Formats: - HTML - YAML - JSON - 2026-09-06T11:23:48.477197
  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_231.68', 'a10': [-0.5, 0.8660254037844386], 'a2': [-0.10452846326765347, 0.9945218953682733], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9781476007338057, -0.20791169081775934], 'a5': [0.9135454576426009, 0.4067366430758002], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 24.82439762755838, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [11, [1]]], 'bad_primes': [3, 7, 11], 'central_character': '231.68', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 231, 'conductor_radical': 231, 'conjugate': 'dirichlet_L_231.17', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 0, 'a^16', 'a^2', 0, 0, 'a^24', 0, 'a^10', 0, 0, 'a^18', 0, 0, 'a^2', 'a^7', 0, 'a^14', 'a^18', 0, 0, 'a^5', 0, 'a^4', 'a^26', 0, 0, 'a^6', 0, 'a^13', 'a^10', 0, 'a^15', 0, 0, 'a^26', 'a^22', 0, 'a^26', 'a^9', 0, 'a^15', 0, 0, 'a^13', 'a^14', 0, 0, 'a^12', 0, 'a^4', 'a^13', 0, 0, 0, 0, 'a^14', 'a^16', 0, 'a^2', 'a^21', 0, 'a^18', 'a^20', 0, 'a^10', 'a^23', 0, 0, 'a^27', 0, 'a^16', 'a^4', 0, 'a^0', 0, 0, 'a^23', 'a^4', 0, 'a^17', 'a^27', 0, 'a^9', 'a^23', 0, 0, 'a^20', 0, 0, 'a^21', 0, 'a^22', 'a^16', 0, 'a^3', 0, 0, 'a^20'], 'euler_factors': [[1, 'a^8'], [0], [1, 'a^2'], [0], [0], [1, 'a^18'], [1, 'a^7'], [1, 'a^14'], [1, 'a^5'], [1, 'a^6'], [1, 'a^13'], [1, 'a^26'], [1, 'a^9'], [1, 'a^15'], [1, 'a^14'], [1, 'a^13'], [1, 'a^16'], [1, 'a^2'], [1, 'a^10'], [1, 'a^27'], [1, 'a^16'], [1, 'a^23'], [1, 'a^27'], [1, 'a^20'], [1, 'a^3'], [1, 'a^13']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-231-231.68-r1-0-0', 'leading_term': '-0.0869166776044291622927446627602+1.04844304192049298877302926597*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/231/68', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 14}, 'plot_values': [-1.052039600489111, -1.9300735700171319, -2.4962346612810373, -2.4867898366252184, -1.7104249967865939, -0.20639664907740238, 1.6539318186581307, 3.227043088170031, 3.8393237761392434, 3.119552682209382, 1.2475994572032711, -1.048639109473975, -2.7998739040163, -3.278972642568414, -2.3989176388394764, -0.7723127455072387, 0.6402904830511565, 1.106566379866575, 0.5654758981430027, -0.366199760081599, -0.8514382639017712, -0.45372051866634233, 0.5246271491786999, 1.2587930514462413, 1.0446044598441313, -0.10485940525091537, -1.3933033870120521, -1.814259996920116, -0.9621926633663107, 0.5638908659351727, 1.552791859320133, 1.144365796651278, -0.3688560209325603, -1.5974157209531303, -1.0414223020011786, 1.6817560161933938, 5.341452825488679, 7.813335374892558, 7.560766812778679, 4.772011446794057, 1.2482377471774364, -0.90978851029953, -0.8062959926052978, 0.7327015290698355, 2.0089567699254878, 1.9197032849297742, 0.7951949042322433, -0.07215287570774831, 0.27287506433889885, 1.5271483165707163, 2.4287083211752436, 1.9801730979452459, 0.42640675141931994, -0.96260832704164, -1.1152858431398114, -0.20710885528726394, 0.5213004386775982, 0.05236929153842668, -1.2683493588323536, -1.9435067702384332, -0.8163228741854122, 1.5485905033127663, 3.037500065311387, 1.7622538340237939, -2.097232423151354, -6.1470394922531115, -7.630779059834004, -5.7166928752753465, -2.166912306539471, 0.2399421509787512, 0.10276445350352516, -1.5693565598225327, -2.5633829930253436, -1.6667550809688283, 0.26599345323157586, 1.3343478082253222, 0.5731154975762247, -1.1314092049380389, -2.0566198799517657, -1.4516741651251857, -0.22081007389991378, 0.1935610659778964, -0.5388979306531426, -1.2890943191332893, -0.8254788432112022, 0.6366788797909716, 1.4992648964209878, 0.5336104767423071, -1.5429834387618702, -2.5203224084263582, -0.931190634713255, 2.202825730632452, 4.093078799829629, 2.8651803985187936, -0.4537351670403397, -2.7646995680581092, -1.8562336472911445, 1.4269080630313689, 4.00507904843084, 3.562138756572251, 0.7019516291563529, -1.8506725734616218, -2.053401026055243, -0.4066298842016507, 0.935251614655989, 0.6275861490356273, -0.5763185900154738, -0.9904425864293368, -0.0985376040412221, 0.8912963728628777, 0.6285288137463032, -0.610332585207672, -1.1422816556676982, 0.09889027924243782, 2.1317751808703695, 2.8960844798698195, 1.6235194371047572, -0.16392681304544582, -0.35863091683588744, 1.150571341864523, 2.069693554002041, 0.20668089308907495, -3.753005966620951, -6.430465928110162, -5.017500313980803, -0.2703473389977482, 4.027778753000258, 4.686745429218724, 2.0536790453036855, -0.7225533573103957, -1.1199406931905476, 0.417567774375784, 1.5693942864159809, 1.0730197724015913, 0.018064013993233936, 0.18308446337002024, 1.6489132165948213, 2.6532989222117216, 1.804468917911899, -0.1382673051835628, -1.1488199312435197, -0.39764018971238774, 0.7768730452605792, 0.6278899858346945, -0.7071458261593836, -1.34213263973738, -0.1788822663443637, 1.3264397684890774, 0.6426659595729122, -2.5785707871061003, -5.409252138172308, -4.435856683280389, 0.4142166462236948, 5.381605269903862, 6.526390548613721, 3.634105769218541, 0.1250520153028388, -0.8021179356976517, 0.6128244220761604, 1.5809376747292334, 0.378079239154636, -1.7049363400770212, -2.200522164863952, -0.5900657336431605, 1.1549486467734844, 1.1116030943516506, -0.28614526377824256, -1.0180549279198867, -0.17682835241777137, 0.9567721111365438, 0.8017671525159731, -0.2582679418233884, -0.34263527540508554, 1.2410158873330575, 2.6984375228798134, 1.8448331475427093, -0.850343597131759, -2.300027079234942, -0.3243865502099871, 3.4546787282710545, 5.100819434045656, 2.8093732101741695, -0.882538622877284, -1.887811291768756, 0.7877688828438898, 3.974271842545087, 4.050667376461645, 1.008666415619992, -1.8387883231656674, -1.8829321335761149, -0.007997555513994515, 0.9919019468793071, 0.01587726911130509, -1.3005061959398452, -1.093759301674153, 0.2392071078770221, 0.832575423123818, 0.13693393882905613, -0.24223936919949052, 1.1380398054883885, 3.276096888518939, 3.759273149156107, 1.9300219887063392, -0.06694114571454794, 0.01118753479501527, 1.471929991285833, 1.4840840265703559, -1.0284579888401226, -3.436781476039016, -2.318105727376908, 2.0679064044773154, 5.422635806877546, 4.042146698983171, -0.9142356482619485, -4.654740218282921, -4.047777019486564, -0.7187147645212154, 1.4423156321329704, 0.9208179564143414, -0.31545129318699433, -0.05997101795725751, 1.1789082073246986, 1.2785932765125283, -0.2316350285859614, -1.3940446467882768, -0.5558973909763747, 1.262115391017756, 1.700378720054311, 0.27535380089392353, -0.9910815033313051, -0.4315042039424555, 0.9116506072099588, 0.8255473982282762, -0.7000320547213639, -1.1374031818673185, 0.9958803910353635, 3.3862798421153206, 2.2007478247285057, -2.9474617054528736, -7.699978983359217, -7.494601380032617, -2.7268634085684673, 1.7510744214662883, 2.1893661039254324, -0.21858914044925384, -1.6151588121578258, -0.5323860918515074, 0.760974749765009, -0.13172953083314487, -2.3589804824361384, -3.1169028893142072, -1.535339906371543, 0.2601403418940321, 0.185143699346414, -1.0462929948755624, -1.2111200463151583, 0.1198293923646763, 1.055887315129998, 0.31940628984343356, -0.746022744681699, -0.1968685924765047, 1.2832834069301193, 0.8621686980078241, -2.4228391432144925, -5.622687474808522, -5.166525858463839, -1.5855652542837324, 0.7085099669385159, -1.2064550180383031, -4.976894401573036, -5.78668065935561, -2.3255841306706926, 1.6724931502943916, 2.1885246576770574, -0.2440364384461091, -1.696274804676877, -0.09664186220003017, 2.42088693016747, 2.7749740918370014, 0.9925464883528239, -0.3259433410955487, 0.13143940915758306, 0.8481903112091965, 0.16825446619343787, -1.0497321677867988, -0.8080387795784796, 0.7465248775883256, 1.1948879598131301, -0.6742084728461847, -2.822220608728667, -2.6117052889658967, -0.5994755897811485, 0.08856611595248075, -1.7339944951217943, -3.26386432709033, -1.4382562141070896, 2.371709978427115, 3.4240133796346144, -0.38216376608292857, -5.335905097609219, -6.057605897718162, -1.8908566084702945, 2.544457273555166, 3.125766779863682, 0.76724819363886, -0.7196525867492842, 0.12323591113505672, 1.190155947261838, 0.5829680522223032, -0.5430438150766458, -0.026753317688757224, 1.7682840916306295, 2.349846055394056, 0.8121771357616592, -0.7281019422265811, -0.18809759081510105, 1.4347550103839875, 1.5872280531747844, 0.02762850290315195, -0.8036453259459955, 0.374124582121603, 1.4042937884748292, -0.18514902518381646, -2.8664099558012315, -2.2604105425163805, 2.9659388626155305, 8.350096915126123, 8.391503524660639, 3.1342437677796875, -1.9249879924270838, -2.4965684779133372, -0.10203112029078407, 0.9408213517739098, -0.5252819601779387, -1.6602453599277733, -0.3371470053177784, 1.7341657704407676, 1.7180540595008917, -0.1500808636596078, -1.0561579285380784, 0.18242905353022945, 1.5199817658318486, 0.8962773752109612, -0.7373502428890135, -1.0925239912176583, -0.17348514945453908, -0.14150504510883968, -1.5662848583376034, -2.033977083107276, 0.25091346967459394, 3.0673458522166457, 2.5904936213202094, -1.1366402552773962, -3.5442280228521876, -1.3426400202134339, 2.849456859384361, 3.6575389289070714, -0.05618450605581191, -3.7547522081227513, -3.2571304833860397, -0.008566030757547412, 1.365642797571227, -0.5473279318403371, -2.471816811030082, -1.4261329504285731, 1.2362803846673622, 2.1634932755280096, 0.7794631494116069, -0.4660402090057729, -0.16221418523067138, 0.15383047488335003, -1.068940337213913, -2.5534045672484895, -2.0980105351145184, -0.27282191009981654, 0.09911522475016879, -1.7568422177906011, -3.066211540509247, -1.5008679528185764, 1.1056978060061968, 1.2003566005095108, -1.0879402829968425, -1.7018798051831259, 1.458615363029888, 4.813251736253029, 3.407948793031861, -2.2132215278129483, -6.144138853179116, -4.423641287289041, 0.21478552656346467, 2.3070063047775045, 0.5777239233675135, -1.4378645193611066, -0.9997751133297218, 0.44644041778736193, 0.36480212738092255, -0.7489751186733142, -0.5127696334816771, 1.1834572703700923, 1.7895519119764003, 0.10321650345983487, -1.6972313297878627, -1.3027927229042062, 0.19694837829820994, 0.06307773499348757, -1.7204886926025917, -2.3513637302155956, -0.7057775285263392, 0.678517144885536, -0.30694365191828343, -1.2502046428649412, 1.962430854700512, 8.655360852844566, 12.751810222406746, 9.944296319603898, 3.2986432207608214, -0.4869514943795983, 0.7576978647817687, 2.944720487848411, 2.093328219004227, -0.550910881600313, -1.3290418565527937, 0.11585334920285553, 0.7651774058932983, -0.7459251272879663, -2.039788661736994, -0.8600570143251537, 1.3543674107896293, 1.6922677138408067, 0.1497653035931302, -0.6559350264820987, 0.2543255618818441, 0.8969204937925119, -0.02550441914193139, -0.6183253240906594, 1.1405847173644994, 3.4965326531080567, 2.9156274387188614, -0.3220624643149707, -1.6067366259834932, 1.6885160559551733, 5.8806796340885406, 5.4431281064119545, 0.5106877073722813, -3.1643898122222818, -1.9067749057899663, 1.2975192346425668, 1.5224989027023155, -1.1719300549558955, -2.4100751192647505, -0.17719304697559285, 2.4954772408919985, 2.2941293343852256, 0.2603646791422609, -0.3665937324211267, 0.8455773895386636, 1.4296789844961313, 0.3777010555496206, -0.3617994193703887, 0.5148479642531727, 1.1750163330842835, -0.3774191999435105, -2.638457114022078, -2.5433202642474493, -0.3572809887142779, 0.36164845967630577, -1.777072600557933, -3.490737494334253, -1.6767754134388826, 1.43637015644986, 1.1006684942198917, -2.727749380887922, -4.559794447827001, -0.8542942562333504, 4.669884972810683, 5.698796887094028, 1.555565200225495, -2.408737367573416, -2.2785383312572556, -0.05003945044557544, 0.48493062463167724, -0.6252467515942786, -0.5791005311766524, 1.1043833747124565, 1.9238109669997367, 0.7800387765425326, -0.11092825621973736, 1.043557759559616, 2.444886179267634, 1.4606311474948177, -1.043763166243692, -1.9019395644116104, -0.6101857934400209, -0.0338320521465305, -1.5681210542687811, -2.6631884940008606, -1.1816837816107726, 0.1901832980209745, -2.7297147990329345, -8.664446599682664, -11.084525893215918, -6.519230922142048, 0.44255117278240363, 2.8568364638961654, 0.0754791249153633, -2.4891051592756157, -1.3853767240974277, 0.8693444649499499, 0.7043149223793497, -1.0348875088360345, -1.1654441374759656, 0.3563756667097546, 0.507118728359014, -1.6562342175176856, -3.3057257594558984, -2.2580063103801944, -0.2704126194300177, -0.02851581800051935, -0.9499184202953957, -0.647755328785132, 0.634749472202959, 0.30627505830169804, -1.8336430844631209, -2.5534513381197, -0.3606335569185193, 1.2413217207883236, -1.470629558300137, -6.179760559572292, -6.800032693333659, -1.9195663495519908, 2.80567170199841, 2.2198105110123585, -1.5363667183783165, -2.659096674101528, -0.06419554711223327, 1.7588106655959728, -0.009131504433308431, -2.4743709057799586, -1.8531642226133416, 0.826924091568075, 1.7448499484971745, 0.20776658974219897, -0.8852385274583572, -0.07926155233247367, 0.6243113560463345, -0.32506578850104606, -1.2129182559695215, -0.17778692174697971, 1.194517395533032, 0.27272027764515683, -1.9357798428474315, -1.9156052012681113, 0.6341753033232058, 1.8008374612572107, -0.5236009726285115, -2.9129639891947514, -1.4405127760109977, 1.8713940242132145, 1.5723518339726292, -2.8541054849307024, -5.467559625798095, -2.083208320070108, 3.623479505562845, 5.100638189357586, 1.6545865103352935, -1.5338316733898798, -1.2304229332889074, 0.16073333480000868, -0.4364520489832932, -1.906897011685901, -1.523640288663174, 0.1952966724081992, 0.5737308043183076, -0.4455294062587708, -0.20442380561783066, 1.8769733983088752, 2.8706915946971985, 0.9902597518316035, -1.3095339318735584, -1.1206090439034395, 0.3614727329657824, 0.16617683159099372, -1.0293622963098794, 0.20954865130873623, 3.695721329883388, 4.42651312442371, -0.16051753797826865, -5.173138264560701, -4.104941322644091, 2.1168680705802054, 6.110722153151018, 3.8761334485311743, -0.5709088527515891, -1.750921183097709, -0.05001937469134621, 0.5219059550173657, -0.7522679697309373, -0.8518929867643559, 1.214551368113368, 2.5005840875132295, 1.0464174088210458, -0.8323004292159105, -0.345995257717881, 1.32134233685394, 1.2362404245411893, -0.3521765972289259, -0.712286619166479, 0.45125290265652307, 0.5377086796442266, -0.9876215575942593, -0.98844617106525, 2.038480411193171, 4.370832218580214, 2.164625576048897, -1.9298367276777417, -1.61978500990581, 3.8883297404833406, 8.119448204376846, 6.137765220456691, 1.1360761733660882, -0.7286149580787158, 0.8920795951740851, 1.186044207972625, -1.6714410769195858, -3.8754569229691014, -2.3591155948937845, 0.4630883686704947, 0.7857916644672349, -0.8248724545318464, -1.1012820293049241, 0.3309643688669083, 0.8493315432987009, -0.22407870136606384, -0.48518500773983436, 1.050197342957144, 1.9523004478929606, 0.6943401058259919, -0.1948192140602951, 1.8300171602844757, 4.479226142211245, 3.6180689068260494], 'positive_zeros': ['1.59847763692419296621304958107', '3.29358000174467762701344538673', '4.83973225132697432978836690139', '5.81157476086979037443157899242', '6.71611889394128124166817594669', '7.788919411245076042369859754731', '8.94806991731036679634982622603', '9.931034953527864311548896250458', '10.7709051244638474670130449669', '12.64250320448196931318701175860', '13.30286758173497240354497765613', '14.63582651094872716789359485831', '14.88832438155688596561916850735', '16.32956212108416992994737519952', '17.25047135050921232518133017240', '17.82730207919817254134120912373', '18.86477578169101289582298548267', '19.84718023145606709467289941336', '21.50891764276463092787813070313', '21.89955305996382014245472867868', '23.08037460277107162444911486600', '23.85840792153123241591652314511', '25.077773767136100607461047172228', '25.43710689680617638622804818813', '26.43370334391496348756071619878', '27.272255174642358353319738506335', '28.222764803054610473882182418198', '29.3336453165989697960411204361', '30.18688471145105570253984085510', '31.31995971869669005073681674499', '32.25793491014363459423535209933', '32.97539062054062969218451354575', '33.7749846550689971093075084809', '34.540535275088368174896382575894', '35.29657295335029604053768028227', '36.5245217242057105628204319620', '36.971824378537643981474269283389', '37.83153718915736856429564897799', '39.078653865562348922030807307053', '40.209689012737685351003555670037', '40.86383555005476293305558993870', '41.88385967426123899007387295857', '42.11862724387214966062175104268', '43.41390227593578888567495859357', '44.15465236564005472958939351665', '44.84547312001783663996204388092', '45.65623644846938815427618845771', '46.32896966362325343323387181782', '47.47731404651773871673236256175', '48.7660336956119625642497422905', '49.26375694948377268416677632406', '50.05511564876074537980344849354', '51.02552647336965230538633482326', '51.81370291726490349346384375550', '52.54127291561859446008471055138', '53.35674797987615597711026158586', '53.84448878938622210865675913220', '54.90510698241003770479823286958', '55.653483973869983899210007647302', '56.79037485654411337022224707585', '57.4310866557790252078981539935', '58.52765510133784353705797448173', '59.37634035741919262823557677257', '60.003185495411486371541394892443', '60.88087334352163302750575548613', '61.6119490162346671397959343785', '61.974994358008654347010173846165', '63.42019852006939724719639976852', '63.7469908565403501663570983124', '64.582319562635502572774568965636', '65.49035508384783686277466224514', '66.50847625204449026814205770334', '67.57176640364804433871512896486', '68.3328421559775029760012843678', '68.76698401820328943638146854084', '69.64675271798295171298326163965', '70.40657461377163032036641294139', '71.299124617707012920745518714843', '71.968849522598924163717734040076', '72.67761676531555588228360750291', '73.325290345015620825915593711796', '74.21464108537713299028780033860', '75.47685000200159689617368471698', '76.22311431960715203893971332568', '76.971805205330290648242166437174', '77.47873499866695037866436130338', '78.6838044020163333704951818804', '79.11468219165086209387168215274', '79.975603514147333087465830563838', '80.70034318929030422572596882906', '81.29155464335759099163060493001', '81.980219391231179047777446225677', '83.279731717074686478266749768452', '83.62894802633375747178997193327', '84.8491197409925793600994175692', '85.59639373144954923966177204340', '86.26124695280133308754547906402', '87.3729373110426714680102100433', '87.76961823137650819431923022843', '88.47678601010018390209124602748', '89.2307416528065748113804693415', '89.91444431148724759513689377365', '91.06445600283454266685931642293', '91.28140438640544169217319548258', '92.30522854559247699768516573302', '93.10258066062292149529729216594', '94.17679234538921879251068877141', '95.106520449564847296547086121871', '95.59823113959815481160372982680', '96.387076122037360952324415307429', '96.8805408282982691670394881283', '97.94293729420985235703570752223', '98.47475612396605920399559924663', '99.38022628929454830852426699097', '99.929170606408882903241422249433', '100.60386568416064595733270812453', '101.40961650637670654866669534298', '102.66800158361409558304384544468', '103.45141058091200434998975413183', '103.976615219943978753761242856431', '104.73335316491703544513951906508', '105.60036721530053962581708012069', '106.21788155505755781172898284131', '107.039250471448151851649858184301', '107.89266174776450576195467762486', '108.0632575662648787086593684199', '109.03806155085458358104175865777', '109.91324834316932827974311933075', '110.721337378326332457517760784620', '111.558764188112387860920378798195', '112.50089348532813888429750612580', '113.05986932997104175696733754914', '113.91395392486421609651925194430', '114.83857065083607964315152252185', '115.38562074765424302291377789244', '115.70115331261885930659066659953', '116.93766704518872312066377536391', '117.2161116757432049403047090277', '118.28979559697136964680529002188', '118.92355976748714958034755976403', '119.57462654871222581300517839173', '120.510956854530781080969173912', '121.54641897985110132670027837987', '122.25710721586437320086262639058', '123.01062557776080333334887792900', '123.53849721171317533344169827550', '124.1682616800446221646752574995', '125.01408466589211449931003538396', '125.8852092514906542907210631066', '126.26464925562013379370216829810', '127.299221499378039578100810228612', '127.75571075230606708198261102519', '128.307355857429059465494445115068', '129.91462413599666133106737373793', '130.21467598494919704713789036127', '131.178545785447149612541942513875', '131.85268823199506264786024419647', '132.37913719382253355651140600130', '133.23868553157515653966919388044', '134.09233727342273864670593378886', '134.62267601612643911317147640906', '135.306206340117598374474080495369', '135.785327139691690786620281549510', '136.843772475476898574898703376086', '137.38089358935648653750779868433', '138.46760205044846867239762735986', '139.235564804166809762940470152925', '139.87499602495941405834531819040', '140.64216680502762287410713545884', '141.61303864673460829680551552046', '141.996963444585242310508451415863', '142.90886327472480167056868187464', '143.30394185266141382370832923420', '144.01281468854779542900616805305', '145.05923385678329959876166387838', '145.39632976596975998187925486583', '146.40201686733952606973384646466', '146.97958324491819034755850350972', '147.85786180048948201298991112702', '148.84823451656017083603114947281', '149.69635184393407550259982490175', '150.146850866833240932301593059999', '150.74844012952147089353005712419', '151.76236249904093327622171311635', '151.955505011858066917370509368261', '152.991650088395327656578772600827', '153.93318862667939543535241288674', '154.042789890342278074161250288400', '155.19220126577910885739029443371', '155.37924419840495609052180435453', '156.85079229483387877857465028440', '157.50638243570896918179344794274', '158.295732584447570119137647835924', '158.87574510612819604193023638374', '159.6132492132922614848213338370', '160.09731395562504118225933881718', '161.328058433561419938438462651901', '161.55007131702443113193131768471', '162.33731502852435474367695526820', '162.8667996932021529133655791097', '163.79143013636365076023244691794', '164.26335028570077807156052456084', '165.41457962328035497206288175631', '166.12094218113728442254802549636', '166.88149774601224638825140355878', '167.49902898177671002223821835287', '168.33823284884791186711947610668', '169.09824021580795637414005554862', '169.707741953705691745930514432963', '170.23849543464590745330696911180', '170.96911496932118607888967826154', '171.6012088114864622393726338667', '172.42783779442720482387345672207', '173.07420927439528965341998240611', '173.876460506231319297070177871', '174.50338823147143103944955299334', '175.420513492730558171843956695539', '176.37827097811866251892454933006', '177.12725478706555531445462089724', '177.39701476952925274540727544546', '178.39696871754386371449768200453', '178.92944244182502256375704633370', '179.415512836198019463664009976072', '180.42526989327099840809854518464', '181.1581809657245264260926809082', '181.60255887618668702359520510249', '182.16433851397700696687367834304', '183.11677788589333945571174199146', '183.96331474651060953250225578501', '184.95098258416905233324991766251', '185.634257270321111144887584466552', '186.08376543366509453576656835616', '186.7130272865250898690615103603', '187.644213027294193163328711784', '188.1877464917846576387249055830', '188.9901495842668953294684958226', '189.57326468865932542561237387138', '190.12356529322483990335695064224', '190.75354316397208345827497341272', '191.71424390799561112846120527044', '192.29964509192916035155428696150', '193.53940279099353581088007642360', '193.92012986287325774342956544990', '194.53097956104670426812835982421', '195.56010193982636566654805822350', '196.095154949325653612060403943355', '196.80666222152021557243346286338', '197.4416700165406070906721117136', '197.937851231168535076097257744856', '198.89524041347080404333079396587', '199.13229728553288359561576568925'], 'prelabel': '1-231-231.68-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.82439762755838, 'root_angle': -0.4736720858821676, 'root_number': '-0.986348761496499320916180992233-0.164669732174197388859267351460*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.473672085882', 'prec': 40}, 'spectral_label': 'r1-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.711455483664921139603950281444+0.576340824748127676541654832312*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.59847763692', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.29358000174', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.83973225133', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 24.82439762755838, 'bad_primes': [3, 7, 11], 'central_character': '231.68', 'conductor': 231, 'conductor_radical': 231, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/231/68'], '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': '1-231-231.68-r1-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-231-231.68-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.82439762755838, 'root_angle': -0.4736720858821676, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59847763692', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_231.68', 'Lhash_array': ['dirichlet_L_231.68'], 'factors': ['1-231-231.68-r1-0-0'], 'label': '1-231-231.68-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/231/68'}