-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1045.37', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9510565162951535, -0.30901699437494745], 'a3': [0.5877852522924731, -0.8090169943749475], 'a4': [0.8090169943749475, -0.5877852522924731], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.30901699437494745, -0.9510565162951535], 'a7': [-0.5877852522924731, -0.8090169943749475], 'a8': [0.5877852522924731, -0.8090169943749475], 'a9': [-0.30901699437494745, -0.9510565162951535], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.37', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.113', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^19', 'a^17', 'a^18', 0, 'a^16', 'a^13', 'a^17', 'a^14', 0, 0, 'a^15', 'a^9', 'a^12', 0, 'a^16', 'a^1', 'a^13', 0, 0, 'a^10', 0, 'a^15', 'a^14', 0, 'a^8', 'a^11', 'a^11', 'a^8', 0, 'a^14', 'a^15', 0, 'a^0', 0, 'a^12', 'a^3', 0, 'a^6', 0, 'a^2', 'a^9', 'a^15', 0, 0, 'a^14', 'a^17', 'a^13', 'a^6', 0, 'a^18', 'a^7', 'a^9', 'a^10', 0, 'a^10', 0, 'a^7', 'a^8', 0, 'a^16', 'a^13', 'a^7', 'a^14', 0, 0, 'a^15', 'a^19', 'a^12', 0, 'a^6', 'a^11', 'a^3', 'a^2', 0, 0, 0, 'a^5', 'a^4', 0, 'a^8', 'a^1', 'a^11', 'a^8', 0, 'a^14', 'a^5', 0, 'a^0', 0, 'a^2', 'a^13', 'a^11', 'a^16', 0, 'a^12', 'a^19', 'a^5', 0, 0], 'euler_factors': [[1, 'a^19'], [1, 'a^17'], [0], [1, 'a^13'], [0], [1, 'a^9'], [1, 'a^1'], [0], [1, 'a^15'], [1, 'a^8'], [1, 'a^14'], [1, 'a^3'], [1, 'a^2'], [1, 'a^15'], [1, 'a^17'], [1, 'a^9'], [1, 'a^8'], [1, 'a^16'], [1, 'a^15'], [1, 'a^6'], [1, 'a^3'], [1, 'a^4'], [1, 'a^11'], [1, 'a^0'], [1, 'a^19'], [1, 'a^4']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1045-1045.37-r0-0-0', 'leading_term': '0.819655058920500474527595999964-2.76006544543547673930390098527*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/1045/37', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.8792005276987744, 1.882634145782626, 0.6290602702748186, -0.813322051151368, -1.6069518317738984, -1.2268062704433826, -0.04004396434945424, 0.9336369938321547, 0.8841016501055903, -0.03712578468068391, -0.8185570721421604, -0.5648750357318912, 0.5276640816697225, 1.2261025093666937, 0.45596516971898376, -1.46982269051135, -2.925816152654949, -2.4838930858599952, -0.42572152268568675, 1.3957630984409095, 1.3940409407192647, -0.06774722738589717, -1.059507438747171, -0.30643549643442597, 1.145946264714366, 0.8797614417486096, -2.094197799832648, -5.75258666111012, -6.757447221507065, -3.9268777139741955, 0.2722712666060999, 2.0780755174061265, 0.28399212385783007, -2.591849778396102, -3.136210336314342, -0.7154481250743554, 2.08942641588951, 2.5977482008317048, 0.9332161338241389, -0.5792446948834651, -0.45538952191551596, 0.38452944448940746, 0.292840833925741, -0.7033034670556142, -1.0927206445182613, -0.28321995567678804, 0.3411308364484952, -0.5429661041563391, -1.829436456163238, -0.9625405593351196, 2.4841293962635387, 5.418337785230634, 4.568318172499732, 0.8289819766415162, -1.1401738907002623, 1.7543283891806525, 7.089449690197206, 9.448561493217387, 6.587624635726448, 1.7705130130184963, -0.41676665180271955, 0.6962616142658178, 2.0166308031964806, 1.3638423321021844, 0.08361226839962713, 0.3922103922729827, 1.7302778257983045, 1.52810521226138, -0.8136409829720802, -2.6796805209182772, -1.7415415055337276, 0.7404199501033946, 1.6065735895482836, 0.11542097865671982, -1.2781551473294832, -0.6842473200835734, 0.555419480503611, 0.21849688536495757, -1.1212080173678243, -0.892787215623817, 1.2308437375391834, 2.3117527324566622, 0.5022423577478394, -1.525831405964593, 0.12551980482922623, 4.503170410257074, 5.8695270072300305, 0.8989816372296523, -6.35775318195795, -8.847398862134229, -4.8613188670404455, 0.45374436677762064, 1.9402494186849437, 0.15345802177575293, -1.0406297511899942, -0.3486208479055486, 0.13617118610766815, -0.7904791483774558, -1.4437202308046837, -0.37938048517681666, 0.9594909180409907, 0.601447422997271, -0.5688276367282628, -0.257843051328928, 1.1192741182097894, 0.685329948753274, -2.0355820221571026, -3.41318495741738, -0.7695149640824337, 3.0272021237608278, 3.019477282563245, -0.6622235832781491, -2.57396139230586, 0.42049866309798983, 4.6285549086938165, 4.815075936691337, 1.5295684617337, -0.251231412345853, 1.2338780609747275, 2.2749819460666068, -0.09018102999500892, -3.295488719552811, -3.2261449842708108, -0.5084292892034898, 0.6865263273751514, -0.8453884718903384, -1.8355775637755696, -0.08198762959529154, 2.050900773972667, 1.5661364390190509, -0.46553510821372546, -0.9505752672482279, 0.19800724560704175, 0.4140452176868788, -0.803979851055015, -1.1594792011512132, -0.005157864916415104, 0.1873989800237833, -1.4426673756253885, -1.4345322033227912, 2.619846230616728, 6.404301874173159, 3.31261876115999, -5.766789962253734, -11.940825986286884, -9.223713486797791, -1.9182390089672592, 1.8046343685280664, 0.45832746263494684, -0.8551643860163383, 0.7326756194971664, 2.3770077948244164, 1.3367570351576519, -0.57286443910213, -0.6562074547557444, 0.15386727796994343, -0.34403601989627797, -1.2862638516094869, -0.5222953995683168, 0.7976770002607165, -0.381126333560292, -3.381599734278074, -3.916942649369106, -0.7389932360945904, 2.0143419826080153, 1.1388115165529293, -0.8167970667201723, -0.26841126382187386, 1.1193475695973585, -0.5262823156008472, -3.8705397002164714, -3.6081593478697487, 0.8072456905749107, 3.363682423199701, 0.4367590995693608, -3.5314465211964636, -2.946589716295553, 0.3551380523275165, 0.4902986504195955, -2.895187708301389, -4.3545192683478815, -1.6155413324343522, 1.0405202787228722, -0.06002849368120113, -2.520597093514168, -2.469558034090422, -0.5996715715172747, 0.11305966588575928, -0.23993862618815914, 0.3244363213902693, 1.1394087262625647, 0.0993152321302728, -1.6568763464085725, -1.0712586442081586, 1.0895196433052148, 0.9800659178227127, -1.1132281429240012, -0.00561078055738942, 5.478299886342854, 8.408941312059929, 3.182938781484028, -5.157295122741029, -7.084862483122594, -1.7314985575557238, 2.784270311030676, 1.6003592160383366, -1.281685362970878, -1.0926527290370835, 0.6011742644256685, 0.3954298221073, -0.6379375781453195, 0.09528287618913858, 1.149803162824356, -0.2969984728103431, -2.6045132616029147, -1.9324125635616474, 0.9570749778050691, 1.657564823915911, -0.5058977107156944, -1.6335745005504283, -0.31337270250885124, 0.15194682408813875, -1.7789538332732822, -2.7405972474004123, -0.602530094084338, 1.4078070323212117, 0.5800769820237588, -0.028784481225969015, 2.7195682449608043, 5.216224027085452, 2.5199975980376212, -2.0879193917726564, -0.7141005781394443, 6.514846307705627, 10.430288435781529, 6.077791628357086, -0.4411400870264936, -1.771122493626089, 0.6233090893726491, 1.1197761912338569, -0.6048868231221163, -0.9384217922831797, 0.2792213116362007, 0.17751101022832244, -1.1293603463656001, -0.9607539031207082, 0.408919167589296, 0.2754665101887498, -0.9664252765402697, -0.45294231883813885, 1.2049187524178921, 0.6911214311509892, -0.8994212430190516, 1.4731363045788364, 7.461009580972415, 9.59057875955746, 4.380287220864375, -1.486885216463963, -1.1826114928028884, 2.010493660176519, 1.0529914946819336, -2.996259377237484, -3.5175667515957265, 0.06326149553368006, 1.8405546165361972, -0.10990452623970855, -1.2444078264183456, 0.5535993690147838, 1.504135975175321, -0.37492423359879834, -1.3251887636941508, 1.0434401772431017, 3.0752261482053647, 1.6034926355856534, -0.41213579561078584, 0.5805080200602292, 2.435275733207967, 1.630157453038223, -0.3414068516833105, -0.29085954301076355, 0.6537724530101021, -0.016926940914209317, -0.7232984327728841, 0.593340564120413, 0.7565614030445851, -3.493856500725854, -7.37803849827044, -3.7386467072480487, 4.376342091805162, 6.28351846847961, -0.38376569526585574, -5.885329946418357, -3.2973292256358784, 1.9827562676144768, 2.3666115442260374, -0.4950521605673581, -0.849127293821261, 1.0418430809800614, 1.210612906054302, -0.10311333177094646, 0.021447374317125227, 0.9495466421030168, 0.3050739674542516, -0.6855883808860974, 0.17283025545049735, 0.7528556974859383, -1.7130899392316374, -4.271004836328796, -2.4325692160905255, 1.5442566805678446, 2.0018261250129257, -0.3056859143516606, 0.0832531427389343, 2.9430712849559857, 2.7355626575788263, -0.4769047376562073, -0.15633122940249167, 4.832274733956286, 7.073255140252078, 2.78390265434801, -1.9158450965072493, -1.6004170852141557, 0.11467215494220337, -1.2565612742179826, -2.372180057956002, 1.1411354480413152, 5.573189184306337, 4.882925739815471, 0.8267908152766272, -0.6166916808049493, 0.7663404802438445, 0.7908004263762779, -0.7573907521640422, -0.777319772661741, 0.37386497505287236, 0.014615813173279113, -0.9056644144038348, 0.15292770926974958, 1.4878081904911649, 0.29792915853655005, -0.8998158507958689, 1.3845219770545056, 3.665180532405409, 0.8662162786967595, -2.6815920193375087, 1.6893978604234117, 11.537207337807097, 14.497719929650556, 6.553804362079022, -2.1247412794989398, -2.9208788289630956, 0.31667977252487134, 0.8609217463408839, -0.29273761844775686, 0.29953680913841224, 0.9190421800392563, -0.7833767167869857, -2.1583106290405087, -0.7545749324771878, 0.6020119741838695, -0.465584151364963, -0.8929855992787568, 1.6117861542112257, 3.3514144294344743, 1.3582703827704437, -0.683935675949583, 0.7578628213398445, 2.4031400652496804, 0.6842850665627686, -1.1872902030016497, 0.394783166792599, 2.0870766404661976, 0.15581129175304376, -1.723964680359661, 0.4621464505279268, 2.2585787043318817, -1.5088433843609672, -5.703251952369813, -2.3749109506118993, 4.998742631747702, 6.308524792197144, 1.0480937380172484, -1.9750217552197906, 0.2738645193464367, 1.9024681966002448, -0.010763614339113124, -1.4221305191752993, -0.37619988193570597, -0.1526674027150099, -1.7552461541113886, -1.9515063124551393, -0.1640548608856945, 0.5297817866644832, -0.12662157888326273, 0.3022591505661264, 0.6958815562832232, -1.667796589023928, -3.9588971207822024, -1.67133135573534, 1.6175711966229058, -1.2350378724665187, -7.466248687835648, -7.1483324540333975, 0.21330523549653, 4.2594020426370065, 0.8010681083474561, -2.3681191737077163, -0.02439650133390839, 2.4821358520201144, 0.6025790344810701, -1.4196889984630627, 0.2919714976410945, 2.124187337015588, 0.8521618820352497, -0.35380707621044727, 0.7799574442439443, 0.8910849123385054, -1.4059755500155118, -1.6006522762670359, 2.0936913047416836, 4.449168268372786, 2.2820020724767107, -0.28561536752001904, 0.036441461912072606, 0.5222146230713516, -0.5831360966503774, -0.3789615274223285, 1.5945106508179367, 1.3884889628800512, -0.8446152392270282, -0.020739593209513397, 2.963718841597215, 0.5412662810145391, -7.19328633017962, -9.537622539818791, -2.286074615776864, 4.351418968755616, 2.0872108393969917, -2.854082930755683, -1.8798048579567093, 2.0004251593641733, 1.7921704391570668, -1.0334180292709025, -1.276438592448352, 0.20820367712525603, 0.07530084151860014, -0.5469266675014223, 0.14676033423686372, 0.0771091948041751, -1.6585429286046103, -1.8189241775274558, 0.15204379748098681, -0.09315193649354815, -3.094718970608615, -3.365893655452741, 0.16859718908900945, 1.3247187960139144, -1.6077541884044049, -2.144128976759283, 1.6453469755032193, 2.3629384250353076, -2.975396459480084, -6.348916638660905, -2.616833499230855, 1.6453484395373228, 0.4918732787412272, -1.5258726060944698, 0.44758230113811803, 2.4087442574799214, 0.5464471191656998, -0.8130960330137506, 1.6982887835951728, 3.1186602167571604, -0.405469682824399, -3.931438690040863, -2.678607502009796, 0.009983438141459959, 0.11150735260830527, -0.20264488843741135, 1.165913380066536, 1.554651153243457, -0.025229039447703976, -0.1648568767796152, 1.5730755226013144, 1.3103551783540301, -0.8302653345381604, -0.7733531738755824, 0.12059315902626833, -2.7914358035462095, -5.351992216677225, 1.5449533080182185, 14.387781634611654, 18.3609069485405, 9.469982245889714, 0.4077017437863737, 0.18861986208604292, 2.7806979723863963, 1.190597195180779, -1.4082067485649994, -0.8754930704234463, 0.0378162175403993, -0.9413299400406298, -0.9585120050622845, 0.7343301230606132, 0.5756268751072215, -1.4804117755301602, -1.4032129995939413, 0.47756057194349866, 0.17823722482914822, -1.067958684661076, 1.0356432311531807, 4.123289760241654, 2.553688408338691, -1.4662828677706092, -1.4839046182532993, 1.2270931926401, 0.9958135194219536, -0.5883024439802403, 1.3190491851131474, 3.4626288809296186, 0.21064258613493944, -4.001890004278122, -1.6173825492876683, 3.4319373017805166, 2.1800542366719635, -3.0488900457408907, -3.228155166694279, 0.8985621332146222, 1.3947002183632624, -1.7416390236009007, -1.9713523191374633, 0.7186701233355647, 1.0120033462553875, -0.8031290347292531, -0.5346538143981697, 0.9573201001976401, 0.40608215342608317, -0.6999497042881333, 0.040096264334652715, 0.50905934376131, -0.6678725843077531, -0.6049174666392557, 0.5467901539895581, -1.9120055145038275, -6.516923793158088, -5.021451377703477, 2.3246129484933, 4.298716767304206, -2.548981151263244, -7.242549580368894, -3.3162531448659145, 0.7343399553307366, -2.1971328838364306, -5.886347391155619, -3.7785559707524072, -0.22525057912595997, -0.37103041457683344, -1.1773529897129544, 0.26878648266146316, 0.8947412072721882, -0.41093597264484916, 0.05542387731565449, 2.090421792703794, 0.9860461414659124, -2.4272918524668636, -2.399834865641312, 0.5663109698690607, 0.6429894817463845, -1.9599251447465686, -2.0721517413574677, -0.06660943333377686, 0.0015346995375763624, -0.6237979712355506, 0.7227765124587493, 0.44970358457420134, -4.046590099433976, -6.436195089250267, -2.1442381712355005, 1.6368758358100666, -1.3958302374441085, -4.067279559051451, 1.124130471896808, 6.955618602679682, 3.7624860602735906, -3.3992225642063834, -4.180322768460422, -0.16782610153080968, 0.8680321878157166, -0.7447494524790785, -0.37344318734197185, 0.8391135721420813, 0.04004048960501729, -0.7943490147057886, -0.09819953673742558, -0.4637945661942216, -2.0667436384371234, -1.3780052217569168, 0.777257656035837, 0.09856381069880862, -1.5965705102976533, 0.7425140464691835, 4.117303648999014, 2.1925562163239753, -1.3674669429934179, 1.0915873852455251, 5.500073988274909, 2.3719744600585435, -5.107687681221526, -6.023552091314594, -0.8066973041875537, 1.231177560521664, -0.7838295866462722, -0.5625594543946044, 1.3263944903784644, -0.005351167590493448, -2.1726437542848935, -0.37253868534974405, 1.9525984083717278, -0.25849544511757633, -3.294018978101383, -2.0014259835960484, 0.43356283439201426, -0.20403383917210324, -0.9236730814037244, 1.0602610182882466, 2.2082183494814074, 0.5920730853278298, -0.08751348232524828, 1.0673869436982828, 0.4275313636717647, -1.3167361935581696, -0.2082729840563728, 1.4782307524022507, -0.337439510353471, -0.6488573619763532, 6.126648822657445, 11.495123933854014, 4.118612534250291, -9.16575239288181, -12.080588786221652, -4.097452822167302], 'positive_zeros': ['0.75677752459343166378909366639', '1.88491358234420071253531288167', '2.80148994348870401926312997289', '3.61009542318800367159670480611', '4.45891268181837633276106106837', '5.683739782615391372425872481791', '6.54918877264244375831244439354', '7.24972551857564788377367541160', '7.93382436031955762715622726740', '9.35151396926867081496144280853', '10.02937414664271471896716417731', '11.00738797761297677022232414805', '12.03338418523844062189648200192', '12.65763009850331153974167238718', '13.22837339150553860566652085628', '14.15157553498441690911696683714', '14.5578261615403308916832418424', '15.41726465225467089481723569694', '16.638080231705663280874383031964', '17.05875376999360162681667040004', '18.62177645176403811962580749910', '18.93397983256259610647448090474', '20.0480152774453119416732401123', '20.164370189628898805171126784329', '21.15581861735395640753869435083', '22.08961141799327346759266942100', '22.830939044357431567983274264738', '23.587421028925708816690533036522', '24.11444214046799900451703674307', '24.83369647019424936160449983748', '25.683270327299610822231124258', '26.239336646339996446699839633', '27.22510261650061099808712818245', '28.402818769391090830959315673407', '29.08601947416849681688319793150', '29.80956391116699070012878491070', '30.08244422755643279671059042673', '31.00932534639703969858899016257', '31.707660642017691979105131357851', '32.24698589126496953853981065108', '32.90624948673918142629931005921', '33.806957135677061867127284964510', '34.635057469883025474474597803922', '35.28382461573648059289882939206', '36.44179397253145548631712598185', '36.66973672404833575067711108577', '37.49215006225097325185683977286', '38.50431598772073257969187945177', '38.92681129149294599191135794909', '39.69727735564105029935359328763', '40.54637282420475238408338533671', '41.19712076454944564746453684096', '41.68629588252820851316896899277', '42.50139389478583905696957014248', '42.862912769002115743891920934644', '43.579377696573817139038087433966', '44.49976441899119594645689694195', '45.72961168056892886231626413264', '46.31447544386527306644666175759', '46.77379883093225280658542946294', '47.69805453990634604673266454143', '48.350206239651462799883984017839', '48.641622891598556344920090806729', '49.47460471298215621809592349540', '49.9521150002237062823055582261', '50.99860633298879894808374201670', '51.71770657022377154094022883464', '52.23489025825852837633752170975', '52.759351061789545028490761216991', '53.697496166788858130823122209756', '54.40390076641062518394583217932', '55.27169254269587905454721636519', '55.68306081589177540259205230193', '56.71029699651311903624453081240', '57.18020094923043035301273446107', '58.28351806390767220923971987431', '58.54372852618658548119682026850', '58.958400163637081639614062400414', '59.70331980036029371812359322780', '60.4607483939553781112968329614', '61.07940985390920772691916015124', '61.562950882448541801629511238669', '62.61207533326224763897358849047', '63.52529325411542603047757575050', '64.21429590787351127077431058085', '64.87033229956450594694990453130', '65.41003960381417332175798434202', '65.91728726453214857766404721164', '66.52542391024548870926317547993', '67.39301217756439001644470632399', '68.06035027415913424383302633254', '68.81927417739561530606714810236', '69.10360300447380679128285841788', '70.06672183803839104168559772244', '70.75733684979822355542418857511', '70.94566772062108946263518773002', '72.02597159741359332162546005612', '72.538585033334473540156812279434', '73.72130373062506179884157226029', '74.293923192579863665521754224662', '74.89274442632337260274119228296', '75.54738558960410267232610448970', '75.983093816510464770850587033', '76.77038705454388817659251094997', '77.25504740167436978663888627232', '77.89225462675188544935201734413', '78.54708165438083917625234058903', '78.952359552170936087875494471311', '80.20560573056663943150891823694', '80.73138964023678757082194902525', '81.33355581692936253808853535009', '82.18215368793152247015934888222', '82.79855148194971333219947330071', '83.360899772023245138739876783514', '84.012064169127527409310937645718', '84.58088625104070016182378936342', '85.52183196207481578563360484942', '85.845962616440752558999893674026', '86.80333357373689002792612395143', '87.26663353496341046418873907140', '87.80834383945381011960954072262', '88.32938536578879030861772940213', '88.83526832481797992109723541255', '89.82837390395454896129562786825', '90.61024993653192823707073402121', '91.4270711525257108781693679819', '92.12644467027439399689067606657', '92.64266961347231329191163288547', '93.4053113464479443278833921444', '93.74325071093339089851901471997', '94.44468245484309712572838118825', '94.9618746536865031863354891254', '95.45206262144983170042833281198', '96.42869582640155877740489112694', '97.137927704334134588729337634182', '97.48898758102118842822430825730', '98.38466775087202681379237027848', '98.76381092625674203075436155909', '99.84086497466624422980376364487', '100.57032564104582806420829828782', '100.72849511512973257651604043074', '101.491495258607742643757807233968', '102.5867799817949887070814846527', '102.97044386764072762449015646498', '103.5949429806523582995651127371', '104.25566345988572665841425133258', '104.69137274104105195198385239622', '105.28646896571450563072450777091', '105.98313913227086218654865603562', '106.42558770553689144718873204036', '107.24339391034995609371873093885', '107.7470684774878536993537692189', '108.961210747522784328929607378633', '109.650390414366086808285259082410', '110.205516059232923707590591549731', '110.54762815698160457461356015482', '111.14060166877767480086821413265', '111.99288197561589700153821995561', '112.40685905130843225793806150964', '112.95552041657659611044969344070', '113.90403941482326176542882484386', '114.274754998987963815092134051924', '115.078503680435820655252315132002', '115.57776264717006598411764897889', '116.266196485499915103859396103555', '116.83140334131225147682356472424', '117.412886954896187287543582717353', '118.22263219269221539102181085992', '119.12481008455835112188452438540', '119.6602531493690066216316972722', '120.31116269902394166759905947239', '121.060578455722394472919413389834', '121.19082572067777578139194006077', '122.21874397623276835321426667802', '122.73885612025889049967676083624', '123.02057953208914089533047397981', '123.5735423085739712129187021151', '124.49938225274211847986478406812', '124.93057191913250807185672860451', '125.92871249032338957505063177031', '126.61342085634136151678367874150', '127.18950648963891600602287156978', '127.87402335208639801488357446622', '128.40422866079636194923538911897', '129.20824332332898851291702757343', '129.51965294294808045498715085064', '130.13593502084838741369132671844', '130.782237625755533923229080067871', '131.81336069647593788144993223108', '132.17722489306091868864112927104', '132.666090311630128139855156880386', '133.19123621502368887457735964829', '133.932648835183726408960533799231', '134.37718251415743541665704896922', '135.02567796075670098698894486560', '136.01692044635553482880418414540', '136.6750896523707951694057442446', '137.325788314355737287253238329797', '138.00034792495175731194157949572', '138.692036790108170806563334931302', '139.087947770202007405823890191463', '139.63597527920076897659279496675', '140.01900375406022266894866022906', '140.90991727805699974688765570316', '141.23664805235826172238360329984', '142.172572907122524212591646748646', '142.66073858689896812965893199547', '143.313338453792302006939728292751', '143.91221269416328049341305564242', '144.840453289501559649986829080659', '145.364297377862014119901838401212', '145.89249898740477377631882383633', '146.62745111164347759981428026104', '147.017636346324999271518178313148', '147.786187229970246442850834677399', '148.74798303773015225218437585504', '149.104959285468917564491172287', '149.445991590177273362984943498005', '150.30717589688841326654941319656', '150.661074728477615465377785953594', '151.4327213022978662275822567951', '152.04865377162179807871102425396', '152.226457526065845819702198669625', '153.08288576339142034097140108245', '154.40496972604645199923912865777', '154.666977392359883409485157989574', '155.42736646071580934422622937079', '156.16908819132619749513540837216', '156.2858384090187715539075553086', '157.05202770542033589198033693402', '157.59127559788712743168516637414', '158.34457232960425974327910903528', '158.78373104547394229573555529709', '159.27874237793767761943021111952', '160.18363076517443720353646584026', '160.786322449618417856423069625376', '161.40161251584815290376729927528', '161.73304169388440006877358042860', '162.51225426087518783812825578396', '163.21311543798957395202757884707', '163.87524586305409803145733217721', '164.61393368758476333287749415060', '165.14319267976899592137022579776', '165.84898347329020087172872582460', '166.41649584932826824794482548184', '166.97302806150549172634498499264', '167.58466608697354877046992552429', '168.11460426312951012421678688599', '168.59178520569419647154392734313', '169.19190796517792251155314293459', '169.5238126659853071070744966651', '170.52623621330692432922661604594', '171.15291560778540207088674162366', '172.07559354359875663222174223777', '172.34428006127747266893991772477', '173.48453685634694083467866058017', '173.65585006503181813990442102845', '174.32845975685069762811327772757', '174.9012669791667038416761360970', '175.30344274603801078995948639343', '176.026088870671399141679553090614', '176.807879228470377539667935745118', '177.270039354214839606662176817207', '178.14018897005071816581752935144', '178.43798285219270966785005069235', '178.92851598831086921971503447977', '179.42036676117659756605846575101', '180.43507936942720369320567696165', '180.84525931598523213085115451604', '181.5164451389576162978026866570', '182.33895379899355702674680502039', '183.140929916280523814998484553958', '183.600289018781378670664577618', '184.1371580474867239125471025815', '184.69628488583204639863993954193', '185.37052249899990184974840985687', '185.47473471073382002043247381059', '186.429153736040429055462860981687', '186.888929507090868792034520119316', '187.44164148026995330017601585197', '188.28130397961289822491238828395', '188.67988337498261162141715913917', '189.47054262907607926880067546252', '190.36859614089141849739570476097', '190.822417095849061812652149961969', '191.330560351427821069914227242359', '191.8744111165315113679082351069', '192.53510634750711104603496637802', '193.10398426606618675411369807207', '193.974576771123847602499965145814', '194.33444626426984810524976612525', '194.8646610023038289585294167365', '195.74862885999012048459966823256', '195.97072671656466916327305650006', '196.627938005211587129735822099771', '197.21425995223156121196625622395', '197.77309100264548663392484879794', '198.175780184264008198369410304871', '199.15498116435821590300884093169'], 'prelabel': '1-1045-1045.37-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.8162243346208732, 'root_number': '-0.837912913260305516403854005021-0.545803948127555892904722397471*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.40811216731', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.51896917312065286831126756972-1.29228327979491688573626393936*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.756777524593', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.88491358234', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.80148994349', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.37', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/37'], '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': '1-1045-1045.37-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': '1-1045-1045.37-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.4081121673104366, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.756777524593', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1045.37', 'Lhash_array': ['dirichlet_L_1045.37'], 'label': '1-1045-1045.37-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/37'}