3.191083967534546, -3.0287291634694165, -2.771333985456801, -2.430515392685798, -2.0218774548963023, -1.5642168687119473, -1.0780893752467422, -0.585170370804529, -0.10721932598553156, 0.33545929096820654, 0.7281418889150464, 1.0575509417126234, 1.3040412685429108, 1.458921821450758], 'positive_zeros': ['1.00598125479172727285268592316388', '1.12365453925280019383108899457634', '2.24084956120762708570795613311607', '2.37753522456644293595311079087663', '2.81721772140154688142432070458050', '3.15891926873810763346200946545697', '3.89130447155569416007337386989962', '3.89842587071899771378089064077086', '4.43417419444974324714972749693211', '4.69006356954258470328763996880126', '5.46150629397672533724213061011470', '5.56691224608062999877867274728538', '6.10927765434231720498422430719132', '6.19415660202671647117484980075136', '6.95637270481319983302452012979892', '7.15945700935716349767501988008935', '7.72689131307410011798144234982194', '7.75434901552065513055240273509444', '8.255778077666497004749933639107470', '8.400251344616668488071078817233872'], 'prelabel': '4-3822e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1629211240750373225, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00598125479172727285268592316', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.12365453925280019383108899458', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.24084956120762708570795613312', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 931.3985971344308, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 14607684, 'conductor_radical': 546, 'degree': 4, 'dirichlet_coefficients': [1, 2, 2, 3, 0, 4, 0, 4, 3, 0, -2, 6, 2, 0, 0, 5, 2, 6, 6, 0, 0, -4, -4, 8, -8, 4, 4, 0, 10, 0, 8, 6, -4, 4, 0, 9, 4, 12, 4, 0, 12, 0, 4, -6, 0, -8, 18, 10, 0, -16, 4, 6, 2, 8, 0, 0, 12, 20, 18, 0, -2, 16, 0, 7, 0, -8, -18, 6, -8, 0, -2, 12, 12, 8, -16, 18, 0, 8, 4, 0, 5, 24, -4, 0, 0, 8, 20, -8, -4, 0, 0, -12, 16, 36, 0, 12, -4, 0, -6, -24], 'euler11': [1, 2, 21, 22, 121], 'euler13': [1, -2, 1, 0, 0], 'euler17': [1, -2, 17, -34, 289], 'euler19': [1, -6, 47, -114, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, 4, 0, 92, 529], 'euler29': [1, -10, 83, -290, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, -8, 70, -248, 961], 'euler37': [1, -4, 28, -148, 1369], 'euler41': [1, -12, 116, -492, 1681], 'euler43': [1, -4, 82, -172, 1849], 'euler47': [1, -18, 175, -846, 2209], 'euler5': [1, 0, 8, 0, 25], 'euler53': [1, -2, -21, -106, 2809], 'euler59': [1, -18, 197, -1062, 3481], 'euler61': [1, 2, 105, 122, 3721], 'euler67': [1, 18, 183, 1206, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 2, 143, 142, 5041], 'euler73': [1, -12, 132, -876, 5329], 'euler79': [1, -4, 34, -316, 6241], 'euler83': [1, 4, 138, 332, 6889], 'euler89': [1, 4, 164, 356, 7921], 'euler97': [1, 4, 100, 388, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, -2, 1, 0, 0], [1, 0, 8, 0, 25], [1, 0, 0, 0, 0], [1, 2, 21, 22, 121], [1, -2, 1, 0, 0], [1, -2, 17, -34, 289], [1, -6, 47, -114, 361], [1, 4, 0, 92, 529], [1, -10, 83, -290, 841], [1, -8, 70, -248, 961], [1, -4, 28, -148, 1369], [1, -12, 116, -492, 1681], [1, -4, 82, -172, 1849], [1, -18, 175, -846, 2209], [1, -2, -21, -106, 2809], [1, -18, 197, -1062, 3481], [1, 2, 105, 122, 3721], [1, 18, 183, 1206, 4489], [1, 2, 143, 142, 5041], [1, -12, 132, -876, 5329], [1, -4, 34, -316, 6241], [1, 4, 138, 332, 6889], [1, 4, 164, 356, 7921], [1, 4, 100, 388, 9409]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3822/2/a/bs'], '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': '4-3822e2-1.1-c1e2-0-8', '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': 0, 'prelabel': '4-3822e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1629211240750373225, 'z1': {'__RealLiteral__': 0, 'data': '1.00598125479172727285268592316', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1275232741455080452166089431152,1424401351132986720372816649821', 'Lhash_array': ['1275232741455080452166089431152', '1424401351132986720372816649821'], 'label': '4-3822e2-1.1-c1e2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3822/2/a/bs'}