-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '987170841665228451958455070281,2879844916835054127047223152603', 'a10': -25, 'a2': 5, 'a3': 0, 'a4': 8, 'a5': -5, 'a6': 0, 'a7': 30, 'a8': -5, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 571.007993663993, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, 5, 25]]], 'bad_primes': [3, 5], 'central_character': '405.1', 'coefficient_field': '1.1.1.1', 'conductor': 164025, 'conductor_radical': 15, 'degree': 4, 'euler_factors': [[1, -5, 17, -40, 64], [1], [1, 5, 25], [1, -30, 557, -10290, 117649], [1, -50, 1169, -66550, 1771561], [1, -20, -1797, -43940, 4826809], [1, -20, 9926, -98260, 24137569], [1, 88, 15654, 603592, 47045881], [1, -120, 2233, -1460040, 148035889], [1, 50, -21889, 1219450, 594823321], [1, 108, -18127, 3217428, 887503681], [1, 80, 102906, 4052240, 2565726409], [1, -400, 91079, -27568400, 4750104241], [1, 280, -1107, 22261960, 6321363049], [1, 280, -25423, 29070440, 10779215329], [1, -1220, 669854, -181629940, 22164361129], [1, -50, -202879, -10268950, 42180533641], [1, -518, 41343, -117576158, 51520374361], [1, -180, -268363, -54137340, 90458382169], [1, 1400, 1205822, 501075400, 128100283921], [1, 820, 946134, 318993940, 151334226289], [1, -516, -226783, -254408124, 243087455521], [1, -660, -136187, -377379420, 326940373369], [1, -3000, 3659938, -2114907000, 496981290961], [1, -1630, 1744227, -1487656990, 832972004929], [1, 450, -827801, 463635450, 1061520150601], [1, 770, -499827, 841399790, 1194052296529], [1, 1320, 2885686, 1617056760, 1500730351849], [1, -3508, 5666574, -4542961732, 1677100110841], [1, 310, -1346797, 447298070, 2081951752609]], 'euler_factors_factorization': [[[[1, -5, 17, -40, 64], 1]], [1], [[[1, 5, 25], 1]], [[[1, -30, 557, -10290, 117649], 1]], [[[1, -50, 1169, -66550, 1771561], 1]], [[[1, -20, -1797, -43940, 4826809], 1]], [[[1, -10, 4913], 2]], [[[1, 44, 6859], 2]], [[[1, -120, 2233, -1460040, 148035889], 1]], [[[1, 50, -21889, 1219450, 594823321], 1]], [[[1, 108, -18127, 3217428, 887503681], 1]], [[[1, 40, 50653], 2]], [[[1, -400, 91079, -27568400, 4750104241], 1]], [[[1, 280, -1107, 22261960, 6321363049], 1]], [[[1, 280, -25423, 29070440, 10779215329], 1]], [[[1, -610, 148877], 2]], [[[1, -50, -202879, -10268950, 42180533641], 1]], [[[1, -518, 41343, -117576158, 51520374361], 1]], [[[1, -180, -268363, -54137340, 90458382169], 1]], [[[1, 700, 357911], 2]], [[[1, 410, 389017], 2]], [[[1, -516, -226783, -254408124, 243087455521], 1]], [[[1, -660, -136187, -377379420, 326940373369], 1]], [[[1, -1500, 704969], 2]], [[[1, -1630, 1744227, -1487656990, 832972004929], 1]], [[[1, 450, -827801, 463635450, 1061520150601], 1]], [[[1, 770, -499827, 841399790, 1194052296529], 1]], [[[1, 660, 1225043], 2]], [[[1, -1754, 1295029], 2]], [[[1, 310, -1346797, 447298070, 2081951752609], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 11, 'label': '4-405e2-1.1-c3e2-0-11', 'leading_term': '8.3904985164556839696709659381432654296609865976095402444255406458025916895709111827594645', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/405/4/e/n', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03515625', 'prec': 34}, 'plot_values': [8.390498516455684, 8.366909373985578, 8.292892571293399, 8.171586682480903, 8.003505188271001, 7.78943933534771, 7.531275659193076, 7.231223864894404, 6.891691176046735, 6.51546482178661, 6.105694967083522, 5.6658397141362915, 5.199648206527766, 4.711148547524275, 4.204612771620335, 3.6845352159151874, 3.155585733715695, 2.622588915370716, 2.0904631229633197, 1.5641944260607312, 1.0487715370704578, 0.5491437454099384, 0.07016489674178893, -0.3834740768917549, -0.8072824081461865, -1.1970621577228997, -1.5489294828558051, -1.8594144378635211, -2.125485285678661, -2.34462401216548, -2.514876436398438, -2.634877342383378, -2.7039339766587736, -2.7219959577706447, -2.68975364238095, -2.60857618054297, -2.4805819381520626, -2.3085823061553508, -2.096085618200764, -1.8472677317553836, -1.5668989542971077, -1.2603333590040031, -0.9333811668415746, -0.5922837476569528, -0.2435729276428931, 0.10600045278490824, 0.4495905657225222, 0.7803787695066, 1.0916783290215832, 1.3770834455362706, 1.6305688426721743, 1.8466305062820303, 2.0203921829457734, 2.1477124814120807, 2.2252916881210334, 2.2507391246630584, 2.2226598347441486, 2.140683999046169, 2.0055153334575078, 1.8189201266687092, 1.5837308455363635, 1.3037878989859888, 0.983899127542756, 0.6297338118450759, 0.24773635405014674, -0.15501484489831793, -0.5709434717542611, -0.9921319052128171, -1.4105023711481592, -1.8179754278058649, -2.206673986630377, -2.5690798325055377, -2.8982283881427517, -3.1878569515183433, -3.4325679921456107, -3.627943960749993, -3.770680715711308, -3.858627244779608, -3.890902964849032, -3.867830355500978, -3.791037416657357, -3.663283549686033, -3.4885249964697094, -3.271670101909363, -3.018572701015881, -2.735765203816671, -2.4303659888285982, -2.109819133006017, -1.7817378443598557, -1.4536591277083104, -1.1328659544517228, -0.8261635339367137, -0.5397163843763321, -0.2788700484273068, -0.04801754441303565, 0.14949851117150903, 0.31148498771816807, 0.4368952068937254, 0.5258776509847092, 0.5796852062473399, 0.6006432067678544, 0.5920087187501004, 0.5578395994296323, 0.5028356838476903, 0.4321248613289372, 0.35109935220617383, 0.26516588322974743, 0.1795803383363329, 0.09921606758783859, 0.028411835001467482, -0.029207297990135953, -0.07083595344537984, -0.09460166157228674, -0.09959317879927095, -0.08589985397543695, -0.05455342412674566, -0.0074826191221118695, 0.05261462923564493, 0.12240426208246212, 0.19808640875055963, 0.2755969090459819, 0.3507945876233705, 0.4196917822177099, 0.478631620915379, 0.5245052590861096, 0.5548828667166597, 0.5681872604454185, 0.563739554468349, 0.5418681108795559, 0.5038474393308748, 0.4519206702361782, 0.3891434717667465, 0.31929874212454123, 0.24668256631911986, 0.1759127225438558, 0.11169375009831889, 0.05855870795207383, 0.02064023980901482, 0.0014128598967853168, 0.0034937969123928535, 0.02845382311375368, 0.07668054891908152, 0.14730350136361456, 0.2381553428020616, 0.3458345377355076, 0.46577999061765063, 0.5924818401786414, 0.719649343402157, 0.8405664725662823, 0.9483047726926923, 1.036190897506575, 1.0980099041285443, 1.1285165105676926, 1.123578248851813, 1.0806434704273595, 0.9987763130760794, 0.8790018099649751, 0.7241902460393518, 0.539221803221651, 0.3307020217942203, 0.10691069394740846, -0.12262840028522907, -0.34742225739712906, -0.5565251227252067, -0.7389985880644887, -0.8844440319109218, -0.9835506166894401, -1.0285801457175598, -1.0138676025865059, -0.9361937543299436, -0.7951143859580873, -0.5931403340530943, -0.3358236047086458, -0.03166778498089498, 0.30805486608158084, 0.669682240365568, 1.0376215785634928, 1.394947047281524, 1.7241250260830052, 2.0076859093743895, 2.229160464364715, 2.3736656182070845, 2.4289181561400617, 2.38561227462691, 2.238318019170516, 1.9855707048022893, 1.6304645580251083, 1.1804088266431778, 0.647281745807117, 0.046857764357689444, -0.6015451448364924, -1.2758823289351464, -1.9522445909674955, -2.605753606224433, -3.211856057578845, -3.747101063611077, -4.19068324532455, -4.524934195635584, -4.736848759261217, -4.8181656200242875, -4.766610228462731, -4.585467077019158, -4.284361261734375, -3.8782528666103397, -3.387702012782908, -2.8373011914139967, -2.2554507904200625, -1.672394516522784, -1.1195799549178047, -0.6275916524708806, -0.22523701638372487, 0.06228984687414679, 0.21436825695533754, 0.21628001818696244, 0.059927344558618485, -0.2555228445358593, -0.7234221354327729, -1.3297549637119555, -2.0535810168015756, -2.8678459015201483, -3.7405367222415884, -4.635945880743846, -5.516508084832557, -6.3441237685071155, -7.082530377533378, -7.698270738070742, -8.163279716198705, -8.455219043490192, -8.559796968562594, -8.47037216325266, -8.189543905903182, -7.728011140129259, -7.105193106134627, -6.347360452033041, -5.4873412512747475, -4.562010992609551, -3.611351137629576, -2.675567624569319, -1.7938197199041388, -1.0014427471005516, -0.3286564800996335, 0.2015783303551628, 0.5745412583886863, 0.7848680637243881, 0.8368877982150249, 0.7445489892378175, 0.5308794009253868, 0.22678572096885988, -0.1303943542556953, -0.4989491624755196, -0.8349771559720156, -1.09482039327471, -1.2376854359099843, -1.2278264065769284, -1.0372120374165996, -0.6468674898800106, -0.049108121354595025, 0.7523362642911977, 1.7410009583710473, 2.888902828487821, 4.156407260936361, 5.4947411662782795, 6.846950636878844, 8.15152350440966, 9.344040501589328, 10.361465051235228, 11.144036683447139, 11.639447851192015, 11.804639237670296, 11.608956933335302, 11.035505938525803, 10.082686313018034, 8.764622402979347, 7.110992356111843, 5.166087140951247, 2.9871809944728622, 0.642214349849088, -1.7930499448631474, -4.238104329395731, -6.611532365379416, -8.83395779747951, -10.832339452242586, -12.542236241692091, -13.911443969703448, -14.90164438310793, -15.490054173776498, -15.670710184423791, -15.453435141568963, -14.864645010916265, -13.943976822282306, -12.744151672545188, -11.326389853403295, -9.758968006410162, -8.112608985084645, -6.458041867162084, -4.862072365403198, -3.3850125753717086, -2.077804142400643, -0.9801816409134163, -0.11913809970194647, 0.49169835836975534, 0.8520767608919751, 0.9744184663768339, 0.8824769393699549, 0.6093798599513299, 0.19549018092574003, -0.31449580726495646, -0.8738769451924531, -1.4370733855314666, -1.9617976710912022, -2.4114424659119775, -2.756915232724027, -2.977577753289695, -3.0624706214542785, -3.009748982223432, -2.826858368832217, -2.529001451495019, -2.1380307111952352, -1.6805467789485098, -1.185865268237142, -0.6840874712882249, -0.203935109442095, 0.22897879425845263, 0.5937234477816516, 0.8752225827720198, 1.0649589027770434, 1.1611533102207063, 1.1687012860001629, 1.098187878461644, 0.9652381637079972, 0.7886868240875241, 0.5894722201957303, 0.38862073196634034, 0.20589768271079156, 0.05821219988321759, -0.041570486225132555, -0.0854695947017417, -0.07099096483526338, -0.0010988073487437381, 0.11595810003143314, 0.26752025772185845, 0.4373315351224843, 0.6070874444501119, 0.7575428198479168, 0.870375966860604, 0.929200393667324, 0.9212752187859451, 0.838079643748699, 0.6764535387727327, 0.4385076333988594, 0.1319456165220091, -0.2307110675079331, -0.6326789911928682, -1.0541509826998468, -1.4735906615429952, -1.8690633696856367, -2.21991303515014, -2.5078303188683377, -2.718411070910005, -2.8417038035307645, -2.873202177585187, -2.813707311101831, -2.6695511408201966, -2.451714678869678, -2.1753578903870063, -1.8583341050058002, -1.5202541327723036, -1.1807805813759948, -0.8585071908244509, -0.5695173510378163, -0.32641213967317784, -0.13748825179030083, -0.006273969117668963, 0.06856168936340579, 0.09293785410258044, 0.07678829881573154, 0.03311670595861068, -0.02307124156164015, -0.07605764436537778, -0.11069452525656961, -0.11363232971167544, -0.07441477639483915, 0.013665760646159167, 0.1530486498986955, 0.3416215456436286, 0.5729400625886448, 0.8366241445043255, 1.1191776165345482, 1.405016310110873, 1.677578061526399, 1.9206754230815024, 2.1196001315828847, 2.2623120011925346, 2.340283462542488, 2.3491195276218484, 2.288874019966621, 2.163999539895573, 1.9829187672687882, 1.7574665048517097, 1.5017542823435561, 1.2313399513255998, 0.9617547850415386, 0.7076154099458498, 0.48135660240301925, 0.29250384405404967, 0.1470347683841158, 0.04707915272293161, -0.008982053733657099, -0.02619412554091776, -0.01234451819984762, 0.022940923232804646, 0.06917043702200189, 0.116172865662209, 0.15499876875686094, 0.17896982734248487, 0.18415664562621636, 0.1699221487917968, 0.1387480503129525, 0.09606693191739946, 0.049444197608507406, 0.0077254885053854964, -0.020182063426170484, -0.026541777730924063, -0.006039288092898284, 0.043140869266827045, 0.11839514612778088, 0.21236496490878062, 0.3126118938179141, 0.40243306444574684, 0.46120305294923836, 0.4664268345809417, 0.3945515242071033, 0.2239804446796057, -0.06408974776378824, -0.4822963044111329, -1.0367904126728378, -1.7243167936073223, -2.5328530720075295, -3.4399363374423824, -4.414452372100039, -5.416723125538516, -6.401282762896853, -7.318811072658042, -8.119296711307934, -8.755507902937081, -9.185565325465788, -9.377282588156072, -9.309095049660181, -8.974510345413611, -8.380534676257556, -7.5507079190252835, -6.522102346406739, -5.347010425552313, -4.0840411429743995, -2.799777995159963, -1.5696008006299431], 'positive_zeros': ['0.77874048376382023360994366937623', '1.57133919639441978373780902946436', '2.27179706799063025876196204963618', '3.31269490309500802344880968338125', '3.84825058831471065364550313731731', '4.08291056000224760857308616580866', '4.85905304328510838075582007155150', '4.87282790617151212743784038035292', '5.64138901843282852954837576541510', '6.08544944814517231495242485933372', '6.64714773366738634578107916292660', '7.40885321315159823090041990850181', '7.53169589096493035022991262687587', '8.458067917910048444916136473812245', '8.706262883731577315153167417337106', '9.002437250714761817255421035696900', '9.712475931479315333238813080642855', '10.51756728298634723215758291633404', '10.73674653544040004898615749891540', '11.88321690357005489384247346627352'], 'prelabel': '4-405e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.88833034402596, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 1136015098943950771, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77874048376382023360994366938', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.57133919639441978373780902946', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.27179706799063025876196204964', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 571.007993663993, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 164025, 'conductor_radical': 15, 'degree': 4, 'dirichlet_coefficients': [1, 5, 0, 8, -5, 0, 30, -5, 0, -25, 50, 0, 20, 150, 0, -25, 20, 0, -88, -40, 0, 250, 120, 0, 0, 100, 0, 240, -50, 0, -108, -40, 0, 100, -150, 0, -80, -440, 0, 25, 400, 0, -280, 400, 0, 600, -280, 0, 343, 0, 0, 160, 1220, 0, -250, -150, 0, -250, 50, 0, 518, -540, 0, -487, -100, 0, 180, 160, 0, -750, -1400, 0, -820, -400, 0, -704, 1500, 0, 516, 125, 0, 2000, 660, 0, -100, -1400, 0, -250, 3000, 0, 600, 960, 0, -1400, 440, 0, 1630, 1715, 0, 0], 'euler11': [1, -50, 1169, -66550, 1771561], 'euler13': [1, -20, -1797, -43940, 4826809], 'euler17': [1, -20, 9926, -98260, 24137569], 'euler19': [1, 88, 15654, 603592, 47045881], 'euler2': [1, -5, 17, -40, 64], 'euler23': [1, -120, 2233, -1460040, 148035889], 'euler29': [1, 50, -21889, 1219450, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 108, -18127, 3217428, 887503681], 'euler37': [1, 80, 102906, 4052240, 2565726409], 'euler41': [1, -400, 91079, -27568400, 4750104241], 'euler43': [1, 280, -1107, 22261960, 6321363049], 'euler47': [1, 280, -25423, 29070440, 10779215329], 'euler5': [1, 5, 25, 0, 0], 'euler53': [1, -1220, 669854, -181629940, 22164361129], 'euler59': [1, -50, -202879, -10268950, 42180533641], 'euler61': [1, -518, 41343, -117576158, 51520374361], 'euler67': [1, -180, -268363, -54137340, 90458382169], 'euler7': [1, -30, 557, -10290, 117649], 'euler71': [1, 1400, 1205822, 501075400, 128100283921], 'euler73': [1, 820, 946134, 318993940, 151334226289], 'euler79': [1, -516, -226783, -254408124, 243087455521], 'euler83': [1, -660, -136187, -377379420, 326940373369], 'euler89': [1, -3000, 3659938, -2114907000, 496981290961], 'euler97': [1, -1630, 1744227, -1487656990, 832972004929], 'euler_factors': [[1, -5, 17, -40, 64], [1, 0, 0, 0, 0], [1, 5, 25, 0, 0], [1, -30, 557, -10290, 117649], [1, -50, 1169, -66550, 1771561], [1, -20, -1797, -43940, 4826809], [1, -20, 9926, -98260, 24137569], [1, 88, 15654, 603592, 47045881], [1, -120, 2233, -1460040, 148035889], [1, 50, -21889, 1219450, 594823321], [1, 108, -18127, 3217428, 887503681], [1, 80, 102906, 4052240, 2565726409], [1, -400, 91079, -27568400, 4750104241], [1, 280, -1107, 22261960, 6321363049], [1, 280, -25423, 29070440, 10779215329], [1, -1220, 669854, -181629940, 22164361129], [1, -50, -202879, -10268950, 42180533641], [1, -518, 41343, -117576158, 51520374361], [1, -180, -268363, -54137340, 90458382169], [1, 1400, 1205822, 501075400, 128100283921], [1, 820, 946134, 318993940, 151334226289], [1, -516, -226783, -254408124, 243087455521], [1, -660, -136187, -377379420, 326940373369], [1, -3000, 3659938, -2114907000, 496981290961], [1, -1630, 1744227, -1487656990, 832972004929]], 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/e/n'], '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': '4-405e2-1.1-c3e2-0-11', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-405e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.88833034402596, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1136015098943950771, 'z1': {'__RealLiteral__': 0, 'data': '0.77874048376382023360994366938', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '987170841665228451958455070281,2879844916835054127047223152603', 'Lhash_array': ['987170841665228451958455070281', '2879844916835054127047223152603'], 'label': '4-405e2-1.1-c3e2-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/e/n'}