-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1431524418486397470340671501251,1446090985835846199039493212949,2076838455855885809259793597576,2292445085240298529669560170595', 'a10': -12, 'a2': 2, 'a3': 0, 'a4': -3, 'a5': -6, 'a6': 0, 'a7': 14, 'a8': 4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64860626.53160265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': '1.1.1.1', 'conductor': 5352009260481, 'conductor_radical': 39, 'degree': 8, 'euler_factors': [[1, -2, 7, -24, 62, -192, 448, -1024, 4096], [1], [1, 6, 297, 2094, 49084, 261750, 4640625, 11718750, 244140625], [1, -14, 249, -1754, 141728, -601622, 29294601, -564950498, 13841287201], [1, -40, 4068, -116616, 7313302, -155215896, 7206710148, -94317907640, 3138428376721], [1], [1, 98, 12397, 986190, 96109736, 4845151470, 299233442893, 11621611896706, 582622237229761], [1, 124, 21504, 1798684, 202620494, 12337173556, 1011674625024, 40013274524596, 2213314919066161], [1, 104, 41844, 3340584, 719588614, 40644885528, 6194413739316, 187319876792152, 21914624432020321], [1, 194, 64761, 7214754, 1694674348, 175960635306, 38521353091281, 2814386319318586, 353814783205469041], [1, 26, 38189, -5395494, 828557428, -160737161754, 33892878073709, 687430176177446, 787662783788549761], [1, 102, 193281, 14822902, 14476248876, 750824455006, 495906166057929, 13256097459097854, 6582952005840035281], [1, 1054, 633469, 261177138, 78839658968, 18000589528098, 3009043783442029, 345060558851234894, 22563490300366186081], [1, -450, 276753, -75560470, 29002070616, -6007586288290, 1749456187899897, -226166675371579350, 39959630797262576401], [1, 96, -19308, 124896, 17303792422, 12967077408, -208125089572332, 107436525417865632, 116191483108948578241], [1, 262, 483789, 119532570, 100466115904, 17795650423890, 10722874106237781, 864538061052158846, 491258904256726154641], [1, -308, 557680, -98956308, 142593856142, -20323547580732, 23523240000912880, -2668202712145721212, 1779197418239532716881], [1, 928, 1041074, 583837824, 364336742755, 132520093129344, 53636522217503714, 10852167574150082848, 2654348974297586158321], [1, -1134, 1218801, -918506522, 562458950376, -276252777076286, 110250766645959369, -30852210005398469898, 8182718904632857144561], [1, -1064, 1201044, -690200040, 504474394630, -247030186516440, 153854077401613524, -48782804764429768984, 16409682740640811134241], [1, 952, 768042, 239296336, 174760946603, 93090342741712, 116231041827456138, 56045750546271053176, 22902048046490258711521], [1, 746, 2156493, 1122200666, 1640976331028, 553288694163974, 524216396218847853, 89409290603033265974, 59091511031674153381441], [1, 404, 1811392, 594579060, 1476544322126, 339972576980220, 592217176797619648, 75523863128086322812, 106890007738661124410161], [1, -1620, 2005896, -1665077532, 1565610279790, -1173828042656508, 996892783613506056, -567577374006126038580, 246990403565262140303521], [1, 2166, 4160745, 5948172454, 5928410141748, 5428736398109542, 3465784104648312105, 1646660473045788260022, 693842360995438000295041], [1, 3002, 5074609, 6286121178, 6844040256812, 6476596935814578, 5386799709921190009, 3283243188598451424802, 1126825030131969720661201], [1, 862, 2191793, 1147591746, 2397433620016, 1254004485831342, 2617115465166186497, 1124714484460808830546, 1425760886846178945447841], [1, 192, 3630660, 1105020096, 5891336887894, 1353697133464128, 5448641659244090340, 352984168784669665344, 2252191588960823337718801], [1, -1442, 5497761, -5315187338, 10779693557660, -6883321743142802, 9220295582477327001, -3131870108955810138938, 2812664781782894485727281], [1, 1566, 3359145, 3543557622, 6182523556564, 5112988662110934, 6993577820017759305, 4704329674883364115518, 4334523100191686738306881]], 'euler_factors_factorization': [[[[1, -2, 7, -24, 62, -192, 448, -1024, 4096], 1]], [1], [[[1, 6, 297, 2094, 49084, 261750, 4640625, 11718750, 244140625], 1]], [[[1, -14, 249, -1754, 141728, -601622, 29294601, -564950498, 13841287201], 1]], [[[1, -40, 4068, -116616, 7313302, -155215896, 7206710148, -94317907640, 3138428376721], 1]], [1], [[[1, 98, 12397, 986190, 96109736, 4845151470, 299233442893, 11621611896706, 582622237229761], 1]], [[[1, 124, 21504, 1798684, 202620494, 12337173556, 1011674625024, 40013274524596, 2213314919066161], 1]], [[[1, 104, 41844, 3340584, 719588614, 40644885528, 6194413739316, 187319876792152, 21914624432020321], 1]], [[[1, 194, 64761, 7214754, 1694674348, 175960635306, 38521353091281, 2814386319318586, 353814783205469041], 1]], [[[1, 26, 38189, -5395494, 828557428, -160737161754, 33892878073709, 687430176177446, 787662783788549761], 1]], [[[1, 102, 193281, 14822902, 14476248876, 750824455006, 495906166057929, 13256097459097854, 6582952005840035281], 1]], [[[1, 1054, 633469, 261177138, 78839658968, 18000589528098, 3009043783442029, 345060558851234894, 22563490300366186081], 1]], [[[1, -450, 276753, -75560470, 29002070616, -6007586288290, 1749456187899897, -226166675371579350, 39959630797262576401], 1]], [[[1, 96, -19308, 124896, 17303792422, 12967077408, -208125089572332, 107436525417865632, 116191483108948578241], 1]], [[[1, 262, 483789, 119532570, 100466115904, 17795650423890, 10722874106237781, 864538061052158846, 491258904256726154641], 1]], [[[1, -308, 557680, -98956308, 142593856142, -20323547580732, 23523240000912880, -2668202712145721212, 1779197418239532716881], 1]], [[[1, 928, 1041074, 583837824, 364336742755, 132520093129344, 53636522217503714, 10852167574150082848, 2654348974297586158321], 1]], [[[1, -1134, 1218801, -918506522, 562458950376, -276252777076286, 110250766645959369, -30852210005398469898, 8182718904632857144561], 1]], [[[1, -1064, 1201044, -690200040, 504474394630, -247030186516440, 153854077401613524, -48782804764429768984, 16409682740640811134241], 1]], [[[1, 952, 768042, 239296336, 174760946603, 93090342741712, 116231041827456138, 56045750546271053176, 22902048046490258711521], 1]], [[[1, 746, 2156493, 1122200666, 1640976331028, 553288694163974, 524216396218847853, 89409290603033265974, 59091511031674153381441], 1]], [[[1, 404, 1811392, 594579060, 1476544322126, 339972576980220, 592217176797619648, 75523863128086322812, 106890007738661124410161], 1]], [[[1, -1620, 2005896, -1665077532, 1565610279790, -1173828042656508, 996892783613506056, -567577374006126038580, 246990403565262140303521], 1]], [[[1, 2166, 4160745, 5948172454, 5928410141748, 5428736398109542, 3465784104648312105, 1646660473045788260022, 693842360995438000295041], 1]], [[[1, 3002, 5074609, 6286121178, 6844040256812, 6476596935814578, 5386799709921190009, 3283243188598451424802, 1126825030131969720661201], 1]], [[[1, 862, 2191793, 1147591746, 2397433620016, 1254004485831342, 2617115465166186497, 1124714484460808830546, 1425760886846178945447841], 1]], [[[1, 192, 3630660, 1105020096, 5891336887894, 1353697133464128, 5448641659244090340, 352984168784669665344, 2252191588960823337718801], 1]], [[[1, -1442, 5497761, -5315187338, 10779693557660, -6883321743142802, 9220295582477327001, -3131870108955810138938, 2812664781782894485727281], 1]], [[[1, 1566, 3359145, 3543557622, 6182523556564, 5112988662110934, 6993577820017759305, 4704329674883364115518, 4334523100191686738306881], 1]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 6, 'label': '8-39e8-1.1-c3e4-0-6', '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': 4, 'origin': 'ModularForm/GL2/Q/holomorphic/1521/4/a/bb', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0126953125', 'prec': 40}, 'plot_values': [1.2040947935075963e-240, 1.2598244195972732e-05, 0.00020125105013144424, 0.0010161303754785812, 0.003199541157561408, 0.0077740470744784166, 0.016026084564339103, 0.02948522831697005, 0.04989932346926815, 0.07920585298247315, 0.11950020391364004, 0.1730005846065932, 0.2420101718153678, 0.328877387260115, 0.4359558572537841, 0.5655615128620445, 0.7199288779220568, 0.9011684152868665, 1.1112278998779936, 1.3518493302004841, 1.624527553866312, 1.9304740018944253, 2.2705904505341716, 2.64543277248788, 3.055179577652212, 3.499611217199816, 3.978106435908591, 4.489617728508466, 5.032655588429884, 5.605289620878827, 6.205176331577996, 6.829547267234314, 7.475211115883121, 8.13858037712786, 8.815734722868136, 9.502418813208404, 10.194060435556414, 10.885821950305031, 11.572698797845709, 12.249519721652243, 12.910975112724728, 13.551688083870676, 14.166342517137378, 14.749675303270152, 15.296505889234313, 15.801818131472261, 16.260907646261753, 16.669354411444917, 17.023042940307597, 17.318243781687112, 17.551766720642505, 17.72090323943086, 17.823427273342887, 17.85766493187835, 17.822639005234834, 17.717974476032836, 17.543872595006228, 17.30115933206897, 16.99140805851458, 16.616807143481946, 16.18010480677982, 15.684630783734221, 15.134387904851392, 14.53388787903344, 13.888070263693352, 13.202297202524038, 12.482410337012269, 11.734547837595201, 10.965046740085254, 10.180416368188078, 9.387363546578916, 8.592609275986694, 7.802788315815787, 7.024411798374708, 6.263869733833683, 5.527268054697411, 4.820341479533728, 4.1484186678822885, 3.516415140392081, 2.9287098378202714, 2.389086185452199, 1.9007130589321106, 1.4661424010410093, 1.0872388110050843, 0.7651592054621443, 0.5003595867650582, 0.2926093275587803, 0.14097840645371965, 0.04385878357932191, -0.0009990474213331941, 0.003551395610465329, 0.05409155877390259, 0.14669543528443296, 0.27699235156272933, 0.44022661895866183, 0.6313324360030569, 0.8450141197919507, 1.0758242789055437, 1.3182370123225773, 1.5667359920155255, 1.8158983214113147, 2.060472099409363, 2.295448714879526, 2.5161392934800344, 2.7182418976262395, 2.897901075824413, 3.0517626785820298, 3.1770175221447055, 3.271435289056518, 3.3333917662855366, 3.3618921586484682, 3.3565697240818686, 3.31767778845926, 3.246077642677333, 3.1432233333738777, 3.0111152332155604, 2.8522523085026528, 2.669583501743467, 2.4664568939449545, 2.2465406901865204, 2.0137486100392517, 1.772167530830169, 1.5259841406720394, 1.2793952740895782, 1.036527076134843, 0.8013588898720413, 0.577648023590975, 0.3688549307923903, 0.1780791897340419, 0.008001707567781548, -0.1391695930745526, -0.26173800588789814, -0.35854634502624505, -0.42899853197892, -0.47307463418307083, -0.4913212401756848, -0.4848351574811798, -0.4552407471387234, -0.40465783381625453, -0.3356475103890247, -0.2511557252217588, -0.15445143141499573, -0.04905350993491752, 0.061350222375118384, 0.17298207901786397, 0.2820578143375459, 0.3848810644650403, 0.47792348391607353, 0.5579005580530971, 0.6218504680573632, 0.6672216787214649, 0.6919228641115479, 0.6943687447036638, 0.6735279973847961, 0.6289754333561064, 0.5608901628740688, 0.4700525985456759, 0.35784291101416504, 0.22623826551114978, 0.07775339581543018, -0.08461518975265249, -0.2574437226669252, -0.4369418616763972, -0.6190562662649034, -0.799565364860047, -0.9741725446664371, -1.1386082752607032, -1.2887475903504486, -1.4207149204364993, -1.5309866445232638, -1.616501978292557, -1.6747557046828458, -1.7038771424001289, -1.7027059250199883, -1.6708720269664175, -1.6088288055702702, -1.517874539211761, -1.4001700199049651, -1.2587539738766251, -1.0974974379824425, -0.9210519189826216, -0.7347935125416952, -0.5447584104015233, -0.35752376879456055, -0.18008945094080847, -0.01975688405195424, 0.11600430049743295, 0.2197187791700625, 0.28405997402854166, 0.3020044438751705, 0.266996772075945, 0.17310800448418442, 0.01518027559137949, -0.211033605245944, -0.5087282818352882, -0.8799418199246588, -1.3254688913688502, -1.8447859122148085, -2.4359877625394333, -3.095774372666172, -3.8194557609585256, -4.600977179342815, -5.4329724221298505, -6.30684922356462, -7.212893322349895, -8.140400808946172, -9.077853464421858, -10.013077577002022, -10.933422268139564, -11.825972690372835, -12.677814474400089, -13.476212609379994, -14.208812684690493, -14.863880293038557, -15.430589648703462, -15.89915723551719, -16.261003004550652, -16.508948265608407, -16.637449107122936, -16.642629403946405, -16.522347676057766, -16.27629357265323, -15.90609618765149, -15.415231388395819, -14.808967691096829, -14.094329127685207, -13.280040637829483, -12.37632678143108, -11.394748566294261, -10.34804008444836, -9.249898802976952, -8.114732835236225, -6.957437625194953, -5.7931526149272425, -4.636949155251064, -3.5036074214351487, -2.407404320980492, -1.3618614389311872, -0.37941258991453763, 0.5287104346128865, 1.3526080421866016, 2.0839003045405944, 2.7159942203856717, 3.2440388068971924, 3.664927405077142, 3.977369480048249, 4.182031020823184, 4.281327590807471, 4.2792939928099365, 4.181528671586311, 3.995188875429531, 3.728669341574507, 3.391378289706282, 2.993585580779607, 2.546301994402892, 2.060927504176052, 1.549003484914506, 1.0220270171406858, 0.49127900029317517, -0.03246501341614221, -0.5391296399068239, -1.0194884598605778, -1.4653117157238476, -1.869521786874052, -2.2262781395090494, -2.5310358611484927, -2.7806110969676348, -2.9731768572674038, -3.1082206232197014, -3.1864956154292745, -3.2099837220182077, -3.181757962718942, -3.1058396928879044, -2.9870668822785578, -2.8309774387864066, -2.6436052023887697, -2.431296550960181, -2.2005502182978427, -1.957875276226903, -1.7096019131101032, -1.4617264650403141, -1.2197849847863664, -0.9887475353412146, -0.7729089498581524, -0.5758141053333056, -0.40021012903046865, -0.2480198421941928, -0.12033882320945995, -0.01745682956601264, 0.06110105521347405, 0.11651533016416099, 0.15058760397962667, 0.16564659307329077, 0.16444477948750347, 0.1500450598133248, 0.12570072762879203, 0.09473918686574881, 0.060447032656224364, 0.02595678679118713, -0.0058490178379528805, -0.032422735329484906, -0.051626574768527646, -0.06179318842601615, -0.06175709065524643, -0.050874805310155265, -0.02903004383423276, 0.0033857805112741395, 0.045510739999841676, 0.09605643428947523, 0.15336856520874526, 0.21551713580833973, 0.28037041742008434, 0.34567110506443494, 0.40912838823224157, 0.4685383326587837, 0.5218441304097482, 0.5671978995631878, 0.6030374815159963, 0.6281854381566143, 0.6418523457689026, 0.6436470672972576, 0.6336023657245923, 0.6122150627424935, 0.5803785798350364, 0.5393327060180342, 0.4906307660266719, 0.43611561158968015, 0.377804667779881, 0.3178032094141888, 0.25823784762724633, 0.20119700131365706, 0.14861776926728257, 0.10220771708733455, 0.06338839790388125, 0.033247290383260436, 0.012477263732359363, 0.0013495841311268097, -0.0002932883963463407, 0.0069653251553297504, 0.022134302669273485, 0.04385621899196017, 0.0704620470432224, 0.10003471587723967, 0.13049204954214463, 0.15967753675366647, 0.185453769488594, 0.20579818534622976, 0.21890306735030673, 0.22326740306608545, 0.21777966142922, 0.20179242573468878, 0.17518057150867367, 0.13838055111789965, 0.09241167202641444, 0.03887967025620246, -0.02004629685045447, -0.08167775768158624, -0.14287115721182025, -0.20011186714974363, -0.24961617536989625, -0.28744811000223847, -0.3096492931009809, -0.31237773485418746, -0.29204385418221684, -0.24544962499738893, -0.16992461932640895, -0.06344596966804206, 0.07525714027781777, 0.24660892433668866, 0.4501179232793008, 0.6843588578869757, 0.9469500814118589, 1.2345526001418088, 1.5429187528702655, 1.867027466411604, 2.201147476945892, 2.5389323526609684, 2.873586635732766, 3.19814462069125, 3.505567014056351, 3.7888809114902116, 4.0414065306270395, 4.257105478187815, 4.430622517916157, 4.557386804160584, 4.633808719752109, 4.657588488768169, 4.627621543700879, 4.5439853708915905, 4.408024869144773, 4.222526281537038, 3.991457030324199, 3.719811947399854, 3.413556480414884, 3.0796313035578624, 2.725574405789605, 2.3592702245643267, 1.9887905791287344, 1.6222751130901618, 1.2675483361306026, 0.9318711529514974, 0.6217747916789175, 0.34292223669204686, 0.0998510760310946, -0.10416160966858663, -0.26716715993448986, -0.38858987984183657, -0.46927081126404285, -0.5114224575381346, -0.518538479982805, -0.49528340964326556, -0.44732491561380106, -0.38112372233447683, -0.3037067092750408, -0.2224303345844708, -0.14469848139787622, -0.07768584328560689, -0.02807473254416703, -0.0018024390795306892, -0.003815458708863072, -0.03786487860497017, -0.10634083507127831, -0.2101428387584228, -0.34860322344258116, -0.5194661974644499, -0.7189197948194813, -0.9416824588961572, -1.1811430198950814, -1.4295489269783122, -1.6782443308877815, -1.9179616931922054, -2.1391120044406566, -2.332101706055657, -2.4876789698241524, -2.597304562286086, -2.653441805964435, -2.6498492508343388, -2.5818693396360954, -2.4466876855190645, -2.2434643227354973, -1.973451004111332, -1.6400664970606234, -1.2488777943710963, -0.8074931119502842, -0.3254342290825283, 0.1860669366440433, 0.7144203522256523, 1.2459714655026772, 1.7663180289310851, 2.260725966811276, 2.714719298069998, 3.1143907981550427, 3.4467450589283306, 3.7001516184872614, 3.864960124725348, 3.933618749278379, 3.9008495670129264, 3.763935130594735, 3.5231235725254892, 3.181413244903642, 2.7444345319792816, 2.2204381878722597, 1.6203449452902732, 0.9572056267844471, 0.2458033823871755, -0.4976451487775767, -1.2557772289876985, -2.010775911944123, -2.74488866781676, -3.4408578819163913, -4.082367577999487, -4.65462213657914, -5.144752211269583, -5.542149499825672, -5.838821553161633, -6.029623255590193, -6.11235509771327, -6.08781659233504, -5.959870729810732, -5.73524189100621, -5.423251012734423, -5.035541449709221, -4.5858108852747845, -4.0892857571852845, -3.56221204576345, -3.0213764255892404, -2.4836450452942285, -1.965372453047318, -1.481887598164267, -1.0470446513754101, -0.6728202974947048, -0.36893746436151686, -0.142588963626836, 0.0017545076087653244, 0.06245582082215569, 0.04071105675871363, -0.0595333630128136, -0.23174736535686252, -0.4670855830453071, -0.7547248755312157, -1.0822430256106208, -1.4360633218341845, -1.8019952383623512, -2.165689389880719, -2.5130955315018975, -2.8309612205333403, -3.1073935920708893, -3.3321490090629777, -3.496915024251976, -3.595613492818819, -3.624720201752331, -3.5831970425948403, -3.472441591130264, -3.2962533011274413, -3.0607773752515977, -2.774085581662392, -2.445822994373488, -2.0868820067998377, -1.7090400253097646, -1.3243946421367014, -0.9449092346175748, -0.5820020458568579, -0.2461124874123122, 0.05371365688845332, 0.3101163994988569, 0.5176633376213187, 0.6730870279191425, 0.7753277941406009, 0.8254877417181179, 0.8267486819967076, 0.7842675993400462, 0.7048273544553527, 0.5964692162565474, 0.4681261035416103, 0.32924234542133207, 0.18923285030965317, 0.05700267177215565, -0.05948532965085035, -0.1536196465133415, -0.22055711610795878, -0.25752753903093706, -0.26405318366094416, -0.24210050848886952, -0.19611906378705757, -0.1329655708859052, -0.061736674921134924, 0.006487271977194942, 0.05902604031518806, 0.0820512478955543, 0.06109513686402037, -0.018379999731893342, -0.1703743098830141, -0.4077487499417822, -0.741634540421067, -1.1808645994743068, -1.7314788096400302, -2.3963035637132535, -3.174623870642778, -4.061992070876911, -5.050126544740039, -6.126923676781805, -7.276632185809101, -8.48027000382957, -9.715968072613347, -10.959434001603947, -12.184618572283574, -13.364682551035502, -14.472556714475404, -15.481614740710622, -16.36655772722301, -17.10459071983459, -17.67579760512692, -18.06363637447698, -18.255635805731593, -18.244323470466018, -18.027057268521688, -17.606018343246546, -16.988395772238917, -16.18672812413038, -15.218083067570838, -14.103469097564677, -12.867444664414155, -11.53783926034471, -10.14450150992153, -8.718352877667808, -7.290660998734682, -5.892434494532198, -4.5531894281465926, -3.3000614307620677, -2.157163782402535, -1.1451241006869384, -0.28031800411475205, 0.42556950972819874, 0.9657246109212418, 1.3381362158518686, 1.5456845349656738, 1.595974962492987, 1.5009284341459088, 1.27608153353688, 0.9401362117574346, 0.5143516265128965, 0.02173182532708368, -0.5140626948364305, -1.069295321359165, -1.6208154606075087, -2.146876570600285, -2.6281650080181014, -3.048060399769214, -3.3929560209997094, -3.652698985797849, -3.821156290153638, -3.895913321177701, -3.878068718132261, -3.772138561105344, -3.5860214051496104, -3.3302294958021132, -3.0172822005767137, -2.6612209375251465, -2.2771638282864317, -1.880434844378423, -1.485905115700979, -1.1074721432084504, -0.7575957913660206, -0.4467408387212711, -0.18302907414227004, 0.027973357275820197, 0.1833874818626303, 0.28304413840604914, 0.32935917071897397, 0.32710894098076615, 0.28312876119491437, 0.20589633547408331, 0.10506261263369537, -0.00905359188278027, -0.1259989654597678, -0.23570011223193976, -0.3289475458732912, -0.39784695682936433, -0.43621896504152474, -0.4398450481126287, -0.40664800253843214, -0.33679266010344094, -0.23266351058790588, -0.09868407906334167, 0.05890999274459886, 0.2323861883041371, 0.4129784704550155, 0.5913447063532244, 0.7580239516462555, 0.9039567309033653, 1.0211179467569507, 1.1028925617106085, 1.144420507974059, 1.142968561429448, 1.0983401425261878, 1.0128400556131858, 0.8912253948600883, 0.7406645176867708, 0.5706650012984567, 0.3925549632031236, 0.21901450758089802, 0.06362842274043679, -0.05961412021988295, -0.13706905453009152, -0.15605992834469695, -0.10544209111224408, 0.023815922195996892, 0.2380872726259887, 0.5407106528762121, 0.9317060295540182, 1.4075387678521831, 1.9611251289035336, 2.5819818540588746, 3.2564677316604533, 3.9681185505270005, 4.698229408503191, 5.426494049721323, 6.131689703992473, 6.7924395363495655, 7.388039295129415, 7.899231947251241, 8.308949301662313, 8.603053276994062, 8.770905652195745, 8.805807594587769, 8.705332179330107, 8.47155968130468, 8.111029258144889, 7.634547468976197, 7.056859635658503, 6.396173597395107, 5.673507468876437, 4.911942940556336, 4.1357752799159675, 3.369560336137344, 2.63725363201797, 1.9613279936595291, 1.361875188116202, 0.8557436437163439, 0.4560051112960556, 0.17145196267997637, 0.006183980375021416, -0.040589383737116756, 0.025577847943736916, 0.19453482452061976, 0.45187376867418566, 0.7796247246783364, 1.156939788007209, 1.560799900824158, 1.966934377523905, 2.3511325913738292, 2.689985180728048, 2.9616482266856363, 3.1468203565504567, 3.2300383375939616, 3.1998767115653526, 3.049228028800704, 2.7757818477618783, 2.3826854464381086, 1.8778886093433842, 1.2736868469099498, 0.5864592913335603, -0.16353730581167855, -0.9534812475713926, -1.7589662314980057, -2.5547765598156635, -3.315666005113816, -4.0177065920523765, -4.639225822605488, -5.161534309245263, -5.569648472451937, -5.852990854114353, -6.005710637460189, -6.026827877865258, -5.920343435121573, -5.694961990239096, -5.363583038294688, -4.942705144070345, -4.4518069914001845, -3.9123335210482266, -3.3466587834041697, -2.777093598763086, -2.224948580233666, -1.7094570664616728, -1.246856059510452, -0.8496378342100984, -0.5259680846355079, -0.27924133642972626, -0.10787370165931502, -0.005325952197845124, 0.039647116027899505, 0.04252306686881422, 0.022344786519535937, 0.0008722669630971472, 0.0015846278106975437, 0.04858717010954707, 0.16545352900455518, 0.3740460567580858, 0.6934292637222443, 1.1388363078935635, 1.720715094526667, 2.443981097711984, 3.3077191963222172, 4.304804830685073, 5.421713905689292, 6.638773909573574, 7.931215446717404, 9.26953339452386, 10.62010929575245, 11.946460814307311, 13.211513139913771, 14.378172121502194, 15.410238927479197, 16.274064332368674, 16.94124660721557, 17.38858294477144, 17.598500724208883, 17.560273954234933, 17.27212277608971, 16.73994551891996, 15.976733909289486, 15.002771559233786, 13.846461928668132, 12.541914484108297, 11.127423019826223, 9.64468910667241, 8.13843559519979, 6.653629392693185, 5.233708609717393, 3.9194743324574848, 2.7482153215819793, 1.751649759275055, 0.9548006851077554, 0.37540056348505385, 0.02345630102194926, -0.09933006125289048, 0.0005302010159715968, 0.30874582685895197, 0.8038050700705102, 1.4578575174959774, 2.23790040808581, 3.1071022204208325, 4.026206206618695, 4.955077427968892, 5.854234158828193, 6.6863550155924285, 7.417794436505799, 8.019686514103467, 8.468892585673684, 8.748862777881866, 8.850440033210905, 8.77175104079889, 8.518022584419075, 8.101368005350633, 7.540503028952941, 6.8594308694265775, 6.086283295164086, 5.252267181294388, 4.390600309885119, 3.5347328068179324, 2.716954865198253, 1.9672431293600225, 1.3121985725699787, 0.773794782635468, 0.3686019863628481, 0.1072987412531358, -0.00564762115782445, 0.02791432066173481, 0.20008601411635818, 0.4974014858865648, 0.9014715277040305, 1.3899152172670415, 1.9374220180353066, 2.516872066044398, 3.100519544971944, 3.6612328549727406, 4.173622920399349, 4.6150679151611556, 4.966667804391306, 5.2139459343351096, 5.347318125456908, 5.362380129173482, 5.2600445160697005, 5.046281646534718, 4.731673683258729, 4.3308316430774045, 3.861695315760886, 3.3445552957018805, 2.801045266755062, 2.2531330447553013, 1.7221318854300534, 1.2277002569799167, 0.786969356716116, 0.41381354036791335, 0.11830250853682628, -0.09366628769444284, -0.22054499534668953, -0.26510072550342667, -0.23411540541883766, -0.13794769267001358, 0.01003986434930617, 0.1942244285280545, 0.3976798606152352, 0.60302228151385, 0.7932712114840019, 0.9527614558745471, 1.0681061951707655, 1.1287876070227723, 1.1276669051527022, 1.0614219808690903, 0.9308612881059732, 0.740809367301038, 0.4998967996904717, 0.22022387422404702, -0.08317712258831877, -0.39309078996110336, -0.6909018093157206, -0.9574613981172669, -1.1740797589951215, -1.3233889860726065, -1.3901573687890254, -1.36207411187365, -1.2304632872742636, -0.990682709493314, -0.642425723292031, -0.189867953045562, 0.358477930317834, 0.9900345158172531, 1.6885308731390534, 2.4346193094357185, 3.2069283516547467, 3.9826842883140836, 4.73842678857222, 5.4510141628055155, 6.099084945479598, 6.663402209693591, 7.127337845382135, 7.477665348022996, 7.705730902315905, 7.807036270295207, 7.781081330373969, 7.631534795739693, 7.366676467853425, 6.998227506624647, 6.540593772955623, 6.010460315364646, 5.426580871456914, 4.8083631117870285, 4.1749689823649625, 3.5447655300711407, 2.9349351677943196, 2.3604804450484274, 1.8337194937618106, 1.3640735060122824, 0.957985505950283, 0.6187211506296141, 0.3464987803992818, 0.13878736586608353, -0.009323213236228853, -0.10466977420788419, -0.1554642071929155, -0.17072742550285083, -0.15974216175527522, -0.13147551725820963, -0.0940915631957289, -0.05456620677710941, -0.018399964846763796, 0.010576683965296495, 0.03024304132971866, 0.040101297115320865, 0.041081635861334086, 0.03523016632168604, 0.025308892431034374, 0.014342532015405331, 0.0051344266990513655, -0.00022911741023780015, -0.0008334878484493813, 0.0026733144736932027, 0.0077741714435708275, 0.009894936244892266, 0.002350197269273821, -0.023572152089459886, -0.07838393203624164, -0.17402146132862373, -0.3233432478037956, -0.5395205486483433, -0.8353663588230612, -1.2225948164518454, -1.711051811902798, -2.3079816484118134, -3.01745894357895, -3.8397900082530185, -4.7710131436807925, -5.8026321437781485, -6.921804643340521, -8.111297968038604, -9.349635938554526, -10.611646947874824, -11.869689623626357, -13.094120843120123, -14.253991179889464, -15.318222637811935, -16.257521171962864, -17.04483053496297, -17.65602817675017, -18.071095031391348, -18.27590397965616, -18.26199921414976, -18.02666169946883, -17.57339526690264, -16.912826564613468, -16.061507737833015, -15.041096648152346, -13.877911996573511, -12.602727399700923, -11.248928575646715, -9.85114718696538, -8.444251751209663, -7.062506885858357, -5.737889278941343, -4.4989131143632966, -3.3697992632810427, -2.369831884418609, -1.5126045035232965, -0.8056892632272219, -0.25059757464549176, 0.15704782211917423, 0.42710551920273676, 0.5742756976135327, 0.6172849677765154, 0.5779188034126392, 0.47991091765041066, 0.3478152034119641, 0.2058631941857786, 0.0768359356237371, -0.018922264729621087, -0.06436527923214912, -0.046467999343365325, 0.043282846149581514, 0.20865777584848197, 0.448601372349186, 0.7573799147966841, 1.1251180014895361, 1.5383278817217327, 1.980532483831612, 2.433162322653858, 2.876944395056488, 3.2925902994697975, 3.6615314285305365, 3.9668223275984325, 4.194223129406806, 4.332579709260186, 4.374203294071137, 4.315743292340839, 4.159914096310505, 3.9136302220183334, 3.5869890065419794, 3.1918263725823284, 2.7389762546990393, 2.2413268739273464, 1.7145095708854652, 1.1791272262164685, 0.6649199193483676, 0.19616210717432767], 'positive_zeros': ['1.12927364861316203486330634664268', '1.14076464411841099358431151572698', '1.63833666428428244574655401782906', '1.80842030511212146768150094984420', '2.02475394237595271426670357684188', '2.35033188474402870840584206708927', '2.43849276021562390482553847027889', '3.02665424742928672294435278307930', '3.28728943102379731908203741438085', '3.65876349281430030392574919349019', '3.79342937202612114688722291302718', '3.88360343977545662423930801983342', '4.26901241580122996639616960403422', '4.27943795959935446084970177264529', '4.50261261544489429955864506275193', '4.65266403210223881873987067869667', '5.12211299158593502553907042954148', '5.30884709906757649436372859700358', '5.31553799592030991497642614207892', '5.64486075152092329768630900112420', '5.89486899117122821424465377837498', '6.25857306493786151174289933494721', '6.29053387196781046624742943523168', '6.63724092095745595669090911253166', '6.81063841629145540808180810488662', '6.93034190532144974186698316386102', '6.98024792562706225848768568502355', '7.50762985356683043206969800482323', '7.63041296321229305743469761374159', '7.932677349973326798111616589450116', '8.035151104432918965706765694939811', '8.171217594136527454123744307537032', '8.397657165430214595242802067257615', '8.453243963833539517429257371485367', '8.900183533793968209737790760981254', '8.921775044660620593159892941507161'], 'prelabel': '8-39e8-1.1-c3e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e4-0', 'trace_hash': 1160888605336673291, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12927364861316203486330634664', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.14076464411841099358431151573', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.63833666428428244574655401783', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 64860626.53160265, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 5352009260481, 'conductor_radical': 39, 'degree': 8, 'dirichlet_coefficients': [1, 2, 0, -3, -6, 0, 14, 4, 0, -12, 40, 0, 0, 28, 0, 15, -98, 0, -124, 18, 0, 80, -104, 0, -261, 0, 0, -42, -194, 0, -26, -2, 0, -196, -84, 0, -102, -248, 0, -24, -1054, 0, 450, -120, 0, -208, -96, 0, -53, -522, 0, 0, -262, 0, -240, 56, 0, -388, 308, 0, -928, -52, 0, 109, 0, 0, 1134, 294, 0, -168, 1064, 0, -952, -204, 0, 372, 560, 0, -746, -90, 0, -2108, -404, 0, 588, 900, 0, 160, 1620, 0, 0, 312, 0, -192, 744, 0, -2166, -106, 0, 783], 'euler11': [1, -40, 4068, -116616, 7313302, -155215896, 7206710148, -94317907640, 3138428376721], 'euler13': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler17': [1, 98, 12397, 986190, 96109736, 4845151470, 299233442893, 11621611896706, 582622237229761], 'euler19': [1, 124, 21504, 1798684, 202620494, 12337173556, 1011674625024, 40013274524596, 2213314919066161], 'euler2': [1, -2, 7, -24, 62, -192, 448, -1024, 4096], 'euler23': [1, 104, 41844, 3340584, 719588614, 40644885528, 6194413739316, 187319876792152, 21914624432020321], 'euler29': [1, 194, 64761, 7214754, 1694674348, 175960635306, 38521353091281, 2814386319318586, 353814783205469041], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 26, 38189, -5395494, 828557428, -160737161754, 33892878073709, 687430176177446, 787662783788549761], 'euler37': [1, 102, 193281, 14822902, 14476248876, 750824455006, 495906166057929, 13256097459097854, 6582952005840035281], 'euler41': [1, 1054, 633469, 261177138, 78839658968, 18000589528098, 3009043783442029, 345060558851234894, 22563490300366186081], 'euler43': [1, -450, 276753, -75560470, 29002070616, -6007586288290, 1749456187899897, -226166675371579350, 39959630797262576401], 'euler47': [1, 96, -19308, 124896, 17303792422, 12967077408, -208125089572332, 107436525417865632, 116191483108948578241], 'euler5': [1, 6, 297, 2094, 49084, 261750, 4640625, 11718750, 244140625], 'euler53': [1, 262, 483789, 119532570, 100466115904, 17795650423890, 10722874106237781, 864538061052158846, 491258904256726154641], 'euler59': [1, -308, 557680, -98956308, 142593856142, -20323547580732, 23523240000912880, -2668202712145721212, 1779197418239532716881], 'euler61': [1, 928, 1041074, 583837824, 364336742755, 132520093129344, 53636522217503714, 10852167574150082848, 2654348974297586158321], 'euler67': [1, -1134, 1218801, -918506522, 562458950376, -276252777076286, 110250766645959369, -30852210005398469898, 8182718904632857144561], 'euler7': [1, -14, 249, -1754, 141728, -601622, 29294601, -564950498, 13841287201], 'euler71': [1, -1064, 1201044, -690200040, 504474394630, -247030186516440, 153854077401613524, -48782804764429768984, 16409682740640811134241], 'euler73': [1, 952, 768042, 239296336, 174760946603, 93090342741712, 116231041827456138, 56045750546271053176, 22902048046490258711521], 'euler79': [1, 746, 2156493, 1122200666, 1640976331028, 553288694163974, 524216396218847853, 89409290603033265974, 59091511031674153381441], 'euler83': [1, 404, 1811392, 594579060, 1476544322126, 339972576980220, 592217176797619648, 75523863128086322812, 106890007738661124410161], 'euler89': [1, -1620, 2005896, -1665077532, 1565610279790, -1173828042656508, 996892783613506056, -567577374006126038580, 246990403565262140303521], 'euler97': [1, 2166, 4160745, 5948172454, 5928410141748, 5428736398109542, 3465784104648312105, 1646660473045788260022, 693842360995438000295041], 'euler_factors': [[1, -2, 7, -24, 62, -192, 448, -1024, 4096], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 6, 297, 2094, 49084, 261750, 4640625, 11718750, 244140625], [1, -14, 249, -1754, 141728, -601622, 29294601, -564950498, 13841287201], [1, -40, 4068, -116616, 7313302, -155215896, 7206710148, -94317907640, 3138428376721], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 98, 12397, 986190, 96109736, 4845151470, 299233442893, 11621611896706, 582622237229761], [1, 124, 21504, 1798684, 202620494, 12337173556, 1011674625024, 40013274524596, 2213314919066161], [1, 104, 41844, 3340584, 719588614, 40644885528, 6194413739316, 187319876792152, 21914624432020321], [1, 194, 64761, 7214754, 1694674348, 175960635306, 38521353091281, 2814386319318586, 353814783205469041], [1, 26, 38189, -5395494, 828557428, -160737161754, 33892878073709, 687430176177446, 787662783788549761], [1, 102, 193281, 14822902, 14476248876, 750824455006, 495906166057929, 13256097459097854, 6582952005840035281], [1, 1054, 633469, 261177138, 78839658968, 18000589528098, 3009043783442029, 345060558851234894, 22563490300366186081], [1, -450, 276753, -75560470, 29002070616, -6007586288290, 1749456187899897, -226166675371579350, 39959630797262576401], [1, 96, -19308, 124896, 17303792422, 12967077408, -208125089572332, 107436525417865632, 116191483108948578241], [1, 262, 483789, 119532570, 100466115904, 17795650423890, 10722874106237781, 864538061052158846, 491258904256726154641], [1, -308, 557680, -98956308, 142593856142, -20323547580732, 23523240000912880, -2668202712145721212, 1779197418239532716881], [1, 928, 1041074, 583837824, 364336742755, 132520093129344, 53636522217503714, 10852167574150082848, 2654348974297586158321], [1, -1134, 1218801, -918506522, 562458950376, -276252777076286, 110250766645959369, -30852210005398469898, 8182718904632857144561], [1, -1064, 1201044, -690200040, 504474394630, -247030186516440, 153854077401613524, -48782804764429768984, 16409682740640811134241], [1, 952, 768042, 239296336, 174760946603, 93090342741712, 116231041827456138, 56045750546271053176, 22902048046490258711521], [1, 746, 2156493, 1122200666, 1640976331028, 553288694163974, 524216396218847853, 89409290603033265974, 59091511031674153381441], [1, 404, 1811392, 594579060, 1476544322126, 339972576980220, 592217176797619648, 75523863128086322812, 106890007738661124410161], [1, -1620, 2005896, -1665077532, 1565610279790, -1173828042656508, 996892783613506056, -567577374006126038580, 246990403565262140303521], [1, 2166, 4160745, 5948172454, 5928410141748, 5428736398109542, 3465784104648312105, 1646660473045788260022, 693842360995438000295041]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/bb'], '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': '8-39e8-1.1-c3e4-0-6', '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': 4, 'prelabel': '8-39e8-1.1-c3e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e4-0', 'trace_hash': 1160888605336673291, 'z1': {'__RealLiteral__': 0, 'data': '1.12927364861316203486330634664', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1431524418486397470340671501251,1446090985835846199039493212949,2076838455855885809259793597576,2292445085240298529669560170595', 'Lhash_array': ['1431524418486397470340671501251', '1446090985835846199039493212949', '2076838455855885809259793597576', '2292445085240298529669560170595'], 'label': '8-39e8-1.1-c3e4-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/bb'}