-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '389883814081993722311464073085,537653665799164867200342067519,1123645786301818305214356809412,1149083002884275632589017633830', 'a10': 0, 'a2': 0, 'a3': 6, 'a4': 0, 'a5': -14, 'a6': 0, 'a7': -28, 'a8': 0, 'a9': -32, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 124973031.45786545, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 28, 294, 1372, 2401]]], 'bad_primes': [2, 7], 'central_character': '1792.1', 'coefficient_field': '1.1.1.1', 'conductor': 10312216477696, 'conductor_radical': 14, 'degree': 8, 'euler_factors': [[1], [1, -6, 68, -302, 2102, -8154, 49572, -118098, 531441], [1, 14, 316, 2250, 39446, 281250, 4937500, 27343750, 244140625], [1, 28, 294, 1372, 2401], [1, -56, 2780, -130424, 5262166, -173594344, 4924939580, -132045070696, 3138428376721], [1, -46, 5180, -228570, 16614646, -502168290, 25002870620, -487806971158, 23298085122481], [1, -136, 22076, -1854904, 168489670, -9113143352, 532860973244, -16127951203592, 582622237229761], [1, -58, 21284, -1222770, 200115766, -8386979430, 1001324531204, -18715886471182, 2213314919066161], [1, 36, 11068, -2483404, -109072922, -30215576468, 1638461219452, 64841495812668, 21914624432020321], [1, 244, 98020, 16054732, 3637039542, 391558858748, 58304581924420, 3539743618112036, 353814783205469041], [1, -80, 98108, -6698256, 4121040902, -199547744496, 87071211135548, -2115169772853680, 787662783788549761], [1, -116, 112292, -16931052, 7096842646, -857608576956, 288110549919428, -15075561816228932, 6582952005840035281], [1, 376, 212316, 51001224, 18244997158, 3515055359304, 1008523132032156, 123095607332129336, 22563490300366186081], [1, 608, 332604, 113978720, 38738414102, 9062106091040, 2102510635549596, 305576308057600544, 39959630797262576401], [1, -504, 371452, -143870104, 56727343558, -14937025807592, 4003961092387708, -564041758443794568, 116191483108948578241], [1, 88, 35956, -40062488, 10958668662, -5964383025976, 796941768754324, 290379196078587704, 491258904256726154641], [1, 38, 123316, 6020190, 81607069814, 1236420602010, 5201534686473556, 329193841108887682, 1779197418239532716881], [1, -130, 528540, 57273642, 122928435190, 13000028534802, 27230578664762940, -1520238992068438330, 2654348974297586158321], [1, -1668, 1986284, -1562559876, 1003433820182, -469960195985388, 179676037168169996, -45380499373019971596, 8182718904632857144561], [1, 408, 545308, -167809544, 48366937318, -60060881702584, 69854109624392668, 18706188293127204648, 16409682740640811134241], [1, -576, 1219532, -601885056, 666382613702, -234143518829952, 184556931654676748, -33910033943962317888, 22902048046490258711521], [1, -472, 994172, -344402424, 659437576006, -169803826726536, 241670741830223612, -56569953303795846568, 59091511031674153381441], [1, -2058, 1798900, -411223106, -157636635434, -235132026110422, 588133037653494100, -384723045340598149374, 106890007738661124410161], [1, 344, 881148, 629036712, 820148016934, 443451381821928, 437914070567703228, 120522602875374911896, 246990403565262140303521], [1, -192, 3197100, -518194304, 4172546665638, -472941950014592, 2663094796958505900, -145964363261676521664, 693842360995438000295041], [1, -650, 1447756, -761380670, 2016738082038, -784451265681670, 1536822167153501356, -710895427244834585650, 1126825030131969720661201], [1, 1264, 2701468, 4120956592, 3607279714918, 4503080533906384, 3225694069399604572, 1649233304360165152912, 1425760886846178945447841], [1, 1644, 4486252, 6018161996, 7997031518518, 7372507226065828, 6732654542443279948, 3022426945218734009508, 2252191588960823337718801], [1, 340, 2451876, 1661713324, 4038136174070, 2151966944266396, 4112041511368387716, 738443715010385192260, 2812664781782894485727281], [1, -2540, 5245428, -6110851860, 8334688000726, -8817329816238420, 10920728017784321652, -7630266522480041413420, 4334523100191686738306881]], 'euler_factors_factorization': [[1], [[[1, -6, 68, -302, 2102, -8154, 49572, -118098, 531441], 1]], [[[1, 14, 316, 2250, 39446, 281250, 4937500, 27343750, 244140625], 1]], [[[1, 7], 4]], [[[1, -56, 2780, -130424, 5262166, -173594344, 4924939580, -132045070696, 3138428376721], 1]], [[[1, -46, 5180, -228570, 16614646, -502168290, 25002870620, -487806971158, 23298085122481], 1]], [[[1, -136, 22076, -1854904, 168489670, -9113143352, 532860973244, -16127951203592, 582622237229761], 1]], [[[1, -58, 21284, -1222770, 200115766, -8386979430, 1001324531204, -18715886471182, 2213314919066161], 1]], [[[1, 36, 11068, -2483404, -109072922, -30215576468, 1638461219452, 64841495812668, 21914624432020321], 1]], [[[1, 244, 98020, 16054732, 3637039542, 391558858748, 58304581924420, 3539743618112036, 353814783205469041], 1]], [[[1, -80, 98108, -6698256, 4121040902, -199547744496, 87071211135548, -2115169772853680, 787662783788549761], 1]], [[[1, -116, 112292, -16931052, 7096842646, -857608576956, 288110549919428, -15075561816228932, 6582952005840035281], 1]], [[[1, 376, 212316, 51001224, 18244997158, 3515055359304, 1008523132032156, 123095607332129336, 22563490300366186081], 1]], [[[1, 608, 332604, 113978720, 38738414102, 9062106091040, 2102510635549596, 305576308057600544, 39959630797262576401], 1]], [[[1, -504, 371452, -143870104, 56727343558, -14937025807592, 4003961092387708, -564041758443794568, 116191483108948578241], 1]], [[[1, 88, 35956, -40062488, 10958668662, -5964383025976, 796941768754324, 290379196078587704, 491258904256726154641], 1]], [[[1, 38, 123316, 6020190, 81607069814, 1236420602010, 5201534686473556, 329193841108887682, 1779197418239532716881], 1]], [[[1, -130, 528540, 57273642, 122928435190, 13000028534802, 27230578664762940, -1520238992068438330, 2654348974297586158321], 1]], [[[1, -1668, 1986284, -1562559876, 1003433820182, -469960195985388, 179676037168169996, -45380499373019971596, 8182718904632857144561], 1]], [[[1, 408, 545308, -167809544, 48366937318, -60060881702584, 69854109624392668, 18706188293127204648, 16409682740640811134241], 1]], [[[1, -576, 1219532, -601885056, 666382613702, -234143518829952, 184556931654676748, -33910033943962317888, 22902048046490258711521], 1]], [[[1, -472, 994172, -344402424, 659437576006, -169803826726536, 241670741830223612, -56569953303795846568, 59091511031674153381441], 1]], [[[1, -2058, 1798900, -411223106, -157636635434, -235132026110422, 588133037653494100, -384723045340598149374, 106890007738661124410161], 1]], [[[1, 344, 881148, 629036712, 820148016934, 443451381821928, 437914070567703228, 120522602875374911896, 246990403565262140303521], 1]], [[[1, -192, 3197100, -518194304, 4172546665638, -472941950014592, 2663094796958505900, -145964363261676521664, 693842360995438000295041], 1]], [[[1, -650, 1447756, -761380670, 2016738082038, -784451265681670, 1536822167153501356, -710895427244834585650, 1126825030131969720661201], 1]], [[[1, 1264, 2701468, 4120956592, 3607279714918, 4503080533906384, 3225694069399604572, 1649233304360165152912, 1425760886846178945447841], 1]], [[[1, 1644, 4486252, 6018161996, 7997031518518, 7372507226065828, 6732654542443279948, 3022426945218734009508, 2252191588960823337718801], 1]], [[[1, 340, 2451876, 1661713324, 4038136174070, 2151966944266396, 4112041511368387716, 738443715010385192260, 2812664781782894485727281], 1]], [[[1, -2540, 5245428, -6110851860, 8334688000726, -8817329816238420, 10920728017784321652, -7630266522480041413420, 4334523100191686738306881], 1]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 1, 'label': '8-1792e4-1.1-c3e4-0-1', 'leading_term': '4.6128048772257960990800646610913437335141211287335631059924292863624074223542312178868139', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3, 3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1792/4/a/m', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0146484375', 'prec': 40}, 'plot_values': [4.612804877225796, 4.569336305924548, 4.511685128933725, 4.4259146840063455, 4.2994172495135725, 4.129486792808808, 3.9227504261533053, 3.6865935858010648, 3.427629385990962, 3.149942852092641, 2.8572592484033867, 2.5536606025348303, 2.244040987295181, 1.933764939952083, 1.6281367719513131, 1.3322360224929848, 1.0507994224976884, 0.7882209833370717, 0.5484993989275659, 0.3352088765658117, 0.15139838111186352, -0.0004910397030910031, -0.11865934771694596, -0.2019780374449403, -0.2500186459955465, -0.2630530248861444, -0.2420465102321438, -0.18864321043161092, -0.10512763788380043, 0.005620851581418484, 0.14017905830134902, 0.29465928525487073, 0.4647919795304271, 0.6460009678424081, 0.8335070753642032, 1.022437479398791, 1.2079212337761203, 1.3851896130792274, 1.5496970926692084, 1.6972215983261654, 1.823949958284472, 1.9265779883719696, 2.0023994842469284, 2.0493690969221414, 2.0661591662562797, 2.05221130365424, 2.007767460872109, 1.9338782155785301, 1.8324011750394564, 1.7059810059891638, 1.5580132401061586, 1.3925876167550846, 1.214415684985175, 1.0287445642318267, 0.841258070452691, 0.6579614313749853, 0.48505735879768663, 0.3288149087355029, 0.19543134463956885, 0.09089157516568906, 0.020827244957696386, -0.009622297249140882, 0.004057943323000996, 0.06563469905091945, 0.17801260712286232, 0.3431359668484282, 0.5619085084402746, 0.8341279291891939, 1.158445613841436, 1.5323424221223507, 1.9521364275219621, 2.413015633800328, 2.9090827069980314, 3.4334177055217365, 3.978203810137406, 4.534857351110893, 5.09412729629968, 5.646249971169094, 6.18120289180836, 6.688842814602166, 7.159045677155617, 7.581952225025558, 7.948253048831367, 8.249265015673918, 8.477099347882236, 8.624955821608724, 8.68726426768042, 8.659717694440397, 8.539453108581146, 8.325209148945289, 8.017308636893947, 7.617653887976335, 7.129848691701906, 6.559077944774318, 5.912019811483049, 5.196805766081666, 4.422907480986507, 3.6008709740736466, 2.7421827765006643, 1.8591443327433628, 0.9645361261978915, 0.0713615918781515, -0.8073158448949037, -1.6586464931050526, -2.470313668673679, -3.2307375812613186, -3.929275269280371, -4.556492013794282, -5.104334898368533, -5.566259245460341, -5.937413350684418, -6.214721707379648, -6.39690607364388, -6.484512489700395, -6.479940476500722, -6.387327080441408, -6.2124326728216, -5.962514332958439, -5.646177302299204, -5.273127972452555, -4.8539424562879825, -4.399801841876092, -3.9222527481599347, -3.432910988167537, -2.943161151147464, -2.4638778209588503, -2.005193108302757, -1.5762322502279948, -1.1848727453187238, -0.8375626642669379, -0.5391830316835082, -0.29291498016031503, -0.10016520304611999, 0.039454548322578366, 0.1281047147230417, 0.16965411040917783, 0.16956616973985325, 0.13474289991286523, 0.07332941842687477, -0.005517115477113059, -0.09188692158638109, -0.17539891163152296, -0.2454978295405182, -0.29175989652339596, -0.3041961386045748, -0.2735467177080338, -0.1915660469421019, -0.05127356349223247, 0.15282983281649518, 0.4245613519561498, 0.7659092261794652, 1.17696991666713, 1.6558766649689731, 2.198774539260829, 2.799938259205183, 3.4518942585541743, 4.145491545737549, 4.870112281639684, 5.614073180266876, 6.364766517939719, 7.108879705459605, 7.8328705849719995, 8.523367815187331, 9.167279624068067, 9.752143726537565, 10.266666210545816, 10.700858024499436, 11.046138746897991, 11.29576797359846, 11.444979535850772, 11.490976676647964, 11.433018609910942, 11.272621999713671, 11.013241010191011, 10.660242856162933, 10.220944359532183, 9.70426286494909, 9.120331930145642, 8.480477369816107, 7.796984204647058, 7.082501228170095, 6.349775208149211, 5.611616726197989, 4.880392253352965, 4.167629732199135, 3.4839028726601318, 2.838700275203905, 2.2400485723925536, 1.6943981584845804, 1.2066415005100244, 0.7800064214665736, 0.4160132293159947, 0.11457779604533971, -0.12587944265730996, -0.3083394884699484, -0.4370018637147895, -0.5170622734506934, -0.5545083707291737, -0.5558911640807198, -0.5280742381791588, -0.477995621001931, -0.41244407690990526, -0.33785175266820344, -0.2601064525232368, -0.18439561820493705, -0.11508441523375275, -0.055630546155070106, -0.008538733330570461, 0.024647645229984888, 0.04331957200840641, 0.047740432894790664, 0.03894928545925166, 0.018643614446380925, -0.010959353930176942, -0.04727623331495935, -0.087514564213195, -0.12883004617777763, -0.16848280965296855, -0.20397517295485804, -0.23316680941169549, -0.25437533908497983, -0.2664454090598969, -0.2687934007614177, -0.26141472091664636, -0.2448652717226137, -0.2202129049311853, -0.18897685942659637, -0.15302714251651067, -0.11447216443733044, -0.07554690821011993, -0.038493241369963786, -0.005426321280658572, 0.021772057920618784, 0.04154914958748194, 0.05277483337376061, 0.05479706799916744, 0.04746763385821503, 0.031154010720426506, 0.00672809362247599, -0.024493231923687093, -0.06082057848427097, -0.1002847613470788, -0.14073663962158817, -0.17997028902955634, -0.21585409640020212, -0.24645739965857943, -0.27013825268545416, -0.2856474445623871, -0.2922267524557628, -0.28963941654380654, -0.27817044096148724, -0.2586363397952287, -0.23234398778587648, -0.20098750918331465, -0.16654250840281828, -0.1311537038230126, -0.09696655531919589, -0.0659607599217182, -0.039794542064772134, -0.019644305084454704, -0.006055662545915018, 0.0011703483364080538, 0.003059721382037388, 0.001509034552655729, -0.0007223932535190609, -7.131340059142624e-05, 0.007715668671361701, 0.027413941749527635, 0.06410279724111657, 0.12290031658783318, 0.20866188896565785, 0.3256519721796955, 0.4772054356860555, 0.6653881278631912, 0.8906658900219014, 1.15161567620455, 1.4447097165927243, 1.7641100029426215, 2.1015514790644465, 2.4464031117752665, 2.7857423464528552, 3.104468058242307, 3.3856635059000895, 3.6111241994625924, 3.761674415954865, 3.8177138015001137, 3.7601578844509875, 3.57100526044585, 3.2338603650814437, 2.7348717809960545, 2.0636625835918396, 1.2135731737334143, 0.1822406583426744, -1.027487040216949, -2.407522147656285, -3.9445804137982323, -5.619852979739774, -7.40905959367042, -9.283242018849252, -11.209187894144046, -13.14983521404408, -15.065446069972237, -16.914734206029294, -18.655784854175323, -20.247309534711633, -21.649967403454248, -22.827625260643746, -23.748636156235797, -24.386871159272175, -24.72258014920232, -24.74355946397425, -24.445785271405676, -23.833420251782524, -22.919040472639, -21.724088966190735, -20.277954869015424, -18.617114114750976, -16.78467224363384, -14.829268704554911, -12.803247206650695, -10.761293201605268, -8.759166482587943, -6.851667371675256, -5.090873566221292, -3.5247510912067876, -2.195541495481786, -1.138265275683028, -0.37964493624615026, 0.06275650530302693, 0.18123918404030234, -0.021761255072100597, -0.5337156871324802, -1.3323412885896906, -2.386291272550188, -3.656154078710294, -5.095728241053249, -6.653489667779663, -8.27425183835812, -9.901059450193594, -11.47700593169, -12.947009760045681, -14.259745654317122, -15.369344180998068, -16.236646704085793, -16.83053587088682, -17.129268408342078, -17.12053686251852, -16.801793130054783, -16.180697086153863, -15.2747635788544, -14.109681061772914, -12.718864536355971, -11.142813205172903, -9.427102052371051, -7.6199035716507835, -5.771228610714718, -3.9314547145399885, -2.1491795672006866, -0.4687812258244943, 1.0700682132601436, 2.4333762562479846, 3.5940519041445818, 4.533641853554225, 5.241729878839667, 5.7155375122094725, 5.960037940208437, 5.988522504884549, 5.8206075219584115, 5.480875405756182, 4.998174874629011, 4.404982019432614, 3.735017920112831, 3.0217555590726435, 2.2974414358238784, 1.5922073237681518, 0.9324292841343821, 0.33983944100492175, -0.16895603980896, -0.5825997546585605, -0.8953969288355065, -1.1072033444725744, -1.2228936133818977, -1.251604617409213, -1.2060906148277462, -1.1017438624433202, -0.9554603101852098, -0.7845279914014921, -0.6055983475434116, -0.43363630988470386, -0.28101344619372176, -0.15678113172167557, -0.06613357043218164, -0.010092332099393558, 0.014565473819265993, 0.015136311770965251, 0.002586930811926498, -0.009061061122855416, -0.003530136330080895, 0.0367755721304573, 0.12973353603555812, 0.2924252124916901, 0.5400870593518685, 0.885100131117432, 1.3360877994108054, 1.8972684940011428, 2.567906752396025, 3.3419763909609674, 4.208213191743024, 5.150414641759792, 6.147686042475509, 7.175220455593698, 8.205541228203819, 9.209212755495027, 10.155807352282626, 11.015751768819456, 11.761543254449379, 12.368281648515445, 12.814928477208198, 13.086175530684308, 13.172249652845597, 13.069058825203626, 12.779178002450955, 12.311967065025641, 11.682315842465526, 10.910247965307985, 10.020763856229731, 9.042306009565086, 8.005268868288534, 6.941217763095856, 5.881456112764567, 4.855548217943574, 3.890178323270249, 3.0082730621129383, 2.2278500264484484, 1.5615020047619086, 1.0160987067885037, 0.5925805797353602, 0.2861288265361567, 0.08670284084361411, -0.020282067704570663, -0.05306632956356588, -0.03243243698492369, 0.01948606851476169, 0.08044966241536274, 0.12935996569910868, 0.14742228856588047, 0.1191767922268886, 0.033353867352461625, -0.11650388510286695, -0.3316853483093085, -0.6082250173810716, -0.9370920801072726, -1.3046808805327952, -1.6935614018628906, -2.0833921692495054, -2.452024487826436, -2.7768107963547854, -3.0358246822124575, -3.209118301057118, -3.2799705230427945, -3.2359338593895446, -3.0696024438023497, -2.779311710663321, -2.3694807599816827, -1.8505516271961673, -1.238785664115111, -0.5557159700340444, 0.1728103031240893, 0.9175977968101674, 1.6473134942072913, 2.3301684952810513, 2.9351748841251615, 3.433403024198259, 3.7996859303742965, 4.013938325298622, 4.061731748402239, 3.9351666456380947, 3.6338288439426885, 3.164486900298837, 2.5407386252394715, 1.7829806100665768, 0.9174828263555184, -0.025015933003186254, -1.0104215651792063, -2.0024754858023037, -2.9646554059266776, -3.8617442828350788, -4.6611161263836856, -5.334208124752764, -5.857758128580336, -6.2147898585916685, -6.395231414678274, -6.396205348224221, -6.22201351898112, -5.8840401233971065, -5.3999881020248965, -4.792856431325713, -4.0898898710066955, -3.3214214967966655, -2.519264287939456, -1.7152366000402373, -0.9398010659725248, -0.22073977036034784, 0.4180675716333564, 0.9575955647461911, 1.3843843656857338, 1.6909484962917516, 1.875878366440801, 1.9436631658282335, 1.9042329916499785, 1.772256321914247, 1.5661569102611355, 1.30701418562067, 1.0174211804081061, 0.7202512247000838, 0.43736555244621456, 0.18857359484109792, -0.009321412168994552, -0.14337283444820675, -0.20501666677999766, -0.19033963689929298, -0.10018040757157347, 0.06013099594210252, 0.2812269247831662, 0.5502599097725069, 0.8518315278911441, 1.1690043504759804, 1.484091348877393, 1.77968210067509, 2.039927453682029, 2.2511099250761233, 2.4022032570602994, 2.485784685023733, 2.4982892054067385, 2.439805209709684, 2.3141123673010617, 2.1286774382189044, 1.893705950478779, 1.6215054443165386, 1.3260473886313355, 1.021953152700378, 0.7234794126965916, 0.44390711282164436, 0.19489780352372402, -0.014313274250407544, -0.17729200909033932, -0.29057173165554456, -0.35380479221777567, -0.369638044253671, -0.3433739593159874, -0.28253803800010346, -0.19628402631378286, -0.09470257520684024, 0.011868296412524607, 0.11356619960037567, 0.2016888714747101, 0.26925898437092377, 0.3114684586545407, 0.3259923923009913, 0.3131148864001596, 0.2756730084573851, 0.21883154478842837, 0.149697766958149, 0.07680295794035902, 0.00948043764992344, -0.04281799878459726, -0.0712313982754078, -0.06814896600377572, -0.02780711395395695, 0.05320005765852518, 0.17559328402320476, 0.3372663317828561, 0.5332358169032159, 0.7558156646693869, 0.9951340831173956, 1.2395540104757647, 1.4762178397387253, 1.691957706352328, 1.8741549788887826, 2.0112525598374993, 2.093518412539622, 2.113979110605618, 2.0686564977058937, 1.9567359354023295, 1.7810065407155258, 1.5477194323864878, 1.2660813455134206, 0.9478914313554555, 0.6071250658264832, 0.25887058000128527, -0.0814906130886815, -0.39896094742773525, -0.6799000521860117, -0.9128868933937673, -1.0892996264407895, -1.2037895756703638, -1.2546551641028174, -1.2438875336771469, -1.1770586391324764, -1.062963499409472, -0.9130247861539075, -0.7405802468607207, -0.560069463509075, -0.3860473888352725, -0.23222941921723694, -0.11060493660013677, -0.03060112554992198, 0.0016025277166992196, -0.01645087799313301, -0.0832351764078083, -0.1932218379692699, -0.3371158311010333, -0.5023441711300586, -0.6737429049187111, -0.8344112464646193, -0.9667454568110285, -1.053540238420171, -1.0790342411235632, -1.0299038791554909, -0.8962715739976613, -0.6724308983410299, -0.3573610329417697, 0.045137335114758474, 0.526360958514163, 1.0728858564431438, 1.6671251409546863, 2.2885827453749576, 2.914508971075842, 3.5207567874775947, 4.083262950459091, 4.579862016770948, 4.9907253257151725, 5.299230457743183, 5.493316095711573, 5.566389835675202, 5.516934278482724, 5.348707474272279, 5.0706271457086185, 4.696541498677274, 4.243989874101571, 3.733304227200996, 3.186360468598464, 2.6258537816089103, 2.073817024388245, 1.550269246718426, 1.0723144874005721, 0.6537153714984528, 0.3040217629053378, 0.028178622820079064, -0.17331821280279036, -0.30403417455402715, -0.37123748677688273, -0.3851200787216247, -0.3578465609442892, -0.3025472065725471, -0.23230576821044133, -0.15917351152174197, -0.09331427008904274, -0.042317441062708364, -0.010754334911030936, 8.248633258521885e-07, -0.008332472476389723, -0.0313192079911552, -0.0624360191637057, -0.09392031964435565, -0.11775217946556278, -0.12670687355636234, -0.11542403887236045, -0.08136942659998884, -0.025604122489731273, 0.0466555117453215, 0.12581558795783815, 0.19803204687148987, 0.24564736451595343, 0.2480781366511439, 0.18303637152324811, 0.02786191712096333, -0.2388349647205025, -0.6352212610391907, -1.174701949248129, -1.864400015513431, -2.7035238707573805, -3.6824481691353497, -4.78237201530485, -5.975064777449017, -7.2231397859619495, -8.481680381880556, -9.699703965662499, -10.821963902045814, -11.791619662460329, -12.553603620542187, -13.057184767990837, -13.258810479585064, -13.124917278158355, -12.63504393370939, -11.78346911580955, -10.580179108088624, -9.051455125344155, -7.24060443813392, -5.206376192515099, -3.0205559458176965, -0.765598826027264, 1.4679690956151692, 3.5861148470734534, 5.495600521143646, 7.108132217031351, 8.344514143903814, 9.138826847458219, 9.441898715227792, 9.224332039135463, 8.478326524728432, 7.218578994376818, 5.482353417536723, 3.3284690741286926, 0.8350690594683186, -1.9035185108651203, -4.780817087267192, -7.682566213524148, -10.491666426191125, -13.093648939447466, -15.381752637426251, -17.261205995999017, -18.653946010482667, -19.502390457445998, -19.77117113122355, -19.448691554522387, -18.548328414016154, -17.106950790646728, -15.1827452879595, -12.85282169661749, -10.209389088898188, -7.355059407077479, -4.398522329908068, -1.4490137859691024, 1.3887797515325697, 4.018418804120998, 6.3559353224387865, 8.33457504568187, 9.90586084918528, 11.04048479328179, 11.730277528290445, 11.987159400588023, 11.840572840633623, 11.335582087548316, 10.530736225466216, 9.492895038919926, 8.293738158110623, 7.0066174623609125, 5.702026541411626, 4.443760419613646, 3.286731912396692, 2.2746966890391236, 1.4382310577268118, 0.7943347896639994, 0.34685093028235303, 0.0871534873134325, -0.004204185925079525, 0.044779094911362935, 0.2000946198881635, 0.4245075509736591, 0.6803974887961654, 0.9324378525094774, 1.1499681691391226, 1.3089026296953918, 1.3930952815241788, 1.3951012221415708, 1.3162839252797918, 1.166264995513502, 0.961796397264808, 0.7252224765145885, 0.48258157515939254, 0.26137479129987196, 0.08836502041594284, -0.012454746285421323, -0.021805203520225764, 0.07333998704537745, 0.2787742112358103, 0.5924096031882485, 1.004354175968875, 1.4976217263099474, 2.0489148087734512, 2.6300352224443087, 3.210306026060255, 3.758082913758356, 4.242409092128576, 4.6356869465510595, 4.915606575635377, 5.0656450417285255, 5.076300936374677, 4.946611546032596, 4.683262060045755, 4.299764903229458, 3.8164473437314217, 3.2588730548848894, 2.655615757371558, 2.036754179204105, 1.432460943223312, 0.8704802869462889, 0.37459074791490643, -0.03636931174249965, -0.3497014386958557, -0.5595085266984827, -0.6666203822087451, -0.6781746953044275, -0.606911859182171, -0.469968984151778, -0.2874757283651811, -0.08096118789206223, 0.12829136404921804, 0.3207887949829582, 0.4801816989942209, 0.5943702940528427, 0.6562383714760129, 0.66399945031681, 0.6211059324180292, 0.5357559506231624, 0.42004767250448055, 0.28883550500048594, 0.15839533752823803, 0.044977764361389096, -0.036636347459122906, -0.0744013781475678, -0.060083752406128864, 0.009966256974385166, 0.13447943658122236, 0.30725661763119855, 0.5175557361257977, 0.7510638054749932, 0.9909311216579523, 1.2189806476195202, 1.4174292356142062, 1.57046225129468, 1.665265149910449, 1.6932551227614199, 1.6513805218474669, 1.542087877509216, 1.3731660920746704, 1.157670569888716, 0.9128983234928, 0.6586888418336765, 0.41595500547068076, 0.2050008405327245, 0.04330393858488779, -0.05627082327102345, -0.08699977729111681, -0.04965509872732253, 0.04674781415047456, 0.18477204311329393, 0.33890202221927396, 0.4766678863099352, 0.5603061943532494, 0.5489034753164992, 0.40105118988080396, 0.07767244442887646, -0.45505367941129043, -1.2227113079427947, -2.2401988770459162, -3.5097271374720767, -5.019240404772735, -6.74177878328332, -8.635745557024658, -10.645954628323146, -12.705606975309816, -14.73895309165866, -16.664661585767583, -18.400174025060476, -19.865549129961355, -20.987420567146135, -21.703665102146385, -21.96734922778952, -21.74851737322084, -21.036935206591494, -19.84498376585476, -18.206272840705253, -16.173314704639388, -13.81670269315628, -11.222766808904451, -8.489477699482475, -5.721610416806794, -3.0273494220761505, -0.5100974881873173, 1.7370223926546366, 3.6338537041912975, 5.109986669486841, 6.10755832598956, 6.593074725982371, 6.5870193519342966, 6.147945795384928], 'positive_zeros': ['0.30756409850774223763801239453450', '0.42413395749772455274837422692366', '0.886400232129827975270809937563225', '0.906466657829368194829004203528487', '1.48067011290612511771299881607392', '1.94350289049325870690326625844528', '2.03517129900038830552400863631676', '2.15747981870927512825627649338780', '2.81903040785615204719242386130041', '3.03545281018653425015010432193778', '3.11513369561883381117652777911908', '3.38644900683686448087483849214959', '3.48974485349875266942384588890820', '3.81978956970797143014292453670720', '3.86159283610387424878072357514023', '3.88213181764830998779885012307909', '4.27969491777478197153508710565343', '4.80175427095701691665028359665099', '4.83307560397835179015911295749090', '5.24844455528242366318362507124391', '5.51729803949494835402234875944498', '5.74641588553499152978448185380295', '5.78874488615390138911736700483091', '5.81770730118823792209960382212351', '6.42678925123111045839744781713952', '6.46970384457129304480787626609339', '6.55173604467279648812718274706562', '6.83739686069532076087261023371189', '7.06016884170994924218344135033974', '7.35835026700612823992992631628488', '7.57243656020601968112317128772179', '7.64165110684621411007787017807163', '7.967639024153905349997496959774426', '8.098945785953584557232524388252865', '8.264028146279698432072309563706977', '8.326245415288009483907919566971055', '8.639004449561982595693620584998308', '8.889444125944267271269828086112854', '8.897902475963633773742409429375268', '9.109821530638101370651880401486497'], 'prelabel': '8-1792e4-1.1-c3e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 10.282578603166, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e4-0', 'trace_hash': 1415799278182342007, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.30756409850774223763801239453', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.42413395749772455274837422692', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.886400232129827975270809937563', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 124973031.45786545, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 10312216477696, 'conductor_radical': 14, 'degree': 8, 'dirichlet_coefficients': [1, 0, 6, 0, -14, 0, -28, 0, -32, 0, 56, 0, 46, 0, -84, 0, 136, 0, 58, 0, -168, 0, -36, 0, -120, 0, -298, 0, -244, 0, 80, 0, 336, 0, 392, 0, 116, 0, 276, 0, -376, 0, -608, 0, 448, 0, 504, 0, 490, 0, 816, 0, -88, 0, -784, 0, 348, 0, -38, 0, 130, 0, 896, 0, -644, 0, 1668, 0, -216, 0, -408, 0, 576, 0, -720, 0, -1568, 0, 472, 0, 98, 0, 2058, 0, -1904, 0, -1464, 0, -344, 0, -1288, 0, 480, 0, -812, 0, 192, 0, -1792, 0], 'euler11': [1, -56, 2780, -130424, 5262166, -173594344, 4924939580, -132045070696, 3138428376721], 'euler13': [1, -46, 5180, -228570, 16614646, -502168290, 25002870620, -487806971158, 23298085122481], 'euler17': [1, -136, 22076, -1854904, 168489670, -9113143352, 532860973244, -16127951203592, 582622237229761], 'euler19': [1, -58, 21284, -1222770, 200115766, -8386979430, 1001324531204, -18715886471182, 2213314919066161], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 36, 11068, -2483404, -109072922, -30215576468, 1638461219452, 64841495812668, 21914624432020321], 'euler29': [1, 244, 98020, 16054732, 3637039542, 391558858748, 58304581924420, 3539743618112036, 353814783205469041], 'euler3': [1, -6, 68, -302, 2102, -8154, 49572, -118098, 531441], 'euler31': [1, -80, 98108, -6698256, 4121040902, -199547744496, 87071211135548, -2115169772853680, 787662783788549761], 'euler37': [1, -116, 112292, -16931052, 7096842646, -857608576956, 288110549919428, -15075561816228932, 6582952005840035281], 'euler41': [1, 376, 212316, 51001224, 18244997158, 3515055359304, 1008523132032156, 123095607332129336, 22563490300366186081], 'euler43': [1, 608, 332604, 113978720, 38738414102, 9062106091040, 2102510635549596, 305576308057600544, 39959630797262576401], 'euler47': [1, -504, 371452, -143870104, 56727343558, -14937025807592, 4003961092387708, -564041758443794568, 116191483108948578241], 'euler5': [1, 14, 316, 2250, 39446, 281250, 4937500, 27343750, 244140625], 'euler53': [1, 88, 35956, -40062488, 10958668662, -5964383025976, 796941768754324, 290379196078587704, 491258904256726154641], 'euler59': [1, 38, 123316, 6020190, 81607069814, 1236420602010, 5201534686473556, 329193841108887682, 1779197418239532716881], 'euler61': [1, -130, 528540, 57273642, 122928435190, 13000028534802, 27230578664762940, -1520238992068438330, 2654348974297586158321], 'euler67': [1, -1668, 1986284, -1562559876, 1003433820182, -469960195985388, 179676037168169996, -45380499373019971596, 8182718904632857144561], 'euler7': [1, 28, 294, 1372, 2401, 0, 0, 0, 0], 'euler71': [1, 408, 545308, -167809544, 48366937318, -60060881702584, 69854109624392668, 18706188293127204648, 16409682740640811134241], 'euler73': [1, -576, 1219532, -601885056, 666382613702, -234143518829952, 184556931654676748, -33910033943962317888, 22902048046490258711521], 'euler79': [1, -472, 994172, -344402424, 659437576006, -169803826726536, 241670741830223612, -56569953303795846568, 59091511031674153381441], 'euler83': [1, -2058, 1798900, -411223106, -157636635434, -235132026110422, 588133037653494100, -384723045340598149374, 106890007738661124410161], 'euler89': [1, 344, 881148, 629036712, 820148016934, 443451381821928, 437914070567703228, 120522602875374911896, 246990403565262140303521], 'euler97': [1, -192, 3197100, -518194304, 4172546665638, -472941950014592, 2663094796958505900, -145964363261676521664, 693842360995438000295041], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -6, 68, -302, 2102, -8154, 49572, -118098, 531441], [1, 14, 316, 2250, 39446, 281250, 4937500, 27343750, 244140625], [1, 28, 294, 1372, 2401, 0, 0, 0, 0], [1, -56, 2780, -130424, 5262166, -173594344, 4924939580, -132045070696, 3138428376721], [1, -46, 5180, -228570, 16614646, -502168290, 25002870620, -487806971158, 23298085122481], [1, -136, 22076, -1854904, 168489670, -9113143352, 532860973244, -16127951203592, 582622237229761], [1, -58, 21284, -1222770, 200115766, -8386979430, 1001324531204, -18715886471182, 2213314919066161], [1, 36, 11068, -2483404, -109072922, -30215576468, 1638461219452, 64841495812668, 21914624432020321], [1, 244, 98020, 16054732, 3637039542, 391558858748, 58304581924420, 3539743618112036, 353814783205469041], [1, -80, 98108, -6698256, 4121040902, -199547744496, 87071211135548, -2115169772853680, 787662783788549761], [1, -116, 112292, -16931052, 7096842646, -857608576956, 288110549919428, -15075561816228932, 6582952005840035281], [1, 376, 212316, 51001224, 18244997158, 3515055359304, 1008523132032156, 123095607332129336, 22563490300366186081], [1, 608, 332604, 113978720, 38738414102, 9062106091040, 2102510635549596, 305576308057600544, 39959630797262576401], [1, -504, 371452, -143870104, 56727343558, -14937025807592, 4003961092387708, -564041758443794568, 116191483108948578241], [1, 88, 35956, -40062488, 10958668662, -5964383025976, 796941768754324, 290379196078587704, 491258904256726154641], [1, 38, 123316, 6020190, 81607069814, 1236420602010, 5201534686473556, 329193841108887682, 1779197418239532716881], [1, -130, 528540, 57273642, 122928435190, 13000028534802, 27230578664762940, -1520238992068438330, 2654348974297586158321], [1, -1668, 1986284, -1562559876, 1003433820182, -469960195985388, 179676037168169996, -45380499373019971596, 8182718904632857144561], [1, 408, 545308, -167809544, 48366937318, -60060881702584, 69854109624392668, 18706188293127204648, 16409682740640811134241], [1, -576, 1219532, -601885056, 666382613702, -234143518829952, 184556931654676748, -33910033943962317888, 22902048046490258711521], [1, -472, 994172, -344402424, 659437576006, -169803826726536, 241670741830223612, -56569953303795846568, 59091511031674153381441], [1, -2058, 1798900, -411223106, -157636635434, -235132026110422, 588133037653494100, -384723045340598149374, 106890007738661124410161], [1, 344, 881148, 629036712, 820148016934, 443451381821928, 437914070567703228, 120522602875374911896, 246990403565262140303521], [1, -192, 3197100, -518194304, 4172546665638, -472941950014592, 2663094796958505900, -145964363261676521664, 693842360995438000295041]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1792/4/a/m'], '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': '8-1792e4-1.1-c3e4-0-1', 'motivic_weight': 3, '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': [3, 3, 3, 3], 'order_of_vanishing': 0, 'prelabel': '8-1792e4-1.1-c3e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 10.282578603166, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e4-0', 'trace_hash': 1415799278182342007, 'z1': {'__RealLiteral__': 0, 'data': '0.30756409850774223763801239453', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '389883814081993722311464073085,537653665799164867200342067519,1123645786301818305214356809412,1149083002884275632589017633830', 'Lhash_array': ['389883814081993722311464073085', '537653665799164867200342067519', '1123645786301818305214356809412', '1149083002884275632589017633830'], 'label': '8-1792e4-1.1-c3e4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1792/4/a/m'}