-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_265.167', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.3546048870425356, 0.9350162426854148], 'a3': [-0.12053668025532305, -0.992708874098054], 'a4': [-0.7485107481711011, -0.6631226582407952], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.970941817426052, 0.23931566428755777], 'a7': [0.9350162426854148, 0.3546048870425356], 'a8': [0.8854560256532099, -0.46472317204376856], 'a9': [-0.970941817426052, 0.23931566428755777], 'algebraic': True, 'analytic_conductor': 1.2306548262188, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [53, [1]]], 'bad_primes': [5, 53], 'central_character': '265.167', 'coeff_info': ['x^52 - 1', '0.992708874098054 + 0.120536680255323*I', '\\\\zeta_{52}'], 'conductor': 265, 'conductor_radical': 265, 'conjugate': 'dirichlet_L_265.73', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^16', 'a^38', 'a^32', 0, 'a^2', 'a^3', 'a^48', 'a^24', 0, 'a^18', 'a^18', 'a^7', 'a^19', 0, 'a^12', 'a^43', 'a^40', 'a^33', 0, 'a^41', 'a^34', 'a^0', 'a^34', 0, 'a^23', 'a^10', 'a^35', 'a^8', 0, 'a^47', 'a^28', 'a^4', 'a^7', 0, 'a^4', 'a^51', 'a^49', 'a^45', 0, 'a^31', 'a^5', 'a^1', 'a^50', 0, 'a^16', 'a^41', 'a^50', 'a^6', 0, 'a^29', 'a^39', 0, 'a^26', 0, 'a^51', 'a^19', 'a^24', 'a^28', 0, 'a^9', 'a^11', 'a^27', 'a^44', 0, 'a^20', 'a^6', 'a^23', 'a^38', 0, 'a^1', 'a^20', 'a^30', 'a^15', 0, 'a^13', 'a^21', 'a^9', 'a^49', 0, 'a^48', 'a^47', 'a^26', 'a^21', 0, 'a^17', 'a^46', 'a^14', 'a^30', 0, 'a^10', 'a^32', 'a^33', 'a^5', 0, 'a^14', 'a^37', 'a^22', 'a^42', 0], 'euler_factors': [[1, 'a^16'], [1, 'a^38'], [0], [1, 'a^3'], [1, 'a^18'], [1, 'a^7'], [1, 'a^43'], [1, 'a^33'], [1, 'a^0'], [1, 'a^8'], [1, 'a^47'], [1, 'a^51'], [1, 'a^31'], [1, 'a^1'], [1, 'a^41'], [0], [1, 'a^28'], [1, 'a^9'], [1, 'a^6'], [1, 'a^1'], [1, 'a^30'], [1, 'a^49'], [1, 'a^26'], [1, 'a^30'], [1, 'a^37'], [1, 'a^11']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-265-265.167-r0-0-0', 'leading_term': '0.966250444685369100931600166719+0.186107163104935519723693958802*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/265/167', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9840100599148569, 1.0601574609079294, 1.0016775221405727, 0.5038570769755509, -0.41169692657040136, -1.3699954212841088, -1.7810311134234849, -1.1187928083824503, 0.753670122803956, 3.38845482379387, 5.844107170581884, 7.085486600141126, 6.519729620727499, 4.366557398238252, 1.6061705856777484, -0.5221222438053047, -1.2056646647449867, -0.5069362850737511, 0.7313152043193499, 1.482831051696728, 1.238657592249289, 0.31530434623624415, -0.4606850616895072, -0.45646415619413916, 0.23011945229086475, 0.8540755058449324, 0.6948483520972684, -0.2256887731885739, -1.0220768884877243, -0.6184421981653587, 1.265911172543095, 3.65192494098371, 4.859746389273875, 3.774115901456591, 0.8406631785985896, -2.083056663753548, -3.0314769912518362, -1.4277289956194978, 1.436103080477185, 3.3829770406815554, 3.0489379917012043, 0.9153631035199727, -1.1822468747821302, -1.645685265747034, -0.43345216681440496, 1.028103124091042, 1.2298204994837847, -0.013534737948710894, -1.4237156562469608, -1.5026675122881443, 0.017811185460231166, 1.8967905836874452, 2.5436287392872936, 1.503758562963376, -0.16289732231766185, -0.9667733272744723, -0.4454577381344279, 0.4785196621359083, 0.6015334319836413, -0.1542167441380048, -0.5660608610964412, 0.529419350711903, 2.699433728629192, 3.9185236254575972, 2.3848495436922152, -1.4868888807725087, -4.949852255106954, -5.082497341242205, -1.3840924754384696, 3.618277047487047, 6.422349045736434, 5.443250041011346, 2.1233452024246215, -0.6558985941616654, -1.2172855667092088, -0.2547050039258515, 0.39039472488257454, -0.1657420783292853, -1.1096515573247614, -1.1715106635402808, -0.2742194088766159, 0.3506494094924675, -0.2942782692084479, -1.600279140946526, -1.853765292724471, -0.1845206822255106, 2.224908758487438, 3.1841877660247904, 1.820996181071209, -0.35536314591217016, -0.9749786468798567, 0.5902903883705797, 2.3843787211881864, 1.8593791126601953, -1.31245972216606, -4.657767812215045, -5.313491172005212, -2.9520479607720276, -0.09306927196510179, 0.5721277122012596, -1.0083720853978793, -2.316275224560952, -1.104746490829875, 2.1026215776048005, 4.555093542938993, 4.1953547638922135, 1.7248617248292315, -0.36128574941497726, -0.5250813978480187, 0.4122976038906925, 0.6335638081431572, -0.36545900950477267, -1.3056275132660597, -0.9210641170104007, 0.33662680951988055, 0.8793220907543914, 0.12316165643789116, -0.6091065878446671, 0.2129549375967522, 1.9974138624829898, 2.158576862792186, -0.9487217379046311, -5.500094623570068, -7.314583589380847, -3.9234926699075627, 2.6337449275963007, 7.464018121791583, 7.375349633497637, 3.613554814548908, 0.0639514800714322, -0.8629108130174201, -0.14186242639722352, -0.13439025362958953, -1.4716858478041763, -2.556736152018212, -1.947717217509429, -0.36892837922597443, 0.22362583350614354, -0.7648386478533403, -1.7339865286620084, -0.9630759735250849, 1.0344387243911415, 1.9677626345588846, 0.6012057868540931, -1.5757558586676466, -2.051075239447738, -0.35056127428548933, 1.3789054933349574, 1.0797901631699642, -0.5900450924605446, -1.1308493954182193, 0.3840371909644465, 1.7016622186330523, -0.0728102508282277, -4.638944801004652, -8.153608631107831, -7.200960455681724, -2.6493999994878172, 1.1501919606617261, 1.0097670446119855, -1.89904993025052, -3.8096489559882083, -2.752188006448376, -0.38144024915144276, 0.5419558921561727, -0.460353947207075, -1.4583484405311657, -0.9558544024331267, 0.2507788374279432, 0.48602204102496194, -0.33970607415405274, -0.7212233287440807, 0.04180515232866303, 0.5662608987349742, -0.6917310249245422, -2.795988971086332, -2.883179359084592, 0.205980489580297, 3.754895593170667, 3.7365030924426956, -0.47352278880347876, -4.9477583760949635, -5.374876580266209, -1.8303511835970518, 1.4793724882444848, 1.1479185772500282, -1.7495036584278096, -3.439372401902952, -2.1492189404415902, 0.14942996951941706, 0.7376332119638922, -0.3601179323006344, -0.8899595841986717, 0.15293758068806232, 0.9926844443713476, -0.42040030224583813, -3.335013900400487, -4.822551083210638, -3.371037709882958, -0.7044239978699591, 0.5382730448066729, 0.08726173460278451, -0.08235591683535606, 1.0948413463128792, 2.1389338230749626, 1.270433025897162, -0.682380802116712, -1.1066317555477132, 0.5987847159833404, 1.5418490402045353, -1.1780935786735318, -6.131756006443469, -8.296939677261909, -4.678916483157144, 1.850943923592093, 5.417489115151603, 3.4967824243344534, -0.7354217821726403, -2.560187875932547, -0.991266662633242, 1.0528910828754359, 1.0697832796230051, -0.190933170850238, -0.5978906037958766, 0.1023522005404421, 0.32183951114393106, -0.5194408095583343, -0.8747294784009758, 0.5284355277893846, 2.3820710590411913, 2.2927936130736857, 0.24499227469290913, -1.0173255993995673, 0.3232459494394267, 2.3509346596612852, 1.712874149917799, -1.6764282092218865, -3.9357310827684406, -1.9281442312501649, 2.565845203979001, 4.824010484363448, 2.9548668428590914, 0.03903195779150299, -0.06813688829310542, 2.339483685928417, 3.5915499025525155, 1.8154876198618193, -0.5777297300520757, -0.3272874772143998, 2.1770832743010313, 3.4608257267366116, 1.6677604370856758, -1.0845510597244001, -1.7269951953465068, -0.25453083526872267, 0.7142642871073817, -0.17055677511907932, -1.3255477434051026, -0.9265973134593529, 0.2873344417979835, 0.28767005066610823, -0.9465337000385209, -1.2715526680558213, 0.2235655848968058, 1.499418765152161, 0.6508864852846643, -0.3857678601584934, 2.523646743027433, 9.898096269700117, 16.370274349413293, 15.914468821642714, 8.725364270615701, 1.1730634064233683, -1.253180070222163, 0.6425436799632145, 2.18436653896535, 1.1162840624415309, -0.48330500065238136, -0.2020173818410072, 1.1498506186603528, 1.2214696476712388, -0.10721448901346112, -0.6786288704042267, 0.4411441990655479, 1.4700126274127485, 0.786794788188419, -0.27445241552208316, 0.7660950791032224, 3.554560709865987, 4.796852630402675, 2.6399059182891227, -0.5928696392154746, -1.4291423086303086, 0.09358108900318453, 0.8168022255744907, -0.6066561655511106, -1.4699757328145764, 0.9932967051748454, 4.976233038541606, 5.808896915956066, 2.162271432734034, -1.7998502897463742, -1.632174927149813, 1.6724195907355066, 3.1674780166946257, 0.5557023889605455, -3.0346169420329208, -3.5435972242919047, -1.2488319684959932, 0.2360300806009374, -0.7956778779304796, -2.2370643319159598, -1.7574616664255382, -0.13703036651555123, 0.37317097699710944, -0.37764975068022355, -0.5671746151974011, 0.29893512071998574, 0.5084055127273577, -0.6957147108049003, -1.1146206516709714, 1.3462626177205297, 4.698298521283347, 4.545366177253141, 0.12773305623099152, -3.683049836873092, -2.125638860618957, 3.119966661944029, 5.70524591023084, 2.520098808864897, -2.6025582319516043, -4.059757714469632, -1.3281416401622863, 1.399075853427028, 1.3409189650864273, 0.1194397245844412, 0.17391519254433938, 0.7962864389792523, -0.2596483118980236, -2.6111143570148863, -3.3580017585664974, -1.4525684779797732, 0.4622462418773716, -0.2151627685285779, -2.2403461907435025, -2.387267359029595, -0.20818717807662093, 1.4406090133387728, 0.7710682687211513, -0.450229211589954, -0.08308815602251403, 0.6655838960429649, -0.8866558585191304, -4.08313539293333, -4.955275562316807, -1.9031008149092559, 1.219014106073147, -0.06928790575795678, -4.334741390489803, -5.467303232218745, -0.6570864827446441, 5.6110582998461105, 7.072861051708695, 3.2739615806656466, -0.7029095821136734, -1.1922762284253587, 0.2517700485366229, 0.49520030522787994, -0.4961436134951154, -0.6298058127702941, 0.294299016443165, 0.313427696070569, -1.1235990606226713, -1.970057083040688, -0.9231227683865648, 0.23964228908917784, -0.4995562892275369, -1.7387806442871057, -0.47178874954364325, 2.8014102501460627, 3.771982273027323, 0.29580650941295605, -3.794798574012546, -3.272334108242362, 1.356122571854134, 4.295863644214531, 2.157145922908739, -1.785119965629172, -2.5283322041363956, -0.14220048338312768, 1.1339167503142815, -0.4877518548651531, -2.03787258775925, -0.8074475533878821, 1.345706246585669, 0.9248920107429138, -1.7668988016262528, -3.061507682090806, -1.4255714612178543, 0.4399133448223235, -0.10436471898368953, -1.7617838894624391, -1.6707081959171703, 0.026947022921924278, 0.6415044076377503, -0.5941954251114229, -1.396626067139615, -0.38559313844838944, 0.5644814488144643, -0.300939014791227, -1.0883942792872927, 0.902624032772975, 3.7060193436178412, 1.7900646391009984, -6.199695329993125, -13.842318975232761, -13.757529962425306, -6.501834336681378, 0.35070308717062, 1.5979591223163159, -0.37369611822193516, -0.623281623667048, 1.317352838828874, 2.126771604786007, 0.5733787294070225, -0.8685177305763845, -0.3460582129994568, 0.6680390356364853, 0.37358297025110293, -0.18142340833391402, 0.7826051500595486, 2.104330740598411, 1.087203617599423, -1.8268642241299615, -2.917573893278489, -0.5828480786395704, 1.921137619882891, 1.1046622656661187, -1.5145908857711259, -1.7367660048651907, 0.7673413695208708, 1.8389435167828094, -0.6225048334638718, -3.0047744065821744, -1.2146129395202505, 2.8719159513409833, 3.689276384365728, -0.07675111234328949, -3.6133098995559, -2.902649373477472, -0.11278854741244101, 0.275660828047975, -1.6802618586824052, -1.8908521160060876, 1.1665958150817044, 4.061916080832062, 3.546823196693419, 1.0088090319008058, -0.2218041137167794, 0.19315684997658278, 0.11854437820742848, -0.8124770401209689, -0.7368245792436542, 0.6163266672284599, 0.9074808809291063, -0.7460635180374758, -1.5759243884021679, 0.5527204744243343, 2.8199999052720095, 0.968806061304958, -3.5566716910024603, -4.103200609341607, 2.2637738141055226, 9.78346301679195, 10.74954073917965, 5.096053140287287, -0.2653919655467261, -0.810756429820666, 0.8975689561070455, 0.6391059421061708, -1.2269197097225177, -1.626133949920479, -0.3153434632577107, 0.1607984810736852, -0.7419162826578909, -0.6178053016349153, 1.3677641638114764, 2.3765607689543744, 0.21377003835234415, -2.798083071800354, -2.9627081591358104, -0.6426367557272048, 0.6425153405229649, -0.060028002404878836, 0.0844399469821848, 2.4816903973817683, 4.224305351873364, 2.647818815930132, 0.010377886025300882, 0.21250254376282857, 2.342937017246774, 1.6926759949343322, -2.583334872006265, -5.12935846529048, -1.8849088676468646, 3.427182341320326, 3.9229691778861406, -1.0369723881030068, -5.218100241389037, -4.221987999763514, -0.7120467558243397, 0.572902015976304, -0.5269223072708802, -0.8982647053861201, 0.16227067094271513, 0.4052897591877695, -0.8420740211187817, -1.3903236017677545, -0.16774629520692388, 0.8005964624087867, 0.019006928894366046, -0.7056571901409618, 0.39287578178717014, 1.1984118985762917, -1.2458412643453216, -4.96100992240702, -4.5863283165393, 0.6176517518818726, 4.450293518026445, 1.8559328770435912, -3.836793432912276, -5.371668210247139, -1.428209585175931, 2.341813728424493, 1.9231360016601702, -0.05729435884204444, 0.34328280373141845, 2.049776457227897, 1.4352307107499929, -1.2832439839108924, -2.407905929263161, -0.9163346497531768, -0.007336007783845266, -1.603690261718312, -3.092621370069986, -1.703289782807384, 0.817798476245403, 0.9882068730471367, -0.8249798049848704, -1.2084190566032036, 0.6301272713157441, 1.8109344297671481, 0.8155182458294549, -0.2289992507057089, 0.10412747191582455, -0.4911291802706951, -3.684808721482622, -5.865421400070193, -2.359624348334007, 4.610397605098908, 7.155278421420095, 2.087710773386521, -4.284563916704671, -4.4562220740297676, 0.5308239843141146, 3.5506744167077517, 1.5908581943791016, -1.3229977320904, -1.2949817689640901, 0.20285676360238544, 0.14776733715292145, -0.8520718998302076, -0.41431405952210665, 1.0054179317844267, 1.0641908485560947, -0.08751089650854138, -0.18489505041894178, 0.603923214961802, -0.5356450589328454, -3.792090483223995, -5.094567568789712, -2.0275974019530025, 1.8038513393080726, 1.6714010902269767, -1.2573165668756978, -2.0456852262404235, -0.14638643765130785, -0.41627932093262476, -4.982992714820269, -8.918627363265818, -7.065202655331658, -1.6674901046002155, 1.0040470133669905, -0.37214761866053814, -1.4405819549475065, -0.0052168103216856995, 0.6181808629373081, -2.225403013866288, -5.462603571807959, -4.772800512241053, -1.249221248048588, 0.4575707786430673, -0.8209051245862604, -1.828582481811178, -0.7277380878597707, 0.38133744441845235, -0.18954992581123273, -0.7430176078531355, 0.288866992327776, 1.1086646883499074, -0.17121173190416955, -1.576172822084911, -0.4281168231028897, 1.224514135678748, -0.8851320367568454, -5.456960403191139, -5.646462293788707, 1.0973600848425078, 7.824543105995833, 6.57952633324323, -0.922912980052851, -5.873069658332312, -4.160953376231559, -0.3428219827500863, 0.44510515677907614, -0.8134878165832143, -0.7480681555438775, 0.3371351810080265, 0.07055990128525695, -0.9533108802985766, -0.20668397595021473, 1.7873792855736435, 1.894959480892439, -0.14105108234151678, -0.8823556884125778, 1.0590264895226806, 2.472875667176775, 0.9059098487607636, -1.0147761472266035, 0.10191031264667996, 2.529020016732719], 'positive_zeros': ['1.12098213807061551953099279964', '2.39428989397704541567421105902', '4.59160695823789408138017552627', '5.44109997478450942114991098733', '6.665940392730947369489415186876', '7.41032217757102857551963740488', '8.37077964893251027798663913335', '9.19005510376974962778097124968', '10.70514579780412454562931945571', '11.72068028152120917760900670312', '12.93176918196667143151762964646', '13.83203008804565769653126434778', '14.68487901971575650093004438075', '15.622202443173765086142468141071', '16.84076263816456381766860608806', '17.63915403648689261717369388461', '18.3819173265937181122017604156', '18.9624564608043521533351536822', '20.202743563681968944409766779525', '21.33485127604635572050484799814', '22.715659580054311166536694889152', '23.51540488193924810901988914958', '24.00756843157673612465764197807', '25.09042994625264624993490827324', '25.54149674801085754951438633350', '26.58629906187135661006620907348', '27.753255366306553343990978511078', '28.348711433906342753432291867856', '29.26439198119167215759359306715', '30.63959889247925767281560418097', '31.08255650262230457796113488233', '31.99327788062909717113657503119', '33.35946906284572667761788676097', '33.92857261411640707794572394730', '34.595727070136576772399477994666', '35.5403205565101110310527321662', '36.28599589755156727318807932046', '36.83193635504283117973581693866', '37.74222858841977436074875193626', '38.94068308282962810937022781531', '40.321153853167578509026501022333', '41.016906475068029184534735641008', '41.18172947498794529659895130140', '42.59831992776934001159246659141', '42.92593231003928745522911752561', '43.90436414937135709551578007379', '44.76918659646963922785631890513', '45.67533075429750612430992512578', '46.452547179018780790013102257088', '47.12682998589513192024458740779', '47.80610970047158686743621059668', '49.24926751877489324753709790461', '49.810238998362987896860805732780', '51.00371445463544308812214774263', '51.45633037674721327511942072795', '52.42531596436232136041520078788', '53.01115599642690030302792705029', '53.73693703324676029999908971469', '54.25728938460477010800103534789', '55.29650940086146491374339676501', '56.221579988437331522995723743702', '57.330344862920357176991561549752', '57.94740838533446215458583918232', '59.03676484702499773918191274611', '59.59877471767235241637005121889', '60.27827595101770720326707523711', '60.88288474770368043277513125923', '62.30176590948674923008755232274', '62.854662381861453464366310716499', '63.16439445343420841755354658567', '64.2592077628419358921976806109', '64.90811374586307417612481672219', '65.53484144534579570039217498534', '66.78375553635678205327787536143', '67.75301041574693889178375896420', '68.56655250630656041912169732696', '69.324636143849878910491274920834', '69.95867384567955554579833605406', '70.45901220200878911998958410178', '71.16510331083955022171119586684', '72.2233874545714673014205398412', '72.766808255386446455381341112280', '73.60888273677118063353895166221', '74.51129528855760238181426301781', '75.63152489412167382112877929236', '75.95017323353927746993260080477', '77.089192863397374211649932571993', '77.550612911918680768765533671331', '78.6135633766582995333237309362', '79.42402834845976511889621510597', '79.962371928540001653209655445139', '80.85110604784789090093346869857', '81.33556009240759416851484280126', '82.150453786985117157684976819047', '82.94162017767690702333183511360', '83.23045897209938317893766569478', '85.07806544963430556469856508661', '85.54486431014962391615336651353', '86.43965312155681126759505773055', '86.9234173281142469532180963129', '87.78797524328722743927762089541', '88.34403675639575151224585642166', '89.25303152971630055706225269374', '89.55608220454105931697016945651', '90.86902443649387293481685205599', '91.54530569427817611155883154666', '92.08335981157923059711340947369', '92.7273498367463545684204650099', '93.895826863555275155126518534223', '94.53847212607699848539171361155', '95.35602109568192820976641894354', '96.4515039523697692782993830326', '96.7098943838456667415453904097', '97.84609010518957516371530184625', '98.30008754007686759880250908293', '98.96510871449266380041247299563', '99.531823338765334098688962633968', '100.18339690139927459573848771012', '101.25768855406872236408860161773', '102.00809123311228198190995940339', '102.95673044173141983669158758789', '103.873296233965651671990042352787', '104.747885679509310379788120107774', '104.908220595836050948709531879034', '105.58401053778396786022800333429', '106.76271167763955750876771492484', '107.149848680089579791725483929297', '108.15165192066732640045603821598', '108.91626088326965772018903022690', '109.39931744234513058686270756007', '109.88785992454829270055235716735', '111.092683512498208244843224934', '111.55646122304945338850857103915', '112.53014993221778603475778070817', '113.67362575865362839691090797653', '114.31546205212553245711250096607', '114.84987572984218780591887949570', '115.52667531063208552889071092388', '116.025372964899154421106775971092', '117.07895918250261420738162165288', '117.38166262423972252781884571706', '118.174527703985831182336900386804', '119.08161198269109328971428756379', '119.9154543884539301529277537101', '120.78406545331507544121887325946', '121.58020368018651210387008967471', '122.12032281570109716307837958553', '122.915522234077150766780323762845', '123.555505769446444920361340903683', '124.579193409911998591463851187592', '124.97937477853034630306195709902', '125.93223464672163490139001521208', '126.4397776304259702002165227544', '127.27251459307489695936027388136', '127.74453906298238129905406622294', '128.34232125942403394904300294246', '129.1505173000143715557245175680', '130.6007496734641512608117643665', '131.18833296744139221959693208855', '131.67929816974418423305019310611', '132.59127135742092769118227529288', '133.21209627784064693837839312553', '133.89611172844334775156195805132', '134.18571136524536680904011068080', '135.12178215996415439394484954321', '135.994123050168462731212442125723', '136.69004581611863971882305875473', '137.412137418812884750249407435172', '138.06641548275817294761894228823', '138.842171475764961989054709174691', '139.68238841848392640449543456539', '140.64236608104677724835655591815', '140.99342778678390497340624697171', '141.77694715424968627488110623911', '142.99919498672113216722550388637', '143.33240040283499478627574491075', '143.79638200126967545006452005298', '144.55256903662691914747817548594', '145.192204637747199643432215605411', '145.87968171758236838711742001415', '146.631516275189330280633659483635', '147.41312385672506748376490199052', '148.724884815009290077903691352052', '149.204269002781117508107921371544', '149.797864961646647354600309552538', '150.71279156673774409833024646051', '151.01423084326926611797256526197', '151.6792334666046150483965403636', '152.520028697393037836183920936924', '153.533060719264810513362313152342', '154.041126274892561891153349202341', '154.35543884953842620585002334379', '155.62702251576614979957666705149', '155.89817993813407915019422648346', '156.70237667749653017566413803374', '157.60245252609804096555948523047', '158.38200174337557516700708694416', '159.46415989549732733826506193712', '159.87518379542474777359360621663', '160.57950853033849908007949982071', '161.06172034183319515551053210126', '161.90900011609091496021842738581', '162.50476932356077106688265383243', '163.04726609996722206922493544518', '163.63951061168311833335665126803', '164.65474697034930732921917149632', '165.412605449496332461569831082691', '166.342233073117305566916037999286', '167.17242958283109796173401745878', '167.426540666459699876307623321321', '168.29422852576445936524422195872', '169.291234382457118012280542985585', '169.36932728698419266325098515774', '170.50767740025885611234701800783', '171.11277783233683218844048241267', '171.78284219872639197848212119953', '172.69380588738485378628174478331', '173.06184823875984505425752727090', '173.33517854733426987378856451779', '174.48192077429044511975602797502', '175.40100493081009114189062148124', '176.21852563168578892669198756994', '177.02141861748300189236018765929', '177.7578247031931564924381871502', '178.16978937215342215023881854793', '178.83950591114800528632183935355', '179.659958458980435771979705867765', '180.06934534067253688029534547286', '180.55208587451798740518609807201', '181.70589675389148624985190498700', '182.36702634503797376282790309152', '183.15363734435562232756697142459', '183.37913917063413085472834018745', '184.81427490497376804029376902909', '185.25647322540609364239035093486', '185.9383951705550217866189746949', '186.35656105985871548514412705573', '187.64814563206778865878049455254', '187.97615395813903928314256241869', '188.904037525393499375448246644714', '189.31634451400877671312269301847', '189.93691384631658500353038639715', '190.59748588069626961983586399147', '191.31010905945021929274878301634', '191.80308562323725027111438928390', '192.77169986151880217841297377916', '193.71320072127751374515464008479', '194.73160842048680293276690043530', '195.11706961933450382148558414575', '195.823974325295488288969680897017', '196.269958766984109283809427854287', '196.908805276370301526486299010112', '197.79112960957873911718376554683', '198.29853078772669920250078381395', '199.176607226471062785636964433810', '199.674669175833622485325538782276'], 'prelabel': '1-265-265.167-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2306548262188, 'root_angle': 0.12113439823614237, 'root_number': '0.928458655622663535509125886422+0.371435761336137742141912418591*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0605671991181', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(52)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.880019361538362775479110142943+0.141918249191571254394456626098*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.12098213807', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.39428989398', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.59160695824', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.2306548262188, 'bad_primes': [5, 53], 'central_character': '265.167', 'conductor': 265, 'conductor_radical': 265, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/265/167'], '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': '1-265-265.167-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': '1-265-265.167-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2306548262188, 'root_angle': 0.06056719911807119, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12098213807', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_265.167', 'Lhash_array': ['dirichlet_L_265.167'], 'label': '1-265-265.167-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/265/167'}