-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1089', 'a10': [-0.9334851442746663, -0.35861606966016646], 'a2': [0.11931882848395176, 0.9928559901462132], 'a3': [0.9897180218885506, 0.14303229407729687], 'a4': [-0.9715260343384347, 0.2369328271950402], 'a5': [-0.46743646674681383, 0.8840266678982341], 'a6': [-0.023918475057802948, 0.9997139123523836], 'a7': [-0.0717006907618376, -0.9974261932314968], 'a8': [-0.35116152500179476, -0.9363148954056076], 'a9': [0.9590835257019713, 0.2831232783207275], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1089', 'coeff_info': ['x^788 - 1', '0.999968211136237 + 0.00797350092461664*I', '\\\\zeta_{788}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.1103', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^182', 'a^18', 'a^364', 'a^258', 'a^200', 'a^582', 'a^546', 'a^36', 'a^440', 'a^49', 'a^382', 'a^324', 'a^764', 'a^276', 'a^728', 'a^459', 'a^218', 'a^432', 'a^622', 'a^600', 'a^231', 'a^43', 'a^564', 'a^516', 'a^506', 'a^54', 'a^158', 'a^15', 'a^458', 'a^269', 'a^122', 'a^67', 'a^641', 'a^52', 'a^400', 'a^96', 'a^614', 'a^342', 'a^16', 'a^463', 'a^782', 'a^299', 'a^413', 'a^294', 'a^225', 'a^711', 'a^746', 'a^376', 'a^698', 'a^477', 'a^688', 'a^775', 'a^236', 'a^307', 'a^340', 'a^450', 'a^197', 'a^626', 'a^640', 'a^279', 'a^451', 'a^618', 'a^304', 'a^582', 'a^249', 'a^108', 'a^35', 'a^61', 'a^234', 'a^50', 'a^582', 'a^146', 'a^278', 'a^534', 'a^8', 'a^631', 'a^524', 'a^197', 'a^198', 'a^72', 'a^645', 'a^520', 'a^176', 'a^717', 'a^481', 'a^33', 'a^595', 'a^395', 'a^476', 'a^118', 'a^407', 'a^287', 'a^105', 'a^690', 'a^140', 'a^188', 'a^558', 'a^85', 'a^92'], 'euler_factors': [[1, 'a^182'], [1, 'a^18'], [1, 'a^258'], [1, 'a^582'], [1, 'a^49'], [1, 'a^324'], [1, 'a^459'], [1, 'a^432'], [1, 'a^43'], [1, 'a^15'], [1, 'a^269'], [1, 'a^96'], [1, 'a^463'], [1, 'a^299'], [1, 'a^711'], [1, 'a^775'], [1, 'a^626'], [1, 'a^279'], [1, 'a^108'], [1, 'a^50'], [1, 'a^146'], [1, 'a^197'], [1, 'a^520'], [1, 'a^395'], [1, 'a^188'], [1, 'a^295']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-4729-4729.1089-r0-0-0', 'leading_term': '0.00952104464438441245186548520151+1.65041648914395718524599675773*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/4729/1089', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-1.6504439517685483, -2.9307931794685724, -3.4713169521490572, -1.6709520691629418, 2.20341935592777, 5.407537218835365, 5.136303584172538, 1.5816289219671709, -1.923600994953586, -2.3283870720299524, -0.1296050623679784, 1.5257184411980664, 0.9029846423939084, -0.34103145040635235, 0.05501367786896005, 1.2931787048086811, 0.3827363657750687, -3.3625974696491165, -6.647000600906778, -6.157590952772197, -2.821525291576688, -0.304913308364161, -0.027005678961592297, -0.03172765146106778, 1.0445532640060922, 1.6280704840113818, 0.3140076167512493, -1.0494242265741416, -0.06558947782283985, 1.87047481947868, 1.412979080102828, -0.9001095429504148, -0.777948072356289, 2.6233857259493165, 3.9144396446021137, -0.8133204787083749, -6.7865397378714345, -6.066515892088299, 1.107782416556637, 6.13884751584344, 3.8269480219278913, -1.2483718989768116, -2.4589105157772724, -0.19189627339835866, 0.903821279785065, -0.09161490673103977, -0.43625706644975765, 0.34186788698775694, 0.16521186973515306, -0.6937963626892433, 0.15428151518389271, 2.010260419965447, 1.4927289671650867, -1.1276237795419741, -1.5880457586911607, 0.8550516304539971, 1.4751336253326561, -1.721135576493238, -3.8655276943499057, -1.3269102003463538, 1.8177772887877448, 0.7822595505149037, -1.7181989114688354, -1.0094073557954744, 0.27899632888026416, -3.2210300789208497, -8.787054651307642, -8.66726258358943, -2.8755893201550213, 0.5860003634803237, -1.261157684847896, -2.6370581099722834, -0.11037684884748301, 1.929667548174843, 0.26572781484544594, -1.3425302574120657, 0.20431660420613623, 1.5731548389756558, -0.2186592924174638, -2.108852531013402, -1.0928107505537195, 0.29561914269389, -0.5263106191646856, -1.3118178806203138, -0.1805947678615386, 0.5156222187085426, -0.33269937433004726, -0.24133066739607986, -0.18589380348073287, -5.355342333614828, -13.812699508492896, -14.373548213327593, -3.081464379386506, 7.979401847830369, 7.243323442549046, -0.11408468835952587, -2.484131694934297, 0.3571331346580022, 1.1472654230197958, -0.5281483058888862, 0.004233786017913892, 1.8080473809383022, 0.8030628516673946, -1.3512929215595346, -0.7492459500747763, 0.7794346327103326, -0.08568453225710272, -1.0709343250822632, 0.46298896200185546, 1.222898977193059, -1.3665540862825711, -3.025454879907758, -0.5569657968418754, 1.656779661028746, 0.13813807782226115, -1.209104222210064, 0.22518495173985284, 0.21455907702300156, -2.7063243397302643, -2.8145185556931347, 1.2811123210958217, 2.4508361270589005, -1.4386769881381125, -2.7406232574652107, 1.0651750713329895, 1.8427191861249468, -3.202529701917244, -4.951913461276069, 0.8780806960885693, 5.314410541927817, 2.0822796661661926, -2.2716374780899757, -1.4735551539746456, 0.6797586964121471, 0.02802134561086021, -0.7987424194575293, 0.09754824632827663, 0.29129846125485503, -0.3751839946820317, 0.2748494346745425, 0.5160356594470233, -1.7871685801112325, -2.7526540688376255, 0.540978271981165, 2.7314159784009244, -0.054640187539985625, -1.8349883407369214, 1.4837125324202245, 3.3268181765968463, 0.2019387480251886, 0.5737471205039859, 8.363767589953346, 12.56863010169309, 5.6101628652755595, -3.09430551082887, -3.566607544133065, -0.14459990075595996, 0.3347153826325088, 0.05202428115527012, 1.2392275859772592, 0.330188374788439, -2.620938126233858, -2.4789665336971085, 0.10091368387688503, -0.0845268393278328, -1.2417920558419298, 1.8664740810231775, 6.05101262999433, 4.993955326328119, 1.128113857535634, -0.05807742231562401, -0.07044416400012461, -1.420505191542431, -1.3698052526501172, 0.3944880821200254, -0.38482566942461716, -2.3308940049154607, -0.1776074642964524, 2.348180714211388, -1.5591478397736824, -5.257531095508874, 1.8372172148607415, 12.449432661972208, 11.212428985024355, 0.8600266310293336, -3.6209196021070196, -0.3779044054372194, 1.1437081102381537, -0.3512180345563522, 0.17681333102139865, 1.2652871008437327, -0.24002647431432933, -0.9538325613303341, 1.2432207448195705, 2.098471886142944, 0.3007365690669738, -0.25592012812773896, 0.3948638517269746, -0.5434997399893025, -0.9819610787480973, 0.3314540248986485, -1.9224420619649123, -8.153869686749678, -8.983949346902545, -2.2470585019566136, 1.3364029646555629, -1.966096452317311, -2.7454685060735633, 1.633429323394124, 2.5551059275671157, -0.861391160486169, -0.5590770102940616, 2.565348117414522, 1.3284948880571994, -1.1868392296949746, 1.6261363016082149, 4.622694153557138, 1.1162986041795702, -3.0655600871472446, -1.6001550254651942, 0.40681079126766795, -1.3284195638661105, -2.0803414846274366, -0.07499625482399801, -0.0752315229001772, -1.8862153039633733, -1.1236635630090128, 0.5241829429701426, -0.1856850003388735, -0.24055572076119153, 1.8562055099622836, 1.7918506604164697, -0.24174715445330772, 0.2680227856750892, 0.4387575810214729, -3.6508894752176486, -3.9483429649133654, 5.491523598864607, 12.053232255996706, 4.608428188510141, -5.07231075656334, -3.166866702494258, 2.616284744209678, 0.8593768376492885, -2.952492644546648, -1.1452946851132642, 1.5899818852503604, 0.7613935023033287, -0.09863884261280766, 0.16901066548469618, -0.7895429653847317, -1.0428866732906994, 0.5098564257819006, -0.6658006889828025, -4.220317280328221, -3.204001221648025, 1.3890569594465427, 1.5647296942321096, -1.5466694883889085, -1.0954917812944216, 0.8907734828881424, 0.05424107600563362, 0.2992639019261593, 3.1540138822131785, 2.46857877233588, -0.4455531256039305, 2.7969351686302613, 8.081976490225154, 4.109696579991787, -4.444161228648816, -4.907549826238684, -0.22088551182956423, 0.10509380640840313, -0.6216487852272733, 2.337098657170575, 2.2266831738445485, -3.5825805580658443, -5.639543210808989, -1.0099370026792176, 1.7375878347571552, 0.13443508543651755, -0.32026011597786347, 0.5667676095809414, 0.04317925430250884, 0.17507501196108263, 1.4202176462042826, 0.5005065850818164, -0.841319470871853, 0.5174629406920536, 0.49544083203819284, -2.408433995637902, -1.2151800091306164, 2.8318843590914256, -1.5488698622146808, -11.245698584422367, -9.826959676711905, 1.7299676182283514, 6.194165210989754, 1.5728989180548034, 0.05755558638162457, 1.9430929261191243, -0.18386491748868375, -2.7909731896636223, -0.6332574420510584, 1.141010156376208, -0.3661253623522174, -0.04332561588866266, 1.8071609639418917, 0.4426399761016251, -0.993113674797133, 1.4083793318062183, 2.5703213126411866, -0.09063129111096885, -0.994590749622242, 0.2281440234118534, -1.2632377668302555, -2.3531672631315077, 1.480545541204714, 4.359696594566613, 1.8157148563081797, -0.2357102753136549, 0.5359621299146261, -0.27680100047539163, -0.28559636134439814, 3.741594425760461, 3.7169259430292017, -2.861701195148449, -1.5010825217727974, 12.017447793223866, 18.880084988309804, 9.959705371379771, 0.5952562342339394, 0.5854160611279763, 1.5883563734817427, -0.5820900484347479, -0.8215132310178364, 0.3225467984628085, -0.32420913874494195, 0.14993317141582058, 2.252134913066148, 1.5667353218513886, -0.5098147075270512, -0.02579241484706143, 0.15053812972176395, -1.407746265653689, -0.0599099488387876, 2.5027545592770686, 0.3831420680824128, -1.6657867481388275, 2.173496831683373, 4.014148994192583, -0.6747751077648277, -0.7423228557031394, 6.903930636392688, 8.519067528880466, 1.285401781082044, -1.872623795320028, 0.496642625594923, -1.1746814359440103, -4.676493358639874, -2.7991069119998286, 0.08054865142955092, -0.3032720161897952, 0.6551222728626085, 2.230476441447223, -1.1468951435415842, -4.640528318140475, -1.6418986870729049, 1.6529459412980985, -0.33955801596531743, -1.5941749513414116, 0.7126826375470807, 1.2347627801931822, -0.14698724827493595, 0.11737538468274801, 0.1795677431820328, -0.3289019423398594, 1.291415065391417, 0.4268733522874629, -6.392899920273988, -8.966096761179257, -2.1133741725972124, 1.1603921759356957, -4.049577681668762, -3.788334989408377, 3.96291949243847, 3.780678695381173, -4.453469734927547, -5.570119119768938, 0.08048056379999649, 1.1865794440973678, -0.4507133432643915, 1.336292383742507, 2.4085773916793283, 0.29779038412866704, -0.20323168119727275, 0.7903414275722673, 0.1428452539596305, 0.0387249881315746, 0.5858016010376381, -1.362319011715628, -1.5825483528327189, 3.744454841481003, 6.261420193680946, 1.2203102337945164, -1.8946558778403466, 0.6138416077557964, 0.7363408075002407, -1.3409916996457703, 0.2186030778857224, 0.09531942901489762, -5.457816365746126, -6.402206102350917, -0.21442646319117248, 1.4304916158063792, -2.1056417579758437, -0.9342590753216029, 1.2092973694033338, -3.599971990605931, -7.165917441992892, -2.5100888012336338, 0.9388133735233337, -1.7283361099105243, -2.4721370821439783, 0.08043102347533695, 0.15800811549485022, -0.4588765067163062, 0.8628551020641185, 0.10266028100344626, -2.106048210920738, -0.7799509159282648, 1.2848244753409395, 0.3286866125807709, 0.002141159591814625, 0.5749934730910415, -1.469334491607324, -1.7394655548506623, 2.125579508314634, 1.7374704513643484, -0.7419819851189468, 9.525459798647402, 26.278424153668016, 25.384066899844175, 8.224172585583023, -1.4212282387405255, 0.6743387313693878, 1.3943808949705896, -0.4167738010970553, 0.18372567568420584, 0.1379581376864122, -0.9621343016551288, 0.6008078408597877, 1.0929104726084735, -2.2601498330747414, -2.9509554115905763, 0.03478264224534024, -0.11948650127129354, -1.6839744835210344, 0.6068579288716301, 2.144454245924387, 0.14881339328270024, 0.6694767910851203, 3.071361265818071, 1.4601828500380356, -0.19395851399047961, 1.9634758843089162, 1.4325497206589928, -1.932618911198726, -0.30529164499545863, 2.0502984755835625, -2.112956374373963, -3.7226928627945655, 2.7412860075226293, 4.25215783174417, -2.711196960022251, -3.8244602712223834, 1.8833646406421858, 1.7455346702156702, -1.882428332426001, 0.44899341088914113, 3.381575655921506, 0.8046566366039458, -1.1045025267022108, 0.2953727287375387, 0.35201529415220983, -0.20796919211426781, 0.5475372045311468, -0.07779820554790884, -0.786030853822268, 0.918376584413587, 0.6553342133808868, -1.6577857970354637, 0.3806640432522075, 1.9422250632814793, -5.2653997473917045, -11.143921968126065, -5.159975721567313, 1.4594022111588163, -0.024528445102786255, 0.1033775524897462, 3.4207391203809308, -0.3673972971112309, -6.272216145339314, -2.8508612686434605, 2.5958587860962123, 0.7262679117441451, -1.3415053068173495, 0.8622461052063098, 1.2275957492458012, -0.09996366462333431, 0.18101779626651937, -1.6974350583142965, -4.583872258577826, -1.5455005789611198, 2.900838436380732, 0.724991871348679, -2.4048789079549806, -0.6508101314469656, 0.5805594586663831, -0.3002431747694442, 0.8011260599779972, 1.178352714156737, -0.999587345755297, -0.7304509540123846, 0.42191767861658114, -1.470439319228938, 0.2758136557874132, 5.279965672470167, -1.3985536132605536, -16.475944924034348, -16.696713664156086, -2.393175599793777, 3.867077742000108, 0.22074799767620285, 0.5356017074852815, 2.634681872640123, -0.37071006819206487, -2.395404139485645, -0.4537750878327557, -0.08851722555771029, -0.684871370583529, 0.2796861395354668, -0.44217970026317954, -1.5712323897154261, 0.8547599897766449, 2.163591776112703, -0.4674443591881082, -0.9446081328537574, 0.5810060194951504, -0.7198850324908762, -0.12501464610810634, 4.039592856459728, 2.141239999837012, -4.016006012441762, -1.9420534652476467, 3.240030308889372, -0.5279174728283363, -4.972028862562295, -0.6978534774806172, 2.7112544763767383, 0.26079005162671354, -0.08501318521413734, 0.4269324280957805, -3.0705903940864125, -3.0914004929551675, 2.139146617204852, 1.4666889064103947, -4.059684394217729, -3.1070364631780483, 1.1501790030289807, 0.4359227950009179, -0.9145603283082049, 0.5574001117635273, 0.5312282695955478, -0.21623902515295362, 0.5525694987561408, -0.6444419161452456, -2.3035364792695296, 0.02823253509835328, 1.4026326867820573, -1.1572683956774137, -1.060407787425492, 0.6953821745076936, -0.8536048289041107, 2.984518696309304, 14.638652246956108, 15.543788349734273, 2.107403153160467, -3.1733696167818133, 4.390580830752195, 5.937495258613116, -0.22794923621240176, -1.1203222629245246, 1.1161185529111428, -0.21838650704653778, -0.7201572134379933, 0.6134862497766965, -0.4960836821619208, -1.0936839495545054, 0.7613622835325895, 0.6496612745464214, -0.04024023421009046, 1.1764181973945835, -1.236444198677843, -5.961558257382993, -3.5091683202902395, 2.1685003956567126, 0.9829781379033404, -2.004071721514249, -0.4728550741821793, 0.13159183366522248, -0.6818997776332317, 1.2436630265994413, 0.6577750697413991, -2.3632033850315497, 3.1714320764476818, 12.140748132865003, 8.869758692110034, 0.4518693889260379, 1.3959089536119214, 3.5436796041213086, -1.3814747090174848, -3.0150484246474427, 1.354575470957974, 1.7630914899633305, -0.44355545590036416, 0.48504645700565147, -0.47315988899213424, -4.082562492883638, -3.19068756529058, -0.0343884530903783, -0.39361360644611115, -0.9841336201513509, -0.01268293575808623, -0.25323624011461443, 0.03541202248487277, 0.35277214947707924, -2.8815449949225997, -3.2438004079512526, 3.0542687348270547, 3.0035499938333374], 'positive_zeros': ['1.08302523822515738912223219137', '2.30832609488876164101909521256', '3.14149299112837087950151340931', '3.94886009412166373749613596018', '4.36107688624320785725764795026', '5.04255084061991802886929487423', '6.67829165065260449497921135561', '6.84598326496332393576078651593', '7.20372720290720603418148521189', '8.17744276882518800159445483733', '8.75991478350810896295144849697', '9.56066543274114199335943837411', '10.08827738719010040875472915204', '10.89956024576524655013300111703', '11.83084246761737833263965716791', '12.72368450826864210160512659620', '13.46399151498713576765189037515', '14.03740008260723959829997617056', '14.55185552305195386686437612927', '15.053509924056032524298074964385', '15.59839472715678707468525119756', '16.42788636450757646180613063803', '17.08720589163564396375356680193', '17.6705588596442202603421539591', '18.54197732635535077569625888490', '19.14569600689238674223803950447', '19.8459322355954821436468473712', '20.06760279972769461231290562434', '21.4459691545594507418810808320', '21.72931064480343706092914836539', '22.51037693311604270502533837515', '23.15724003775006874514474092802', '23.722824416061257040349196793864', '24.349473713733542874480313383588', '25.19604892931410750603713062656', '25.502068371303022900615604243338', '26.28982499479792438006625193408', '26.76537769191935678518649470360', '27.276923367288858122022811529396', '27.46147429447711923337405314998', '28.819694606183767920541221260690', '29.68178208359861921425387173159', '30.274446143070810066868390293711', '30.829341605782842479749709998153', '31.24932123948843611699666761218', '31.974215767398126342974056212445', '32.62155481041842037749614254222', '33.109181207153035825825388207400', '33.68026114432796017862806559818', '34.24093172653553525279707632038', '35.05144121163479653036102003512', '35.64295118275406765210966085562', '36.2092840787498345313178019608', '36.59307982481793976655587246618', '37.40765550596348177615114043232', '38.022513421186015085563512065576', '38.67091049405692188075511899744', '39.1973034422967204883611592022', '39.96194343153438136326337865064', '40.744666345313136260221264349718', '41.42597741984779525910788212488', '41.88094122677908041731602114495', '42.47059050521150744489671163388', '42.929503187591815002372798954028', '43.358781078985887455568749647537', '43.848350974124074723394745569821', '44.64648272553546290681115878551', '45.30795960055115223669737720711', '45.827428569213079685682525951772', '46.58304562538200985391201520421', '46.83264435492540848280951510975', '47.98822912693324689311462418669', '48.770554726310424158189196900524', '49.20818273115156183985445957074', '49.34879634036749168518475217712', '50.03670715554468017941739436975', '50.92041891985803392709887483986', '51.23445531864954409967757235522', '51.74284526872547921726019294770', '53.01528897139262145547701195247', '53.19545174683886543261848656157', '53.403930499147391323571033953946', '54.289610023810211165131558616197', '54.63233520043698347855703416466', '55.32674128207864399044367465520', '55.85499975891347433893714048999', '56.51168192537374026316097036984', '57.52965848332124703709340888399', '58.1580460946413459162119521619', '58.66739686210615873411391768266', '59.02824021459072985670335731306', '59.65096829190726741087257034530', '60.15990594183781561888391529059', '60.99704823589494851401353638754', '61.351083758619894826437564138960', '61.75107412115003685830126286056', '62.403420694903579389032695359012', '62.65274440876808475292448639351', '63.86408143865582889813676395601', '64.22521342794823119578466739070', '64.88975398257241538172408082865', '65.54061733414857498505029717264', '65.99072214284475051412730708442', '66.68240197019155728678992395887', '67.06970657924857639981833642218', '67.87478760990889096507634235989', '68.617424660369846879669484616559', '68.87895387373555180258583881341', '69.70144523844575539119902946339', '69.98555308143066065377834674084', '70.79632036720990175686490916250', '71.20318622802092731009946719329', '71.60786867449792589032272418524', '72.44720246559667192169207251116', '72.75718711933590929858980609172', '73.17624786789759567801309312804', '73.90741923563391701081047661452', '74.80861207000851633940575716813', '75.45582703849949499945218022406', '75.99206402005611755613771940223', '76.66010745000662031769133062156', '77.37909912231619637009702913643', '77.600450113067385906902974658925', '77.91644379674026911209781046146', '78.63956790013974438253860693291', '78.99153806712869146873212305170', '79.895229709916725982775444431202', '80.4600131314828656550000436023', '81.07482497521764977714243155170', '81.57542266609689667892193424088', '81.82689228476063804336686869732', '82.728246781448199044155392569432', '82.94622137962539926649780239688', '83.88756743820938224161463419236', '84.71049403000767307819757933773', '85.0188344384849861759031509960', '85.404988953114816399756118570237', '86.07219614418571431426693503314', '86.94020234912687899748865293913', '87.524161719884440944891370668663', '87.90953515345672980335888867887', '88.455752151803919555584793323193', '88.69609044087101970232769937016', '89.45309385414269476716488248844', '89.91259401940045310633676417737', '90.37314655541158188892203739651', '91.01840757214523524637317693082', '91.508009712382248812707140867408', '92.451351820757458200198509140863', '93.27422688650059791702640357794', '93.42565857077678811258859693075', '94.047541860593772986578824177019', '94.7503029592797824689457422090', '95.2438834226561024873694284995', '95.631687042580617702316284824932', '96.30392493456068907793598102830', '96.73154454997242166392119047142', '97.48986800719993997986831218177', '98.032369861432240301073371341979', '98.254836739131496371907874535417', '98.96865527106763243965474539598', '99.89751988214333261312682705871', '100.13037057581870238703508843705', '100.56988299328560319018627415742', '100.97031494045171215768685335723', '101.742186364245688738619660975662', '102.23332562558416139367781977767', '103.49289182671486078156627104903', '103.66522195175425639425961890629', '104.29389865813535875458476289218', '104.869334747117192460157169605679', '105.20632766234950152209191595305', '105.59928181255116845353087040101', '106.455603469767558367975861405783', '106.88176802839966173449909996262', '107.222207169541223788132718637747', '107.81838992423950782656513471952', '108.469171141586543596751773293000', '108.92461858326519681061776347015', '109.64506614565802403232316646499', '110.03966113631699339223159271803', '110.998345909328239355957887494127', '111.486356916111920082821836651812', '111.77427535258933928282514170406', '112.79024559401467349957669760139', '113.00636983199542271719336569243', '113.33676669625672219570047304801', '113.9912601256975498440163673185', '114.79584754688671711110142970', '115.27795178658981314946287052714', '115.849483846930681774015259236726', '116.51318649203179360165866527287', '116.82744100713179592662726861469', '117.254287929681314948701105105929', '117.60259773166113397339461970813', '118.15284911696624910561794374261', '119.15981311651102032021984181808', '119.4704359667167646589683377785', '120.15386551210998321047035243186', '120.7702998865185526133969778479', '121.55705904321341485382592301006', '122.05175363012456949989348736710', '122.33162267681095565690376090661', '123.17534799961050105346975820758', '123.49501315192580645181873632605', '124.11293832183266803619058401775', '124.35988467929672048440029822491', '124.825352783176864076053885309668', '125.43029526183730490380020460915', '126.317436065404594632588479539020', '126.80828618647731513878820136037', '127.2789572648730067771918361443', '127.78470230148748125851113681891', '128.133047804596539693856081926080', '129.07432287785780846070240922126', '129.50121684239180334767599996648', '130.078634542746148112723058110533', '130.438362272957966488996032367514', '131.39884326646515447981226973166', '131.715594292597969868776983606040', '132.48714430712189223936307214863', '132.85187102662242300473683623104', '133.25182332013004472580470876631', '133.7630226362268334472454655949', '134.46081494044012958118100369578', '135.0836321067289082200259729074', '135.31171322522516770879030027940', '135.754295730322524779170271175335', '136.398849490045605332884851918135', '137.010515822498968761501271120', '137.25042350739400641409524712358', '138.647442376781821281831999500640', '139.000322225162383148120490710235', '139.58629486729588504174910212266', '139.95043646692979713224186294955', '140.34398584782457576536061697910', '140.85488865265344708773705530666', '141.37182067890408288901386524130', '142.18274338699378559839966367716', '142.482010424028112391760490245295', '143.067156566474478173401864508545', '143.77982902414058723255200811124', '143.962333176792009809695360458664', '144.86675351796104222454024110704', '145.05422687890470003575947150195', '145.744655126649234189197409519980', '146.27390814825126396677160412065', '146.75402471052988883333470828982', '147.38260192550973684462068143850', '148.00952836689262677154560937706', '148.6409610732859492662047605962', '149.18659981748767668084407444170', '149.6563085261746397940800134851', '150.38594246924601183248245767106', '150.87614224676511625012426673628', '151.36451175609644350956989922888', '151.6690274902633907012359392279', '152.170558438412645591130830599477', '152.66768243591961892805341154193', '153.20351042477315872029887752253', '153.71902332932110690227815269232', '154.18713397138154715473208451312', '155.19823572000892065836478665852', '155.622170357011004703537623737174', '155.927501554492948532557708132130', '156.54680010398108732696521606767', '157.31507817213002058023153310074', '157.8728077918511653741581963162', '158.33297476808572494481703842828', '159.01295925876177779658289490313', '159.23447461780560278426831967386', '159.47791243854517639897889286043', '160.3965910419996582942695499612', '160.98777690790164106663330901848', '161.64548394536145646727422963040', '162.05603911820264000064482550749', '162.34738220210752441489485548497', '162.984093738192512643887717281158', '163.55779035810765557640477527448', '163.85174890956467521380200279914', '164.358292521354884882049764042261', '164.96810558671798200279610896556', '165.99856327579802170805517140990', '166.58614185914356514330092974473', '166.814574205289972599123577596097', '167.4718438427208968648787106863', '168.2223791639238970204169396837', '168.40532697836179384681165742104', '168.97162817094320090350732001750', '169.29387953848287674838224051392', '169.91751934508063716924880354642', '170.572962304468508958879927860627', '171.09353286751359526278606238205', '171.44451688315133163228608648939', '171.88599426532703606410239454839', '172.59843189612148395048272571075', '173.21618072449022572727644565345', '173.72605394382231197633030894572', '174.41104392222421124754540196402', '175.0345445072467133854067715987', '175.32992020486097359180728920824', '175.68391673893772871266924893904', '176.431735016323781119745267392095', '176.955448681977418729973484552160', '177.70112376292252164661627017751', '178.18115986694496959869822481606', '178.644307783023298895608164545838', '179.204923930061955192157944323730', '179.48435342222393557520450468169', '179.91067652820463569357782176923', '180.62229966667796591563138150137', '181.12117210236423642115256224723', '181.69896196529647181391137251237', '182.044236692118906450385503028208', '182.3699428457754156438293746046', '183.49158644236296977913817970502', '183.90195245879346504360018870770', '184.67349320838598624750757133568', '185.12489934106481218745982468188', '185.592113069167202096535319602703', '186.0819705342514134060465192066', '186.479007280741343507271527392849', '187.0616869513582797195570282140', '187.66738346174890881464692246859', '187.829594179629800572445430193', '188.35237462682290864295035030028', '189.230000811681222690338306244556', '189.76207385832813013449796825688', '190.38865593570612391196112347803', '190.65992209798859239272321422176', '191.08341415788780287625960797125', '191.6185959949378750801244320188', '192.07737953324905665834816216044', '193.16315063255508465422785938349', '193.31944511464806696525626924027', '193.98853228178356339880657537365', '194.59038782011860794031259668148', '195.211133073109940263749871229188', '195.52119127273501145116508395067', '195.88894203606003962899620576501', '196.88196463832068687743890229635', '197.09681609797979435841245808737', '197.81984906508995713996140105303', '197.985355996377271199860974399086', '198.42731358193211295869962615915', '198.807681727198507334560930360026', '199.546788282414617791087159878120'], 'prelabel': '1-4729-4729.1089-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.4981637307686415, 'root_number': '-0.999933442402378623123589535968+0.0115373638812751599764254565966*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(788)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.910421122054506994315414484194+0.811522876151046584537212193273*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.08302523823', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.30832609489', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.14149299113', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1089', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1089'], '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': '1-4729-4729.1089-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': '1-4729-4729.1089-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.4981637307686415, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08302523823', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1089', 'Lhash_array': ['dirichlet_L_4729.1089'], 'factors': ['1-4729-4729.1089-r0-0-0'], 'label': '1-4729-4729.1089-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1089'}
Lfunction data - 1-4729-4729.1089-r0-0-0