Lfunction data - 6-475e3-1.1-c3e3-0-0

Formats: - HTML - YAML - JSON - 2025-12-08T16:56:42.848446

• 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
  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': '535476762261349641270865502932,1244346861832122562913198047177,1372203451440934376441245525781', 'a10': 0, 'a2': -3, 'a3': -1, 'a4': 3, 'a5': 0, 'a6': 3, 'a7': 35, 'a8': -1, 'a9': -16, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22012.99025540451, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [19, [1, 57, 1083, 6859]]], 'bad_primes': [5, 19], 'central_character': '475.1', 'coefficient_field': '1.1.1.1', 'conductor': 107171875, 'conductor_radical': 95, 'degree': 6, 'euler_factors': [[1, 3, 6, 10, 48, 192, 512], [1, 1, 17, -118, 459, 729, 19683], [1], [1, -35, 1176, -21691, 403368, -4117715, 40353607], [1, -16, 3942, -41410, 5246802, -28344976, 2357947691], [1, 65, 7335, 280762, 16114995, 313742585, 10604499373], [1, 29, 5514, 503573, 27090282, 699989501, 118587876497], [1, 57, 1083, 6859], [1, -101, 31877, -2079558, 387847459, -14951624789, 1801152661463], [1, -377, 81935, -13844910, 1998312715, -224248392017, 14507145975869], [1, 140, 51757, 5897128, 1541892787, 124250515340, 26439622160671], [1, -290, 105187, -19377292, 5328037111, -744060658610, 129961739795077], [1, -956, 508879, -163355096, 35072449559, -4541099654396, 327381934393961], [1, -570, 145938, -24674476, 11603092566, -3603176937930, 502592611936843], [1, 66, 280158, 10764012, 29086844034, 711428211714, 1119130473102767], [1, 817, 657711, 260089834, 97918040547, 18108283042393, 3299763591802133], [1, -265, 458145, -77293258, 94093361955, -11177841414865, 8662995818654939], [1, -988, 726644, -371638582, 164934381764, -50902129868668, 11694146092834141], [1, -207, 842361, -117000634, 253351021443, -18724885108983, 27206534396294947], [1, -846, 1246593, -603857484, 446169347223, -108372840197166, 45848500718449031], [1, 627, 811566, 342245479, 315712970622, 94886559883203, 58871586708267913], [1, -382, 809229, -432705284, 398981456931, -92859408009022, 119851595982618319], [1, -766, 1679713, -797249332, 960438057131, -250436326000654, 186940255267540403], [1, 172, 1270123, 165585880, 895397341187, 85480782045292, 350356403707485209], [1, -2450, 4122563, -4668536612, 3762551940899, -2040781412076050, 760231058654565217], [1, -150, 1535091, -777559652, 1581605792391, -159228022590150, 1093685272684360901], [1, 338, 2671697, 628733204, 2919435447719, 403589676226802, 1304773183829244583], [1, 935, 1959361, 698655446, 2400301477523, 1403182878978815, 1838459212420154507], [1, -1895, 5037695, -5135170502, 6523961118155, -3178104710043695, 2171893279442309389], [1, -2134, 4836447, -5428593652, 6978494866959, -4442885040067606, 3004041937984268273]], 'euler_factors_factorization': [[[[1, 3, 6, 10, 48, 192, 512], 1]], [[[1, 1, 17, -118, 459, 729, 19683], 1]], [1], [[[1, -35, 1176, -21691, 403368, -4117715, 40353607], 1]], [[[1, -16, 3942, -41410, 5246802, -28344976, 2357947691], 1]], [[[1, 65, 7335, 280762, 16114995, 313742585, 10604499373], 1]], [[[1, 29, 5514, 503573, 27090282, 699989501, 118587876497], 1]], [[[1, 19], 3]], [[[1, -101, 31877, -2079558, 387847459, -14951624789, 1801152661463], 1]], [[[1, -377, 81935, -13844910, 1998312715, -224248392017, 14507145975869], 1]], [[[1, 140, 51757, 5897128, 1541892787, 124250515340, 26439622160671], 1]], [[[1, -290, 105187, -19377292, 5328037111, -744060658610, 129961739795077], 1]], [[[1, -956, 508879, -163355096, 35072449559, -4541099654396, 327381934393961], 1]], [[[1, -570, 145938, -24674476, 11603092566, -3603176937930, 502592611936843], 1]], [[[1, 66, 280158, 10764012, 29086844034, 711428211714, 1119130473102767], 1]], [[[1, 817, 657711, 260089834, 97918040547, 18108283042393, 3299763591802133], 1]], [[[1, -265, 458145, -77293258, 94093361955, -11177841414865, 8662995818654939], 1]], [[[1, -988, 726644, -371638582, 164934381764, -50902129868668, 11694146092834141], 1]], [[[1, -207, 842361, -117000634, 253351021443, -18724885108983, 27206534396294947], 1]], [[[1, -846, 1246593, -603857484, 446169347223, -108372840197166, 45848500718449031], 1]], [[[1, 627, 811566, 342245479, 315712970622, 94886559883203, 58871586708267913], 1]], [[[1, -382, 809229, -432705284, 398981456931, -92859408009022, 119851595982618319], 1]], [[[1, -766, 1679713, -797249332, 960438057131, -250436326000654, 186940255267540403], 1]], [[[1, 172, 1270123, 165585880, 895397341187, 85480782045292, 350356403707485209], 1]], [[[1, -2450, 4122563, -4668536612, 3762551940899, -2040781412076050, 760231058654565217], 1]], [[[1, -150, 1535091, -777559652, 1581605792391, -159228022590150, 1093685272684360901], 1]], [[[1, 338, 2671697, 628733204, 2919435447719, 403589676226802, 1304773183829244583], 1]], [[[1, 935, 1959361, 698655446, 2400301477523, 1403182878978815, 1838459212420154507], 1]], [[[1, -1895, 5037695, -5135170502, 6523961118155, -3178104710043695, 2171893279442309389], 1]], [[[1, -2134, 4836447, -5428593652, 6978494866959, -4442885040067606, 3004041937984268273], 1]]], 'gamma_factors': [[], [0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '6-475e3-1.1-c3e3-0-0', 'leading_term': '1.98914648376562192621693191670715070660869300412164037499980246410369518535294978956868495', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/475/4/a/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0234375', 'prec': 30}, 'plot_values': [1.989146483765622, 1.9738209617384979, 1.9503099284791414, 1.910633185175799, 1.850780232467862, 1.7731737590276846, 1.6809079557718303, 1.5757721084053342, 1.458642863131544, 1.3306278347757279, 1.1934328703545367, 1.0490151076930088, 0.89936591645891, 0.7464600898157684, 0.5922865855909352, 0.43887523428727004, 0.2882483101773604, 0.14236874642661274, 0.003123926033954225, -0.12771986212516398, -0.24853507710537864, -0.3578545001904676, -0.4544128371530303, -0.5371568070148045, -0.6052721047538074, -0.6582040375894403, -0.6956639287390388, -0.7176479355249938, -0.7244383593766501, -0.7166074759688271, -0.6950167694307195, -0.6608040970027836, -0.6153778965427593, -0.5603957933809711, -0.4977404773484055, -0.4294983559821526, -0.35792248188299086, -0.28539690145943836, -0.2144004182530137, -0.14745942495125772, -0.08710209918990841, -0.035813170728638474, 0.004018332640375746, 0.030148707121323826, 0.04052685287033172, 0.033344339842681925, 0.007080028357270409, -0.03945843001321322, -0.10709616891493778, -0.1962597648687863, -0.30695166226565074, -0.43873045476498296, -0.5907021710394769, -0.7615189261517072, -0.9493813670414231, -1.152063768966652, -1.3669356640518564, -1.5909921476723017, -1.8209170146846354, -2.0531175857188586, -2.2837951263683034, -2.509027429088951, -2.7248149779382578, -2.9271962351717646, -3.1123125884036056, -3.2764804337450406, -3.4163264547148957, -3.5288064333596436, -3.611324077421669, -3.6618213089391545, -3.678764477526896, -3.6612978198188584, -3.609229032118323, -3.523021685199886, -3.403923882363027, -3.25384284280695, -3.075371240150157, -2.8718062091695256, -2.6469760404544314, -2.405272904374686, -2.1515329136749726, -1.8908829184336418, -1.6287207058133817, -1.3705082079871918, -1.1216655559372917, -0.8874612067199488, -0.6728151609876335, -0.48221615611900936, -0.31956356192582386, -0.18803900709337426, -0.09002827427244557, -0.027000788124735817, 0.0005440077142625795, -0.006874807504023317, -0.04769771024951025, -0.11933451905982505, -0.21819955908893895, -0.33978895995261754, -0.4787639113647217, -0.6290916721700288, -0.7841941504949494, -0.9371211275597858, -1.0807626468218052, -1.208046884948203, -1.3121800238810475, -1.3868744389861247, -1.426568273483424, -1.426663498800526, -1.3837248552792942, -1.2956618526932149, -1.1618945171756667, -0.9834790881582631, -0.7631780760299316, -0.505510670068277, -0.21674714671695963, 0.09516799662240759, 0.42071551182061195, 0.7489737257049462, 1.067823889511268, 1.3642382815080938, 1.624569813246798, 1.8348666178641635, 1.9813343312810774, 2.0506256123930986, 2.0302760863893523, 1.9091928931646343, 1.6778705639201916, 1.328920995433361, 0.8573559801779309, 0.26075379625130274, -0.4602724791745121, -1.3021516034305605, -2.258177039936568, -3.3183695730509144, -4.469853991646581, -5.69672629378754, -6.980397546548225, -8.300115124945897, -9.633029484383504, -10.954906561239959, -12.24069552942183, -13.464898421776406, -14.602345845971321, -15.628841113604599, -16.521682017149267, -17.260275274432814, -17.82685301923088, -18.206840295084376, -18.389249950705043, -18.367303973602336, -18.13843259438246, -17.70445600921677, -17.0718432235588, -16.251356389270793, -15.257953821658303, -14.110559478468632, -12.831479986980629, -11.445939739819783, -9.98148431092012, -8.467257854416722, -6.933244618694115, -5.409530804299463, -3.925517737763802, -2.509132165812181, -1.1861218882463889, 0.020624648641578053, 1.091631872942055, 2.0113753062455486, 2.7686082780307877, 3.3565786474922525, 3.773219789800901, 4.021002403665507, 4.1068416658883145, 4.0417534344343595, 3.84036532888738, 3.520536917290076, 3.102491891450365, 2.6082424852646247, 2.060957270302262, 1.4838429849461559, 0.8996795163614794, 0.33009244494267703, -0.205448951460867, -0.6898871808822671, -1.1090962350827553, -1.45254440958969, -1.7132405593504794, -1.8878034385698, -1.976731608966514, -1.9839366814433501, -1.916366443371333, -1.7838966946203765, -1.5984877111112707, -1.3735641015272184, -1.123589353095194, -0.8630976890291834, -0.6060706081020921, -0.36536531047160475, -0.15196525265663965, 0.025460968856996277, 0.1609852694640468, 0.2517270187234376, 0.29796244322423, 0.3031546423723372, 0.27377506627089765, 0.21899922711826061, 0.15028906644126522, 0.08082501890240419, 0.024857358347055918, -0.0030041246623255437, 0.011453004750631626, 0.08128298363283704, 0.21766069671424093, 0.42920742659464606, 0.7214019697682486, 1.0961902687612688, 1.5516192291259707, 2.081650581706608, 2.676401132170105, 3.322130088808436, 4.001598922237364, 4.695019600200263, 5.380275762669742, 6.033812442221128, 6.632063537240983, 7.151733957283883, 7.570928339079267, 7.8706800514554764, 8.035107708292895, 8.052236195348796, 7.915365345769794, 7.622806861735035, 7.177955726239975, 6.590353594810176, 5.874687852464432, 5.050090135660336, 4.140752710697288, 3.1741264800866333, 2.1798052407438755, 1.1895422464559302, 0.23509959504362896, -0.6529108476438307, -1.4455126623377126, -2.1171481474981992, -2.646637472899559, -3.0176994871603036, -3.2198696781306206, -3.249033033921041, -3.107426954594623, -2.803617466431711, -2.3523507815798026, -1.7738256615907475, -1.0929165525325995, -0.33828263875899367, 0.45888121058598746, 1.2660737283168413, 2.05075810736792, 2.7817872387546903, 3.4306115694053507, 3.972338314103739, 4.387017445424328, 4.660218044100302, 4.783455936508513, 4.755025316589848, 4.579523240188762, 4.267548959690088, 3.8358227554177193, 3.3057345977552646, 2.702437499167144, 2.0542778834892372, 1.390864943793854, 0.7418346498316296, 0.13600153303412713, -0.40046524971721237, -0.8451363289359185, -1.1799311059188649, -1.392322588944792, -1.4757903446311966, -1.4298711689219012, -1.2603662363104495, -0.9789743120093958, -0.6026855532951393, -0.152943173768842, 0.34528382313552997, 0.8647204264277476, 1.3771757254094976, 1.8546279182496428, 2.270754032648442, 2.6020745425796328, 2.8288859952960683, 2.936478683486748, 2.915488069531014, 2.762416689784594, 2.4799103894975456, 2.076313843805105, 1.5654874137301984, 0.9660674649447054, 0.30048128516662764, -0.405987212688658, -1.1264547606830113, -1.8336798682174138, -2.5012983517457132, -3.1050027946106264, -3.6236661680207893, -4.0401690745137255, -4.342161152649718, -4.522555280512792, -4.579554591956651, -4.5168253101941005, -4.3430413609448095, -4.071231974807511, -3.7182809149851512, -3.303773863407481, -2.8489864463067462, -2.37592114322886, -1.9060902476462116, -1.4594660651910971, -1.0536277391478843, -0.7029752174176589, -0.4180334593718822, -0.20522863870366198, -0.06671195492682884, -0.00039090903799506894, -0.0003709580338093686, -0.05740698754549202, -0.1596504214162569, -0.29341453320305927, -0.4441290528192196, -0.5972699620250527, -0.739129018190854, -0.8578304839902997, -0.9438430376372793, -0.9905387396500859, -0.9946518748708212, -0.9561864889067394, -0.8785202985511459, -0.7680441593219496, -0.6336145918389063, -0.4860777837413165, -0.337402798336298, -0.19991403052666396, -0.08549296633233999, -0.004745120577184425, 0.03369283874369664, 0.02374154490674857, -0.037690884990758775, -0.15047675770942773, -0.3112111878056312, -0.5133861721561931, -0.7477836311819255, -1.0028991847123858, -1.2657598462990003, -1.5225978721762867, -1.7595959374936283, -1.9639983328208903, -2.1245040841930076, -2.232184052292245, -2.2811269111567554, -2.2683519614536443, -2.1945459548060775, -2.063716723364426, -1.8827871085480699, -1.6616968815167898, -1.4122792731636018, -1.147721205692471, -0.8819358907904228, -0.6283849585584771, -0.39948197242650546, -0.20578905950173232, -0.055310021968395705, 0.04692388818279866, 0.09916467979868306, 0.1030272546506921, 0.06337367924389477, -0.01206976395808772, -0.11321445191877176, -0.22830138290788068, -0.3447161547115497, -0.44983752417367806, -0.5319008990656362, -0.5808272882973052, -0.5889284925373062, -0.5514544211721719, -0.4669777373322788, -0.3375177030184353, -0.1684933682587602, 0.03167402778165838, 0.2519960759790699, 0.4796660708402455, 0.7010444204208683, 0.9023078872883202, 1.0707449438044545, 1.1955589743220183, 1.268475746608512, 1.284932623991134, 1.2440326948297877, 1.148967296645536, 1.0071975752998876, 0.8296400289880143, 0.6305822254303157, 0.4266470082673686, 0.235691380227786, 0.07600629008320227, -0.03517324787764414, -0.08268647456899297, -0.05453819576292252, 0.057142531454906734, 0.25543299461263, 0.5381509733788258, 0.8978273890285576, 1.3218157766303356, 1.7928940497203623, 2.290120314470143, 2.7899084513174324, 3.2672946057284618, 3.697486902917491, 4.057252736577024, 4.326243516163244, 4.488651382786175, 4.533824494769771, 4.457323219843622, 4.2615629239664505, 3.9552481589095216, 3.553813723224761, 3.078322711365467, 2.554163496039343, 2.0104580828656404, 1.4777580169782691, 0.9866344691560808, 0.5661611159718197, 0.2418194153650663, 0.03435190825462659, -0.04161647587919934, 0.02148276652281017, 0.2237510102515199, 0.5576582984800148, 1.0083663104424072, 1.5545850199687297, 2.1696738429211635, 2.8229201039350307, 3.481552679288652, 4.11229340769962, 4.683076674904881, 5.165205682704113, 5.534519757252811, 5.772683933061004, 5.868397194938648, 5.81765456842362, 5.6237614383818215, 5.297239459266516, 4.8549380776054, 4.318757442609691, 3.714550142101569, 3.070372813212007, 2.414782252602163, 1.7752992710351374, 1.1768123337804852, 0.6403372956288791, 0.18184696513428977, -0.18815640575793077, -0.4650419146768806, -0.6500269692938474, -0.7493442746605233, -0.7737918307119654, -0.7374122784524465, -0.6561516580815784, -0.546824201286401, -0.42540444962035584, -0.3060278881970582, -0.20001754655253498, -0.11496860142837628, -0.054557873876574764, -0.01842181386371249, -0.0024827403937203755, 0.00034067306750066895, -0.0007747480236909341, 0.004285813143864953, 0.025329327138072497, 0.07057832716273296, 0.1455502394184063, 0.2520734694131409, 0.3875700656377291, 0.5448713715353057, 0.7122072827687391, 0.8735863957539721, 1.0099965570712888, 1.1003965261656945, 1.1230721277103082, 1.0577680230800208, 0.8870347203981894, 0.5977546283560985, 0.18303032279116604, -0.3570223780829338, -1.0146988266074441, -1.7741764040932368, -2.612025940304215, -3.49814399462972, -4.397086714481909, -5.269915649066107, -6.076087026506732, -6.776443702761525, -7.3351953062042305, -7.721674372783827, -7.913922328121357, -7.898973061125745, -7.673684508631263, -7.247121825272873, -6.638243897823911, -5.87552238803368, -4.996626480944959, -4.0444462489084065, -3.0654871565322552, -2.1072275901043143, -1.2142845730127325, -0.4262475998699848, 0.22520478939094266, 0.7184782271890761, 1.0433333350886607, 1.2019196011679334, 1.2085300122856986, 1.0886684654401004, 0.8775886812933775, 0.6177441471455336, 0.35584149169559726, 0.13970122273866703, 0.014700471494107841, 0.02043820611626405, 0.18772793938040414, 0.5360668362627156, 1.0718162085263625, 1.7874252828486936, 2.6612501788600555, 3.6585401480995547, 4.733873772523947, 5.833088106251971, 6.897118895113212, 7.866414469487862, 8.68369919331195, 9.298829198326084, 9.672614753809567, 9.778842736610258, 9.606886856987375, 9.163204509352962, 8.47086569970859, 7.567843418970172, 6.5059458984401815, 5.346887765103826, 4.157282751776041, 3.005772064162087, 1.956921171310712, 1.066101908794674, 0.37629259832311657, -0.08668948765793259, -0.3166622640685337, -0.32826872218892633, -0.15745308545150824, 0.1399727472237691, 0.4909600316738033, 0.8092162977236604, 1.0002038098560897, 0.9669110155038227, 0.6160943593577174, -0.1354238925660145, -1.3548091039978751, -3.0880007711186894, -5.355588604375099, -8.149818580298291, -11.433706027448567, -15.141079713317952, -19.178698954041234, -23.430989061105574, -27.76310949401598, -32.029314441576794, -36.08005714898205, -39.765913021672525, -42.95073428141912, -45.51486183516062, -47.35897537363562, -48.416709840933514, -48.65014802210105, -48.053402668028845, -46.657772055339464, -44.52186563085564, -41.7331137769611, -38.40354665585657, -34.65951256797802, -30.639344885963318, -26.48445846875147, -22.33210420962226, -18.310248109689383, -14.530772894099137, -11.086025461971266, -8.045161352407376, -5.452504637607734, -3.327954634604341, -1.6677385843717467, -0.4471346813638764, 0.37584159858542104, 0.8562398047036218, 1.0574749249019837, 1.0464858413339135, 0.889304703693955, 0.646865676981845, 0.3719730286989815, 0.10712925865453445, -0.11722726815235739, -0.28243180489475506, -0.3808983736079115, -0.41510949820029386, -0.39487829920136575, -0.334906800814885, -0.2525349520933207, -0.16474325020456948, -0.08606544197924228, -0.027179011414814543, 0.006355814664686967, 0.014232278386417871, 0.0008871786594347325, -0.02559616918256707, -0.05515713048538224, -0.07773907975860844, -0.08548648356341339, -0.07466011056651636, -0.047418196625082724, -0.012949998052577483, 0.012059268100077522, 0.003677773954606175, -0.06814042200473003, -0.23774256378344757, -0.5411644041631773, -1.0132797954256205, -1.684445027968905, -2.5772765723412867, -3.7037759510790025, -5.062755819593798, -6.638339878970419, -8.399181818583438, -10.298794309168331, -12.277075491958309, -14.263133237327764, -16.178051500145514, -17.939709547833317, -19.46814925454155, -20.688117508810496, -21.53651517428903, -21.96593771385073, -21.945205700267863, -21.46677167983659, -20.544371371937633, -19.211595278305012, -17.525346019960427, -15.557906600290988, -13.394204406187178, -11.129458073901889, -8.86010032190423, -6.6800658900775085, -4.675607552597008, -2.9191461460236074, -1.4660872576251667, -0.3517331249892189, 0.41031679178465863, 0.8283499372510177, 0.9311127802385473, 0.7651955309516322, 0.39133899743809564, -0.12031802805791476, -0.6953282536095607, -1.2602529821567034, -1.7478790801921698, -2.101641190050342, -2.279276554679023, -2.255642792946831, -2.0235245188631685, -1.5936590686890142, -0.9938435964596277, -0.26636567100009634, 0.5368102861543094, 1.3602845106117265, 2.147326604629528, 2.8357573109421876, 3.363924594467967, 3.6913153172943485, 3.8310546900186466], 'positive_zeros': ['0.42241668340230481051776815579773', '0.981616591833813509542561010687230', '1.08247765685109220844021774055649', '2.15506696931849794623376472593150', '2.17075433587517844871797033345540', '2.68830346625041858979088412528481', '3.03238743106983099750173163075430', '3.86676459926048703157287418770577', '4.25640372100472110897810053269765', '4.66034568682703804988250649926320', '4.89325207441706797424285493400749', '4.91283871887317861925698601151322', '5.63100643969690231456477576395974', '5.93973126883544044364403939593712', '6.38062699982005776042183722939448', '6.61675634312065184113569977841847', '6.97102109035760990027347337903409', '7.54716449145074726078191911487664', '7.57002309337987325001596970057507', '8.017505772753163634616575100962675', '8.074038146281281106556226935227298', '8.659694557468588902537564026628358', '8.762422921597023549809201507134360', '9.043350233772598800900331803726950', '9.436482581375267902912533771777381', '9.505831241616103377866340785823355', '10.10798712722594660623811537152652', '10.14427045917877166297628027787467', '10.74517060590801912081719777040602', '11.14257607317209084995767334606640'], 'prelabel': '6-475e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.293950061412254, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e3-0', 'trace_hash': 2066514202043038336, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.42241668340230481051776815580', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.981616591833813509542561010687', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.08247765685109220844021774056', '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': 22012.99025540451, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 107171875, 'conductor_radical': 95, 'degree': 6, 'dirichlet_coefficients': [1, -3, -1, 3, 0, 3, 35, -1, -16, 0, 16, -3, -65, -105, 0, -33, -29, 48, -57, 0, -35, -48, 101, 1, 0, 195, 151, 105, 377, 0, -140, 27, -16, 87, 0, -48, 290, 171, 65, 0, 956, 105, 570, 48, 0, -303, -66, 33, 49, 0, 29, -195, -817, -453, 0, -35, 57, -1131, 265, 0, 988, 420, -560, 47, 0, 48, 207, -87, -101, 0, 846, 16, -627, -870, 0, -171, 560, -195, 382, 0, -456, -2868, 766, -105, 0, -1710, -377, -16, -172, 0, -2275, 303, 140, 198, 0, -27, 2450, -147, -256, 0], 'euler11': [1, -16, 3942, -41410, 5246802, -28344976, 2357947691], 'euler13': [1, 65, 7335, 280762, 16114995, 313742585, 10604499373], 'euler17': [1, 29, 5514, 503573, 27090282, 699989501, 118587876497], 'euler19': [1, 57, 1083, 6859, 0, 0, 0], 'euler2': [1, 3, 6, 10, 48, 192, 512], 'euler23': [1, -101, 31877, -2079558, 387847459, -14951624789, 1801152661463], 'euler29': [1, -377, 81935, -13844910, 1998312715, -224248392017, 14507145975869], 'euler3': [1, 1, 17, -118, 459, 729, 19683], 'euler31': [1, 140, 51757, 5897128, 1541892787, 124250515340, 26439622160671], 'euler37': [1, -290, 105187, -19377292, 5328037111, -744060658610, 129961739795077], 'euler41': [1, -956, 508879, -163355096, 35072449559, -4541099654396, 327381934393961], 'euler43': [1, -570, 145938, -24674476, 11603092566, -3603176937930, 502592611936843], 'euler47': [1, 66, 280158, 10764012, 29086844034, 711428211714, 1119130473102767], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, 817, 657711, 260089834, 97918040547, 18108283042393, 3299763591802133], 'euler59': [1, -265, 458145, -77293258, 94093361955, -11177841414865, 8662995818654939], 'euler61': [1, -988, 726644, -371638582, 164934381764, -50902129868668, 11694146092834141], 'euler67': [1, -207, 842361, -117000634, 253351021443, -18724885108983, 27206534396294947], 'euler7': [1, -35, 1176, -21691, 403368, -4117715, 40353607], 'euler71': [1, -846, 1246593, -603857484, 446169347223, -108372840197166, 45848500718449031], 'euler73': [1, 627, 811566, 342245479, 315712970622, 94886559883203, 58871586708267913], 'euler79': [1, -382, 809229, -432705284, 398981456931, -92859408009022, 119851595982618319], 'euler83': [1, -766, 1679713, -797249332, 960438057131, -250436326000654, 186940255267540403], 'euler89': [1, 172, 1270123, 165585880, 895397341187, 85480782045292, 350356403707485209], 'euler97': [1, -2450, 4122563, -4668536612, 3762551940899, -2040781412076050, 760231058654565217], 'euler_factors': [[1, 3, 6, 10, 48, 192, 512], [1, 1, 17, -118, 459, 729, 19683], [1, 0, 0, 0, 0, 0, 0], [1, -35, 1176, -21691, 403368, -4117715, 40353607], [1, -16, 3942, -41410, 5246802, -28344976, 2357947691], [1, 65, 7335, 280762, 16114995, 313742585, 10604499373], [1, 29, 5514, 503573, 27090282, 699989501, 118587876497], [1, 57, 1083, 6859, 0, 0, 0], [1, -101, 31877, -2079558, 387847459, -14951624789, 1801152661463], [1, -377, 81935, -13844910, 1998312715, -224248392017, 14507145975869], [1, 140, 51757, 5897128, 1541892787, 124250515340, 26439622160671], [1, -290, 105187, -19377292, 5328037111, -744060658610, 129961739795077], [1, -956, 508879, -163355096, 35072449559, -4541099654396, 327381934393961], [1, -570, 145938, -24674476, 11603092566, -3603176937930, 502592611936843], [1, 66, 280158, 10764012, 29086844034, 711428211714, 1119130473102767], [1, 817, 657711, 260089834, 97918040547, 18108283042393, 3299763591802133], [1, -265, 458145, -77293258, 94093361955, -11177841414865, 8662995818654939], [1, -988, 726644, -371638582, 164934381764, -50902129868668, 11694146092834141], [1, -207, 842361, -117000634, 253351021443, -18724885108983, 27206534396294947], [1, -846, 1246593, -603857484, 446169347223, -108372840197166, 45848500718449031], [1, 627, 811566, 342245479, 315712970622, 94886559883203, 58871586708267913], [1, -382, 809229, -432705284, 398981456931, -92859408009022, 119851595982618319], [1, -766, 1679713, -797249332, 960438057131, -250436326000654, 186940255267540403], [1, 172, 1270123, 165585880, 895397341187, 85480782045292, 350356403707485209], [1, -2450, 4122563, -4668536612, 3762551940899, -2040781412076050, 760231058654565217]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/4/a/f'], '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': '6-475e3-1.1-c3e3-0-0', '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': 0, 'prelabel': '6-475e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.293950061412254, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e3-0', 'trace_hash': 2066514202043038336, 'z1': {'__RealLiteral__': 0, 'data': '0.42241668340230481051776815580', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '535476762261349641270865502932,1244346861832122562913198047177,1372203451440934376441245525781', 'Lhash_array': ['535476762261349641270865502932', '1244346861832122562913198047177', '1372203451440934376441245525781'], 'factors': ['2-475-1.1-c3-0-6', '2-475-1.1-c3-0-29', '2-475-1.1-c3-0-35'], 'label': '6-475e3-1.1-c3e3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/4/a/f'}