Lfunction data - 4-3e4-1.1-c21e2-0-0

Formats: - HTML - YAML - JSON - 2024-04-25T07:10:52.347741

• 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': '499978996465706018335479911013,1577157603667616301750730882372', 'a10': 663919416, 'a2': -666, 'a3': 0, 'a4': -1285756, 'a5': -996876, 'a6': 0, 'a7': 679896112, 'a8': 611332056, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 632.6714463549673, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.5', 'prec': 14}, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '9.1', 'coefficient_field': '1.1.1.1', 'conductor': 81, 'conductor_radical': 3, 'degree': 4, 'euler_factors': [[1, 666, 1729312, 1396703232, 4398046511104], [1], [1, 996876, 479727216206350, 475347518920898437500, 227373675443232059478759765625], [1, -679896112, 1147317924110377614, -379753161363905240551080784, 311973482284542371301330321821976049], [1, 219869122968, 24368468203545949073734, 1627086464988032548830592684714248, 54763699237492901685126120802225273763666521], [1, 48468909956, -87046554991999245321666, 11974948412982611194223033020835828, 61040881526285814362156628321386486455989674569], [1, -11333529041436, 163049233709759468659315558, -783055439532061324977538663508749563612, 4773695331839566234818968439734627784374274207965089], [1, -11960585011624, 173516252603875318424026518, -8542363389349695341123216061496859614456, 510095203738582479622335815880298130716653502143703561], [1, -146508390063504, 70350674583296071946138208046, -5782918242779264795609305039610334909418992, 1558005952997140033806173725098810522409738596181909282129], [1, -1798520043674052, 7587059836229882944079722961758, -9231520492051562840021502973477889595578670708, 26346074268992142099064516382762907506814419719803282255713641], [1, -11169107526944992, 65110043582704149302277695219262, -232602320210870623007501051321922263773442097952, 433701716541192355457229753999917360820651622584523552060436161], [1, -12736264858660012, 1169087614331349951957049436247054, -10896280818239554894640017446830763986122907759644, 731934824502651514621160916115101341995441470527191525223322819769], [1, 122972020616468052, 11537437518922444803031032170525302, 908379449125753770406320291339230453947357267743732, 54565982855941191947249368879497196495421462536627690767330656099281], [1, -288455418162270040, 60588844480912796894264501569866630, -5793169933804356783766057296019576226939705287291720, 403343566675122500462878634623535631588559593930513766350645748813849], [1, 837243745741596960, 435212250071069604210871713333695710, 108869675554582995594015122856205129417057809732945120, 16908692777708688563979281162874109375742132033178319498546247522565409], [1, -43007964012775764, 3035046442171135358103872093607580846, -69717554565147509777049671721234831423614484987104292, 2627764996340071914932060028590629703016273743509013665720935053615458009], [1, -3523823330903857224, 22496141078639900048146408173821413798, -54313322564229040580479664885632358969825116705752821016, 237566111385928825180581197186581724740035515556906717126291161106235417081], [1, 1779023128451013860, 54581477540293900337554820522490345438, 55221491112909501494787800089051446776599515682427437460, 963502998275379493962849646581354683437407419033192428674820139330228382121], [1, 16454068667621610296, 483672984740847466171511634737330990838, 3663061094560387395932853428920480093626820350342458517032, 49561188616996901345349189252156955439051753759670367683995836545268981893289], [1, 17379227131150420944, 1578450641853831735097967952041073581326, 13075424043949467210334580080473301273554066026655005544624, 566044592922467932920289630256783944174352087720184706882390017513705742761841], [1, -50891146268473989076, 1519084761764201093580550328041283444406, -68615509976601001711116009132924028044303191525431646748148, 1817858708606516392063752284490078897342614279715947003348265995414509863302929], [1, 54055785594190591040, 14861294583513934634248604408585443331358, 382834528332584185944153812342805357187985297840513506996160, 50157725483905227341761748890141694180076101090840037071925071763978352502147041], [1, 111108429277666677288, 39997912234158986996837338981425633593878, 2220173670617504285341283509603621514972856652400421129437304, 399282135658682469334331901689876886678820965774126540592961885129481494196023689], [1, 226920767965448065524, 171269531303391580490166794691127246306198, 19636513668421346803287292967855386289346105454176845265130836, 7488249032982960608606585095904734981347282237297075167277004918963148603698150321], [1, 128331469252795746236, 780378418922367967273197315773085057717318, 67692349189173687709577926593180875355911033379402282012741692, 278235691213844046805607971221988942088139032625098384397060765968745910963026076609], [1, -1486652631697148916852, 2172815480654891353525709392799286916187854, -1832138721399887088895531011529230532017445391581145250423506052, 1518789894633344114558187057241532359566305770497313080998093132114937103884488614201], [1, 110997725102286224720, 2199223251100409323717601332097364304123470, 206488465479885950601572915673293466086839431300471734778490160, 3460695893531817996658349481083474517849949869415850595461675555044106143967951861809], [1, -811468735372666299240, 8230981820381533710790412182124736870463750, -3359936914059459781364974805852705252310141286575716489616658680, 17144256780108035603880534575647498377121472595621714814881607371777034087912296215449], [1, 162920020974569929796, 11980728189555603184974304825665859230634878, 995247084621833926301544098892531402904342490611043946771142964, 37317531966144644223023469252436379373897973663646166843862654536796454569588761033481], [1, -2108125891845462086172, 14808625093442879504293386178372866127082278, -27450095228027725716789658915871588576508217375172960717658598236, 169548763280838543075970667041682503721606000913649454670696321095954881733907235299169]], 'euler_factors_factorization': [[[[1, 666, 1729312, 1396703232, 4398046511104], 1]], [1], [[[1, 996876, 479727216206350, 475347518920898437500, 227373675443232059478759765625], 1]], [[[1, -679896112, 1147317924110377614, -379753161363905240551080784, 311973482284542371301330321821976049], 1]], [[[1, 219869122968, 24368468203545949073734, 1627086464988032548830592684714248, 54763699237492901685126120802225273763666521], 1]], [[[1, 48468909956, -87046554991999245321666, 11974948412982611194223033020835828, 61040881526285814362156628321386486455989674569], 1]], [[[1, -11333529041436, 163049233709759468659315558, -783055439532061324977538663508749563612, 4773695331839566234818968439734627784374274207965089], 1]], [[[1, -11960585011624, 173516252603875318424026518, -8542363389349695341123216061496859614456, 510095203738582479622335815880298130716653502143703561], 1]], [[[1, -146508390063504, 70350674583296071946138208046, -5782918242779264795609305039610334909418992, 1558005952997140033806173725098810522409738596181909282129], 1]], [[[1, -1798520043674052, 7587059836229882944079722961758, -9231520492051562840021502973477889595578670708, 26346074268992142099064516382762907506814419719803282255713641], 1]], [[[1, -11169107526944992, 65110043582704149302277695219262, -232602320210870623007501051321922263773442097952, 433701716541192355457229753999917360820651622584523552060436161], 1]], [[[1, -12736264858660012, 1169087614331349951957049436247054, -10896280818239554894640017446830763986122907759644, 731934824502651514621160916115101341995441470527191525223322819769], 1]], [[[1, 122972020616468052, 11537437518922444803031032170525302, 908379449125753770406320291339230453947357267743732, 54565982855941191947249368879497196495421462536627690767330656099281], 1]], [[[1, -288455418162270040, 60588844480912796894264501569866630, -5793169933804356783766057296019576226939705287291720, 403343566675122500462878634623535631588559593930513766350645748813849], 1]], [[[1, 837243745741596960, 435212250071069604210871713333695710, 108869675554582995594015122856205129417057809732945120, 16908692777708688563979281162874109375742132033178319498546247522565409], 1]], [[[1, -43007964012775764, 3035046442171135358103872093607580846, -69717554565147509777049671721234831423614484987104292, 2627764996340071914932060028590629703016273743509013665720935053615458009], 1]], [[[1, -3523823330903857224, 22496141078639900048146408173821413798, -54313322564229040580479664885632358969825116705752821016, 237566111385928825180581197186581724740035515556906717126291161106235417081], 1]], [[[1, 1779023128451013860, 54581477540293900337554820522490345438, 55221491112909501494787800089051446776599515682427437460, 963502998275379493962849646581354683437407419033192428674820139330228382121], 1]], [[[1, 16454068667621610296, 483672984740847466171511634737330990838, 3663061094560387395932853428920480093626820350342458517032, 49561188616996901345349189252156955439051753759670367683995836545268981893289], 1]], [[[1, 17379227131150420944, 1578450641853831735097967952041073581326, 13075424043949467210334580080473301273554066026655005544624, 566044592922467932920289630256783944174352087720184706882390017513705742761841], 1]], [[[1, -50891146268473989076, 1519084761764201093580550328041283444406, -68615509976601001711116009132924028044303191525431646748148, 1817858708606516392063752284490078897342614279715947003348265995414509863302929], 1]], [[[1, 54055785594190591040, 14861294583513934634248604408585443331358, 382834528332584185944153812342805357187985297840513506996160, 50157725483905227341761748890141694180076101090840037071925071763978352502147041], 1]], [[[1, 111108429277666677288, 39997912234158986996837338981425633593878, 2220173670617504285341283509603621514972856652400421129437304, 399282135658682469334331901689876886678820965774126540592961885129481494196023689], 1]], [[[1, 226920767965448065524, 171269531303391580490166794691127246306198, 19636513668421346803287292967855386289346105454176845265130836, 7488249032982960608606585095904734981347282237297075167277004918963148603698150321], 1]], [[[1, 128331469252795746236, 780378418922367967273197315773085057717318, 67692349189173687709577926593180875355911033379402282012741692, 278235691213844046805607971221988942088139032625098384397060765968745910963026076609], 1]], [[[1, -1486652631697148916852, 2172815480654891353525709392799286916187854, -1832138721399887088895531011529230532017445391581145250423506052, 1518789894633344114558187057241532359566305770497313080998093132114937103884488614201], 1]], [[[1, 110997725102286224720, 2199223251100409323717601332097364304123470, 206488465479885950601572915673293466086839431300471734778490160, 3460695893531817996658349481083474517849949869415850595461675555044106143967951861809], 1]], [[[1, -811468735372666299240, 8230981820381533710790412182124736870463750, -3359936914059459781364974805852705252310141286575716489616658680, 17144256780108035603880534575647498377121472595621714814881607371777034087912296215449], 1]], [[[1, 162920020974569929796, 11980728189555603184974304825665859230634878, 995247084621833926301544098892531402904342490611043946771142964, 37317531966144644223023469252436379373897973663646166843862654536796454569588761033481], 1]], [[[1, -2108125891845462086172, 14808625093442879504293386178372866127082278, -27450095228027725716789658915871588576508217375172960717658598236, 169548763280838543075970667041682503721606000913649454670696321095954881733907235299169], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 0, 'label': '4-3e4-1.1-c21e2-0-0', 'leading_term': '0.96852262296885567480552682324647931293185993580147227195311489837901669142220829301002569', 'load_key': 'CMFs-workshop', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21, 21], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/9/22/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.048828125', 'prec': 37}, 'plot_values': [0.9685226229688557, 0.9447083010086975, 0.8991779132786096, 0.815964343579003, 0.699154986664099, 0.5566655765761851, 0.3923552819587429, 0.2100384496517389, 0.015428808404731726, -0.1852372801686392, -0.38570028247985766, -0.5796854980203259, -0.7608716793809299, -0.9232095051906329, -1.0610404341517605, -1.1693007645485218, -1.2436088661697, -1.2804347390758255, -1.2771755376523972, -1.2322598178961568, -1.1451886546411374, -1.0165720500155169, -0.8481286952943043, -0.6426523798550815, -0.40396632123912857, -0.13682434853545652, 0.1531789059443817, 0.45976039756477055, 0.7760779608136522, 1.0949176368461524, 1.4088553728345272, 1.710455090016121, 1.992453902799263, 2.247943855532664, 2.470570198391021, 2.654670237179938, 2.795472753712226, 2.8891715128290456, 2.933112689974166, 2.925787846962586, 2.8669955678120203, 2.7577481768152237, 2.600394188071696, 2.3984433149220012, 2.1566383379419993, 1.8807124917213929, 1.5774033266958203, 1.2541639179394808, 0.9191172804482688, 0.580746979120261, 0.24779822247220662, -0.0710260693439739, -0.3672032030683591, -0.632665888203502, -0.8599578684202464, -1.0424616350217126, -1.17454655282966, -1.2517352895220084, -1.2708197069672165, -1.229956670456792, -1.128731754829091, -0.9681790505416248, -0.7507809562080521, -0.4804102689803565, -0.16226449098995122, 0.19726762939242493, 0.5907286414634874, 1.0097946189275315, 1.4454375590368411, 1.8881839141183718, 2.3282948955669367, 2.7560621641351224, 3.1619834318162003, 3.5370690777396576, 3.8729940913763667, 4.162383184456881, 4.398926540757565, 4.5776085004123965, 4.6947807254136755, 4.748303174549668, 4.7375725112628135, 4.663553465988672, 4.528762978177552, 4.337183510210117, 4.094204971956567, 3.8064269975715628, 3.4815618810292626, 3.1281477119081758, 2.755417206116716, 2.372955395105502, 1.9905420325308112, 1.6177942248987898, 1.2639942273137719, 0.9377578950388054, 0.6468646889402395, 0.39798720141925154, 0.19654492217619055, 0.04651966317832702, -0.04964261476619915, -0.09111852812641806, -0.07873424317440535, -0.014954788593172182, 0.09617670432030066, 0.24913726504603592, 0.43707710006428696, 0.6519900671732933, 0.884948062793124, 1.1263261389291623, 1.3660916329772859, 1.594066289252057, 1.8002306829894825, 1.9750064313909221, 2.1095293579027707, 2.1959353049530783, 2.227555863152672, 2.1991909022905514, 2.107188931600612, 1.9496884339304112, 1.7265599014471247, 1.4395972473375442, 1.0923178180549173, 0.690085866518147, 0.23978698318053054, -0.25013057128681987, -0.7700740628523243, -1.3093518815363079, -1.8566427939804162, -2.400118736265548, -2.9279223962611196, -3.4283425597229744, -3.8902605878124277, -4.303342598636185, -4.6584213219191986, -4.9476647308317805, -5.1648668570634175, -5.305555517503173, -5.367172980923606, -5.349095905374224, -5.252693890790985, -5.0812508725569545, -4.839896754152159, -4.535438311280266, -4.1761667731628025, -3.771624191967495, -3.3322984926213484, -2.869364783816229, -2.3942890941875374, -1.9185905498611493, -1.453385264402377, -1.0092133087573338, -0.5955636291528474, -0.22080020828830696, 0.1082855787440468, 0.38642918121051545, 0.6102676396735526, 0.7781692769626469, 0.8904984855851368, 0.9493308439435791, 0.9585856520831829, 0.9236490715614516, 0.8513711348841999, 0.7496290939038576, 0.6272055252577172, 0.4933302496718901, 0.3574734597454382, 0.2289072309589667, 0.11645935424808089, 0.028134474666334813, -0.029121261758382234, -0.049704309372794325, -0.029531295926752778, 0.03379756159199228, 0.1409162163191199, 0.2906622527431089, 0.48011416871150014, 0.704688274237161, 0.9583046806436888, 1.233586795804647, 1.522150187838044, 1.8148619467256173, 2.102232680175665, 2.3746802256138713, 2.6229930829591512, 2.838538304688548, 3.013755486350154, 3.142253822800688, 3.219290302980073, 3.2417157267123065, 3.208390064540434, 3.1199595364212107, 2.979167223698803, 2.7904693395491122, 2.5602107121674402, 2.2961134612781526, 2.007304635144723, 1.703729988194754, 1.396043499490671, 1.0950091193511218, 0.8112862015874585, 0.5548820641593214, 0.33488783371791603, 0.15903667572782432, 0.03345586892041415, -0.03762822131017414, -0.052056662836873796, -0.009862809464506048, 0.0866949553381238, 0.23318218656379727, 0.42311916261154275, 0.6481868642483661, 0.8985230137456703, 1.163048493803064, 1.4299024019925444, 1.6868348240305875, 1.9217320560711693, 2.1230083551548415, 2.280159142115283, 2.3840777301399285, 2.4275719134811276, 2.405534443275268, 2.3153657232614298, 2.15694177913747, 1.9328993951420224, 1.6483729980333304, 1.3111158218293026, 0.9310135331967171, 0.5200347820216292, 0.09156782516196112, -0.3397849869715926, -0.7589685301844271, -1.1508005430686306, -1.5007317328602012, -1.7952357690726015, -2.0224663804445173, -2.1726402882165754, -2.2385054758303817, -2.2156375439342013, -2.102664988269504, -1.9014024839651378, -1.6168198234553202, -1.2569525478084962, -0.8326425325740083, -0.35719785900044804, 0.1540336798379163, 0.6842404266218879, 1.2156592215787467, 1.730325495745454, 2.2105836823930463, 2.63991189380785, 3.003346711456705, 3.288262597282293, 3.484639710361207, 3.5856815220527496, 3.58787263889887, 3.4913450655112075, 3.2996960336406103, 3.02005861317946, 2.6626766363051444, 2.24068919672618, 1.7694902973304396, 1.2662875232190416, 0.7493063998652907, 0.2372204582005875, -0.2517090810559477, -0.7002184777890702, -1.0928527597027355, -1.4164586853260892, -1.660825321156178, -1.819000407169127, -1.8876535380894386, -1.8671624496844639, -1.7616338542354069, -1.5787369864215177, -1.3293802645765256, -1.0272970607499694, -0.6884478052230396, -0.3303871937507774, 0.028475364519702992, 0.36967600918543625, 0.67540532976857, 0.9294048695536407, 1.1174684465861993, 1.2283463721000398, 1.2538955147610717, 1.18989159378425, 1.0357495204703902, 0.7951442759705158, 0.47530636419776806, 0.08736839168793355, -0.35467682233741293, -0.8339505979466911, -1.3319176118804394, -1.8286717119190115, -2.3041768221554375, -2.738784597525394, -3.1143255044029736, -3.414716239592582, -3.626779034225419, -3.740763908305898, -3.7508260762258665, -3.6552957071822463, -3.4567970390675833, -3.162146323149085, -2.782144309597661, -2.331061268504992, -1.8261727045816776, -1.2868808530161402, -0.734090491538067, -0.18909794314135037, 0.3270801337089801, 0.794865542585563, 1.1967187287837358, 1.5181472340950464, 1.7481233437204666, 1.879773160248211, 1.910520568407473, 1.842350817517288, 1.6816271617554435, 1.4389018933448061, 1.1284072173818365, 0.7674638184598362, 0.3757117773215495, -0.025769799732656053, -0.4153679182726432, -0.7719487190892236, -1.0757387755694314, -1.3092954634491356, -1.458202466902728, -1.5118271384522786, -1.4637039131429048, -1.3119357619566754, -1.0592065323232647, -0.7127309077241656, -0.2839208413373104, 0.21214851327421844, 0.7573121601398768, 1.3312933897078147, 1.9123530290883433, 2.4785988437005435, 3.0085264612545948, 3.482486418315103, 3.8829532233792565, 4.195942816124727, 4.410899582878815, 4.521863017813795, 4.526934297710007, 4.429039305017119, 4.235011757771902, 3.9558818935925046, 3.6056791463295745, 3.201273840469525, 2.7610495361620515, 2.304416368959919, 1.850525905645829, 1.4176377617611482, 1.0220460471498043, 0.6775010129782051, 0.39448660439195316, 0.17987239520536222, 0.03662944407392673, -0.03617728546907001, -0.043217140228157286, 0.007463168866453115, 0.10500657124761364, 0.23640557556633643, 0.3873290196888036, 0.5429572303941779, 0.6888783785290192, 0.8119349466706848, 0.900981105975267, 0.947573989320696, 0.9464101675068598, 0.8957243640534067, 0.7972924087288324, 0.6564551451601462, 0.4816729495361074, 0.28416501857646115, 0.07710376637456477, -0.1250614823008748, -0.3075988346995553, -0.45634414235717047, -0.5586712031049674, -0.60432172548379, -0.5861496454583399, -0.5007160424329065, -0.3486670210149737, -0.13489992874616913, 0.13147008283837971, 0.43750165023137544, 0.7668108021609191, 1.1005492516933146, 1.4179855785152073, 1.6979827449536558, 1.9195659197797004, 2.0637069544829156, 2.1136522951033796, 2.056756073048286, 1.8843704959634913, 1.5934597699032091, 1.18592405015024, 0.6697769303727994, 0.057872245406284197, -0.6314741118305276, -1.3762721092357075, -2.1507898196848925, -2.9276636577975634, -3.6782691653262223, -4.374874644081911, -4.991254309989818, -5.504563571678644, -5.895966594111642, -6.151928872004855, -6.264649221882572, -6.232551178157596, -6.060366030787574, -5.758749950447366, -5.343946202807841, -4.836629737561292, -4.261170394733102, -3.643969026599911, -3.01243548463153, -2.3931885672453093, -1.8109382964478726, -1.2869464530825518, -0.8380474429404197, -0.4756984403980585, -0.20537385123632926, -0.026390250734777344, 0.06814226526060538, 0.09071830761115166, 0.05884898832692988, -0.006143359657512304, -0.08028908233220983, -0.13848260019985253, -0.15601004707087085, -0.11002322962391604, 0.018901425756834424, 0.24563769166746374, 0.5792975307120306, 1.0226777436068355, 1.5717167901970128, 2.2156191441413915, 2.9371502936224125, 3.7134211851532495, 4.516979473424105, 5.317124020058772, 6.081537501320267, 6.777912049364978, 7.375713744300164, 7.847844442604891, 8.172077572814585, 8.332465979032818, 8.32005711082887, 8.133789128604525, 7.7802642788345615, 7.273958728243935, 6.636058997991435, 5.893940155347458, 5.079290091366304, 4.226969267862025, 3.372801509289591, 2.552088855258463, 1.7974999007508732, 1.1376259009987577, 0.5953569406427187, 0.18687785649838334, -0.07918298204615079, -0.20202459601144057, -0.18861147526987104, -0.053116915496285264, 0.18403399648430657, 0.49740544288642446, 0.8582336719489352, 1.2360023293896114, 1.6005571097258946, 1.923551452562199, 2.180618630504451, 2.35223893050893, 2.4255784352687124, 2.3944673174604314, 2.260560628061736, 2.0323554408035855, 1.7254935771132418, 1.3609252842417565, 0.9642619863288145, 0.5636688354657212, 0.18867972134651873, -0.13261999979421604, -0.3752385810877451, -0.5174063426567899, -0.5425556769404415, -0.44468553618952616], 'positive_zeros': ['0.39441388374342991176490321880907', '1.24415797490543756439724998455968', '2.47909800498750747947282194614459', '3.14767765435172049491292905416815', '4.75658686997557929485351830652178', '4.93956968454570441006330021794746', '5.98136708677993779512077036755493', '7.40498662748837978922671546409585', '8.174762702916693838669892475364335', '8.327728500524252218697218219586175', '9.881748268042164303783479361148596', '10.01631058338208857695815856530219', '11.09432143062809884988752872425474', '11.85078522177591995827296343639784', '12.81626208261011362283744084378735', '13.52145812722002435240906711501711', '14.07258330141691945639913971775284', '15.05653681714102024596849310279350', '15.71950741249817679745562138072350', '16.28840568283866407544562494978522'], 'prelabel': '4-3e4-1.1-c21e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.015272772824584, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c21e2-0', 'trace_hash': 253949802517954802, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39441388374342991176490321881', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.24415797490543756439724998456', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.47909800498750747947282194614', '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': 632.6714463549673, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 81, 'conductor_radical': 3, 'degree': 4, 'dirichlet_coefficients': [1, -666, 0, -1285756, -996876, 0, 679896112, 611332056, 0, 663919416, -219869122968, 0, -48468909956, -452810810592, 0, -1651516028016, 11333529041436, 0, 11960585011624, 1281739298256, 0, 146432835896688, 146508390063504, 0, -478733454446974, 32280294030696, 0, -874180505380672, 1798520043674052, 0, 11169107526944992, 4767644351391840, 0, -7548130341596376, -677772116546112, 0, 12736264858660012, -7965749617741584, 0, -609422254657056, -122972020616468052, 0, 288455418162270040, 282698044070843808, 0, -97574587782293664, -837243745741596960, 0, -685059200997661070, 318836480661684684, 0, 62319191789386736, 43007964012775764, 0, 219182251827847968, 415642288015366272, 0, -1197814349086918632, 3523823330903857224, 0, -1779023128451013860, -7438625612945364672, 0, 4481700578904069184, 48317493081297456, 0, -16454068667621610296, -14572152966200585616, 0, 451396229619710592, -17379227131150420944, 0, 50891146268473989076, -8482352395867567992, 0, -15378393942205627744, -149488161854793100416, 0, -54055785594190591040, 1646356691944478016, 0, 81899365730567722632, -111108429277666677288, 0, -11298123096710553936, -192111308496071846640, 0, -134413042994944262208, -226920767965448065524, 0, -32953823431962491072, -188374041574490649024, 0, 557604334663903575360, -11923220144047686624, 0, -128331469252795746236, 456249427864442272620, 0, 615534411455923502344], 'euler11': [1, 219869122968, 24368468203545949073734, 1627086464988032548830592684714248, 54763699237492901685126120802225273763666521], 'euler13': [1, 48468909956, -87046554991999245321666, 11974948412982611194223033020835828, 61040881526285814362156628321386486455989674569], 'euler17': [1, -11333529041436, 163049233709759468659315558, -783055439532061324977538663508749563612, 4773695331839566234818968439734627784374274207965089], 'euler19': [1, -11960585011624, 173516252603875318424026518, -8542363389349695341123216061496859614456, 510095203738582479622335815880298130716653502143703561], 'euler2': [1, 666, 1729312, 1396703232, 4398046511104], 'euler23': [1, -146508390063504, 70350674583296071946138208046, -5782918242779264795609305039610334909418992, 1558005952997140033806173725098810522409738596181909282129], 'euler29': [1, -1798520043674052, 7587059836229882944079722961758, -9231520492051562840021502973477889595578670708, 26346074268992142099064516382762907506814419719803282255713641], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -11169107526944992, 65110043582704149302277695219262, -232602320210870623007501051321922263773442097952, 433701716541192355457229753999917360820651622584523552060436161], 'euler37': [1, -12736264858660012, 1169087614331349951957049436247054, -10896280818239554894640017446830763986122907759644, 731934824502651514621160916115101341995441470527191525223322819769], 'euler41': [1, 122972020616468052, 11537437518922444803031032170525302, 908379449125753770406320291339230453947357267743732, 54565982855941191947249368879497196495421462536627690767330656099281], 'euler43': [1, -288455418162270040, 60588844480912796894264501569866630, -5793169933804356783766057296019576226939705287291720, 403343566675122500462878634623535631588559593930513766350645748813849], 'euler47': [1, 837243745741596960, 435212250071069604210871713333695710, 108869675554582995594015122856205129417057809732945120, 16908692777708688563979281162874109375742132033178319498546247522565409], 'euler5': [1, 996876, 479727216206350, 475347518920898437500, 227373675443232059478759765625], 'euler53': [1, -43007964012775764, 3035046442171135358103872093607580846, -69717554565147509777049671721234831423614484987104292, 2627764996340071914932060028590629703016273743509013665720935053615458009], 'euler59': [1, -3523823330903857224, 22496141078639900048146408173821413798, -54313322564229040580479664885632358969825116705752821016, 237566111385928825180581197186581724740035515556906717126291161106235417081], 'euler61': [1, 1779023128451013860, 54581477540293900337554820522490345438, 55221491112909501494787800089051446776599515682427437460, 963502998275379493962849646581354683437407419033192428674820139330228382121], 'euler67': [1, 16454068667621610296, 483672984740847466171511634737330990838, 3663061094560387395932853428920480093626820350342458517032, 49561188616996901345349189252156955439051753759670367683995836545268981893289], 'euler7': [1, -679896112, 1147317924110377614, -379753161363905240551080784, 311973482284542371301330321821976049], 'euler71': [1, 17379227131150420944, 1578450641853831735097967952041073581326, 13075424043949467210334580080473301273554066026655005544624, 566044592922467932920289630256783944174352087720184706882390017513705742761841], 'euler73': [1, -50891146268473989076, 1519084761764201093580550328041283444406, -68615509976601001711116009132924028044303191525431646748148, 1817858708606516392063752284490078897342614279715947003348265995414509863302929], 'euler79': [1, 54055785594190591040, 14861294583513934634248604408585443331358, 382834528332584185944153812342805357187985297840513506996160, 50157725483905227341761748890141694180076101090840037071925071763978352502147041], 'euler83': [1, 111108429277666677288, 39997912234158986996837338981425633593878, 2220173670617504285341283509603621514972856652400421129437304, 399282135658682469334331901689876886678820965774126540592961885129481494196023689], 'euler89': [1, 226920767965448065524, 171269531303391580490166794691127246306198, 19636513668421346803287292967855386289346105454176845265130836, 7488249032982960608606585095904734981347282237297075167277004918963148603698150321], 'euler97': [1, 128331469252795746236, 780378418922367967273197315773085057717318, 67692349189173687709577926593180875355911033379402282012741692, 278235691213844046805607971221988942088139032625098384397060765968745910963026076609], 'euler_factors': [[1, 666, 1729312, 1396703232, 4398046511104], [1, 0, 0, 0, 0], [1, 996876, 479727216206350, 475347518920898437500, 227373675443232059478759765625], [1, -679896112, 1147317924110377614, -379753161363905240551080784, 311973482284542371301330321821976049], [1, 219869122968, 24368468203545949073734, 1627086464988032548830592684714248, 54763699237492901685126120802225273763666521], [1, 48468909956, -87046554991999245321666, 11974948412982611194223033020835828, 61040881526285814362156628321386486455989674569], [1, -11333529041436, 163049233709759468659315558, -783055439532061324977538663508749563612, 4773695331839566234818968439734627784374274207965089], [1, -11960585011624, 173516252603875318424026518, -8542363389349695341123216061496859614456, 510095203738582479622335815880298130716653502143703561], [1, -146508390063504, 70350674583296071946138208046, -5782918242779264795609305039610334909418992, 1558005952997140033806173725098810522409738596181909282129], [1, -1798520043674052, 7587059836229882944079722961758, -9231520492051562840021502973477889595578670708, 26346074268992142099064516382762907506814419719803282255713641], [1, -11169107526944992, 65110043582704149302277695219262, -232602320210870623007501051321922263773442097952, 433701716541192355457229753999917360820651622584523552060436161], [1, -12736264858660012, 1169087614331349951957049436247054, -10896280818239554894640017446830763986122907759644, 731934824502651514621160916115101341995441470527191525223322819769], [1, 122972020616468052, 11537437518922444803031032170525302, 908379449125753770406320291339230453947357267743732, 54565982855941191947249368879497196495421462536627690767330656099281], [1, -288455418162270040, 60588844480912796894264501569866630, -5793169933804356783766057296019576226939705287291720, 403343566675122500462878634623535631588559593930513766350645748813849], [1, 837243745741596960, 435212250071069604210871713333695710, 108869675554582995594015122856205129417057809732945120, 16908692777708688563979281162874109375742132033178319498546247522565409], [1, -43007964012775764, 3035046442171135358103872093607580846, -69717554565147509777049671721234831423614484987104292, 2627764996340071914932060028590629703016273743509013665720935053615458009], [1, -3523823330903857224, 22496141078639900048146408173821413798, -54313322564229040580479664885632358969825116705752821016, 237566111385928825180581197186581724740035515556906717126291161106235417081], [1, 1779023128451013860, 54581477540293900337554820522490345438, 55221491112909501494787800089051446776599515682427437460, 963502998275379493962849646581354683437407419033192428674820139330228382121], [1, 16454068667621610296, 483672984740847466171511634737330990838, 3663061094560387395932853428920480093626820350342458517032, 49561188616996901345349189252156955439051753759670367683995836545268981893289], [1, 17379227131150420944, 1578450641853831735097967952041073581326, 13075424043949467210334580080473301273554066026655005544624, 566044592922467932920289630256783944174352087720184706882390017513705742761841], [1, -50891146268473989076, 1519084761764201093580550328041283444406, -68615509976601001711116009132924028044303191525431646748148, 1817858708606516392063752284490078897342614279715947003348265995414509863302929], [1, 54055785594190591040, 14861294583513934634248604408585443331358, 382834528332584185944153812342805357187985297840513506996160, 50157725483905227341761748890141694180076101090840037071925071763978352502147041], [1, 111108429277666677288, 39997912234158986996837338981425633593878, 2220173670617504285341283509603621514972856652400421129437304, 399282135658682469334331901689876886678820965774126540592961885129481494196023689], [1, 226920767965448065524, 171269531303391580490166794691127246306198, 19636513668421346803287292967855386289346105454176845265130836, 7488249032982960608606585095904734981347282237297075167277004918963148603698150321], [1, 128331469252795746236, 780378418922367967273197315773085057717318, 67692349189173687709577926593180875355911033379402282012741692, 278235691213844046805607971221988942088139032625098384397060765968745910963026076609]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9/22/a/e'], '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': '4-3e4-1.1-c21e2-0-0', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21, 21], 'order_of_vanishing': 0, 'prelabel': '4-3e4-1.1-c21e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.015272772824584, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c21e2-0', 'trace_hash': 253949802517954802, 'z1': {'__RealLiteral__': 0, 'data': '0.39441388374342991176490321881', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '499978996465706018335479911013,1577157603667616301750730882372', 'Lhash_array': ['499978996465706018335479911013', '1577157603667616301750730882372'], 'label': '4-3e4-1.1-c21e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9/22/a/e'}