-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '91684427970109063453369642187,1435076622814952535721449317324', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5012.964553428746, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 9]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '1200.1', 'coefficient_field': '1.1.1.1', 'conductor': 1440000, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, 0, 9], [1], [1, 0, -286, 0, 117649], [1, 32, 2918, 42592, 1771561], [1, 0, -1030, 0, 4826809], [1, 0, -8382, 0, 24137569], [1, -8, 13734, -54872, 47045881], [1, 0, -17934, 0, 148035889], [1, 164, 55502, 3999796, 594823321], [1, -16, 59646, -476656, 887503681], [1, 0, 80170, 0, 2565726409], [1, 492, 198358, 33909132, 4750104241], [1, 0, 115562, 0, 6321363049], [1, 0, 7650, 0, 10779215329], [1, 0, 195050, 0, 22164361129], [1, 1184, 761222, 243168736, 42180533641], [1, -1148, 783438, -260574188, 51520374361], [1, 0, -571942, 0, 90458382169], [1, 1536, 1305646, 549751296, 128100283921], [1, 0, -466670, 0, 151334226289], [1, -816, 1152542, -402319824, 243087455521], [1, 0, -1116678, 0, 326940373369], [1, -1020, 1670038, -719068380, 496981290961], [1, 0, -1561150, 0, 832972004929], [1, -1332, 2504158, -1372360932, 1061520150601], [1, 0, -975454, 0, 1194052296529], [1, 0, -981142, 0, 1500730351849], [1, 4156, 6908142, 5382140524, 1677100110841], [1, 0, -760030, 0, 2081951752609]], 'euler_factors_factorization': [[1], [[[1, 0, 9], 1]], [1], [[[1, 0, -286, 0, 117649], 1]], [[[1, 16, 1331], 2]], [[[1, 0, -1030, 0, 4826809], 1]], [[[1, 0, -8382, 0, 24137569], 1]], [[[1, -4, 6859], 2]], [[[1, 0, -17934, 0, 148035889], 1]], [[[1, 82, 24389], 2]], [[[1, -8, 29791], 2]], [[[1, 0, 80170, 0, 2565726409], 1]], [[[1, 246, 68921], 2]], [[[1, 0, 115562, 0, 6321363049], 1]], [[[1, 0, 7650, 0, 10779215329], 1]], [[[1, 0, 195050, 0, 22164361129], 1]], [[[1, 592, 205379], 2]], [[[1, -574, 226981], 2]], [[[1, 0, -571942, 0, 90458382169], 1]], [[[1, 768, 357911], 2]], [[[1, 0, -466670, 0, 151334226289], 1]], [[[1, -408, 493039], 2]], [[[1, 0, -1116678, 0, 326940373369], 1]], [[[1, -510, 704969], 2]], [[[1, 0, -1561150, 0, 832972004929], 1]], [[[1, -666, 1030301], 2]], [[[1, 0, -975454, 0, 1194052296529], 1]], [[[1, 0, -981142, 0, 1500730351849], 1]], [[[1, 2078, 1295029], 2]], [[[1, 0, -760030, 0, 2081951752609], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 0, 'label': '4-1200e2-1.1-c3e2-0-0', 'leading_term': '0.086996781297609430109583911816131292011308919591124719244591787650704546774937644189042931', '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/1200/4/f/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [0.08699678129760942, 0.07037967828294618, 0.021922798995199715, -0.058305562758856185, -0.16867648879648772, -0.3069810842299713, -0.47074125653488175, -0.6569422770308456, -0.8620720797324944, -1.0822556535065255, -1.3133027346512325, -1.5507434005654135, -1.7899233059116926, -2.0260727212360536, -2.254395297682561, -2.470135233345481, -2.6686804813490723, -2.845628589969135, -2.9968915448568954, -3.1187514752147782, -3.207968535687742, -3.26181637571509, -3.2781903255366918, -3.2556127664173675, -3.193339384893374, -3.0913262978036546, -2.950329913443349, -2.771831502092963, -2.55812400797504, -2.3121947549680537, -2.037790588232655, -1.7392646796383866, -1.4216109996335446, -1.0902852135420695, -0.7512020274196046, -0.4105414176380639, -0.07470852228876103, 0.24986493107845367, 0.5567909670553469, 0.8399205717876526, 1.0934307198342879, 1.3120086242849625, 1.4909384705109123, 1.6262659820073837, 1.7148681501584415, 1.7545868781499174, 1.7442686725793088, 1.6838536190445759, 1.5743773839430395, 1.418001944771552, 1.2179762015974942, 0.9786008078744444, 0.7051442016089609, 0.40374492553503405, 0.0812787211741469, -0.2547854294715167, -0.5965716986900849, -0.9359606411880202, -1.2648302898533046, -1.575206694271112, -1.8595521266575037, -2.1108746498850617, -2.323041209518972, -2.4908304833040487, -2.6102316812872743, -2.6784403844819615, -2.694094657018349, -2.657223168192317, -2.5693738067102663, -2.4335259399416733, -2.2540818853148137, -2.0367523545718047, -1.7884044456900803, -1.5169238489276768, -1.2309392636510985, -0.9396604510081306, -0.6525219539425086, -0.37899612905614405, -0.12821260847741903, 0.09124686010116852, 0.2716975500899132, 0.40655292669442505, 0.4905991517650844, 0.5201576219590651, 0.4932550244236167, 0.4097117266994152, 0.27118771827058186, 0.08117309357100326, -0.15510243368241616, -0.4307800132212379, -0.7376034516487715, -1.0661107901022895, -1.406000850160054, -1.7463686699005625, -2.076182057763311, -2.3845170875934323, -2.661097261573579, -2.8964886336740374, -3.082634690015603, -3.2129790146061397, -3.282920738812928, -3.289841467596174, -3.233413848246122, -3.1155165509034375, -2.9403520085474195, -2.714239275012061, -2.4455312227908896, -2.144283108699505, -1.8219953391952874, -1.4911703761033248, -1.1649330909203215, -0.856513564262486, -0.5788080766054108, -0.34385090163721904, -0.16238198940597323, -0.04338448621240028, 0.006275010344220404, -0.017828603066330617, -0.11745536407216343, -0.29156089002615987, -0.5362661394573321, -0.8449151157702249, -1.208280065280232, -1.6147890365312305, -2.050980435074928, -2.5018437344115756, -2.9514964177695044, -3.3835660040491065, -3.782018174332866, -4.1315049801433155, -4.418238969534947, -4.630236288924645, -4.758118995480839, -4.795189629188343, -4.738057263351907, -4.5864921021749865, -4.343806743891021, -4.016458739099936, -3.6141657864099694, -3.149256778713708, -2.636541663968642, -2.0924608381208807, -1.5347577680209021, -0.981528648060727, -0.4507647253994803, 0.040560949827207156, 0.47699937435746986, 0.8453600573521634, 1.1351711249032088, 1.3391217796586647, 1.453378571090621, 1.4776770840692721, 1.4154075729160023, 1.2733613069230878, 1.0615335165130968, 0.7925848836792257, 0.48136841606604125, 0.14420218914411456, -0.20180566834695124, -0.5395582963298583, -0.8527186898075799, -1.1264634418930992, -1.348153999938645, -1.5079229760721826, -1.5991336307204773, -1.618691262337805, -1.5672063149575188, -1.4489523516480913, -1.2717136505839308, -1.0463649127199728, -0.7864411275468498, -0.5073938679221128, -0.22595734616676397, 0.04078228469222109, 0.27612623170320394, 0.4646920947739821, 0.5931404333271221, 0.6509096162207774, 0.6307975716487115, 0.5293568401882406, 0.3471990967219158, 0.08898733516563523, -0.23664306149737047, -0.617468145643823, -1.0381802183515618, -1.481052503417365, -1.9268153978999814, -2.355471198707837, -2.7473873729408083, -3.084118336051341, -3.349495000503599, -3.53031134764951, -3.617181368496573, -3.6049575796857316, -3.4931808091946923, -3.2861198011949093, -2.9927387891916375, -2.6262917571894246, -2.20384322502128, -1.7454284926930936, -1.2732452815922979, -0.8105003491151259, -0.38042857290338905, -0.005045261946397861, 0.29583549833583633, 0.5056804258585575, 0.6120433674972696, 0.6072471741964138, 0.4888456659865547, 0.2597781587218056, -0.07165278020229403, -0.4921508389513947, -0.9840053098726562, -1.5258630452127118, -2.093824948495079, -2.662432716709684, -3.206104434012736, -3.7001376153999304, -4.12219307103566, -4.453138137001978, -4.678247984635973, -4.787748492640224, -4.777457869579535, -4.648928239799373, -4.4093855722771895, -4.071415606094935, -3.65223568059019, -3.172933783396194, -2.657264973709094, -2.13054186856209, -1.618236570923068, -1.1447301056165526, -0.7320059116162541, -0.39853849590414525, -0.1583247814169171, -0.020179680525767386, 0.01270918538032083, -0.05708647106024374, -0.22142370195049083, -0.4670348989068484, -0.776365832507004, -1.1284458750175168, -1.5002778388972395, -1.8678695396322245, -2.20795106193646, -2.4988810666869954, -2.7223662310766237, -2.864002475889611, -2.914643766299599, -2.8704251646456282, -2.7334985836625925, -2.511485885184762, -2.217454007953712, -1.8688485092604246, -1.48677368140215, -1.0945545191671369, -0.7165586811124983, -0.37662159571468345, -0.0967457281166401, 0.1043165331167696, 0.21214378820855934, 0.21760882991059946, 0.1174602329750941, -0.08537587037110189, -0.381894720693792, -0.7574103327000101, -1.19239823603177, -1.663430707570824, -2.144693994924324, -2.6091408450529485, -3.030472087886978, -3.3841248497733667, -3.64937861709712, -3.8098550635310704, -3.8553311667832633, -3.7815662693211705, -3.591439469718665, -3.2940746587392096, -2.905080382831442, -2.4450792910125627, -1.9390682479540542, -1.4145644550425076, -0.9003426849957967, -0.42448579343417114, -0.012915481756334017, 0.31232209190056776, 0.5342840114645662, 0.6422828027571238, 0.6325178067249325, 0.508415377834175, 0.2804739328340656, -0.03428475100954218, -0.41327687839531496, -0.8296292495261803, -1.2538239854784141, -1.6552993058283083, -2.00453965203989, -2.2744807013367616, -2.4427158045868302, -2.4922154304959374, -2.4132601215248584, -2.203182402261091, -1.8676298675075822, -1.4193329006375774, -0.8783925240693294, -0.270344225158515, 0.37460230940830047, 1.0237971333379727, 1.643721162846156, 2.2020992188409863, 2.669780459112695, 3.022385810106575, 3.2418757358061634, 3.3175111656209193, 3.24655303845251, 3.0344615055429576, 2.694401693090449, 2.246758644083435, 1.7174378628867863, 1.136925380786142, 0.5376655137163677, -0.04696873458777391, -0.585746336905238, -1.0502569604739629, -1.4178901692984607, -1.6717611195481887, -1.8031064852071406, -1.8102237825627854, -1.6999316015132457, -1.4855500844753795, -1.1872792855498253, -0.8295212824808716, -0.4402730117415565, -0.04828601084048584, 0.3181949470029926, 0.6338809637108562, 0.8778576358212004, 1.0351748103129088, 1.0978936863189983, 1.0655384907709944, 0.9453678135278428, 0.7516561667990254, 0.5050283146519308, 0.23079690601598063, -0.04252100604886072, -0.285359646204068, -0.4690583944175194, -0.5679183104317748, -0.5611632980406676, -0.4342975452153598, -0.18061565454396827, 0.1985745573379284, 0.6932526852503705, 1.2857212292000821, 1.9509065254791766, 2.6584091264484933, 3.373772806135724, 4.061006249319839, 4.684545312069223, 5.211571187757193, 5.614179078020469, 5.870894170438648, 5.9684503019722, 5.902142638861812, 5.676689676624387, 5.305348731303871, 4.809616574666036, 4.217276485909202, 3.5610958039557774, 2.876155291230862, 2.198064666127882, 1.5600495244765569, 0.991386939380835, 0.5147883962855592, 0.1456885104320357, -0.10955540486223007, -0.2531766325015132, -0.2965925258017102, -0.2587614361179997, -0.16544861282362067, -0.04678992221582215, 0.0645033526278435, 0.13584592230438358, 0.13701998053425724, 0.042569516671021254, -0.16626628680653355, -0.4999974440586119, -0.9598762594422324, -1.5375948199530545, -2.215464900586982, -2.9675781002503054, -3.760999811414863, -4.55830098434286, -5.319261649990411, -6.004319379988034, -6.576159544891022, -7.003313461644932, -7.261095212439045, -7.334474595110449, -7.218021365187701, -6.917353688160841, -6.447995149176662, -5.835115247828499, -5.111446364506957, -4.3155440716283575, -3.489127440995132, -2.6745101031040375, -1.9118961010909257, -1.23682353770355, -0.6780306779189383, -0.25567128523317134, 0.019703413141054196, 0.14767291100242452, 0.13757944043312575, 0.0076530787216903175, -0.21658870071589764, -0.5044371550367001, -0.8222582936883944, -1.1363493113775818, -1.4150698242128823, -1.631801505425737, -1.76619083090739, -1.8064851830925392, -1.7494411519040367, -1.601423310310062, -1.376959519099752, -1.0983245510942832, -0.7930978474843281, -0.49243317908705864, -0.2282106429867984, -0.030637557546148067, 0.07433610941602316, 0.06720439022873313, -0.06336963934364047, -0.3193986442777468, -0.6930964166805336, -1.1672432865076312, -1.716037160946914, -2.307007799306087, -2.90288260479302, -3.464655865326983, -3.953795054835887, -4.335799648533488, -4.581877970690089, -4.6722377613503, -4.596449126517966, -4.355785375465855, -3.9618586978526995, -3.4375546807760617, -2.8140646811212244, -2.130302587068747, -1.4289658467703452, -0.7547356698046375, -0.1502907155212838, 0.34602350695064554, 0.70331560223135, 0.9001123865921841, 0.9259604423857628, 0.7822242771580862, 0.4818914905267336, 0.048815124687689525, -0.48415612704049615, -1.077310680496207, -1.6871383727354485, -2.2691533839587157, -2.78139539378769, -3.1870223183568203, -3.457339910111203, -3.5733618377182674, -3.5275099134397614, -3.3237051256811214, -2.9772112327861793, -2.51327865825526, -1.9651772963743606, -1.3716952942825704, -0.7740120851064276, -0.21298121360140063, 0.27435683430760976, 0.6577458987045954, 0.9154671901823954], 'positive_zeros': ['0.07232626084317088969834298938276', '1.13207584373531598017376621626743', '1.69514718777245378304922472095923', '2.45513548357055589123168139409733', '2.73015135607053421510211272934149', '3.61656439470327130558174019376062', '3.64455583785418963353136530214535', '4.52854576293546265263863441657304', '4.91928112569723091465625334720218', '5.40127581696242711437081352273480', '5.66541438332756006412181027523662', '6.34421325173085146227280498293054', '6.55644521572146388225158567391093', '7.35270528791872588849527886742627', '7.38574212423257680935513288630126', '8.075888973887839536725615142313828', '8.207360814132493406067201718296703', '8.876090310148763839061158426436170', '9.090669181978706203389298612803743', '10.02866430860871430518041470067754'], 'prelabel': '4-1200e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.414409783632408, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 1376846434420838495, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.07232626084317088969834298938', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.13207584373531598017376621627', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.69514718777245378304922472096', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5012.964553428746, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 1440000, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -9, 0, -32, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -164, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -492, 0, 0, 0, 0, 0, 0, 0, 286, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1184, 0, 1148, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1536, 0, 0, 0, 0, 0, 0, 0, 816, 0, 81, 0, 0, 0, 0, 0, 0, 0, 1020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 288, 0], 'euler11': [1, 32, 2918, 42592, 1771561], 'euler13': [1, 0, -1030, 0, 4826809], 'euler17': [1, 0, -8382, 0, 24137569], 'euler19': [1, -8, 13734, -54872, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -17934, 0, 148035889], 'euler29': [1, 164, 55502, 3999796, 594823321], 'euler3': [1, 0, 9, 0, 0], 'euler31': [1, -16, 59646, -476656, 887503681], 'euler37': [1, 0, 80170, 0, 2565726409], 'euler41': [1, 492, 198358, 33909132, 4750104241], 'euler43': [1, 0, 115562, 0, 6321363049], 'euler47': [1, 0, 7650, 0, 10779215329], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 195050, 0, 22164361129], 'euler59': [1, 1184, 761222, 243168736, 42180533641], 'euler61': [1, -1148, 783438, -260574188, 51520374361], 'euler67': [1, 0, -571942, 0, 90458382169], 'euler7': [1, 0, -286, 0, 117649], 'euler71': [1, 1536, 1305646, 549751296, 128100283921], 'euler73': [1, 0, -466670, 0, 151334226289], 'euler79': [1, -816, 1152542, -402319824, 243087455521], 'euler83': [1, 0, -1116678, 0, 326940373369], 'euler89': [1, -1020, 1670038, -719068380, 496981290961], 'euler97': [1, 0, -1561150, 0, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 9, 0, 0], [1, 0, 0, 0, 0], [1, 0, -286, 0, 117649], [1, 32, 2918, 42592, 1771561], [1, 0, -1030, 0, 4826809], [1, 0, -8382, 0, 24137569], [1, -8, 13734, -54872, 47045881], [1, 0, -17934, 0, 148035889], [1, 164, 55502, 3999796, 594823321], [1, -16, 59646, -476656, 887503681], [1, 0, 80170, 0, 2565726409], [1, 492, 198358, 33909132, 4750104241], [1, 0, 115562, 0, 6321363049], [1, 0, 7650, 0, 10779215329], [1, 0, 195050, 0, 22164361129], [1, 1184, 761222, 243168736, 42180533641], [1, -1148, 783438, -260574188, 51520374361], [1, 0, -571942, 0, 90458382169], [1, 1536, 1305646, 549751296, 128100283921], [1, 0, -466670, 0, 151334226289], [1, -816, 1152542, -402319824, 243087455521], [1, 0, -1116678, 0, 326940373369], [1, -1020, 1670038, -719068380, 496981290961], [1, 0, -1561150, 0, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1200/4/f/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': '4-1200e2-1.1-c3e2-0-0', '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': '4-1200e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.414409783632408, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1376846434420838495, 'z1': {'__RealLiteral__': 0, 'data': '0.07232626084317088969834298938', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '91684427970109063453369642187,1435076622814952535721449317324', 'Lhash_array': ['91684427970109063453369642187', '1435076622814952535721449317324'], 'factors': ['2-1200-5.4-c3-0-1', '2-1200-5.4-c3-0-41'], 'label': '4-1200e2-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1200/4/f/h'}