-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '913897711702361378808689237512,1843605374438876913017091710430', 'a10': 0, 'a2': 0, 'a3': -4, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 7, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.765404812333806, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 4, 9]], [5, [1, 0, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '240.1', 'coefficient_field': '1.1.1.1', 'conductor': 57600, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, 4, 9], [1, 0, 5], [1, 4, 102, 196, 2401], [1, 0, -62, 0, 14641], [1, -16, 402, -2704, 28561], [1, 0, -398, 0, 83521], [1, -68, 1878, -24548, 130321], [1, 0, 562, 0, 279841], [1, 0, -62, 0, 707281], [1, 28, 2118, 26908, 923521], [1, -112, 5874, -153328, 1874161], [1, 0, -2642, 0, 2825761], [1, 16, 3762, 29584, 3418801], [1, 0, -2798, 0, 4879681], [1, 0, -3998, 0, 7890481], [1, 0, -6782, 0, 12117361], [1, 92, 9558, 342332, 13845841], [1, 64, 10002, 287296, 20151121], [1, 0, -7202, 0, 25411681], [1, 212, 21894, 1129748, 28398241], [1, -44, 12966, -274604, 38950081], [1, 0, 802, 0, 47458321], [1, 0, -4322, 0, 62742241], [1, -244, 33702, -2295796, 88529281], [1, 0, 10018, 0, 104060401], [1, -92, 23334, -976028, 112550881], [1, 0, -22718, 0, 131079601], [1, -172, 31158, -2043532, 141158161], [1, 0, -16718, 0, 163047361]], 'euler_factors_factorization': [[1], [[[1, 4, 9], 1]], [[[1, 0, 5], 1]], [[[1, 2, 49], 2]], [[[1, 0, -62, 0, 14641], 1]], [[[1, -8, 169], 2]], [[[1, 0, -398, 0, 83521], 1]], [[[1, -34, 361], 2]], [[[1, 0, 562, 0, 279841], 1]], [[[1, 0, -62, 0, 707281], 1]], [[[1, 14, 961], 2]], [[[1, -56, 1369], 2]], [[[1, 0, -2642, 0, 2825761], 1]], [[[1, 8, 1849], 2]], [[[1, 0, -2798, 0, 4879681], 1]], [[[1, 0, -3998, 0, 7890481], 1]], [[[1, 0, -6782, 0, 12117361], 1]], [[[1, 46, 3721], 2]], [[[1, 32, 4489], 2]], [[[1, 0, -7202, 0, 25411681], 1]], [[[1, 106, 5329], 2]], [[[1, -22, 6241], 2]], [[[1, 0, 802, 0, 47458321], 1]], [[[1, -142, 7921], 1], [[1, 142, 7921], 1]], [[[1, -122, 9409], 2]], [[[1, 0, 10018, 0, 104060401], 1]], [[[1, -46, 10609], 2]], [[[1, 0, -22718, 0, 131079601], 1]], [[[1, -86, 11881], 2]], [[[1, 0, -16718, 0, 163047361], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 0, 'label': '4-240e2-1.1-c2e2-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/240/3/l/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.248026798209371, 1.2345138068892425, 1.2054349528426351, 1.1532236237995062, 1.0788911693999435, 0.9851623868482233, 0.8728325750149709, 0.7427808865984414, 0.5969646604612683, 0.43801881297899353, 0.2691588891224038, 0.09433153985830364, -0.08161147360005559, -0.2530125636445349, -0.41335064738856264, -0.5554083991925964, -0.6713201598708595, -0.7528508649043085, -0.7916155448320696, -0.7794314705258254, -0.7087313166833386, -0.5729345999842642, -0.36703306805234925, -0.0878972456107673, 0.26504541678608673, 0.6896699596968489, 1.1805220009711783, 1.7289403070240477, 2.3226534856206595, 2.9462280791860715, 3.581084823475881, 4.2062648609564945, 4.799014202239205, 5.3357619969308905, 5.793323119387356, 6.149873505100031, 6.38667664926613, 6.488752207074741, 6.446873048212905, 6.257590951090234, 5.925123169687379, 5.460454777211216, 4.882689320930411, 4.217104756491506, 3.495622001207655, 2.753933870711315, 2.030958116731607, 1.3654343081667857, 0.7945398056889622, 0.3505769782899664, 0.0592610206334341, -0.06279099587903746, -0.009353297945967967, 0.21429311063587822, 0.5912713636557501, 1.0936434126090673, 1.6840845056853335, 2.317825369087361, 2.9461796842675914, 3.5191336154522963, 3.990217679732149, 4.318627599019238, 4.474399318195914, 4.438916901898268, 4.209094778669312, 3.795507914557213, 3.224459085105441, 2.533694133173888, 1.771846317047884, 0.9925653624277228, 0.2517230947582928, -0.39852002970941397, -0.9135011033093233, -1.2603061632960406, -1.4208201750143867, -1.3929733263519195, -1.1914817023120898, -0.8457631073000151, -0.3976125729598146, 0.10328433961671145, 0.6042744330212969, 1.0546738836834915, 1.4116723734247014, 1.6434391025651343, 1.7338332887974242, 1.6819992142707865, 1.5040731940449772, 1.228975963387935, 0.8965449516328002, 0.5508856293316579, 0.23600033889519012, -0.010741895368447786, -0.16309871412883162, -0.20967463745725406, -0.1558641787931104, -0.023193449568391648, 0.1529443253772036, 0.3279088439839814, 0.4539451579692742, 0.48637159555035125, 0.3911363684914567, 0.14920096606061667, -0.2380643482444844, -0.7490320879880678, -1.3416043382670981, -1.958489855629516, -2.532952040948367, -2.9970871688120004, -3.2913053460091777, -3.371559462903922, -3.2180226639619995, -2.837232274924168, -2.265142344741434, -1.5623897140296117, -0.8090907873922555, -0.09503711563053287, 0.49253335030123785, 0.878789522219576, 1.0156263882907706, 0.8855214682557827, 0.5114755089415292, -0.04912003923747817, -0.7036225102818883, -1.3397805217955898, -1.8340936329626605, -2.071675732878745, -1.9587244447235852, -1.4387268650004152, -0.5007592884132293, 0.8145213497736771, 2.418121584446264, 4.1784977816352935, 5.938732895703966, 7.529298286559731, 8.79472466086506, 9.604137946698026, 9.87782264182238, 9.586534324214485, 8.767810944614023, 7.510235080135688, 5.954112416639468, 4.264619096807932, 2.6193323399854003, 1.1804888712058148, 0.07870054780711676, -0.6042415797460657, -0.8441570889837862, -0.6746136582526895, -0.18115612768378833, 0.5134229440350839, 1.2681509791379062, 1.9434636804454375, 2.424511750422947, 2.6331271589193754, 2.5436133233809937, 2.1790929554900083, 1.6122032849543642, 0.9469000975360155, 0.3052904960092525, -0.19556151801008567, -0.46112718869538366, -0.4352313885249506, -0.10959022414425774, 0.4754870197452697, 1.2371237144734732, 2.062615978160714, 2.8292224967914805, 3.4202173356151633, 3.7482353786207656, 3.7623515344449525, 3.4626635773327483, 2.8917792378098124, 2.133949729656597, 1.2943988444820755, 0.48617424380547936, -0.19121461179251495, -0.6663702045728377, -0.905891311991919, -0.9191257528441796, -0.7516900272181996, -0.47644685096043743, -0.1763826718425867, 0.07203491051371787, 0.21403316627805466, 0.22873726649443762, 0.131465993975152, -0.02785876056551653, -0.17698283758331643, -0.23621725860298298, -0.1364093713866862, 0.16361654054697436, 0.6665935454593316, 1.3308098324361939, 2.0750151403900805, 2.7910482286836724, 3.360315596511689, 3.679547480125964, 3.675285016467216, 3.3274388010572733, 2.6678364023822754, 1.7867416592301746, 0.8116783550971315, -0.10658824739023597, -0.8245822385434026, -1.2293358049138452, -1.259909652875542, -0.9207380259902662, -0.280502144494988, 0.5377947829055498, 1.3790041341322754, 2.0863471461451617, 2.5275095912915733, 2.6275754940946396, 2.3774707664253247, 1.8477954296122518, 1.1689787318286515, 0.5169130991116444, 0.073801827853568, -0.0030365343690623324, 0.3839655813252711, 1.2500758633828986, 2.5196829959036235, 4.034609232850942, 5.5758253477134865, 6.905028733784525, 7.798155785788552, 8.099325005660477, 7.736824376929918, 6.758391273450047, 5.3100660963573505, 3.6331395368623483, 2.0109515065962773, 0.7339337584267581, 0.042168297593470225, 0.0879326814299089, 0.9060329408122324, 2.4065466433381544, 4.386598778477022, 6.566468738167064, 8.627791436380795, 10.277047512492002, 11.276402474542184, 11.500313216862555, 10.93011935544273, 9.675060196283377, 7.9272020867571, 5.943386372916352, 3.9849629073514, 2.2836034993583203, 1.000515497670094, 0.20751956960004458, -0.11421538582118834, -0.061391215475525646, 0.2214722416676314, 0.5768326299138126, 0.8666203419265455, 1.0025342383719773, 0.9540473295802099, 0.7529125888791827, 0.4717346962135429, 0.20373922795497787, 0.031001437181173916, 0.0013977286947252465, 0.11256111500211932, 0.3100654514414251, 0.49812748181753375, 0.5646540387907651, 0.4057301085699801, -0.040513210671526384, -0.7810793016936445, -1.7523960437117838, -2.834809321303291, -3.8681751126330735, -4.685214474553009, -5.1459682014475545, -5.163676105940063, -4.729672559865627, -3.909635579166606, -2.838006159066215, -1.686155183203979, -0.6307007497178271, 0.18116043687856384, 0.6631289026957029, 0.7987821713665628, 0.6469419148188974, 0.31728866730295285, -0.0532509560642022, -0.3379779976427441, -0.44975216501773535, -0.3601936717044628, -0.10540856983404857, 0.2283005012221496, 0.5310921307150559, 0.7022917854500185, 0.6880154781135307, 0.499079441813235, 0.22528504192865037, 0.01638460099258206, 0.056724635327408186, 0.5193826074739646, 1.5206805220240518, 3.083358789750848, 5.113706435465107, 7.40473249193269, 9.6670786461522, 11.568910171825037, 12.811702273630855, 13.167814191350873, 12.555480100919377, 11.029643042347685, 8.808674826091897, 6.207135337170458, 3.603904311646103, 1.3522434968983053, -0.27386211449862335, -1.1354267617524305, -1.249182758691217, -0.7759735941149226, 0.018740072851094965, 0.8249232987814361, 1.363909901527839, 1.4397221368462607, 0.9959126376505543, 0.10867528772648971, -1.0156413357193257, -2.1069564506557357, -2.8827875895440846, -3.126680514052011, -2.734410476307314, -1.7484860492977692, -0.34669838872445913, 1.183964699896054, 2.522471856940794, 3.3637120197239154, 3.5105041634360803, 2.8893217984939725, 1.5977755500007154, -0.14263788510389525, -2.008702768478284, -3.659425951776743, -4.796814158678688, -5.22718633130022, -4.9010979695609125, -3.9103254842116733, -2.4698805972124283, -0.8618314270762899, 0.6255922124584297, 1.7539900728866686, 2.3880146039576005, 2.502227056955282, 2.186911281169214, 1.6022748685146615, 0.9420558940262713, 0.3766717211300959, 0.016589790238351873, -0.10860663853544654, -0.04950498571684643, 0.08846941688588511, 0.18140907383125915, 0.1261225673155578, -0.12505858539644946, -0.5526777024128107, -1.0718068000340493, -1.5582586525926383, -1.8845963313417256, -1.9548582889894466, -1.7379268362480733, -1.272961774803912, -0.665175553646201, -0.05498309586316998, 0.4213135138893965, 0.6664931586443793, 0.6585326143262757, 0.45004265148379224, 0.16540566788773464, -0.04161028490871212, -0.025337865433311305, 0.30339117897207957, 0.9481766053820188, 1.816447189512726, 2.7389748403612377, 3.5040632837496055, 3.9208075442025296, 3.857785297044948, 3.3004012056669563, 2.3437271199938077, 1.195262792506101, 0.11245537234101097, -0.6477542236666107, -0.9011041767027036, -0.5849975883357694, 0.2203116523424448, 1.3025608772075623, 2.3641413491385546, 3.097231909110747, 3.250704273307811, 2.710930005284875, 1.517978738073624, -0.11757542155893257, -1.8762708425411938, -3.390816456783057, -4.339493565254327, -4.525493360918671, -3.9227617398193297, -2.6924247398939865, -1.1431536179546677, 0.3427132990580307, 1.3914366800803109, 1.747838183243508, 1.3125905327842042, 0.20095426812738085, -1.3166441505375988, -2.846068147766383, -3.991374900104384, -4.429393995762411, -4.00325720154799, -2.750208059062854, -0.902550272352424, 1.1792767013596968, 3.0764799009863997, 4.43341165327713, 5.011335351148373, 4.773146783873122, 3.851820001593907, 2.5413321750107585, 1.1933141026092042, 0.14416072664451005, -0.37766875130676186, -0.30174198643783234, 0.27420324876813507, 1.116572342340772, 1.9215271616872154, 2.4063887197513205, 2.3740866662534303, 1.7826458661045488, 0.7372427626054121, -0.5205694296996008, -1.690484218761201, -2.484017684778192, -2.7007253338314174, -2.2815618306191516, -1.3163475660805128, -0.023045801162721282, 1.3110871131827124, 2.4069076906061824, 3.0513719252661557, 3.1610249837139577, 2.7760851939473055, 2.0586273529873904, 1.225817399083519, 0.49986802920269124, 0.04278456539630951, -0.07878130544925561, 0.09842231627677478, 0.45529772828945614, 0.8330006331985882, 1.0884522003090102, 1.1303079065580972, 0.9516182627533055, 0.6151327592478231, 0.2345952397599885, -0.07446509082282106, -0.23400531519376824, -0.23101490336037964, -0.12401121761817933, -0.01707351552708724, -0.02100887980775785, -0.2035914509392771, -0.5520078412068717, -0.9583280032856608, -1.2384952685512154, -1.1736600812928109, -0.5829927136956609, 0.6245128297084932, 2.391847801426184, 4.5159831500131284, 6.672215487704783, 8.478632372986722, 9.596349692597544, 9.790010181466457, 9.021588129016017, 7.428826214565028, 5.334151372592167, 3.13595249972578, 1.239089795431078, -0.05809967119624642, -0.6241577951122124, -0.5184805116787241, 0.03624956924596458, 0.7279231660981123, 1.2558323174319652, 1.4139574286378933, 1.1683088455882846, 0.6519324541650822, 0.14066890508965996, -0.04580366711001111, 0.3580456809685983, 1.465413624140529, 3.178624352958371, 5.189008316890364, 7.0426222130261715, 8.23278318222883, 8.356612408479071, 7.1879900918676425, 4.794716508976126, 1.4937952827809622, -2.1536738055211053, -5.52587435634546, -8.049905929428327, -9.314037204500591, -9.183246731103544, -7.900151637502032], 'positive_zeros': ['0.72093817613293607114905671851471', '1.45434820455017486105777129164190', '3.14551828905361041951591584772631', '3.25400737175870062306895408962451', '4.39793582494968958516912021908045', '4.92482270008296073106892430764828', '5.68422698109558736905296363283065', '5.94632777445677102714009961556571', '6.33933711002365588561088727038202', '7.19655001376276928028719173630825', '7.55759314885657683149523693394111', '8.025773303184323858916193764338350', '9.005573745742292200058942456801920', '9.267594117484508364717482258331059', '9.910082970761950223351205460748541', '10.13884717696738528414571348664143', '10.91809737861071506096622982978650', '11.35444133131044377004341116583401', '11.61463529123126255680878263802741', '11.84635163800132264612389136373850'], 'prelabel': '4-240e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.557249761882309, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c2e2-0', 'trace_hash': 1596304907814102299, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.72093817613293607114905671851', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.45434820455017486105777129164', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.14551828905361041951591584773', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 42.765404812333806, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 57600, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, -4, 0, 0, 0, -4, 0, 7, 0, 0, 0, 16, 0, 0, 0, 0, 0, 68, 0, 16, 0, 0, 0, -5, 0, 8, 0, 0, 0, -28, 0, 0, 0, 0, 0, 112, 0, -64, 0, 0, 0, -16, 0, 0, 0, 0, 0, -86, 0, 0, 0, 0, 0, 0, 0, -272, 0, 0, 0, -92, 0, -28, 0, 0, 0, -64, 0, 0, 0, 0, 0, -212, 0, 20, 0, 0, 0, 44, 0, -95, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 112, 0, 0, 0, 244, 0, 0, 0], 'euler11': [1, 0, -62, 0, 14641], 'euler13': [1, -16, 402, -2704, 28561], 'euler17': [1, 0, -398, 0, 83521], 'euler19': [1, -68, 1878, -24548, 130321], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 562, 0, 279841], 'euler29': [1, 0, -62, 0, 707281], 'euler3': [1, 4, 9, 0, 0], 'euler31': [1, 28, 2118, 26908, 923521], 'euler37': [1, -112, 5874, -153328, 1874161], 'euler41': [1, 0, -2642, 0, 2825761], 'euler43': [1, 16, 3762, 29584, 3418801], 'euler47': [1, 0, -2798, 0, 4879681], 'euler5': [1, 0, 5, 0, 0], 'euler53': [1, 0, -3998, 0, 7890481], 'euler59': [1, 0, -6782, 0, 12117361], 'euler61': [1, 92, 9558, 342332, 13845841], 'euler67': [1, 64, 10002, 287296, 20151121], 'euler7': [1, 4, 102, 196, 2401], 'euler71': [1, 0, -7202, 0, 25411681], 'euler73': [1, 212, 21894, 1129748, 28398241], 'euler79': [1, -44, 12966, -274604, 38950081], 'euler83': [1, 0, 802, 0, 47458321], 'euler89': [1, 0, -4322, 0, 62742241], 'euler97': [1, -244, 33702, -2295796, 88529281], 'euler_factors': [[1, 0, 0, 0, 0], [1, 4, 9, 0, 0], [1, 0, 5, 0, 0], [1, 4, 102, 196, 2401], [1, 0, -62, 0, 14641], [1, -16, 402, -2704, 28561], [1, 0, -398, 0, 83521], [1, -68, 1878, -24548, 130321], [1, 0, 562, 0, 279841], [1, 0, -62, 0, 707281], [1, 28, 2118, 26908, 923521], [1, -112, 5874, -153328, 1874161], [1, 0, -2642, 0, 2825761], [1, 16, 3762, 29584, 3418801], [1, 0, -2798, 0, 4879681], [1, 0, -3998, 0, 7890481], [1, 0, -6782, 0, 12117361], [1, 92, 9558, 342332, 13845841], [1, 64, 10002, 287296, 20151121], [1, 0, -7202, 0, 25411681], [1, 212, 21894, 1129748, 28398241], [1, -44, 12966, -274604, 38950081], [1, 0, 802, 0, 47458321], [1, 0, -4322, 0, 62742241], [1, -244, 33702, -2295796, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/240/3/l/a'], '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': '4-240e2-1.1-c2e2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-240e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.557249761882309, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 1596304907814102299, 'z1': {'__RealLiteral__': 0, 'data': '0.72093817613293607114905671851', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '913897711702361378808689237512,1843605374438876913017091710430', 'Lhash_array': ['913897711702361378808689237512', '1843605374438876913017091710430'], 'label': '4-240e2-1.1-c2e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/240/3/l/a'}