-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_43.19', 'a10': [-0.9888308262251285, -0.14904226617617444], 'a2': [0.2225209339563144, 0.9749279121818236], 'a3': [-0.9555728057861407, 0.2947551744109042], 'a4': [-0.9009688679024191, 0.4338837391175581], 'a5': [-0.36534102436639504, 0.9308737486442042], 'a6': [-0.5, -0.8660254037844386], 'a7': [0.5, -0.8660254037844386], 'a8': [-0.6234898018587335, -0.7818314824680298], 'a9': [0.8262387743159949, -0.5633200580636221], 'algebraic': True, 'analytic_conductor': 4.620991766168876, 'analytic_normalization': 0, 'bad_lfactors': [[43, [1]]], 'bad_primes': [43], 'central_character': '43.19', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 43, 'conductor_radical': 43, 'conjugate': 'dirichlet_L_43.34', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 'a^19', 'a^18', 'a^13', 'a^28', 'a^35', 'a^27', 'a^38', 'a^22', 'a^24', 'a^37', 'a^20', 'a^2', 'a^32', 'a^36', 'a^8', 'a^5', 'a^25', 'a^31', 'a^12', 'a^33', 'a^10', 'a^4', 'a^26', 'a^29', 'a^15', 'a^11', 'a^23', 'a^41', 'a^16', 'a^3', 'a^1', 'a^17', 'a^6', 'a^14', 'a^7', 'a^34', 'a^39', 'a^40', 'a^30', 'a^21', 0, 'a^0', 'a^9', 'a^19', 'a^18', 'a^13', 'a^28', 'a^35', 'a^27', 'a^38', 'a^22', 'a^24', 'a^37', 'a^20', 'a^2', 'a^32', 'a^36', 'a^8', 'a^5', 'a^25', 'a^31', 'a^12', 'a^33', 'a^10', 'a^4', 'a^26', 'a^29', 'a^15', 'a^11', 'a^23', 'a^41', 'a^16', 'a^3', 'a^1', 'a^17', 'a^6', 'a^14', 'a^7', 'a^34', 'a^39', 'a^40', 'a^30', 'a^21', 0, 'a^0', 'a^9', 'a^19', 'a^18', 'a^13', 'a^28', 'a^35', 'a^27', 'a^38', 'a^22', 'a^24', 'a^37', 'a^20', 'a^2'], 'euler_factors': [[1, 'a^9'], [1, 'a^19'], [1, 'a^13'], [1, 'a^35'], [1, 'a^24'], [1, 'a^20'], [1, 'a^8'], [1, 'a^25'], [1, 'a^10'], [1, 'a^23'], [1, 'a^16'], [1, 'a^7'], [1, 'a^30'], [0], [1, 'a^18'], [1, 'a^22'], [1, 'a^36'], [1, 'a^5'], [1, 'a^4'], [1, 'a^11'], [1, 'a^41'], [1, 'a^14'], [1, 'a^40'], [1, 'a^19'], [1, 'a^24'], [1, 'a^32']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-43-43.19-r1-0-0', 'leading_term': '-0.125037550182888563650964319839+0.180553023983371747470827294133*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/43/19', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.21962191016671917, -0.7905451740331237, -1.4736282741224203, -2.255874670228134, -3.0789394403111863, -3.8372913380518314, -4.395496741385522, -4.619340182927093, -4.4138126310759045, -3.758602764373398, -2.7299238100972176, -1.4985598613510605, -0.2990953328543528, 0.6261456065468506, 1.0951780894687075, 1.0457800413607155, 0.5641263961572612, -0.13284769827268567, -0.7626741672293267, -1.0737062927758496, -0.9411266983976305, -0.42568591592659705, 0.23331511088091705, 0.6975900340157386, 0.6602910802183927, -0.01887307432033039, -1.2292124058788547, -2.6179022593931998, -3.7015166918046996, -4.047194669675153, -3.455809738909292, -2.0694434125537686, -0.34816460718152653, 1.0887635094720043, 1.70335434876213, 1.2652636761897038, -0.03539866018404558, -1.6473116781107426, -2.875917428217147, -3.1741529645028317, -2.380497531601967, -0.7945423780150337, 0.9512686182659655, 2.1721168553896355, 2.4374757864399816, 1.7599534331211624, 0.573814537316748, -0.4891755975077211, -0.9175559177809961, -0.571761113735645, 0.2610719602494391, 1.040495341350101, 1.2848521935285804, 0.8534432032497149, 0.038478194309648106, -0.5959967614704269, -0.5518025880265546, 0.2720072991433922, 1.4487169069953985, 2.191421434137028, 1.7544400320344704, -0.13398320890092702, -3.0466460992974618, -5.98413292027262, -7.814663258274444, -7.8140011734516674, -6.0249919510898975, -3.2404296846764544, -0.6098024894580493, 0.925335286332962, 1.066231617144946, 0.23114744346742533, -0.7600495645328583, -1.1991594106135564, -0.8976838580748691, -0.2524089152609134, 0.06109242367067419, -0.4305657644507312, -1.6496144214393158, -2.9770897295745593, -3.6246919304616956, -3.1390559396428537, -1.7148161559308903, -0.10275682781037321, 0.8478626532348641, 0.7336679322467028, -0.12266120022079013, -0.8551853446251347, -0.609256484596192, 0.8711742802500718, 3.0050166057909733, 4.663624593394735, 4.837916262900541, 3.2809224026954973, 0.7170544570122556, -1.53581124291523, -2.3209541358088153, -1.3192235132310923, 0.7708254917029427, 2.6638640890426335, 3.262884329106762, 2.2956584505148294, 0.42161235450511236, -1.2389110900664724, -1.8297217464702114, -1.2595922152992693, -0.1638557664872951, 0.6160636574077889, 0.650498650790167, 0.1943068401577679, -0.07429998449133027, 0.35196082105253557, 1.3334890395559011, 2.105056041056163, 1.8180970082193981, 0.2356557410558822, -1.9343060948000697, -3.3606608316866797, -2.908663806778136, -0.4290306808253303, 3.033191401562474, 5.795850885420629, 6.535116235603433, 5.079728193356868, 2.4805434151053856, 0.3086478726660245, -0.3480040113359169, 0.4798887655456053, 1.7847302516401704, 2.3700288864027246, 1.7109764786785076, 0.2809482924293216, -0.8648874060630164, -0.9169244026725852, 0.07421148645671938, 1.2504089375844254, 1.6169076667010083, 0.8165897977543013, -0.5853571646033773, -1.5288827070171984, -1.2767613572815422, 0.005504656392754569, 1.3641869376843263, 1.7936140965565632, 1.0324453459981875, -0.21078231057279903, -0.8123114878892636, -0.17193052127761668, 1.1888010374939875, 1.8765437018166073, 0.608542769668657, -2.761026792861845, -6.941150488255626, -9.90693880148666, -10.159225092693688, -7.675054849426157, -3.886903630196918, -0.7160518260358955, 0.6456631805767227, 0.3547286420883019, -0.44893463035329695, -0.6420759061640207, 0.03962640627767828, 0.9375243593004301, 1.1640131115645196, 0.4357362849147266, -0.6589812183985337, -1.1760217220484923, -0.6696196145030762, 0.3563121240412659, 0.8201568187333689, -0.008707832364146285, -1.7858246713003119, -3.2157710026598183, -3.00469828333588, -0.9307703248624772, 1.8309074071507612, 3.453062061708613, 2.763122424196225, 0.13351653181905968, -2.7425319043561798, -4.049753442229567, -3.1330629211690795, -0.9001787108371897, 0.9438519271022833, 1.2191670984949967, 0.12042562009338188, -1.046670537854301, -0.993598164109097, 0.48262114816259677, 2.343800157686097, 3.167270961007976, 2.295633251291361, 0.34064207684606146, -1.3474502415405685, -1.7756788065553346, -1.0469398305997808, -0.14396402476360112, 0.01517952094415051, -0.5982425725785285, -1.1548962659276458, -0.833095769341659, 0.2594684867367757, 0.9800501823970287, 0.053584419392861224, -2.7203652626157435, -6.003860350205982, -7.705293691493634, -6.499824486945957, -2.914331772913516, 0.9210818215013632, 2.73081733671186, 1.6768106613181466, -1.1309947103644615, -3.5574896151861632, -4.042273218231091, -2.6249227067734053, -0.6595291339869104, 0.43485711554322604, 0.29362700039723466, -0.3064854270621591, -0.3602008589706036, 0.34577684334801007, 1.0439598471489786, 0.7831583382204478, -0.5463069193657558, -1.9408646053215612, -2.0759218876802974, -0.4961701328740378, 1.8684961847822692, 3.3831153270430665, 3.0555195388219705, 1.3954960442940552, 0.002201988264044606, 0.1831142454753889, 1.7753585397684186, 3.2147930366395157, 2.8507883929428246, 0.4176655461953098, -2.606403965656046, -4.110368911088767, -3.042581564516456, -0.28078793382403217, 2.053358982427728, 2.2715668051367652, 0.40276585867782666, -1.950066382016272, -2.9990251185437415, -2.1955955207814544, -0.5101880721885479, 0.5775805036034838, 0.40896489143102827, -0.38981492479742796, -0.6558249455442557, 0.11854564181148555, 1.2937223556933624, 1.7420774567173865, 1.0000376760072855, -0.23112212478447758, -0.7747081910715256, -0.24505540105101276, 0.34435185050161127, -0.6630149131734795, -3.991343080340233, -8.427428469638565, -11.40005411407345, -10.82473841819235, -6.752052684634529, -1.435598026432468, 2.284475785084978, 2.9876952136214867, 1.4660712750646616, -0.25011493731212103, -0.6976269218106718, -0.0459856996959689, 0.4015545095267294, -0.3279514653126454, -1.8660069274180764, -2.864277334309443, -2.3305992179373747, -0.6344017257507358, 0.7886349418550981, 0.7577598336457094, -0.5595569414603497, -1.8256321344515742, -1.820845991299823, -0.6178898633292366, 0.4904778697196197, 0.26335152439483367, -1.2263931550496499, -2.58176639922692, -2.3987543550836, -0.696940629887594, 0.9337056325059572, 0.7191893038860802, -1.5811004597505822, -4.225750396784525, -4.83251182824308, -2.414033321896654, 1.6710174517892609, 4.727053266437607, 4.858060047192001, 2.4128013952709577, -0.45827653761919185, -1.6694502215750955, -0.8221744494565317, 0.7668158979799551, 1.487134833455328, 0.8900489128581404, -0.1384271327815396, -0.493629752025898, -0.03445497146657624, 0.37231306669751946, -0.05867574205467294, -0.9942432842811756, -1.1558164760597978, 0.36751104470299306, 2.9566912784997683, 4.714417579653829, 4.073367000940368, 1.3293756277248614, -1.4010195244571666, -1.9101783489117636, 0.16368314695621586, 2.9540673663744497, 3.9464335914374673, 2.1503068918150094, -1.0660657962179847, -3.2077881513967084, -2.81658509679076, -0.6183193027049598, 1.3130253151916906, 1.5058572764353377, 0.3121331752748341, -0.6735485009358169, -0.3261891387799464, 0.8777443226509738, 1.389417450255564, 0.2052999350420695, -2.0531560496481944, -3.667002786823216, -3.4254000978929997, -1.723846569152174, -0.09167418447421531, 0.3418186124661759, -0.1195043125772692, -0.2439276463891764, 0.6321290794976494, 1.7168230435131615, 1.5089305917879547, -0.4750392013214715, -2.7580799131816343, -2.884928135320421, 0.37605157109213827, 5.616956353998106, 9.599727019371791, 9.740755613801602, 6.149189323617458, 1.4440834902003596, -1.449058205286773, -1.546000553342465, -0.1803018819983709, 0.6146243812999199, 0.043979867014928974, -0.9906210232311672, -1.145435128774917, -0.1630013507468751, 0.9078112570424759, 0.9388965320945681, 0.019647951716482003, -0.5967105439821893, 0.13336362594085927, 1.810676009334481, 2.8703443817373815, 2.184030204042756, 0.36537898325723955, -0.6505771563137972, 0.5208659877592787, 3.197289760924814, 5.047761718620519, 4.181782516225185, 0.9624361575479303, -2.2274800843759177, -3.1098459449937392, -1.538267727483951, 0.4937426708466315, 0.8535607694193552, -0.6619833414158673, -2.1807813269297975, -1.6432590225562274, 1.1337549866957268, 4.214433396102807, 5.320557112245463, 3.8763838583105032, 1.377083195728208, -0.16352197340856303, -0.06662212899846626, 0.6593012909446837, 0.6599866445910919, -0.25165585131472623, -1.0074998645637003, -0.6292682787271575, 0.5369352729267972, 1.1127622477701604, 0.24486148865372243, -1.281056413044196, -1.7125065937445354, -0.255947860219352, 1.731173273928987, 1.7092295785112872, -1.6203707263822924, -6.736601838636333, -10.235608171162326, -9.605098298008237, -5.351307988623722, -0.52854482370029, 1.8742207113676752, 1.275062735678778, -0.48297635304963576, -1.211654366026711, -0.3991356920832019, 0.7136796489974588, 0.8073254650375763, -0.012763920967201196, -0.4592362662963119, 0.32911248987262154, 1.662341533909255, 1.949571703987272, 0.46106804490865144, -1.7143881644837886, -2.6280000525581895, -1.4217544005991183, 0.7593391646322711, 1.892625309684496, 1.1091360939105304, -0.49231633567085964, -1.1332663223579336, -0.407754918438753, 0.1173932324239764, -1.483205683858364, -5.2436879182560725, -8.796124074704883, -9.316227409657554, -6.149972029777774, -1.5540898704728372, 1.2426927332368265, 0.8451475143948719, -1.2849142316229707, -2.4693140112629224, -1.413028109329642, 0.7714672708175851, 1.9556484174999789, 1.2169441837771804, -0.3883510456865953, -1.1340436020897395, -0.4686864673981096, 0.5813244334713169, 0.7484766586637005, -0.009832354869210858, -0.5939092763463817, -0.2604978059083679, 0.2600598378468135, -0.5345535091701987, -3.015241122841847, -5.442903338608073, -5.2592960585037725, -1.60799145429531, 3.444481211414278, 6.42592432087835, 5.455760862676763, 1.8901078531798967, -0.9907849082897505, -0.9936527476827992, 1.1708771390177453, 2.916951056017315, 2.469086006424977, 0.4626488061163718, -1.0252195563179258, -0.8093577668740987, 0.22530668207293536, 0.26438689044191627, -1.3232925511959717, -3.2308206583463464, -3.6099319152830427, -2.0652076124714522, -0.07001365024837305, 0.6261403782166349, -0.16148776299798523, -0.9731598413970108, -0.4415353706363111, 1.1107073392993465, 2.018853680578639, 1.2068688940445398, -0.4738581873786687, -1.091012496736446, 0.15674697981191982, 1.8086724236103582, 1.5176211691199133, -1.3328422651754488, -4.536854203595944, -4.867488039615043, -1.1749881849821175, 4.273003032835916, 7.629831561768859, 6.784093061383314, 3.0078895021765173, -0.5068753191211336, -1.6094508822571894, -0.7309844376359527, 0.23610176353775109, 0.19156662742235486, -0.2618101864711655, -0.0002820079929135799, 0.9665403017540789, 1.3920578713594194, 0.3480535619643256, -1.4497567216997087, -2.2234928581321514, -1.0987860361754778, 0.76376529056701, 1.2917683767069732, -0.2034065770728723, -2.0830812631209654, -1.9921883782315388, 0.5432357371593248, 3.3180452877363646, 3.4686494178946736, 0.35692115343016123, -3.6548301523997715, -5.407860765205033, -3.931500860318484, -1.2002913811941478, 0.028692942392372224, -1.013379940643048, -2.5787610508871976, -2.5227416447516346, -0.691924965176965, 0.9720469280059146, 0.6238059463919965, -1.450848237347922, -3.151963681935564, -2.815894692344356, -0.9086363770169523, 0.6256596412536989, 0.5253151713033593, -0.5594999588447227, -1.0524773145486803, -0.3846272517771848, 0.42792864843773437, 0.21885478416941606, -0.6523863223926508, -0.5353721856114938, 1.4133891825470022, 3.6458271499679498, 3.2474534576698226, -1.1160562107254905, -7.329595464859659, -11.223058994656672, -10.142895748439239, -5.2804096593654455, -0.47185979306982695, 1.3134915546840766, 0.3371193292919935, -0.8393296519386213, -0.307606559891936, 1.387118653557959, 2.2757028491507776, 1.3783374782459852, -0.26834621372486384, -0.963506147229289, -0.3271720516887135, 0.43259933970463166, 0.20372477196610314, -0.48972531880224435, -0.02058655577178398, 2.2737855362395836, 4.932287827440201, 5.641865244527333, 3.686063890166646, 0.8413982352454172, -0.4061291160833928, 0.5296583746214967, 1.7715211950285377, 1.1470172001476933, -1.2686271332254742, -3.0968035202430846, -2.2600188475347585, 0.5600262145824518, 2.3760562109111616, 0.9208767276850033, -2.9184943640075844, -5.867495449192452, -5.468222044163068, -2.3975681453872397, 0.43011173713279727, 0.881316916014506, -0.48487484784034496, -1.4557825199863106, -0.749004852888857, 0.7760074423654056, 1.4285920333418365, 0.7696273251313203, -0.010243375169258362, 0.26490789580661755, 1.2026973437796753, 1.336980110633377, 0.09320390906602384, -1.2361835880508938, -0.8908768450237862, 1.0719184585272494, 2.388600622802061, 0.9071466658311151, -2.7389396669842063, -5.180598503219916, -3.4153674520286366, 2.071863014052554, 7.453238652488676, 8.964534699414186, 6.200346669029121, 2.078541569070902, -0.2505856128890316, -0.2135430826655296, 0.4028330293182635, 0.010858890086540776, -0.9690831576216699, -0.9817037787311299, 0.40225559584753845, 1.6784738981641234, 1.0715735427529363, -1.2962862576261827, -3.3350069950248606, -3.1860047543678447, -1.2061904500196992, 0.5244156756683291, 0.5744254411375084, -0.3533249715267768, -0.5262335480957314, 0.4929961874297384, 1.1544896916477114, -0.18721778130196715, -2.979473382011645], 'positive_zeros': ['3.8383850762264910680237064742', '5.25453097316806927785063194337', '6.76247294655105446528772989248', '7.80648260500463909647171327985', '10.06599665881085891590828952233', '11.24293473418147683348526763184', '12.95054336231972744487933334669', '14.52793885838560990517512245428', '15.53461791301013505519421119880', '16.88964009332190311468665058748', '17.73192081559039749101038780988', '19.04575664179352193173705494481', '21.344753184180159899802725286912', '22.255206404919201343271479106734', '23.607797341067793153549119689573', '23.85034845937961424691500453278', '25.96085633523626948889151544693', '26.835276573044053013835297554743', '27.65745932255504095658480468503', '29.46190713043536766419962681439', '30.5167949925419022818496158567', '31.94360930159370394327566410156', '33.17471762289274137055758676357', '34.21193183255826171626548445883', '34.49681834576204887027177984933', '35.9725399282413266096826784374', '37.22823400173506059039588649817', '39.13571347654349655652181006007', '39.55591013072822892335107810551', '40.99869815340013674686180949065', '41.856600660477808592627504678472', '42.99607290027532130719906749630', '44.06136401136788386457188331692', '45.255406732271097605788789754845', '45.98096713691891378147049453752', '46.94622591800458807581150475289', '49.174254181677814332053273981942', '49.81966330891105108263157876443', '50.61189079937415914430054049231', '51.68412639482883595627665152882', '52.70221887264299194945207230611', '53.435633067478337063302662596829', '54.79142600693793910140774790228', '55.95096175173639576212057206884', '57.3163154002115162329135537868', '58.15199107689765237169421818658', '58.98062702757969443883058030658', '60.365149203798849488870279610430', '61.65251936373710679592666820389', '61.889301794794706517466755349736', '63.05616089830378233639718182543', '63.75846929524339474820646370913', '65.54015414643103117067917619948', '66.44489960269636626190008252631', '67.95471025244497376541226918247', '68.583755865291504545853854008749', '69.24795632261236300576411434065', '70.20235917135217024461206133552', '71.31723260915226043290288261151', '72.81345288676265972989706621138', '73.06092378920626190735102275652', '74.41681547716470012943627602840', '75.65526684990854131800350643509', '76.61321035234257985793884971772', '77.92190734099853700741435899941', '78.598663705204472099390472720829', '79.34235721050324062517744518695', '80.560957496202649477974979774690', '81.34316187674274743110225352349', '81.75425326915271557983906878750', '83.847067526599157785468974379495', '84.94119866328996181995748342627', '85.643349476525743934755961361470', '86.16263157206891532543260203676', '87.61412302173664788971566780929', '88.32325891339299073259031938895', '89.519235240600517475511404581863', '90.071123777927137889969753827338', '91.36137534810101849939149538164', '91.998470033018191743979462828435', '93.3122518977438829929911854385', '94.62886656520474092206210007976', '95.46979192856116318704032724218', '96.51326128994692768084061836594', '97.20501801544516093222418985875', '97.79031125077076966229625465603', '98.697726622556098865994252015151', '100.13452281738627189410759621772', '100.91955645328741006864016052571', '102.08415911526720294449614287906', '103.206945041281251662807149768801', '104.13582888314060098223160880903', '104.77929333170076001138473705386', '105.65677738545400929826150476156', '107.21468245962185736159673317678', '107.74270210368799385672622498764', '108.25068023588129600183551678041', '109.31498361721364621339113559042', '110.28703058529242616646206550100', '111.995693131683044848043059436644', '112.85544996078046812559214181089', '113.45046442675563758032141237547', '114.41526218915906811487205460135', '115.31856345657649840284396563644', '115.906686502328785749107833106', '117.2565281724000034467871974585', '117.73064717892641141546051751492', '119.145123645090024791741574137842', '120.22093943828511696267736050104', '120.826932275363333759441989126370', '121.76591050784809589257449293135', '123.37715977692343771755529355188', '123.77976897972784679549799423365', '124.6138023008247174146839947625', '125.48574746734629123683293204905', '126.30045184821427149755406081545', '127.22471349897173928813652035021', '128.006366093186287316082540064181', '129.731370575883210659338009420294', '130.5340302106787055064765652661', '131.34872931207493689836866661022', '132.18294484175951993676065019660', '132.726618060814350042317756399525', '133.815108802754145176288997480064', '134.88827239949116904479875282227', '135.83563445041729922448041495109', '136.7082922634001523957465615267', '136.9400826603894966499039100767', '138.88260574524604361610525376654', '139.50685365010344567317125206745', '140.51322422116384512205736391802', '141.48269797736630276269847804948', '142.31500058944161044927574631643', '143.12152811850044281592855249053', '143.869587608772451303076067628664', '144.25358243129973074825833364017', '145.723716406712560295711681633515', '147.04921312969209815489805712458', '147.66098233867949346638190336640', '148.82209126097647057121160960878', '149.61108218661935526632390169757', '150.07760968494207780961476198843', '151.57694559880543360488286898026', '152.141644043499513883952825642685', '152.91012516074628173176907213384', '153.969668155285514520668951045178', '154.66070419103294227210818018386', '155.50279471219505674729315293918', '156.63094154410602589968597370318', '158.066352826938202476650054979770', '158.95542708077678571129104595366', '159.49221623141865826088953120377', '160.00011721351272316758279670297', '160.99936714444984815293982578731', '162.051193124569170714184376220821', '162.78200011235668397887392109327', '163.69592250729099530222180932935', '164.71424832029264073590287010770', '166.20007925133314648767322029367', '166.29464030138461315803750377148', '167.60403958736046975211301540736', '168.23540991351702389176040831477', '169.52642973882591135216370205685', '170.157609847146865749082982617022', '171.059833031231564451496267910920', '171.64351564738685781712435398203', '172.30318977612921075312522902174', '173.37620764784425339077476185073', '175.044584623541669020500843087357', '175.69335181851463443751960770128', '176.31329034127233982628837213120', '177.44349893534927334238553993621', '178.23254701324114169608628704607', '178.83416346314130335486342918530', '179.379397713006697256695495135797', '181.07408150817917532606911974792', '181.44429156980361641983839746333', '182.34943275254666040382212978855', '183.37826142177898692922231797480', '184.14718501855232172999588149044', '185.5596020824137833226239128272', '186.15404713550537980292542880720', '187.02635826270316944151439145925', '188.116092147063970632108375705711', '188.302458522623238060816626733809', '189.39291755342568359949446382256', '190.157013647219040065164418825904', '191.02431994676553571834304934256', '192.081981962981585492406070029960', '193.68721665993311907718379241066', '194.15137123314442132990517023866', '194.69116003743721010822955279098', '195.5500423502011609415863927291', '196.40678997592667868950418003760', '197.68813939951445642405579763353', '198.31830584259692192467458171266', '198.934924846032876845369810203297', '199.6622998443675684290718441525'], 'prelabel': '1-43-43.19-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.620991766168876, 'root_angle': -0.6144046239060322, 'root_number': '-0.351724544687294996486203138310-0.936103543773078035163890591708*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.307202311953', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.427511556448818009546145846833+0.374808131312487732819483311161*I']], 'z1': {'__RealLiteral__': 0, 'data': '3.83838507623', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.25453097317', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.76247294655', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.620991766168876, 'bad_primes': [43], 'central_character': '43.19', 'conductor': 43, 'conductor_radical': 43, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/43/19'], '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': '1-43-43.19-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-43-43.19-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.620991766168876, 'root_angle': -0.3072023119530161, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.83838507623', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_43.19', 'Lhash_array': ['dirichlet_L_43.19'], 'label': '1-43-43.19-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/43/19'}