-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_3528.5', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.36534102436639504, -0.9308737486442042], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 16.38396312037708, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '3528.5', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 3528, 'conductor_radical': 42, 'conjugate': 'dirichlet_L_3528.2117', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^29', 0, 0, 0, 0, 0, 'a^40', 0, 'a^40', 0, 0, 0, 'a^32', 0, 'a^28', 0, 0, 0, 'a^17', 0, 'a^16', 0, 0, 0, 'a^32', 0, 'a^21', 0, 0, 0, 0, 0, 'a^25', 0, 0, 0, 'a^22', 0, 'a^41', 0, 0, 0, 'a^12', 0, 0, 0, 0, 0, 'a^38', 0, 'a^27', 0, 0, 0, 'a^27', 0, 'a^60', 0, 0, 0, 'a^27', 0, 'a^21', 0, 0, 0, 'a^3', 0, 'a^23', 0, 0, 0, 0, 0, 'a^0', 0, 0, 0, 'a^23', 0, 'a^61', 0, 0, 0, 'a^16', 0, 0, 0, 0, 0, 'a^15', 0, 'a^35', 0, 0, 0], 'euler_factors': [[0], [0], [1, 'a^29'], [0], [1, 'a^40'], [1, 'a^40'], [1, 'a^32'], [1, 'a^28'], [1, 'a^17'], [1, 'a^32'], [1, 'a^21'], [1, 'a^25'], [1, 'a^22'], [1, 'a^41'], [1, 'a^12'], [1, 'a^38'], [1, 'a^27'], [1, 'a^60'], [1, 'a^21'], [1, 'a^3'], [1, 'a^23'], [1, 'a^0'], [1, 'a^23'], [1, 'a^16'], [1, 'a^35'], [1, 'a^43']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-3528-3528.5-r0-0-0', 'leading_term': '0.109633164207001500330986080443-0.957688416544809516330475739634*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/3528/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9639432212937356, -0.0865259677682928, -1.0175572992140252, -1.0121045276329301, 0.2577699506363564, 1.5795998186920217, 1.1800448642549453, -1.2070460648410577, -3.599425067800982, -3.634286785808507, -1.2529720370092159, 1.0342782057842939, 0.9922243188921265, -0.6564566568874823, -1.1995133605899884, 0.44734287440651316, 2.18831177895267, 1.571234854888142, -0.6533623893327328, -1.2963533566726968, 0.8653332138315093, 3.10327141737681, 2.2943421905641994, -0.6809784141408172, -2.005825738017635, -0.18769115533140154, 1.9688735203920982, 1.5823068337713089, -0.1381096493286188, -0.07487002418151856, 1.599430848953235, 1.4154339186618046, -1.843282563204985, -4.603659214821771, -3.379162296956984, 0.06049459319989148, 1.2579832501797084, -0.39124764707061177, -1.1968027474673246, 0.6156114663085102, 2.0608695402714754, 0.4904897074314554, -1.814790890588997, -1.3321747342764765, 0.6784001375587525, 0.021960651921117468, -3.347137187380753, -4.7171271698164405, -1.9248757967600887, 1.1828972412169527, 0.8621282456483267, -0.8694412774415364, -0.23712403276838565, 1.6967818506760124, 1.182918760466659, -1.2025075328896526, -1.1953714325634495, 1.5915798992364263, 2.4030779256130934, -0.825313551371565, -3.6991071549429644, -2.3767094613545936, 0.348669929792675, 0.12134093852830818, -1.7178899206294127, -1.1908175197640263, 0.8106194322246576, 0.24044997944373095, -2.2722408606047204, -1.9739860794106532, 1.5061039561495324, 2.9293447439720763, 0.2704373403023146, -1.7550118898594214, 0.17916107168606726, 2.4930993490461275, 1.3787836005253045, -0.5595699233317728, 0.4600937127966595, 2.2793699487127426, 1.0830166119159954, -1.0115693724398827, 0.3646353345608794, 3.2736538100266275, 2.1903309591604763, -2.1971580029216913, -3.7745686493042885, -1.229003520224643, 0.4844865634548462, -0.5067190003163017, -0.349786480228847, 2.11953067788374, 2.5309373394225205, -0.5113813214509164, -1.9441760443405602, 0.820144295471545, 2.9511910622324584, 0.8953855208586475, -1.1706968755205374, 0.8356346160093843, 3.3690213922092385, 1.9522268659656876, -0.7317278348675081, -0.4284796124467978, 0.6497153274247306, -1.0948725857786716, -2.7436330917732388, -0.22416920556329414, 3.0325541896799457, 1.4901091574812648, -2.37064211337255, -2.2970710985097775, 0.7972754273538961, 1.3791531827141708, -0.25861706595532336, 0.2935501055628104, 1.981553959769154, 0.3701578467746408, -2.715817322774544, -1.7478827989477592, 1.8933195254756272, 2.0557722669530234, -0.7915610972481713, -0.7473537542758334, 2.0206801778417676, 1.7156118391314823, -1.7621771150466916, -2.7097297454338616, -0.5032805213977943, 0.12573683560861715, -0.7129243958874021, 1.4243331687853313, 4.942573404096592, 3.6518573740266556, -1.4299882439554152, -2.992504340937593, -0.15962049280925794, 0.9512427700084853, -0.8291373947749778, -0.7584951925314383, 1.0987319209993287, -0.06801202173017715, -3.2473225784879975, -2.76010476906235, 0.49711760581699105, 0.614536651679833, -1.5061012696980094, 0.1412687944352023, 4.383241332712469, 4.511447558617082, 0.8610811165409876, -0.3494273491401036, 1.0317251230619053, 0.30455799897476515, -1.3490384810822955, 0.542091845440811, 3.3603398877593644, 1.7086570320883454, -1.4382996477655883, 0.09880845717597549, 3.631308676965613, 2.683397242439414, -0.7385571244279053, -0.8078093481939678, 0.7203076157017994, -0.6720442541615022, -2.3107639557302253, -0.38128018545579073, 1.137583461299825, -1.6847450855125785, -3.9126243457725645, -0.9896781183421266, 2.078242483519804, 0.4917006900889909, -1.1563278698283643, 1.3606694602448044, 3.431917821179084, 1.361776665772843, -0.4248547287091083, 0.7192144264763812, 0.31581899776452227, -2.5536470009159338, -1.8732409935848882, 2.8909137320158194, 4.279723678768562, 0.6912778546131957, -0.9683016243485655, 0.9729296964298233, 0.7400275723808276, -2.1223391259211066, -2.127485025677673, 0.1483437956747065, -0.4251543388960131, -1.9526977423378782, 0.5718103288808256, 3.562178983728467, 0.9444289359016707, -3.399968177622131, -2.706399593646512, 0.10574273144651139, -0.420414524951173, -1.1634078901250475, 1.725066589078978, 3.763801889451519, 1.4844622764024207, -0.25954573946256704, 0.9811562463249108, -0.14964329709798638, -4.533918118780531, -4.9665870029949115, -0.2692220324108974, 1.8038783958967755, -0.6658107367184137, -1.3163456550755086, 0.819010293360299, 0.6614918855775265, -0.779007030818644, 1.0648961312480139, 2.9174040674679556, -0.36645308875708343, -4.104723721733825, -2.1342054116603975, 1.1799063999730857, 0.25149322264129786, -0.7087731285854112, 2.2733895404130227, 3.9530874866166625, 1.002556797178906, -1.1341944740945722, -0.10460705573961565, -0.8782804957212403, -3.398792146569612, -1.7594312627206143, 2.22215629440052, 1.075748399195796, -3.2611700017035714, -2.9510460404557612, 0.5213555241524833, 0.5975883063278649, -0.9757556804297186, 0.12109324645742217, 0.40354888441855813, -2.8679189111481103, -3.948075468959555, -0.39736098233848066, 0.8226331865130133, -2.5961505840233072, -3.565968326777342, -0.5119280348833324, -0.21765397926318952, -3.0026209228462823, -2.3916497906719423, 0.6772886042947038, 0.2730103109975823, -1.5726656154249803, -0.22716645670227179, 0.5236411109790353, -2.683603859768406, -3.605499247979106, 1.2054966802584197, 4.168474152873455, 1.1625937494580425, -1.123014053634278, 0.4742272798249014, 0.7546243894706222, -0.6239036289945955, 1.3341492343660242, 4.206991419710033, 2.2788684650817252, -0.5824214447237165, 1.3949864653328237, 3.410442726701697, 0.3591337524658382, -2.0317146832651565, 0.6237789899025024, 2.3467027568998806, 0.031173097718876705, -0.5257638739708963, 1.8047163527841188, 1.306505007760277, -1.1113533134898121, -0.12518741531056568, 0.8569345275103568, -3.5465193325751305, -7.60060409616998, -4.727236514197445, -0.3872404703018674, -0.4475793088517778, -0.46555202560222625, 2.305049186788056, 2.5547675482355405, -0.10644054909442388, 0.4740119892973704, 2.999558305652368, 1.3868955503788047, -1.040704976315811, 1.744865019082563, 4.684821515775341, 1.618281928271257, -1.9836203624822508, -0.7800657148106788, 0.3432992148611079, -1.2184989152551207, -0.2039860624248609, 3.118491025245608, 2.4224792216101294, -0.38207816577863435, 0.9077718011232035, 2.577373963970853, -0.9959625293400729, -4.092182634108687, -1.042410034802507, 2.0557545472389083, 0.4517335522625642, -0.5092948203403643, 1.2180224160433957, 0.5260211615903788, -1.410131591511835, 0.8847180816074611, 3.439678575589419, 0.07842202332641016, -3.7462948951987913, -1.788228543924318, 0.39592775781380923, -1.7380201260297323, -2.3346939970005147, 0.814943647087242, 1.3578248138541826, -0.9651645174250542, -0.27365269558984395, 1.289225330032928, -1.3150038228509526, -3.1995421101136308, 0.2848730870820712, 2.418195140686133, -0.9286762093660158, -2.4330555531850675, 0.8057664428062501, 1.698971429575119, -0.8872657769156277, -0.9245880572958375, 0.3653635546706099, -1.3486856299922154, -1.5716796548076548, 2.9948677498983653, 4.843000743330307, 0.5363344455296799, -1.7030207481936739, 0.966167524584264, 1.3955986340735353, -0.9392123910302699, -0.015995638817786078, 1.7769377835555256, -0.8255371379815388, -3.164528178379306, -0.8409773603852015, 0.6402078174963912, -0.696615718273341, 1.597591524501306, 6.296074785053062, 4.732817391029476, -1.0268626802230316, -1.9820461425588123, 0.25399321100527167, -0.29413988478653225, -0.7602091229945214, 1.0121241211194727, -0.556760834500046, -4.975826263074358, -4.204829239452276, 0.2777999302211295, 0.2056758120224689, -1.9901285453451036, 0.2655026852326534, 2.530198800495231, -0.15882281674919943, -1.8775158865792607, 0.6218217133012995, 1.2237098557364179, -0.7029529038205866, 0.4607345991121737, 1.9162174660475553, -1.689691781041146, -4.503750900787962, -1.1459088213819826, 1.2137803697080547, -1.8205734171409873, -2.9753350728678045, 0.08752746783168858, 0.6937239261669881, -1.0273693850467611, -0.08646159276008018, 0.01793518860219898, -4.047347851171158, -5.197708879439884, -0.5428527045924365, 1.4200193226219975, -1.3455662099130166, -1.0784318152359165, 1.7323971183543692, 0.19583801528852818, -2.6629914330000197, -1.0971167114590281, 0.34885573489540966, -1.7010449790118802, -1.6055503651465846, 0.7663350540187255, -1.3075013137092049, -4.79127107368487, -1.8863412497750154, 2.7062909272802167, 1.4566859635928087, -0.6916049364230361, 1.1593929224300115, 1.5786134805248881, -0.8954555699392364, -0.34198059628948396, 1.5109329439812806, -0.878265891553877, -2.594475780888342, 1.2236643587639906, 3.2895497353268346, -0.3285442784990939, -1.6110348920326794, 1.5420738403898415, 1.642599424930407, -0.8480185350431999, 0.16899474707070716, 1.4993229733704854, -0.9006456499953291, -1.3687322189059212, 1.708464232434102, 0.8361599724519837, -3.203647497558671, -2.0907236888767984, 1.4639088926903117, -0.15497599302054466, -2.5899774658258887, -0.15167386909827624, 1.6451980209911898, -0.1434783821622962, 0.2640567080848875, 2.259346694770792, 0.3773933221555943, -0.9141941727516074, 3.452795733906476, 5.877314083498919, 1.4575712554780877, -1.4913756339455877, 0.5972073471054129, 0.8988827512777405, -0.5594274329231772, 1.617793363305071, 3.425182941241821, 0.3625304965412741, -1.3620583018128043, 0.8360816393408945, 0.002614664713749765, -3.0912208578736022, -0.8359767628898266, 2.9858020870640876, 0.6032137480117211, -2.800472091421672, -1.0612610967067637, 0.3881293551144424, -1.106471043031963, -0.06772450842252348, 2.0565681890555507, 0.14888497331306144, -0.3592417089921156, 5.02654566043479, 7.69221668087855, 3.1714243882454975, -0.07894083477166383, 0.45510029539480445, -1.547383123736212, -4.016650076769719, -1.3701613856065287, 1.304548999707288, -0.2309845197385869, -0.02403649697929183, 2.533066310973652, 0.49864144843718267, -3.0883027260871065, -0.6781047875420919, 2.409114771472027, -0.377749766095661, -2.4942141150248, 0.22105528979836825, 1.0345549442540078, -1.0063155491611437, -0.1881269813778209, 0.7923798478174773, -1.651967826141613, -0.7156676790251648, 5.398404657840458, 6.690928873787037, 1.7166295213915626, -0.2126622010928831, 0.7910221860305602, -1.1943984032395112, -2.0955699542087274, 1.6042287230493346, 2.9226530640598365, 0.15541038234297808, 0.27901242926779507, 1.8514217958155543, -0.5994497593754876, -1.4317091068258003, 3.5349466858108975, 5.373111072394193, 0.5472634725134697, -1.8877413712014253, -0.08544770115979962, -0.46023746883576244, -1.09489265111295, 1.452794173187418, 1.1733540730012055, -3.078736160287904, -2.962369836313855, 0.5416350828115898, -0.7538369390223831, -3.0713813342930365, 0.3938905287171195, 3.3877522081631692, 0.948864316358909, -0.23439033664446152, 1.4312594187379641, 0.1319353810713206, -1.293917308211682, 1.9053942563370962, 3.3593088791608574, -0.0007561254272331341, -0.036880984693545255, 3.524149326481348, 2.002834208436186, -1.9997152546439645, -0.5352248337204842, 2.001880759572592, 0.43037798564278845, 0.2219478995886386, 2.474675544451352, 1.3429563698343234, 0.06686023571599761, 3.9720897723749364, 5.9676898187142635, 1.625841215923717, -0.17741804202270603, 3.0712523995200307, 2.915003284692355, -0.12075624454692109, 0.5775034289118944, 1.331565073833672, -1.5400202806956163, -1.8026588004315776, 0.9206843370749764, -0.6190615401256367, -3.3164915110524316, -0.5204023871015685, 1.3905242170542382, -2.715076580048402, -4.51168850252598, -0.9021068614003882, 0.440293789594803, -0.1452644468598745, 2.8019703357173293, 4.573687476515774, 1.42142164401576, -0.13118367205868026, 0.20014249300658432, -4.400510705002003, -9.03333963296708, -5.335002234382497, -0.026185640380768375, -0.6054116660960687, -1.3299820693726718, 0.34873700875422886, -1.0659045171742636, -2.876755385139829, 0.09563507354331201, 1.6054166277862731, -1.8371757569807823, -2.260559075904351, 0.8061574411130876, -0.6499052034207563, -3.335092344693601, -0.22162236930695345, 2.3646666556830644, -0.7875122723022674, -2.4170729858176485, -0.297433953394615, -0.20613826992089923, 0.16551556593414293, 4.027219248415575, 3.884929814922161, -1.8077832153838218, -2.727102844535813, 1.3488006573997993, 0.9346448784813969, -1.8321193117974688, -0.44949165063522667, 0.354066058082108, -1.9495597814865575, -0.8922177461303185, 1.9246524460974475, -0.23768873774734725, -2.455550775891307, 0.220387965551042, 0.508312856460135, -3.137790984542265, -1.949309265831144, 2.2075984150598953, 0.6948214679928938, -2.2908372099542755, -0.5133129405476303, 0.7761210857077774, -0.24137359463288388, 1.6383645256584185, 2.636295772424821, -2.2154518789604225, -4.604370290974948, 0.011342245953032603, 2.1104317558482775, -0.5843364375519047, 0.042361817358570614, 2.2301921315340625, 0.07483498217294784, -1.2434516671821427, 1.1142132377665674, 0.40174562435600547, -2.1607283259743424, 0.10305926976981519, 1.969344533198272, -1.7310385032374809, -2.99036373579574, 0.6033151804898969, 0.03776291760283499, -3.7326611990599563, -2.457967403502432, 0.3199122668743229, -0.6159181391563011], 'positive_zeros': ['0.28718233495788146320039007864', '1.19942195472134668339807211843', '2.0503012411169910228109173199', '3.26936994613448900951285240054', '3.94216486259679295493579798778', '4.623551656947223840342044248404', '5.53092290676321687728423793197', '6.153043160439909942025216045836', '7.11536221231245913249350456798', '7.83441100091976509080812410500', '8.71720122132875768138121258129', '9.079692840806542069761847527395', '9.84660818567222540315089377887', '10.93107673422131130148451012096', '11.50103796601640555487189127800', '12.10561877969249059871169517471', '12.86871275018481669541553189233', '13.627841337209863569127958008353', '14.06515573044854126152627193419', '15.16277307392823809868211870095', '15.761514191963634361465228607644', '16.28675072708897315825162521408', '17.026369238289142393304972826', '17.64610046329141915591987460752', '18.37427028877570984749492360149', '19.318260840599059396630432156805', '19.70823410557808717538642158947', '20.48226711177909940934775897338', '20.96949516456643291823299948827', '21.74780107640735047099754352478', '22.52528066704333018735033935632', '23.10689192647535096011473138093', '23.93376253090512312096428114281', '24.306600748213927764593907749720', '25.1306040331462716678387953176', '25.58662642373100350213426636865', '26.408729597111640182316661534944', '27.33909675034313107180499705215', '27.69182427730560395696285202247', '28.18009167468019044697929473870', '29.01527461907867389362776076486', '29.61618730597198090960243618586', '30.40345412424820394247956023429', '30.85578585981976629088319226804', '31.763798619888356432146324391583', '32.27049546118133060068083174414', '32.67368925507278644899980310839', '33.45460974038034254398896746791', '34.174070879068083295115619144869', '34.91394863220827045971080352257', '35.56302276646218792580630843850', '35.88581878604265946521072276575', '36.59622818519288506744254490973', '37.33136548320221291824244940841', '38.031544951522368070294055804138', '38.52590118219346872793743024544', '39.22087154437955238239571901023', '40.09108090222198530796490279425', '40.35469290913130252945836948959', '40.79988159473730934490465876974', '41.78368399204309567186097887906', '42.517309372971297111033707484468', '42.990091183102966362781011873788', '43.555487621461492302568090088541', '44.055573630745214239791865571910', '44.94328699890441640487787492807', '45.39657913501990717078214040428', '45.926350390049433388408304888893', '46.97538839385537309516254361386', '47.2772343049687240928098508235', '47.85697001677641546419839909596', '48.38691298763935601641848702759', '49.203397290416881439904559503541', '49.67932810660376703345136111011', '50.54216114069846065906429442877', '51.06960811953321170214534004432', '51.47441652035646558912667665394', '52.22937499487598342773318469515', '52.67033383901552647769726888816', '53.509227903720701554880381862', '54.11618563290503381494755401288', '54.56247675618996814834541365057', '55.479837898820262136006889173720', '55.78643219684863384682600880745', '56.289174341339720146215016142042', '57.00597852553171816160801688860', '57.87400438407073011035204083236', '58.29787626891454568483784527931', '58.835125991934460297093319435379', '59.65753895542630050387187440923', '59.9302299885350511516289984170', '60.580732590700791362165855519417', '61.30795496806579720826248271672', '62.16644951106947403848777533470', '62.4196156521013005312480871705', '62.97428559168319114785296607487', '63.93665772891902192414017826237', '64.166566911323091989455581776629', '64.67413341409606383604245851742', '65.643273654904764053292729634844', '66.17649368898954238666330211466', '66.75318403587118277583066683088', '67.29700525361275799602565099054', '67.69640285995663898039117384515', '68.41461623847462802343505846722', '69.22789451406881063103955352264', '69.72306737555404436555424663754', '70.10925362444826091458052521260', '71.028902129388366585425528717772', '71.60299771189111328045090060151', '71.71149859495009765337837008547', '72.62334658599493041608815223027', '73.19970955824893492788221997468', '74.00391468799379682472849172184', '74.46951733925943220520030183188', '74.97877323190669093154479579025', '75.36853676000257585659080612937', '76.28476842447381943436522717076', '76.660584965904672766739753920833', '77.569864935511882000198196687629', '77.77825619864831685671362255707', '78.66380226610942710576909879984', '79.0993367663813810017486568826', '79.719834565533888626607796640214', '80.076449496995794174386225901122', '80.87127958499740212037271092724', '81.65983732344786575835306601745', '82.11417813539733977299438022113', '82.64144332475283531364145554899', '82.99158697312634854160055050638', '83.95137484560076945604546131053', '84.23705069923098133576636399235', '85.026775464062177716114821059087', '85.57130905456248445982545837583', '86.25387135993983134465648681038', '86.64194927628047025557977362942', '87.33394338840400833414622195862', '87.82908662614526024176471977591', '88.22474071903029438356295598784', '89.459944597141971718419096455841', '89.55467145585526080026135345936', '90.06601908707921127147251164794', '90.92043256050257112565713746994', '91.1888033337750732174010554850', '92.00178053995274158843237053033', '92.36810677110004269563150977697', '93.22998231135868372633300407662', '93.86371886694268012210029523349', '94.15259489337823598681250687731', '94.70700561776001654723736987879', '95.55638349282533855173373113237', '95.83045660570831950258702782263', '96.5001829911949657230823197545', '97.25877363933906364842778157815', '97.87336764318360099130932478345', '98.23112793319715492860974545156', '98.8149123443321911159288682077', '99.30211148737025349248783369798', '100.00460462828625608848485481651', '100.805118832579776683620119760483', '101.04474533114941584636412091226', '101.79632193824680618112211340196', '102.360122045158430472497078535271', '102.848231234040498423305230642493', '103.32508477521494942696633156932', '104.042716866185194193260534335531', '104.61750517278054663899373607254', '105.24218744876420713730675482106', '105.8285115718026419474544195327', '106.41356832063686127370577904347', '106.68573780026526001136589355359', '107.31716961232021356057805432937', '108.16059954178051954597624030877', '108.65158507276002139494900243795', '109.23554572750203154939231039782', '109.68939661455211761131856679151', '110.245682306696303079267933990544', '111.029509913848938245958963959455', '111.39873582135410650608022460764', '111.75091206164547795943930505301', '112.7469231944698829091567688916', '113.38481479887157143553335795554', '113.68927310799061179869288120652', '114.20019317627286642211302529518', '114.64285470003410218065491136658', '115.59859417867239113580545019982', '115.961265846930809215422261950193', '116.54053362834743685524235838169', '117.17402067445221500439459790442', '117.744936303591189087768242094761', '118.30574243897883849291174957360', '118.693613415398905196231299608862', '119.26586378929427078077089342938', '120.08332628425832780509638319704', '120.47371002355395867156408648996', '121.24055532814829227347698171648', '121.6755812914271709739369655023', '122.2029706332144400035166860859', '122.502317972636648950496771914298', '123.473922061147901680014463687973', '123.9222354471738814086368254367', '124.48120916145545962794752600325', '125.01665468478982869528701707655', '125.76196152202340539264911650314', '126.02094735816915333493659665696', '126.74629672085977857585469044394', '127.08192773348971199549970352536', '127.91607790679911561687095474440', '128.5843091954347712229941022890', '128.91578580243007694012676160796', '129.56773924570091661696714831369', '130.04200964748745157633456991267', '130.54901383113503811616192730268', '131.170762020833217147889147191272', '131.85007925531107866102415919996', '132.35599036660713331837991001596', '132.99521963139023335446628506159', '133.41593298786784415733702070954', '133.966943327547328524186870263918', '134.51725792273820762597514067859', '135.06222714927937029226548507843', '135.779136653444523090933189924507', '136.23668881768672763905321477006', '136.88854250138790953166680152074', '137.47426652131839986351791992377', '137.77397502292585430470505617977', '138.475456127176639425216918330248', '138.84930413357002977107407144639', '139.7789175289296576127425896708', '140.23905233257517339053829751100', '140.77217133573119095669326949073', '141.08470330624171044986819994204', '141.90524919086416495331026457924', '142.38742925795241786887628452924', '142.81274659902024027729777953987', '143.49042331406201917136924985147', '144.10250111322250285425806463223', '144.81643791068498032676850211530', '145.10126545207214250302314535899', '145.63259103162585421889731583519', '146.26655499541677584842967367008', '146.59635893588892232583419575343', '147.7800853316247209457122116002', '147.92445357412708871331863405477', '148.27365447866050351186292179788', '149.17039541889523851012706768319', '149.65116352811746233074670468471', '150.00305177294323903672684590538', '150.659127079372591305466963276248', '151.295728836650281799253878448528', '151.84686125177889479150835297746', '152.47776686736860156732085571843', '152.96276125323796119833323781154', '153.46500095570995984671929080605', '153.87687349201837880303511304291', '154.419094897096933603148339514443', '155.47084111706764418808070450267', '155.687369029107507911157253493', '156.115942523954027316138479385061', '156.75705744393318648218331466177', '157.52317937999214945624129293241', '157.768205068130875474409474882607', '158.38252927345784217574391116946', '158.86475167368616488893495830429', '159.7215706101307977601263313005', '160.33295517594114420698680703179', '160.52521651827199406684109495951', '161.09264023103191215435933210731', '161.65466009832006488858182161696', '162.43161625694023432243493514739', '162.74100173353149871226585724862', '163.41306987422534918198447029251', '164.1747176390424731651961703976', '164.42675471170755787121047218797', '165.01504858447774527087583615713', '165.47605900865196464204479389065', '166.24992419571608599670265382443', '166.56615809295270158404579027035', '167.31894278443949437134092302112', '167.85809396428382476504009384601', '168.51292196074426879370173575900', '168.70905284506329075885386900739', '169.56871137926641143217723486085', '169.670775722356948197996119204471', '170.75862703361880806555984475053', '170.96460363409499049999745083247', '171.85382714827286848286955204954', '172.095426401645786682966811422316', '172.66338464098577102717284738391', '173.312371984914045908190943002934', '173.69565215870946403237845308606', '174.41429933517640218829678718430', '174.8267644670231036918810745160', '175.71777967475797015815373855038', '176.064901219801403596671454451478', '176.28626211792296683115630672327', '177.36045801551600794842433934472', '177.553428037080237997862357646665', '177.845515323967108189663824633770', '179.066032934527550420590477812', '179.28039949121444431795421384094', '179.915224302206028659965983463201', '180.184197568644648802775636737455', '180.929852498794371948261182934695', '181.41473583509037053599158965758', '182.086161786181401275975147091119', '182.443396580330658016093205177330', '183.13973595773373252797071854052', '183.68930689658422183293129191180', '184.442909623788537971830646147255', '184.61699258013213337217121002495', '184.97860607199558628019695966364', '185.83802059636643053109917056489', '186.45095002686776952678457803450', '186.96069177070439501392541694502', '187.56036202523985566049780805669', '187.87225540231237945165589645875', '188.515910705057131865468288512140', '189.04334379097101881196210934526', '189.66559435186596955442953244158', '190.04913164970692640478096271129', '190.75174556572082458100702267585', '191.30314677406869777089667417443', '191.934786299277672992037023138146', '192.38937154220915821173838891695', '192.608203381493756730521534191632', '193.319232027008553604538037003515', '194.06181606021548859461520409834', '194.61520039202163695042098826337', '194.99533054674734011570484837686', '195.632346088105474344139089374067', '196.11063436375160305617623122906', '196.60213205463096338942935021142', '197.17913109712865974325518972600', '197.69281522051521012075474835180', '198.38011331429431443273644494945', '198.75314307033220220069563227368', '199.61458592118272687731828939874', '199.8758747202715373003447853849'], 'prelabel': '1-3528-3528.5-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 16.38396312037708, 'root_angle': -0.9274376417233561, 'root_number': '-0.974129132836495420143401384224-0.225992107294076666848503063454*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.876605514598442484401642285099-0.341855775518270844150783035115*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.287182334958', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.19942195472', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.05030124112', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 16.38396312037708, 'bad_primes': [2, 3, 7], 'central_character': '3528.5', 'conductor': 3528, 'conductor_radical': 42, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3528/5'], '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': '1-3528-3528.5-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': '1-3528-3528.5-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 16.38396312037708, 'root_angle': -0.46371882086167804, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.287182334958', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_3528.5', 'Lhash_array': ['dirichlet_L_3528.5'], 'label': '1-3528-3528.5-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3528/5'}