Lfunction data - 8-39e8-1.1-c3e4-0-5

Formats: - HTML - YAML - JSON - 2023-09-29T14:23:56.913885

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': '1273096206173794896638147932582,1612366474714555065771215221619,1946042192550349988883005840030,2172797831928004395827280037774', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, '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, 0, 0, 0, 115, 0, 0, 0, 4096], [1], [1, 0, 0, 0, 3742, 0, 0, 0, 244140625], [1, 0, 1372, 0, 705894, 0, 161414428, 0, 13841287201], [1, 0, 0, 0, -1486370, 0, 0, 0, 3138428376721], [1], [1, 0, 19652, 0, 144825414, 0, 474351505988, 0, 582622237229761], [1, 0, 27436, 0, 282275286, 0, 1290750791116, 0, 2213314919066161], [1, 0, 48668, 0, 888215334, 0, 7204610645852, 0, 21914624432020321], [1, 0, 97556, 0, 3568939926, 0, 58028583903476, 0, 353814783205469041], [1, 0, 119164, 0, 5325022086, 0, 105758488642684, 0, 787662783788549761], [1, 0, 202612, 0, 15394358454, 0, 519846959180308, 0, 6582952005840035281], [1, 0, 0, 0, -315317810, 0, 0, 0, 22563490300366186081], [1, 1808, 1543852, 800627600, 274591480246, 63655498593200, 9759248985924748, 908687442381812144, 39959630797262576401], [1, 0, 0, 0, -19480835090, 0, 0, 0, 116191483108948578241], [1, 0, 595508, 0, 132986166774, 0, 13199054367208532, 0, 491258904256726154641], [1, 0, 0, 0, 78746477470, 0, 0, 0, 1779197418239532716881], [1, 0, -876820, 0, 295244076822, 0, -45174094647212020, 0, 2654348974297586158321], [1, 0, 1203052, 0, 542750293014, 0, 108826137585179788, 0, 8182718904632857144561], [1, 0, 0, 0, -234490873970, 0, 0, 0, 16409682740640811134241], [1, 0, 1556068, 0, 908005357734, 0, 235486346833071652, 0, 22902048046490258711521], [1, 0, 1622300, 0, 1144139233542, 0, 394360779091718300, 0, 59091511031674153381441], [1, 0, 0, 0, -633473875010, 0, 0, 0, 106890007738661124410161], [1, 0, 0, 0, -926581329650, 0, 0, 0, 246990403565262140303521], [1, 0, 3650692, 0, 4997832029574, 0, 3040924234618260868, 0, 693842360995438000295041], [1, 0, 4121204, 0, 6369120903606, 0, 4374741090737443604, 0, 1126825030131969720661201], [1, 3392, 8685532, 13558790720, 17110836621286, 14816056707093440, 10370979431176118428, 4425790639548797625536, 1425760886846178945447841], [1, 0, 4900172, 0, 9004382111094, 0, 7353836849680618028, 0, 2252191588960823337718801], [1, 0, 5180116, 0, 10062600665046, 0, 8687573117769237556, 0, 2812664781782894485727281], [1, 0, 5771588, 0, 12491710515654, 0, 12016167751937073092, 0, 4334523100191686738306881]], 'euler_factors_factorization': [[[[1, 0, 0, 0, 115, 0, 0, 0, 4096], 1]], [1], [[[1, 0, 0, 0, 3742, 0, 0, 0, 244140625], 1]], [[[1, 0, 343], 4]], [[[1, 0, 0, 0, -1486370, 0, 0, 0, 3138428376721], 1]], [1], [[[1, 0, 4913], 4]], [[[1, 0, 6859], 4]], [[[1, 0, 12167], 4]], [[[1, 0, 24389], 4]], [[[1, 0, 29791], 4]], [[[1, 0, 50653], 4]], [[[1, 0, 0, 0, -315317810, 0, 0, 0, 22563490300366186081], 1]], [[[1, 452, 79507], 4]], [[[1, 0, 0, 0, -19480835090, 0, 0, 0, 116191483108948578241], 1]], [[[1, 0, 148877], 4]], [[[1, 0, 0, 0, 78746477470, 0, 0, 0, 1779197418239532716881], 1]], [[[1, 0, -438410, 0, 51520374361], 2]], [[[1, 0, 300763], 4]], [[[1, 0, 0, 0, -234490873970, 0, 0, 0, 16409682740640811134241], 1]], [[[1, 0, 389017], 4]], [[[1, 0, 811150, 0, 243087455521], 2]], [[[1, 0, 0, 0, -633473875010, 0, 0, 0, 106890007738661124410161], 1]], [[[1, 0, 0, 0, -926581329650, 0, 0, 0, 246990403565262140303521], 1]], [[[1, 0, 912673], 4]], [[[1, 0, 1030301], 4]], [[[1, 848, 1092727], 4]], [[[1, 0, 1225043], 4]], [[[1, 0, 1295029], 4]], [[[1, 0, 1442897], 4]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 5, 'label': '8-39e8-1.1-c3e4-0-5', '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/y', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0126953125', 'prec': 40}, 'plot_values': [-5.5931092494314185e-242, 9.60464725604094e-06, 0.00015341943764040546, 0.0007745384575568731, 0.002438444959594882, 0.005923581859107921, 0.012208345973488764, 0.02245464030829679, 0.03798816138862597, 0.06027572400155544, 0.0909001668369196, 0.13153263719431468, 0.18390272896012536, 0.2497672090008815, 0.3308785992304886, 0.4289515389302905, 0.5456285984406813, 0.6824470664894646, 0.8408091219253577, 1.0219484749427945, 1.2268985067811837, 1.4564646586652852, 1.7112050440097604, 1.9914030087355041, 2.297043741622951, 2.6277993476216848, 2.983028233554187, 3.3617572930097817, 3.762671330352983, 4.184116111522183, 4.624122859997383, 5.080400767855374, 5.550340752116103, 6.03103889406187, 6.519349128177683, 7.011883249159948, 7.505027160180631, 7.9949835898071715, 8.477851999709443, 8.949629905735097, 9.406236521851978, 9.843570092295264, 10.257609825713804, 10.64440993759223, 11.000123127571728, 11.32106496027383, 11.603828995277658, 11.845264156619272, 12.042489411845368, 12.192956002559981, 12.294564599856049, 12.3456178374153, 12.344818281150292, 12.291319392634941, 12.184833053275339, 12.025552408315427, 11.81412779141981, 11.551699245416318, 11.239984380239893, 10.881171665120528, 10.477873075203544, 10.033134565670839, 9.550497812440836, 9.033869922879623, 8.48745649051892, 7.915751010438317, 7.3235690194383665, 6.715905715416415, 6.097857845306665, 5.47459774655007, 4.85138380455949, 4.233421412263149, 3.625785577048469, 3.0333890172784597, 2.460977527012208, 1.9130109731113265, 1.3935997293924864, 0.9064780743356288, 0.45499586430579114, 0.04203421484746227, -0.3300327146120994, -0.6593485271107362, -0.9445750756115724, -1.1849327754618217, -1.3802063145428933, -1.5307325864942947, -1.6373846164677546, -1.701566318416835, -1.7251849934215333, -1.7106148389330822, -1.6606608760174641, -1.5785152997809395, -1.4677032705424564, -1.33202691111908, -1.1755123947374178, -1.0023427125725515, -0.816789553075684, -0.6231485233874537, -0.4256787963319277, -0.2285318423298179, -0.035685892633333126, 0.14911331325023894, 0.32240682724754977, 0.4810778893906553, 0.6223984842327492, 0.7440686868329234, 0.8442508871373832, 0.9215938563892215, 0.9752481809876967, 1.004875166874981, 1.0106506081249036, 0.9932505454598429, 0.953831123308456, 0.894003688556578, 0.8158050104486313, 0.7216483217786406, 0.6142725156233633, 0.4966889497078525, 0.3721242910766002, 0.2439503573624842, 0.1156161930094364, -0.009419656762483675, -0.1277587493992951, -0.23613413700155886, -0.33147649897602927, -0.4109774577947446, -0.47215115391903456, -0.5128860683905878, -0.5314901876955721, -0.5267307354097918, -0.49786699850560223, -0.4446672693446635, -0.36741927363988436, -0.2669324866555963, -0.1445273293213179, -0.002012631663787794, 0.1583424353024206, 0.33384734667920807, 0.5214486086416404, 0.7177832606298492, 0.919237186292646, 1.1220172564188662, 1.3222479286693387, 1.5160355853433167, 1.6995383474315602, 1.8690525727561278, 2.021126414405219, 2.1526086163444202, 2.260705600965284, 2.3430577236733967, 2.3978419323251794, 2.423780388469907, 2.420162403724505, 2.3868872672849637, 2.3245295029121333, 2.234292783022899, 2.117983615600246, 1.97800651723532, 1.8173751146792116, 1.6396129519538394, 1.4486804808330564, 1.2489227638681604, 1.0450255798464723, 0.8418822958580077, 0.6444914718763955, 0.4578730149957731, 0.28698599848244927, 0.1365941353816365, 0.011163066223684954, -0.08522711936942114, -0.14897204873604575, -0.17704224366831123, -0.16705371435056832, -0.11732731685702497, -0.026951883970723917, 0.10418126262486145, 0.2753651467070231, 0.4850711579214191, 0.7309413569780344, 1.0098300077364224, 1.3178567433332093, 1.6504634891967396, 2.002473783571978, 2.3681981238094174, 2.7415412089106543, 3.1161107286244323, 3.485333039781579, 3.8425881540388245, 4.181339589094001, 4.495265186771506, 4.778398020150696, 5.0252441850099245, 5.230893328028828, 5.391131337146179, 5.50256399426769, 5.562672613172107, 5.569866126371896, 5.5235381331620035, 5.42413342237537, 5.27311372899455, 5.0729287337306905, 4.826995928009158, 4.539687064269652, 4.216204427237316, 3.862473844414073, 3.4850507739245744, 3.091030192657548, 2.6878640807617353, 2.2832064273643047, 1.8847748141040939, 1.5002144450154975, 1.1369097051665136, 0.8018298177123913, 0.5013927619872128, 0.24133213866839318, 0.02656131058559496, -0.13892849204329552, -0.25215293738580324, -0.31121493387584304, -0.3153434650130884, -0.2649060143733347, -0.1614084651969892, -0.00749014960228846, 0.193148654925187, 0.4358320308118936, 0.7149980890101023, 1.0242904208878332, 1.3567198549213986, 1.704822417303566, 2.0608105689067506, 2.4167178880290603, 2.764598166626218, 3.0967049346477373, 3.405651604192025, 3.6845513602903153, 3.927189752609878, 4.128166105308569, 4.283003198811977, 4.388219726185202, 4.441423882435215, 4.441370132629155, 4.387974219963541, 4.282274628639448, 4.126426160437057, 3.9236567466463073, 3.6781764084546014, 3.395021577444022, 3.0799681441181943, 2.7394113406315093, 2.3801963741580248, 2.009382093033055, 1.6341270789411393, 1.2615465677289384, 0.898523002510558, 0.5514570295891731, 0.226193954602106, -0.07207747089884528, -0.33896701430269105, -0.5710696684511015, -0.7659448460817877, -0.9221257200555871, -1.039163218476263, -1.117697646878149, -1.159326218837182, -1.166506680866733, -1.1424912486254308, -1.0912748645155348, -1.0173802066321371, -0.9256859220505321, -0.8212839506385691, -0.7093463004661963, -0.594894369736546, -0.48261664619613864, -0.37671722092584475, -0.2807781904086141, -0.19759283567441058, -0.1290475663466662, -0.07603734906051797, -0.03840478475003792, -0.014897553109905228, -0.003168833594811095, 0.00018870527079089638, -0.0004216930463290517, 0.0003017896344984119, 0.00843091854036464, 0.03065195668425746, 0.07408520806385288, 0.14608485184991968, 0.2540236640274546, 0.4050682984063361, 0.6059555798389183, 0.8627645615281362, 1.1806927898849084, 1.563853343428088, 2.0151219285996964, 2.535961411764469, 3.126272945851379, 3.7843106801530113, 4.506714135375629, 5.288432689742035, 6.12270386405669, 7.0011476507393935, 7.9140536882790515, 8.850393697368837, 9.797922720078697, 10.743453241835248, 11.673390276065476, 12.573757926352961, 13.430360050889387, 14.229168313835718, 14.95701828872432, 15.601540202077548, 16.15127913743628, 16.596087808054687, 16.92784436033223, 17.140186605319425, 17.2284963977291, 17.190186339516252, 17.025296751068133, 16.735989099473667, 16.326346104063248, 15.802484216242643, 15.172935677622295, 14.447941743103412, 13.63909249559049, 12.759267537716783, 11.822790408537127, 10.844642704469232, 9.840036229931902, 8.824253866818378, 7.81264493889499, 6.819923459170685, 5.859800349632925, 4.944835161627181, 4.086388775754582, 3.2941523423498213, 2.57595177328178, 1.937711459734224, 1.383475511172638, 0.9152415907105916, 0.5329876824596856, 0.23479449695916052, 0.016991871347571914, -0.12572953297082898, -0.20010346885729427, -0.21403619099252522, -0.17635654946978616, -0.09654325414978311, 0.015572648237510598, 0.15009670807841738, 0.2973376206083943, 0.4480826711228724, 0.5938461039538127, 0.7270811969746747, 0.8413556157415577, 0.9314950042891533, 0.9936801244750392, 1.0254996215632945, 1.025960405902942, 0.9954426564863803, 0.9356171677643459, 0.8493271843851151, 0.7404336565689869, 0.6136215393803424, 0.47419288145619826, 0.3278437974484939, 0.1804223356975806, 0.03769736966514879, -0.09486109427309532, -0.21229618232824812, -0.31037260602562333, -0.38572024810701483, -0.43595374311807944, -0.45977079352130273, -0.4570205431279798, -0.42868439927941965, -0.3768366759853788, -0.3045786804146108, -0.2159288620970859, -0.11565372813117047, -0.009094322276463205, 0.09802827452195423, 0.19984895918134468, 0.29058249672491204, 0.36473462603901574, 0.41732174148462486, 0.44411345576011735, 0.44178232788078214, 0.40803294014460034, 0.341726874097356, 0.24300310251802432, 0.1132586049138683, -0.04488454159999971, -0.22762299903573902, -0.43004514308913105, -0.6463270744216234, -0.8699225761957459, -1.0937620910547534, -1.3104917380112127, -1.5127555319271346, -1.6934491707031494, -1.84597400906511, -1.9645240531142292, -2.0443066266037526, -2.0817215253754124, -2.0745304575682755, -2.0220395179113853, -1.9251272403214552, -1.7862358726885121, -1.6093492627562378, -1.3999632544253093, -1.1648780851451346, -0.9119770452110837, -0.6499995022201965, -0.38829935332186244, -0.1364779050468953, 0.0959637598041619, 0.2999586713445073, 0.4672081547524079, 0.5905415750247367, 0.6642262786472614, 0.6842385464997011, 0.6485029393273467, 0.5570649759324032, 0.41219857375167235, 0.21845354701198147, -0.017362123939242156, -0.2862983376262264, -0.577439308033069, -0.8781455432849785, -1.1743738501357914, -1.4510483784211756, -1.6924700324858206, -1.8827736869839817, -2.006435764068657, -2.0487400535016875, -1.9962515961177685, -1.8372952032606995, -1.5624089357701192, -1.1646940332658395, -0.6401430623303981, 0.01209156933399375, 0.789567289823442, 1.686469161348609, 2.6935761926533037, 3.798363675261584, 4.985369599556675, 6.236384796873759, 7.53072099098487, 8.845692784176407, 10.157471072080885, 11.441383207091931, 12.672334228875046, 13.825512019366256, 14.877526699515487, 15.806556738552448, 16.59268199856064, 17.218555808908924, 17.670518080995333, 17.938345474179005, 18.015275746472867, 17.898406526538793, 17.589491827338634, 17.09420107179943, 16.421745220867955, 15.584889151359494, 14.600287223226928, 13.487365167661267, 12.267640629862147, 10.964414769590238, 9.60270374673932, 8.20803200638024, 6.805686003653848, 5.4202946757803865, 4.075574595117973, 2.793377673867669, 1.5931543898582226, 0.49167198026062237, -0.49716343531970664, -1.3627574286758524, -2.0979697726978523, -2.699093397954459, -3.1657783866730553, -3.500937193718257, -3.710485298394208, -3.8030147995574035, -3.78945577294933, -3.682608557052769, -3.4966509040430496, -3.2466610827980262, -2.9481670411530425, -2.616604729234244, -2.2668484306489076, -1.9128096704347524, -1.5670913506816575, -1.2406513655924232, -0.9425721067324715, -0.6799121256426376, -0.45762469974109343, -0.27855730468981665, -0.14353201154811254, -0.051486456600918135, 0.0003294370724750124, 0.016083137270880163, 0.0010654375011178029, -0.03862329030328491, -0.09641240017239443, -0.16559804145478443, -0.23965033191847668, -0.31250190608337075, -0.3788267054195008, -0.4342266534419529, -0.4753664554488439, -0.5000727892286236, -0.5074016661540179, -0.4975694013005301, -0.4718495379523381, -0.432445771706484, -0.3823371194303103, -0.3250142675399061, -0.26422572011453205, -0.2037326072117524, -0.14706486016736384, -0.09724561224385991, -0.05656853643896484, -0.026418819272316874, -0.007132948322788935, 0.002101041356905433, 0.003272615314016294, -0.0004823913981591421, -0.004972538060388347, -0.00510098831045093, 0.004930815740536755, 0.031373512946634666, 0.08063618071544286, 0.15897522374222686, 0.27217251431824446, 0.4252099580643106, 0.6219545334485211, 0.864886775334477, 1.1548645016806123, 1.4909369745318777, 1.8702438926174765, 2.287970362048931, 2.737364680351314, 3.209849687857561, 3.695280621364159, 4.182175239575911, 4.658006887495491, 5.109606181866451, 5.523728382156568, 5.887422389578246, 6.1884432638080025, 6.415757062237843, 6.5601777035875015, 6.614619570285688, 6.5743735473330975, 6.437439943191498, 6.204923655539376, 5.880943178509545, 5.47255983526611, 4.989730639240628, 4.445254826043203, 3.854284915196821, 3.2338766859466075, 2.602551262146217, 1.9798232190076062, 1.385486064763622, 0.8389667792366817, 0.35871081165325513, -0.038432283715349194, -0.3378278535559178, -0.5275831722505329, -0.5990023429645743, -0.5469528876853381, -0.37009438204072853, -0.07101315448965709, 0.3437634753120292, 0.8639457509194793, 1.4757355488703745, 2.1621573178320768, 2.903547327997707, 3.6783116162385046, 4.463479028069922, 5.235313687759328, 5.9701044196095925, 6.645238659544311, 7.239675401855311, 7.734484679344195, 8.11356630231757, 8.364606768354546, 8.47909758773751, 8.452466576901138, 8.28438466114394, 7.97922964895879, 7.545492005525737, 6.995371438202906, 6.344548213393257, 5.612035803823755, 4.8191362305194145, 3.9886646067204605, 3.144350982326244, 2.310284407174866, 1.509829888267318, 0.7648535207977879, 0.09512138918550941, -0.4822567209219824, -0.9534989146765419, -1.3085428464654674, -1.5412863044033904, -1.6497599646754442, -1.6361396574184126, -1.5065728606262812, -1.270902723907172, -0.94231335247249, -0.536769828258748, -0.0723998662066167, 0.43115939781352547, 0.9534701358358625, 1.474054847826629, 1.9731043535725117, 2.43215412654544, 2.8347623278942704, 3.1670244157664076, 3.417980601215914, 3.579950474989048, 3.6488129602789674, 3.6239979702055725, 3.5083863438906455, 3.308136857700941, 3.0324353266777604, 2.6930023627669657, 2.3035723614855157, 1.8793385787371635, 1.4363510534919, 0.99085451845076, 0.5586652445922741, 0.15457276019238567, -0.20822909157038402, -0.5185848970746766, -0.7677475003567199, -0.9496709652766097, -1.0611861739224329, -1.1019983742080763, -1.0746237924454516, -0.9842235397931864, -0.8382615846364627, -0.6461278774154335, -0.4187385504786685, -0.16803567581776557, 0.09369395732920172, 0.35425479217597033, 0.6019757100890536, 0.8262284283000585, 1.0180848115414045, 1.170456206741183, 1.2782482117308354, 1.3385936317591909, 1.3511667861064802, 1.3178592050131914, 1.2425359008903627, 1.1308833801882834, 0.9903016615329814, 0.8292478465454001, 0.6567427432277487, 0.4819970749493452, 0.31408076393931916, 0.161284404303365, 0.030697294669459883, -0.07207531962470676, -0.14313047153608277, -0.18054113822432744, -0.18442456864198895, -0.15688501902452126, -0.10188234771640498, -0.025020731023922802, 0.06678889903130344, 0.16573494929779753, 0.26355394028770973, 0.35203781802540834, 0.42355360102100176, 0.4715459559257672, 0.4910103293087596, 0.47891427585799395, 0.4345337601092284, 0.3596944770279933, 0.25890823230731097, 0.13937713335497878, 0.01087397157916754, -0.11450165716332619, -0.22269367898610604, -0.2981663447319641, -0.3244738718515874, -0.28490991529684045, -0.16320621741042907, 0.055758616622986264, 0.3852366865298281, 0.8359230675418585, 1.4153976735066447, 2.12758372074232, 2.972283726991056, 3.9449046431706796, 5.03654564709731, 6.233899931478511, 7.519311944947476, 8.871176826264296, 10.264912711469607, 11.673250259351128, 13.06674365002581, 14.414742623317572, 15.687055091711466, 16.854236049688367, 17.888175036817035, 18.76321686295208, 19.457969611702676, 19.95509353298707, 20.241498295615628, 20.309105368851082, 20.156196573139194, 19.786408493228762, 19.208273100771923, 18.435327238359847, 17.486666120023358, 16.385267272513403, 15.156986642935747, 13.830103537819143, 12.435181970583328, 11.0032360757912, 9.56462254833599, 8.148430094364592, 6.782097059720707, 5.490050244820758, 4.293009393390102, 3.2076930170420996, 2.246691176120425, 1.4179807038323444, 0.7249282453217688, 0.16655449548131288, -0.2620991664305722, -0.5696230760071948, -0.7676458966568144, -0.8701427247127378, -0.8927265903284924, -0.8519129621323003, -0.7643619730655519, -0.6461659488652864, -0.512213013440849, -0.3756278769358441, -0.24732329043773474, -0.13567844041301397, -0.04635186672022525, 0.017754701948065766, 0.056404879705862, 0.07181211732795093, 0.06830543498014632, 0.051894344264703754, 0.029774542481401, 0.009784697568908752, -0.0001583044907893835, 0.0074000850459221635, 0.038942151470905476, 0.09952433657411032, 0.19244264581028928, 0.3189806028582734, 0.4782423208825273, 0.6671272922681344, 0.8805414804866079, 1.1115661359847577, 1.3517137121323342, 1.591359373030112, 1.8204459095723065, 2.0288488168759953, 2.206804967985508, 2.3455009067266483, 2.437878819348663, 2.478781738112425, 2.4651590770927223, 2.3963953087169925, 2.2747480101517, 2.104978029840103, 1.8940841057769784, 1.6511384913807796, 1.3871392703588576, 1.114191421968505, 0.844869283435532, 0.5916883205677604, 0.3665690894147783, 0.17998758141323767, 0.0403679837562015, -0.046389765184165405, -0.07734412477981276, -0.052887587469559086, 0.02311573087102891, 0.14333717792207376, 0.29709543191638493, 0.4706954206728079, 0.6479216710501915, 0.8106414542924655, 0.9395287134387739, 1.0149020366796269, 1.0175889035712467, 0.9298150965109643, 0.7361353036658854, 0.42421323377761655, -0.014482764838219492, -0.5840703771895994, -1.2837666116157875, -2.107699160609415, -3.0448491538370708, -4.079183231286505, -5.190093563645747, -6.352930351765379, -7.539652598896784, -8.719738975159506, -9.861537329892704, -10.933109080346028, -11.903174152061014, -12.742356899853498, -13.424902922461492, -13.929109383013328, -14.237903941259171, -14.339758936330618, -14.23002247487738, -13.910347659901818, -13.388417451800569, -12.678054509747279, -11.79966262708407, -10.77860734654653, -9.644101593555655, -8.428539574104887, -7.167102921340114, -5.89566237262839, -4.6493616889545715, -3.4616951074125217, -2.3638443806372074, -1.3829762544575952, -0.5412676205168314, 0.14459174434592725, 0.6636293160009205, 1.0112320760780296, 1.1891898169603783, 1.2053615580027603, 1.0730963214817235, 0.8107542864664373, 0.4408852978804239, -0.010803262186001668, -0.5166431219865315, -1.0480434718090388, -1.5766020010654678, -2.075253563652252, -2.519458230616071, -2.8879830529418733, -3.1635901834273694, -3.333650616109096, -3.390683028243748, -3.3323237541900554, -3.1611936370215656, -2.8846759883644744, -2.51457258341197, -2.0662964616232222, -1.558069524717206, -1.0100959317275666, -0.4436500006205507, 0.11994875564400698, 0.6602340641188802, 1.1584345840955876, 1.5983193373676086, 1.9667591216232894, 2.254126268487864, 2.454608716069142, 2.5664687044613594, 2.591799077827712, 2.536203804968431, 2.4084454848852386, 2.220050378908049, 1.9844674460543432, 1.7163084963122028, 1.4306608837094907, 1.1424362548606037, 0.8655161944963916, 0.6121092478563667, 0.3922703830945954, 0.21354053023403252, 0.08061726147552817, -0.0047388593152488945, -0.043624023171621666, -0.039772817265539114, 0.0007631198070968466, 0.07008050628749593, 0.15898261254154303, 0.2575989520416133, 0.3560123235150594, 0.44488490208970644, 0.5160493331144032, 0.5630310837982305, 0.5814467281065478, 0.569292945609476, 0.5271037089238393, 0.45794312553262456, 0.36725697157517245, 0.2626007300076139, 0.15322955628650006, 0.04953933688319737, -0.03749984718595012, -0.0969631178027194, -0.11864066046914092, -0.09372125176196809, -0.015314943752267851, 0.12106468741127442, 0.3170952237083824, 0.571410425952723, 0.8795474152928531, 1.2339842847702853, 1.6243468241235886, 2.0379106216095715, 2.46006346572688, 2.8748425326969067, 3.265650964734238, 3.6162627147339483, 3.9114101474424476, 4.137397965329923, 4.282835117536697, 4.339527879730753, 4.302653720656954, 4.170937229720296, 3.9468672837220886, 3.6369196301520392, 3.2510486491358286, 2.802214138418876, 2.3059182043098527, 1.7796725326200595, 1.2420437711618888, 0.7118056733835577, 0.20713887055018015, -0.2551810572193775, -0.6605892644410121, -0.9973750254060163, -1.257199889459921, -1.435478648876416, -1.5315165601730407, -1.5484903157217513, -1.493242608448492, -1.3758079271953427, -1.208848347099033, -1.0069955683912213, -0.7860035120374079, -0.5616177485908751, -0.34883177072345867, -0.16111105434351697, -0.009479845449999812, 0.09855064035566106, 0.15918255149251997, 0.17257075743390102, 0.14313475949746254, 0.07983732060891965, -0.004540562394885303, -0.09398954920915673, -0.16981976554583975, -0.21138637810684532, -0.19744436857095043, -0.10723509499767017, 0.07848506576051577, 0.37621771798634673, 0.7985728616841177, 1.353459341049272, 2.0433607659663795, 2.864500720886992, 3.8067220674689786, 4.85363950741359, 5.982861074897407, 7.166199409990791, 8.370799851879902, 9.56033971822742, 10.696203728764047, 11.738658370841607, 12.6486360989059, 13.389344890716469, 13.927707159890375, 14.23568155124655, 14.291647564921778, 14.081451150917044, 13.599147584100805, 12.847452369140555, 11.83789918160655, 10.590652961523913, 9.133975095238274, 7.503287868077719, 5.740070705610969, 3.890541345921514, 2.0040579845247333, 0.13117534312448695, -1.6779267885841462, -3.375070889169767, -4.915840366267974, -6.261462926455613, -7.37975950394377, -8.246073300007515, -8.84417890055554, -9.167027724746394, -9.216414964412499, -9.002679123008773, -8.544287353118012, -7.867042140384448, -7.0027238951380655, -5.987856770704591, -4.862307997624171, -3.667368481110052, -2.4442976820256535, -1.2330587679593472, -0.07098459984282539, 1.008714490962967, 1.9776935312094623, 2.8130944434410368, 3.4987145046406414, 4.027301718694005, 4.398421557992551, 4.6171874637968875, 4.692279176440393, 4.6319011950412365, 4.44765735454599, 4.155506959017697, 3.7794160987115313, 3.3596639449069987, 2.9327900404319287], 'positive_zeros': ['1.00429582563569572043564346386120', '1.27193287679133555141862337287842', '1.53515660561355164867993949042964', '1.71403526455697741416538416984582', '2.13409999330796236444640788121655', '2.21194569838360631144232425907100', '2.73129345536957542935029507038888', '2.81889130521058540160829223360598', '3.24681318391671947977094535206338', '3.56493847822622501583319031591195', '3.57470470352467855535306473402517', '3.59149591061077614802528530241056', '4.34302551539624240450587668861258', '4.41636826877582856312733702960575', '4.66267163451729961046086568385759', '4.82528943994074521641636881511210', '4.97316708748453382701676845351529', '5.27584693661184407968128493906893', '5.40733163364397188505797768214788', '5.59841777465940521575435540803973', '6.06178690426260958289221079158181', '6.37291978815668365772005135821140', '6.39890592584817335997313572898787', '6.68613027365212190681432055115129', '6.71455830302494320646054356259680', '6.74959183188466457389478152586075', '7.23495663221123530047904824185698', '7.31494027396041057658711801638821', '7.68261532937547794948260948360872', '7.82218769075698239804512182984723', '8.092123795331436383180762764707027', '8.247429746656681197432700436545549', '8.483897910118657352071753898325558', '8.572961381240159222404037465507809', '8.735445194946338423989297481951584', '8.820524125677110181469314497387606'], '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': 720056639438426618, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00429582563569572043564346386', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.27193287679133555141862337288', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.53515660561355164867993949043', 'prec': 103}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 64860626.53160265, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 5352009260481, 'conductor_radical': 39, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -115, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1808, 0, 0, 0, 0, 0, -1372, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 0, 0, -1486370, 0, 0, 0, 3138428376721], 'euler13': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler17': [1, 0, 19652, 0, 144825414, 0, 474351505988, 0, 582622237229761], 'euler19': [1, 0, 27436, 0, 282275286, 0, 1290750791116, 0, 2213314919066161], 'euler2': [1, 0, 0, 0, 115, 0, 0, 0, 4096], 'euler23': [1, 0, 48668, 0, 888215334, 0, 7204610645852, 0, 21914624432020321], 'euler29': [1, 0, 97556, 0, 3568939926, 0, 58028583903476, 0, 353814783205469041], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, 119164, 0, 5325022086, 0, 105758488642684, 0, 787662783788549761], 'euler37': [1, 0, 202612, 0, 15394358454, 0, 519846959180308, 0, 6582952005840035281], 'euler41': [1, 0, 0, 0, -315317810, 0, 0, 0, 22563490300366186081], 'euler43': [1, 1808, 1543852, 800627600, 274591480246, 63655498593200, 9759248985924748, 908687442381812144, 39959630797262576401], 'euler47': [1, 0, 0, 0, -19480835090, 0, 0, 0, 116191483108948578241], 'euler5': [1, 0, 0, 0, 3742, 0, 0, 0, 244140625], 'euler53': [1, 0, 595508, 0, 132986166774, 0, 13199054367208532, 0, 491258904256726154641], 'euler59': [1, 0, 0, 0, 78746477470, 0, 0, 0, 1779197418239532716881], 'euler61': [1, 0, -876820, 0, 295244076822, 0, -45174094647212020, 0, 2654348974297586158321], 'euler67': [1, 0, 1203052, 0, 542750293014, 0, 108826137585179788, 0, 8182718904632857144561], 'euler7': [1, 0, 1372, 0, 705894, 0, 161414428, 0, 13841287201], 'euler71': [1, 0, 0, 0, -234490873970, 0, 0, 0, 16409682740640811134241], 'euler73': [1, 0, 1556068, 0, 908005357734, 0, 235486346833071652, 0, 22902048046490258711521], 'euler79': [1, 0, 1622300, 0, 1144139233542, 0, 394360779091718300, 0, 59091511031674153381441], 'euler83': [1, 0, 0, 0, -633473875010, 0, 0, 0, 106890007738661124410161], 'euler89': [1, 0, 0, 0, -926581329650, 0, 0, 0, 246990403565262140303521], 'euler97': [1, 0, 3650692, 0, 4997832029574, 0, 3040924234618260868, 0, 693842360995438000295041], 'euler_factors': [[1, 0, 0, 0, 115, 0, 0, 0, 4096], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 3742, 0, 0, 0, 244140625], [1, 0, 1372, 0, 705894, 0, 161414428, 0, 13841287201], [1, 0, 0, 0, -1486370, 0, 0, 0, 3138428376721], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 19652, 0, 144825414, 0, 474351505988, 0, 582622237229761], [1, 0, 27436, 0, 282275286, 0, 1290750791116, 0, 2213314919066161], [1, 0, 48668, 0, 888215334, 0, 7204610645852, 0, 21914624432020321], [1, 0, 97556, 0, 3568939926, 0, 58028583903476, 0, 353814783205469041], [1, 0, 119164, 0, 5325022086, 0, 105758488642684, 0, 787662783788549761], [1, 0, 202612, 0, 15394358454, 0, 519846959180308, 0, 6582952005840035281], [1, 0, 0, 0, -315317810, 0, 0, 0, 22563490300366186081], [1, 1808, 1543852, 800627600, 274591480246, 63655498593200, 9759248985924748, 908687442381812144, 39959630797262576401], [1, 0, 0, 0, -19480835090, 0, 0, 0, 116191483108948578241], [1, 0, 595508, 0, 132986166774, 0, 13199054367208532, 0, 491258904256726154641], [1, 0, 0, 0, 78746477470, 0, 0, 0, 1779197418239532716881], [1, 0, -876820, 0, 295244076822, 0, -45174094647212020, 0, 2654348974297586158321], [1, 0, 1203052, 0, 542750293014, 0, 108826137585179788, 0, 8182718904632857144561], [1, 0, 0, 0, -234490873970, 0, 0, 0, 16409682740640811134241], [1, 0, 1556068, 0, 908005357734, 0, 235486346833071652, 0, 22902048046490258711521], [1, 0, 1622300, 0, 1144139233542, 0, 394360779091718300, 0, 59091511031674153381441], [1, 0, 0, 0, -633473875010, 0, 0, 0, 106890007738661124410161], [1, 0, 0, 0, -926581329650, 0, 0, 0, 246990403565262140303521], [1, 0, 3650692, 0, 4997832029574, 0, 3040924234618260868, 0, 693842360995438000295041]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/y'], '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-c3e4-0-5', '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': 720056639438426618, 'z1': {'__RealLiteral__': 0, 'data': '1.00429582563569572043564346386', 'prec': 103}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': '1273096206173794896638147932582,1612366474714555065771215221619,1946042192550349988883005840030,2172797831928004395827280037774', 'Lhash_array': ['1273096206173794896638147932582', '1612366474714555065771215221619', '1946042192550349988883005840030', '2172797831928004395827280037774'], 'label': '8-39e8-1.1-c3e4-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/y'}