-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_99.31', 'a10': [1.0, 0.0], 'a2': [0.9135454576426009, -0.4067366430758002], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.6691306063588582, -0.7431448254773942], 'a5': [0.9135454576426009, 0.4067366430758002], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9781476007338057, -0.20791169081775934], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.4597540671534385, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [11, [1]]], 'bad_primes': [3, 11], 'central_character': '99.31', 'coeff_info': ['x^15 - 1', '0.913545457642601 + 0.406736643075800*I', '\\\\zeta_{15}'], 'conductor': 99, 'conductor_radical': 33, 'conjugate': 'dirichlet_L_99.16', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 0, 'a^13', 'a^1', 0, 'a^8', 'a^12', 0, 'a^0', 0, 0, 'a^4', 'a^7', 0, 'a^11', 'a^6', 0, 'a^12', 'a^14', 0, 0, 'a^10', 0, 'a^2', 'a^3', 0, 'a^6', 'a^8', 0, 'a^4', 'a^10', 0, 'a^5', 'a^9', 0, 'a^3', 'a^11', 0, 'a^13', 'a^7', 0, 'a^5', 0, 0, 'a^9', 'a^2', 0, 'a^1', 'a^1', 0, 'a^2', 'a^9', 0, 0, 'a^5', 0, 'a^7', 'a^13', 0, 'a^11', 'a^3', 0, 'a^9', 'a^5', 0, 'a^10', 'a^4', 0, 'a^8', 'a^6', 0, 'a^3', 'a^2', 0, 'a^10', 0, 0, 'a^14', 'a^12', 0, 'a^6', 'a^11', 0, 'a^7', 'a^4', 0, 0, 'a^0', 0, 'a^12', 'a^8', 0, 'a^1', 'a^13', 0, 'a^14', 'a^0', 0, 'a^0'], 'euler_factors': [[1, 'a^14'], [0], [1, 'a^1'], [1, 'a^8'], [0], [1, 'a^4'], [1, 'a^6'], [1, 'a^12'], [1, 'a^10'], [1, 'a^8'], [1, 'a^4'], [1, 'a^3'], [1, 'a^7'], [1, 'a^5'], [1, 'a^2'], [1, 'a^9'], [1, 'a^13'], [1, 'a^11'], [1, 'a^10'], [1, 'a^6'], [1, 'a^3'], [1, 'a^14'], [1, 'a^11'], [1, 'a^0'], [1, 'a^14'], [1, 'a^14']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-99-99.31-r0-0-0', 'leading_term': '1.62748974389093081649132755030-0.519056583348368005689075666391*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/99/31', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.7082571829755169, 1.845852840162672, 2.118424147617836, 2.1456857925262574, 1.7836531350255156, 1.075779975627836, 0.20820719091889528, -0.5494833242175968, -0.936606126573362, -0.8079071623211617, -0.2126128043561789, 0.5973510245602233, 1.2505337151202742, 1.4102633081228066, 0.9384312429455541, -0.012143495502851482, -1.0382031915374779, -1.6634180401116265, -1.5839086388442263, -0.8622627906446461, 0.04500926287631544, 0.47184948226999507, -0.12487927258050799, -1.8423584584994526, -4.1974710740385435, -6.2842115064556054, -7.178682945641764, -6.402976984521651, -4.20204577677291, -1.464074835647979, 0.7019149691345224, 1.5223205410588139, 0.9477103191462538, -0.3506187823420376, -1.3849991065854212, -1.4293006273810633, -0.430645020975245, 0.9941124532344788, 1.9753395850223183, 1.9580280638692011, 1.053667569917292, -0.05675356698473959, -0.6077634710105271, -0.29465344573353547, 0.5038196803130036, 0.9986652196626638, 0.587623246383509, -0.6432650110925292, -1.896197149248294, -2.1813663030192, -1.0512076930294145, 0.9706433142990997, 2.6159328541740754, 2.6636949226828626, 0.7908171553221743, -2.113926113000346, -4.4364907534317055, -4.844037022084264, -3.148687469651521, -0.4326339023494845, 1.6684725256962736, 2.041677125423594, 0.7913399392501166, -0.9226336165948814, -1.7661642474953148, -1.17973680075137, 0.29404937907659956, 1.5171115688793446, 1.6769179809067616, 0.8947917783736591, 0.05327258858914947, 0.0025039294607645296, 0.8090555072239096, 1.681334060426218, 1.6530987311327898, 0.46712024944740305, -1.0983553296403492, -1.7881867862368088, -0.9072719686563238, 1.0126903421256035, 2.5228952234710698, 2.377850370753795, 0.6063029252617049, -1.3600240532280066, -1.6892517463451255, 0.43510180920852326, 4.0848839809188835, 7.15556886066163, 7.841827735468437, 5.906054081293711, 2.772686814156617, 0.40030617568531124, -0.15849919073909566, 0.6201873662075073, 1.3597359769046873, 1.0627284206610057, -0.06448161822052524, -0.9133897027185642, -0.5763429087020683, 0.7660127494521037, 1.9771957617828464, 1.9933879373044543, 0.8046102540280533, -0.5256360868515869, -0.8471542581991679, -0.02243719842936548, 0.902075412778397, 0.6768971830334799, -0.8685450794521357, -2.4471235972829746, -2.3006443116236404, 0.2138960516904055, 3.827119198350891, 6.147949845703879, 5.4925710412575395, 2.257300635630555, -1.3408907296246277, -2.9794677521726594, -1.9898169102074657, 0.2851070314041395, 1.7731983003026741, 1.4359010780507713, -0.010765007865484788, -0.9611120389804132, -0.49119375396770565, 0.8272828195484481, 1.5716525731154316, 0.8925915099962664, -0.6675942115468543, -1.7315011048280327, -1.4465029541085814, -0.29940780940555933, 0.423892871857232, 6.123592216156944e-05, -0.9257758536500169, -0.959542394277424, 0.5358338856817704, 2.5386029221718602, 3.0806245973325255, 1.0552153950831022, -2.5390896923751987, -5.187067761029653, -4.899882432116981, -1.9383623392581166, 1.3621847506980864, 2.5683310983360035, 1.1899638975583091, -1.0225368496924625, -1.7500665258286654, -0.1875213635172518, 2.3471811273693626, 3.746591056259115, 3.0542853529429497, 1.1871363117384761, -0.13747473948310668, -0.10665451592513583, 0.5509254155596301, 0.5456838751096464, -0.47777794098170406, -1.5239139809824884, -1.3456957887153567, 0.11099614984146952, 1.4891186386352246, 1.347039321390956, -0.29582362681307145, -1.8449846068859166, -1.696028093425161, 0.03348850266514544, 1.4197525100531423, 0.5472479111284465, -2.464596172171516, -5.263749915947206, -5.254784512525974, -1.9930835619438736, 2.284439363999736, 4.551547297612578, 3.577447644945576, 0.8241746591848567, -1.0954818262546244, -0.8383015137559816, 0.6770580287948049, 1.506514555514116, 0.7406160133174701, -0.7183435517382981, -1.3284562759699459, -0.6574914629218368, 0.18937391463058167, -0.12196507059615183, -1.5832578756496156, -2.7622568238804996, -2.337694654734743, -0.5905693562605735, 0.8164324366560435, 0.6093687342596984, -0.6713421477307582, -1.2167680780443808, -0.012818197104949365, 1.7592307693643374, 1.6357037405267323, -1.6170061903521566, -6.39268852316186, -9.317452433026046, -8.159606807666883, -3.834540935474053, 0.4376208840220424, 2.0084405952358257, 0.9436863742041011, -0.5290282136019836, -0.5092817641413275, 0.7574134257877879, 1.477143055437641, 0.48181805399212757, -1.434690869245416, -2.401745290302731, -1.5146612730655113, 0.23490006292362253, 1.116947530299013, 0.5604424964971653, -0.34627390576459016, -0.281119958338593, 0.6327463361034447, 0.8868300276326618, -0.589211537314899, -2.9023053725093235, -3.851644432686152, -2.2751685950319986, 0.4133302030929068, 1.3453542776367127, -0.9496481319571826, -4.8621974145325595, -7.057734288337679, -5.6434072792171985, -1.9886442633577874, 0.6468629589053844, 0.27961943907148856, -2.036419611842462, -3.538869297459624, -2.6536884979929676, -0.4201737260849754, 0.8894582982693083, 0.27975678101823026, -1.0731534666060065, -1.3597072471165037, -0.2264275892173034, 0.9522498897962928, 0.8139243933046294, -0.3560689814829851, -1.0284220095960928, -0.3771896409246469, 0.5830050210032574, 0.12455390304305143, -2.0189735951722496, -4.011539341685728, -3.7602860712689083, -1.3239566569319077, 0.8852708496796071, 0.5686824177383626, -1.8779186234276937, -3.556504084019432, -2.0322463081414766, 1.9809470914099605, 5.114212877194926, 4.6102972258176935, 1.0140140087474179, -2.4612075669479934, -3.1371703084028537, -1.2674756565372503, 0.7188724154280155, 1.019705428231893, 0.14738051439314065, -0.16120028347626092, 0.7327679238664108, 1.6190362905322409, 1.0520628207182545, -0.7168266961273592, -1.8781821036191335, -1.1528021838836187, 0.662322328177389, 1.5843279942820951, 0.7669566609822075, -0.5221676080176912, -0.5223664136821208, 0.6702947857796184, 0.9260058046711303, -1.446520614789701, -5.302041664732098, -7.27128328291832, -5.078498561090585, -0.10556544771382505, 3.6853606571979687, 3.5191008011238054, 0.3809409243829057, -2.240778645845333, -1.990130444895656, 0.23864843048595288, 1.7619768035532133, 1.2409331692351164, -0.06882307880542951, -0.13289250339791137, 1.3337038170057478, 2.616470223984951, 2.177026453548496, 0.5311461647071754, -0.42776308817823844, 0.23063697267683608, 1.364330087495004, 1.2362122398597608, -0.2673461758472645, -1.4725767117904602, -1.0911350155480457, -0.04393241024939544, -0.5035583502467602, -3.0646779521184704, -5.4380077733969605, -4.561265287282505, -0.05486773682854481, 4.88263573585605, 6.415675005951544, 3.848733203441202, 0.18062337781837118, -1.1477724837405665, 0.2585073948375551, 1.7571967479166357, 0.9338037202872642, -1.68112060508573, -3.4099180219611345, -2.586231133652926, -0.33424563639495714, 0.9407423697751992, 0.3479334519220423, -0.7501057650341694, -0.7263674258758939, 0.23840340257863082, 0.585992627564346, -0.34983516409688287, -1.2501372360473306, -0.4206019089936623, 1.8602979354191524, 3.3254866196538844, 2.313256827975479, -0.09938007668578644, -1.1874022760149943, 0.16454788350971566, 1.8969080319821137, 1.0036407848860187, -2.8085960827407486, -6.307436152155152, -5.9631610442025265, -1.7620091745679114, 2.6600124231167497, 3.75343003180809, 1.540326311368202, -0.8824886687642326, -0.9856624879991884, 0.6547785248587703, 1.5874996077466588, 0.6446163287615218, -0.8480279248041529, -1.0280794971398022, 0.07238694752257635, 0.7032422953308605, -0.17791218927868002, -1.4479439556954188, -1.253033103780114, 0.49861968404422136, 1.8504792501413911, 1.21081533489726, -0.5542852999063602, -1.1167476785625965, 0.32143744643344746, 1.8198584610087538, 1.0419661149411246, -1.5327059109272545, -2.601517522796798, 0.3265479541916533, 5.705141757889126, 9.049760819888773, 7.426943718538018, 2.4350468851063254, -1.5919300129877594, -2.0494948055512454, -0.22434821625421267, 0.9276984685352501, 0.3855613743800133, -0.2184260739366228, 0.772891888457049, 2.6528821691448092, 3.2068441236486556, 1.5735146724826294, -0.6155985962970452, -1.2471121445595448, -0.26929688525498496, 0.47038769567543176, -0.20985491304212797, -1.27833944850062, -1.026791434941062, 0.35067136494680673, 0.7051010386047394, -1.2192372550058646, -3.6144931440322776, -3.2246950977943065, 0.7764306325756004, 5.294148463348307, 6.352961421334312, 3.4252041344816773, 0.04255568795505265, -0.12059968791311429, 2.7707924054738573, 5.182446445095039, 4.4077700194088925, 1.4997969711756514, -0.32089467941462074, 0.4302462049944518, 2.04321055281019, 2.082670254772719, 0.43989605701175766, -0.8073027905798046, -0.26263004770744786, 1.0417985976067932, 1.1922534042140682, 0.0244350039442791, -0.7185936743778089, 0.1178944371214091, 1.3770850844079616, 1.09828327700643, -0.6376377320072775, -1.4209047928249352, 0.49453874406470044, 3.6146464346640688, 4.587249056538301, 2.2135512809486193, -0.8014109336857704, -0.7939877991878357, 2.5091733835060555, 5.473855842894269, 4.662774678747894, 0.793812604324965, -2.100915922285509, -1.266938312342348, 1.855964120192827, 3.633355907949035, 2.467882406981544, 0.18334313122500517, -0.6938991501820867, 0.009520735772359365, 0.4797368946074438, -0.21259069825885124, -0.7906639402727238, 0.27409602606074557, 2.325406900581105, 3.0617340807786033, 1.4700815234941877, -0.7554070002786495, -1.321505145198222, -0.27684066013958375, 0.15833611851465487, -1.2270386075995674, -2.680706965106201, -1.6396695155579362, 1.5157572275985347, 3.092279268148584, 0.13507429586119177, -5.741409540055748, -9.558776985923867, -8.14919919035972, -3.3991242090164775, 0.11774923769222606, 0.17811917249832462, -1.2725477885555074, -1.2322942606101597, 0.5522080742426126, 1.725567583537631, 0.7576421608311273, -1.0294477263003676, -1.354163250300266, -0.041223076298258284, 0.8744130126246796, 0.023821565664081137, -1.416082666958983, -1.3807396984065174, 0.19408364865139027, 1.2518325262437342, 0.4761387256235712, -0.8137455814082357, -0.49681196810997885, 1.1396124559846543, 1.3431495459607534, -1.4588787579051639, -4.9056905571107725, -4.813150503757181, -0.08467271606705237, 5.5198038907256795, 7.2144453943234925, 4.2910941513633905, 0.5311424214743785, -0.38933507591729305, 1.1383581052195546, 1.8920869626513075, 0.2561070600430813, -1.86669531818961, -1.8078713615051516, 0.31943486253960596, 1.8730553250158553, 1.1505617627570175, -0.609271036698332, -1.1521940394585437, -0.21128314383125713, 0.49848415662666934, 0.05616941103692002, -0.20601226949749518, 1.2642735557151892, 3.566433178600074, 4.026805432210324, 1.6947605012783369, -1.0169979159554858, -1.1152670994136267, 1.0908598893792387, 2.172109356232167, -0.03955415943752798, -3.3409905977296566, -3.524465517584172, 0.4370083197273689, 4.812592063527562, 5.261993932661925, 1.7433157116979583, -1.706508006027435, -1.8327373876695263, 0.3905112828048791, 1.6477819472884652, 0.6133555763896927, -0.8589587621857999, -0.738688823685427, 0.39682942772440016, 0.47779194390620683, -0.9057994983259917, -1.8613897277970954, -0.9265210055904236, 0.7520944496227294, 0.9579930387397332, -0.42743540717467726, -1.1347382344934835, 0.31290273888267994, 2.304209995414843, 2.1237313863109186, -0.2420516250434139, -1.7506062304136265, -0.2975222072630795, 2.0568604559794643, 1.2178884715284513, -3.6968420614638986, -8.600467011037512, -8.72961040420442, -3.991142179832109, 1.0625348884823926, 2.46021158338556, 0.8163032561732715, -0.4038854303491973, 0.4540373819054583, 1.7068313628218992, 1.3580417063191996, 0.08144404243643094, 0.0994466478134293, 1.8036805873627286, 3.010807545566695, 1.9163943747692855, -0.4028120954323816, -1.4347863042346316, -0.5872345800264898, 0.24282592523437718, -0.3793130243850652, -1.2600747871730855, -0.46834809969309704, 1.2978974585777572, 0.9305816089328102, -2.9420127057163157, -7.286191862317853, -7.567447861881417, -3.1409308205295288, 1.6351401490944129, 2.2775135311080765, -0.7924073104987751, -3.1849948160267116, -2.081986746702268, 0.6285063020308475, 1.2700953625320408, -0.7979771243483653, -2.684209908373769, -2.024972625884445, 0.04494670399471835, 0.7710836387855717, -0.41568207723461986, -1.414392935534239, -0.654525397608699, 0.723219326155489, 0.7100738522045689, -0.5367254196717589, -0.9502163208521255, 0.2496204094125996, 1.14803328071104, -0.19316278583294072, -2.657422003162322, -3.2229764623401604, -1.1905523701836276, 0.32281293537017547, -1.8227688431992966, -6.3674084631803405, -8.618548577847466, -6.025055807647735, -1.3798422523680007, 0.5464762560999148, -1.239945534348981, -3.0567128499909155, -1.4627096202811247, 2.434707370689285, 4.629139168764169, 3.3103753765086097, 0.7241587367205231, -0.18024471972858083, 0.5813931947608164, 0.8080976026637363, -0.325888846987605, -1.2043713223821342, -0.5047568790246072, 0.5409510018307291, -0.14969873776762127, -2.260255442113465, -3.1444710426529623, -1.4061471855748446, 1.0094955119369868, 1.358491188178447, -0.13438009966121695, -0.6877260550738579, 0.7699641967806321, 1.486064104314691, -1.6228052291761634, -7.175070111963421, -9.909450751396442, -6.601050811695413, -0.07592477014941923, 3.8497384768372336, 2.805036226826344], 'positive_zeros': ['1.9521091757370593796784068178', '3.209631067049269452206597961233', '4.68394985081248898287004760791', '6.23227741673729814443600767401', '6.840276150876243358404262744193', '9.254931443619730196157566683191', '10.23157751944238948418235142110', '11.34550492197366526558428302941', '12.793882027668931996939249863787', '13.55974329655421568899838885421', '14.540471926149625330566361904632', '15.79361333761909694286806296570', '16.96445421571938369511279981848', '18.48930082368885436023090462665', '19.513755623762059308364095870336', '20.56613129513058825837795358118', '21.90887177163920934977004459140', '22.18575287949439551621796976396', '23.52757769087656591081971907659', '24.53083020811975046272244130466', '25.71129730680532279564982511617', '26.51803687722878725462153931712', '28.54372814628933050030762126370', '28.848040554080091401404420977456', '29.983273395100588527779758029942', '30.775123713035495074395892083453', '32.04768585943082178161961409284', '32.81879458982677733812756018580', '33.59713071789397059747330180021', '34.667735287927482723371170639202', '36.12249333181882493963711426697', '37.14776613727577048414578030045', '38.12269715483025857681452043727', '38.87276438242357596806353570556', '39.870727279348925345721505366613', '41.02538350071127650527584317080', '41.56252151687972465694755110297', '42.41387751346258508329909434315', '43.53488698638883138531087000437', '44.85774061935704819817535428340', '45.785108857728248724575685094282', '46.586506897867212446756098464745', '48.06979373082101516989883983130', '48.49145642270249213484946437732', '49.25358551993972857052626608297', '50.292253254975061570865569026710', '51.202135965010384088029539604503', '52.18216513629153878903528563425', '52.88273573948748285829653015122', '54.20304587438537425521013201454', '55.41390819914843369252760215688', '56.11592209086885031801220521667', '57.029901949656269569493762632948', '58.02644401500693177134689858210', '58.39749176549844200740338370619', '59.79035453517111857261680748432', '60.46844830798531054204959059694', '61.252146836225275076946025436062', '62.06434517133300759050807278408', '63.709263266720078380619295971660', '64.55178287900395930697462336081', '65.14055605130270411315474242661', '66.018690287959363234520270594906', '67.14234536954205628235965407882', '67.984808562257121995830362697273', '68.54568254315077453444510307063', '69.28521316850788676445219198156', '70.571552787532320739038264379512', '71.16044781088361254968916947341', '72.69988759962044628247326861337', '73.17105159466433863495599981276', '74.44096299830895198048531710099', '75.06345392350808744958506037250', '75.9861198059258044875046176838', '76.78557986884915857458914056430', '77.60391651195191376638902490943', '78.15040734058836063349663880300', '79.53207643399064581835874352794', '80.08774661266902716707064212749', '81.1054697480360688979409588699', '82.265055579649361731709668328299', '83.30107774602767853614154803765', '84.12128286633624145661477581227', '84.46586890903245172147121354673', '85.50562223879104296488751244813', '86.448523509217595777471061622326', '87.35540013182956110995498007806', '87.96137375762974000262269490892', '88.60319971576976190771743429005', '90.00651191287958859877350412137', '90.97202308529775292373531411607', '91.843195933509632399795896755931', '92.79076683193879835273285178642', '93.167408658673564025605761476630', '94.491354095197569972402138976140', '94.93750235575305778714744166828', '95.88864943567343813682452009690', '96.89991978726948533876043339032', '97.04435346094353331582143813545', '98.440642616119079346488158713335', '99.70761835064575719309180396787', '100.271942509837097136518649225258', '101.058988130501425926356547754438', '102.2394020880986147570486202087', '102.9006718165678187572006873503', '103.67462570374976523131145636570', '104.28612183837827747941884882295', '105.06621311182087921628499388612', '106.23596223647519166883511140598', '106.850177154604600297106687190844', '107.60007226513649415723039341267', '108.859970521595691458250568198131', '109.860971504672049246586762500956', '110.510038950540709588551798054602', '111.372740462404965900044033341001', '112.168709886685333041218126103474', '112.77217207299120661891147253618', '113.67125230040553135538801534431', '114.58557500729386419094946550485', '115.26037642629538474993104669580', '116.07158455715597197611075820337', '116.85318597388079896989110895411', '118.28504313532905517796804469914', '119.10028760577132365690638195711', '119.82140736249861009230644011003', '120.137326608955052667858139584960', '121.46132789446135916234263597116', '122.26058887166892257697925924941', '122.75526560039932427857461373512', '123.67051796343900215719101035646', '124.21691184069554884128021991445', '125.263424479444291850373427360393', '126.568815851695006926704741767495', '126.89499588367861857900353167041', '128.333932725791781769471331840069', '128.659009786166785374984781683610', '129.765745739173906537009172135241', '130.37385520302876313983865587361', '131.25590760803497120811947076747', '131.848395824526524356677342214197', '132.70467300001431214145228003563', '133.38434316738165209852060683488', '134.58477622996276772270552363650', '135.097456167411635732537471033740', '136.31242220248933561075501264126', '137.00871663053773774205135393359', '138.157262668177823203672986918702', '138.74675293293190535968616303344', '139.30623394469464937066591636988', '139.952109515689857155577322067842', '141.12997209455040495671912702591', '141.95982793778461863126989298355', '142.25405436100824606808961967062', '143.29435755578551079035779494568', '144.070698566767597888599016180188', '145.60560314770874764290225410408', '145.97838373893722906269780617839', '146.7882344664696214007301570359', '147.62435400801606491520103967095', '148.446065960088676307042205963086', '149.067369453465955102378072881319', '149.96512140237160006279435331632', '150.72496484818977581674684416399', '151.35185534267095878980588361761', '152.058517309622825258941602102672', '153.12934863668582632697291335907', '154.44793178206398209420166270243', '154.79395615987968967941954215446', '155.65791634210336727362234426868', '156.52030313346668417188704521856', '157.38449971107528523842154769568', '158.18472805797341244786519690929', '158.77515140370259085236315618891', '159.14614419397199080616632265066', '160.48627079965933520901657892832', '161.1091837807386244349452585208', '161.87142137274606434094914425039', '162.78528552108458425358601856351', '163.88292095487225099328049986017', '164.635225919756203980183372483703', '165.42317158194403376732082584147', '166.13556705565943920140472038453', '166.69336859646005818289628545056', '167.66070326409535600141495476785', '168.35170290562134307003321672323', '169.01715970869814441027212221550', '169.97061742833138841188533534128', '170.66025983113122712859574541838', '171.34820635163268123172755390668', '172.730756732868134045552233314224', '173.584922427940443385186355087398', '173.96013290777236643647026662708', '175.02910222175019539459737061009', '175.28013443148222351358759841927', '176.50404140928557127124386355966', '177.35328583734739332740107260144', '177.696224954165775989806987318942', '178.51788451067001181765593891454', '179.163700867889405194220935101399', '180.49704273203044927348433219181', '181.18083614657905512964002752889', '182.106601784033430184512106565136', '182.71486437918229436100144849672', '183.74217251338477167050513978017', '184.28992061684319739809216627387', '185.134245874494858755604985692430', '185.80955184525996017535962928251', '186.511177487664172228285828789151', '187.16140768694963470594370021128', '188.30221892950491257991601599174', '188.554172087873571498810709869419', '190.13827216968918928985133767593', '190.4617623374445977882086344104', '191.37239854695470242470422840790', '192.648481588991401461900858703477', '192.92280396402608228979516209114', '193.676571661656959571849332836203', '194.497510620280634728237487078637', '194.97173121578582531260037139225', '196.10312147716799549186565664052', '196.84780789145383615700438187253', '197.36511350480672319597402513651', '198.01020388654937520056526094235', '199.37890381070655932615860901737'], 'prelabel': '1-99-99.31-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.4597540671534385, 'root_angle': -0.09827268562516234, 'root_number': '0.815348477882473832191501400268-0.578970517051372038240776577471*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0982726856252', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(15)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.62912458982073238852443895776-0.380804301307132655957251072719*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.95210917574', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.20963106705', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.68394985081', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.4597540671534385, 'bad_primes': [3, 11], 'central_character': '99.31', 'conductor': 99, 'conductor_radical': 33, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/99/31'], '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': '1-99-99.31-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': '1-99-99.31-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.4597540671534385, 'root_angle': -0.09827268562516234, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.95210917574', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_99.31', 'Lhash_array': ['dirichlet_L_99.31'], 'factors': ['1-99-99.31-r0-0-0'], 'label': '1-99-99.31-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/99/31'}
Lfunction data - 1-99-99.31-r0-0-0