Lfunction data - 6-855e3-1.1-c3e3-0-2

Formats: - HTML - YAML - JSON - 2025-09-29T02:44:34.727930

• 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': '1368264008669956573517621265338,1635900508809230899911472738875,2425061945738123267197964747027', 'a10': -15, 'a2': 1, 'a3': 0, 'a4': -8, 'a5': -15, 'a6': 0, 'a7': -24, 'a8': -8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 128379.75916951911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, 15, 75, 125]], [19, [1, 57, 1083, 6859]]], 'bad_primes': [3, 5, 19], 'central_character': '855.1', 'coefficient_field': '1.1.1.1', 'conductor': 625026375, 'conductor_radical': 285, 'degree': 6, 'euler_factors': [[1, -1, 9, -9, 72, -64, 512], [1], [1, 15, 75, 125], [1, 24, 1139, 16084, 390677, 2823576, 40353607], [1, -70, 4835, -176852, 6435385, -124009270, 2357947691], [1, -20, 5853, -73388, 12859041, -96536180, 10604499373], [1, 100, 10947, 840456, 53782611, 2413756900, 118587876497], [1, 57, 1083, 6859], [1, -56, 17593, -493872, 214054031, -8290009784, 1801152661463], [1, -140, 75885, -6842196, 1850759265, -83275264940, 14507145975869], [1, 422, 143289, 27255644, 4268722599, 374526553382, 26439622160671], [1, -140, 85789, -7838540, 4345470217, -359201697260, 129961739795077], [1, -130, 191013, -15920460, 13164806973, -617513551330, 327381934393961], [1, 286, 164595, 24348004, 13086454665, 1807909832014, 502592611936843], [1, -792, 503249, -178039856, 52248820927, -8537138540568, 1119130473102767], [1, 434, 371431, 126415236, 55297532987, 9619332729986, 3299763591802133], [1, -478, 663817, -194030340, 136334071643, -20162295080398, 8662995818654939], [1, 650, 737535, 294381908, 167406431835, 33488243334650, 11694146092834141], [1, 1060, 1208081, 657646872, 363346065803, 95885885099140, 27206534396294947], [1, 796, 1246957, 575726472, 446299626827, 101967826001116, 45848500718449031], [1, -218, 656551, -33841388, 255409500367, -32990861331002, 58871586708267913], [1, 1314, 1289277, 789056444, 635663842803, 319416916554594, 119851595982618319], [1, 326, 884365, 103390668, 505668410255, 106582561718294, 186940255267540403], [1, 502, 1939413, 707861436, 1367226043197, 249484608062422, 350356403707485209], [1, -968, 1472769, -2040866588, 1344156501537, -806316900771272, 760231058654565217], [1, -342, 3017243, -679195028, 3108668480143, -363039891505542, 1093685272684360901], [1, -1304, 3018805, -2463307472, 3298729731235, -1557044194673816, 1304773183829244583], [1, -1400, 3944697, -3281117136, 4832423446971, -2101022492588600, 1838459212420154507], [1, 748, 2397923, 714328104, 3105379824767, 1254470882909068, 2171893279442309389], [1, 514, 1157411, -790562332, 1670024859667, 1070123200841026, 3004041937984268273]], 'euler_factors_factorization': [[[[1, -1, 9, -9, 72, -64, 512], 1]], [1], [[[1, 5], 3]], [[[1, 24, 1139, 16084, 390677, 2823576, 40353607], 1]], [[[1, -70, 4835, -176852, 6435385, -124009270, 2357947691], 1]], [[[1, -20, 5853, -73388, 12859041, -96536180, 10604499373], 1]], [[[1, 100, 10947, 840456, 53782611, 2413756900, 118587876497], 1]], [[[1, 19], 3]], [[[1, -56, 17593, -493872, 214054031, -8290009784, 1801152661463], 1]], [[[1, -140, 75885, -6842196, 1850759265, -83275264940, 14507145975869], 1]], [[[1, 422, 143289, 27255644, 4268722599, 374526553382, 26439622160671], 1]], [[[1, -140, 85789, -7838540, 4345470217, -359201697260, 129961739795077], 1]], [[[1, -130, 191013, -15920460, 13164806973, -617513551330, 327381934393961], 1]], [[[1, 286, 164595, 24348004, 13086454665, 1807909832014, 502592611936843], 1]], [[[1, -792, 503249, -178039856, 52248820927, -8537138540568, 1119130473102767], 1]], [[[1, 434, 371431, 126415236, 55297532987, 9619332729986, 3299763591802133], 1]], [[[1, -478, 663817, -194030340, 136334071643, -20162295080398, 8662995818654939], 1]], [[[1, 650, 737535, 294381908, 167406431835, 33488243334650, 11694146092834141], 1]], [[[1, 1060, 1208081, 657646872, 363346065803, 95885885099140, 27206534396294947], 1]], [[[1, 796, 1246957, 575726472, 446299626827, 101967826001116, 45848500718449031], 1]], [[[1, -218, 656551, -33841388, 255409500367, -32990861331002, 58871586708267913], 1]], [[[1, 1314, 1289277, 789056444, 635663842803, 319416916554594, 119851595982618319], 1]], [[[1, 326, 884365, 103390668, 505668410255, 106582561718294, 186940255267540403], 1]], [[[1, 502, 1939413, 707861436, 1367226043197, 249484608062422, 350356403707485209], 1]], [[[1, -968, 1472769, -2040866588, 1344156501537, -806316900771272, 760231058654565217], 1]], [[[1, -342, 3017243, -679195028, 3108668480143, -363039891505542, 1093685272684360901], 1]], [[[1, -1304, 3018805, -2463307472, 3298729731235, -1557044194673816, 1304773183829244583], 1]], [[[1, -1400, 3944697, -3281117136, 4832423446971, -2101022492588600, 1838459212420154507], 1]], [[[1, 748, 2397923, 714328104, 3105379824767, 1254470882909068, 2171893279442309389], 1]], [[[1, 514, 1157411, -790562332, 1670024859667, 1070123200841026, 3004041937984268273], 1]]], 'gamma_factors': [[], [0, 0, 0]], 'group': 'GL2', 'index': 2, 'label': '6-855e3-1.1-c3e3-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3], 'order_of_vanishing': 3, 'origin': 'ModularForm/GL2/Q/holomorphic/855/4/a/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.01953125', 'prec': 34}, 'plot_values': [-1.957244841772855e-180, 0.0003198647117271411, 0.002552460454935899, 0.008578308412423227, 0.020213896859281617, 0.03918076725705496, 0.06707567452836025, 0.10534229551820937, 0.1552454944633556, 0.21784700273642246, 0.29398390223033233, 0.38425187647040826, 0.48898874273346904, 0.6082623829730657, 0.7418664167152922, 0.8893128183682069, 1.0498311295761398, 1.2223793239352654, 1.4056454042666893, 1.5980586543664268, 1.7978175016574864, 2.002898499401669, 2.211079117480573, 2.419983158660768, 2.6270940209947717, 2.829787172293943, 3.025392178711355, 3.211205787014357, 3.384530895850499, 3.542752595767128, 3.683345612416786, 3.8039154310973644, 3.902284063122627, 3.976485957040021, 4.024806123406539, 4.045869826019973, 4.038621379160472, 4.002353830382312, 3.9367956602649206, 3.842068055248257, 3.7187010843329467, 3.5677100247471643, 3.3905287468167637, 3.1890084542689645, 2.9654766543092386, 2.7226470978411648, 2.46359904008315, 2.1918132824299117, 1.9110624187661835, 1.6253710940904462, 1.339025973891152, 1.0564534589997054, 0.7821643266169481, 0.520737773778909, 0.2766967792920271, 0.05444343475474541, -0.1417789816659402, -0.3080007406008381, -0.4405908505402318, -0.5363091855396167, -0.5923984283327772, -0.6066394352607878, -0.5774066203349555, -0.50372539438371, -0.38530717287179306, -0.2225951984640501, -0.016778892556391315, 0.23020055299058848, 0.5156267183871039, 0.8360403640407417, 1.1872691067357815, 1.5644368630007464, 1.9620405012763225, 2.3740159181009974, 2.793786363968234, 3.2143741884475414, 3.6284987506234194, 4.028663148849325, 4.40728588804698, 4.756820198069024, 5.069871128835003, 5.339327714881606, 5.5584882526067645, 5.721192227021031, 5.821932097852287, 5.855965934188664, 5.819442575492369, 5.709474224060707, 5.524217425136774, 5.262966574575452, 4.9261742539308715, 4.515484386526488, 4.033769735452682, 3.48509587807682, 2.874696446487955, 2.208935107477807, 1.495220072015011, 0.7419200039794854, -0.041760113575933316, -0.8458957546961771, -1.6599776570229623, -2.473120760819096, -3.2741846133234236, -4.051940580938898, -4.795351199066665, -5.493660941979344, -6.136570061565299, -6.714557977140239, -7.218911043443487, -7.641873706668901, -7.9769810717345555, -8.218996481291585, -8.364012256687893, -8.409753551645194, -8.35541067309752, -8.201668652271513, -7.950948042305154, -7.6071333884706265, -7.175522483493941, -6.662979792621915, -6.077580654428492, -5.428485496761892, -4.725996630405192, -3.9811542914998634, -3.2055557103096115, -2.41132346055358, -1.6107009328511566, -0.8158479978670927, -0.038745528586636414, 0.7091584387520359, 1.4171383194566896, 2.075313752003849, 2.6749070782021156, 3.208380992628845, 3.669547495035483, 4.0536978315962875, 4.357659501766041, 4.579854470642486, 4.7202915304265725, 4.7805290013753226, 4.763657831419205, 4.674170244552564, 4.517833158504781, 4.301590351691537, 4.033343140288478, 3.7217580544793316, 3.3761028964419424, 3.0059903007178863, 2.6211574489292477, 2.231268890907214, 1.845678622128949, 1.4732261254341672, 1.1220498840682886, 0.799416570518722, 0.511574583480658, 0.263623236753969, 0.0594399216981322, -0.09838019793062837, -0.20856404941063542, -0.2711293975247016, -0.2873497114114617, -0.2596864402147174, -0.19167376311555442, -0.08780065784115473, 0.04665769386791558, 0.20579757343025507, 0.38325558124759207, 0.5724489371908201, 0.7667225851425675, 0.9595254025588781, 1.144677224350997, 1.3164542033479245, 1.4697278443066741, 1.6002088714452278, 1.7044345915068115, 1.7798365969849272, 1.8249192401055032, 1.8391373623774563, 1.822877866529556, 1.7775490613984377, 1.705365307493784, 1.6092511213035003, 1.492842273096254, 1.3602183175023919, 1.2157592324894848, 1.064083196333946, 0.9097819872329718, 0.7572734056521044, 0.6107172571650515, 0.47380813839227015, 0.3496680402929237, 0.24078613547435018, 0.1489082932802808, 0.07500254494625085, 0.019258133378792373, -0.018914860710588986, -0.040836175408858984, -0.04848348239557616, -0.044398820388524496, -0.03156995750632669, -0.013299530242361402, 0.00694172207843079, 0.02566631769036836, 0.03952136657791413, 0.0454357057124423, 0.04075596774689933, 0.02336611946378239, -0.008213364006858799, -0.054749478945238225, -0.11625881065991324, -0.19198434737111073, -0.2804064311670641, -0.3793172169617777, -0.485871175058087, -0.5966822519677185, -0.7080101576645575, -0.8158512682749908, -0.9160919451734684, -1.004771994892533, -1.0781613012222337, -1.1329178184470423, -1.166367386333075, -1.176507624020516, -1.162113307413919, -1.1229629580065912, -1.0597282334818872, -0.9739826221426359, -0.868318531359635, -0.7461140458785851, -0.6114306112056892, -0.46899758899498567, -0.3238893166846552, -0.18133547942971065, -0.04659424976735697, 0.07539184816565438, 0.18021472593920182, 0.26417658355266127, 0.32456908121214695, 0.3598442601564416, 0.3697530105396917, 0.35548113113436547, 0.3197002732354513, 0.2665866106381159, 0.20176932465445507, 0.13221944347477613, 0.06610083427916547, 0.012537415546614389, -0.01865405396055444, -0.017270560709082262, 0.026921964147227702, 0.1238241285597932, 0.2826146709568702, 0.5113684509575804, 0.8166937880420077, 1.20339097585697, 1.6741456925630138, 2.229280782983119, 2.8666119305803455, 3.5812894438523792, 4.365755948695695, 5.209928367213817, 6.101201533585105, 7.024650453662191, 7.963605225515088, 8.899756790590473, 9.813571410369596, 10.685235544149322, 11.494740488658667, 12.22240835017452, 12.850091452129753, 13.361081572571205, 13.740603072526643, 13.977083597369623, 14.06175000412489, 13.988941735340804, 13.757248562550995, 13.368720157528358, 12.8288958390561, 12.14764020322869, 11.337991924389597, 10.41588488414012, 9.400596194649196, 8.313364881762364, 7.176871936425494, 6.015324196919602, 4.853052767291094, 3.7138972893773907, 2.6210508175787677, 1.5958739680955127, 0.6573658736108824, -0.17804239327971674, -0.8972615878433021, -1.4908221249369562, -1.9529422073695586, -2.281791424629426, -2.4794233894198867, -2.551575453239164, -2.507454582669027, -2.3593341212248626, -2.1220591296702307, -1.8125113705132476, -1.4489837331922302, -1.0504796808792802, -0.6360936554437403, -0.22434789832922275, 0.16753911489250906, 0.5241123321268915, 0.8321827516196871, 1.081387246975573, 1.264311364568947, 1.3766842089342417, 1.4176060318373185, 1.389280562014377, 1.2968555098560408, 1.1482575665675412, 0.9536204332104, 0.7248420844351012, 0.47509185633884854, 0.2181304214897577, -0.032249708346867204, -0.26287355360182013, -0.4617327787194943, -0.6184561310130939, -0.7248937990150838, -0.7753371410769908, -0.7667262823076828, -0.6989745546355561, -0.5747716879886433, -0.3994490261868202, -0.18094537703578478, 0.07074888964570182, 0.34402377549532576, 0.6260077056653898, 0.903297701622055, 1.1625319031054595, 1.3909139554261196, 1.5768685264095732, 1.710540959447439, 1.7842639840426107, 1.7929137135560091, 1.7341434548844699, 1.6085858993834306, 1.4197907927430113, 1.1740933484072629, 0.8804430675490669, 0.5499559681992418, 0.19545276898955244, -0.16904916596331637, -0.5289933333745598, -0.8699135297461827, -1.1781029567516792, -1.4412251719146656, -1.6488767201715682, -1.7931624599868863, -1.8690175913688238, -1.8744828241194957, -1.8109470681135569, -1.6830447092184997, -1.4985213222181097, -1.2680163124410528, -1.0045617282639965, -0.723067165308953, -0.43968570305875965, -0.171098326708786, 0.06620527222013099, 0.2567655381557161, 0.3868066720564495, 0.4448945104361767, 0.4226668381892104, 0.31516104738112677, 0.12115337220236899, -0.15652291137687557, -0.511121998604292, -0.9321146420413243, -1.4054603153707825, -1.9141867662059473, -2.438965082627568, -2.9589488834251747, -3.452570425194915, -3.898364831322808, -4.276146298569877, -4.567693524994178, -4.757515887191025, -4.834002842737042, -4.789681796724805, -4.621618649236069, -4.332171089727755, -3.928634382442419, -3.4230849355349675, -2.832501490499367, -2.1778243474627943, -1.4832458707056466, -0.7756944538103159, -0.08354337137917141, 0.5644432445277576, 1.1400205548689073, 1.61673869361973, 1.9709955596191302, 2.182923328133245, 2.237288835773622, 2.124184277844452, 1.8394390569327423, 1.3849316088236217, 0.7686748370189067, 0.00442839894186867, -0.8885536902964954, -1.8860749805802217, -2.960263774141415, -4.080124233894852, -5.21252967969349, -6.324171072244186, -7.381989847181167, -8.35425679391169, -9.212792293342654, -9.932865150865437, -10.493971261047724, -10.881847705219887, -11.087582763887662, -11.107821590916757, -10.946194173741572, -10.611648010592447, -10.118022539851044, -9.484735691786218, -8.734625783528207, -7.893071129281925, -6.988044137084259, -6.047929956502253, -5.100532495050046, -4.172807380675485, -3.2891426126487233, -2.4706238001277376, -1.7348223991246767, -1.0948703651357956, -0.5592447560984639, -0.13189602860675273, 0.187817570101963, 0.4047765472541526, 0.5275511030580172, 0.5678188188979573, 0.5396159795396193, 0.45851393402394663, 0.3407839819281173, 0.2025724283386628, 0.059100554537187086, -0.07600635533150318, -0.1912916148145774, -0.2779328768047195, -0.3299733140992704, -0.34444045629262876, -0.32129776432581186, -0.26320015447441575, -0.17516517250724317, -0.06404539020177283, 0.06199338815970507, 0.19404545521146493, 0.3232351923671143, 0.4411891044868442, 0.5405503495190818, 0.6156583340349372, 0.6626738294656795, 0.6797725966043021, 0.6674582614321072, 0.628215285854382, 0.5662840932112607, 0.4875176931473569, 0.3986714659310157, 0.3068758874714957, 0.21918077184030224, 0.14177888246505663, 0.07945640117627373, 0.03513862697837343, 0.009397413636392675, 0.00019408266664930595, 0.002759692235876841, 0.009625621670588481, 0.010854969769049776, -0.005563733980312558, -0.05315086387826708, -0.1462455174402305, -0.29919052663869633, -0.5254597718780233, -0.8367728285033487, -1.2422223604379032, -1.7474592327785055, -2.3540078694089543, -3.0588440034788458, -3.8539616361757787, -4.726244416643539, -5.657936870345848, -6.626703686572587, -7.606201591402355, -8.567617512994035, -9.480031754363615, -10.311534361814763, -11.031625055583692, -11.611443656972991, -12.025012937694676, -12.251959683335421, -12.277104214790128, -12.091309571659087, -11.693836574547493, -11.090946403745276, -10.295953602622752, -9.330645678639712, -8.222904460599032, -7.005864874372302, -5.718178565089775, -4.401067084753093, -3.096861830198328, -1.8483377170881023, -0.6959022470524531, 0.32392232619813693, 1.179507713940263, 1.846052629038787, 2.306528782377437, 2.5523234230100695, 2.5838061901018565, 2.4102659315425137, 2.0496579552937946, 1.5277784315860268, 0.8771415777920434, 0.13571648485154117, -0.6548244519327795, -1.4509104296202966, -2.208981419547065, -2.887376767725896, -3.448154314780078, -3.8589393065530433, -4.0941483111725265, -4.1361301286522405, -3.976195141299562, -3.614684756627638, -3.0610025335182667, -2.3333325210853366, -1.4575797369442511, -0.4663048210951879, 0.6028761302386546, 1.708946939618394, 2.8091939806621222, 3.8616322306644566, 4.826437006413393, 5.667565970479912, 6.355213125830316, 6.866256730112079, 7.185123189939291, 7.30549115746015, 7.2293800626586435, 6.966903512647119, 6.536783339815766, 5.964253451843452, 5.2798229206965255, 4.51867026322248, 3.7180205756572824, 2.915456296150646, 2.147725249372762, 1.4484593152495515, 0.8467541356836918, 0.3661415997122621, 0.023366000702074834, -0.17217541119354274, -0.21866374728719926, -0.12175692948586452, 0.10592030445321468, 0.4455773239860799, 0.8734035040643855, 1.361889410934697, 1.8814056982669818, 2.401700048448768, 2.8934276073254246, 3.329891809684169, 3.6880989751791775, 3.94982618326102, 4.102837732618462, 4.14095183029318, 4.064204937595394, 3.8791073579293647, 3.597653033281958, 3.236561967494933, 2.816589208832502, 2.3608947124562247, 1.8937646904772212, 1.4394282324248355, 1.0204800036128767, 0.6567055056275379, 0.3640824744797464, 0.1538952079446847, 0.03221747951160528, -0.00032274450662223925, 0.05155173480357344, 0.1781324864896119, 0.36545888160067225, 0.5962079159730642, 0.8507365187705536, 1.108518529927941, 1.3492691321441292, 1.5541329068990224, 1.7072157341323428, 1.79628530374792, 1.8135044933026203, 1.7563990985320923, 1.6276951824000223, 1.4352174237071984, 1.1919039354668681, 0.9147673925174051, 0.6239812635886812, 0.3420192723032291, 0.09215064278934522, -0.10286975228742277, -0.22201714823483717, -0.24734404718672984, -0.16507576879055108, 0.03354685814795638, 0.35159950698372094, 0.786105568144533, 1.3281671778639341, 1.9631303374054345, 2.6711120035313507, 3.4282991697802645, 4.207648015807011, 4.980052236567874, 5.716508404577187, 6.38873602665365, 6.970432173095854, 7.439646225467417, 7.778691600975496, 7.974898888152305, 8.022491102750056, 7.921454649163626, 7.67745191972006, 7.302755441112497, 6.814217490053515, 6.23241082726368, 5.5816300594566295, 4.887521362481334, 4.175887262552283, 3.4721747595964745, 2.7994962658586875, 2.1776828451786807, 1.6228540810711305, 1.1463975493461904, 0.7547153849630788, 0.4493345882165853, 0.2269956558781904, 0.08018346706327235, -0.0021298805207251937, -0.03360358480312389, -0.02951057944553022, -0.005670849891136853, 0.02261410340978241, 0.04153965652878947, 0.03965536577120128, 0.008522979133396391, -0.05682557424893705, -0.1577049377224868, -0.29181140433081604, -0.45347656673019876, -0.634298106936491, -0.8237242875128971, -1.0098283882259358, -1.1804847884297565, -1.3240320436205553, -1.4301037205172373, -1.4908065470050416, -1.5009356566434626, -1.4583767239637784, -1.3647526524195497, -1.2249067636903217, -1.0466352960905967, -0.8405637507002127, -0.6190227881244214, -0.3952508233128732, -0.18268819983073176, 0.006274077435576392, 0.16116837282426397, 0.2742199687447052, 0.34113786732736323, 0.36153851395920217, 0.3392131964328083, 0.2820753553573025, 0.20182257551628505, 0.11341327527741114, 0.0342012000789576, -0.01707539937848621, -0.021425249282205065, 0.039151555953486926, 0.18044627049653353, 0.4149070957172109, 0.7506210010682594, 1.1905063227903268, 1.7319245565377657, 2.366328273609169, 3.0793100270770943, 3.8514777102739823, 4.658781175381366, 5.473447355021984, 6.26612320369635, 7.00642542724997, 7.664335900284936, 8.213065509732889, 8.629118600275222, 8.893465108994743, 8.994264594487152, 8.925855551521511, 8.689105026007171, 8.2932178556046, 7.753517979382297, 7.090773415631901, 6.33176554560657, 5.5063105877633145, 4.645873976493916, 3.783166378254563, 2.9492665287624256, 2.1722112836138874, 1.4763204941894212, 0.880306937088899, 0.3965595665331488, 0.0309562820850518, -0.21754795761913906, -0.356562733642347, -0.3995527572473344, -0.3649115231138027, -0.2746839601675234, -0.15312538788857605, -0.02513520690748595, 0.08531660842470709, 0.15670395683620356, 0.1712463936878349, 0.1160044098661236, -0.01633700466562003, -0.22708569421777547, -0.511452122045169, -0.8590124512941821, -1.2543231513094888, -1.677839415494743, -2.10755984257176, -2.5201141439447943, -2.892165804557876, -3.202601881753328, -3.4332591238605485, -3.5700328246842297, -3.60471777471213, -3.5346871277585823, -3.363088354674551, -3.0996402427463137, -2.7591153158103428, -2.3604999002301135, -1.926615585435292, -1.4818923458164548, -1.0509345651863926, -0.6574550080596213, -0.32224632045224433, -0.061949694786433696, 0.11184237910675537, 0.19361647963237863, 0.18426945973302547, 0.09106079473174265, -0.07277438266714187, -0.2887881738070079, -0.5342700570777039, -0.7836875000513939, -1.010574480803087, -1.189919722362474, -1.299036161822692, -1.318054465770702, -1.23037326686776, -1.0269692418934575, -0.7094028186332406, -0.287221236223121], 'positive_zeros': ['1.07936998446071228773184587362428', '1.29049795623076368498402229596037', '1.91303656173200413242620524073437', '2.50099128529680571385869148109683', '3.05357319592563533486386149242945', '3.19678315757022229518468754332544', '3.79783593194605209821380201096510', '3.91908660709431843905414852700777', '4.03867307012425869315325639928868', '4.55796526101795424970465093244261', '4.81074398574573681903946592377802', '4.85402443712847381015375013034923', '5.65967362772067972446472043144120', '5.94850693522825607018159331739329', '6.22788560388344168381363198123744', '6.44002768763588746075948840896815', '6.76830283830114143597177815930291', '7.10357901444265296883012492660255', '7.23579614311568472240361213329455', '7.67820923139396924227578617089046', '7.890728102340781892484261233475946', '8.483861580723993486093273981591713', '8.660635412070971518501897665752460', '8.838251710388559922359644130456247', '9.221170252323708547241436853609742', '9.224249074668043066024368723731000', '9.292774099883049864309557025034749'], 'prelabel': '6-855e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.102579324084191, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3e3-0', 'trace_hash': 305172369580686855, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07936998446071228773184587362', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.29049795623076368498402229596', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.91303656173200413242620524073', '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': 128379.75916951911, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 625026375, 'conductor_radical': 285, 'degree': 6, 'dirichlet_coefficients': [1, 1, 0, -8, -15, 0, -24, -8, 0, -15, 70, 0, 20, -24, 0, 1, -100, 0, -57, 120, 0, 70, 56, 0, 150, 20, 0, 192, 140, 0, -422, -7, 0, -100, 360, 0, 140, -57, 0, 120, 130, 0, -286, -560, 0, 56, 792, 0, -563, 150, 0, -160, -434, 0, -1050, 192, 0, 140, 478, 0, -650, -422, 0, 40, -300, 0, -1060, 800, 0, 360, -796, 0, 218, 140, 0, 456, -1680, 0, -1314, -15, 0, 130, -326, 0, 1500, -286, 0, -560, -502, 0, -480, -448, 0, 792, 855, 0, 968, -563, 0, -1200], 'euler11': [1, -70, 4835, -176852, 6435385, -124009270, 2357947691], 'euler13': [1, -20, 5853, -73388, 12859041, -96536180, 10604499373], 'euler17': [1, 100, 10947, 840456, 53782611, 2413756900, 118587876497], 'euler19': [1, 57, 1083, 6859, 0, 0, 0], 'euler2': [1, -1, 9, -9, 72, -64, 512], 'euler23': [1, -56, 17593, -493872, 214054031, -8290009784, 1801152661463], 'euler29': [1, -140, 75885, -6842196, 1850759265, -83275264940, 14507145975869], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, 422, 143289, 27255644, 4268722599, 374526553382, 26439622160671], 'euler37': [1, -140, 85789, -7838540, 4345470217, -359201697260, 129961739795077], 'euler41': [1, -130, 191013, -15920460, 13164806973, -617513551330, 327381934393961], 'euler43': [1, 286, 164595, 24348004, 13086454665, 1807909832014, 502592611936843], 'euler47': [1, -792, 503249, -178039856, 52248820927, -8537138540568, 1119130473102767], 'euler5': [1, 15, 75, 125, 0, 0, 0], 'euler53': [1, 434, 371431, 126415236, 55297532987, 9619332729986, 3299763591802133], 'euler59': [1, -478, 663817, -194030340, 136334071643, -20162295080398, 8662995818654939], 'euler61': [1, 650, 737535, 294381908, 167406431835, 33488243334650, 11694146092834141], 'euler67': [1, 1060, 1208081, 657646872, 363346065803, 95885885099140, 27206534396294947], 'euler7': [1, 24, 1139, 16084, 390677, 2823576, 40353607], 'euler71': [1, 796, 1246957, 575726472, 446299626827, 101967826001116, 45848500718449031], 'euler73': [1, -218, 656551, -33841388, 255409500367, -32990861331002, 58871586708267913], 'euler79': [1, 1314, 1289277, 789056444, 635663842803, 319416916554594, 119851595982618319], 'euler83': [1, 326, 884365, 103390668, 505668410255, 106582561718294, 186940255267540403], 'euler89': [1, 502, 1939413, 707861436, 1367226043197, 249484608062422, 350356403707485209], 'euler97': [1, -968, 1472769, -2040866588, 1344156501537, -806316900771272, 760231058654565217], 'euler_factors': [[1, -1, 9, -9, 72, -64, 512], [1, 0, 0, 0, 0, 0, 0], [1, 15, 75, 125, 0, 0, 0], [1, 24, 1139, 16084, 390677, 2823576, 40353607], [1, -70, 4835, -176852, 6435385, -124009270, 2357947691], [1, -20, 5853, -73388, 12859041, -96536180, 10604499373], [1, 100, 10947, 840456, 53782611, 2413756900, 118587876497], [1, 57, 1083, 6859, 0, 0, 0], [1, -56, 17593, -493872, 214054031, -8290009784, 1801152661463], [1, -140, 75885, -6842196, 1850759265, -83275264940, 14507145975869], [1, 422, 143289, 27255644, 4268722599, 374526553382, 26439622160671], [1, -140, 85789, -7838540, 4345470217, -359201697260, 129961739795077], [1, -130, 191013, -15920460, 13164806973, -617513551330, 327381934393961], [1, 286, 164595, 24348004, 13086454665, 1807909832014, 502592611936843], [1, -792, 503249, -178039856, 52248820927, -8537138540568, 1119130473102767], [1, 434, 371431, 126415236, 55297532987, 9619332729986, 3299763591802133], [1, -478, 663817, -194030340, 136334071643, -20162295080398, 8662995818654939], [1, 650, 737535, 294381908, 167406431835, 33488243334650, 11694146092834141], [1, 1060, 1208081, 657646872, 363346065803, 95885885099140, 27206534396294947], [1, 796, 1246957, 575726472, 446299626827, 101967826001116, 45848500718449031], [1, -218, 656551, -33841388, 255409500367, -32990861331002, 58871586708267913], [1, 1314, 1289277, 789056444, 635663842803, 319416916554594, 119851595982618319], [1, 326, 884365, 103390668, 505668410255, 106582561718294, 186940255267540403], [1, 502, 1939413, 707861436, 1367226043197, 249484608062422, 350356403707485209], [1, -968, 1472769, -2040866588, 1344156501537, -806316900771272, 760231058654565217]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/855/4/a/h'], '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': '6-855e3-1.1-c3e3-0-2', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3], 'order_of_vanishing': 3, 'prelabel': '6-855e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.102579324084191, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3e3-0', 'trace_hash': 305172369580686855, 'z1': {'__RealLiteral__': 0, 'data': '1.07936998446071228773184587362', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '1368264008669956573517621265338,1635900508809230899911472738875,2425061945738123267197964747027', 'Lhash_array': ['1368264008669956573517621265338', '1635900508809230899911472738875', '2425061945738123267197964747027'], 'factors': ['2-855-1.1-c3-0-40', '2-855-1.1-c3-0-57', '2-855-1.1-c3-0-82'], 'label': '6-855e3-1.1-c3e3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/855/4/a/h'}