-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_143.57', 'a10': [1.0, 0.0], 'a2': [0.5877852522924731, -0.8090169943749475], 'a3': [0.30901699437494745, -0.9510565162951535], 'a4': [-0.30901699437494745, -0.9510565162951535], 'a5': [0.5877852522924731, 0.8090169943749475], 'a6': [-0.5877852522924731, -0.8090169943749475], 'a7': [0.9510565162951535, -0.30901699437494745], 'a8': [-0.9510565162951535, -0.30901699437494745], 'a9': [-0.8090169943749475, -0.5877852522924731], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.57', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.138', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^17', 'a^16', 'a^14', 'a^3', 'a^13', 'a^19', 'a^11', 'a^12', 'a^0', 0, 'a^10', 0, 'a^16', 'a^19', 'a^8', 'a^8', 'a^9', 'a^1', 'a^17', 'a^15', 0, 'a^10', 'a^7', 'a^6', 0, 'a^8', 'a^13', 'a^14', 'a^16', 'a^7', 'a^5', 0, 'a^5', 'a^2', 'a^6', 'a^9', 'a^18', 0, 'a^14', 'a^1', 'a^12', 'a^0', 0, 'a^15', 'a^7', 'a^1', 'a^4', 'a^18', 'a^3', 'a^4', 0, 'a^12', 'a^5', 0, 'a^10', 'a^17', 'a^11', 'a^9', 'a^13', 'a^18', 'a^4', 'a^11', 'a^2', 0, 0, 'a^15', 'a^2', 'a^6', 'a^19', 'a^3', 'a^3', 'a^19', 'a^6', 'a^2', 'a^15', 0, 0, 'a^2', 'a^11', 'a^4', 'a^18', 'a^13', 'a^9', 'a^11', 'a^17', 'a^10', 0, 'a^5', 'a^12', 0, 'a^4', 'a^3', 'a^18', 'a^4', 'a^1', 'a^7', 'a^15', 0, 'a^0'], 'euler_factors': [[1, 'a^17'], [1, 'a^16'], [1, 'a^3'], [1, 'a^19'], [0], [0], [1, 'a^8'], [1, 'a^1'], [1, 'a^10'], [1, 'a^14'], [1, 'a^7'], [1, 'a^9'], [1, 'a^1'], [1, 'a^0'], [1, 'a^1'], [1, 'a^12'], [1, 'a^9'], [1, 'a^18'], [1, 'a^15'], [1, 'a^3'], [1, 'a^19'], [1, 'a^2'], [1, 'a^13'], [1, 'a^5'], [1, 'a^7'], [1, 'a^12']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-143-143.57-r0-0-0', 'leading_term': '0.970773506532697861906889090311-1.39714123718529332514898304598*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/143/57', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.7012950472006443, 1.5939088325830233, 1.512516075831154, 1.1531045102036925, 0.5529700227175255, -0.06286893520391397, -0.4229090036623749, -0.34646892452465994, 0.1460613735634111, 0.8032739973655194, 1.229134047200778, 1.068588058817271, 0.21328209530596137, -1.084938214101141, -2.279727189502961, -2.7771874887137393, -2.2584569011147595, -0.9035252288873012, 0.6352146986999768, 1.539504469509257, 1.2763210069998991, -0.05502218888132805, -1.7062798510069472, -2.6519223098410385, -2.173599166194696, -0.3244163660933077, 2.0274488722230584, 3.646473347721855, 3.635815523197046, 1.9818194301844512, -0.41480180998658256, -2.267624811492618, -2.6786940019883323, -1.6671437470374306, -0.10461011204907834, 0.9019615669605513, 0.7613007374767801, -0.23611901315147016, -1.18972077404769, -1.2930236728827254, -0.4434757203797196, 0.7059647340688624, 1.2964005262100406, 0.98252609320468, 0.23296373632078105, -0.07063578102094868, 0.5448376287670919, 1.5662549306703866, 1.6992496367656977, -0.19070509914113204, -4.064008466066097, -8.431181107453433, -11.139140742366273, -10.746053852789117, -7.51309169582935, -3.261624330098806, -0.16041934021352594, 0.6875591729002384, -0.17112363414755266, -1.1820876756699985, -1.1001283270509614, 0.07710917650292075, 1.2741155071486319, 1.3973221392133675, 0.3488356481708914, -0.8835699078125311, -1.1241990341195485, -0.08900806413778722, 1.3272598512495875, 1.8352218081078746, 0.9227076535307239, -0.6436990435373477, -1.4722841973996148, -0.8005251212646647, 0.7824202336456085, 1.8414531039752169, 1.4224528735762478, 0.0029080028177761734, -0.8580062587806885, 0.05793711240466, 2.3825216975471344, 4.279244368301029, 3.94622315032812, 1.2547325517942691, -1.94411706776997, -3.215252291748334, -1.5181521538097014, 1.9119568646150298, 4.552100671757827, 4.614288220180807, 2.3832467882464288, -0.22156148485668312, -1.375021373913309, -0.786209054362579, 0.3685629966920931, 0.7899199274468893, 0.29104094699904953, -0.24850233019040074, -0.04740696057166356, 0.5870436786185731, 0.5346132759287313, -0.8418655165002674, -2.7522177928026283, -3.496364913995471, -2.092897234467503, 0.5577310191964663, 2.2555088846083025, 1.4657556500680886, -1.129256847273567, -3.051743040011741, -2.1870815260188468, 1.2458847543656084, 4.764871178348853, 5.7364377887484235, 3.6241199972609746, 0.32965501069428915, -1.6231521530008268, -1.2999139166986473, 0.09879298560451515, 0.7384823270157862, 0.08847187008706262, -0.6555626170197231, -0.00785145024217943, 2.0753396166113, 4.001273410267957, 4.097121112791545, 2.3018181412856005, 0.2353378838383837, -0.42244102950519435, 0.44852559604534303, 1.4632657431474054, 1.3475336833029232, 0.3322386087975176, -0.212458130257896, 0.49239383045795626, 1.5016072616465141, 1.0265001278798678, -1.4368863300886554, -4.0214263531525605, -3.8691186023521995, 0.11233793641221809, 5.806788196740295, 9.370092046400828, 8.42879862239465, 4.044039456011914, -0.3811841470691719, -2.1437369233462564, -1.317090659319154, -0.047528593398073006, -0.07396734184174675, -1.112545663113535, -1.6031772617608133, -0.7262100495377591, 0.6462147217882159, 1.0472378236078979, 0.18436727663232685, -0.719926537013615, -0.4248033659143603, 0.7571041517668099, 1.2302963184986633, 0.04780084430188741, -1.6891865397819623, -1.732633506969191, 0.8691782187464285, 4.418009152558543, 5.962560723414696, 4.187142527680485, 0.8002887056023044, -1.124794416076019, -0.2103629563998281, 1.9473417150018042, 2.617609768912967, 0.9192927676909499, -1.245891317647366, -1.2966460379208153, 1.1741328438670928, 3.8773084673936786, 4.184371569534578, 1.8138346245617043, -0.9982563448886944, -1.913384016401006, -0.8015064983815137, 0.47892788350230503, 0.3678142895766046, -0.7338496090288856, -1.225064946934747, -0.4092115720365643, 0.644477623431929, 0.4882411146009882, -0.8191963218678145, -1.717894535019898, -1.1392355376732404, -0.05836658570360956, -0.510563680482006, -2.958050935404332, -5.097687634077121, -3.875790142662905, 1.1287958384166872, 6.637963043778779, 8.402694640887791, 5.1615361898472925, -0.1961947640341603, -3.4533662792797273, -2.9394224897788837, -0.5601153160889105, 0.7397581603407969, 0.060058556258836264, -1.084223139364254, -1.0618025973633818, -0.10552255608572803, 0.30644783102156803, -0.3562106063666043, -0.8135287699489144, 0.3958995344007834, 2.8132327169107567, 4.206610478190261, 3.003696143307505, 0.19102735092845285, -1.6535103751169267, -1.1692810159532854, 0.41067975805077783, 0.9515278909424172, 0.14092343109055255, -0.10710963830218392, 1.814244371912281, 4.747894802732455, 5.546317043585234, 2.510963836297264, -2.3653232037983147, -5.112462520216074, -3.7873982700961477, -0.40536732813786464, 1.341199012370717, 0.03136693381160526, -2.2185989880588823, -2.4109054149572957, -0.07399004540153861, 2.4042393609471615, 2.6453073876428306, 0.8565743855551633, -0.7595226006664071, -0.7422360228363611, 0.16726647054069305, 0.4111338498293515, -0.20448987081616263, -0.4246008867022955, 0.4418007584337281, 1.258419932003899, 0.47920838275643607, -1.4286771355976862, -1.8908719363193138, 0.8743893276155936, 5.21655977007221, 7.136026346412946, 4.387708164694281, -0.8606140789868435, -3.995621545321739, -2.601820387769594, 1.2571964931490631, 3.533266520236414, 2.522354105503847, 0.1953249871037373, -0.628833407388407, 0.3657291993886799, 1.0373189190382814, -0.1756987438619492, -2.1916541025311966, -2.7160801447876843, -1.2177712861961212, 0.3725198938889782, 0.09730091851836295, -1.584936152902559, -2.447533788274894, -1.3740463561767489, 0.23235742251633892, 0.3137151372224925, -1.1165762348528698, -1.9404359077047422, -0.6974186795846244, 1.4200857186395424, 2.0173274807349038, 0.6279877495790324, -0.5842825599224328, 0.28168552833129523, 1.9254691245737148, 0.8592816113226992, -4.347398060094346, -10.564953562916731, -12.68531157737315, -8.765776027566623, -2.0578228654179247, 2.3287109521425284, 2.350128073194727, 0.21917369353242588, -0.8906255804508072, -0.3348184345641998, 0.21046249579730528, -0.34917160233852595, -1.0303105896773697, -0.4448201690173299, 0.9663113382271298, 1.3680791022906067, 0.08050625575165957, -1.3242809048441089, -1.068016652459693, 0.2805564062657323, 0.3228631873553187, -1.949246423072037, -4.387780087989114, -4.014094405424225, -0.8483884273200036, 1.6253144650365157, 0.3361108758341591, -3.635602330301412, -6.0703010112244655, -4.351877163773214, -0.3606853341543086, 1.8685582205374252, 0.8008296220285595, -1.2207119230937236, -1.2680172812663806, 0.5387559717169375, 1.5409222589181684, 0.2629416318240442, -1.5863308665427345, -1.36400257896049, 1.0182245923697972, 2.9010042104109943, 2.176757510131109, -0.1904225223981374, -1.5498346850403395, -0.8701798647729663, 0.3463818139385159, 0.47084738408100246, -0.03900108948120415, 0.33392721021100286, 1.5143353962805601, 1.5949715517634604, -0.26526317773291463, -1.760961427651202, 0.3770379905666422, 6.034937674325221, 10.743195540165956, 10.007554662104765, 4.285886429183091, -1.300569918014935, -2.398852643640189, 0.2179142769261419, 2.2316742478509055, 1.0434744464882546, -1.6499777971175504, -2.598162404478381, -1.1073954132810995, 0.5998881856452842, 0.6541019378054359, -0.22004964719365586, -0.2504588994559205, 0.6248749026393126, 0.8158792071368812, -0.22877760692267618, -0.7508440573855949, 1.035733689981339, 4.093678947905584, 5.289460611188063, 3.1722081741941945, -0.04893308020135938, -1.123666363634019, 0.23985191831703823, 1.2048316137985062, -0.2399308697966927, -2.4111544460194976, -2.077874958158235, 1.0541759655882308, 3.487328080240281, 2.120137853272204, -1.7371722485324903, -3.75127376999674, -1.7810797612071902, 1.5701311336517916, 2.2125504104460285, -0.5200956243282133, -3.371526732079724, -3.371352205299877, -1.2158769050368736, 0.21059854261559563, -0.2694507937213113, -1.0552929308665409, -0.5169542081509867, 0.6195729988663817, 0.5545416781132075, -0.7225102875746038, -1.288273026720192, -0.13489146579090694, 1.1842605342822794, 0.7333485312462297, -0.7724690372114742, -0.6923501085248331, 1.5139938780393243, 2.475014476815014, -1.454470403892131, -9.101187473037056, -14.567183878110683, -13.146842419557936, -6.3525479282679225, -0.12483540814089644, 1.5329471918851056, -0.03266153883647041, -1.0933099246752787, -0.3840034656030114, 0.28796527858288723, -0.42696251187292716, -1.2102947089980909, -0.2023248071479635, 1.890069766618811, 2.3975617812498844, 0.31808635294819276, -2.120513904310455, -2.270877141730833, -0.4660124483618383, 0.6365263904945959, -0.20362488230856451, -1.2251479566481003, -0.41126216992912534, 1.4117839475666842, 1.6622374964285334, -0.14429096123673155, -1.3465404079831447, 0.25559484587074316, 2.968728931526802, 3.015918105608214, -0.35425532410648275, -3.280579812665328, -1.8120858871789194, 2.972537018371803, 5.92028381674992, 3.866395616128242, -0.7248699330050764, -2.957805478269435, -1.2830654404245196, 1.33111116221439, 1.7086798646743797, 0.23483598026456692, -0.5002165980496762, 0.4116213021537222, 1.3163157618743064, 0.8430405609663753, -0.09347127789596697, -0.022122179154995897, 0.542468299282816, -0.09689636102333785, -1.7060890142475909, -1.633315393052214, 1.6062487169996755, 5.461594774704268, 5.775863799392999, 2.009430918533985, -1.620380212410927, -1.0708787483173308, 2.601935209721452, 4.719095756762754, 2.99890710921424, 0.3070958676670682, 0.6640333099395437, 3.916381256733614, 6.054501018709876, 4.486209326872417, 1.1266015618024396, -0.530906372966085, 0.009001239160173861, 0.23325086665783953, -1.28233725585572, -2.7466392739794356, -1.9381339973572858, 0.2992127212712781, 0.9957363521236364, -0.8589477350897085, -2.89897341182049, -2.626964069948862, -0.6969088341777607, 0.32043613437509394, -0.32264427092132564, -0.8374874466214981, -0.1067564515184118, 0.27704557342037106, -1.3867355237344476, -3.3480711052665098, -1.7388951813883484, 4.013265982464759, 8.97098951035425, 7.6189585649313205, 0.452955865979334, -6.112931076474011, -6.747203402490543, -2.651118117755626, 0.8568137515542074, 0.9179305556933541, -0.49701006092137723, -0.48074920409730376, 0.7713037145544125, 1.0537250999521628, -0.09270631462683791, -0.7973355549578119, -0.006658929651543653, 0.7429736030133406, -0.2454896467112284, -1.9357749264492066, -1.8202318197666747, 0.29010043198693036, 1.65562011170684, 0.4488246219084586, -1.4051771315354729, -0.8177746425604822, 1.8025091784805518, 2.6020575693450763, -0.5016346356614801, -4.492699366804558, -4.738722677884752, -0.9278736809186818, 2.497360315986053, 2.0461654814046084, -0.6375780164734868, -1.5833515087200052, -0.12924079808692618, 0.47803380043859417, -1.8631093803107308, -4.701189048056785, -4.132487407400928, -0.09882512073444916, 3.4141587534464373, 3.4019772393658916, 1.1710424992805386, -0.15357589250283085, 0.12491226190818266, 0.20860721286350284, -0.7305995042540022, -1.2131253497455357, -0.14976555185008986, 0.9771877634427665, 0.2258021082776632, -1.4942943481490862, -1.35184473315946, 1.0371012670890352, 2.3447381104673184, 0.05009898979107072, -3.200440167727544, -2.10114658405684, 4.378228441593038, 10.754884807212168, 11.020875699342177, 5.553527653764005, 0.2674645810236236, -0.5911637849001304, 1.3363890608644113, 2.000992987951813, 0.5174340831467833, -0.6403522287298283, -0.012750865579718534, 0.8192971864169277, 0.15435667283480833, -0.9711339943999127, -0.5364680001227093, 0.9397350883763791, 0.8306313105291628, -1.5455928499220635, -3.385692240187793, -2.07754570427178, 1.0149456077429964, 2.2640275372934178, 0.7067677523875543, -0.8692457058246468, -0.1967657621906564, 1.2194484584274923, 0.7656968013347925, -0.7161813830139535, 0.34394313670938753, 4.696244052867914, 7.954733246993357, 5.63884533068915, -0.7404784857494664, -4.965535444056728, -3.4716216188005777, 0.749965715271614, 2.5353773698022914, 0.9783206366675515, -0.4990363088764366, 0.3800391263506265, 1.8276681844632006, 1.2434271095166205, -0.7677000072753579, -1.5019836958933903, -0.2669756415899109, 0.8525075327116195, 0.4182040656504763, -0.31017092317835915, 0.20985337642528512, 1.0763602568727575, 0.603539905977595, -0.1402537640677579, 1.916663314676777, 6.90587264152983, 10.156800247265455, 7.33993879981135, 0.4432326020968532, -3.843843119776531, -1.9595795691295224, 2.5075964480209443, 3.7741592234896775, 1.028934703382704, -1.5204135040270008, -0.964127239062285, 0.7696577142415411, 0.5432329039360486, -1.1933506877521647, -1.4701432752317751, 0.3664522582488199, 1.5897534317394961, 0.3227071133916889, -1.489783688597403, -0.9242952450368043, 1.5438840012702857, 2.699849588856269, 1.243169582538779, -0.5422986361919978, -0.4372618264942058, 0.47466781409175857, -0.09411794917109048, -1.6494880000917427, -1.5057730087427228, 0.7480642716343444, 2.0020156311906265, 0.1224194385428505, -2.346451835748686, -1.3992636593024215, 2.303790167861179, 3.4646377034829934, -0.831216642438221, -6.528218293234793, -7.180920654971189, -1.9688824393448245, 3.416912360245852, 3.9430188650333946], 'positive_zeros': ['1.526433299841239666634110166307', '2.425052668006634599057543512098', '3.80607662232747198743761026819', '5.48964594953182135326530027883', '6.55208641733410707258323049604', '7.8559904260276820480673465979', '9.32044241226579780145065545245', '10.64794222417523569145493299472', '11.497879020873651665684601758633', '12.616639969396615596789595383694', '13.885569274262829200710811617153', '14.14171146076412207790501741421', '15.29229156478985210444341016112', '17.526130860781960619018343191245', '18.08038898639763807737741972330', '19.045400368848677166407012966808', '20.07944579754882302579464263185', '20.95655161645955884032585582110', '22.057069316517838310348501158324', '22.9761216730911839280807237621', '24.06313708158533464909247695119', '24.67750424620730997032057605811', '26.05237132756430142704168773295', '27.01971910655450572753097022404', '28.40547952153029459457411580318', '29.26651741113811620285209205824', '30.13472454965469982238780228921', '30.65011176771725289481877494604', '31.405812264549956120162100662452', '32.74667506194408890914547354733', '33.623466783405784686562206148545', '34.58824781009232311725444505052', '35.97328795831390729038046065111', '36.85122221204744848521809581050', '37.52786970985577788001295433187', '38.12660588067570827656311353374', '39.73964864904601025827374213777', '40.19157005645223618517841492888', '41.36667757257589070828165918335', '41.71783910222281669322815768221', '42.6535835915577677564781202948', '43.74351307237820747903645473553', '45.27842627225834381710591540887', '46.270979619747714076424260307633', '46.52873980049739887429067169029', '47.65644652358853907827768605402', '48.4874373318885902829924441336', '49.1826678690808842642317295904', '50.008212491354855327606483490043', '50.85724090682560542906481649669', '52.27506543664081348646254346449', '52.84433393351464855919571779514', '53.86774162174836080890256621397', '54.56394974253665904849153210945', '55.81213958948438157375122824119', '56.73000808680296650874110849926', '57.30181893831876840932896254327', '58.22888291543195610295270841905', '58.88290015054000913734835320768', '60.0358110939519867179005494751', '60.15750303577335412252998755650', '61.50311800050644119141903847452', '62.80010626887169039776163804996', '63.83642918240289310799273274160', '64.38964867647231643084361424739', '65.349956444036066734312558200038', '65.80731081605778167629842110924', '66.49875846885992247225215807304', '67.8345281136128967993893472806', '68.66334225898217714388110083099', '69.42519296272302966632396982759', '69.72453071466825163074690511220', '71.09715276324618726104616600567', '72.230203972712010608459228142828', '72.81667534601383930000093084271', '73.75789727230010066238419710949', '74.82330880944094691829491674673', '75.56321311312132108202019282803', '76.15896286468340322714530466267', '76.7497209713809021875651255548', '77.58278930913188824703223188567', '78.36748502646319308660961420658', '79.63479003407350858968416632541', '80.524095170531050587403315886054', '81.596228022472512161971148900996', '82.09791004369287403644367740581', '82.78439025117305060968508106266', '83.96073891432363203733344228222', '84.39769317955232440998607099395', '85.56609109349143118797035965561', '86.02411310423452242431514963437', '86.97417059000767299896646794905', '87.930330433451779209868057823452', '88.38475441877891566428953962500', '89.13343002821174773921884590599', '90.73763590872912625020495744045', '91.59801886789738701262054258278', '92.3168809326372873122509552060', '92.680029363314011916176618332969', '93.53795281961172284098635125661', '94.389492112850263810731717160687', '95.24163721861999924939993794479', '95.69245270218508799617154674900', '96.95298672696959045058075402972', '97.53140547709862282956184042430', '98.781292737731485286998180720223', '99.48670362042670783759932306215', '100.22699322224765188925645708678', '100.976752174798845283986128832904', '101.75657180705030466579561638298', '102.78676583441817463252588068161', '103.64194630363165840468688169417', '104.337186267110178882373786219446', '104.54515089276833047809925256829', '105.58887506635127226506325942164', '106.22171214891459829237666066062', '107.72010403077069138677380285126', '108.41546170832956177402280880263', '109.18172380254808732066054903305', '110.17614863415171297947527627098', '110.85072144415538626433735576960', '111.35186737043699072593528133995', '112.12951250063815457976815574580', '112.6823929465235346439068965017', '114.05653633793651508108201463126', '114.6446663952740678800842679038', '115.2801688960184138171605901087', '116.15748364021358126312900950609', '117.050074867430858130637929790481', '117.96787510438415387777901856583', '118.70306053930539437327799409538', '119.90836623340366241009828136642', '120.223813180363822146734831219711', '121.06820554689394323873561192032', '121.71098280708143692139713652291', '122.525410597248308737135341031166', '123.27178677759993297676401074082', '123.867733865347967357759192841', '124.61115087120265438454078113599', '126.25954640598745520274546789360', '126.86950049973913315977073524638', '127.61834975363565675318057763811', '127.997844404022158977200823286', '128.78171580958669147243759311065', '129.72265372958680915958612476170', '130.70771424505067762152841927772', '131.203245500823981007699036797582', '131.94514671701066689438160015463', '132.79099936963005288618085908466', '133.40796141801317115077162599992', '134.34754966650529907708965730826', '135.12774352457982845677357013185', '136.19744820502748448215002417171', '137.01283390590379764961234545166', '137.864206140146010648059185298384', '138.33403287518615283699515341093', '139.329653733286568450661055422580', '139.698831734883337649703384599980', '140.29068101202923298605292996701', '141.12462311376334176498557644726', '142.33099159395158994135490572094', '142.91531694756911737656823131774', '144.15174434914836451547902108076', '144.23057585935272114703161923613', '145.77268329628948666926911275332', '146.24674149872044872487154915656', '146.63962573202580454463379314029', '147.7668350427800176728084500466', '148.3255443897002939262194684862', '149.51724528208217562405431161742', '149.89266198605085184003997208882', '150.659719549152135793475196789990', '151.02995547307213946785506057352', '151.98663349597121792665905544803', '153.142470284749910104820906927738', '154.26697105833397590851923308503', '154.87816350157159535259672616826', '155.439126108284192532064964044400', '156.22790112360132000045989515340', '156.87677317910544170663890946553', '157.45448831749021279960995660508', '158.398510468815573210458731995839', '159.12701748406965192930022320573', '159.7931192175387824654304759782', '160.5888086810280980475958414978', '161.62811895896945743554160821513', '162.4224524450061698241518427342', '163.14965180504607453630998784595', '163.54096290546519344510237181528', '164.69429465841478723894725242964', '165.85650533806551533128609659728', '166.17713131943810110867525405390', '166.65592977242872588050095503858', '167.53081832986609597638363720751', '168.1655042968439699943379211358', '168.94051608616386445370794681016', '169.69177861781056620631627754262', '170.43554835050706279412645228477', '171.90218418307409002913344781878', '172.29853988546783438330796801145', '173.22071877675947348928980443750', '173.753455601319651828479369755825', '174.41175543487010339105745798713', '175.11193177588422795170532597698', '175.75697572741366537512137651166', '176.768875930798799665697349147874', '177.60550045479287169411204955107', '178.163148625471497197132722543498', '178.89434100088925204827142065835', '179.33697117468554259079334682527', '180.58941020218483045803541800784', '181.50248773985300635868156335329', '182.34259355588898259586554495180', '182.73833154583823873257617949540', '183.6296071270104162610812268944', '184.42779151275974467115453074929', '185.13885152992983114824354082331', '185.55794935272445766939839657387', '186.43172047221913905531947463137', '186.63547111092049740285878962727', '188.1459268850351906158340747729', '188.882471310902061177040887126341', '189.78378212291386821316337475895', '190.46911758203425664284255642323', '191.040193194663551388334747441660', '191.82138098070068197443842641020', '192.546715977587115781362878900068', '193.25007068540269845657262239', '194.25163161555476648354852376987', '194.8172973709248291431992804876', '195.29164655415961767063757646708', '196.15632240731871919813846437009', '196.88793192006572862669090840866', '197.624825263337842176537503008952', '198.39441068103296810320880452997', '199.47137185100210715226823901189'], 'prelabel': '1-143-143.57-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': -0.3067073723754718, 'root_number': '-0.348811756576782316438814408319-0.937192807523521041673822213683*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.306707372375', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.21124995851346485135508544815-1.00058154385764075635849056104*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.52643329984', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.42505266801', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.80607662233', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.57', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/57'], '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': '1-143-143.57-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': '1-143-143.57-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': -0.3067073723754718, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52643329984', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_143.57', 'Lhash_array': ['dirichlet_L_143.57'], 'factors': ['1-143-143.57-r0-0-0'], 'label': '1-143-143.57-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/57'}
Lfunction data - 1-143-143.57-r0-0-0