Lfunction data - 1-1480-1480.1029-r0-0-0

Formats: - HTML - YAML - JSON - 2024-04-25T04:07:48.960117

• 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': 'dirichlet_L_1480.1029', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.766044443118978, 0.6427876096865394], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9396926207859084, -0.3420201433256687], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.17364817766693036, 0.984807753012208], 'algebraic': True, 'analytic_conductor': 6.87309110492009, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 5, 37], 'central_character': '1480.1029', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 1480, 'conductor_radical': 370, 'conjugate': 'dirichlet_L_1480.909', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^20', 0, 0, 0, 'a^17', 0, 'a^4', 0, 'a^21', 0, 'a^23', 0, 0, 0, 'a^4', 0, 'a^20', 0, 'a^19', 0, 'a^6', 0, 0, 0, 'a^24', 0, 'a^12', 0, 'a^9', 0, 'a^5', 0, 0, 0, 0, 0, 'a^7', 0, 'a^14', 0, 'a^9', 0, 0, 0, 'a^15', 0, 'a^16', 0, 'a^24', 0, 'a^10', 0, 0, 0, 'a^4', 0, 'a^10', 0, 'a^14', 0, 'a^3', 0, 0, 0, 'a^26', 0, 'a^26', 0, 'a^2', 0, 'a^9', 0, 0, 0, 'a^20', 0, 'a^17', 0, 'a^8', 0, 'a^22', 0, 0, 0, 'a^14', 0, 'a^1', 0, 'a^22', 0, 'a^11', 0, 0, 0, 'a^6', 0, 'a^25', 0], 'euler_factors': [[0], [1, 'a^20'], [0], [1, 'a^17'], [1, 'a^21'], [1, 'a^23'], [1, 'a^4'], [1, 'a^20'], [1, 'a^6'], [1, 'a^12'], [1, 'a^9'], [0], [1, 'a^14'], [1, 'a^9'], [1, 'a^15'], [1, 'a^10'], [1, 'a^10'], [1, 'a^14'], [1, 'a^26'], [1, 'a^2'], [1, 'a^9'], [1, 'a^17'], [1, 'a^22'], [1, 'a^1'], [1, 'a^6'], [1, 'a^15']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1480-1480.1029-r0-0-0', 'leading_term': '1.47803323590177645908353144970+1.74671353041672024183339503941*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/1480/1029', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.288141255205001, 3.2365038075240533, 4.051542454671893, 3.756019517458599, 2.2486147902061098, 0.5488189623674047, -0.009236999976522605, 1.0251564704289526, 2.687135133333337, 3.369352562258828, 2.3296175891888886, 0.4752768334897141, -0.5073843096605298, 0.06496926504717845, 1.0664025083116555, 0.7848228636617589, -0.9856505306911033, -2.3615820461023436, -1.2533087095670656, 2.138088986349776, 5.088951342658363, 4.981453726762058, 2.0794058936650717, -0.7156238114871644, -1.0088044509603737, 0.5728231182042369, 1.4068389709976734, 0.17501965842477632, -1.6111944601760722, -1.7220598751844882, -0.20904012305110475, 0.65743051766993, -0.4945787660937873, -2.1123889481839404, -1.6850929540194146, 0.7171594775135617, 2.1620414539815624, 0.5877325049826116, -2.198764581665537, -2.4599039485893552, 0.7586932188346005, 4.20981657698352, 4.337858880285729, 1.5432860582181505, -0.6654453477402978, -0.3199260587019383, 0.8757315987102636, 0.5771436224174876, -0.6103864204502407, -0.22304289914453684, 1.9835575904696963, 3.1902738957112984, 1.4842465873606323, -1.0628224835416529, -1.0406155529074699, 1.3623982426698509, 2.317724499569224, -0.31209985940949553, -3.6922687797053255, -3.661883711381558, -0.3835451259899021, 1.9379878870016398, 0.8227255936523818, -1.4517318520084344, -1.620097235956927, -0.13025635145735076, 0.11807953250236193, -1.3675114535987998, -1.9777375718797194, -0.5207899982830189, 0.4099650169897505, -1.5890783358566984, -4.392287206205301, -3.8333269105006345, 0.1028672069351576, 2.7294117062136816, 1.0776961023086078, -1.974029224526772, -2.001719171828501, 0.6249078774281838, 1.7270729265951226, -0.19568942777596807, -1.987611712627281, -1.0647937773091916, 0.66382980431743, 0.24173079244235635, -1.4186230490967322, -1.2512938997335226, 0.5639222824887298, 0.7286404729331055, -1.3641586922192568, -1.81107538007769, 1.8580310417879853, 6.0198135763152365, 5.489147343098397, 0.9395884941345143, -2.0464030448373514, -0.899829287554094, 1.0474243930262317, 0.5576857929187364, -0.6243992894065246, 0.5047324287094668, 2.6578205341840366, 2.2951666584091357, -0.33563585009632163, -1.5032936972058226, -0.181881800124449, 0.46441624350936794, -1.0078448274734386, -1.2084024531518005, 2.4447082293734246, 6.36866744285877, 5.294876725945802, 0.2604410915179399, -2.5960975552079777, -0.8641794983840726, 1.3516422132566746, 0.5191426447000432, -1.1778058676388639, -0.44254950977598073, 1.348729950986354, 0.9855267720571289, -0.5986260712016692, 0.029303595658864742, 2.4280720981895842, 2.699886162223417, 0.4252415616860607, -0.07228204083367867, 2.9519391372813586, 5.031569843472532, 2.370954374537804, -1.7530703855599088, -1.9355779964689177, 0.8827866192888818, 1.2440043439187427, -1.8924900739477515, -3.8374464431433846, -2.0685024311462796, 0.22902070682923964, 0.23600537977112393, -0.13682911412154575, 1.0340311482399491, 1.2482585211559756, -1.8350033793678941, -4.953048426470147, -3.62660350992335, 0.2909161286145905, 1.227611429005366, -1.0091126524620257, -1.0132622607738244, 2.8981266725855583, 5.559755306137158, 3.3789185490024383, 0.0481996310147659, 0.1624502547974012, 2.015442414899879, 1.5312593453284988, -0.42911014340781817, -0.29340925212654156, 1.2755941638221322, 0.7563712201775636, -1.2924784759784416, -1.0768523904501763, 0.8700676373410431, -0.3205220091766818, -5.07986401245564, -7.283106931951932, -3.68233355448083, 0.6281795218274915, 0.2300531580456824, -2.4689858595311507, -2.2842339546065973, -0.051709678711909374, -0.11524537281812913, -2.052142860443025, -1.7924862193257542, 0.5282634777453136, 0.7896214100150083, -1.3790228718731754, -1.9443434376850228, -0.13467381912660456, 0.18303196706808028, -1.5882811433753712, -0.5878378084010162, 4.680682874718851, 8.066385387592833, 4.900896371531609, -0.3545815886206626, -1.1397574989902297, 1.3723960381993345, 1.8306115458995305, 0.17563329698028657, 0.3267301530335852, 1.958234129801462, 1.221128530702231, -1.4656116816130917, -1.848103691689252, 0.13384184643480151, 0.16488354702890445, -2.0640304036137778, -1.9079688621510775, 1.2807025452015246, 2.0530758185904365, -1.4512800224263331, -3.3358698049134325, 0.3079466174343038, 4.463520848617261, 3.3847314151886305, -0.3498021684378161, -1.192541699013547, 0.15338289578245332, -0.22030257109907403, -1.3865965445510438, -0.026498856997715266, 2.2386234933225913, 1.5453940800826813, -0.553467846015425, 0.1522617640794829, 1.9834991741560586, -0.17459527288171364, -4.911886830381853, -5.533999719031765, -1.395717754509644, 0.8984815630166816, -1.1176655307119825, -2.1095603194233075, 0.8436508325861029, 3.061103385191416, 1.0580315630081456, -1.4134252452134446, -0.6909548606669349, 0.6035414335450175, -0.36575934459457643, -1.1437640817746564, 0.12416380776610565, -0.1285707348560029, -3.853107800827117, -5.833332381130771, -1.9243075458916448, 2.951058854115073, 2.46737749423067, -0.702348641941734, -0.27770984172698243, 2.466850293230318, 1.8799478054830403, -1.265378195028226, -1.5143070154576066, 1.045706550780491, 1.5178177904842058, -0.3683736718660544, -0.5221771209457726, 0.9062179582629686, 0.12044330826370567, -1.9092168656356656, -0.7261627672588413, 2.3608531751116173, 1.7659638611525437, -1.5519337586874133, -0.6858646026456258, 4.816218600276497, 7.270848159639547, 3.6079020841663314, -0.11629332766108304, 0.2294865171962518, 0.9575440204243272, -0.7433426244742752, -1.5605325930678822, 0.2672418279256459, 0.7672935703151313, -1.780965935573207, -2.9455726174498453, -0.6461728267521353, 0.706141533048352, -0.9894046881203015, -1.2394577577413664, 1.592675027218015, 1.578018097384281, -4.078984119287076, -8.40385546981601, -5.547690933929217, -0.21582587518968094, 0.9565645031106211, -0.2604693029103989, 0.5133374975922058, 1.4969124927489206, -0.280480420974347, -1.8787217139836632, -0.1645609447210412, 1.5777740868107084, 0.17626653035311374, -0.7486537796501247, 1.9329617425276102, 3.774325264078633, 0.8935131285686861, -1.7963933344902558, 0.9066377980288253, 4.5760378800852255, 2.924354898356629, -0.9450494676824267, -0.674287614140079, 1.8644969063092987, 1.0673698182574285, -1.7029012956318614, -1.6259032050938225, 0.20994610112556097, 0.21683984509972945, 0.19610322578989656, 2.846136920109081, 4.607137343367208, 1.9901011008551026, -0.5140828814748128, 1.9214150377153796, 4.803376881405368, 2.029583917442601, -2.694684240595519, -2.4274262603406234, 0.7055599058000898, 0.3896436454600568, -2.008515622355432, -1.214350259518096, 1.1596736715331053, 0.1938126678021598, -2.4114965343845, -2.009441456174082, -0.08521370529726632, -0.27043439104328615, -0.4501257219414244, 1.9151451948851088, 2.514415093860005, -2.159540211458792, -6.1936802326996565, -3.3135368900481867, 1.8475420664721183, 1.7855045812038979, -1.1106711668057059, -0.4054492526242816, 2.2335160848388593, 1.569300855561268, -0.5460440969378386, 0.3831901302325188, 2.132907989046351, 0.7405657747976094, -1.0620005305514957, 0.39815020753779856, 2.014264208644817, 0.5929248279122542, -0.0808983632120137, 2.6003945714407317, 3.108225788986519, -2.145447814524358, -6.492008725156503, -3.9864691134199473, 0.13863329495050294, -0.692074717787109, -3.0571053491602798, -1.4223469463919602, 1.4228137491240962, 0.9856090575613075, -0.35331482327110736, 0.24509217460477745, -0.29107836810600735, -3.400059272189023, -4.076734662648816, -0.3759037646750163, 1.9329994040584215, 0.17100472267327796, -0.384523307762692, 2.0914080010700613, 1.4344253776894917, -3.924770133216328, -6.0817034468984605, -1.395915754633396, 2.932258680300342, 1.7512420648330842, -0.453167573903192, 0.012449474276426682, -0.08931210416031371, -2.0577752887224188, -1.8859681936501271, 0.5652241964705678, 0.4119898609860613, -1.989161216579506, -1.3162938699339497, 1.342994147858581, -0.08291459323222092, -3.8842125888193677, -2.568823305487972, 2.80795743673094, 4.045185732058792, 0.7384108941685998, -0.014083435314425019, 2.3549137427497437, 1.93342401941686, -1.078625310196449, -1.1442221364700413, 1.2016658788103944, 1.1146172978173228, -0.3775994610760842, 0.5195938715957056, 1.5522935752048344, -0.2929557928558203, -0.7801755070703246, 3.3875722481531176, 5.856565133141296, 1.1702536387772084, -4.349736962605081, -3.2815096523134146, 0.40819042748902074, 0.2849375726732705, -0.8706086034130744, 1.1966333474682078, 2.742736667165986, 0.20020230854018878, -2.0133428787600876, -0.3882664446101099, 1.0745486168780898, -0.07250861261112491, 0.019879484490360318, 1.9891640484360358, 0.9865423076730417, -2.229108083610157, -0.9832256251651068, 3.734842776230749, 3.414776222543612, -2.2251117861938496, -4.267281963507595, -0.7438103718281064, 1.057476304682122, -0.9221459076203422, -1.3547823704566928, 0.3318271168526206, -0.30201670527991065, -2.1100213959030483, -0.6363501796563648, 1.8662232040765723, 0.911381089986585, -0.531829228373708, 1.6020171035991222, 3.262220832333747, 0.6764176558831632, -0.6918918523849567, 3.2991443740018, 5.983855677614372, 1.9121033279544315, -2.5436811981331666, -1.043318140789551, 1.7263692060676856, 0.4563903252700311, -1.2292672712806094, 0.061500157053548866, 0.7644486806464694, -0.6333095084749348, -0.05307752350648556, 2.3350679807016665, 1.455826096141691, -1.3630057043310284, 0.05095494712080963, 3.728532135890732, 2.4560313918567553, -1.9264396610053136, -2.040240489514649, 0.2928187979595977, -1.8622971075540942, -5.915047056192386, -4.443699308486763, 0.41172845517431106, 1.545363761236654, -0.09466287154774214, 0.08651056646760508, 0.3204457805760075, -1.7871840072013594, -2.347793531538671, 0.40367107303630057, 1.1641334868075566, -1.4013735139358388, -0.9826892676284107, 3.0694195322979674, 2.929735028031155, -2.3570391789167107, -4.045697084753415, 0.028028121261085642, 2.1519741324304706, 0.12736096739817315, 0.01060070176451875, 2.5066266170267317, 2.203752476958965, -0.2080005130020257, 0.4096281922499376, 2.4074598567995182, 1.1892745554901747, -0.7362738197486361, 0.29082381125767265, 0.7242143510975015, -1.5376599993266136, -0.4479229173516258, 5.878402580603331, 8.504851744773672, 3.0119807416287077, -2.093034699329075, -0.7550878577077554, 1.380698420606758, 0.03406852209556447, -0.5876389128748019, 0.8992342364339172, -0.24221013963513172, -3.516310569040135, -3.1179467395705727, 0.1420639601978715, 0.7695700322258208, -0.054305166772370635, 1.405211865997188, 1.5906898762470887, -2.6453105510826096, -4.708039567090795, 0.2723872054216736, 4.888559723291426, 2.625954462173652, -0.46571194435375896, 1.5430966025532262, 3.5325807412929304, 1.030611901456001, -1.1370584276235953, 0.13221484303188458, 0.5905602375812351, -0.8303385861154708, -0.07019801184874298, 1.5240622639608388, -0.8249292961892547, -3.99517894077037, -2.1438238667251657, 1.0557496447486183, -0.2302976193052176, -1.6593048946973203, 1.966685074088743, 4.7143116353078085, 0.7788568181108909, -3.5282300574200476, -1.767782778352691, 1.1183926659677996, 0.07459705077750627, -0.795654647670592, 1.2679460754222656, 1.9298147293872088, 0.12833388807207557, -0.006793117879132201, 0.37912070532833253, -2.8722885362216077, -5.7712539056998695, -2.4125829523522193, 2.304930812046277, 1.2995320988531358, -0.9535151357785893, 1.9171848340117417, 4.891548212294978, 2.1042500681159817, -1.0905493159919004, 0.70136139684403, 2.612256340604209, 0.7590702510642379, -0.14250804052145283, 2.0004468985575787, 2.3390858363874534, 0.29583553176701977, 0.35193563124350313, 1.103979164357908, -1.5009326590434113, -3.3142014186627646, 0.438635935705221, 3.45689235420425, -0.6843399654288032, -5.4192783324314755, -3.3886536403870386, 0.07627167934385365, -1.2855642747315834, -2.9641774827452108, -0.8805459461793632, 0.26979881957812507, -1.6585425952887562, -1.6452777704708827, 0.7336815778898036, 0.23078032563843737, -2.1118938718636255, -1.198914425313009, 0.5373414076584268, -1.3244961864844114, -2.609507537942574, 0.20454914480228606, 0.32317604821102186, -6.1368092772249865, -10.152837131698643, -5.490410398275082, 0.22793235279978274, 0.41653794085161533, -0.42599160279147885, 0.8798608063196429, 0.3905570765275821, -1.7587646729023492, -0.7065006888891987, 1.6478401969796903, 0.033903383254096746, -2.5648370627983157, -1.210675368672347, 0.4498620558288313, -0.7698699453272465, 0.7363324341241027, 6.722953946170922, 8.430700595310109, 2.812139707578723, -0.9022907853425015, 1.3697652176067847, 2.316234085294445, -0.6057797511094621, -1.1567298833657653, 1.3297221587958121, 1.2792482912483365, -0.5470425992423047, 0.16634321334338156, 0.9793487575851962, -0.8602286873730608, -0.7400497223286018, 2.844253582840676, 2.8951107322965384, -1.7680091314091797, -2.551645644979133, 2.010903828916447, 3.297419278689512, 0.12348909555688678, 0.07642154880032029, 2.735180190634231, 0.9470692203436556, -3.3934340994752343, -3.1304699099761173, -0.17355699817678666, -0.06715606153011389, -0.6972771862941028, 0.5928454551717808, 0.16545734365915543, -2.1513546517654714, -0.7441228921298663, 2.8220823202396907, 1.1411411825353688], 'positive_zeros': ['1.76380450167558610196679699371', '1.88431595453149608843041992664', '3.536942835264645606476697359532', '4.043684780324986249641390571099', '4.844629617552570665766160018692', '5.75519486419085556397332594675', '7.08406693754415302277464415233', '7.709507726092541356474369072759', '8.46535294783316709371067933479', '9.41694613102859801606141287109', '9.910704232491058774911011481959', '10.85107415095083640725211158902', '11.625625969440819931531471346277', '12.44127768615735077183352637270', '13.615478336215259503825919719685', '14.136708370235389377625703118629', '14.828566708622700426758284932859', '15.35306388217173764098711215753', '16.4140802469302109521588263456', '17.02312514062583686734609028580', '17.7866125268491808333830481889', '18.784280909162495700336835864058', '19.47813796979866159426665064652', '20.34624270073680966259152789295', '20.661536291283888720378150294573', '21.65986969173255232948018418400', '21.99207652653138658503264641165', '23.117338938271133813221445321515', '23.84984206574235882357509967546', '24.61559416399714458245355427039', '25.288724708592340350632866478907', '26.10436862258332695165428598514', '26.608141092599573856816584899740', '27.40009131608967777069292939928', '27.93843744089088488907928419884', '28.62487187410004299679300891556', '29.75315369804485067954876498007', '30.4300027640478466844524679970', '31.051273732415510206836674564605', '31.48608375717229651660202141039', '32.45970811253864450480379239974', '33.16161826240790265216350367814', '33.56683096161554174968454108767', '34.20059601628251864270000708216', '35.3291868466056747614582581433', '36.03080714885958719540178026620', '36.64082792734780906707567524563', '37.25690152459569154000504419004', '37.98805974868224439853781071162', '38.43304099148841377776279449079', '39.44432649057330041916733323683', '39.7011343926694264983608205232', '40.78685693985867005269069686228', '41.462801142094728688714527899223', '42.01997845280622038792183110158', '43.075036232089825532803005100332', '43.5345060745950928768365163223', '43.81529121229635631329747826532', '44.53586703844228236352630653238', '45.59751627690987748046737139041', '46.11875421917579847168014091761', '46.66512631577621957300143709485', '47.82054584204517034336062679235', '48.09464276657017519333599659797', '48.97956356765638550967055988230', '49.433095521427642527350731565531', '50.11118318980739682451647924034', '50.78490224307497645676776787887', '51.22074061236850579948082038093', '52.43155726150084519591412327912', '52.839514398156303247075269471200', '53.76038300008091007916708019254', '54.03916176359583175529333292260', '54.92367353005056083214603303782', '55.43944848786384460514909143482', '56.275511312874682913405660554778', '56.60289282128817195878477993260', '57.2334462927900620555177560274', '58.40880440447347103786259282213', '58.89790775660076599913398344766', '59.739564852165307751489035963779', '59.91362053925171526076746633809', '60.76531896804192256184289780338', '61.53861878504671984672319940219', '61.90358081615250875894888440189', '62.69271966833862645378412749452', '63.32711092720009163831150081708', '64.04413036621644707893678619973', '64.964087773660929856007737820674', '65.57913464796413624610235274488', '65.884868253579376687397203876653', '66.56571222176656429598754165794', '67.3933552073265758630860370653', '67.79000614225332735190045826449', '68.42508545107688389511380438210', '69.48981908361264829906504817345', '69.86902586353733568614363257375', '70.554095124030657253187566433800', '71.35355778081621194341079067051', '71.99584182297729551420277397756', '72.426201377770785813987303162273', '73.09742538717689878994292786291', '73.41908285011089323679907500366', '74.478061186190501242338311229233', '75.22656009723665671790976908887', '75.65720028184490890697090188721', '76.43031909622758528228072694629', '77.06158334511998303025762811219', '77.74810985923912351018229176532', '78.233902232178835792469693648642', '78.76705202202801676524950763445', '79.444486420412482806126272290906', '80.15769115564447451720642437302', '80.67278469105227986433813636627', '81.854595810182530880290434796', '82.137632316397492660814361579', '82.70283091632685340212909528691', '83.39741157254061144548653825592', '83.86877695424606197023334035056', '84.76698344401010477303641144697', '85.1633041331572244346205170487', '85.775421923308983881529697259437', '86.36194512998536912242628573806', '87.51873536894505771791461556551', '88.03354891666624675775847172048', '88.33000002687427098286157710749', '89.02837025508603797828894261475', '89.70682186155720517084803763639', '90.338413404003845517413302417290', '90.75109955184410670746604751859', '91.63123241659782622717724322792', '92.12353583461089753000817731940', '93.02877425508140488117342760907', '93.51468613453963760128227127655', '94.17463484403796629129351935953', '94.9517326106623742547377417014', '95.411103440804211233334077919101', '95.56422506687651977534739258397', '96.74978507979722332212386908719', '97.0130421490351852492323659427', '97.930480240477618383924898341529', '98.66437409666013703376761941432', '99.11087674161650358202541032192', '99.82560495121602516496816228392', '100.33436451711556879416449854304', '101.277916713432676219133132458039', '101.46573657875468235762895064120', '101.95982969756405469737185569071', '102.69632208393493446086653950542', '103.617105049202988952103081962398', '104.237632131148419604189899479585', '104.73193468933503731012244695770', '105.51351251505657142227717221974', '105.88172237933172859440018218686', '106.653889326559618784505186819895', '107.13671061842833984571346378019', '107.91656395154032456167050526467', '108.14267003072542454167729148393', '108.95802170720068897025339584008', '109.98012769037158573548099101820', '110.22745635894580574441450149780', '111.06874960009868463051197679058', '111.74515826472608412184210607325', '112.10402473149063663429507047919', '112.45429978464967367614057906813', '113.466214225008944026480561705742', '114.08715779563841689679303939370', '114.43772976608217307086866957817', '115.09778447036829193466151645709', '116.01084256700278959456801976737', '116.77123877771725523009495827218', '117.18343562694917986787660740620', '117.47962096448908225067309484685', '118.35740720849180221492939819101', '118.805497099153328089172618417775', '119.51191591320560382482253745980', '119.993205100616960903634175390426', '120.77373928460836752489749151754', '121.65548544844108255020162423489', '121.877640054792832705892135708263', '122.69257163124680164276220419160', '123.27246685246119463699004556331', '123.950578033254002755053716202061', '124.279821607594439325204498352920', '124.96153731662866733448942371624', '125.39762681210695026331193044300', '126.30273748128369202864083244706', '127.137562202384856029706774266439', '127.54886765032311788520181675689', '127.99174629405084481906199108350', '128.767866883066217742415929613579', '129.42426144127977718994723713060', '129.983027157892734599351913255779', '130.3086921317873913005441839528', '131.02740749380892786995250739357', '131.62905316654679288772086310885', '132.38134590917138165798386229292', '133.18923725072759102214162392416', '133.62610307313948365149784785695', '134.30023644367274509253339537163', '134.63882090788344072709839273793', '135.377007793034735181244290895213', '136.06730968566369099150505447891', '136.38363072053670868354810330834', '137.25417054249383604857483578691', '137.58767000632028879719874999133', '138.5397076520347866018398357327', '139.152536436936482900166239191858', '139.74331204585097310189255305466', '140.30210560345881956050524266239', '140.80230466165187526111711491984', '141.25728685885227155702484996082', '142.01654399197171558052949475019', '142.49580935415854918464537465435', '143.28887127766498485284831508710', '143.99350026045847814016424660813', '144.20616768468995057606271800587', '145.28009682326840113135674968529', '145.91241388040813892169166395272', '146.22234694397189244992386756444', '146.63216166040130727276987728981', '147.45698598062974464026188642236', '147.964638473838671458088086289745', '148.52006226101639637005053299596', '149.24283001463040112713895195801', '149.99803862797220999126494797124', '150.645084441284878959974978925836', '150.93580573736917970271588512575', '151.835675784101932276740858923627', '152.12558964732307681213455776075', '152.96090250780740324918996233517', '153.385311184854968829593996097125', '153.86522504024179149069978708773', '154.404111499119172381047377171', '155.45401369819023221683259653280', '156.01240192833363224442458812730', '156.56806592513618497914069956412', '157.00234138943524921503164206068', '157.47468541818978032309245026139', '158.4205900132348941881865353948', '158.97883548860127620629671309075', '159.10327285701975567536996292538', '159.83020634599743561994488807618', '160.61229163817176880881236095940', '161.46658845874197922926726322828', '161.716778898418618569494350851266', '162.59743952378800740706530901046', '163.10154183384382596285439197078', '163.56735065421780606752672576925', '164.07277917339720042823113761335', '164.62062960870947907951863078112', '165.48504492372610468295762334357', '165.911716339563900099194541486127', '166.432574465778777487004404056936', '167.228890093280470775387119812212', '167.96260309540261367001843154363', '168.448906258777124940196790806842', '168.89791408566537044788546788796', '169.71606632930666946407418340092', '170.00210792015474407145159085463', '170.38102012163268291330237670153', '171.38189055022113895042957154358', '172.000583877973323183589294041700', '172.35378225163434941824336858537', '173.28066574327924051954413512712', '173.67934990495150323762820275834', '174.49067528128257715754348412482', '174.72167599418999074319490758922', '175.70818711733924723537930159121', '175.830681325576801063252869661678', '176.4252807647706943044971473387', '177.16106692405446751649598935303', '177.778577235175416479409789329057', '178.732299511709739075705704077124', '178.89123544281696936669846199681', '179.807488863582485732808662855736', '180.06636463567258524127684304731', '180.83014440526125176431538874394', '181.27896010550275223323474314170', '182.03304303979672634659627096913', '182.34240494094623930640057257134', '183.104804613065942319397868157174', '183.46238980997136638521707263651', '184.66546757173938350246119383504', '185.08381295599393295287497891351', '185.43931858859941223936942561793', '185.99117464396047235457280608629', '186.63803508430598745496879312223', '187.190687578290144487068518025424', '187.970201705607699495747722176295', '188.27835581121472848744935222199', '188.69296924149176691298741307127', '189.85300912833983063128532155144', '190.17601479763131231062932957536', '190.87516265681049960080990414904', '191.39816037558980016575422542909', '192.06740762537088615998254661366', '192.468966982018537421329430256', '193.001019467702404632103255292', '193.513326025827003768190848596', '194.260022776206490275584870723039', '194.8713730410521954797135425202', '195.639905772053203391303435925659', '195.92768221904389589538532375676', '196.626016826916092943320010513877', '197.531524919933179008926049214834', '197.79393395140257812480041150439', '198.31125309152132823743845969695', '198.77302960483256752562290151702', '199.4335697603325523298383617339'], 'prelabel': '1-1480-1480.1029-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': 0.552919823285637, 'root_number': '-0.165487718498088086079207748238+0.986211850986540089394674985661*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.276459911643', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.38405315672655775996165025159+0.610647717702433474896440788189*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.76380450168', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.88431595453', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.53694283526', 'prec': 44}}
• 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': 6.87309110492009, 'bad_primes': [2, 5, 37], 'central_character': '1480.1029', 'conductor': 1480, 'conductor_radical': 370, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1480/1029'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-1480-1480.1029-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1480-1480.1029-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': 0.2764599116428185, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.76380450168', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_1480.1029', 'Lhash_array': ['dirichlet_L_1480.1029'], 'label': '1-1480-1480.1029-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1480/1029'}