Lfunction data - 6-2475e3-1.1-c3e3-0-6

Formats: - HTML - YAML - JSON - 2025-01-13T07:57:56.485068

• 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': '1265001090054643217345018300524,1286287211200289494955515850413,2011219642919260859859468961738', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': -8, 'a5': 0, 'a6': 0, 'a7': 16, 'a8': 12, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3114037.3861829336, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [11, [1, 33, 363, 1331]]], 'bad_primes': [3, 5, 11], 'central_character': '2475.1', 'coefficient_field': '1.1.1.1', 'conductor': 15160921875, 'conductor_radical': 165, 'degree': 6, 'euler_factors': [[1, 1, 9, 5, 72, 64, 512], [1], [1], [1, -16, 856, -11150, 293608, -1882384, 40353607], [1, 33, 363, 1331], [1, -45, 6871, -192794, 15095587, -217206405, 10604499373], [1, -58, 15434, -572224, 75827242, -1399979002, 118587876497], [1, 169, 28098, 2360147, 192724182, 7950753889, 322687697779], [1, 155, 41944, 3812131, 510332648, 22945562795, 1801152661463], [1, -277, 68543, -12078682, 1671695227, -164766059917, 14507145975869], [1, 173, 42261, 6587230, 1258997451, 153538136813, 26439622160671], [1, -60, 3724, 9069062, 188631772, -153943584540, 129961739795077], [1, 44, 133902, 3107666, 9228659742, 209004586604, 327381934393961], [1, 109, 228873, 16964786, 18197005611, 689028572341, 502592611936843], [1, 270, 208054, 52560216, 21600790442, 2910388138830, 1119130473102767], [1, -148, 385579, -33949544, 57403844783, -3280325447092, 3299763591802133], [1, -684, 535726, -196887298, 110026870154, -28851485010444, 8662995818654939], [1, 1038, 631795, 333327140, 143405460895, 53478148586718, 11694146092834141], [1, -314, 854861, -187279700, 257110558943, -28403932001066, 27206534396294947], [1, -1459, 1463380, -997438583, 523759799180, -186898314240739, 45848500718449031], [1, 1170, 1393615, 839920876, 542139926455, 177061044758130, 58871586708267913], [1, 506, 1295660, 507308816, 638810910740, 123002252493626, 119851595982618319], [1, -347, 1599297, -390027914, 914457233739, -113448309559043, 186940255267540403], [1, -607, 1367067, -593095898, 963739855923, -301667643613327, 350356403707485209], [1, -1263, 3146554, -2315882599, 2871774878842, -1052043642225327, 760231058654565217], [1, 813, None, None, None, 863015882438613, 1093685272684360901], [1, 1303, 2625717, 2003487426, 2869191860259, 1555850142377287, 1304773183829244583], [1, 355, 1875089, 1217781166, 2297064653827, 532759274906395, 1838459212420154507], [1, 13, 3229007, 208494854, 4181657706203, 21802301440933, 2171893279442309389], [1, -1394, 2528303, -1571224028, 3648080813791, -2902240743136946, 3004041937984268273]], 'euler_factors_factorization': [[[[1, 1, 9, 5, 72, 64, 512], 1]], [1], [1], [[[1, -16, 856, -11150, 293608, -1882384, 40353607], 1]], [[[1, 11], 3]], [[[1, -45, 6871, -192794, 15095587, -217206405, 10604499373], 1]], [[[1, -58, 15434, -572224, 75827242, -1399979002, 118587876497], 1]], [[[1, 169, 28098, 2360147, 192724182, 7950753889, 322687697779], 1]], [[[1, 155, 41944, 3812131, 510332648, 22945562795, 1801152661463], 1]], [[[1, -277, 68543, -12078682, 1671695227, -164766059917, 14507145975869], 1]], [[[1, 173, 42261, 6587230, 1258997451, 153538136813, 26439622160671], 1]], [[[1, -60, 3724, 9069062, 188631772, -153943584540, 129961739795077], 1]], [[[1, 44, 133902, 3107666, 9228659742, 209004586604, 327381934393961], 1]], [[[1, 109, 228873, 16964786, 18197005611, 689028572341, 502592611936843], 1]], [[[1, 270, 208054, 52560216, 21600790442, 2910388138830, 1119130473102767], 1]], [[[1, -148, 385579, -33949544, 57403844783, -3280325447092, 3299763591802133], 1]], [[[1, -684, 535726, -196887298, 110026870154, -28851485010444, 8662995818654939], 1]], [[[1, 1038, 631795, 333327140, 143405460895, 53478148586718, 11694146092834141], 1]], [[[1, -314, 854861, -187279700, 257110558943, -28403932001066, 27206534396294947], 1]], [[[1, -1459, 1463380, -997438583, 523759799180, -186898314240739, 45848500718449031], 1]], [[[1, 1170, 1393615, 839920876, 542139926455, 177061044758130, 58871586708267913], 1]], [[[1, 506, 1295660, 507308816, 638810910740, 123002252493626, 119851595982618319], 1]], [[[1, -347, 1599297, -390027914, 914457233739, -113448309559043, 186940255267540403], 1]], [[[1, -607, 1367067, -593095898, 963739855923, -301667643613327, 350356403707485209], 1]], [[[1, -1263, 3146554, -2315882599, 2871774878842, -1052043642225327, 760231058654565217], 1]]], 'gamma_factors': [[], [0, 0, 0]], 'group': 'GL2', 'index': 6, 'label': '6-2475e3-1.1-c3e3-0-6', '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}], 'nu_real_doubled': [3, 3, 3], 'order_of_vanishing': 3, 'origin': 'ModularForm/GL2/Q/holomorphic/2475/4/a/v', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.016927083333333332', 'prec': 67}, 'plot_values': [-7.93168148350827e-181, 0.00038585974657478773, 0.003077772860679057, 0.010336396301912822, 0.024332278521171397, 0.04710287743311132, 0.08051140096134686, 0.12620838080256366, 0.18559828683199187, 0.25980786486721985, 0.3496594742223249, 0.45565408718740996, 0.5779522874889118, 0.7163633197544057, 0.8703499749487671, 1.0390228477751058, 1.2211469612386618, 1.4151719784147234, 1.619237587946707, 1.831197162885539, 2.0486741130814017, 2.2690737229125197, 2.489620867771617, 2.7074404106648005, 2.9195688133122952, 3.123000779224302, 3.3147887384076564, 3.492046418543275, 3.65199771718807, 3.7920878722420346, 3.9099711626931515, 4.003554596387783, 4.071111682941388, 4.111247658576843, 4.122930888114201, 4.105599537411278, 4.059100147757674, 3.9837010480215485, 3.88018285694147, 3.7497496502271725, 3.5940210693038086, 3.4150995109770363, 3.215457135435399, 2.9979064902744637, 2.7656403235119074, 2.522101725310129, 2.270936560433491, 2.0160057320527742, 1.7612492005595417, 1.5106268246134986, 1.2681070923053082, 1.0375379864621022, 0.822585418002189, 0.6267062885711064, 0.45303965159849996, 0.3043532642451832, 0.18301167512425293, 0.09089955787575134, 0.02938662530660597, -0.00069735470665969, 0.0009011964372919722, 0.03385111878167213, 0.09722954385922779, 0.1895289915383476, 0.30867980412276186, 0.4520693297531934, 0.6165889455946136, 0.7986869793312993, 0.9944173806286071, 1.1995168953524067, 1.4094825496096712, 1.6196471404904484, 1.8252715177266206, 2.021635716586286, 2.2041323802440713, 2.368356003323658, 2.510193230611119, 2.625920059087719, 2.7122697820896353, 2.766506673831254, 2.7865096642654796, 2.770803963063133, 2.718603864697822, 2.6298654493008744, 2.50527324234036, 2.346242270731168, 2.154925649552899, 1.9341562909224452, 1.6874051292384686, 1.4187360011865477, 1.1327119406009165, 0.8343146350295512, 0.5288478938337152, 0.2218266812664985, -0.08112908752401833, -0.3744314834561294, -0.6526287566447775, -0.9105177820075735, -1.1433017602417688, -1.3466619585891022, -1.5168539083284611, -1.6508606136982036, -1.7464095942381368, -1.8020315495417139, -1.8171827904096838, -1.7921937378186836, -1.7282745279305283, -1.627584728442845, -1.493111662104263, -1.3286170821017824, -1.1386416934234826, -0.9283255899708728, -0.7033021112406973, -0.46963782272865623, -0.2336202600450827, -0.0016170957894577791, 0.22003339796139834, 0.42523305465110245, 0.6082717464346244, 0.7639588656168048, 0.8877953797090928, 0.9760967410578067, 1.0261110665404607, 1.0361200463573546, 1.0055066845802725, 0.9348245140410896, 0.8258066855304796, 0.6813572208871599, 0.5055434864553089, 0.30350995650734913, 0.08138618194395586, -0.15380976539870406, -0.39433714568593675, -0.6318970285621359, -0.8578096055291743, -1.0632268239903515, -1.239341324562153, -1.3776146291810047, -1.469992814681633, -1.5091191838183895, -1.488565570739877, -1.4030057847822788, -1.248386330864314, -1.0221034497450003, -0.7230982422721305, -0.35194454916262985, 0.08908385040504106, 0.5960136751128049, 1.1631935086135554, 1.7833778593193899, 2.4478153252562613, 3.1463837654072235, 3.8678423379252975, 4.599973582290989, 5.329812035581737, 6.044050180861027, 6.729179889253519, 7.371771609524971, 7.95898959449708, 8.478668211677912, 8.919584193972103, 9.272013059798248, 9.527680286893293, 9.679966490036588, 9.724426483008667, 9.658574756546491, 9.481974529571598, 9.196646764473437, 8.80668080090485, 8.318181568246999, 7.7395178272107765, 7.080786004565411, 6.35362092823512, 5.5712665402769, 4.747955765857911, 3.898622136481605, 3.038814915301639, 2.184081828729592, 1.3496442681173257, 0.5502132232258647, -0.20053163587352554, -0.8902284433121377, -1.5080383414215797, -2.0449901447176555, -2.494158862375991, -2.8508110933065653, -3.1125255824920783, -3.27921625236449, -3.3531543936375705, -3.3388613562149345, -3.242963356601857, -3.0740616942171504, -2.8424401231422065, -2.5597783333425275, -2.2388851983802747, -1.8933008475797402, -1.536930592730644, -1.1836983840745976, -0.8471427193080667, -0.5400539071129133, -0.2741344851676456, -0.05968339858960501, 0.0946791685356486, 0.18224903417284097, 0.19839937407779176, 0.14070380391869144, 0.008991575549139801, -0.1946663092971812, -0.46601398856641885, -0.7987801841798103, -1.184836635088772, -1.614418080008976, -2.0765090943458064, -2.559072121485869, -3.0493721615633684, -3.5345236995283904, -4.001688349334204, -4.438418679180172, -4.833270836521011, -5.1758734286264785, -5.45719979017171, -5.670138024170392, -5.809361589126968, -5.871458336967856, -5.855363345277078, -5.762010988702303, -5.59428780776978, -5.357271628151279, -5.057701993666189, -4.703772299865909, -4.305171282679325, -3.8724582380547132, -3.4167547043376567, -2.9496370403613494, -2.4825309931799238, -2.026391855673368, -1.5915346271523294, -1.187160821666754, -0.8211199045963615, -0.4997753070274062, -0.2277446050234348, -0.007812386048751596, 0.1590877508013145, 0.2738921034699573, 0.3393157406246749, 0.35971766681468437, 0.34091189341026656, 0.2899230831083881, 0.21471800511970568, 0.12389219401993942, 0.02634270053191767, -0.0690631348184541, -0.15381670340217332, -0.22008288179253757, -0.2609912757635475, -0.2708796903859374, -0.24550429658858383, -0.1821875291125421, -0.07991318151937755, 0.060628667605820495, 0.23710865022766403, 0.4456162849215844, 0.680790230217614, 0.9361158446518874, 1.2040818878705433, 1.4764410876981846, 1.7446903690013882, 2.000228966093962, 2.2346626330704313, 2.4403669452112564, 2.610538903840882, 2.739443037708273, 2.8229350718587187, 2.8583247140897217, 2.844479372167288, 2.782199383347126, 2.6738650835881903, 2.5233595697088056, 2.336234533899321, 2.119183374874061, 1.8798047001645317, 1.6265654243039958, 1.3682018681446093, 1.1134014134994799, 0.8706355340423618, 0.6476224141185473, 0.451036675797778, 0.28632742252036764, 0.15736699583046243, 0.0662959117841746, 0.013444371842402535, -0.0027569121094941393, 0.014271363508909445, 0.05936150099276069, 0.1257730339885667, 0.20544716407307426, 0.2893026877992301, 0.3675977382667355, 0.43032362823690185, 0.4676203567786275, 0.4701955935803289, 0.42973860370448747, 0.3393199372934082, 0.1937253131328301, -0.010245476319924254, -0.2735533534784763, -0.5947768872539663, -0.9700348606727094, -1.3930659625060795, -1.8553065423646111, -2.3460745800792617, -2.853010060397036, -3.362312326038094, -3.8591407107598594, -4.328371292079061, -4.754856363068295, -5.12392138933042, -5.422299267356459, -5.638240810796543, -5.761947210024633, -5.786485165095607, -5.707601500091639, -5.523940981978102, -5.237745924886795, -4.8543068071603255, -4.381877056155062, -3.8320222328840936, -3.218749752928367, -2.5581277602122627, -1.8682549488906783, -1.168221401856922, -0.47753810202666624, 0.18418377786472423, 0.7982189634071637, 1.3473112031312566, 1.8161044390202294, 2.191849182297754, 2.4648060576920363, 2.6285741503429834, 2.680357921451165, 2.621046737384449, 2.4552654808432752, 2.19116356451196, 1.840124775093756, 1.4164651559478227, 0.9368449851765025, 0.4196827038719031, -0.11544500436812927, -0.6485547157465381, -1.1599634998621036, -1.6310152642515436, -2.044734392834245, -2.386431986581975, -2.644325352195373, -2.809868169678391, -2.878058637755685, -2.847735856748851, -2.7214717288367063, -2.505476589107335, -2.2094504556395482, -1.8460736012314254, -1.430537329814729, -0.9799707391919679, -0.5127099825060412, -0.047610060675016136, 0.3967884103222877, 0.8029456790010043, 1.1549940430817467, 1.4395719136093938, 1.6462038296642008, 1.767716465908062, 1.8008048250444628, 1.7459381208991533, 1.6073627708967715, 1.3932157182883427, 1.1149452103670576, 0.786881834804999, 0.42586670330690635, 0.05034329424370638, -0.3203703654563003, -0.6667990938924413, -0.9702713433598736, -1.2136998618947155, -1.3823737591947702, -1.4646659305480652, -1.45258801356067, -1.3423442341309517, -1.1345538097818688, -0.834364733618788, -0.4515242684371713, -4.0725070810611844e-05, 0.5022180435386545, 1.0340219490186524, 1.5715673088071234, 2.089293563580805, 2.56082940742713, 2.9599705969617807, 3.261663672653543, 3.4431035350662738, 3.4845776979367056, 3.3702991304851744, 3.0892671795901925, 2.6357089029346916, 2.009479192936209, 1.2163294569978673, 0.26783034590474053, -0.8188093146316051, -2.0212709207222486, -3.3126344526064075, -4.662100977320684, -6.036299338505031, -7.399955912866712, -8.716938530002523, -9.952097656229768, -11.071732702109049, -12.044626937568626, -12.844026660845019, -13.447569012570739, -13.83797614353927, -14.004746064628028, -13.943357008515733, -13.655399136718547, -13.149653550382055, -12.44061158784308, -11.548007448860895, -10.497162080550112, -9.317078308860795, -8.039535129629215, -6.698802791922228, -5.329720540134748, -3.9666554277835644, -2.6428764904029842, -1.389040266820287, -0.23235531577234367, 0.8040227413696011, 1.7017894324395584, 2.447857676770211, 3.0346348838088066, 3.4600092568683944, 3.727148284661798, 3.8442997813225603, 3.8241076042890976, 3.682937201194986, 3.440254283011241, 3.1175925298355445, 2.7376543277445426, 2.323491231873391, 1.8975124706106665, 1.4806696111972804, 1.0917412418239518, 0.7467044706559364, 0.45826191772595865, 0.23549417270231407, 0.08374649153538272, 0.004617690687667787, -0.00389274883868618, 0.052961344848481924, 0.16707007917259845, 0.32805696350340363, 0.5238588276660688, 0.7413355501378248, 0.967097534106325, 1.1880224199467992, 1.3918213158959591, 1.5678317739431866, 1.7072210651008237, 1.8032935044608562, 1.8520146246711704, 1.8517913799181676, 1.8034256977476462, 1.7102602478461673, 1.5776008580214844, 1.412370968929604, 1.2229271985743932, 1.0183284105932398, 0.8078637601817804, 0.6007122730233503, 0.40531331021028155, 0.22898146723033566, 0.07762863703874319, -0.044563557357267684, -0.13527880212870128, -0.19411553547641072, -0.22254355512370022, -0.22374220356216012, -0.20237870972042094, -0.1642760897558326, -0.11603929630008299, -0.0646588888342299, -0.01707933759241261, 0.020211764253308548, 0.041564952044649627, 0.04249227044551683, 0.019929083420735544, -0.027595855979814836, -0.09987879160560031, -0.1950417405367138, -0.3096857966292058, -0.43905214964409567, -0.577276079711822, -0.7178381507490597, -0.8538383208770071, -0.9783749818529863, -1.0851381710756178, -1.1685984396914886, -1.2243218357226697, -1.2494855029807064, -1.2428084232957606, -1.2046392483961752, -1.1372088661164634, -1.04424086508483, -0.9307530544794828, -0.8029821545485456, -0.6677603195859937, -0.5321087263001236, -0.4029252002021544, -0.28633325834603296, -0.18725592805022484, -0.109077726427501, -0.05320851300371226, -0.018855742296727408, -0.0028989387854472487, 0.00015823895811404012, -0.0019320668574330738, 0.000600888682605983, 0.019180601395582447, 0.06640986603470757, 0.15549424816149382, 0.29960091103324793, 0.5111862458761414, 0.8012934818151104, 1.1788813106045641, 1.65021356877268, 2.2183688525715364, 2.882781058611483, 3.6389541163370285, 4.478519826994567, 5.389113444649152, 6.354565250364901, 7.355703841785493, 8.370500232339504, 9.374703305535538, 10.343355084914421, 11.250956913606988, 12.07233134013975, 12.78458010092676, 13.366938175169972, 13.80153854304527, 14.075396082256804, 14.17966819377552, 14.11002031170765, 13.8682210542982, 13.46071290983325, 12.89842309706882, 12.197709586101048, 11.378395947046577, 10.463088894507292, 9.477461529509831, 8.44812419809065, 7.40170959317287, 6.364719873377576, 5.361699015885911, 4.414445204597986, 3.5417845778992905, 2.7584353053171164, 2.0746609910752873, 1.496310212747548, 1.0245412074682154, 0.6560545411557959, 0.3835655980146075, 0.1962750648317943, 0.08058459866059955, 0.020923696289158848, 0.0006169340304213038, 0.0027900635008707556, 0.011260681634871818, 0.011362251650130651, -0.009326719148507318, -0.06040246894355181, -0.14820698631459964, -0.27556307964593096, -0.44179380723216116, -0.6428118547776055, -0.8714038109485813, -1.1179172772877577, -1.3707217203198752, -1.6168880148194162, -1.8433475059867646, -2.037382583994414, -2.1873754507505496, -2.2840518701943484, -2.3206258307964593, -2.293262386324486, -2.20198591914162, -2.050246419195401, -1.8448701787881525, -1.5963572007644478, -1.3178947968029873, -1.024802536147987, -0.7342074208469692, -0.46378900094519626, -0.2309597110180989, -0.05217713218360901, 0.05815427803158033, 0.08839455456566388, 0.030300266213749556, -0.12041348751838556, -0.3638098104130702, -0.6955486526558037, -1.1070216446540446, -1.5856889588645378, -2.115545224060642, -2.6778101617883183, -3.2517550844623417, -3.8157256521673775, -4.347994845384262, -4.8277473984452, -5.236320861310431, -5.5577387683031665, -5.779442474927763, -5.893315225842911, -5.89553416468455, -5.786742568491007, -5.57252219040555, -5.262486873254933, -4.869832742495351, -4.411178659463364, -3.905151158722526, -3.371529006476831, -2.8306646761807563, -2.302036733570113, -1.803392244070871, -1.350156982973209, -0.9544545165479312, -0.6246566497155827, -0.3651911959543923, -0.17633223820765034, -0.05438594721014466, 0.007895698426090522, 0.020778850591829278, -0.0032059187971890542, -0.05017707391068953, -0.1058393194295408, -0.1564634150745115, -0.18991082508517723, -0.1964630072983777, -0.1695604753915883, -0.10644007216131707, -0.008414760273390965, 0.11900519996967439, 0.2662310996577268, 0.42003552976145536, 0.5641525751900952, 0.680192927203347, 0.7486210101214824, 0.749840265828927, 0.6655548846346828, 0.47983466595477714, 0.18019801604497357, -0.24120360348922304, -0.7869334209881341, -1.4537160739026294, -2.2320761371694764, -3.1063971718754697, -4.055222715128668, -5.052101025532477, -6.066282539409893, -7.063831997249826, -8.009610484454482, -8.868164940639037, -9.605234043498687, -10.190342531406213, -10.597241228213573, -10.80517885691183, -10.801322236145653, -10.580197429909761, -10.1441584611823, -9.504903411211075, -8.68172991990533, -7.700949082009635, -6.596130613679361, -5.405476367092038, -4.170375629142758, -2.934535724420298, -1.7411848259346, -0.6313504867274764, 0.357507327420837, 1.1936148045495671, 1.852151533277246, 2.3163026804628344, 2.578058325779431, 2.638459075419491, 2.507682921167171, 2.204367648698089, 1.7546840109074882, 1.191262475785104, 0.5514414012846367, -0.12448752350947577, -0.7951528627608802, -1.4201272633812663, -1.9618053364187904, -2.3873081037188646, -2.6699133792994627, -2.790289506703223, -2.737581477886618, -2.509688127793959, -2.1133515654703543, -1.563868674343743, -0.8842012742502474, -0.10390713873090755, 0.7425356587836041, 1.6172503170666448, 2.4807083697686543, 3.294245274421918, 4.021368063460897, 4.629414430902584, 5.0920301343871035, 5.389484935856692, 5.509527587452711, 5.448990368683041, 5.212754623283624, 4.813449819298593, 4.271748275242132, 3.614208385369916, 2.8719829937692474, 2.079941456302938, 1.274113581305453, 0.4900118860727208, -0.23878800199790598, -0.8826962360088548, -1.4174024160885836, -1.8250119304856898, -2.094889970468497, -2.2239816838649076, -2.217029577039585, -2.0860206487279767, -1.8493868354584508, -1.531148963890657, -1.1593493027215076, -0.7644893906122373, -0.37799553945137293, -0.030404216953636813, 0.25027132679948677, 0.43999536976761866, 0.5199767586388606, 0.47766571973726807, 0.30735800136715047, 0.01045790937519981, -0.4045634421016158, -0.9228470171273301, -1.5238131602812617, -2.182152820567199, -2.8696360691615, -3.556152950720161, -4.211202216924772, -4.806432561734479, -5.316199641350463, -5.7185446397131505, -5.996841483621653, -6.139896458625818, -6.1431786099192935, -6.011885494899953, -5.7573662375775445, -5.393622711036254, -4.932284759771653, -4.388465167969355, -3.7884061567268246, -3.1812867605536215], 'positive_zeros': ['0.997909905006072522647684163778713', '1.01470169380167116607799455431039', '1.58657254811156824820093674792715', '1.94673506044199708653465687081367', '2.20645791519083836536642427675502', '2.46813537405271466369895016292912', '3.04222779260184957883982800014294', '3.40810718077426570558115688269136', '3.48787369225175766709524233710032', '4.08011478932058509051533724221926', '4.23634240468506285450847731495322', '4.37735124843775149016248548821631', '4.91837487161020108513765943129512', '4.93216022047827053506083889211235', '5.14508688907335366592253377243270', '5.61497713994008519672382193004804', '5.87006247369572543624364456081716', '6.16322256798716487300231275938458', '6.40070387776346695537497493812788', '6.60156393568827618328371755523298', '6.85983408587648447115154863048058', '7.33304568780582597426060088345831', '7.68689843590326600292642929956056', '7.70404876003238400828711026515238', '8.118317832921700573298589410103506', '8.284371968034373313405544638986731', '8.353269635687547896373284706757444'], 'prelabel': '6-2475e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 12.084276033929713, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3e3-0', 'trace_hash': 2142427456641024199, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.997909905006072522647684163779', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.01470169380167116607799455431', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.58657254811156824820093674793', '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': 3114037.3861829336, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 15160921875, 'conductor_radical': 165, 'degree': 6, 'dirichlet_coefficients': [1, -1, 0, -8, 0, 0, 16, 12, 0, 0, -33, 0, 45, -16, 0, -7, 58, 0, -169, 0, 0, 33, -155, 0, 0, -45, 0, -128, 277, 0, -173, -53, 0, -58, 0, 0, 60, 169, 0, 0, -44, 0, -109, 264, 0, 155, -270, 0, -600, 0, 0, -360, 148, 0, 0, 192, 0, -277, 684, 0, -1038, 173, 0, 184, 0, 0, 314, -464, 0, 0, 1459, 0, -1170, -60, 0, 1352, -528, 0, -506, 0, 0, 44, 347, 0, 0, 109, 0, -396, 607, 0, 720, 1240, 0, 270, 0, 0, 1263, 600, 0, 0], 'euler11': [1, 33, 363, 1331, 0, 0, 0], 'euler13': [1, -45, 6871, -192794, 15095587, -217206405, 10604499373], 'euler17': [1, -58, 15434, -572224, 75827242, -1399979002, 118587876497], 'euler19': [1, 169, 28098, 2360147, 192724182, 7950753889, 322687697779], 'euler2': [1, 1, 9, 5, 72, 64, 512], 'euler23': [1, 155, 41944, 3812131, 510332648, 22945562795, 1801152661463], 'euler29': [1, -277, 68543, -12078682, 1671695227, -164766059917, 14507145975869], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, 173, 42261, 6587230, 1258997451, 153538136813, 26439622160671], 'euler37': [1, -60, 3724, 9069062, 188631772, -153943584540, 129961739795077], 'euler41': [1, 44, 133902, 3107666, 9228659742, 209004586604, 327381934393961], 'euler43': [1, 109, 228873, 16964786, 18197005611, 689028572341, 502592611936843], 'euler47': [1, 270, 208054, 52560216, 21600790442, 2910388138830, 1119130473102767], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, -148, 385579, -33949544, 57403844783, -3280325447092, 3299763591802133], 'euler59': [1, -684, 535726, -196887298, 110026870154, -28851485010444, 8662995818654939], 'euler61': [1, 1038, 631795, 333327140, 143405460895, 53478148586718, 11694146092834141], 'euler67': [1, -314, 854861, -187279700, 257110558943, -28403932001066, 27206534396294947], 'euler7': [1, -16, 856, -11150, 293608, -1882384, 40353607], 'euler71': [1, -1459, 1463380, -997438583, 523759799180, -186898314240739, 45848500718449031], 'euler73': [1, 1170, 1393615, 839920876, 542139926455, 177061044758130, 58871586708267913], 'euler79': [1, 506, 1295660, 507308816, 638810910740, 123002252493626, 119851595982618319], 'euler83': [1, -347, 1599297, -390027914, 914457233739, -113448309559043, 186940255267540403], 'euler89': [1, -607, 1367067, -593095898, 963739855923, -301667643613327, 350356403707485209], 'euler97': [1, -1263, 3146554, -2315882599, 2871774878842, -1052043642225327, 760231058654565217], 'euler_factors': [[1, 1, 9, 5, 72, 64, 512], [1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, -16, 856, -11150, 293608, -1882384, 40353607], [1, 33, 363, 1331, 0, 0, 0], [1, -45, 6871, -192794, 15095587, -217206405, 10604499373], [1, -58, 15434, -572224, 75827242, -1399979002, 118587876497], [1, 169, 28098, 2360147, 192724182, 7950753889, 322687697779], [1, 155, 41944, 3812131, 510332648, 22945562795, 1801152661463], [1, -277, 68543, -12078682, 1671695227, -164766059917, 14507145975869], [1, 173, 42261, 6587230, 1258997451, 153538136813, 26439622160671], [1, -60, 3724, 9069062, 188631772, -153943584540, 129961739795077], [1, 44, 133902, 3107666, 9228659742, 209004586604, 327381934393961], [1, 109, 228873, 16964786, 18197005611, 689028572341, 502592611936843], [1, 270, 208054, 52560216, 21600790442, 2910388138830, 1119130473102767], [1, -148, 385579, -33949544, 57403844783, -3280325447092, 3299763591802133], [1, -684, 535726, -196887298, 110026870154, -28851485010444, 8662995818654939], [1, 1038, 631795, 333327140, 143405460895, 53478148586718, 11694146092834141], [1, -314, 854861, -187279700, 257110558943, -28403932001066, 27206534396294947], [1, -1459, 1463380, -997438583, 523759799180, -186898314240739, 45848500718449031], [1, 1170, 1393615, 839920876, 542139926455, 177061044758130, 58871586708267913], [1, 506, 1295660, 507308816, 638810910740, 123002252493626, 119851595982618319], [1, -347, 1599297, -390027914, 914457233739, -113448309559043, 186940255267540403], [1, -607, 1367067, -593095898, 963739855923, -301667643613327, 350356403707485209], [1, -1263, 3146554, -2315882599, 2871774878842, -1052043642225327, 760231058654565217]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2475/4/a/v'], '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': '6-2475e3-1.1-c3e3-0-6', '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}], 'nu_real_doubled': [3, 3, 3], 'order_of_vanishing': 3, 'prelabel': '6-2475e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 12.084276033929713, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3e3-0', 'trace_hash': 2142427456641024199, 'z1': {'__RealLiteral__': 0, 'data': '0.997909905006072522647684163779', 'prec': 107}}
• lfunc_instances •

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

  
  {'Lhash': '1265001090054643217345018300524,1286287211200289494955515850413,2011219642919260859859468961738', 'Lhash_array': ['1265001090054643217345018300524', '1286287211200289494955515850413', '2011219642919260859859468961738'], 'label': '6-2475e3-1.1-c3e3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/4/a/v'}