Lfunction data - 1-1491-1491.1490-r1-0-0

Formats: - HTML - YAML - JSON - 2026-03-24T21:46:32.292918

• 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': 'dirichlet_L_1491.1490', 'a10': [-1.0, 0.0], 'a2': [-1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [1.0, 0.0], 'a7': [1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 160.2302028687859, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [71, [1]]], 'bad_primes': [3, 7, 71], 'central_character': '1491.1490', 'coeff_info': ['x^2 - 1', -1, '\\\\zeta_{2}'], 'conductor': 1491, 'conductor_radical': 1491, 'conjugate': 'dirichlet_L_1491.1490', 'degree': 1, 'dirichlet_coefficients': [1, -1, 0, 1, 1, 0, 0, -1, 0, -1, 1, 0, 1, 0, 0, 1, -1, 0, -1, 1, 0, -1, 1, 0, 1, -1, 0, 0, -1, 0, 1, -1, 0, 1, 0, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 0, -1, 0, 1, 1, 0, 1, 0, 0, 1, -1, 0, 1, -1, 0, 1, 1, 0, -1, -1, 0, 0, 0, 0, -1, -1, 0, -1, 0, 0, 1, 1, 0, 1, 1, 0, -1, -1, 0, -1, 1, 0, 0, 1, 0, 1, -1, 0, 1, 0, 0, 1], 'euler_factors': [[1, -1], [0], [1, 1], [0], [1, 1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [0], [1, -1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-1491-1491.1490-r1-0-0', 'leading_term': '2.03272159872126411049435070267', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/1491/1490', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.0327215987212646, 1.5716783033208626, 0.45545124758311595, -0.6093610060886757, -0.8669633580328363, -0.15319635531100187, 0.7617875596998481, 0.6985890272201211, -0.7509337279419068, -2.479397298911502, -2.561202655868079, -0.09584984065242053, 3.48915614806881, 5.246989678330358, 3.280876312653306, -1.2713870255986468, -4.9946162233366405, -5.248683239552033, -2.5694447207811226, 0.08491124807999155, 0.4927205659757648, -0.6605230064220401, -0.9426374718796353, 0.7595173339879226, 2.8927914195861315, 3.1704309310834997, 1.3712044731565791, -0.4614896725823527, -0.616992531355253, 0.24814603996382725, 0.25225827976146165, -0.9832100121766617, -1.7777954658645108, -0.8505900775661263, 0.6223046700927231, 0.4670568394791993, -1.2398712391128406, -1.7563140524707506, 0.7708616261832122, 4.293618165050453, 4.860593012210158, 1.639187142661616, -1.5537328541444462, -0.7204318829012246, 3.244913413065415, 5.529718401273229, 3.4227716648332565, -0.3324121333402773, -1.1954662085800043, 1.3750296218507199, 3.580179155172264, 2.5241619629204566, -0.22955924600892574, -1.3210522188323106, -0.25146755886232214, 0.5455427134209447, -0.2416963378338982, -0.9791725673256195, -0.05826352062399608, 1.2598929701945825, 0.7658376596080165, -0.9772970469676828, -1.1738388791431011, 0.8764760283883839, 2.373287199906245, 1.1223270772355785, -0.9385094966881732, -0.5487936031800738, 1.6303111945435855, 1.6112076723786675, -1.6766160312669558, -3.823556863353119, -0.7616522742935766, 4.873095286427033, 6.419985760301039, 1.850445894637483, -3.561581706648901, -4.26298657155668, -1.2031171131402336, 0.7025719730414131, -0.20702600376753272, -1.096789515174978, -0.08529144079517913, 0.8563860909143004, -0.24566486429006992, -1.7004967046597255, -0.8835346391841706, 1.2735201041023418, 1.6411974553915303, -0.04647417782641389, -0.832161866933177, 0.48337565022375173, 1.37810806492081, 0.058339371009199184, -1.243890661026166, -0.07538263221554387, 1.5675700083415474, 0.2392665825870849, -2.38970648013177, -0.6834392157334878, 6.306656345165901, 11.797132873331071, 9.710592180023232, 2.91064124817704, -0.8984042303473777, 0.494785884698533, 2.3095857815165557, 1.1698918481345248, -0.2640428858907846, 1.1517002957367424, 3.3861416328710368, 2.700664285061161, -0.1235680987860609, -1.2821423653624011, -0.23354318166211593, -0.056074983413674756, -1.7360653165094793, -2.5244309994358844, -0.9754399232764506, 0.4981269642734816, 0.07759655081623686, -0.20134593121210226, 1.4305072639699328, 2.401383212121282, -0.048417352746270466, -3.0070952768194354, -1.350410181938246, 3.813742951690774, 5.858599311382621, 2.6148499308845907, -0.1343598099627158, 2.194383692529158, 5.597348243738183, 3.8535835427739964, -1.5501045451108753, -3.822800631543693, -1.348765403293072, 0.668998967550162, -0.8410782843764365, -2.4954280585744963, -1.0260636910406395, 1.3011004393423622, 1.1684116806003249, -0.1976206449105265, 0.012043447229856489, 0.8988269829027123, 0.06881401503890706, -1.2533535844263253, -0.27648866862401855, 1.7024203757468852, 0.9947354355759523, -1.7408714634833462, -2.0621537703149238, 0.6008630692882418, 1.7709216061458315, -0.0798685132310342, -0.5752766006356282, 2.3418740740390387, 3.2729366288879453, -2.282663303961586, -9.19471975987598, -9.149716447079932, -3.017156179364569, 0.6823184897871752, -1.3453666115800293, -3.550175284621248, -1.6560567639350865, 1.1504980570635037, 0.9799154415702083, -0.34026355916185264, 0.215179038100601, 1.1436639568872877, 0.05830718675525211, -1.0364835056098478, 0.6772253554495087, 3.137758278648763, 2.6660454657477146, 0.43717285722668076, 0.13560029676488017, 1.168710179796233, 0.21917970400063427, -1.895209147442789, -1.5161067518520275, 0.4122891082025257, -0.4795749120653099, -2.9348470127657484, -0.2725227746321544, 8.025190489138431, 12.982274042078005, 8.774607718180253, 1.5847849984149405, -0.011650510480858647, 2.6075567171008194, 2.554337932982493, -0.5663564187009256, -1.5026486535484507, 0.5148219484577357, 1.124913014830291, -0.5009747668631028, -0.46237200810832674, 1.9687946678932309, 2.7314660060370297, 0.5250453228723697, -0.897629151355948, 0.2784836513271225, 1.123096402357533, 0.15682027009277957, -0.049150912507779865, 1.1616136987863714, 0.5200131948740542, -2.2619658976809913, -2.3473010245588197, 1.6579151391645102, 3.9291870496036605, 1.1597627347174777, -0.8770975819417587, 3.0147614943304895, 7.650897306508169, 5.45855333428351, -0.8384199069377813, -2.8181998641080046, -0.13480101016666482, 0.28513975721080576, -2.957942381075764, -3.9961547615915656, -0.8998166121484472, 1.124907656577519, -0.5945640004124666, -2.0779702272931386, -0.6829554591632754, 0.6410982173037557, -0.13836723522623484, -0.6055760030113649, 0.25845400515819245, -0.3714710691995262, -2.8257684372248484, -3.0305750274773713, -0.029123573576294644, 1.561165867827827, -0.12487152694986225, -0.804322597076273, 1.2860316566565049, 1.3392672807995922, -2.5638262134570167, -4.252960213985354, -0.03086652745605477, 3.6278022022158933, 0.7372760503486945, -3.2283061016658343, -0.29065123954658106, 6.211820324832188, 7.069851726736471, 2.071547955586099, -1.1450015407788603, -0.20788388226207918, 0.4259753463911791, -0.6366351902150582, -0.25350424066182375, 1.4497630567070938, 0.9569489379661208, -1.1446548038348454, -0.8960002467451739, 1.163530525361264, 0.8923821336725921, -1.325258320611555, -1.447819713782145, 0.06433451104246928, -0.6765536172134048, -2.7257810711705153, -1.9102300829942338, 0.4300105224940797, -0.1574866388681335, -1.2366839072160352, 3.273206105238511, 10.175439815558699, 9.321946408874226, 0.21361717499050828, -5.871530846782023, -3.116779646779406, 1.3466667595367887, 1.0396321412010647, -0.4603279896941028, 1.0370650079678696, 2.257146255639122, 0.1158731534157076, -1.776596179031979, -0.49885304685675996, 0.4251652327361656, -1.6787253850730355, -3.2516424631390217, -1.5888545506727785, 0.1400911865709464, -0.3892890253505087, -0.4084285471273267, 1.3365889700038724, 1.5427682283385349, -0.36995853876741164, -0.3182801787017682, 1.7174339475601124, 0.3887334161583908, -4.06310504800265, -4.047166540608165, 1.7980852347226846, 4.491696757837083, -0.29633195069606083, -4.6018781237481035, -2.1945895227099173, 1.1309819540501458, -0.8285865732195622, -3.5930032092168256, -1.4402491953187042, 1.738866062239698, 0.3446751836140097, -2.580632712985402, -1.8983623565859697, 0.21364354622172807, -0.30639931349739913, -1.5186641053666472, -0.4957953485881275, 0.5349672759051161, -0.4127163369911032, -0.4835316648987539, 1.6188419652151658, 2.1258368927351294, -0.025424231555039853, -0.24241895244646097, 2.490829547786775, 2.754664705313754, -0.6811215445994657, -1.737653372544653, 1.1006771226972032, 1.234639304650315, -2.8818299089636183, -3.4662331181394896, 1.8390403119711427, 3.86815501809612, -2.2716741646444603, -7.897085193916201, -5.284679736945624, 0.2708108369213146, 1.265089291033847, -0.14572766560694228, 0.568698942151424, 1.2561250788998113, -0.6718706105925476, -1.944071751000076, -0.2618938870697909, 0.9722990803057436, 0.03173197849944171, 0.30298608071415245, 2.3511830121770174, 1.8202975213661294, -1.5762061403633079, -2.641612034942246, -0.4894647480915941, 0.3443523365665504, -0.4346526649990369, 0.8669610586747294, 2.1116309017747943, -1.7366128638888996, -6.360592199012823, -2.7495916518920405, 6.08228694379526, 7.964992662433378, 1.4837163188185456, -2.3969482955896977, 0.5352234779143817, 2.6408252081354533, 0.07635563942898546, -1.6753642674869376, -0.17113811274828453, 0.07767153415843983, -1.8732713568779369, -1.588314348119205, 0.8738547276248775, 0.8601221665985271, -1.1569374288240812, -0.6306932454810952, 1.6150086381817597, 1.3029286366490551, -0.5195437201386214, -0.30380912476792177, 0.45849890367004653, -0.353061281226158, 0.6025426797395976, 4.8044836882637885, 6.083113220699631, 1.363861692603242, -2.0030736589203815, 0.7533951510568373, 2.199662805377071, -3.4573493831811954, -8.502316485501856, -5.200411335769173, 0.39544659915079566, 0.008212551142461666, -2.7484673883092623, -1.5643944018890135, 0.20484556350748398, -2.2227721916742693, -4.732228271766668, -2.6465062221296596, 0.23969831992724341, -0.3014148648875622, -1.3434858234852927, -0.1712651629481173, 0.4338536784123186, -0.6046448985068064, -0.08923612316358909, 1.6199854533419282, 0.5462389330722219, -1.9257094725525188, -1.0106607138912773, 1.2508648438349317, -0.4428471310489339, -3.328596596296353, -1.5572475155344718, 1.5362890737673909, -0.16008332386276097, -2.2825939672165667, 2.0281749222860994, 7.175671023943414, 3.9635606021841157, -3.0656356434381076, -3.3031161867714802, 1.398398833000098, 1.79926542377048, -1.5837772011816134, -1.7035442585826712, 0.8728496181773203, 0.9383458901669958, -0.43062158796479266, 0.2738555854051407, 1.0192460676298738, -0.3099316851586938, -0.379005256371873, 2.1304250806121567, 2.6424954234680214, -0.050790093229132444, -0.915829676149894, 1.1063999869158154, 1.3118546094503922, -0.43626560064932796, 0.11904959533619815, 1.2592327468518478, -1.5287978701161102, -4.1892127646202795, -0.6299473318661821, 3.298483469684279, -1.4250139078357136, -9.156216192448973, -7.861294540757797, 0.049514980870783785, 2.809196425454903, -0.2895061743051484, -0.8869952367871944, 1.635358586093309, 1.6391949868563191, -0.13314169166657763, 0.25920715955788, 0.4397810396689963, -2.5716210508086714, -4.6078524019002245, -2.2169722212717202, 0.3792027332357966, -0.13424748052340493, -0.4866593066539263, 0.8144519716243537, 0.412847585995414, -1.3096643504092311, -0.2927953406141021, 1.788193485036043, 0.5997942539367476, -0.4723560702444854, 3.40086562974688, 6.595861377197786, 2.4222041429764403, -2.3046959836757757, 1.6936695807028364, 8.493006340863925, 7.163759700016815, 0.8731529682141119, -0.8664083476330496, 0.44540132747990363, -1.2548004289166255, -2.7480264594916015, 0.8922977748820416, 4.8145219655916, 3.338879528159262, 0.2824840222895182, 0.2780121359647071, 0.6349152581986507, -0.6886234932686763, -0.48167988759612074, 1.4614980926216743, 1.1169429592139357, -0.8177363424505039, -0.4045863713788592, 0.5035863708472206, -1.402904205783001, -2.122488388756279, 1.9447747012730976, 4.92202583385849, 2.1457998601575965, -0.1449642763254751, 2.5370510935841963, 3.3908718716777484, -1.1081810209542158, -2.1917097838771533, 4.2488995568472046, 8.073664193093887, 3.176383335627911, -1.553122904387162, 0.6619117153743636, 3.420877916250376, 1.4720467594444173, -0.42597869447592407, 0.6964210035412869, 0.7832502487573693, -0.9987057088321971, -0.860683155013716, 0.27094196109876867, -1.1489087181568516, -2.665636548853802, -0.9215771964883517, 0.5389659088389582, -1.1872838217664714, -1.7086638691781846, 1.1526699397909266, 2.279792834446598, 0.22370868202799973, 0.05344811279216018, 1.3607638153553419, -1.0906711753626304, -3.5128603718787668, 2.1193873381937705, 10.159997398553408, 8.005056847545088, -1.3825634021421203, -4.180994361205621, 0.5773158012569785, 2.4550628378002797, -0.024107864524547887, -0.1094040840852916, 1.7147565658303696, 0.5231660761513914, -1.484003490446605, -0.5388886591138777, 0.037195504261049755, -2.2254478112988796, -2.773162371860548, 0.194227661190775, 1.6135149210483042, 0.07513339598849207, -0.22567005112326216, 0.5097052735252248, -1.180459602042809, -2.8876304357012077, -1.1674474953633749, 0.20667909396296597, -1.1300990560409445, 0.8094239707313173, 7.0908294098508895, 7.473568245160863, -1.2071099499639584, -6.751566158792624, -2.449757273259735, 2.1152643678974425, 0.48545789894924424, -0.26279245140542407, 3.4355302987191205, 4.283132968513216, 0.13950622508738875, -1.6716105574913362, 0.44247601337590853, 0.541643346348708, -1.341685899778465, -0.2314217665512399, 2.1843899970154594, 1.3410740099964216, -0.5192155017017278, -0.10676865375723024, -0.06093112768191199, -1.6229953659200664, -1.2937566093707915, 0.06168049351856292, -2.168110154338092, -5.161827257910002, -2.8380204950723242, 1.0571666519356424, -0.1680683471845113, -2.252417329636827, 0.64813193828394, 2.472636918669718, -2.165257147177537, -4.7748946290221355, 1.1762830360567182, 6.318502057835274, 2.5951052773944454, -2.2448366788408802, -0.7586802362342365, 1.2554697441467233, -1.0769757585065656, -2.3722281244009245, 0.16577003923037986, 1.4096176273297476, 0.00021045940638319042, -0.06675793576235658, 0.631112267969059, -0.69120874614968, -1.141057666461568, 1.3694203172382369, 1.9334351866174297, -1.4143967078173252, -2.8786997314780893, -0.7035373667341303, -0.03328487696612254, -0.8959140057312501, 1.0049467248057844, 2.4446849441659113, -1.2913711047350134, -3.717574880773443, 1.4446158426155586, 5.411007186421894, -0.4232109370018658, -6.9320884757890555, -3.578732673620719, 2.5237351850787313, 1.3590045282070502, -2.3227440504443866, -1.2882640761318007, 0.8194726896785582, 0.1532635945165775, 0.2637128420603689, 1.7279680784048426, 0.19035613957287467, -2.700008996570819, -1.6533957167171687, 1.0211800290582211, 0.4503730622171678, -0.7636089824561899], 'positive_zeros': ['0.74336781637499039065117755217', '1.60923750094764345412384583210', '2.36676163979979082239351189184', '3.44612011975552358339387530808', '4.605269718755504051478388992156', '5.922267483970132438378317581592', '6.39757427677316629592801578000', '7.07992637540804087550758305348', '8.334596939933070244744331596218', '8.96864128439067658380166116921', '9.45813373343059461384668233068', '10.474510936150074013368641199890', '11.03574539889433144521312988512', '11.80656543504499494180520767431', '12.94335565718873151347547443509', '13.50413871400265146215522818422', '14.65340705415135426387262329248', '15.173503494096832334894604308265', '16.22063352545108620536193509719', '16.933798274866534610615627353632', '17.43532609945437478758693951691', '18.13666368778423201145535413653', '18.886610340369039557332970594533', '19.573578509713560823214029199541', '20.46146250304026018732547831344', '21.02017154425432879576410349514', '21.73580935108156694126511868425', '22.542703503912729250089883400754', '23.5302430431700340612316378205', '24.51086527888857618501537010671', '24.95694970399008998460467906311', '25.64275243026280218512763348804', '26.2070073499372588690478504083', '26.999785801231119043505134300198', '27.80434306308350802106845983414', '28.34818078577604301173324740933', '29.07196275339651954361666944985', '29.698642721274128034532910448458', '30.33840057045903319556816672495', '30.97755492957028070009923362313', '32.367377262610404892452823014552', '32.751758103643846976126773839304', '33.637525710577549011613557616154', '33.886993438380267728030560619182', '34.984996566774237246154974397572', '35.699033829950723875192084757244', '35.91854557573696450224545035338', '37.03700929585251476863723842269', '37.52740152431001027176530763930', '37.87708370442232335048218299595', '38.74587740239718951666181684576', '39.462717626504716706252861342428', '40.571936092126956095139479235781', '40.70789443172849768703273361147', '41.783364385671970200520945431620', '42.6461827956680423439004949547', '43.01116992518252451402125240331', '43.86858638334837131254366150325', '44.62603719596306631159603058979', '44.9963484861846860218944420340', '45.63810534654685283876986934439', '46.289449823216199750797858360954', '46.989736367039541181696842412162', '47.74711476976467405647690604054', '48.42565485206559312034815198715', '48.83566613510306353784027632763', '49.59123424704256891697704552128', '50.81742192825786416838727917334', '51.114274247464459629812839017859', '52.03289132976551797026617113316', '52.70071941416327760853530644299', '53.072079779507230536576469226286', '53.76036046186236456823065039762', '54.29564723279003816033521174745', '55.42902347874802086683990363764', '55.56992865033073819295869037363', '56.280856545857314268514613415329', '57.10001851451604479447230174458', '57.4366315240870668472485862398', '58.13801959446741337027099763874', '59.512777691816322633509516245365', '59.6896829644161257240750943477', '60.566762389338140905549789987836', '61.17654339253390880632520587731', '61.78198555180133933678423039693', '62.25989734957061256014225067900', '63.19313747644927076699590488703', '63.69758053931171150212111126105', '64.42337548988414719335813115523', '64.70450245433773116669913536189', '65.37732887989991944059626998406', '66.13564134819591301032800272382', '66.977095804147196867191418986777', '67.31041659607653101560916842174', '68.39049333474074263480229898219', '69.07898653158713167516168329820', '69.41332575931634007703235967447', '70.39687557530016515992167974836', '70.86291150395938924700609585770', '71.672465356602794521444730287195', '72.15109926255062513272684609396', '72.717392524680169198533263067516', '73.057986469203302318539657425558', '74.06537041683807948492563142182', '74.6688919553923223245859242907', '75.141620305415303547313548044623', '75.75248923444873004270163988779', '76.56423213200306837478923270522', '77.23163143830386058539728632587', '77.8266711518180654035474158986', '78.89292094066778902189777988328', '79.41763705819908661009613491549', '79.825696426402641939592330684039', '80.35929858509145190044362689222', '81.07235596624417958799087043098', '81.693692247984238124255308202163', '82.31260543373758583747357991531', '83.103475884443886626327664223580', '83.31023271641676793862918372028', '84.29632661429115900839385753215', '84.6620657006039640007976954858', '85.14182725363072954480182056783', '86.256929549503808074888204077446', '87.06310724899612690967154508334', '87.65954550198716445135142619874', '87.97374432525069347174153070094', '88.76228242923796232668812688759', '89.45866425016201163293517782107', '89.789367711906630012831017998549', '90.8792619019408831881454634170', '91.1187030491353225283115873844', '91.65022735806046224610910042527', '92.43613065378391403811626776616', '92.86376486741852428594773911795', '93.46765312114276626202499898203', '94.28672914591981309189112216224', '94.98556451399991949299347766275', '95.78530503144124644291678630377', '96.17824214785674532320828631951', '96.98718988664554813153051172119', '97.531780430111987980881308160170', '98.38625181567172896110895475629', '98.68654318567261300590157769790', '99.470317247410418342919526824724', '99.89787261785302588601406918684', '100.40135277185622103257538731345', '101.24610741495650553434712279522', '101.59948607776943247057351626754', '102.44044570267925247383833148099', '103.01353942758346361308730035177', '103.54521528379111485437977749104', '104.27783278062636945645201463367', '104.909916268017440665255441409390', '105.91628759389628943769985541325', '106.50812719761824390593439340136', '106.74190466687429052869530266496', '107.414834690010167511974911393819', '108.16261242808613489358948352413', '108.76032731586417222416117671706', '108.994708011462738424988789567945', '109.85915405836003937890558813773', '110.70497789301805721712020928645', '111.06147631986857250324361398442', '111.43010066394247580429460001575', '112.08948137553094379211243696635', '112.9095418467875458223910758665', '113.82002737287014760852212352461', '114.33444779680458786358409093063', '115.00727042393632213017649226837', '115.65826493353336827502626521540', '115.953886764496723240857722538460', '116.75668525366896394221290120907', '117.31477597756626379360614647580', '117.89578839116719135049720365122', '118.64097444687842927592961178140', '119.143313732307782269155807412774', '119.57458013383798912840395274661', '119.926302131738750611004158804818', '121.01653594874732425576943407813', '121.50375531855749299036009572218', '122.03358956514939266354490193231', '123.0897839642108294602734750036', '123.43834170036518498768244003156', '124.27060412897348078809900207199', '124.44963702731449425185426905832', '125.57755361527139750252323792085', '125.87805566790518830476003951394', '126.59864593865522366336237019910', '127.0166791522297048479770799584', '127.515581146847954640673269890010', '128.18608502050386232473698478102', '128.86278280283825096608556515859', '129.33428441499893038009420637797', '130.12522008932217445326467640710', '130.61069036471272153737252341591', '131.14911161315914255688228686819', '132.03666561877194106628765375045', '132.71263526326238966617651412231', '133.28876051105540795719229167821', '133.94698788054433465957112644110', '134.55745031719309540706566313396', '134.939275958555534630468161197932', '135.56349806194861078601134677650', '135.99830440941536922471769516837', '136.86908938568812266140566527581', '137.34294375307830613647106577919', '138.03164426815303969924260564573', '138.416634431050466801223296485911', '138.94005956068788742687940417687', '139.72172328770654274613314609671', '140.25757580315168462483018501212', '141.247752930553263439706874456961', '141.84632178755577853301903733503', '142.30280401512613131246337889150', '143.08749482817995580905563173655', '143.36639135821382185296688515565', '143.820247026444618196180389068337', '144.91826917601776210214174474322', '145.27799253616312727345951229903', '145.752147434447137740965817833756', '146.31805751838595930686478697130', '146.91100771879732010930691368145', '147.58195505034396139993792042338', '147.884712071649545268247722709602', '148.86770172943151524494603591954', '149.30051810850704797042986799818', '150.37542019750247354937199404490', '150.797893512382032434274285167679', '151.09614242486382680344906489793', '151.82106594053313125995711960897', '152.88705939136521464679582788473', '153.02206144325868679297928838645', '153.60112307837433125779949478693', '154.14201918352149851331191506251', '154.85052023967127772948947119799', '155.39446034857193474519287080112', '155.7537728023847652181818258945', '156.441060129198070695353610447979', '157.40356949623592063986021739711', '157.54632284843297950430906034853', '158.36813047222219293527304348932', '158.88281075052123453041200396434', '159.84651020473817331327487888931', '160.26168901504480711736313764255', '161.11266951184729561875866453760', '161.41924479993627866212449044053', '162.01281557070002479223755628631', '162.68658158186636585586154134190', '162.94502748957083729097946896468', '163.87173217439991678063581172023', '164.20547597200381464875191454324', '164.88849727867026657130690284747', '165.66564582740838926542102721182', '165.92596186909061552447328375769', '166.47416741761203685599714455678', '167.11069809412342697341921118457', '168.07435974085953704864045779277', '168.714270083997116918482890908360', '169.37154067190463173330124267965', '169.70562356243796664046868992461', '170.374545463351760356297151105300', '171.05053381520268858866775875603', '171.25976518528589313296307828875', '172.16846336342908826273262528137', '172.82815504206573168326696564178', '173.195364414162299721080561328644', '173.59181355944854471361912528541', '174.54769329070250550609206936219', '174.76372321241303215512399932177', '175.25794078231118630456345579130', '176.211488143229191878477694310317', '176.99739975896213134234573826121', '177.55754314937394728093418306477', '177.84676398354496269953434913534', '178.7604130289520307988534308089', '179.312603026826923254306234554406', '179.771651841247543240325154896170', '180.3383520329052280120115272491', '181.12680541241750230878062012943', '181.59997356617156779284822898717', '181.85731943788081342665538042476', '182.758165455430578512946502683261', '182.862552714394600481449481767154', '183.94517093047722161844539830051', '184.35850625049937357036510197977', '184.95131673335465807325911924679', '185.50940377830626214307369516965', '186.20376911563048338391741543000', '187.005288502850919203739360370', '187.571606020971773423065494745584', '188.01763503406181968498260722457', '188.73214080984970544616570016739', '189.37505170991844290642750313588', '189.70826081156950508786516417743', '190.1907512142247931073747389112', '190.78742066096827682085642413699', '191.44519911298796823058899338993', '192.322640582542120448619124868243', '192.48761902008915927723607924251', '193.01262200791978427691942595353', '193.6688076972849099336106263985', '194.31040106274950761208933801424', '194.98500422572133705890522781883', '195.78013431977288134768841383659', '196.34558577179776308060400630964', '197.022146897078931027930567438333', '197.55128579977279138512277977602', '197.74140370461683761505957157180', '198.45560183874670371651969398407', '199.22912391418260161026029829957', '199.76257984443270923692809960086'], 'prelabel': '1-1491-1491.1490-r1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 160.2302028687859, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r1-0', 'st_group': 'mu(2)', 'symmetry_type': 'orthogonal', 'types': ['DIR'], 'values': [[1, '0.976320249653709537211012696139']], 'z1': {'__RealLiteral__': 0, 'data': '0.743367816375', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.60923750095', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.3667616398', 'prec': 40}}
• 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': 160.2302028687859, 'bad_primes': [3, 7, 71], 'central_character': '1491.1490', 'conductor': 1491, 'conductor_radical': 1491, 'degree': 1, 'dirichlet_coefficients': [1, 1, 0, 1, -1, 0, 0, 1, 0, -1, -1, 0, -1, 0, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, 0, 1, 0, 0, -1, 1, 0, -1, 1, 0, -1, -1, 0, -1, 1, 0, 0, 1, 0, -1, -1, 0, 1, 0, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, -1, 0, 1, 0, 0, -1, -1, 0, 1, -1, 0, -1, -1, 0, -1, -1, 0, 0, -1, 0, 1, -1, 0, -1, 0, 0, 1], 'euler11': [1, 1], 'euler13': [1, 1], 'euler17': [1, -1], 'euler19': [1, -1], 'euler2': [1, -1], 'euler23': [1, 1], 'euler29': [1, -1], 'euler3': [1, 0], 'euler31': [1, 1], 'euler37': [1, 1], 'euler41': [1, -1], 'euler43': [1, 1], 'euler47': [1, -1], 'euler5': [1, 1], 'euler53': [1, 1], 'euler59': [1, -1], 'euler61': [1, 1], 'euler67': [1, -1], 'euler7': [1, 0], 'euler71': [1, 0], 'euler73': [1, -1], 'euler79': [1, 1], 'euler83': [1, 1], 'euler89': [1, 1], 'euler97': [1, 1], 'euler_factors': [[1, -1], [1, 0], [1, 1], [1, 0], [1, 1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 0], [1, -1], [1, 1], [1, 1], [1, 1], [1, 1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1491/1490'], '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': '1-1491-1491.1490-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1491-1491.1490-r1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 160.2302028687859, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.743367816375', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_1491.1490', 'Lhash_array': ['dirichlet_L_1491.1490'], 'factors': ['1-1491-1491.1490-r1-0-0'], 'label': '1-1491-1491.1490-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1491/1490'}