-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_6223.891', 'a10': [-0.9888308262251285, 0.14904226617617444], 'a2': [-0.7330518718298263, 0.6801727377709194], 'a3': [-0.7330518718298263, -0.6801727377709194], 'a4': [0.07473009358642425, -0.9972037971811801], 'a5': [0.8262387743159949, 0.5633200580636221], 'a6': [1.0, 0.0], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.6234898018587335, 0.7818314824680298], 'a9': [0.07473009358642425, 0.9972037971811801], 'algebraic': True, 'analytic_conductor': 28.89949050399846, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [127, [1]]], 'bad_primes': [7, 127], 'central_character': '6223.891', 'coeff_info': ['x^21 - 1', '0.955572805786141 + 0.294755174410904*I', '\\\\zeta_{21}'], 'conductor': 6223, 'conductor_radical': 889, 'conjugate': 'dirichlet_L_6223.1334', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 'a^13', 'a^16', 'a^2', 'a^0', 0, 'a^3', 'a^5', 'a^10', 'a^16', 'a^8', 'a^6', 0, 'a^15', 'a^11', 'a^19', 'a^13', 'a^14', 'a^18', 0, 'a^3', 'a^20', 'a^16', 'a^4', 'a^14', 'a^18', 0, 'a^9', 'a^2', 'a^13', 'a^19', 'a^8', 'a^6', 0, 'a^0', 'a^11', 'a^1', 'a^19', 'a^5', 'a^9', 0, 'a^18', 'a^11', 'a^7', 'a^7', 'a^11', 'a^3', 0, 'a^12', 'a^11', 'a^1', 'a^13', 'a^5', 'a^18', 0, 'a^6', 'a^17', 'a^13', 'a^10', 'a^2', 'a^0', 0, 'a^6', 'a^8', 'a^16', 'a^19', 'a^14', 'a^12', 0, 'a^6', 'a^8', 'a^13', 'a^19', 'a^17', 'a^9', 0, 'a^6', 'a^17', 'a^13', 'a^10', 'a^17', 'a^12', 0, 'a^0', 'a^5', 'a^1', 'a^19', 'a^5', 'a^15', 0, 'a^15', 'a^5', 'a^19', 'a^16', 'a^11', 'a^9', 0, 'a^0', 'a^20'], 'euler_factors': [[1, 'a^8'], [1, 'a^13'], [1, 'a^2'], [0], [1, 'a^16'], [1, 'a^6'], [1, 'a^19'], [1, 'a^14'], [1, 'a^20'], [1, 'a^9'], [1, 'a^13'], [1, 'a^11'], [1, 'a^9'], [1, 'a^18'], [1, 'a^11'], [1, 'a^13'], [1, 'a^13'], [1, 'a^2'], [1, 'a^19'], [1, 'a^6'], [1, 'a^13'], [1, 'a^17'], [1, 'a^12'], [1, 'a^5'], [1, 'a^9'], [1, 'a^19']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-6223-6223.891-r0-0-0', 'leading_term': '0.0281373706697317497959375655460+0.172087378637973347493032176606*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/6223/891', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.1743725251141795, 0.8768266939769738, 1.0522329897424967, 0.14179323109436537, -1.097196430883667, -1.0213818071096434, 0.5417164224304857, 1.2463243530656225, -1.1777038618452376, -5.171016827300484, -5.737981805079404, 0.011434353140874652, 8.423047270529429, 12.322600856427588, 8.828434244744374, 2.4092371299695765, -0.7985617621948281, 0.04804213480413198, 1.1492193312066332, 0.2974751186850737, -0.7471376282225112, -0.3058708639833069, 0.2519775235201549, -0.5345622883604165, -1.0418733917979375, 0.700485328130048, 2.9027362755711774, 2.2919284500565436, -0.32407538529457736, -0.8890753321475553, 1.2792745601150288, 2.1655296557537493, -0.19575685697076453, -2.233585540226834, -0.9560270879108139, 0.8176489814082804, -0.2722590300878644, -1.349005305136453, 2.1750861955086096, 7.604734103506692, 7.711324762835488, 2.1089711496386654, -1.6742108842677286, 0.14679538581789478, 2.5003253399106944, 1.0464967067866486, -0.6024532210273562, 1.6898920381249567, 4.415416433600161, 2.339209405177984, -2.2247638113214956, -3.277677704903286, -0.8474880275210739, 0.39520661575693034, -0.3554227957720566, -0.16677082613523023, 0.9114523788766716, 0.3704992358699775, -1.0069380053859427, -0.6734143219886415, 0.2138667758594887, -0.3281761304241767, 0.5659404443556397, 5.401011914959653, 8.480352942914454, 3.1515211324609, -5.40090244340068, -5.961315635580532, 1.1761448044680707, 4.791401786638408, 1.0879679018256898, -1.6900658697334683, 1.056958567175276, 3.28244018005933, 0.7802398025254349, -1.6787326870217896, -0.46148882350390585, 0.719710983174666, -0.6164003288162759, -1.0727609538730052, 0.6508989862948049, 0.8122919347365676, -1.1745956717660961, -1.2007668485589251, 0.7168158267130058, 0.0060138298354030055, -2.8215300219252026, -2.5490988740967406, 0.2495484833032615, 0.022166780014141685, -2.7400359332916535, -2.5944871956053124, -0.06811223049932787, 0.08159406679136876, -0.9404259778461308, 0.48860508430844474, 0.774406403648452, -3.9566073242394673, -6.800769738510037, -0.4650574193647847, 7.472040320887551, 5.41633708197469, -2.450486588399645, -3.6294098082151858, 1.6899897592488262, 3.6447878839732915, 0.8858689985508941, -0.14102744628694264, 1.213259501827188, 0.9805900421773869, -0.023547503822668354, 0.6139482566341398, 0.6626277276642074, -1.157605790066426, -1.2635644131784998, 1.0215423623652127, 1.3630998259492648, -0.4150521203530126, -0.28017513193206356, 0.13056676717918533, -3.388738984158148, -6.5013397158497375, -3.1018801451176348, 1.124054041072867, -1.723015640907529, -5.216408536563473, 0.46208523281703395, 9.108406728363606, 8.662385646323894, 1.9358948965307905, -0.7831644569909996, 0.031329435642942834, -1.1990332937340729, -2.1789450126644385, 0.22939885132979698, 1.6589843535908895, -0.04573221888940315, 0.3144296835178454, 3.3420729180384177, 2.519802992414845, -2.060379309072924, -2.9200565650513104, 0.42517905818568474, 1.5774848555120773, 0.07222481068933914, -0.09942387630912454, 0.09645071401021935, -1.024476511114978, -0.3412814440538762, 2.1412414499383834, 1.3642895491953535, -1.2490528152145162, 0.58491621202416, 3.3151404835064158, -0.8330035584443494, -5.701493539017421, -0.45078853328061325, 8.130452614859347, 6.146934811648667, -2.1030739216328325, -3.0689104113787784, 1.5541609574011397, 1.7296654217922962, -0.9688422602553943, -0.056739931137247124, 1.694956759927051, 0.17064616551349798, -1.192063706088615, -0.23790478995563719, -0.18585531250685836, -1.0164515590425056, -0.163829986487311, 0.3408321723432651, -0.41248952634109587, 2.4644187554478703, 8.307885354864409, 8.303911330748358, 1.9308052484886207, -1.2529035774721817, -0.03432538430576676, -1.7055085341484495, -4.638585631975591, -2.319044329013704, 0.6804603833169925, -2.0573801424995692, -4.058666587656989, 0.3983072089572657, 3.4529340358444105, 0.5746054278324307, 0.48977986318523803, 5.940563940323694, 7.082800478545375, 1.7942240564518894, -0.7611159371698073, 0.8704106419962746, 0.2992915602870323, -1.2321853114575139, 0.7430257524576791, 2.359204681163485, 0.09696548134066335, -1.2769061179531858, 0.3410853020367016, 0.5074229878695786, -0.8006884446124676, -0.09756459453747035, 0.41005232382959106, -1.3009870211799845, -1.222727673633639, 0.48275464008770447, -1.057501767584484, -1.6463087384742467, 4.747272246906557, 7.615041195234889, -4.4806285964991845, -18.343556838562574, -15.34297455385524, -2.923646001975082, 1.1503612147939133, -1.6056803538965536, -1.2372175430275403, 0.4941182780354815, -0.2607033113751803, -0.05940138170009145, 1.2139553937145386, -0.33006061110899354, -1.8804282926392177, 0.19517586577904994, 1.4755364930417711, -0.0829379943316598, 0.8905073056582851, 3.925780019348909, 2.7184070188036737, -0.5081891272454726, 0.10788495741382345, 1.1556630641721295, -0.8502836047177235, -0.839349524195628, 1.7146908352967176, 0.2509519163865517, -2.8333459161151, -0.4336738025871533, 2.0342928981464987, -2.304861770842424, -5.328695432564577, -0.8395151054216401, 1.8061880747396202, -1.3368110343518698, -0.3624445824750948, 4.908110941760226, 2.9290383653725516, -4.398985769104349, -4.83941646204936, 0.015158444118824157, 0.6977810948160582, -1.072421558540987, -0.2497972401586357, 0.31909111665810647, -0.8374733423694636, -0.5668513932616398, 0.04400852966860766, -0.7886374559233789, 0.1382891549429949, 2.1655253222249815, 0.6998722729189277, -0.5940632770083241, 3.0484870460958593, 4.317808626309596, -1.0553588219206809, -2.2268961803467615, 4.375710241673603, 5.645142793400091, -1.0612038922173257, -2.7255309195191626, 1.0129011651531268, -1.3706900198857164, -6.693145575189198, -4.294092621530217, 1.017048154228007, 0.6054732483409349, -1.1793849280993352, -0.09260511649731, 0.10640817252611916, 0.15219877838815973, 3.202482007893095, 4.214388602071116, 0.4743185650847016, -0.9681900456513616, 1.220151138328806, 0.16708198937421742, -2.5980970532270624, -0.8490602274361421, 1.6182160192460036, 0.12573345213595535, -0.7943348269149083, 0.553069191553841, 0.10537740583110004, -0.3544012374739345, 0.8215197831268165, -2.1923962113682123, -6.400750840583283, 0.47788359749180687, 12.412334948137314, 10.245340824578344, -1.977626583727964, -4.253799501514277, 1.9894541308353946, 2.0326712028710676, -1.7577339149852835, -0.4977939318277592, 1.5471573736521067, 0.15944409108293167, -0.017801015384770125, 1.0600574379656265, -0.3498417665983445, -1.102340258301217, 0.8485926195875245, 1.029009941667812, -0.13684053702469892, 1.2647926822521094, 2.011026669695951, 0.1419704138229564, 0.8480304567918063, 2.6608294774029035, -0.1981015269715068, -0.9461960419426751, 7.027853934999103, 11.988459364785934, 5.453274311717552, -0.7665563326130036, -0.017287732557999588, -1.708251332200101, -6.040709948355811, -3.4225597527261247, 2.0611291420336797, 1.4666172145498284, -0.31635800095883676, 0.8204742144532697, -1.1262630535763634, -4.202716111677378, -0.436409328458496, 4.480482935187881, 1.9039439659391353, -1.9092076265122735, -0.6530993804395626, 0.42553606259202936, -0.6672107606982076, -0.12617302077745984, 0.040764602384066866, -1.8963331755935904, -1.4783791450598118, 0.5604076936277324, -0.06167415304688122, 0.48284791805199945, 4.0456609224131705, 3.4290347260336596, -0.21295472161390028, 1.1291539805368285, 0.8713390362755078, -8.53769027238616, -12.658874458672235, -1.3748196781746542, 7.527780895780638, 1.7945853182356626, -4.064939165062977, -1.1501625722625135, 0.5089429064728771, -1.8084236134617322, -1.177931943751144, 0.6702577707225498, -0.14049748143310548, -0.4089767159555936, -0.003199342789790491, -1.316165054952363, -0.8966462658454739, 1.2585827059212136, -0.5788428987329853, -2.7794872784259312, 1.4862908621859081, 5.352491953346134, 2.103477754132104, -0.838110640108451, 0.20430447612226665, -0.8054885284189858, -2.0777526927232346, 0.5907025244886249, 0.5420689324729154, -3.1524132561350187, -0.24827643428688473, 5.917932081426123, 2.903340836338645, -2.7582725092828353, 0.5618798437666112, 4.278640597648208, 0.4180428513218686, -1.4070309004530346, 1.8265333345365224, 0.8793727087983674, -2.566626469796715, -1.1493043152042834, 0.4295277536717822, -1.597072029072509, -1.078609596325549, 1.884390845321663, 1.3218103083628256, -0.4134898542178904, 0.11536247464450347, 0.03344878501120831, -0.21160769451910688, 0.9153527106748464, -0.7279530182657401, -3.4002276154531224, -0.7425089087072174, 0.5515778777072171, -5.777831004718685, -6.068278232022026, 5.853696850965349, 10.344717089069299, -0.2246930569596139, -6.479049131718272, -1.5349552965836293, 0.9048129655301065, -1.2014959935456335, -0.30085408669187086, 0.6133282388800645, -0.5190656473407937, 1.9653973916799359, 5.185916218124134, 2.776461608605403, -0.1704608983736298, 0.21586514789283387, -1.0072467277905464, -2.4906699340122174, 0.11440660837319135, 1.18809822907773, -1.8460872901979604, -1.6607299935971644, 1.2284747913879352, 0.3935236562110219, -0.4902860807795749, 1.579907875325231, 0.5979723630503715, -1.73713986515722, 1.0444709018242553, 2.852064934282694, -0.6977728613646533, -1.107692148378138, 0.4076550108123204, -5.429333342485254, -8.674833045502087, 2.3522617107563963, 11.958540828410296, 6.146186068893769, -0.9438192840095176, 1.3365445078126412, 3.0251729796278473, 0.4229150677608272, 0.17150955817211927, 0.9563772196090773, -0.08842008791618078, 0.27696778599828326, 0.9560942934017377, -0.4214662670202837, 0.11281169790950031, 2.048297973148962, 0.6665285178401138, -0.12302266860383333, 1.9991830152328167, -0.3402782421993483, -5.232792079602918, -2.9873134321874026, 1.0248689831364486, -0.9429327036602654, -0.34263593287945615, 4.14023844088937, -0.8525852522965269, -10.919145418455585, -8.98005078186808, -0.5924195762315038, -0.041473230098741945, -1.9723195468841956, 0.07852011858470725, -0.0659383046575369, -1.9242276449167357, -0.20026386453688155, 0.4553629691820432, -1.351659092956108, 0.9578992176893145, 3.43238333575473, -0.9225185094857937, -4.428661039519875, -1.3686377618261063, 0.540044948557859, -0.8295098722053408, -0.333806619977321, 0.022258328221958317, -1.2638505328413165, -0.18534430231621424, 1.0194516176201325, -0.009994165165926128, 1.8310307627583073, 3.3105706183270955, -2.2110479491129102, -2.771075179343776, 9.971140581309317, 16.278274449766112, 5.233759218153019, -3.0285024179123488, 0.7550027645326103, 1.8774129084329652, -1.4070892795107657, 0.8364884136643136, 3.6489462183897547, 0.8814535711355622, -0.7019445021929708, 0.45768119215097286, -0.5613085417936708, -1.090415027268507, 0.4075502933892591, -0.3797852973928861, -1.3067472408853014, 0.507747734237392, 0.5435528865536763, -0.22273060306648346, 2.2119949508657646, 0.9239562202936182, -5.976948796776463, -6.1727019289576175, 0.40263464036474667, 1.050622676518962, -1.392524434508728, 1.2077541489052468, 1.9695803530976899, -0.9223288418725853, 1.6236591371342548, 4.851255747694739, 0.49151907092751124, -1.604643280032224, 3.076002071639475, 2.285765619314201, -3.2123072779738933, -1.8856957807097763, 1.028898086754405, -1.9001951676426494, -2.4067750257106146, 1.8653384142292606, 2.2808527976291453, 0.024689576312377386, 0.3069452807996343, 0.18751897643763185, -0.08619952873158598, 2.276292670633548, 2.329727897501799, -0.8413939967319697, -0.668504321989922, 0.9830672266604448, -0.03816856429917339, 0.3208502216728645, 0.19435354599345162, -4.054918842228026, -0.6602301099614754, 13.099924538079181, 15.395435436855594, 2.3639120884041085, -1.6127182073274922, 6.239179599656552, 5.795798899500065, -1.5282063727076285, -1.9988138531027895, 0.3304358615162797, -0.35818217183875933, 0.4003150317449085, 1.5507098770261716, 0.2486542716324751, 0.28764935462747526, 0.12867611991296243, -3.162706845711423, -2.496751031604421, 2.9203160671550776, 3.0285225690242266, -0.7173393243579771, -0.4230882533695143, -0.33744863521900176, -2.9541617153087634, -1.9180718001461896, 0.37435606309247127, -0.7738864024788338, 0.11583139864396284, 1.752870684354855, -2.8403090311610195, -5.228258485057147, 0.631810914651844, 1.3145156354604555, -5.119242769096065, -3.5657459450168156, 2.4754196291066166, 0.4007661897090881, -1.386849772849108, 3.7679199676056694, 4.146641471581407, -0.8610531184356616, -0.012099133214335247, 2.8401984742777335, 0.5661766533276443, -0.8249416797620308, 0.6814874978867237, 0.12074665812057661, -0.6117379447206936, 0.041162426240848204, -0.7501192885187202, -0.621733007924678, 0.7537689581496765, -1.1606862074195856, -1.49105740698539, 3.35896636400232, 2.326345180077525, -4.789834155096635, -2.9099610907411106, 3.3181224804767635, -0.802193725232207, -5.352857725603912, 0.36135508046668585, 3.3667231641861814, -0.8821977523716648, -0.6041086471369932, 1.599491484446723, -1.926150970138524, -3.3697990512281404, -0.09234404496234892, -0.29491598707442507, -1.45485764765281, 1.0639602165257933, 1.1861586543398133, -1.0132659811013862, -0.08336601097982999, -0.7186318454849056, -4.230169800180964, -2.5968177487512127, 1.3521700364473097, 0.21703993268718355, -0.649962707688942, 1.584597372124883], 'positive_zeros': ['0.970161742269896888334436501532', '1.77763915695471891054942970230', '2.39413928640575868619909807814', '3.4370653559321934670280240209', '4.86279631658911307037245826950', '5.303568698518774245372852952191', '6.00313030119604002177632337001', '6.67185900232424835619427763445', '7.02973103248647053274453866832', '7.72326503575486852069470864501', '8.70696213258983434193194198450', '9.21175454328129494838402190763', '9.9800258876568192474476812988', '10.75337649454665208609073472613', '11.20809915164956372611811659129', '11.73627167448846328650467457838', '12.93389011871885132678782358162', '13.42365382298797950005753044041', '14.19507115225278216349634841678', '14.5196105365608302247241575314', '15.46503021535445140251045144952', '16.37800169960932340631374683207', '16.748106229728276145667973622778', '17.23374622916936122861069283861', '17.88714632081489321033135198334', '18.62561872850328652036166604024', '18.93175333872824449324975329361', '19.30421415613031814290142811356', '20.41823702094124200019294763117', '21.20117313352612762214125754054', '21.94778368508319220192364043853', '22.41490931444383032716920639215', '23.19324959887077451210147820411', '23.82068182011121025400454825420', '24.2631733808602560016747651155', '24.89016699100924081081617725284', '25.44725186703718643079937695890', '26.12222413762323995866248308303', '26.5632312690164289415519616150', '27.46468675019286094206682806489', '27.81542337976028695019603774712', '28.7618877598149548817795805364', '29.0820127949430156401652301644', '29.61400264445888077178190691868', '30.07707447690021757769763140064', '30.952607509278315793009005454480', '31.76845863796117074561200669372', '32.404674781694905216372231822500', '33.252749032227467692445600576487', '33.48132850132725917114472080277', '34.35065305717118284388085415805', '34.45999798327605992811809063437', '35.12770414030287001108678573093', '35.80252011390112594198890093206', '36.48014501901466415560301579148', '36.94673780272211274544371927390', '37.21337766018951471653216393646', '38.30761538193944499723061074437', '38.64044442838904923146740486003', '39.35976711950997568864705260230', '40.44517963311166146926057953685', '40.90896333621598298388513836244', '41.00585643870655702711235034872', '41.85116867051419326542630846613', '42.4914548756894860167227571750', '42.76910978476399675812258438120', '43.60863954916301005185723169804', '44.33495050517807204738952170144', '45.01922577434945311948091600374', '45.36201071553867505006144036268', '45.66403711755010125728000276958', '46.29358212230903704531918154204', '47.012346820853410748014256166831', '47.4515922679470524002949011602', '48.086258812758848084637074212622', '48.76442696703929037333995619011', '49.59654833397186948825219472093', '50.1999510642556879755812579780', '50.80196427544018055974729569738', '51.257120657671564368556551962442', '51.8978410871639951972903881451', '52.59290184177547183073080464232', '52.7323219428992692201590544677', '53.4772593679956202411596871638', '53.86802539403655406611265884776', '54.178327865319328925906339511755', '55.42632648506433380026003344858', '55.95675018900470867871081229493', '56.01385748901227333923768183894', '57.057478756807498539706973601146', '57.33374235862766866420736739', '58.103196358368806473497939079507', '58.81352903958272956352807654032', '59.01377139207434240790466521474', '60.12762261112630669651485764925', '60.47486811250501303809028442086', '60.98055777453297534162388221933', '61.48383427835568292831176220227', '62.198050701515921942080863568784', '62.75242562244507179381042330220', '63.23243548052592920231367362789', '63.771786269003358919777229553926', '64.15916955356643927900480681290', '64.8769712877419639610547948629', '65.18147045452331145678524253561', '65.73729906759751106892360976739', '66.47722992849082094658358773906', '67.61650078356780128088468946982', '67.95364178032868771090659574246', '68.612919970824296953057390046634', '68.9902433916002351951178483233', '69.38756149606863225177881101517', '69.960182502791378982753838397803', '70.6032521695269150919750405889', '71.229767363888135239683875487314', '71.445765777188700930401110941928', '72.427404375606946443219538171448', '72.795918958859677506201339829461', '73.32407337254330512949652220286', '73.848463380274896705645459684017', '74.39537438420397209340086293212', '75.031049090438723582774675378483', '75.500579627226865390789104099344', '76.29852349483055234757139717086', '76.7550640776361734564025554047', '77.210073911158151238961279239244', '77.93288633141984185397405574935', '78.74871752640413975236647747659', '79.16697013799169824950657858780', '79.74120383933083951763212292733', '80.09818566935345900149590814722', '80.814756937186697789610118547002', '80.9693437725290899765739168712', '81.54347461243080127088939854541', '82.26924083853185546962976021624', '82.58447749032029334856406626600', '83.38154419755089092718098937783', '83.87264309627282900051963101572', '84.63766523297660408039412028558', '85.210228116880939738824704467809', '85.54544149225433280846472348328', '86.47828559635066649727050414657', '86.947523278947598096279029366832', '87.523283586520806879990527551800', '87.85753953642337227231476008552', '88.09168013201234343108820793435', '89.10249328341659118931876930361', '89.51794235467786242060894809529', '90.01597686857892811542073284353', '90.7006629995482352005144361529', '91.2674794093025913046631244839', '91.74388433823774895698004893172', '92.21251164445766297306893346440', '92.58914407314090126460309968817', '92.97679389131804045479236797704', '93.73812147770708873978987409712', '94.62970209325595538550970940682', '95.20641390425582633299767845031', '95.76947887465925816216529610274', '96.29914019318005333319797834596', '96.907642156585953399990928254571', '97.191910011950015252338682948118', '97.76000321122644293108798511572', '98.31279081681904161057365434466', '98.97755727588066973684589480867', '99.15330929608524828215871564224', '100.03778607105699013576276628511', '100.169725286788503766721866831954', '100.92201248759380442040215194858', '101.30848364106836500122004065135', '102.42282242352685580194424555979', '102.81704967215086326939608574445', '102.95534399528323228129320588638', '103.91894389819800158465199231437', '104.55672938121688248227149773885', '104.80213947954402752186005791146', '105.21562363333415151369016587925', '105.958343029370307489340877227198', '106.68035637482156528138782748526', '107.28256421163769072602708356914', '107.62762933195895969606978902110', '108.15919479930115887730953263537', '108.44685267248491064489972357662', '109.25866112061666814441062242407', '109.6718112061980059996135579769', '109.935666179279140839007494140735', '110.90480583092833161848568992941', '111.122887207029477728899203470193', '111.60655759691588639678538157469', '112.530456644203529143139298402469', '113.187694340441514598891531117105', '113.847856325565535205123727885702', '114.14398084684590691664950060910', '114.84202774610819755819420545297', '115.27795581641087933172238217483', '115.8052096528327479580323979876', '115.93558504509142029501213113474', '116.67464519751137551681870881623', '117.13669238785629040620735786558', '117.73588537471310688328208152306', '118.59441446726482953205867800439', '119.00438795713352220387787812785', '119.25352303793835572935843804621', '119.94004907115970567986888382642', '120.35944559529064421835993568384', '120.948578485074525166961399829007', '121.68672413347003050102363602663', '122.15902349734594437537737216252', '122.839789955401291166828868695049', '123.26866946735599363562951057820', '123.81729600599424713144867323345', '124.50681023614596386070222121677', '124.782611173063293386839361394466', '125.41756272889705296757182122310', '126.130342735107320751291612358111', '126.51890959780127015807816893174', '126.88831150442664615426348949811', '127.2543222307140637784769841235', '127.74130964077003234982365950301', '128.495568065369599478307944727250', '128.794108094400583891316063869862', '129.548912423509974574287949686234', '130.30670786702695405976705750613', '131.032146492560661240869301573732', '131.38490721343169714777108422187', '131.92038485737978747911880169905', '132.33322893627258732697130097063', '132.64063420614804346584535420591', '133.70503423921976959219405768681', '133.95993956854797068082588607867', '134.21906885978952514677120586933', '134.989239397910193513229429320122', '135.448836052573434278632751503104', '136.09630328451188521000146377294', '136.6201209227441169143908550199', '136.96500820593063620544441540135', '137.55768616580375493544487978648', '138.04652112331579150111196048636', '138.692656355432180302313081014986', '139.1924497200460243999183740011', '139.42577804136487650557340932316', '140.262104059692202067751300595888', '141.16670779910253554502667577796', '141.46051518534362666800093703889', '142.26412850043596630667531761634', '142.45291294278184340853136148822', '143.09585460098701891614962695445', '143.36533239380486697973317408340', '143.97281625289790646062915774167', '144.35844607733106002438739046107', '145.09977186899183196000395909025', '145.33683473899313275484190422741', '145.91744554195813999133049924187', '146.74549611229946859621678631605', '147.089154003092511433069379314039', '147.523445398244117079053082147925', '148.09928537982344707852789871462', '149.10162629259525231851461110134', '149.370440170840924753350742561217', '149.98860009226840339235328588268', '150.30308905109991594164989074833', '150.96368848939258068037522800439', '151.32519438251728114689324027109', '151.80085132415278035967156059379', '152.452555767502449433980480740', '153.25222846407386501465184995296', '153.57276305699121626944853633113', '154.15021028229184939780918806975', '154.38180693510642318420512832747', '155.02685026236689025239887246732', '155.61724255019010148042618898486', '155.68452558139566672152398806187', '156.46022060049018314630350006915', '156.96564978714242009611046676620', '157.94713736668999970493569356896', '158.39229771917090094665726377377', '158.90698491136445638556680377068', '159.315461553862024202876665965139', '160.08628321092618148120636250718', '160.4851139073038408847168915380', '160.835418784646284151710813518456', '161.46263369742243085685530476354', '161.80929054394733271244259215184', '162.42000989331254625206093701379', '162.92534101975099433588082903536', '163.17542831544490233520935427583', '163.79804217378215714518869322613', '164.66395440152747294474389198479', '165.098837721251691148545922881351', '165.5212272084877939917725756713', '166.12712412485512542510943761329', '166.45364518664273897457817596086', '167.21504559489122807717654872705', '167.62327833635287069494834039044', '168.243159314348472452968992669967', '168.88754257574564605639839845462', '169.21940803727660531382333233188', '169.8641989049837804073198782829', '170.632377487373861879766059448704', '170.82398408638326264794628061455', '171.30887699630595541521296611968', '171.58263717677728267621419999900', '172.40783313050668893802545808207', '172.90464685964441793195526165703', '173.426926754627274169198380298482', '173.67512225619056602143833288991', '174.082584227183768474431693146068', '174.70587560095542693588571296453', '175.69249089681703610719288591882', '176.015194005182750190676921652020', '176.79590215912421618020359366732', '177.41333380003046109936257374750', '177.70044377759792773210678619303', '178.05470385831174174604296270926', '178.83438805905101564849832884572', '178.95160073239990607861480983784', '179.3926962486917254392602138656', '180.14324256130238126884158028047', '180.85825944561290393876338845793', '181.34532984114736599182720435943', '181.496995001037440331597411881804', '182.398125269658984654493660708395', '182.65968884858025281920593411472', '183.11189671191244039291440228002', '183.59988935131993616054316648306', '184.34322407497573349310282692449', '184.75671928588007176183304693423', '185.46839099237538524458193976335', '185.96462336055506503524825642568', '186.35676635497596633179139866435', '187.11953528386097728879001349054', '187.50097694581440597015880707049', '188.18279554504486725645933109527', '188.60578743106619626156860217340', '189.08804560070060327147373152912', '189.64248046108214369814522525468', '189.765981758852265864773292439234', '190.422824715006325291683497335003', '190.80681874053016149407042730525', '191.35977951996514004922347111154', '191.974447001420651848319894159447', '192.6174436341748630755170650406', '193.09254759427772159261026779137', '193.73463070189367537932217641196', '194.30782094777425363843624869214', '194.74201770765712911135188451406', '195.18077099281447284953659423139', '195.9495980620875455762252004741', '196.205621649708546322360926870396', '196.76023650485757620306339420209', '197.330331020959593101717870148329', '197.83074947580207738499405731308', '198.033970367216778601138844624422', '198.92231365667108851951267090979', '199.40208933650799596831166617894', '199.78787955185457927389963205196'], 'prelabel': '1-6223-6223.891-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 28.89949050399846, 'root_angle': 0.4484108292899301, 'root_number': '-0.947923605780299682305144574161+0.318497782730861407058211946824*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(21)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.591101256180453656076995757950+0.0649999697880156301826147346826*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.97016174227', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.77763915695', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.39413928641', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 28.89949050399846, 'bad_primes': [7, 127], 'central_character': '6223.891', 'conductor': 6223, 'conductor_radical': 889, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6223/891'], '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': '1-6223-6223.891-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': '1-6223-6223.891-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 28.89949050399846, 'root_angle': 0.4484108292899301, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.97016174227', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_6223.891', 'Lhash_array': ['dirichlet_L_6223.891'], 'factors': ['1-6223-6223.891-r0-0-0'], 'label': '1-6223-6223.891-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6223/891'}