-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '640876523517425607176655289856,1190752132491711044739038755720,1815961786435117613370912127581,2639914956720571990228649577625', 'a10': 0, 'a2': 2, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': -2, 'a9': 4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5490.140660461492, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 3, -2, 1]], [7, [1]], [11, [1, -2, 3, -2, 1]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.1', 'coefficient_field': '1.1.1.1', 'conductor': 1350439223056, 'conductor_radical': 154, 'degree': 8, 'euler_factors': [[1, -2, 3, -2, 1], [1, 0, -4, 0, 7, 0, -36, 0, 81], [1, 0, -8, 0, 39, 0, -200, 0, 625], [1], [1, -2, 3, -2, 1], [1, 0, 36, 0, 662, 0, 6084, 0, 28561], [1, 0, -2, 0, -285, 0, -578, 0, 83521], [1, 0, -30, 0, 539, 0, -10830, 0, 130321], [1, -4, -34, -16, 1603, -368, -17986, -48668, 279841], [1, 24, 332, 2952, 18870, 85608, 279212, 585336, 707281], [1, 0, -60, 0, 2639, 0, -57660, 0, 923521], [1, -4, -62, -16, 4123, -592, -84878, -202612, 1874161], [1, 0, 100, 0, 5862, 0, 168100, 0, 2825761], [1, -16, 268, -2320, 19606, -99760, 495532, -1272112, 3418801], [1, 0, -76, 0, 3567, 0, -167884, 0, 4879681], [1, -24, 326, -3456, 29163, -183168, 915734, -3573048, 7890481], [1, 0, -100, 0, 6519, 0, -348100, 0, 12117361], [1, 0, -90, 0, 4379, 0, -334890, 0, 13845841], [1, -4, -122, -16, 13483, -1072, -547658, -1203052, 20151121], [1, 40, 884, 12520, 125446, 888920, 4456244, 14316440, 25411681], [1, 0, 54, 0, -2413, 0, 287766, 0, 28398241], [1, -16, 34, -1024, 22819, -80896, 212194, -7888624, 38950081], [1, 0, 316, 0, 38742, 0, 2176924, 0, 47458321], [1, 0, -128, 0, 8463, 0, -1013888, 0, 62742241], [1, 0, -96, 0, 21122, 0, -903264, 0, 88529281], [1, 0, -194, 0, 27435, 0, -1978994, 0, 104060401], [1, 0, -188, 0, 24735, 0, -1994492, 0, 112550881], [1, -40, 986, -16000, 194347, -1712000, 11288714, -49001720, 131079601], [1, 20, 82, 2000, 45643, 218000, 974242, 25900580, 141158161], [1, 72, 2396, 47736, 620934, 5394168, 30594524, 103888584, 163047361]], 'euler_factors_factorization': [[[[1, -1, 1], 2]], [[[1, 0, -4, 0, 7, 0, -36, 0, 81], 1]], [[[1, 0, -8, 0, 39, 0, -200, 0, 625], 1]], [1], [[[1, -1, 1], 2]], [[[1, 0, 18, 0, 169], 2]], [[[1, 0, -2, 0, -285, 0, -578, 0, 83521], 1]], [[[1, 0, -30, 0, 539, 0, -10830, 0, 130321], 1]], [[[1, -2, -19, -46, 529], 2]], [[[1, 6, 29], 4]], [[[1, 0, -60, 0, 2639, 0, -57660, 0, 923521], 1]], [[[1, -2, -33, -74, 1369], 2]], [[[1, 0, 50, 0, 1681], 2]], [[[1, -4, 43], 4]], [[[1, 0, -76, 0, 3567, 0, -167884, 0, 4879681], 1]], [[[1, -12, 91, -636, 2809], 2]], [[[1, 0, -100, 0, 6519, 0, -348100, 0, 12117361], 1]], [[[1, 0, -90, 0, 4379, 0, -334890, 0, 13845841], 1]], [[[1, -2, -63, -134, 4489], 2]], [[[1, 10, 71], 4]], [[[1, 0, 54, 0, -2413, 0, 287766, 0, 28398241], 1]], [[[1, -8, -15, -632, 6241], 2]], [[[1, 0, 158, 0, 6889], 2]], [[[1, 0, -128, 0, 8463, 0, -1013888, 0, 62742241], 1]], [[[1, 0, -48, 0, 9409], 2]], [[[1, 0, -194, 0, 27435, 0, -1978994, 0, 104060401], 1]], [[[1, 0, -188, 0, 24735, 0, -1994492, 0, 112550881], 1]], [[[1, -20, 293, -2140, 11449], 2]], [[[1, 10, -9, 1090, 11881], 2]], [[[1, 18, 113], 4]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 8, 'label': '8-1078e4-1.1-c1e4-0-8', 'leading_term': '7.0992275534972200504735982970422825760807236326594593446466694897280725635606358689459504', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1078/2/e/s', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.015625', 'prec': 27}, 'plot_values': [7.099227553497222, 7.0913273856467995, 7.066610631500302, 7.025260857996835, 6.9674987565283, 6.89351631540273, 6.80336766341806, 6.697112040424804, 6.574839461267124, 6.436701199335128, 6.282905002481388, 6.1137060894092965, 5.929413382571497, 5.730375133928004, 5.5169733075345295, 5.289648195321958, 5.048910503053966, 4.795356939869527, 4.529647112406001, 4.2525161086003305, 3.964789761740005, 3.667391964466029, 3.361322729390975, 3.047668263096263, 2.727622630551134, 2.402484542566404, 2.07363233843099, 1.7425305456810845, 1.4107508599692313, 1.0799516133044276, 0.7518565459063764, 0.4282579152504654, 0.11102793908771236, -0.19791524964532298, -0.4966255526307515, -0.7831298409787781, -1.0554349830566914, -1.3115648196938023, -1.549577496319217, -1.7675734229953282, -1.9637189777751978, -2.136278475056649, -2.283633113370135, -2.404298956608851, -2.496955319461884, -2.5604686017891947, -2.5939135932547526, -2.5965989315524873, -2.56808504591473, -2.5081994979795406, -2.417060254711251, -2.2950964635717575, -2.1430470393119503, -1.9619664520741418, -1.7532466446443866, -1.5186162552631663, -1.2601196758120072, -0.9801111049445083, -0.6812662625914457, -0.3665497726290608, -0.0391791442261442, 0.2973942326392848, 0.6394965890420609, 0.9832918913687155, 1.3248278458117977, 1.6600676044804772, 1.9849336539696403, 2.295377799312864, 2.587431878778825, 2.8572510954420802, 3.1011836155835324, 3.3158308409423487, 3.4980947345825526, 3.645228081279912, 3.754907493673121, 3.8252688757853024, 3.854941036337023, 3.8430898308982147, 3.7894679196202716, 3.694415902784214, 3.558872152124637, 3.384389304133819, 3.1731438679636614, 2.9278983563906, 2.651978429045708, 2.3492433316234793, 2.0240530946811517, 1.6811933548594782, 1.3258136525609099, 0.9633519939002296, 0.5994683655509593, 0.23994221217948258, -0.10942479228044344, -0.4429068596818776, -0.7549382854323727, -1.0402265772589352, -1.2938624637924598, -1.5114060926650648, -1.6889670024002308, -1.8233064419067955, -1.9119180430184626, -1.9530728507724329, -1.9458700143030496, -1.8903019998303143, -1.7872639775803478, -1.6385412589831654, -1.4468102834287326, -1.2156387593201377, -0.9494075460416527, -0.6532376671938496, -0.33293296215072354, 0.005100866783751364, 0.35400048218680596, 0.7065672361700552, 1.0553781155723967, 1.3929289110987593, 1.711800164201628, 2.0048011849823393, 2.265112927423546, 2.4864378051309792, 2.663138495554247, 2.790364048103603, 2.864182416290603, 2.881669785341647, 2.8409818498120814, 2.7414216147669372, 2.583505458610241, 2.3689491856388667, 2.100647732479726, 1.7826542194041461, 1.420137128639585, 1.0192634756312406, 0.5870864624761928, 0.13142526604188504, -0.3392823540600874, -0.8161623535650528, -1.2900820690735044, -1.7518464790899289, -2.1923933041084847, -2.6029819149918896, -2.9753891059068276, -3.302114379491592, -3.5765433411504692, -3.793079544685029, -3.9473014347397757, -4.03608430180294, -4.057668375952939, -4.011684816795645, -3.8992179559655273, -3.722775989829066, -3.4862365845668424, -3.19475284459171, -2.854683899084439, -2.47341599000433, -2.059198985945848, -1.6209593664060096, -1.168109464867017, -0.7102929922901239, -0.25716263653543137, 0.18184280983684073, 0.5977310096836044, 0.9821854480611344, 1.3277701297047249, 1.6281139234888322, 1.8780671246142655, 2.0738222911624935, 2.213026043654404, 2.294849163880802, 2.319978505245566, 2.2905888864482535, 2.21032011773268, 2.0841842320335835, 1.91838789620973, 1.7201673282906549, 1.4976378860625918, 1.2595584462111045, 1.0150589677254438, 0.7734019783029157, 0.5437623114874088, 0.33494650848851254, 0.15513527796040033, 0.01166738179598774, -0.0891536672920906, -0.14225722340655592, -0.14395156430646386, -0.09202629910402947, 0.014187080043809952, 0.17378342666231728, 0.38429841388187286, 0.6417707525898724, 0.9408754820589225, 1.2750506400320705, 1.6366570994394285, 2.0171950950035797, 2.407599000010647, 2.7984378650858197, 3.180146423586846, 3.5433190874916183, 3.8790482023912203, 4.179082403144017, 4.436027577095089, 4.643593167778738, 4.796837148661122, 4.892186456583302, 4.927520958181693, 4.902255417421431, 4.817407833944901, 4.675449347628977, 4.480231855256545, 4.236868711360884, 3.951628838580895, 3.6316640592393234, 3.2848077077755344, 2.919325856601153, 2.543714447325975, 2.166410797848394, 1.7955555996704156, 1.438752535413719, 1.1028815797005969, 0.793908511764151, 0.5167333601974164, 0.27507680821922514, 0.07140818448925204, -0.09307632101244404, -0.2184378942199141, -0.3059404862453192, -0.35797277622003576, -0.37790585900821405, -0.3699260197068005, -0.3388576445871401, -0.28998061501806843, -0.22880663749459687, -0.16086309647643063, -0.09149595848460082, -0.02568388624128638, 0.032142088240571534, 0.07824234040216771, 0.10967974741203483, 0.12440465718274651, 0.12129646894071996, 0.10016623499568038, 0.061726675709060895, 0.007525807139888148, -0.06015510273817938, -0.13842355840578408, -0.22392318157824287, -0.3130145789295433, -0.4019340036770784, -0.48695337987851756, -0.5645572391783656, -0.6316303255933394, -0.6855540938787011, -0.7243000966845583, -0.7465338936991095, -0.7516995129972054, -0.7399781266456462, -0.7122547999773122, -0.6700925624553202, -0.6156767386637902, -0.5516476094921708, -0.4809621759899929, -0.40676740098147696, -0.33226341543912274, -0.26050229453579243, -0.19423628435482646, -0.13579261626146552, -0.08696589732265979, -0.04890142171541099, -0.022036632873419844, -0.006082099481389894, -3.15261974471295e-05, -0.002200105012008868, -0.010310416046406097, -0.021608332956997454, -0.03299931052850634, -0.041214922109888134, -0.04299420576861228, -0.03526449905537444, -0.015321722972062945, 0.01899128943623929, 0.06913381650641258, 0.13574412002528835, 0.21854278639063934, 0.31628151158741047, 0.42673669294461963, 0.5467404899505603, 0.6722599405936167, 0.7985377179134447, 0.9202468393878296, 1.031680806251717, 1.1269970650765733, 1.2004754821344188, 1.2467404180610135, 1.261007836821788, 1.239363466448558, 1.1789624569755117, 1.0781744964007876, 0.936731045045594, 0.7558505816576128, 0.5382306190222853, 0.28800777250675463, 0.010687302142760174, -0.28700794753135955, -0.597355826822626, -0.9118626552936737, -1.2215540596802756, -1.5173454039873684, -1.7903244044812303, -2.032048467981333, -2.234925554088788, -2.392571918979939, -2.4999659655003215, -2.5536363779718956, -2.5519239851354563, -2.4950811717608095, -2.385172228054203, -2.2260260887853036, -2.0232137185213745, -1.7838169659080096, -1.5160921797702764, -1.2291999947338594, -0.9329097908731758, -0.6371894631237383, -0.3517922972188963, -0.08591571459410602, 0.15214574622953891, 0.35533689969744664, 0.5181069273746796, 0.6366055237253758, 0.7088092622912461, 0.7345887681898101, 0.7156751556809642, 0.6555617853264433, 0.5593044076526003, 0.43329023656776555, 0.2849336193964098, 0.12232562466203538, -0.0461513436731042, -0.21219820314146576, -0.3679755133336141, -0.5064621878483495, -0.621758896196478, -0.7093570399530977, -0.76633046716504, -0.7914288035700434, -0.7850959570421798, -0.7494505048845814, -0.6881447576247339, -0.6061134992740316, -0.5093009148932525, -0.40436797808197805, -0.2983054295857724, -0.19802332540560363, -0.10998280902427286, -0.03984934041957621, 0.007847811598448632, 0.029981811648992617, 0.025013621772052585, -0.006895169147423226, -0.0638658405565368, -0.14238086293049304, -0.237449225516867, -0.34287392191547117, -0.45158331662920864, -0.5560086423754048, -0.6485233797189363, -0.7219422503194135, -0.7699366719452073, -0.7874378621545559, -0.7710522482355097, -0.7194103536067881, -0.6333138749301686, -0.5158386741882265, -0.3723919253805559, -0.21058545164441972, -0.03993489242172307, 0.12847882704176744, 0.2824251414098257, 0.4091120412952758, 0.49579601638875587, 0.5303853799086392, 0.5020746954220671, 0.40201959006448584, 0.22386132314001245, -0.03582592467961905, -0.3771682621722464, -0.7967134879999614, -1.2873915680712702, -1.8386247080222917, -2.4365646090125956, -3.0644799683853856, -3.7033138417368945, -4.332407538802955, -4.930233400160859, -5.475308053706598, -5.947046434675225, -6.326660598126696, -6.597904155283938, -6.748008016972207, -6.768255631171911, -6.654378984858061, -6.406796802754306, -6.0310107361048, -5.537401412918852, -4.940738218963099, -4.259703190133769, -3.5165111185360503, -2.7358897465158956, -1.9439552842416339, -1.167274679210146, -0.43198852301548607, 0.23745392523742587, 0.8193430769472969, 1.2955185738496664, 1.6520923694198064, 1.8801199014675625, 1.9759232352094036, 1.9412058737800082, 1.7830062982300288, 1.5133355760863803, 1.1486025721491349, 0.7088891791391457, 0.21702566774554585, -0.3024690309436626, -0.8244576024154879, -1.324338394158873, -1.779263678721851, -2.169061038453571, -2.4770683903806576, -2.690984363738243, -2.8034941012089916, -2.8123559430113403, -2.7204171642184996, -2.535582107569847, -2.270393848972082, -1.9411946698505635, -1.5672994721889473, -1.1701127035885872, -0.7720366383313506, -0.3952535608879676, -0.06063444862348592, 0.213285398769873, 0.41120907460306344, 0.5218597955165799, 0.5385334056953721, 0.45940486874504055, 0.2875817820618708, 0.030929074830848897, -0.2983857037179048, -0.6845426479615271, -1.1088756529203767, -1.5508497171866473, -1.989240276155941, -2.4031336253347897, -2.7729813585862666, -3.081656088781843, -3.315420446579155, -3.464390666514251, -3.52304969898521, -3.490600042820375, -3.3708816344265076, -3.1718819333632133, -2.9053417349743733, -2.586148748860821, -2.231249041726613, -1.8585615549926917, -1.4860537662479942, -1.1307075084134441, -0.8073637963375382, -0.5278916745727914, -0.30058626731865834, -0.1296796395711365, -0.015116786378937876, 0.047318944241684174, 0.06564276928293142, 0.051046686651748274, 0.017011977970989488, -0.02174149938695518, -0.05041659357082913, -0.055394481815291594, -0.02545596160957551, 0.0471033736765699, 0.16551949793389156, 0.32785115316374, 0.5265665201510839, 0.7484685370396716, 0.9750422081147023, 1.1831232226148407, 1.3459039920600135, 1.4343311122805529, 1.418862723872363, 1.2712212385213868, 0.9663057465928788, 0.4842245482475152, -0.18775160543695588, -1.0536362537988946, -2.1073651850121027, -3.331889819311986, -4.698655811914759, -6.167621378839141, -7.687927868222288, -9.19940969384724, -10.634196690041813, -11.91869326048795, -12.976657924847387, -13.732529177437867, -14.114293945279691, -14.056363301028457, -13.503681914233873, -12.41450946323437, -10.762592712933161, -8.539020089790917, -5.7547566039761024, -2.4406250641099057, 1.3531191903070816, 5.557459753352488, 10.0856038088893, 14.836085962064377, 19.696357676589056, 24.54604649981972, 29.260663230604315, 33.7160667559487, 37.79383727117116, 41.385366498232656, 44.3949927953687, 46.743325617364476, 48.37187692542838, 49.245105399170015, 49.3498799041791, 48.695888515131564, 47.317520203978304, 45.27171612502169, 42.63351755664322, 39.49352134327022, 35.95669504791256, 32.13675535627724, 28.150335282565834, 24.1133102694149, 20.138088221472444, 16.32797770944376, 12.773208589051368, 9.54866038006703, 6.7121139870472675, 4.302094481832013, 2.3375388596710147, 0.8184085220964369, -0.2733449237777688, -0.9717631819229596, -1.3241242669921678, -1.3879902761476073, -1.2279814752583857, -0.911917893828428, -0.5073006589339277, -0.0781115299114847, 0.3182187454101011, 0.6333740041003305, 0.8299594749896533, 0.8827918636926038, 0.7794329316258936, 0.5198679377522213, 0.11567209163976183, -0.41128439095057034, -1.030953337161846, -1.7075203261980414, -2.401748554563733, -3.0735265885967227, -3.684715309532389, -4.201395049414384, -4.595531244123233, -4.846602482325403, -4.942981813582392, -4.882146205384778, -4.6701907475151, -4.321461021801657, -3.857745914293865, -3.3063324656782735, -2.6978634001700095, -2.064800240696478, -1.4395539590443045, -0.851975895335019, -0.32758427827967923, 0.11338312273570608, 0.45705988523480706, 0.6970819576267248, 0.8343399645635593, 0.8763051629063695, 0.8364186108635132, 0.733179212764218, 0.588179051212248, 0.4243599898281615, 0.2644405801269455, 0.12918403801349895, 0.03560906595921887, -0.004226803665401395, 0.015911164451841407, 0.09588151746215488, 0.22915724371094098, 0.4033375639223939, 0.6010730504207514, 0.8014155241130433, 0.9814966621264737, 1.118406233158969, 1.1912556085787487, 1.18308109233353, 1.0825557067018903, 0.8855125752129895, 0.5961328035443285, 0.2273357589172676, -0.19925991001257584, -0.6537887792838682, -1.0993371105851109, -1.4937960995854616, -1.791985740283725, -1.9480734908894293, -1.9184211265517073, -1.6643662598404714, -1.1548838326811308, -0.3690257746696738, 0.7022163141255214, 2.0544318866731492, 3.668845805197747, 5.512275775145498, 7.538473437422352, 9.689157031320596, 11.895865284814416, 14.082911323460568, 16.171720237834766, 18.083404527649257, 19.74222639436258, 21.079427442292218, 22.037985126512375, 22.57423936683203, 22.66014458409578, 22.284855672922685, 21.45689374701395, 20.202842698617182, 18.566166763235547, 16.60522642946985, 14.391706113999671, 12.006615623027207, 9.536248508602895, 7.06816558766228, 4.687540534120473, 2.472974816092828, 0.4927566253758859, -1.1981143649544659, -2.5604985820583392, -3.572480008029433, -4.22980806581374, -4.545651806970459, -4.549959381588317, -4.286942924590826, -3.812035912264278, -3.1887892583030797, -2.4856187125142393, -1.7714436306374757, -1.1117796137206557, -0.5653710475867808, -0.1811718933298396, 0.004347826810156981, -0.03109542861495245, -0.29471602166171706, -0.7786259950928869, -1.4606856665407193, -2.306064100417044, -3.269539407115736, -4.298692175644781, -5.336966866633819, -6.326854196923605, -7.21350091439981, -7.948535544738673, -8.492205682603117, -8.815322993091609, -8.90129405625913, -8.747500893382817, -8.3643831461902, -7.7744900665327625, -7.011458781964673, -6.118202935684171, -5.143518585832169, -4.139128294880565, -3.1568577247657474, -2.2457158896977445, -1.448681517985025, -0.8003261001975013, -0.3250349485801408, -0.03579446170216344, 0.06641860964704352, -0.007606206352846887, -0.23628741879249876, -0.5888413260899672, -1.0273988035385604, -1.5095481901552983, -1.9910733825327138, -2.4289397528644, -2.783934240826113, -3.023063592582948, -3.1214998704316645, -3.0643988578840586, -2.847506492032793, -2.477141796428463, -1.9696837976561063, -1.350773625189686, -0.6532486472520573, 0.08518480750547441, 0.8243022709712386, 1.5238633440993035, 2.146461763301251, 2.65986745276841, 3.0389934685855904, 3.2677053400943064, 3.3397641131788522, 3.2589974780667403, 3.0390782054693277, 2.7029506116783675, 2.280980880206395, 1.8088598252359838, 1.325420843255698, 0.8702890342613633, 0.4810090823605169, 0.19060996637623404, 0.025523100028552802, 0.0038462043832596577, 0.1340494273825107, 0.41437725630892164, 0.8329153582060403, 1.3683082767610097, 1.9909894228519274, 2.6649258015764947, 3.3499993853671595, 4.00454109909907, 4.58769251166252, 5.061897337818438, 5.395609644562138, 5.565188448351491, 5.55607218940391, 5.363762434115967, 4.994455668402565, 4.46454838589216, 3.7994413332333132, 3.0321039831123424, 2.201163598632552, 1.348580714513904, 0.5170441525310993, -0.2526432114356258, -0.9239803001738044, -1.4668157269645978, -1.8591164840260648, -2.088408718214351, -2.1522654887617536, -2.058351121775413, -1.8238500424176265, -1.4744137801330417, -1.0423195237612248, -0.5645685235692086, -0.08054387791607058, 0.3704726917632865, 0.751700332430377, 1.0309821732323157, 1.1827575006728475, 1.189549778209841, 1.0428972724681056, 0.7438036663184823, 0.3024857577262036, -0.26235463604484616, -0.9246192290188802, -1.6524794243853462, -2.4106852780566155, -3.1623619190554706, -3.870950694828888, -4.502714323585678, -5.028913629082113, -5.426618762939997, -5.679768187381798, -5.780678420952525, -5.7300079647810715, -5.535711715672977, -5.212454440719059, -4.7812925250626535, -4.267562224001151, -3.6988702872027077, -3.103656018187943, -2.509887118364356, -1.942924633506701, -1.4241714933340075, -0.9702492701128272, -0.5923619284229459, -0.2958565052770889, -0.08041749463726096, 0.05941294068022347, 0.13344603047742434, 0.15475971280717588, 0.13847109020959306, 0.10047809085419805, 0.05615146996438299, 0.01918409692143981, 0.0006533758496760761, 0.008306852057907325, 0.04614998034347808, 0.11437665897225033, 0.20956285758178134, 0.32514760069641, 0.4522425269665628, 0.5804855957256039, 0.6989914191542117, 0.7973759292342933, 0.8668291902965138, 0.9007969355804547, 0.8955727260573759, 0.8506778798757595, 0.7691141476903919, 0.6570460220599426, 0.523361625464135, 0.37903517098969797, 0.2364485644094024, 0.10834378352297015, 0.006838935786229667, -0.057450631699665855, -0.07615738597954598, -0.04389831519793055, 0.04129153108134469, 0.17780628309395793, 0.3605424997477382, 0.5811924667297942, 0.8287969023325621, 1.090456977975898, 1.3522236702823631, 1.600048141193415, 1.820633334560828, 2.0022617100708686, 2.1356619991679953, 2.214530625667455, 2.2357322545230565, 2.1994330798789536, 2.1091624544224024, 1.9713259997011396, 1.7945858541754856, 1.5892571224259773, 1.3666469881793346, 1.138134408756341, 0.9144191249572513, 0.7048916639434274, 0.5170873318302984, 0.356324284581774, 0.22556046942375158, 0.12539029492767875, 0.05424070031863296, 0.008806970883029905, -0.015468147754395695, -0.02387817729947853, -0.021852563881277574, -0.014395075782757082, -0.005655738662143501, 0.001387691787618231, 0.005102119563312093, 0.005181403247746998, 0.0024682335982689372, -0.0013717416208755043, -0.004306832988049836, -0.004452590978256004, -0.0006060265732283906, 0.0072507806342868115, 0.017569537745404554, 0.026992878459317596, 0.030295085854692642, 0.020568272194429554, -0.010393429167134092, -0.07152775680529742, -0.1716538834703165, -0.31855042093386815, -0.5180756402655948, -0.7732167816411555, -1.0830217000152174, -1.4420277132601795, -1.8399834292934074, -2.2615920570564416, -2.686534717976431, -3.090279240718678, -3.4451879683584195, -3.7215680665731403, -3.889166770218476, -3.919064513405304, -3.7855809623150027, -3.4679183446453927, -2.951832658561234, -2.231074358845557, -1.308346254246444, -0.1959111053305274, 1.0842690364025906, 2.50096829432879, 4.015120905221562, 5.581120706490373, 7.148413276198147, 8.663749199809319, 10.074706309902854, 11.331650152276069, 12.389469317796493, 13.210009998594158, 13.765643309422915, 14.039426546937495, 14.025158176065114, 13.72819686557127, 13.166790973049599, 12.369361784748227, 11.372523195133121, 10.219954380247957, 8.961004768039691, 7.646728126644299, 6.327297190486173, 5.0502807930060305, 3.858467638189541, 2.7873503068192504, 1.8639026098002556, 1.106037658674281, 0.5220742275176561, 0.1109313505404795, -0.13700327766232723, -0.2386384453101703, -0.21662490496448042, -0.09751743592532268, 0.09008673062949027, 0.3174416546293037, 0.5575849123913644, 0.786701888355684, 0.985221051828156, 1.138665848388166, 1.238202376579233, 1.2803637018723957, 1.2666295847987614, 1.20273005200582, 1.0977630735131696, 0.962916593626572, 0.8103387691542643, 0.6520031442024836, 0.498739323289153, 0.3594254763125327, 0.2404807717698627, 0.14559081839928026, 0.07571442794663294, 0.029403995710299426, 0.003292746452402418, -0.007295996302148072, -0.007657381288629579, -0.0029743165070898053, 0.0022921170732047476, 0.004870575851386494, 0.002981338403628001, -0.003582737289502228, -0.01359303390405046, -0.02470981903102976, -0.033992103479590835, -0.03850994121643347, -0.03593080679196571, -0.02506784153294835, -0.006364028933655731, 0.017777896874054844, 0.04286931504680725, 0.06254346834551312, 0.06941267715648206, 0.05600771953971675], 'positive_zeros': ['0.50556243447685142525612914077542', '0.939337805131261358351192474321794', '1.43254125869397259724395104169472', '1.73414405094382841272524904422434', '2.08252570246507862304766255652513', '2.47782074971000954998203089854586', '2.82963158174833831468337548854148', '2.90454780051418567248627330186604', '3.47508202460065744691953011093412', '3.66286346539957141566501866203703', '3.78314046931653629738575030484481', '4.21907368570579354291815534309574', '4.22470240037869523938341830626293', '4.35159464175674344870093384405270', '4.70370248902019579022030748297038', '5.06790717818188946222630863934975', '5.26135419763845999217246132756733', '5.54364405496541873922930200555310', '5.59123617697526498404469089650913', '5.86302115455856576529990933301807', '5.99810773635683109634343046609400', '6.41612098810812933989532338710653', '6.60033486625472391882394591365534', '6.87814900858078444822581643881482', '6.98599038472824670738269954011491', '7.37785589597875927836448293495843', '7.44423854655493122260310435010301', '7.50666885545617956566347665268325', '7.71481036913765700133474152412758', '8.025883698479201246532506719681928', '8.526733060473410109455209796330345', '8.643543572871857644141732871365095', '8.753731866630101218626904909304034', '9.073776633135855967380822835828714', '9.261872825460911455779991529314142', '9.274681054265508098785914302673548', '9.492900956805119002456625676851024', '9.646495696127967982052008463983326', '10.06676973981224527880344011634022', '10.29605990375114096964612624319556'], 'prelabel': '8-1078e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 1919186585428784769, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50556243447685142525612914078', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.939337805131261358351192474322', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.43254125869397259724395104169', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5490.140660461492, 'bad_primes': [2, 7, 11], 'central_character': '1.1', 'conductor': 1350439223056, 'conductor_radical': 154, 'degree': 8, 'dirichlet_coefficients': [1, 2, 0, 1, 0, 0, 0, -2, 4, 0, 2, 0, 0, 0, 0, -4, 0, 8, 0, 0, 0, 4, 4, 0, 8, 0, 0, 0, -24, 0, 0, -2, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 16, 2, 0, 8, 0, 0, 0, 16, 0, 0, 24, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 3, 0, 0, 4, 0, 0, 0, -40, -8, 0, 8, 0, 0, 0, 0, 16, 0, 9, 0, 0, 0, 0, 32, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 8, 8], 'euler11': [1, -2, 3, -2, 1, 0, 0, 0, 0], 'euler13': [1, 0, 36, 0, 662, 0, 6084, 0, 28561], 'euler17': [1, 0, -2, 0, -285, 0, -578, 0, 83521], 'euler19': [1, 0, -30, 0, 539, 0, -10830, 0, 130321], 'euler2': [1, -2, 3, -2, 1, 0, 0, 0, 0], 'euler23': [1, -4, -34, -16, 1603, -368, -17986, -48668, 279841], 'euler29': [1, 24, 332, 2952, 18870, 85608, 279212, 585336, 707281], 'euler3': [1, 0, -4, 0, 7, 0, -36, 0, 81], 'euler31': [1, 0, -60, 0, 2639, 0, -57660, 0, 923521], 'euler37': [1, -4, -62, -16, 4123, -592, -84878, -202612, 1874161], 'euler41': [1, 0, 100, 0, 5862, 0, 168100, 0, 2825761], 'euler43': [1, -16, 268, -2320, 19606, -99760, 495532, -1272112, 3418801], 'euler47': [1, 0, -76, 0, 3567, 0, -167884, 0, 4879681], 'euler5': [1, 0, -8, 0, 39, 0, -200, 0, 625], 'euler53': [1, -24, 326, -3456, 29163, -183168, 915734, -3573048, 7890481], 'euler59': [1, 0, -100, 0, 6519, 0, -348100, 0, 12117361], 'euler61': [1, 0, -90, 0, 4379, 0, -334890, 0, 13845841], 'euler67': [1, -4, -122, -16, 13483, -1072, -547658, -1203052, 20151121], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 40, 884, 12520, 125446, 888920, 4456244, 14316440, 25411681], 'euler73': [1, 0, 54, 0, -2413, 0, 287766, 0, 28398241], 'euler79': [1, -16, 34, -1024, 22819, -80896, 212194, -7888624, 38950081], 'euler83': [1, 0, 316, 0, 38742, 0, 2176924, 0, 47458321], 'euler89': [1, 0, -128, 0, 8463, 0, -1013888, 0, 62742241], 'euler97': [1, 0, -96, 0, 21122, 0, -903264, 0, 88529281], 'euler_factors': [[1, -2, 3, -2, 1, 0, 0, 0, 0], [1, 0, -4, 0, 7, 0, -36, 0, 81], [1, 0, -8, 0, 39, 0, -200, 0, 625], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 3, -2, 1, 0, 0, 0, 0], [1, 0, 36, 0, 662, 0, 6084, 0, 28561], [1, 0, -2, 0, -285, 0, -578, 0, 83521], [1, 0, -30, 0, 539, 0, -10830, 0, 130321], [1, -4, -34, -16, 1603, -368, -17986, -48668, 279841], [1, 24, 332, 2952, 18870, 85608, 279212, 585336, 707281], [1, 0, -60, 0, 2639, 0, -57660, 0, 923521], [1, -4, -62, -16, 4123, -592, -84878, -202612, 1874161], [1, 0, 100, 0, 5862, 0, 168100, 0, 2825761], [1, -16, 268, -2320, 19606, -99760, 495532, -1272112, 3418801], [1, 0, -76, 0, 3567, 0, -167884, 0, 4879681], [1, -24, 326, -3456, 29163, -183168, 915734, -3573048, 7890481], [1, 0, -100, 0, 6519, 0, -348100, 0, 12117361], [1, 0, -90, 0, 4379, 0, -334890, 0, 13845841], [1, -4, -122, -16, 13483, -1072, -547658, -1203052, 20151121], [1, 40, 884, 12520, 125446, 888920, 4456244, 14316440, 25411681], [1, 0, 54, 0, -2413, 0, 287766, 0, 28398241], [1, -16, 34, -1024, 22819, -80896, 212194, -7888624, 38950081], [1, 0, 316, 0, 38742, 0, 2176924, 0, 47458321], [1, 0, -128, 0, 8463, 0, -1013888, 0, 62742241], [1, 0, -96, 0, 21122, 0, -903264, 0, 88529281]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/e/s'], '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': '8-1078e4-1.1-c1e4-0-8', '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': 0, 'prelabel': '8-1078e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1919186585428784769, 'z1': {'__RealLiteral__': 0, 'data': '0.50556243447685142525612914078', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '640876523517425607176655289856,1190752132491711044739038755720,1815961786435117613370912127581,2639914956720571990228649577625', 'Lhash_array': ['640876523517425607176655289856', '1190752132491711044739038755720', '1815961786435117613370912127581', '2639914956720571990228649577625'], 'label': '8-1078e4-1.1-c1e4-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/e/s'}