-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '466889053684543129597591753987,1027392263236626941890492442604,1335559464959411049383543285097,1363057497390075335203833136689,1391032603695121495278399290530,2217143448471885462386148662846', 'a10': 0, 'a2': -3, 'a3': 0, 'a4': 3, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 2, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.964496036380636, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 3, 6, 7, 6, 3, 1]], [19, [1]]], 'bad_primes': [2, 19], 'central_character': '2888.1', 'coefficient_field': '1.1.1.1', 'conductor': 580207226143679709184, 'conductor_radical': 38, 'degree': 12, 'euler_factors': [[1, 3, 6, 7, 6, 3, 1], [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, -6, 0, 15, 0, -20, 0, 15, 0, -6, 0, 1], [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, -3, 3, -4, 9, -9, 6, -9, 9, -4, 3, -3, 1], [1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, -6, 0, 15, 0, -20, 0, 15, 0, -6, 0, 1], [1, 0, -6, 0, 15, 0, -20, 0, 15, 0, -6, 0, 1], [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], [1, -3, 3, -4, 9, -9, 6, -9, 9, -4, 3, -3, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], [1, -3, 3, -4, 9, -9, 6, -9, 9, -4, 3, -3, 1], [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, -6, 0, 15, 0, -20, 0, 15, 0, -6, 0, 1], [1, 6, 21, 50, 90, 126, 141, 126, 90, 50, 21, 6, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1]], 'euler_factors_factorization': [[[[1, 1, 1], 3]], [[[1, 0, 0, 1, 0, 0, 1], 2]], [[[1, -1, 1], 3], [[1, 1, 1], 3]], [[[1, -1], 6], [[1, 1], 6]], [[[1, 0, 0, 1, 0, 0, 1], 2]], [[[1, -1, 1], 3], [[1, 1, 1], 3]], [[[1, -1], 6], [[1, 1, 1], 3]], [1], [[[1, -1, 1], 3], [[1, 1, 1], 3]], [[[1, -1, 1], 3], [[1, 1, 1], 3]], [[[1, -1], 6], [[1, 1], 6]], [[[1, -1], 6], [[1, 1], 6]], [[[1, 0, 0, 1, 0, 0, 1], 2]], [[[1, -1], 6], [[1, 1, 1], 3]], [[[1, -1, 1], 3], [[1, 1, 1], 3]], [[[1, -1, 1], 3], [[1, 1, 1], 3]], [[[1, 0, 0, 1, 0, 0, 1], 2]], [[[1, -1, 1], 3], [[1, 1, 1], 3]], [[[1, 0, 0, 1, 0, 0, 1], 2]], [[[1, -1, 1], 3], [[1, 1, 1], 3]], [[[1, 0, 0, 1, 0, 0, 1], 2]], [[[1, -1, 1], 3], [[1, 1, 1], 3]], [[[1, 0, 0, 1, 0, 0, 1], 2]], [[[1, -1], 6], [[1, 1, 1], 3]], [[[1, 0, 0, 1, 0, 0, 1], 2]], [[[1, -1, 1], 3], [[1, 1, 1], 3]], [[[1, -1], 6], [[1, 1], 6]], [[[1, 1, 1], 6]], [[[1, -1, 1], 3], [[1, 1, 1], 3]], [[[1, 0, 0, 1, 0, 0, 1], 2]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 3, 'label': '12-2888e6-1.1-c0e6-0-3', 'leading_term': '0.202232287024250990136980900447992339157628605199220167525924023750896788814577243182046689', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0, 0, 0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2888/1/k/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.009765625', 'prec': 37}, 'plot_values': [0.20223228702425095, 0.20232121342262527, 0.20228947727633642, 0.20215395894942598, 0.20193076178851835, 0.2016349881616588, 0.2012788170042605, 0.2008579533165841, 0.20035105931183206, 0.19973310228867733, 0.19897791555850777, 0.19805832373646057, 0.19694732219443933, 0.19561792276816514, 0.194041827126663, 0.19218945746138183, 0.1900300185352465, 0.18753034230878096, 0.18465466883953685, 0.1813659895844761, 0.17762545639074792, 0.17339369799712848, 0.16863128712900827, 0.16329893097502454, 0.15735818037862734, 0.15077182781169748, 0.14350416911650163, 0.13552166343179006, 0.1267934417441816, 0.1172920960995957, 0.1069943717980361, 0.0958819606243519, 0.08394260646837458, 0.07117057234491238, 0.057567173281444804, 0.043141446671660755, 0.027910852655787213, 0.011902176569103844, -0.004847192214963766, -0.02228952593027178, -0.04036658498988577, -0.05900924386017167, -0.07813721806223502, -0.09765883232023247, -0.1174705194829569, -0.13745784888078286, -0.15749616038074885, -0.17745108745396093, -0.19717961909537188, -0.21653142943064008, -0.2353488965441708, -0.25346931007432466, -0.2707266679940387, -0.28695373339869606, -0.3019852191999621, -0.31565883178018694, -0.3278166098806684, -0.3383080113756014, -0.34699271700891127, -0.35374483358255276, -0.35845442597242255, -0.36102880669475, -0.3613944821002646, -0.3594998832435185, -0.355319318642167, -0.3488541925507413, -0.3401326586121243, -0.3292103882272491, -0.31617113720877815, -0.3011287423290636, -0.2842271799066834, -0.2656374235669001, -0.24555577388293434, -0.22420190156839423, -0.20181754924370832, -0.17866457373417366, -0.1550190537577016, -0.13116692721273512, -0.10739962595600741, -0.0840098999921443, -0.06128803286330908, -0.0395147484355621, -0.018955457399769487, 0.00014485937690833956, 0.017566463998654497, 0.03311901200868951, 0.04664693482009947, 0.05803368209977722, 0.06720470739230619, 0.07412966318186937, 0.07882380780237833, 0.08134880670943964, 0.08181228657358887, 0.08036572469907173, 0.07720121059903219, 0.07254739634054837, 0.06666413916519948, 0.059835426890466725, 0.052361584196981406, 0.04455013352277667, 0.03670617164058417, 0.02912206573373697, 0.022065863761190848, 0.015769920095511657, 0.010419589372104682, 0.006142037255595016, 0.0029956708627266538, 0.00096001376001061, -7.295199380225091e-05, -0.00030592607578812527, -4.1738644798887704e-05, 0.00031317619512801967, 0.00024766588852136303, -0.0008526512106300822, -0.0037012660872890804, -0.009103908035870384, -0.017948529084019588, -0.031192282826075945, -0.049845888696877394, -0.074955358237987, -0.10758129505453441, -0.14877535391441207, -0.19955451638745508, -0.26087512275954583, -0.33360569223647574, -0.4184993259368593, -0.5161655261133239, -0.6270423072876875, -0.7513730972188872, -0.8891838317982962, -1.0402628126480038, -1.2041438334161865, -1.3800924650955526, -1.5671004502642885, -1.763888323420093, -1.9689066453453978, -2.180344222949973, -2.3961443462395358, -2.614026175563609, -2.831514756114203, -3.0459848778766916, -3.254693476736808, -3.454825277544435, -3.6435404550649126, -3.8180218435257007, -3.975533043992617, -4.113490579635495, -4.229512820405528, -4.321471331944296, -4.387531360063371, -4.426197163042327, -4.436360722125699, -4.417367802313584, -4.369034338583459, -4.291640976047903, -4.185939106890392, -4.053150079763169, -3.8949679628824065, -3.7135755419637437, -3.5115663258380443, -3.2918867247700936, -3.057783346122992, -2.8127447832480947, -2.5604541389827364, -2.3047148514075997, -2.049337049586032, -1.7980486702836296, -1.5544143904153336, -1.3217639305737447, -1.103110656096891, -0.901078303963746, -0.7178218721062785, -0.5549721681643961, -0.41359930704622727, -0.2941835621345504, -0.19659953161420213, -0.1201220176870849, -0.06344126740346055, -0.02470090967882988, -0.0015521405671889937, 0.008776794325757344, 0.009395850090310786, 0.0036576893904474352, -0.004949194457475878, -0.012915863213253383, -0.016832826331375436, -0.013509973384858235, -9.334040398232338e-05, 0.025823350885722664, 0.0660941134679823, 0.12193254741206506, 0.1938417557063631, 0.2815633504623307, 0.3840475805351527, 0.4994449590336397, 0.6251294802317864, 0.757748451844602, 0.8932963590569024, 1.0272132866617911, 1.154509882573702, 1.269916019523417, 1.3680430265371204, 1.4435588237953467, 1.4913711429719754, 1.5068216092691258, 1.4858861821692186, 1.4253460291647517, 1.3229467028649529, 1.1775392568207514, 0.9892030561316065, 0.7593543134127826, 0.49078050507400595, 0.18764268857542296, -0.14456233579331565, -0.49907712456514003, -0.8679847845257256, -1.2423896906970442, -1.612638337622277, -1.9685726090061608, -2.2998060789497807, -2.596019051684177, -2.847289342165253, -3.0444322260368843, -3.17933530220296, -3.245292912339722, -3.2373036103463204, -3.152344137130475, -2.989590055759231, -2.7505900101991325, -2.439386528509162, -2.0625882387581207, -1.629348215718005, -1.1512369193000693, -0.6420608062963579, -0.11760963453401141, 0.4046622829185808, 0.9060216060400984, 1.3669496065939235, 1.7676581845203758, 2.088634278956869, 2.311207092189018, 2.418127077046122, 2.394175000406116, 2.2267038616975956, 1.9061337861741312, 1.426393635932989, 0.78529050201918, -0.015208161219130833, -0.9687938478685982, -2.0647837751957616, -3.288193061691266, -4.619934284178769, -6.037152185663353, -7.513666953403688, -9.020558222073968, -10.526828870522031, -12.000179565389322, -13.40788962334056, -14.717649853403387, -15.898463090265246, -16.921607388629337, -17.761495595618044, -18.396589695361413, -18.81003312961771, -18.990218207692923, -18.931283794935272, -18.633545026879915, -18.103729619981376, -17.354801401282575, -16.405629958340835, -15.280556126554812, -14.008804335453283, -12.62386823364242, -11.162396921736663, -9.66293054701531, -8.164677399490945, -6.70622224200095, -5.3242563096704245, -4.052195516875182, -2.918734233259861, -1.9466274183526395, -1.1516130458239222, -0.5415054541474857, -0.11545234628910142, 0.13658616198177156, 0.23400475609942373, 0.20544125576407385, 0.08838032531193836, -0.07153981508111742, -0.2215713074422022, -0.3031972354106686, -0.25371322835504273, -0.008024321474270414, 0.49931204339019725, 1.331895072441021, 2.5492475495219264, 4.204617004887137, 6.342814193983653, 8.997988112876444, 12.191644306519521, 15.931036873473305, 20.20785836805358, 24.997524446010754, 30.258356791979406, 35.931243265077306, 41.940133657276775, 48.19283703226535, 54.58244908735034, 60.989606046361324, 67.28415585889334, 73.32782898190237, 78.97717430032856, 84.08672134867271, 88.51256136194311, 92.11660843294474, 94.76965425930989, 96.35458405573739, 96.76962295044727, 95.93133647447283, 93.7775439100552, 90.27044097704419, 85.39750877080071, 79.1723878034064, 71.63546322582188, 62.85389139607264, 52.92104076228361, 41.955234575305596, 30.0972405012059, 17.50765798756937, 4.363959424448088, -9.142965580940237, -22.812839559168612, -36.44098860637925, -49.82227911483095, -62.755200710704415, -75.04615000748487, -86.51332393316683, -96.99089959831265, -106.33413209279999, -114.42099931266357, -121.15429282063708, -126.46303929540865, -130.30342542235047, -132.65984691841783, -133.54668758978988, -133.00584475467886, -131.104172686409, -127.93108386955633, -123.5959271236467, -118.22556940044863, -111.96292551819424, -104.961196324067, -97.37918030032671, -89.37754964553937, -81.11525378513637, -72.74664111017998, -64.41895930322461, -56.26787400055998, -48.41476262729867, -40.96488247300693, -34.00611847176365, -27.608264663055596, -21.822627221871194, -16.681777920067308, -12.200239607528065, -8.375729297260728, -5.190749014016573, -2.6143741631584687, -0.6043091724527303, 0.8907436249281675, 1.9286528031739907, 2.5714803879749746, 2.8831831832126134, 2.92747961909692, 2.7659497374489503, 2.4562035898589483, 2.050492477182329, 1.5946686317524816, 1.1274782904225094, 0.680200105313148, 0.2765738556595466, -0.06698705589136429, -0.3408698006804794, -0.5415175283536989, -0.670525176412775, -0.7336447307241247, -0.7397631594453421, -0.6997993756098645, -0.6256653473526715, -0.5293410890911832, -0.4220845597292872, -0.3138064943303135, -0.21262052831600378, -0.12453048029884568, -0.05332962152513751, -0.0006760930125086078, 0.033687460094203724, 0.05159831270614709, 0.056057254748361963, 0.050766467565519564, 0.03965316068767907, 0.026423854960557994, 0.014184015468144358, 0.005153070760787125, 0.0004963121429281705, 0.00028825755496440433, 0.003615831216377723, 0.008816907073119416, 0.013841157747669164, 0.016710838175537257, 0.016054673220057145, 0.011675797544822793, 0.005113916965198231, 0.0001596218492936318, 0.0032791479626463373, 0.023911628174521974, 0.07459453543674716, 0.17089247553474202, 0.3311190124755747, 0.5758419750393878, 0.927172694602827, 1.4078425318397751, 2.040067791232913, 2.8443483146207043, 3.838172210069807, 5.034670540527029, 6.441304203013713, 8.058633585991894, 9.879326114453772, 11.887440392144146, 14.05788758375359, 16.356251394507936, 18.73897760587265, 21.15416562926593, 23.54280663260133, 25.840041790064664, 27.976902109918477, 29.882375309938364, 31.48595394592813, 32.72058370359898, 33.52512080056627, 33.846691719775585, 33.64305364605126, 32.88495034434722, 31.558519133821648, 29.66639261897803, 27.22867466518464, 24.282977362566893, 20.88411353983842, 17.103634151683995, 13.027942553372757, 8.755910951511602, 4.396148623430971, 0.06353443247150807, -4.124205998622708, -8.050475977935095, -11.603962725589597, -14.68260778177533, -17.1976537268694, -19.077043326749813, -20.268334500730187, -20.741035999023065, -20.48819033865326, -19.52731588131223, -17.90087703844604, -15.67505423019333, -12.937655643691523, -9.795426663717725, -6.370639047000069, -2.797186778608363, 0.7836048180273794, 4.228458076124109, 7.397423059941181, 10.158992861447818, 12.395052656845591, 14.005421392614402, 14.911377682179433, 15.059228601334869, 14.422835952053836, 13.00509454232484, 10.838485853068391, 7.984172080004975, 4.529380552713202, 0.5851966701083126, -3.7167797374478773, -8.228791121879427, -12.792012721892533, -17.242406233562722, -21.417762350566967, -25.162429096973334, -28.332512639771274, -30.801180846686286, -32.46303700626396, -33.238386332260745, -33.0776860260613, -31.961957756729372, -29.903221017481567, -26.94386103663688, -23.155130386936662, -18.63518296424582, -13.506807230950267, -7.911662778721022, -2.004739401270923, 4.050979811890058, 10.08995282893386, 15.94936247228692, 21.47438167624323, 26.524258965572656, 30.97680135501907, 34.731876147039, 37.71406410892851, 39.87463280600582, 41.19281006433958, 41.67539252391696, 41.35528100650987, 40.28915867366896, 38.554491296317046, 36.246033221161184, 33.47183836227829, 30.348226515103363, 26.99486796420501, 23.53011315842539, 20.066607582077097, 16.707340510175506, 13.542429936336077, 10.646072696878381, 8.074543030981935, 5.865122243452841, 4.035957080948977, 2.5867594796131828, 1.5002504757495843, 0.7441818472264194, 0.2740133877276706, 0.036079111426314384, -0.029008897952063, 0.01711098650546591, 0.1139570187838772, 0.2053924512298421, 0.2424319632710616, 0.18554153707430157, 0.006361386820089994, -0.3112112617212132, -0.7706650620565879, -1.3632624116569767, -2.0689698010303172, -2.857952020897704, -3.6925484706256504, -4.5296972139118985, -5.323813005932078, -6.029340401922079, -6.6033016417027826, -7.007735906675197, -7.211881450589722, -7.194131429146495, -6.943310683318007, -6.4590826833870745, -5.751996207020605, -4.8430494931246955, -3.7627194179327885, -2.549432243378995, -1.2476742637781406, 0.09432293536776781, 1.426901048954838, 2.7014366950712843, 3.8727127772222203, 4.900876658675674, 5.753367270040191, 6.406231300557076, 6.8450979747590255, 7.065725074853553, 7.07356181968303, 6.883151553844631, 6.5173117377955405, 6.005496029837428, 5.382085375789652, 4.684121755796681, 3.949194556530428, 3.2135153551124387, 2.510207635987891, 1.8675117521662383, 1.3073070523898922, 0.8442207834023898, 0.4852621590657227, 0.22992476787065666, 0.0707166595213871, -0.006009176491464882, -0.01873506210023414, 0.010847196505694542, 0.05961504719563014, 0.10483464416400622, 0.12592574288414105, 0.10607919668281986, 0.033582742376777296, -0.09723783554566354, -0.2855244100655944, -0.5238742514816875, -0.7987992984550215, -1.0917073370017358, -1.3803223414985848, -1.6404607350881215, -1.8480827666611583, -1.9814264369669685, -2.0230958929258493, -1.9620810849578911, -1.7954663718428416, -1.5297209299627987, -1.1813749203976314, -0.7770393676962197, -0.35273298304683326, 0.047426006984492446, 0.37326617527589573, 0.5713061017311053, 0.5880228841595696, 0.3735114976707499, -0.11464693968878724, -0.9074722386482446, -2.0207725073080747, -3.4517952019290554, -5.176456242744957, -7.147403297693048, -9.293100840904986, -11.517730929922239, -13.702479167232724, -15.708027795764592, -17.378275298329335, -18.54519763510149, -19.034444835192932, -18.671786316125743, -17.290276824839612, -14.73781260253173, -10.884629287671634, -5.629302792134528, 1.0946587778748844, 9.313098213011513, 19.006707267225018, 30.10791385853305, 42.50178572925308, 56.02693693071991, 70.47713662775114, 85.60488134303264, 101.12653974707803, 116.73238297985009, 132.09669860064662, 146.88410433219505, 160.76157486632653, 173.40709253933707, 184.52172047881558, 193.8429813306086, 201.14804454994157, 206.26106467649194, 209.06256235095756, 209.49241617030407, 207.55587095495972, 203.31798722822325, 196.89977151678178, 188.47544845400546, 178.27078530613107, 166.55635009942642, 153.6338607202075, 139.82411719087509, 125.45702843777266, 110.86245734508535, 96.36401869658731, 82.26507844010447, 68.83737044228671, 56.314031380006085, 44.88425965342883, 34.69042529419862, 25.82604889440576, 18.333337130581576, 12.204898969901361, 7.3875584034309325, 3.7876622354017724, 1.2774777152149934, -0.29754755411618544, -1.1107347373932508, -1.3455526430018445, -1.1870528477971733, -0.8137422188236565, -0.39013275121654994, -0.06030282375740777, 0.057371404544232237, -0.12595567187176648, -0.6673120025802833, -1.591184397987214, -2.890295548975665, -4.527786452539809, -6.440688011872335, -8.544588161238732, -10.73902494755648, -12.913276828656405, -14.952500082187402, -16.743940691591305, -18.182855177462297, -19.177746980713206, -19.654525202163967, -19.55995387597222, -18.86414321151801, -17.56205196305328, -15.673312671394095, -13.240890744920812, -10.329043180588382, -7.020446354677872, -3.4125328021790025, 0.38711195469655896, 4.265372879268063, 8.108092871489418, 11.80447342803708, 15.251294094226283, 18.357300345312275, 21.04620923786343, 23.258593667170036, 24.953280303963044, 26.10805878185568, 26.720077689935913, 26.80477933663966, 26.39410849398818, 25.53406055595781, 24.28200929781642, 22.70398019481322, 20.871446530654744, 18.8580446370585, 16.736838625687852, 14.577437683891281, 12.443565569371557, 10.390992930940406, 8.466275144600122, 6.70600290229371, 5.136510137577004, 3.7737967689112693, 2.623778514382463, 1.683593898499756, 0.9429751561420455, 0.3856814840536163, -0.009029709091575671, -0.2651034539014936, -0.4078786374926489, -0.4625507165129924, -0.4530081096565171, -0.4009076681554605, -0.3250805700754977, -0.2409548403415854, -0.16025997753344004, -0.09110610304844971, -0.038257502412889804, -0.0035704957135556355, 0.013510019844425247, 0.015381693359045432, 0.005645659659850275, -0.01150147757354725, -0.03180624171995923, -0.05140175279158222, -0.06715748901689061, -0.07690467506515791, -0.07953717332835487, -0.07499727365746248, -0.06416276146416687, -0.04866630677733475, -0.030655540522911334, -0.012520540262329011, 0.003377480729722648, 0.014954991444646015, 0.02060822446864029, 0.019360716906015665, 0.010945458092546328, -0.0041837593497853496, -0.02490876492818178, -0.04956376420808631, -0.07609654608357697, -0.10226120543842661, -0.12582788996437022, -0.1447847813228499, -0.15751798977840067, -0.16295249109105028, -0.16064870012555169, -0.1508466122517911, -0.13445369878229513, -0.11296926624520112, -0.0883626463801896, -0.06291673380450513, -0.03904545762177733, -0.019097721552132234, -0.005163190891352326, 0.0010945639547840517, -0.0014260603313681977, -0.013168432037560823, -0.03386964076499383, -0.06257387796938704, -0.09770389776597999, -0.13716772299676863, -0.17850115707501218, -0.21903932845971255, -0.2561250345185433, -0.28730658617098864, -0.31050971751807055, -0.32417191741492635, -0.327345792244237, -0.3197850411977283, -0.30196559415441715, -0.27502037933616724, -0.24065580567980485, -0.20101247143842793, -0.1585169495635038, -0.1157128443571712, -0.07505097724743431, -0.038715572066732776, -0.008475706175923355, 0.014431310545995446, 0.029374065981927436, 0.03636126946360653, 0.036014179593777146, 0.029490313935720883, 0.018367647349844838, 0.004500616674204453, -0.01015238740134638, -0.023709401886181238, -0.03453340201279823, -0.0413772320643779, -0.04349077941326844, -0.04068730400519499, -0.03335689943537, -0.022421034972730892, -0.009233340764442497, 0.00456815061432803, 0.01724922996893723, 0.02718824471633525, 0.03309301831008785, 0.03420845460994655, 0.030496738021910073, 0.022774315670277417, 0.012789681834584756, 0.0032234970338818505, -0.0023848013782386667, 0.00021298876449064207, 0.015750035245034464, 0.04915645339210075, 0.10522000634118109, 0.18822109762128497, 0.3015613904064382, 0.4474153088929308, 0.6264229679659552, 0.8374476638934006, 1.0774335725700765, 1.3413529986313621, 1.6222910294226929, 1.911638071944026, 2.1993695964162385, 2.4744545562798432, 2.7253928404181442, 2.9407770634116392, 3.109891030607253, 3.223243308278279, 3.2731105950365436, 3.25404915617182, 3.1633919897806657, 3.0014950794722, 2.7717662680427217, 2.480628767463909, 2.137348687832441, 1.7537380881671738, 1.3437188434340774, 0.9226120750025487, 0.5064413486345724, 0.11121790188967087, -0.2477948551177507, -0.5568497664358322, -0.8044026810304908, -0.9816536239321879, -1.08295142543451, -1.1060566600445356, -1.052311993233568, -0.9265582460865187, -0.7368333886423813, -0.4939300638680408, -0.21083965762471385, 0.09786539763892599, 0.41677044762024695, 0.7304411328813165, 1.0241908185679776, 1.2847838536413592, 1.5010510399235286, 1.6644108701396731, 1.769226819881613, 1.81299470801921, 1.7963658528453783, 1.7230095097894582, 1.599352995723629, 1.4341058774869613, 1.2377051010775382, 1.0216931827499722, 0.7980412968495791, 0.578536460925473, 0.3741338885007973, 0.19439459263414335, 0.04703792150785844, -0.062401615232519504, -0.1308037368168039, -0.1574840745641259, -0.14409566553829367, -0.09441704121444126, -0.014036773520475705, 0.0900415419541062, 0.20988764827068418, 0.3371738363041318, 0.4636631237091116, 0.5816609335185521, 0.6844169809490938, 0.7664758312880583, 0.8239465137796483, 0.8545944277235862, 0.8578407805291287, 0.8346839596721762, 0.7875515933051886, 0.7200458804758262, 0.636655193979514, 0.5423848157540742, 0.44241147249493273, 0.34177586747304617, 0.24507731534943314, 0.15622905331164502, 0.07828491929566296, 0.013327043613779607, -0.03756013601506693, -0.07425281194806604, -0.09748658925066221, -0.10870257424023572, -0.10986119301305428, -0.10323727453593524, -0.0912129879893888, -0.07608297666730408, -0.05989097642432488, -0.044306275797131554, -0.03054690995293345, -0.019353025834777802, -0.011005491278247846, -0.005388790199260353, -0.0020873894117821954, -0.0005040014558969043, 1.2815150944578685e-05, 4.518474929212291e-05, 1.647383678710719e-07, 3.181322041904009e-05, -8.775121377453559e-07, -0.0005349367753384075, -0.002262294541221122, -0.006050612164425179, -0.01283216728608435, -0.023469524802886905, -0.03860880327285279, -0.05853679878594234, -0.0830672376976989, -0.11144832825239592, -0.14230712447634555, -0.17364240998037503, -0.202869298590285, -0.2269263655906047, -0.24247052361537724, -0.24605415129942002, -0.23433658694174084, -0.2043189882967157, -0.1535722572512028, -0.08047063676058851, 0.01556529641175479, 0.13398289661451046, 0.27305325915636935, 0.42987821624371375, 0.6004597171753177, 0.7798253058165856, 0.9622130509413115, 1.1414011051088082, 1.311018004442883, 1.4648469417817698, 1.5971351748263025, 1.7028956782182687, 1.7782384428014442, 1.8205675248467668, 1.8286729711773726, 1.8027770904524891, 1.744506430054694, 1.6568356344277666, 1.5439591140067273, 1.4109562044272892, 1.2634840417097137, 1.1074675037704667, 0.9488008770602963, 0.7930655051448864, 0.6452390185050247, 0.5094353905711009, 0.3887458585347838, 0.2851639363545768, 0.199582669015917, 0.13184328266274134, 0.08086153574424333, 0.044801861674041946, 0.02129664733016147, 0.007683933232422094, 0.001241857404735769, -0.0005928489059217671, -4.08365356315996e-05, 0.0011555722084610899, 0.0018103356490313458, 0.0013103745804892344, -0.0004283543988562994, -0.003059192561528082, -0.0059471292904229745, -0.008339858572390318, -0.00955054508443754, -0.009135056655772472, -0.0070448780720988695, -0.0037400505219802563, -0.0002485430828989533, 0.0018363540509215095, 0.00042158887076720224, -0.0069571994920972794, -0.02295131607659075, -0.05017225577694427, -0.09094851549960316, -0.14707569329627374, -0.21957875602229432, -0.3085087183212455, -0.4127940951351526, -0.5301889975727921, -0.6573266989771791, -0.789803639950453, -0.9223494791078395, -1.0490806829867638, -1.1638505591897303, -1.2606387708734554, -1.333994225178201, -1.3793421858998363, -1.3932854737744091, -1.3739064760778292, -1.3209645522072866, -1.2359655316451963, -1.1222104942244862, -0.9845624842362652, -0.8291916352053692, -0.6632509750023493, -0.49442638931761845, -0.3304994364305023, -0.17890357028433676, -0.04622033998908041, 0.06223143326402372, 0.142723637578474, 0.19332277934840691, 0.21397817972426503, 0.2064999618800892, 0.17441370087559865, 0.12266725767821061, 0.05723862268147547, -0.015312550635683424, -0.08832533881034481, -0.15552073381399747, -0.2114714393400606, -0.2519938056580453, -0.27442514287031244, -0.27777863721283236, -0.26276992111165076, -0.2317274566397488, -0.18833671749141895, -0.13727205957715433, -0.08375130328012227, -0.03304343835980108, 0.010028959737353823, 0.0415513424830866, 0.05892500810918495, 0.061158250333683654, 0.04901745440054596, 0.025023172953796618, -0.006719968919220355, -0.04085915970192869, -0.07123770541188569, -0.09144576312207249, -0.09543643334085526, -0.07815985697687751, -0.03616988637827307, 0.03186998248970407, 0.12485324890266115, 0.23906027278873399, 0.3681663979907439, 0.5034379668593203, 0.6341714445492691, 0.7484434253955214, 0.8339001883652495, 0.8786125074727474, 0.8719386986267679, 0.8053994148329988, 0.6735581243459026, 0.47495702332947737, 0.2123507863677387, -0.10727333578497886, -0.47283336262560105, -0.8695536257395939, -1.279561471335509, -1.6826734572954156, -2.0578384219671206, -2.384463950924707, -2.6436822470655565, -2.819576845321009, -2.9003452838893953, -2.8790822865691124, -2.7544697768248914, -2.531011052255254, -2.2188657467587247, -1.833392336151233, -1.3942163450741636, -0.9239894458443609, -0.4469821546335148, 0.012466399122137544, 0.43151245287066997, 0.7903243663762755, 1.0733827093380506, 1.270487650896251, 1.3773618430157326, 1.3958312029297337, 1.3335700068595748, 1.203321172149241, 1.02178126618441, 0.8082351360847034, 0.5828728774798336, 0.3650619478886016, 0.17165740404635613, 0.015575230070106623, -0.09525630823403433, -0.15847849791910965, -0.17741316761792486, -0.16052029009721844, -0.12022127890070272, -0.07116922733785414, -0.028062770786917976, -0.0031434747039594513, -0.0035321859113315378, -0.028612335834221438, -0.06769444217863017, -0.09817714044617235, -0.08440288338383233, 0.02264894258992164, 0.2846807683516884, 0.7743293047519417, 1.5723430483626555, 2.7637543347783975, 4.433293995828756, 6.660457447779646, 9.51389458160854, 13.045658173485128, 17.28578822414422, 22.23779843612417, 27.875026141790265, 34.13946582023207, 40.940210329458516, 48.15372882175556, 55.62714675389005, 63.18184181369589, 70.61929360845318, 77.7313808954134, 84.3064146100559, 90.13851856511637, 95.03613313656187, 98.82898340364643, 101.37724742665414, 102.58314749601753, 102.3937822515833, 100.80313527452644, 97.85067642246509, 93.62016230330534, 88.23820943926904, 81.87448095095446, 74.73052198958543, 67.02725847895752, 58.99552219722633, 50.86669261956892, 42.864674724510245, 35.199490084682246, 28.053967338775003, 21.57629785698688, 15.875955884333706, 11.021654851186826, 7.041609113519921, 3.9251279211702146, 1.6250015926056796, 0.0631509803053083, -0.8621852866116526, -1.2685847461321764, -1.2812950178917244, -1.0252723839606148, -0.6178091363037078, -0.16208209038254345, 0.257824379307436, 0.580207073316701, 0.7671801543703212, 0.8043059262362139, 0.6985009266423711, 0.4744440523570317, 0.16982654464372127, -0.17017016031643703, -0.4986342852318055, -0.7724682945213192, -0.9574260838297022, -1.0321094899386498, -0.9905847004663304, -0.8434481736945313, -0.6172707611531562, -0.35245788651986987, -0.09967416277208996, 0.08490005580330386, 0.14509604250928498, 0.030636986016214354, -0.2970981017224665, -0.8599136012424193, -1.6587085578943037, -2.670785446593199, -3.8488352394221432, -5.1217981614178125, -6.397671762621395, -7.568173044455136, -8.514736958611365, -9.115758475361309, -9.254689589087615, -8.828247273059743, -7.753935995720243, -5.977314485130291, -3.4774449900114215, -0.2708150146217884, 3.5871053026877964, 8.00406010303233, 12.853295521193331, 17.978632917955782, 23.20140100914209, 28.329081610819493, 33.16784345415242, 37.53132637540726, 41.24915285949702, 44.17714893384342, 46.20430859989049, 47.26138476607443, 47.32357494797101, 46.40877589071494, 44.57655221539343, 41.92596168478534, 38.59031885770452, 34.72902904068118, 30.515638442303754, 26.128290609579892, 21.74075431255014, 17.514953643614923, 13.592356291791537, 10.085611324958903, 7.074473825755219, 4.604176279027453, 2.6860851269052457, 1.3002743819896088, 0.3990413380175374, -0.08708187115735445, -0.24215271254325668, -0.15726732899673207, 0.07681802199932536, 0.37643000243351754, 0.6706954581946916, 0.9057129457356188, 1.0469255279515506, 1.0796285672842632, 1.0076766456404815, 0.8505535988540046, 0.6390166956403869, 0.4099438993230617, 0.2008727641612299, 0.04473988920924465, -0.03465172580622702, -0.02598078971849191, 0.06782697161229473, 0.22966288064982107, 0.4301791922095321, 0.6314706128827968, 0.7922309339542486, 0.8740125077031897, 0.8479498075511802, 0.7013275464932082, 0.44321778553866353, 0.10864433656011671, -0.23932073494840217, -0.5100691334013843, -0.5889610099752637, -0.34372746490996303, 0.36637817836612796, 1.6789272468802454, 3.714722288843244, 6.56345422350213, 10.26951473758806, 14.818554475295683, 20.1258827353314, 26.02771883305116, 32.27748611480139, 38.549117448846246, 44.44210861387024, 49.4919596893567, 53.18605472294367, 54.985217866861554, 54.351137290913805, 50.777976636012134, 43.81835080353691, 33.110623928028645, 18.406293079847064, -0.40648459379955976, -23.28472856283157, -50.01174018565165, -80.19711069162997, -113.28152721384124, -148.5524004124776, -185.16466789807188, -222.16431945208268, -258.51692700356153, -293.14907587780687, -324.9998386446407, -353.06568008723156, -376.4352681228832, -394.3269259743765, -406.12377871820155, -411.4016271195975, -409.9445765643745, -401.7472813533014, -387.01371665509737, -366.15006474926014, -339.784193364059, -308.7881400160499, -274.19566996008973, -237.1504339530599, -198.85725967723064, -160.45120013251585, -122.69238804498546, -86.14970323825362, -51.27653273037654, -18.417401258623556], 'positive_zeros': ['0.36831052152737027040768285476321', '0.810469590793909577491085084232151', '1.05357064850437119726910331810708', '1.07526277125942176532524721439521', '1.09733123894287451397950762082560', '1.74901778776636730931783788249792', '1.78165928957934329060036778495267', '1.82621902203459743614142187764917', '2.07592113183844305123237163760006', '2.28733973991170197725997292149224', '2.41194007802340266673115447422979', '2.76738339141353640070273612831841', '2.80825583896444296002341311009018', '2.85177531042252682158178136984509', '3.21606771023013407189258209557484', '3.59732534699859407151847611648324', '3.71863990237356771452906315787256', '3.85757521192815391971078139964190', '3.94815570727009404188752212724605', '3.95307650904102647586440589976850', '4.03402513160551732087726176584641', '4.03723646811873972787289549515553', '4.42397315127002355419516279147264', '4.58768929848599925020705763822825', '4.71816454638715442129940559055976', '4.90559113488590231640626798433430', '5.20813550873666993337407558324609', '5.22238252801421634228110642133526', '5.27368729736430391520583308510884', '5.47783112961325386666246636624426', '5.71160676567331818298568769049656', '5.72978629874290861574503459940514', '5.78422545339988296104524075135954', '5.94603380500026527013267250421199', '5.99425158177577190382029920821501', '6.17042089850362100298032707036700', '6.57971796465804316119024589594933', '6.64344738235392602283199797012028', '6.65567159223329309352848942021192', '6.87401846674390821780177885823712', '7.16769427035594273135207871221473', '7.27682866423810615815885230601159', '7.30826158546439051407038919306959', '7.41960632250225210865092661946731', '7.46836445295394718609899827261675', '7.64334318047952149915461409435246', '7.65393448501170312365360368818229', '7.87434131349372631516717230213078', '7.942450421150700281042733495018715', '8.033848983258140730640090005896951', '8.119581355924151838569181100761182', '8.134508895292597931747914002797708', '8.430638847626936748346153350040889', '8.541883933848905682685522657645316', '8.734244492170545490508121988998622', '8.790502181771245745105051728810270', '8.996450550409292916188266202609641', '9.159541622255110431546318405927731', '9.179900369418957763537576264330089', '9.181104827217375139045018642952977'], 'prelabel': '12-2888e6-1.1-c0e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2005414430514723, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e6-0', 'trace_hash': 1371689822940891403, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.36831052152737027040768285476', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.810469590793909577491085084232', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.05357064850437119726910331811', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 8.964496036380636, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 580207226143679709184, 'conductor_radical': 38, 'degree': 12, 'dirichlet_coefficients': [1, -3, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -9, 3, 0, 0, 0, 0, 0, 0, 0, -3, 0, -2, 0, 0, 0, 0, 9, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 9, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -18, 0, -9], 'euler11': [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], 'euler13': [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], 'euler17': [1, -3, 3, -4, 9, -9, 6, -9, 9, -4, 3, -3, 1], 'euler19': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler2': [1, 3, 6, 7, 6, 3, 1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], 'euler29': [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], 'euler3': [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], 'euler31': [1, 0, -6, 0, 15, 0, -20, 0, 15, 0, -6, 0, 1], 'euler37': [1, 0, -6, 0, 15, 0, -20, 0, 15, 0, -6, 0, 1], 'euler41': [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], 'euler43': [1, -3, 3, -4, 9, -9, 6, -9, 9, -4, 3, -3, 1], 'euler47': [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], 'euler5': [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], 'euler53': [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], 'euler59': [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], 'euler61': [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], 'euler67': [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], 'euler7': [1, 0, -6, 0, 15, 0, -20, 0, 15, 0, -6, 0, 1], 'euler71': [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], 'euler73': [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], 'euler79': [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], 'euler83': [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], 'euler89': [1, -3, 3, -4, 9, -9, 6, -9, 9, -4, 3, -3, 1], 'euler97': [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], 'euler_factors': [[1, 3, 6, 7, 6, 3, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, -6, 0, 15, 0, -20, 0, 15, 0, -6, 0, 1], [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, -3, 3, -4, 9, -9, 6, -9, 9, -4, 3, -3, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, -6, 0, 15, 0, -20, 0, 15, 0, -6, 0, 1], [1, 0, -6, 0, 15, 0, -20, 0, 15, 0, -6, 0, 1], [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], [1, -3, 3, -4, 9, -9, 6, -9, 9, -4, 3, -3, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], [1, 0, 3, 0, 6, 0, 7, 0, 6, 0, 3, 0, 1], [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1], [1, -3, 3, -4, 9, -9, 6, -9, 9, -4, 3, -3, 1], [1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2888/1/k/b'], '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': '12-2888e6-1.1-c0e6-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '12-2888e6-1.1-c0e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2005414430514723, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e6-0', 'trace_hash': 1371689822940891403, 'z1': {'__RealLiteral__': 0, 'data': '0.36831052152737027040768285476', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '466889053684543129597591753987,1027392263236626941890492442604,1335559464959411049383543285097,1363057497390075335203833136689,1391032603695121495278399290530,2217143448471885462386148662846', 'Lhash_array': ['466889053684543129597591753987', '1027392263236626941890492442604', '1335559464959411049383543285097', '1363057497390075335203833136689', '1391032603695121495278399290530', '2217143448471885462386148662846'], 'label': '12-2888e6-1.1-c0e6-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2888/1/k/b'}