-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1697575245951401028418689452788,1977495811188291852300919057912,2323771290500531875893498469351,2638268186036710931605911007174', 'a10': 0, 'a2': 0, 'a3': -4, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -8, 'a8': 0, 'a9': 8, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8430.113313630305, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 4, 8, 12, 9]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '1200.1', 'coefficient_field': '1.1.1.1', 'conductor': 2073600000000, 'conductor_radical': 30, 'degree': 8, 'euler_factors': [[1], [1, 4, 8, 12, 9], [1], [1, 8, 32, 120, 386, 840, 1568, 2744, 2401], [1, 0, 20, 0, 342, 0, 2420, 0, 14641], [1, 0, 0, 0, 338, 0, 0, 0, 28561], [1, 0, 0, 0, -254, 0, 0, 0, 83521], [1, 0, -44, 0, 1206, 0, -15884, 0, 130321], [1, 0, 0, 0, -958, 0, 0, 0, 279841], [1, 0, 52, 0, 2358, 0, 43732, 0, 707281], [1, 32, 508, 5024, 33670, 155744, 488188, 953312, 923521], [1, 32, 512, 5280, 38066, 195360, 700928, 1620896, 1874161], [1, 0, -100, 0, 5862, 0, -168100, 0, 2825761], [1, 8, 32, 408, 5138, 17544, 59168, 636056, 3418801], [1, 0, 0, 0, 3682, 0, 0, 0, 4879681], [1, 0, 0, 0, -3854, 0, 0, 0, 7890481], [1, 0, 172, 0, 14358, 0, 598732, 0, 12117361], [1, 24, 460, 5256, 49974, 320616, 1711660, 5447544, 13845841], [1, 24, 288, 3336, 33458, 223512, 1292832, 7218312, 20151121], [1, 0, -28, 0, 10278, 0, -141148, 0, 25411681], [1, 32, 512, 6432, 64418, 469536, 2728448, 12448544, 28398241], [1, 0, -316, 0, 37446, 0, -1972156, 0, 38950081], [1, 0, 0, 0, -12878, 0, 0, 0, 47458321], [1, 0, 100, 0, 18342, 0, 792100, 0, 62742241], [1, -32, 512, -7200, 84866, -698400, 4817408, -29205536, 88529281], [1, 0, -340, 0, 49302, 0, -3468340, 0, 104060401], [1, 24, 288, 4200, 56066, 432600, 3055392, 26225448, 112550881], [1, 0, 0, 0, 8786, 0, 0, 0, 131079601], [1, 0, -236, 0, 37686, 0, -2803916, 0, 141158161], [1, 0, 0, 0, 18562, 0, 0, 0, 163047361]], 'euler_factors_factorization': [[1], [[[1, 4, 8, 12, 9], 1]], [1], [[[1, 4, 8, 28, 49], 2]], [[[1, 0, 10, 0, 121], 2]], [[[1, 0, 0, 0, 169], 2]], [[[1, 0, 0, 0, -254, 0, 0, 0, 83521], 1]], [[[1, 0, -22, 0, 361], 2]], [[[1, 0, 0, 0, -958, 0, 0, 0, 279841], 1]], [[[1, 0, 26, 0, 841], 2]], [[[1, 8, 31], 4]], [[[1, 16, 128, 592, 1369], 2]], [[[1, 0, -50, 0, 1681], 2]], [[[1, 4, 8, 172, 1849], 2]], [[[1, 0, 0, 0, 3682, 0, 0, 0, 4879681], 1]], [[[1, 0, 0, 0, -3854, 0, 0, 0, 7890481], 1]], [[[1, 0, 86, 0, 3481], 2]], [[[1, 6, 61], 4]], [[[1, 12, 72, 804, 4489], 2]], [[[1, 0, -14, 0, 5041], 2]], [[[1, 16, 128, 1168, 5329], 2]], [[[1, 0, -79], 4]], [[[1, 0, 0, 0, -12878, 0, 0, 0, 47458321], 1]], [[[1, 0, 50, 0, 7921], 2]], [[[1, -16, 128, -1552, 9409], 2]], [[[1, 0, -170, 0, 10201], 2]], [[[1, 12, 72, 1236, 10609], 2]], [[[1, -28, 392, -2996, 11449], 1], [[1, 28, 392, 2996, 11449], 1]], [[[1, 0, -118, 0, 11881], 2]], [[[1, 0, 0, 0, 18562, 0, 0, 0, 163047361], 1]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 25, 'label': '8-1200e4-1.1-c1e4-0-25', 'leading_term': '22.0135154661209392770419839265786231661234885109671191919705487672838816900856729025067538', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 4, 'origin': 'ModularForm/GL2/Q/holomorphic/1200/2/v/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0146484375', 'prec': 40}, 'plot_values': [3.0404960001339905e-239, 1.0147256110713986e-06, 1.6232413753795717e-05, 8.214844809659682e-05, 0.00025950394482834155, 0.0006333281534326063, 0.0013129797821229685, 0.0024320993541996016, 0.004148513585056479, 0.006643689681945604, 0.010122709236320948, 0.014813993668246267, 0.02096910109897231, 0.028862352380638116, 0.03878960278938064, 0.05106750589346155, 0.06603239157686128, 0.08403915165936703, 0.10545922331839579, 0.13067902501869524, 0.16009835206521975, 0.19412809589244526, 0.23318563554095156, 0.27769241528398375, 0.32807191363290067, 0.3847457118453573, 0.44812560990999223, 0.5186113802901816, 0.5965879400890564, 0.6824190034454288, 0.7764359509456876, 0.8789365158085862, 0.9901810205874156, 1.1103835637736528, 1.239699410870268, 1.3782244388089029, 1.5259905763763868, 1.6829568348328592, 1.8489958004483082, 2.0238943758460444, 2.207349894348965, 2.398963780588057, 2.5982277187212657, 2.8045268729384487, 3.0171401098122117, 3.2352367296396802, 3.457865139244904, 3.68396079279509, 3.912351901198239, 4.141760343204524, 4.370797330586969, 4.5979771349899075, 4.821727460674657, 5.04039762756894, 5.252265571757248, 5.4555541361011795, 5.648446784885388, 5.829106633612208, 5.995693290242957, 6.146379431118954, 6.279372991569082, 6.3929454933302345, 6.485454588790894, 6.5553601625704605, 6.601252874881706, 6.6218797224803785, 6.616174373637785, 6.5832704683107925, 6.522525744772714, 6.433537825921389, 6.31618253321539, 6.170619605507037, 5.997292967324964, 5.796941696691337, 5.570641227654987, 5.319784191433527, 5.046055535930448, 4.751438274596137, 4.43824746269154, 4.109071259664949, 3.766733149896855, 3.4142876710162535, 3.0550268522506316, 2.692395448247332, 2.3299438726229913, 1.9713073044589575, 1.62017954030549, 1.2802236988254347, 0.9550174997638546, 0.6480111019553207, 0.36248907670338976, 0.10148721326593219, -0.1322656033928792, -0.3363927406175253, -0.5089029482475314, -0.6482580442552268, -0.7534180242488066, -0.8238646856216976, -0.8596207784346692, -0.8612884703985736, -0.8300542040403281, -0.7676808505012288, -0.6765033368670592, -0.5594141299143914, -0.41982078715056664, -0.2616035390690251, -0.08907228859905351, 0.09310881627049668, 0.2800005757752069, 0.46646349318410046, 0.6472534756505115, 0.817131658450476, 0.970965357452169, 1.1038303322763114, 1.2111399801916125, 1.288755910517925, 1.3330881583969372, 1.3412052072642744, 1.3109534944080288, 1.2410372995409835, 1.1310908405819817, 0.9817530641062132, 0.7947397340983215, 0.5728620833201977, 0.32003703874104944, 0.04129008047592736, -0.25725088490863435, -0.5684203967554248, -0.8840897971690822, -1.1952521699613636, -1.4921256026268706, -1.76430191455115, -2.0009009071748642, -2.1907385570727076, -2.3225181060602496, -2.3850321248218176, -2.3673682512757113, -2.259128161862382, -2.05065857739872, -1.7332586829344225, -1.2993869031175151, -0.7428646228789159, -0.059081893977745166, 0.7548477933926407, 1.6999503192666618, 2.7752696734166964, 3.9777586752762577, 5.3022390919085804, 6.741389901634934, 8.285748605360835, 9.923775496554963, 11.641968920873731, 13.424965142976623, 15.255694914743275, 17.115690453454825, 18.985288162192692, 20.843808956836266, 22.669887067098294, 24.44200574771095, 26.138639170543865, 27.738496573010032, 29.221016304482802, 30.56692635405504, 31.7582750001108, 32.778701194780886, 33.613946089778494, 34.25225644028177, 34.684299799393685, 34.903413924117004, 34.905829072857046, 34.69095127581776, 34.26114602993995, 33.62177108118332, 32.781047906600705, 31.75025493645286, 30.543379708439613, 29.176724259451692, 27.668641118701935, 26.03962726375856, 24.311736368461666, 22.507938869050232, 20.651848516974614, 18.767715500865254, 16.87961493281392, 15.01089296360883, 13.183950220362435, 11.420084339502772, 9.738785122374775, 8.157400063213508, 6.691020349976899, 5.352288048922144, 4.151045698960265, 3.094258010141244, 2.186015499881232, 1.4275308327393839, 0.817147623698455, 0.3504985283547228, 0.02069080756637809, -0.18146553136172372, -0.26718368185153746, -0.24936767045341884, -0.14226062664152864, 0.038913689129713866, 0.27835072378467735, 0.5600658164470036, 0.8682745327120232, 1.1877503840951509, 1.5041882448798867, 1.8045166785391635, 2.077165688148596, 2.3122964569276, 2.50197441699084, 2.6402823113441998, 2.723391253617316, 2.7495577446537713, 2.719054741611187, 2.634067654178001, 2.4985455110565757, 2.317963435228419, 2.099078974976232, 1.8496761473783454, 1.5782516437166245, 1.2936732919114933, 1.0048889185191867, 0.7206291064692306, 0.4490912138047624, 0.19765039672526877, -0.027344509618488274, -0.2207644695540341, -0.37885851495127554, -0.49937456993931106, -0.5815788751941191, -0.6262356948832037, -0.6355525203616388, -0.6130890674276729, -0.5635655787911207, -0.49265257097360354, -0.40674738294380214, -0.31271257394394025, -0.21757578675724434, -0.12824976427187373, -0.051254171607488554, 0.00757287044819475, 0.04331292524240675, 0.05217513670352044, 0.03168061733689136, -0.019211847381251628, -0.10005060648379566, -0.20886134519324617, -0.342189215272364, -0.495233964230538, -0.6619977690473519, -0.835472071600429, -1.007910682335748, -1.171187164201297, -1.3170662908760908, -1.4375268977103532, -1.5251295676894223, -1.5734432997804355, -1.5772937417826653, -1.5330275956296304, -1.4387878374337164, -1.294809513056057, -1.1034652712625364, -0.8692999536251954, -0.5990579643263595, -0.3016788944083005, 0.011954264960702057, 0.3292639504555563, 0.636247502822034, 0.9178303734219596, 1.1583397218401141, 1.341950706807088, 1.4531585740598454, 1.4773449272200294, 1.40126813720783, 1.2135074683812983, 0.9049178473999456, 0.46914931612626093, -0.09708709230074977, -0.7938103838647045, -1.6175715553270973, -2.5612441295973616, -3.614148425451657, -4.762218393346785, -5.988198875866349, -7.27189177417909, -8.590650529505176, -9.919892773054153, -11.233665231766915, -12.505268781911399, -13.707910688194943, -14.815377779735243, -15.802765718575982, -16.647176205560744, -17.328248860269618, -17.828733409000936, -18.135037402621727, -18.237654003180896, -18.13134663391556, -17.815375253684564, -17.293569568919104, -16.57426999724746, -15.67009855637274, -14.597702034398706, -13.377337402762874, -12.032274058878588, -10.588268874619502, -9.072969992056288, -7.515206982768148, -5.944009892747826, -4.388072218074673, -2.8751787754147866, -1.4314710266102095, -0.08038338850215408, 1.1575209722878264, 2.264796360791273, 3.227607636019127, 4.0365301676490475, 4.686124785001858, 5.1747349495044155, 5.504580688210104, 5.68208720263387, 5.7169580546808545, 5.621600201830416, 5.410842096242203, 5.1018618711629715, 4.71306015329212, 4.263346720562329, 3.7717177097793577, 3.2570267622500433, 2.737028828921881, 2.2278295783219013, 1.7436154914695714, 1.2965302334922193, 0.896166573312425, 0.5494026191903071, 0.26044854712895765, 0.030983012527209555, -0.13983919376283668, -0.2551576345968678, -0.3200693700458539, -0.3412600875339967, -0.32665255965684176, -0.2849762140086313, -0.22532610799057115, -0.15674756922828192, -0.08784222443083847, -0.026403138879902723, 0.02089274487582157, 0.048724945042096846, 0.053310097274657124, 0.032506458657125384, -0.014160099267922404, -0.08554887764965866, -0.1790181337015927, -0.2905997038459891, -0.41523424258360897, -0.5470636399594254, -0.6797165300486717, -0.8066184062967536, -0.9213236225299939, -1.017845555154897, -1.0908977790840182, -1.1361396502916674, -1.1503871081196893, -1.131759391322585, -1.079738100360925, -0.995194598124207, -0.8803241945280735, -0.7385681024908847, -0.5744646714927235, -0.3934327962384245, -0.20148115911312703, -0.0050276106094513705, 0.1893734784513362, 0.3753811895532354, 0.5471037361071461, 0.6992821678952973, 0.8275266966557904, 0.9285413529208121, 1.0001336767658908, 1.0413065166075843, 1.0523257232256256, 1.0346115350809166, 0.9905890436011807, 0.9236376984786584, 0.8379123144952881, 0.7380365158771429, 0.6288977176019193, 0.5155042507232577, 0.4026804492956422, 0.29482331721087135, 0.19575858125229773, 0.10860898043329625, 0.03562969448715579, -0.021846050607281474, -0.06339970048706894, -0.08951364490582461, -0.10149718567158286, -0.10135390659951256, -0.09162543094417999, -0.07521929738268332, -0.05520188636994635, -0.034589314466264676, -0.016149091137138773, -0.002217229294491863, 0.005465372807694166, 0.005878207105468241, -0.0011965495840284132, -0.0151376953269239, -0.03449660522964256, -0.057058954678395696, -0.07995363026012915, -0.09980663020651208, -0.11292486058225003, -0.11550546055396198, -0.103864628009246, -0.07467027715999762, -0.025156879194904256, 0.04667032361217192, 0.14186182725531307, 0.2604143873285405, 0.4011865211949871, 0.5618584674379726, 0.7389760105533053, 0.9280924839426615, 1.12387485293866, 1.3202842270470405, 1.5108310934418334, 1.6889320487132553, 1.8481220567353167, 1.9823294931761273, 2.0861615428484774, 2.1553050151421473, 2.186658779833108, 2.178439717146389, 2.1303192066362144, 2.043660577284709, 1.9213671257199723, 1.7676922793548921, 1.5881438162199086, 1.3894421250232143, 1.1790606743642607, 0.9648588944403559, 0.7548189293824824, 0.556778751837568, 0.37793970762304513, 0.22453987504920567, 0.10161424831588775, 0.012768925872692908, -0.04004131937411108, -0.05659720439852762, -0.03842122306473632, 0.011292436291343098, 0.08782525980906829, 0.18515776607856815, 0.2962657764007457, 0.4134751980827277, 0.5288437111508257, 0.6345533727588258, 0.7233132028337992, 0.7887611965660282, 0.8257889210758713, 0.8308064532347172, 0.8019504277229155, 0.7392409611867627, 0.6445801603556977, 0.521665893581823, 0.37583667043417157, 0.21384050957162812, 0.04347924497922685, -0.12678323559434587, -0.2882515671552801, -0.43246808981991686, -0.5516539993669275, -0.639126415540606, -0.6896908573014319, -0.6999724092335942, -0.6685934329029896, -0.5962912532511436, -0.4859391782222883, -0.3424453888363802, -0.17250261427064917, 0.015720025030744773, 0.21297652318500243, 0.4094590141900575, 0.5953069599877527, 0.7611063584703902, 0.898410830027914, 1.0003309025628482, 1.0618632540805266, 1.0801319909231948, 1.0546153505533826, 0.9873630831107958, 0.8827561079514887, 0.7472241140831873, 0.588955226438088, 0.4175402867702346, 0.24323207140151976, 0.07628976058163944, -0.07362733851663879, -0.19806581737334386, -0.2904786347515014, -0.3467209332962985, -0.365386154856134, -0.3479959475956682, -0.2990154636248583, -0.22560384333185862, -0.1371314462988896, -0.044496045811513577, 0.04081427047534988, 0.10784806186704889, 0.147450465731485, 0.153624667694531, 0.12495666995553767, 0.0659875343601332, -0.011515271512183317, -0.08745694843653917, -0.13258489078606067, -0.1079694538632267, 0.03514563094209552, 0.3549955945089259, 0.9185268534612392, 1.8001834111632484, 3.080207001877896, 4.842321533030091, 7.171166427683815, 10.149430805564473, 13.854774608398278, 18.356224860747403, 23.710774095551233, 29.960359048649476, 37.12880045658495, 45.21880380617224, 54.209732613931045, 64.0564195345523, 74.68754880462207, 86.00589244821025, 97.88942262574147, 110.19197567508532, 122.74468199899717, 135.36171418377106, 147.84395555205168, 159.98042565113616, 171.55353498526551, 182.3505724591336, 192.16506158513073, 200.79893834510906, 208.07092884774437, 213.82841016353493, 217.94411238929752, 220.31814285235927, 220.8865792121947, 219.62688843092698, 216.551520247002, 211.70858206178377, 205.1843116455895, 197.10279210158686, 187.61744842859542, 176.9087808938793, 165.1791250954863, 152.65039823197245, 139.55513205050627, 126.12976645042771, 112.60795976876864, 99.21809007466294, 86.17539177522771, 73.67482172842726, 61.88749419602681, 50.959545833375316, 41.00718184021897, 32.11424427060766, 24.332495276549817, 17.68288153224929, 12.155732305829899, 7.71311038637611, 4.292173255981354, 1.8090774888842778, 0.1630476915664651, -0.7590738858494556, -1.078114821676888, -0.9177523128352431, -0.40011880053602467, 0.35823163343705255, 1.2499968087466988, 2.180088273853901, 3.067826443924141, 3.848542582322538, 4.474225001769554, 4.913550166579843, 5.1512745895442125, 5.186794205044585, 5.032169811458747, 4.710057796099175, 4.251201178333137, 3.691502936745302, 3.0693974466442935, 2.423423868339036, 1.7897530566624944, 1.2001728164558014, 0.6805813046115854, 0.2497757505353202, -0.08114962873875294, -0.3088654579645953, -0.4375227012573616, -0.4780504142170752, -0.44691088359822817, -0.3647291253696066, -0.25476200013375466, -0.14117437611176384, -0.0473777936534395, 0.005464584370507995, -0.00016993333461478845, -0.07709179733301073, -0.2326732041506278, -0.46839435517076633, -0.779793233185877, -1.1569280870433563, -1.5849537981316, -2.0449945562538177, -2.5153445145009745, -2.973053481363285, -3.395129071754821, -3.759816975404094, -4.047955193060915, -4.244482955380926, -4.339043536999824, -4.326450834985877, -4.207098280083113, -3.987321421192565, -3.678671401753731, -3.297135438391433, -2.8623291012090513, -2.39658327303361, -1.9233527131617119, -1.4657991086464814, -1.0454911948429553, -0.6811862317530111, -0.38755742666584436, -0.17426919637415741, -0.04535234899817439, 0.0011288076589640195, -0.02690095298558099, -0.11586605187780373, -0.24719977279050656, -0.39831043141729544, -0.5437757151113648, -0.656704205171265, -0.7102263691043336, -0.6790548358149268, -0.5409130480134555, -0.27787696358054076, 0.12244794185110426, 0.6661092498100394, 1.352234551892907, 2.1726989072256515, 3.112259071234467, 4.1493658403449745, 5.25672579008433, 6.402199469171366, 7.550273466917908, 8.664199391957498, 9.707007078610054, 10.642919107437507, 11.439074106980557, 12.067859021251575, 12.507301241259823, 12.741713134007707, 12.762528621332423, 12.569678465645346, 12.170629573913606, 11.579534325494757, 10.816867118074548, 9.909444989742694, 8.888217663660742, 7.786568518282415, 6.6392590926284445, 5.481566788999922, 4.347029016935252, 3.266081910702685, 2.265252848861672, 1.3664016226657476, 0.5857235288398447, -0.06650923732686939, -0.585863557934215, -0.9735859597754378, -1.2361352144336986, -1.3843856551575273, -1.4327151209560862, -1.3980846010023282, -1.2988977243083755, -1.1538929592036855, -0.9811391263910817, -0.7971959458513446, -0.6163332217274771, -0.4499653216606174, -0.30632607987753785, -0.19036863479578733, -0.10386032332022693, -0.04567386428517577, -0.012249831833814508, 0.0018105189875318387, 0.0030656983073535037, -0.0014693953468375412, -0.005017899332237203, -0.0016768675414170573, 0.0130589373934274, 0.041895677121757194, 0.08549267565631237, 0.14243290483931353, 0.2093171878468392, 0.28099046134417394, 0.350945416925156, 0.41195447046016215, 0.4565660985817474, 0.4776451971606492, 0.4689974968945406, 0.4261067683882662, 0.34639345752616135, 0.22943993556136155, 0.07721999688332039, -0.10569346938092793, -0.31254524630947056, -0.5347922013449684, -0.7624771198099721, -0.9846835277533919, -1.1904003336468876, -1.3692032961802696, -1.5118474521928758, -1.610879581975793, -1.6612279265863286, -1.6605259653805542, -1.6092933878567313, -1.511024143308353, -1.3719871195552251, -1.2008271812609124, -1.008056965516964, -0.8054642980683357, -0.6052969295848902, -0.41943291756831624, -0.2585901536701371, -0.13159777890225982, -0.044704944177262146, -0.0010691331426458414, -0.000440434606665688, -0.03904724840850311, -0.10970536979291455, -0.2021541805113862, -0.30361129522475117, -0.3995268048457333, -0.474449612702559, -0.5130087270148515, -0.5009669020325113, -0.4262320287876301, -0.27974050359198327, -0.056286893346255154, 0.24487224635509283, 0.6197470005119636, 1.0594589726399277, 1.5503421230089878, 2.074543167162056, 2.61085596670905, 3.1354743836080643, 3.623127172957838, 4.048482063941106, 4.38766351371465, 4.619274507390554, 4.725681858409085, 4.693997573367946, 4.517438613326146, 4.19557728088065, 3.7344066559436073, 3.1462722107853054, 2.450183178856048, 1.6705992122878481, 0.8360843986304937, -0.021694266791489013, -0.8688824330973927, -1.67157602714869, -2.397451653882491, -3.0170571444691143, -3.505123692620109, -3.841987618732479, -4.014422736587085, -4.016286802911714, -3.84881450871783, -3.5204404695077525, -3.046351007989928, -2.447855688634405, -1.7512406798061142, -0.9863974052712433, -0.18544509821749428, 0.6187771747625885, 1.3943074370439448, 2.111552993880921, 2.7445779854329357, 3.272152288072695, 3.6786587539151894, 3.9546680548587405, 4.097040899139455, 4.108753395515552, 3.998603656082106, 3.7804963516176433, 3.472353407748119, 3.09503563360217, 2.671212311581885, 2.224031088728644, 1.7758888617286326, 1.3473566427865424, 0.956152101697381, 0.6164353556508299, 0.3383475138818323, 0.12772435522036182, -0.013963671794210925, -0.0892356684950351, -0.10413976071761027, -0.0676511308178168, 0.009172714320260735, 0.11406868871255008, 0.23437463818705873, 0.3578608600736002, 0.47362972772001255, 0.5726129831982599, 0.6479331653423911, 0.6951889569053404, 0.7127178227958553, 0.701290153953318, 0.6637298051561364, 0.6045539793490003, 0.5296230644455071, 0.4453695260671864, 0.3581717107944949, 0.2738891338552244, 0.1974874096373004, 0.1325696459027898, 0.08118211107315691, 0.0438119694100582, 0.01950923586136954, 0.006104456190980006, 0.0005971200029204033, -0.0003705244399316568, -2.948773136638107e-06, -0.0008349761506260906, -0.004254109100407604, -0.010111356192137134, -0.016451942758633386, -0.019400399754136568, -0.01321894063823044, 0.009460799407172602, 0.05724097565435373, 0.13940526950848092, 0.26524894155448575, 0.44333421772091236, 0.680759521876119, 0.9824277128907448, 1.3503534353383984, 1.7831366331002343, 2.275815608879827, 2.819654244153984, 3.402105608838284, 4.007226124571528, 4.616694585036661, 5.210221758239787, 5.7662709533188, 6.263376209763436, 6.681798423760783, 7.003959153196401, 7.215275184706409, 7.30530799942404, 7.269021715485103, 7.106400822260772, 6.822479678575291, 6.427294025011228, 5.9361138476798825, 5.367961178568668, 4.74445450403126, 4.088868159108898, 3.425533335991604, 2.7779822693017024, 2.16748101960094, 1.6121743877446046, 1.126507379588225, 0.7202464357177106, 0.3982108000891096, 0.16038297690139933, 0.0021667608743392423, -0.08533861860032677], 'positive_zeros': ['1.33915074520200397122627638468511', '1.55996913568475495543508443069330', '1.83313232375084836687615780898272', '2.08122662945271656368633171479431', '2.88691164004279061749837348432162', '2.95623639703052422194080173490803', '3.32330537809552337108992570987565', '3.54269177073260169902359654027159', '3.59892778277536946967825673883038', '3.91058196048793774274400447394915', '4.08462660640692026455977735693365', '4.60051738945155253587241994299233', '4.95349925205421325153156435037442', '5.10517222830260620554518905651139', '5.16720725357775466167810705883156', '5.47889022127029328100287014697127', '5.79472229497362126952728517986010', '5.95040283240010447057077064633713', '5.98950487083743241321939682912534', '6.14338251429471009493355995329834', '6.59456570505574244109479947746156', '6.64770209205872827267057240311354', '6.90312460301925017665630973448362', '7.08865658340810206136314088578409', '7.33141066806559101920320673994498', '7.47806463586219298492644490378356', '7.57115418735111793086113010730479', '7.62934124188293452706202665145415', '8.483409082891017258129605252003649', '8.548203821529180701599916673453375', '8.828958013841248821221912085448069', '8.962281830009273131701615833614292', '8.979428040061995763163173640277380', '9.402822132059400201473778505125988', '9.408721572497026155637185590260440', '9.561461758858264014432520071590913'], 'prelabel': '8-1200e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.095488368990207, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 1661874678965644465, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33915074520200397122627638469', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.55996913568475495543508443069', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.83313232375084836687615780898', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 8430.113313630305, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 2073600000000, 'conductor_radical': 30, 'degree': 8, 'dirichlet_coefficients': [1, 0, -4, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -12, 0, 0, 0, -32, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, -64, 0, 0, 0, -24, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 32, 0, 0, 0], 'euler11': [1, 0, 20, 0, 342, 0, 2420, 0, 14641], 'euler13': [1, 0, 0, 0, 338, 0, 0, 0, 28561], 'euler17': [1, 0, 0, 0, -254, 0, 0, 0, 83521], 'euler19': [1, 0, -44, 0, 1206, 0, -15884, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, 0, 0, -958, 0, 0, 0, 279841], 'euler29': [1, 0, 52, 0, 2358, 0, 43732, 0, 707281], 'euler3': [1, 4, 8, 12, 9, 0, 0, 0, 0], 'euler31': [1, 32, 508, 5024, 33670, 155744, 488188, 953312, 923521], 'euler37': [1, 32, 512, 5280, 38066, 195360, 700928, 1620896, 1874161], 'euler41': [1, 0, -100, 0, 5862, 0, -168100, 0, 2825761], 'euler43': [1, 8, 32, 408, 5138, 17544, 59168, 636056, 3418801], 'euler47': [1, 0, 0, 0, 3682, 0, 0, 0, 4879681], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, 0, 0, -3854, 0, 0, 0, 7890481], 'euler59': [1, 0, 172, 0, 14358, 0, 598732, 0, 12117361], 'euler61': [1, 24, 460, 5256, 49974, 320616, 1711660, 5447544, 13845841], 'euler67': [1, 24, 288, 3336, 33458, 223512, 1292832, 7218312, 20151121], 'euler7': [1, 8, 32, 120, 386, 840, 1568, 2744, 2401], 'euler71': [1, 0, -28, 0, 10278, 0, -141148, 0, 25411681], 'euler73': [1, 32, 512, 6432, 64418, 469536, 2728448, 12448544, 28398241], 'euler79': [1, 0, -316, 0, 37446, 0, -1972156, 0, 38950081], 'euler83': [1, 0, 0, 0, -12878, 0, 0, 0, 47458321], 'euler89': [1, 0, 100, 0, 18342, 0, 792100, 0, 62742241], 'euler97': [1, -32, 512, -7200, 84866, -698400, 4817408, -29205536, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 4, 8, 12, 9, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 8, 32, 120, 386, 840, 1568, 2744, 2401], [1, 0, 20, 0, 342, 0, 2420, 0, 14641], [1, 0, 0, 0, 338, 0, 0, 0, 28561], [1, 0, 0, 0, -254, 0, 0, 0, 83521], [1, 0, -44, 0, 1206, 0, -15884, 0, 130321], [1, 0, 0, 0, -958, 0, 0, 0, 279841], [1, 0, 52, 0, 2358, 0, 43732, 0, 707281], [1, 32, 508, 5024, 33670, 155744, 488188, 953312, 923521], [1, 32, 512, 5280, 38066, 195360, 700928, 1620896, 1874161], [1, 0, -100, 0, 5862, 0, -168100, 0, 2825761], [1, 8, 32, 408, 5138, 17544, 59168, 636056, 3418801], [1, 0, 0, 0, 3682, 0, 0, 0, 4879681], [1, 0, 0, 0, -3854, 0, 0, 0, 7890481], [1, 0, 172, 0, 14358, 0, 598732, 0, 12117361], [1, 24, 460, 5256, 49974, 320616, 1711660, 5447544, 13845841], [1, 24, 288, 3336, 33458, 223512, 1292832, 7218312, 20151121], [1, 0, -28, 0, 10278, 0, -141148, 0, 25411681], [1, 32, 512, 6432, 64418, 469536, 2728448, 12448544, 28398241], [1, 0, -316, 0, 37446, 0, -1972156, 0, 38950081], [1, 0, 0, 0, -12878, 0, 0, 0, 47458321], [1, 0, 100, 0, 18342, 0, 792100, 0, 62742241], [1, -32, 512, -7200, 84866, -698400, 4817408, -29205536, 88529281]], 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1200/2/v/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': '8-1200e4-1.1-c1e4-0-25', 'motivic_weight': 1, '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}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 4, 'prelabel': '8-1200e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.095488368990207, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1661874678965644465, 'z1': {'__RealLiteral__': 0, 'data': '1.33915074520200397122627638469', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1697575245951401028418689452788,1977495811188291852300919057912,2323771290500531875893498469351,2638268186036710931605911007174', 'Lhash_array': ['1697575245951401028418689452788', '1977495811188291852300919057912', '2323771290500531875893498469351', '2638268186036710931605911007174'], 'label': '8-1200e4-1.1-c1e4-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1200/2/v/a'}