Lfunction data - 8-7e8-1.1-c7e4-0-0

Formats: - HTML - YAML - JSON - 2024-05-18T16:17:30.155542

• 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': '31803825405086001085070378814,1176752324640720674339498477943,1245508035335456514857985681799,5189919045640943493320639228368', 'a10': -990, 'a2': 3, 'a3': -94, 'a4': 42, 'a5': -330, 'a6': -282, 'a7': 0, 'a8': -417, 'a9': 5718, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 54896.56233136906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[7, [1]]], 'bad_primes': [7], 'central_character': '49.1', 'coefficient_field': '1.1.1.1', 'conductor': 5764801, 'conductor_radical': 7, 'degree': 8, 'euler_factors': [[1, -3, -33, 642, -15772, 82176, -540672, -6291456, 268435456], [1, 94, 3118, 126336, 8588223, 276296832, 14913297342, 983273201082, 22876792454961], [1, 330, -52950, 1848000, 11584094375, 144375000000, -323181152343750, 157356262207031250, 37252902984619140625], [1], [1, 2844, -29998230, -2524834944, 913217889351659, -49201890300503424, -11391822850291787663430, 21046310841470207327844084, 144209936106499234037676064081], [1, -5068, -75826328, -109594359700, 10371750960332446, -6876883542739564900, -298556793281488797080792, -1252123033344246590225965084, 15502932802662396215269535105521], [1, -1488, -796315678, 32955515712, 468363501153159843, 13522922585292730176, -134081903116815758050464862, -102808797662556994526670898896, 28351092476867700887730107366063041], [1, 32810, -821175938, 3606756053600, 1839903037090471423, 3223977305780209210400, -656125064666031132407480498, 23433213553699574878155948107390, 638411683925748518131605316913942641], [1, -6576, -6776719822, -67816341504, 34771829644557187923, -230902805275261452288, -78561403713703370837749013998, -259565137177693515194553301360848, 134393854047545109686936775588697536481], [1, -41280, 31585266636, -1355201959258560, 852538515923370936086, -23377066170924617349455040, 9398456118802053798513129719916, -211883747002016507748134342956845120, 88540901833145211536614766025207452637361], [1, -391836, 61486586290, -14507193586161024, 3491887927172886021459, -399130818969622483220609664, 46541898589645663151931646999090, -8160183123160971676981333145668812516, 572964121067545096123347421337293637543041], [1, 367392, 71124113482, -46295428199372928, -17748494037413105303877, -4394911901642494228542455424, 640974870323088962412612301307098, 314315574212693127795844497595894540704, 81217248802771228597652036390959994837496721], [1, -1469328, 1345354841148, -878020599652429296, 448345733172319524366950, -170998264337869068520172017776, 51028269427682023245554965314120828, -10853748296027474111697941344006778872848, 1438626275603521989270100382252682485138269921], [1, 960952, 1419861053212, 832492459806292600, 626705823045432495819286, 226286944181596476790851908200, 104906941295593475091212244956072188, 19299198017135121469152378495176639704936, 5459046029871041534743397034507955551606171601], [1, -1089108, 170819098322, -2277212013836928, 173308342809438672698163, -1153688256405896796981857664, 43843623149602575138922598784828818, -141620448294750154551686407461443684410476, 65877941798660252683780571409941608871644628161], [1, 2858844, 3786130953938, 5824711062825811056, 8263676154313847119746603, 6842352971833292223777756637872, 5224657257545591070069052615116858722, 4634295464533915213468466466790641877043532, 1904251686165483303166544735375573842653419591761], [1, 160170, -4336274439298, -98564469827644800, 12769192305753103403435343, -245292614186965756533724291200, -26856222327663411755854533978129981778, 2468729007728428565129494144069784326734030, 38358032782038398419973086399760468678777161743121], [1, -864646, -5008356465590, 457844324641237856, 20904794089308848958760759, 1438886971279123272933465610976, -49466698078009816857261056460397405190, -26838909872063241939972656321945816337574606, 97551820892064552722266841889541788960852432978481], [1, -328648, -11479536848678, 175457560334425472, 96884390925000887875815403, 1063397672160512931146021987456, -421668932291412165525202786891126467062, -73164742831907511903300999332642658907533016, 1349256365417755877454657051946796697206085388680241], [1, 15000432, 113352705437468, 564689055383387840304, 2003789613416572729728703590, 5135914810840222585335899893590864, 9376673029405710902265311769220053753308, 11285715283096462477451867339702782722649043472, 6842798698940938981814244812733146152009703886272161], [1, 4301244, -253409836502, -14369111007814970064, 25287014549336098331795043, -158741295668475501478820987312208, -30927407053696477565313398622838019318, 5799280861878000001089333505080608059764637212, 14894985451961941943846586557477384171894488107677281], [1, -6408440, 8995491286882, 40598787702696064000, -128805799996156739126344157, 779655423990966447121159778176000, 3317448314284700636285551406683580999842, -45385930067980202092684240857836652040222810760, 136006152866792691625201101984747368303641150837104961], [1, -23318148, 304841358243152, -2602065765792171554820, 15982578156929982653681375406, -70609789298899194523782620281852140, 224474587030995530118116984994827133414608, -465944290399291069084742161581305883801464556684, 542233801012015735135407853098133122208235840693558641], [1, 9772260, 11684070451002, -45437830420574079600, 844244467709952656523623363, -2009775894258667425236471330108400, 22858843799021250101224806496589176670682, 845639289792046111192071386246734093585638739140, 3827543948647425430322045212330289877339037312647605281], [1, -21525504, 493072305760828, -5799315660339570969600, 67352210862524748148928647686, -468574756502492399951829461388364800, 3218954886118174624788227831822468091196732, -11354283884731657703311586665241483877444407129088, 42619520516862344959898006540158454742326868747150111361], [1, 12778314, -50354358654870, -10061683851102563904, 16640770135855225759470729959, -1078748695849126372822401957136704, -578810367978917509924984510023092087172870, 15747891184828940382271690029824146854807926637714, 132129096689825080931822600853816049099831724850779782801], [1, -3763556, 44251097224738, 1038972976960438272256, -15962721968184521063933479997, 127780571124631861871459039817340672, 669337549757032281542552514519881945990722, -7001322797124704778753770253907921430943237377468, 228792767573726113549107350198718474022130892363602038561], [1, 23121312, 103333922501322, 2545768608160503608832, 74356548775816680049417346843, 408794807438441120509580533760549376, 2664500480439078017809841116456198957101978, 95735234524603909230383039684869806124667281212384, 664883836375406516433586250657527435394385613490936917201], [1, 2420280, -211807363325078, -358062771412417960800, 12890013003395009023436221323, -65455275384994397091783412040575200, -7078023905910626986924750393186323164718758, 14785025189411904407278183926934536361500295346520, 1116713952456127112240969687448211536647543601817400964721], [1, -32536848, 700269167153052, -14741284975865638617840, 282662410111560661047354656006, -3468042782306977084366371302255735280, 38758165562301603438042671730247044786118428, -423665199253354546573262017966728451648746178731024, 3063348575248001425954190006610728401266477888045839853121]], 'euler_factors_factorization': [[[[1, -3, -33, 642, -15772, 82176, -540672, -6291456, 268435456], 1]], [[[1, 94, 3118, 126336, 8588223, 276296832, 14913297342, 983273201082, 22876792454961], 1]], [[[1, 330, -52950, 1848000, 11584094375, 144375000000, -323181152343750, 157356262207031250, 37252902984619140625], 1]], [1], [[[1, 2844, -29998230, -2524834944, 913217889351659, -49201890300503424, -11391822850291787663430, 21046310841470207327844084, 144209936106499234037676064081], 1]], [[[1, -2534, -41123742, -159004742078, 3937376385699289], 2]], [[[1, -1488, -796315678, 32955515712, 468363501153159843, 13522922585292730176, -134081903116815758050464862, -102808797662556994526670898896, 28351092476867700887730107366063041], 1]], [[[1, 32810, -821175938, 3606756053600, 1839903037090471423, 3223977305780209210400, -656125064666031132407480498, 23433213553699574878155948107390, 638411683925748518131605316913942641], 1]], [[[1, -6576, -6776719822, -67816341504, 34771829644557187923, -230902805275261452288, -78561403713703370837749013998, -259565137177693515194553301360848, 134393854047545109686936775588697536481], 1]], [[[1, -20640, 15579628518, -356037447017760, 297558232675799463481], 2]], [[[1, -391836, 61486586290, -14507193586161024, 3491887927172886021459, -399130818969622483220609664, 46541898589645663151931646999090, -8160183123160971676981333145668812516, 572964121067545096123347421337293637543041], 1]], [[[1, 367392, 71124113482, -46295428199372928, -17748494037413105303877, -4394911901642494228542455424, 640974870323088962412612301307098, 314315574212693127795844497595894540704, 81217248802771228597652036390959994837496721], 1]], [[[1, -734664, 402811824126, -143078953866510984, 37929227194915558802161], 2]], [[[1, 480476, 594501933318, 130602318990246932, 73885357344138503765449], 2]], [[[1, -1089108, 170819098322, -2277212013836928, 173308342809438672698163, -1153688256405896796981857664, 43843623149602575138922598784828818, -141620448294750154551686407461443684410476, 65877941798660252683780571409941608871644628161], 1]], [[[1, 2858844, 3786130953938, 5824711062825811056, 8263676154313847119746603, 6842352971833292223777756637872, 5224657257545591070069052615116858722, 4634295464533915213468466466790641877043532, 1904251686165483303166544735375573842653419591761], 1]], [[[1, 160170, -4336274439298, -98564469827644800, 12769192305753103403435343, -245292614186965756533724291200, -26856222327663411755854533978129981778, 2468729007728428565129494144069784326734030, 38358032782038398419973086399760468678777161743121], 1]], [[[1, -864646, -5008356465590, 457844324641237856, 20904794089308848958760759, 1438886971279123272933465610976, -49466698078009816857261056460397405190, -26838909872063241939972656321945816337574606, 97551820892064552722266841889541788960852432978481], 1]], [[[1, -328648, -11479536848678, 175457560334425472, 96884390925000887875815403, 1063397672160512931146021987456, -421668932291412165525202786891126467062, -73164742831907511903300999332642658907533016, 1349256365417755877454657051946796697206085388680241], 1]], [[[1, 7500216, 28549732695406, 68215365733886712456, 82721210695570328927708881], 2]], [[[1, 4301244, -253409836502, -14369111007814970064, 25287014549336098331795043, -158741295668475501478820987312208, -30927407053696477565313398622838019318, 5799280861878000001089333505080608059764637212, 14894985451961941943846586557477384171894488107677281], 1]], [[[1, -6408440, 8995491286882, 40598787702696064000, -128805799996156739126344157, 779655423990966447121159778176000, 3317448314284700636285551406683580999842, -45385930067980202092684240857836652040222810760, 136006152866792691625201101984747368303641150837104961], 1]], [[[1, -11659074, 84453675852838, -316381226555834425398, 736365263311636486061599129], 2]], [[[1, 9772260, 11684070451002, -45437830420574079600, 844244467709952656523623363, -2009775894258667425236471330108400, 22858843799021250101224806496589176670682, 845639289792046111192071386246734093585638739140, 3827543948647425430322045212330289877339037312647605281], 1]], [[[1, -10762752, 188617737573662, -869611897863379646976, 6528362774606076144776040769], 2]], [[[1, 12778314, -50354358654870, -10061683851102563904, 16640770135855225759470729959, -1078748695849126372822401957136704, -578810367978917509924984510023092087172870, 15747891184828940382271690029824146854807926637714, 132129096689825080931822600853816049099831724850779782801], 1]], [[[1, -3763556, 44251097224738, 1038972976960438272256, -15962721968184521063933479997, 127780571124631861871459039817340672, 669337549757032281542552514519881945990722, -7001322797124704778753770253907921430943237377468, 228792767573726113549107350198718474022130892363602038561], 1]], [[[1, 23121312, 103333922501322, 2545768608160503608832, 74356548775816680049417346843, 408794807438441120509580533760549376, 2664500480439078017809841116456198957101978, 95735234524603909230383039684869806124667281212384, 664883836375406516433586250657527435394385613490936917201], 1]], [[[1, 2420280, -211807363325078, -358062771412417960800, 12890013003395009023436221323, -65455275384994397091783412040575200, -7078023905910626986924750393186323164718758, 14785025189411904407278183926934536361500295346520, 1116713952456127112240969687448211536647543601817400964721], 1]], [[[1, -16268424, 217803773854638, -3827318346065453958408, 55347525466347647961440563489], 2]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '8-7e8-1.1-c7e4-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, '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': [7, 7, 7, 7], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/49/8/c/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [0.009194601971934134, -0.00443779334120885, -0.04644857718139873, -0.11530367380332708, -0.20840926609803162, -0.3218765379093291, -0.45120816460939145, -0.5914998486085911, -0.7376242363761935, -0.8843867972875544, -1.0262764895339378, -1.1577428164704076, -1.27345473188956, -1.3685530957407084, -1.439076745948529, -1.4820055648388633, -1.4953307537370533, -1.4781440732752409, -1.4306856798961751, -1.3543735834724446, -1.2517950892074066, -1.1266776101337521, -0.9838516980601533, -0.8290577400329675, -0.6687594659956445, -0.5099556893767915, -0.35997368911691463, -0.22618888271935678, -0.11575973586674877, -0.03537069467284923, 0.009027506788874708, 0.012489979212946601, -0.028690823452046207, -0.11678463965526033, -0.2524510797741805, -0.43461351673823817, -0.6603868019145558, -0.9250567989733148, -1.2221222165565888, -1.5433929325571925, -1.8791423928098738, -2.218323297994647, -2.5488678343904905, -2.857987844733587, -3.132515343208329, -3.359300694403368, -3.525688218419675, -3.6198869631262087, -3.631359828182209, -3.5512439418892714, -3.3728015084989598, -3.091671135853132, -2.706115345927834, -2.217253745788676, -1.6292423491045027, -0.9492509862718278, -0.18741941851408642, 0.6432591482246767, 1.5272119918505445, 2.446603902115252, 3.3816913319798276, 4.311310627901085, 5.213616782122745, 6.066532870880397, 6.848262440592077, 7.537991248277284, 8.116891123748331, 8.56840027030832, 8.878617079839474, 9.036925446773662, 9.036913510145945, 8.876179639478881, 8.55633450590732, 8.083259831260378, 7.4675946549485746, 6.723933868536895, 5.870326429188079, 4.928036046963824, 3.9214311663605015, 2.8767378225626263, 1.8211837374486866, 0.78238763172791, -0.21221764789322836, -1.1366386554529424, -1.9671504725227549, -2.682926828854478, -3.2667021080011436, -3.7054980218218674, -3.9909896565650245, -4.119752594972044, -4.093572948158076, -3.9192992829413447, -3.60850021409272, -3.177113636170821, -2.645172422950594, -2.0358447788211413, -1.3745070810507891, -0.6879303099820326, -0.003562098363598427, 0.6517499255489682, 1.2527956636273678, 1.7768285879808683, 2.2042651848229156, 2.5195913453157806, 2.711928135608077, 2.775352689247559, 2.7090720867015374, 2.5174710214463696, 2.209865872589644, 1.8000690816503464, 1.3058355765309737, 0.7480749634590566, 0.1499366840580402, -0.46416346786756807, -1.0695332187857143, -1.6422803463360331, -2.1603232556073775, -2.6043064425853513, -2.9583816222302386, -3.2108432515144125, -3.354585440104732, -3.387358688645811, -3.311762943881031, -3.1350281426029363, -2.8686376071209554, -2.5277437674290444, -2.130290536692315, -1.696154234461296, -1.246245017538362, -0.8014825681662161, -0.3815762729172616, -0.0042417150218427395, 0.31551581405042334, 0.5661377096165364, 0.7402738913161874, 0.834801686235432, 0.8507823113436233, 0.7933882817001764, 0.6717244467101017, 0.4979721524398482, 0.28659918477548185, 0.05358395541745847, -0.1844737794257983, -0.4114813467685193, -0.6127587178181406, -0.7758371984092344, -0.8912648586459846, -0.9531404603577538, -0.9593729730846308, -0.9117860319570092, -0.8161184942049007, -0.6815470285363641, -0.5200515415620053, -0.34569032912862374, -0.1737801926934368, -0.019831544879490612, 0.10146006036839414, 0.17715701848853796, 0.19696311966290955, 0.1539340439727105, 0.04498160286010634, -0.12882849668171234, -0.36223137061344424, -0.6460379839880679, -0.967590777932473, -1.3114504320034417, -1.660409531341553, -1.996448754671847, -2.3017205046863594, -2.559671155836128, -2.7563856928061967, -2.8811867499394777, -2.9271627446540736, -2.8917389497663937, -2.7772933711718317, -2.5905687514506845, -2.3421236869411928, -2.0458553546789915, -1.7184991901860673, -1.3780850590862446, -1.042711382842285, -0.7295497062298469, -0.4539433466692848, -0.22809397905445944, -0.06028262493055196, 0.04553915324365864, 0.08989367135933157, 0.07780834379126597, 0.018381774060731593, -0.07596477902606409, -0.1904968835075635, -0.30925561102455223, -0.41627124533724447, -0.4968257014272098, -0.5387203668231749, -0.5331790347617318, -0.4755437598387506, -0.36574579174658817, -0.2084726959977117, -0.012744690968932241, 0.20874332410872432, 0.44053570327373287, 0.6656844767708164, 0.8671834578040944, 1.0293492932038288, 1.1392103672299896, 1.1879531963903978, 1.1717666804612958, 1.0923538443661578, 0.9571841392270972, 0.7794544225032068, 0.5771409397447839, 0.3717919237774638, 0.18710215274209746, 0.0472290436006179, -0.025250751237598363, -0.011231314375687479, 0.10321136296408133, 0.3253662614718036, 0.6548553243466465, 1.083108769961086, 1.5934398289549778, 2.161953538587342, 2.7587441582007424, 3.3495303832453898, 3.8979409076713925, 4.368692137437541, 4.7296316554154, 4.953849280293838, 5.022105653102087, 4.925591130317169, 4.665926620073817, 4.2551116297848575, 3.715504075110451, 3.079515120200555, 2.3863887257234184, 1.6794198460527625, 1.0033743527097287, 0.4016246956928765, -0.08786961066026944, -0.43540498431110225, -0.6217000782714788, -0.6397522728750273, -0.4956918354046157, -0.20833210621495302, 0.19207944160261353, 0.6658034923822335, 1.1670313737189328, 1.6477007282185248, 2.061442659208758, 2.367700925584424, 2.5358026192509393, 2.5481155089541145, 2.402320112613383, 2.112820844006354, 1.7105477025074218, 1.241365064764248, 0.7632936796324856, 0.3426477173425336, 0.04900891604115389, -0.05031674119629822, 0.10398859525032113, 0.5578989053285678, 1.3393176382972247, 2.454226696435065, 3.884365610174934, 5.587574192134612, 7.498685233475079, 9.531858699530707, 11.585469503616567, 13.55089426585075, 15.317719577282816, 16.779864465989426, 17.84395216752509, 18.440634135386006, 18.526311908213543, 18.085413149280242, 17.134086710875476, 15.724746857674967, 13.938334443816265, 11.87825809122185, 9.665721659607692, 7.4348002369881785, 5.318921363291262, 3.441162447631248, 1.9068699884281048, 0.7967996809902236, 0.15880709438278182, 0.004324687727159339, 0.3076774706083648, 1.0070623696866978, 2.0083998573936452, 3.1922177038944066, 4.422090941991382, 5.554089428176728, 6.447655482390605, 6.9761170457909225, 7.036117778663899, 6.55543413667447, 5.498804379506368, 3.87120963277282, 1.7181260386429829, -0.8781569334450062, -3.8033449226990994, -6.9179428473694955, -10.066917036584803, -13.093137680576225, -15.845510043042452, -18.187408722098922, -20.00654333509341, -21.22642925501283, -21.806109502423006, -21.740189573708, -21.059717623931334, -19.83297428691685, -18.15437607763537, -16.13599499414349, -13.900903476016502, -11.576720919052875, -9.283340566292976, -7.125340689840313, -5.187209037190298, -3.5298602249972304, -2.1874785225857334, -1.1682414085097566, -0.4570493674964125, -0.019350198865309892, 0.1934203771310346, 0.23766047283256983, 0.17162065538817695, 0.04991239965697303, -0.08139704930287017, -0.1880630065418708, -0.2493784181301093, -0.2584393804510191, -0.22079416418861483, -0.15183243583526956, -0.07335036005082227, -0.009633368696773607, 0.016466744733398618, -0.013020834309987794, -0.10849468327108104, -0.271245772927512, -0.49316408992164124, -0.7574633907847226, -1.0405402200700897, -1.3152081512454092, -1.5536524998271541, -1.7303914457713847, -1.825410053660451, -1.827438685470539, -1.734588196358301, -1.5543579899235156, -1.3032265639232903, -1.005669863894562, -0.6906311293106868, -0.38825127915611823, -0.12690804317597731, 0.06948622500148913, 0.18453764043504356, 0.21108192676014698, 0.1517089703860886, 0.01803770631611821, -0.17051558566028904, -0.3889138378151109, -0.6094790248798537, -0.8056438396327569, -0.9545251679933648, -1.039185193674927, -1.0506122761664736, -0.9892081843015902, -0.8637753964487969, -0.6900445076748591, -0.48880976616780397, -0.28345350795847046, -0.09641112628643483, 0.05365908188398514, 0.15412982025895047, 0.20016949464684483, 0.19537818235404622, 0.15120109509556134, 0.08543903428081766, 0.019973566252911225, -0.02234931109986796, -0.020918934037009333, 0.03966120777838878, 0.16716183212529137, 0.36023974747059845, 0.6079917009142921, 0.8907509448988107, 1.1825086216495293, 1.4536620679994527, 1.6742150833314027, 1.817622653022838, 1.8652710452911012, 1.8082238106173547, 1.6483305183752492, 1.398870247900696, 1.0842791055680414, 0.7362286487012886, 0.389789742471686, 0.07958101886784881, -0.1645531758265496, -0.3222271261615375, -0.3852744686574271, -0.359121422380223, -0.26296411235731565, -0.12743715108142756, 0.009413437958652108, 0.10714084307329012, 0.12867926841991592, 0.04669757675510377, -0.15114154142428315, -0.4584233977156614, -0.8481299518699901, -1.2733875568140425, -1.6708362413052504, -1.9664723418939387, -2.0839042195056643, -1.9532459705378198, -1.5203152220262253, -0.7554643235897146, 0.33928754012224804, 1.7270600972265011, 3.3355208945845574, 5.060049841380694, 6.772712869086245, 8.33253706672755, 9.597345570668395, 10.438616922549969, 10.760204977758123, 10.507279445745908, 9.673661011357527, 8.308549213902596, 6.521001768901808, 4.468506096392039, 2.344949735428266, 0.36736189060744473, -1.2416205734100605, -2.277671727398828, -2.573579116277002, -2.0154365554733698, -0.5584085228082316, 1.7665866582563268, 4.853853259495695, 8.528635323499065, 12.557157267820285, 16.66773097393351, 20.573654537886807, 23.996541876253612, 26.69035856984068, 28.46316568398833, 29.19289191774051, 28.837655247941278, 27.440535260750153, 25.12285250271916, 22.071971753364483, 18.52443992852081, 14.74442797658829, 10.998721780914593, 7.533933498039107, 4.555729040925745, 2.2110088472636575, 0.5793965100625404, -0.3293985525588951, -0.5728308676300214, -0.26583154779616447, 0.43633455682191236, 1.3557837513434845, 2.3110840618806976, 3.138574390340705, 3.707397847746411, 3.9294833444553143, 3.766408340042975, 3.232887446152232, 2.3881556895448983, 1.3251231051848753, 0.15846357921099125, -0.9891509573071023, -2.0042420113934827, -2.795094114319528, -3.3005467447863808, -3.4958696661988258, -3.393732700227893, -3.039868513147385, -2.505321483329662, -1.8764020791459808, -1.24297410057859, -0.6870127514476098, -0.2727152706441796, -0.03939228489915348, 0.0014340510277069801, -0.13414403819636353, -0.4060364060959009, -0.7576736175805833, -1.124607036310342, -1.4431367682953522, -1.6591469092780762, -1.736436776363145, -1.6596497279238367, -1.4350756714313548, -1.089428897042956, -0.6655729735956015, -0.21485500910592842, 0.21002853375429847, 0.5621616559259239, 0.8079011072737835, 0.9304002691172617, 0.9305444915600009, 0.826264395474844, 0.6500842601330361, 0.4421269848386448, 0.24334965148044785, 0.08938468128178967, 0.004967615081735953, -0.0004438206873173062, 0.06600825617821209, 0.1817755317310294, 0.3125804604095488, 0.4180666480286329, 0.458309947796781, 0.4005850897173261, 0.22583612260453578, -0.06778778750112446, -0.4636048102489172, -0.9273993944991189, -1.411487382992784, -1.861265932355144, -2.2223023567841365, -2.4481602257274173, -2.5090492287469206, -2.39573715371543, -2.121225911261531, -1.7208045159965357, -1.2498915326160855, -0.775346673168934, -0.3668634168714717, -0.0886051117195723, 0.009447477866812215, -0.10049739585594902, -0.4200871872043268, -0.9240289305560659, -1.5622124647217508, -2.26585197448165, -2.955904440181389, -3.5528858870846793, -3.987793211615372, -4.210187520739328, -4.193867662869596, -3.9404989322394828, -3.4808656417247987, -2.8681341888486047, -2.1699765703063765, -1.4603261118131574, -0.8105410789552625, -0.2778022411246027, 0.10193895231170176, 0.3171970180471439, 0.3811056120853768, 0.3289063037858865, 0.2109148494998869, 0.08321798813936367, -0.0022469380312597808, -0.00682540957104507, 0.08738740663700377, 0.27338100054797865, 0.5194410743176252, 0.7731236292065253, 0.968715926599006, 1.0377621545950682, 0.9211080834185958, 0.5791548353854655, 0.0007091770872456403, -0.7913355000450476, -1.740863593097774, -2.763179681057022, -3.752666178715438, -4.595298382231083, -5.187912274059835, -5.449790625159983, -5.332674344927515, -4.830635949727105, -3.988880178223981, -2.8957221579375556, -1.6724859184554317, -0.4620216333105181, 0.58560438304454, 1.3347639107735771, 1.6811549986473933, 1.5643109404903415, 0.9756363765992438, -0.039105571226851654, -1.384441675693327, -2.9262467920327278, -4.509659100561551, -5.976189202149001, -7.180907511083929, -8.009949569215536, -8.39744478912324, -8.327191970814164, -7.830872713317868, -6.98351903406156, -5.894790757233798, -4.68862640139142, -3.4865501453003436, -2.393745065662104, -1.4871347551681997, -0.8071427907705679, -0.3573249719629663, -0.10920274094662759, -0.011499263397402003, -0.003573576843563964, -0.028688142370994766, -0.04543840077783638, -0.03614431961077198, -0.00893447399844476, 0.006463712482928927, -0.03191196117612501, -0.16397676998984168, -0.4106357118993684, -0.758369753028253, -1.1471959026569734, -1.4636012431869332, -1.5431547748501075, -1.1821498542121753, -0.15719306236251615, 1.7493518126450258, 4.718707746546693, 8.86412528893617, 14.203982992272943, 20.64930105006649, 27.99381080332451, 35.91386882971942, 43.98776026904196, 51.747097821457814, 58.70267597507661, 64.37711842275876, 68.35555693053621, 70.36025833451592, 70.24931555867796, 68.01880505158441, 63.815863532379566, 57.95786132862626, 50.86624066551338, 43.0182483985092, 34.914065460445734, 27.04853687501055, 19.843998637618345, 13.615930424912678, 8.559694734931742, 4.748147488282775, 2.132377355597888, 0.5635059536026047, -0.17609281932253598, -0.338546161719317, -0.17512875127645813, 0.09440560889701122, 0.30431136292710703, 0.35547380735681805, 0.21689311872082653, -0.08314813748719183, -0.4736278191211504, -0.862913844385677, -1.1610784871642863, -1.299158631359658, -1.2436394478914399, -1.003759951299741, -0.62832003585951, -0.19631383407663403, 0.19774226921721183, 0.4632505922131408, 0.5311699456805434, 0.3676097284542397, -0.017020635679363197, -0.5656381683460945, -1.1829581742238775, -1.7485689156932074, -2.1341875030546804, -2.2260139657558393, -1.9429841014902105, -1.2496471112326593, -0.16479314357875177, 1.234729852663186, 2.8255145125327266, 4.453515870103101, 5.952442271763637, 7.16460582718764, 7.9635906081761085, 8.270203659791347, 8.061932021188145, 7.375697168223645, 6.301168459526, 4.967509765890977, 3.5254695672458727, 2.1260133699905284, 0.9009692547792911, -0.05232094152001522, -0.6818802439334795, -0.9861661203227977, -1.0078295102243195, -0.8231164014095608, -0.5279730602590154, -0.22164308670472113, 0.010518065121429401, 0.10960466926628025, 0.05090085404291993, -0.15494829099536378, -0.4665926226127318, -0.820915394910839, -1.145713070902927, -1.3761958645437387, -1.4661888246128003, -1.3959171465035414, -1.1769223900692432, -0.8530597198741509, -0.4912652119547639, -0.17036562971255165, 0.031063303051798278, 0.04780950772828868, -0.16011594142047755, -0.6005118362749291, -1.2468517631399099, -2.041694371872369, -2.904500191297287, -3.7421653221351527, -4.462247104878196, -4.988760357004102, -5.269376039934966, -5.280149015008371, -5.0288612618046145, -4.556060744656322, -3.922865641529256, -3.2005601732936904, -2.4619663141443966, -1.7733401906880872, -1.183403921913629, -0.7194369215662084, -0.3877394994614729, -0.1766922556818035, -0.06166644270854354, -0.012237865658158199, 0.0008560791745452098, 0.00028909368096323516, -0.0009582409606770326, 9.276773506089067e-05, -0.0012938841349567506, -0.013369383353552611, -0.04291338992223715, -0.09070089073155464, -0.14850264795450135, -0.19873470290956236, -0.21661581695812765, -0.1744864224804915, -0.04784171988093871, 0.17788514998238786, 0.5025449924405451, 0.9084144710208113, 1.3602686490268125, 1.810063625744075, 2.2034708412675745, 2.487652697592486, 2.6206951200228077, 2.582348977729016, 2.3762201792570314, 2.0293208322280583, 1.5895757606626604, 1.1201177154667434, 0.684986356500109, 0.3369800015846609, 0.10788740877557142, 0.0010129499232580505, -0.01251715574292129, 0.01005757258343024, -0.007529030059226665, -0.14689985517028054, -0.4786616488197571, -1.0464436578526435, -1.8542996078249891, -2.8607352801537678, -3.979602882794031, -5.088374872688617, -6.044700142454563, -6.711945439671359, -6.979435087329781, -6.781310349844971, -6.1132662976376295, -5.043496814027971, -3.7020208151578826, -2.26451886445296, -0.9302954162004584, 0.10768965109419466, 0.6959792344380429, 0.7454796102254142, 0.2489994922359375, -0.7109169772408772, -1.9738074370274443, -3.3238284806641385, -4.520959076851107, -5.341715621256827, -5.6173189597088795, -5.26209876137851, -4.292499447306477, -2.8339844006501007, -1.0993067380519115, 0.64567269733254, 2.1247738109909915, 3.102352109832691, 3.435266743986732, 3.109862079162693, 2.2623375204940466, 1.1794375810414583, 0.27156107306539745, 0.024617687257569208, 0.9361927054133763, 3.443446753294105, 7.852668348227118, 14.27822047094647, 22.60296982037661, 32.48157368496999, 43.354882830860696, 54.48578429310259, 65.03359775409953, 74.18557791649182, 81.21357527492079, 85.53223254923988, 86.77699175583966, 84.90198450370461, 80.12322588079348, 72.87132002099601, 63.76046568080918, 53.55840555132429, 43.04759685758886, 32.937299013089145, 23.811938365861486, 16.096626636355484, 10.010655699092297, 5.573481770386559, 2.638694436124503, 0.9408862845461627, 0.14964407505736177, -0.07274288682363124, -0.022021174227335003, 0.08299452701468109, 0.11714080471665755, 0.04636547342664185, -0.09044619774064232, -0.21107890176150867, -0.22372284232890785, -0.057869509491992, 0.3123328453828105, 0.8580835314697388, 1.5002332943550742, 2.123767502362662, 2.60193123445592, 2.82929707392562, 2.7447549637476283, 2.347051921960115, 1.703300481219467, 0.9467191635441528, 0.25176890052443074, -0.19444181087361664, -0.2226585636016225, 0.2855859620055725, 1.3722660818933115, 2.991666530560542, 5.01146404666086, 7.226153053259393, 9.386223686682944, 11.233118647923163, 12.53600911035309, 13.127350671988573, 12.925096587520544, 11.943229151491227, 10.290164965944435, 8.152602773386187, 5.765338699984257, 3.37932757733431, 1.2278996877416797, -0.5077616352805128, -1.7158991538132902, -2.3608986482879017, -2.482337868534703, -2.184753506807826, -1.6097669455042678, -0.910633301515701, -0.22955987133290875, 0.32310925548681796, 0.6822869865621939, 0.8299614152593069, 0.7899223043374745, 0.6172679128244292, 0.380970773283129, 0.1475659843345776, -0.03159874305877295, -0.12870281052127303, -0.14177758008678737, -0.09062704751171571, -0.00858441586495576, 0.0678552662907734, 0.10922116873165671, 0.100335065218071, 0.043397332134815995, -0.044210433477331355, -0.13577740930938734, -0.20313263451653749, -0.22550417393652034, -0.1976735309816348, -0.13147611662099978, -0.05355263798271568, 0.00017006620661681791, -0.006104259554989652, -0.09593940208495931, -0.2719762834421012, -0.5110059648498878, -0.7629313395496243, -0.958030095912929, -1.0201282733269155, -0.88242903498782, -0.5025583937507206, 0.1222631183874516, 0.9459763306294708, 1.8737117530274183, 2.7744216964216433, 3.495759186021692, 3.884986727808583, 3.815379366573229, 3.214550322274301, 2.076110285363582, 0.4657016663181097, -1.4807068250113686, -3.572397166631884, -5.59147194228069, -7.320610008715598, -8.57285918815952, -9.224294191765217, -9.227185915270129, -8.612986846345537, -7.487463794992628, -6.016303629904394, -4.394122487009682, -2.815026657133621, -1.4451214888422117, -0.3977766787179734, 0.2764523688156682, 0.5894063329501437, 0.6070447338044175, 0.4327849640719976, 0.17995351580814956, -0.050821184198697744, -0.1891046282452323, -0.20629664635765826, -0.11675535109670315, 0.03144882630576751, 0.17206886824288373, 0.2407833022948577, 0.1944470442759777, 0.0243777145679352, -0.2378512600079648, -0.5233999335767489, -0.740097958416024, -0.7921229963687604, -0.6021960245471163, -0.13195564437221258, 0.6052736199068706, 1.5400425085070093, 2.553347322777759, 3.4986064980736957, 4.225134738559676, 4.602356761197732, 4.546249958493444, 4.045744410849916, 3.1599191974030223, 2.00796223914891, 0.7537662034223435, -0.41907285537526034, -1.346843671180373, -1.914128605147312, -2.0736522499268264, -1.8592096952322128, -1.3781786971432683, -0.7895972038708209, -0.2750471181748501, -0.004414487081746128, -0.09846165843370185, -0.6036150951850056, -1.4807349715053681, -2.608998117866156, -3.8067448198045524, -4.864183087361525, -5.583600024988654, -5.823339376086169, -5.523773862207087, -4.719862508901085, -3.540895388010974, -2.1943459141236468, -0.9185569387419175, 0.06403029524485743, 0.5899584082562855, 0.5938019721195762, 0.13342451412520645, -0.6130846996568786, -1.3714961737117077, -1.809753062137301, -1.597868249601939, -0.4715826703656575, 1.7133207502495564, 4.951167016661487, 9.069675740197065, 13.738556177994397, 18.50734960575152, 22.878335648554007, 26.370725165721083, 28.584944875792235, 29.264801671433755, 28.349751476555912, 25.96415837047183, 22.39139635125253, 18.035902312127984, 13.380863176859691, 8.923411802907443, 5.094834334743883, 2.173248712213645, 0.20589777553193958, -0.8922904826261737], 'positive_zeros': ['0.02508879449854715529057705770449', '0.928293904037008866802961245610335', '0.982532596214772184443320792705623', '1.75726161055369082433443254209854', '2.55567370112560081484936489260573', '3.06266857769061002064685138621627', '3.50765660173953933289187791822907', '4.09412423636808436741260114282623', '4.41326621161018922925570076706779', '4.84825714580521549277265772677978', '5.00927588556670901337779833129949', '5.76549339113643247114425151038716', '5.88192375036138314900487261931119', '6.22063181565621774895178007957224', '6.70367444730053676539023240613080', '6.75497765690762189786919674210666', '7.46246722991508891355055170505298', '7.64216893711663855605284134698932', '8.102266347097256257706145081525558', '8.142213158378598940137063543048840', '8.991030869677108127569912963837435', '8.997978190536007208183678678370035', '9.427429547037717235024023194463873', '10.18944660592757677094838528661218', '10.32414483489172003628331996400157', '10.56931933679201237815089407358534', '10.61738147462117534885287599102800', '11.17502244981212223953357858122895', '11.31583574794860340925320329319072', '11.73770732820498273068828516859132', '11.94935981401560838802492228092014', '12.01494686897313148211593149474323', '12.54042004921085844324047848305593', '12.74765448836882240156536961570705', '12.85305606597544783675881219480853', '13.17872448563672881956088621543290', '13.66266717521733392648881779183047', '14.48565992895514204953621537761962', '14.57603445854337241221628525122966', '15.32512747656932663890602698592841'], 'prelabel': '8-7e8-1.1-c7e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.912399040067612, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c7e4-0', 'trace_hash': 1129743107360121553, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.02508879449854715529057705770', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.928293904037008866802961245610', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '0.982532596214772184443320792706', 'prec': 107}}
• 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': 54896.56233136906, 'bad_primes': [7], 'central_character': '1.1', 'conductor': 5764801, 'conductor_radical': 7, 'degree': 8, 'dirichlet_coefficients': [1, 3, -94, 42, -330, -282, 0, -417, 5718, -990, -2844, -3948, 5068, 0, 31020, 13981, 1488, 17154, -32810, -13860, 0, -8532, 6576, 39198, 161850, 15204, -370736, 0, 41280, 93060, 391836, -33642, 267336, 4464, 0, 240156, -367392, -98430, -476392, 137610, 1469328, 0, -960952, -119448, -1886940, 19728, 1089108, -1314214, 0, 485550, -139872, 212856, -2858844, -1112208, 938520, 0, 3084140, 123840, -160170, 1302840, 864646, 1175508, 0, 1584729, -1672440, 802008, 328648, 62496, -618144, 0, -15000432, -2384406, -4301244, -1102176, -15213900, -1378020, 0, -1429176, 6408440, -4613730, 20307821, 4407984, 23318148, 0, -491040, -2882856, -3880320, 1185948, -9772260, -5660820, 0, 276192, -36832584, 3267324, 10827300, 3162348, 21525504, 0, -16261992, 6797700], 'euler11': [1, 2844, -29998230, -2524834944, 913217889351659, -49201890300503424, -11391822850291787663430, 21046310841470207327844084, 144209936106499234037676064081], 'euler13': [1, -5068, -75826328, -109594359700, 10371750960332446, -6876883542739564900, -298556793281488797080792, -1252123033344246590225965084, 15502932802662396215269535105521], 'euler17': [1, -1488, -796315678, 32955515712, 468363501153159843, 13522922585292730176, -134081903116815758050464862, -102808797662556994526670898896, 28351092476867700887730107366063041], 'euler19': [1, 32810, -821175938, 3606756053600, 1839903037090471423, 3223977305780209210400, -656125064666031132407480498, 23433213553699574878155948107390, 638411683925748518131605316913942641], 'euler2': [1, -3, -33, 642, -15772, 82176, -540672, -6291456, 268435456], 'euler23': [1, -6576, -6776719822, -67816341504, 34771829644557187923, -230902805275261452288, -78561403713703370837749013998, -259565137177693515194553301360848, 134393854047545109686936775588697536481], 'euler29': [1, -41280, 31585266636, -1355201959258560, 852538515923370936086, -23377066170924617349455040, 9398456118802053798513129719916, -211883747002016507748134342956845120, 88540901833145211536614766025207452637361], 'euler3': [1, 94, 3118, 126336, 8588223, 276296832, 14913297342, 983273201082, 22876792454961], 'euler31': [1, -391836, 61486586290, -14507193586161024, 3491887927172886021459, -399130818969622483220609664, 46541898589645663151931646999090, -8160183123160971676981333145668812516, 572964121067545096123347421337293637543041], 'euler37': [1, 367392, 71124113482, -46295428199372928, -17748494037413105303877, -4394911901642494228542455424, 640974870323088962412612301307098, 314315574212693127795844497595894540704, 81217248802771228597652036390959994837496721], 'euler41': [1, -1469328, 1345354841148, -878020599652429296, 448345733172319524366950, -170998264337869068520172017776, 51028269427682023245554965314120828, -10853748296027474111697941344006778872848, 1438626275603521989270100382252682485138269921], 'euler43': [1, 960952, 1419861053212, 832492459806292600, 626705823045432495819286, 226286944181596476790851908200, 104906941295593475091212244956072188, 19299198017135121469152378495176639704936, 5459046029871041534743397034507955551606171601], 'euler47': [1, -1089108, 170819098322, -2277212013836928, 173308342809438672698163, -1153688256405896796981857664, 43843623149602575138922598784828818, -141620448294750154551686407461443684410476, 65877941798660252683780571409941608871644628161], 'euler5': [1, 330, -52950, 1848000, 11584094375, 144375000000, -323181152343750, 157356262207031250, 37252902984619140625], 'euler53': [1, 2858844, 3786130953938, 5824711062825811056, 8263676154313847119746603, 6842352971833292223777756637872, 5224657257545591070069052615116858722, 4634295464533915213468466466790641877043532, 1904251686165483303166544735375573842653419591761], 'euler59': [1, 160170, -4336274439298, -98564469827644800, 12769192305753103403435343, -245292614186965756533724291200, -26856222327663411755854533978129981778, 2468729007728428565129494144069784326734030, 38358032782038398419973086399760468678777161743121], 'euler61': [1, -864646, -5008356465590, 457844324641237856, 20904794089308848958760759, 1438886971279123272933465610976, -49466698078009816857261056460397405190, -26838909872063241939972656321945816337574606, 97551820892064552722266841889541788960852432978481], 'euler67': [1, -328648, -11479536848678, 175457560334425472, 96884390925000887875815403, 1063397672160512931146021987456, -421668932291412165525202786891126467062, -73164742831907511903300999332642658907533016, 1349256365417755877454657051946796697206085388680241], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 15000432, 113352705437468, 564689055383387840304, 2003789613416572729728703590, 5135914810840222585335899893590864, 9376673029405710902265311769220053753308, 11285715283096462477451867339702782722649043472, 6842798698940938981814244812733146152009703886272161], 'euler73': [1, 4301244, -253409836502, -14369111007814970064, 25287014549336098331795043, -158741295668475501478820987312208, -30927407053696477565313398622838019318, 5799280861878000001089333505080608059764637212, 14894985451961941943846586557477384171894488107677281], 'euler79': [1, -6408440, 8995491286882, 40598787702696064000, -128805799996156739126344157, 779655423990966447121159778176000, 3317448314284700636285551406683580999842, -45385930067980202092684240857836652040222810760, 136006152866792691625201101984747368303641150837104961], 'euler83': [1, -23318148, 304841358243152, -2602065765792171554820, 15982578156929982653681375406, -70609789298899194523782620281852140, 224474587030995530118116984994827133414608, -465944290399291069084742161581305883801464556684, 542233801012015735135407853098133122208235840693558641], 'euler89': [1, 9772260, 11684070451002, -45437830420574079600, 844244467709952656523623363, -2009775894258667425236471330108400, 22858843799021250101224806496589176670682, 845639289792046111192071386246734093585638739140, 3827543948647425430322045212330289877339037312647605281], 'euler97': [1, -21525504, 493072305760828, -5799315660339570969600, 67352210862524748148928647686, -468574756502492399951829461388364800, 3218954886118174624788227831822468091196732, -11354283884731657703311586665241483877444407129088, 42619520516862344959898006540158454742326868747150111361], 'euler_factors': [[1, -3, -33, 642, -15772, 82176, -540672, -6291456, 268435456], [1, 94, 3118, 126336, 8588223, 276296832, 14913297342, 983273201082, 22876792454961], [1, 330, -52950, 1848000, 11584094375, 144375000000, -323181152343750, 157356262207031250, 37252902984619140625], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2844, -29998230, -2524834944, 913217889351659, -49201890300503424, -11391822850291787663430, 21046310841470207327844084, 144209936106499234037676064081], [1, -5068, -75826328, -109594359700, 10371750960332446, -6876883542739564900, -298556793281488797080792, -1252123033344246590225965084, 15502932802662396215269535105521], [1, -1488, -796315678, 32955515712, 468363501153159843, 13522922585292730176, -134081903116815758050464862, -102808797662556994526670898896, 28351092476867700887730107366063041], [1, 32810, -821175938, 3606756053600, 1839903037090471423, 3223977305780209210400, -656125064666031132407480498, 23433213553699574878155948107390, 638411683925748518131605316913942641], [1, -6576, -6776719822, -67816341504, 34771829644557187923, -230902805275261452288, -78561403713703370837749013998, -259565137177693515194553301360848, 134393854047545109686936775588697536481], [1, -41280, 31585266636, -1355201959258560, 852538515923370936086, -23377066170924617349455040, 9398456118802053798513129719916, -211883747002016507748134342956845120, 88540901833145211536614766025207452637361], [1, -391836, 61486586290, -14507193586161024, 3491887927172886021459, -399130818969622483220609664, 46541898589645663151931646999090, -8160183123160971676981333145668812516, 572964121067545096123347421337293637543041], [1, 367392, 71124113482, -46295428199372928, -17748494037413105303877, -4394911901642494228542455424, 640974870323088962412612301307098, 314315574212693127795844497595894540704, 81217248802771228597652036390959994837496721], [1, -1469328, 1345354841148, -878020599652429296, 448345733172319524366950, -170998264337869068520172017776, 51028269427682023245554965314120828, -10853748296027474111697941344006778872848, 1438626275603521989270100382252682485138269921], [1, 960952, 1419861053212, 832492459806292600, 626705823045432495819286, 226286944181596476790851908200, 104906941295593475091212244956072188, 19299198017135121469152378495176639704936, 5459046029871041534743397034507955551606171601], [1, -1089108, 170819098322, -2277212013836928, 173308342809438672698163, -1153688256405896796981857664, 43843623149602575138922598784828818, -141620448294750154551686407461443684410476, 65877941798660252683780571409941608871644628161], [1, 2858844, 3786130953938, 5824711062825811056, 8263676154313847119746603, 6842352971833292223777756637872, 5224657257545591070069052615116858722, 4634295464533915213468466466790641877043532, 1904251686165483303166544735375573842653419591761], [1, 160170, -4336274439298, -98564469827644800, 12769192305753103403435343, -245292614186965756533724291200, -26856222327663411755854533978129981778, 2468729007728428565129494144069784326734030, 38358032782038398419973086399760468678777161743121], [1, -864646, -5008356465590, 457844324641237856, 20904794089308848958760759, 1438886971279123272933465610976, -49466698078009816857261056460397405190, -26838909872063241939972656321945816337574606, 97551820892064552722266841889541788960852432978481], [1, -328648, -11479536848678, 175457560334425472, 96884390925000887875815403, 1063397672160512931146021987456, -421668932291412165525202786891126467062, -73164742831907511903300999332642658907533016, 1349256365417755877454657051946796697206085388680241], [1, 15000432, 113352705437468, 564689055383387840304, 2003789613416572729728703590, 5135914810840222585335899893590864, 9376673029405710902265311769220053753308, 11285715283096462477451867339702782722649043472, 6842798698940938981814244812733146152009703886272161], [1, 4301244, -253409836502, -14369111007814970064, 25287014549336098331795043, -158741295668475501478820987312208, -30927407053696477565313398622838019318, 5799280861878000001089333505080608059764637212, 14894985451961941943846586557477384171894488107677281], [1, -6408440, 8995491286882, 40598787702696064000, -128805799996156739126344157, 779655423990966447121159778176000, 3317448314284700636285551406683580999842, -45385930067980202092684240857836652040222810760, 136006152866792691625201101984747368303641150837104961], [1, -23318148, 304841358243152, -2602065765792171554820, 15982578156929982653681375406, -70609789298899194523782620281852140, 224474587030995530118116984994827133414608, -465944290399291069084742161581305883801464556684, 542233801012015735135407853098133122208235840693558641], [1, 9772260, 11684070451002, -45437830420574079600, 844244467709952656523623363, -2009775894258667425236471330108400, 22858843799021250101224806496589176670682, 845639289792046111192071386246734093585638739140, 3827543948647425430322045212330289877339037312647605281], [1, -21525504, 493072305760828, -5799315660339570969600, 67352210862524748148928647686, -468574756502492399951829461388364800, 3218954886118174624788227831822468091196732, -11354283884731657703311586665241483877444407129088, 42619520516862344959898006540158454742326868747150111361]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/8/c/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': '8-7e8-1.1-c7e4-0-0', 'motivic_weight': 7, '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': [7, 7, 7, 7], 'order_of_vanishing': 0, 'prelabel': '8-7e8-1.1-c7e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.912399040067612, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7e4-0', 'trace_hash': 1129743107360121553, 'z1': {'__RealLiteral__': 0, 'data': '0.02508879449854715529057705770', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '31803825405086001085070378814,1176752324640720674339498477943,1245508035335456514857985681799,5189919045640943493320639228368', 'Lhash_array': ['31803825405086001085070378814', '1176752324640720674339498477943', '1245508035335456514857985681799', '5189919045640943493320639228368'], 'label': '8-7e8-1.1-c7e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/8/c/e'}