-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3525.128', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.565467801802006, 0.8247703711489686], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.3604923302504147, 0.9327621775300636], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.816969893010442, 0.5766803221148672], 'a8': [-0.9731614129083754, 0.2301235851149864], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 16.37003117894819, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [47, [1]]], 'bad_primes': [3, 5, 47], 'central_character': '3525.128', 'coeff_info': ['x^460 - 1', '0.999906715964522 + 0.0136586737659511*I', '\\\\zeta_{460}'], 'conductor': 3525, 'conductor_radical': 705, 'conjugate': 'dirichlet_L_3525.3167', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^71', 0, 'a^142', 0, 0, 'a^185', 'a^213', 0, 0, 'a^126', 0, 'a^359', 'a^256', 0, 'a^284', 'a^403', 0, 'a^258', 0, 0, 'a^197', 'a^21', 0, 0, 'a^430', 0, 'a^327', 'a^32', 0, 'a^8', 'a^355', 0, 'a^14', 0, 0, 'a^89', 'a^329', 0, 0, 'a^454', 0, 'a^395', 'a^268', 0, 'a^92', 0, 0, 'a^370', 0, 0, 'a^41', 'a^17', 0, 0, 'a^398', 0, 'a^103', 'a^364', 0, 'a^256', 'a^79', 0, 'a^426', 0, 0, 'a^413', 'a^85', 0, 0, 'a^182', 0, 'a^131', 'a^160', 0, 'a^400', 'a^311', 0, 'a^102', 0, 0, 'a^65', 'a^333', 0, 0, 'a^6', 0, 'a^339', 'a^156', 0, 'a^84', 'a^163', 0, 0, 0, 0, 'a^337', 'a^441', 0, 0], 'euler_factors': [[1, 'a^71'], [0], [0], [1, 'a^185'], [1, 'a^126'], [1, 'a^359'], [1, 'a^403'], [1, 'a^258'], [1, 'a^21'], [1, 'a^32'], [1, 'a^8'], [1, 'a^89'], [1, 'a^454'], [1, 'a^395'], [0], [1, 'a^17'], [1, 'a^364'], [1, 'a^256'], [1, 'a^413'], [1, 'a^182'], [1, 'a^131'], [1, 'a^102'], [1, 'a^333'], [1, 'a^156'], [1, 'a^337'], [1, 'a^70']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-3525-3525.128-r0-0-0', 'leading_term': '0.918768963029619421949746831525+1.65448590084798496060977522217*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/3525/128', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.8924745714358457, 2.3991765981787134, 1.771208497589123, -1.0525763598172309, -5.128441536531989, -7.769284889544098, -6.919413299116366, -3.339589643274964, -0.12754164624746478, 0.3123139942448912, -1.293432321752169, -2.105096832707546, -0.6084244182781372, 1.6283834707425182, 2.0820601358122595, 0.5669399008852536, -0.6392007262201695, 0.013097330166787541, 1.2676539500041861, 1.0422000782366447, -0.4061249516534807, -0.8626040829259193, 0.36228458034119165, 1.1647844671109668, -0.14610775998088057, -1.8954448927691996, -1.264315186643612, 1.189008261001521, 1.819445440306913, -0.6587937424831054, -2.632607787920705, -0.622932647533893, 2.945432099330262, 2.3465473054490853, -3.240225662780101, -7.7319869111910915, -5.928384469685894, -0.33817863953774496, 2.613787102767586, 1.224843358378929, -0.4732888139514212, 0.22736133443197537, 1.0611810474982777, -0.40691215725449337, -2.236968880540862, -1.3955291029974373, 1.0177231167235796, 1.5560712771735086, 0.040765715267527286, -0.6253814820643235, 0.17280148463614753, -0.12033404646180511, -2.075034447131599, -2.629956726750559, -0.505433442108226, 0.8996562032072858, -0.8789196704195639, -2.6023354035174053, -0.5689124270823507, 2.336327887254896, 0.6302295844755046, -4.175683455919707, -4.745979752011914, 0.6650763511904209, 4.853694432352978, 2.464625050787289, -2.11430355754597, -2.2063364972740533, 0.9525364970921814, 1.5011515801280984, -1.0789468012624712, -2.1762152958926286, -0.5379713678403124, 0.43886358208413034, -0.276609902656009, 0.24999299496563854, 2.5332273172091226, 2.9758098314284167, 0.3974510333100155, -1.5441674924263908, -0.7585490819991036, 0.07005237413634507, -0.6409801147456079, -0.1560880745113658, 2.4061765008623475, 2.7197897423736754, -1.24090247693368, -4.2095408833300665, -2.053207778245054, 0.361915130011428, -2.9076485760952244, -7.903527825660488, -6.64374904230936, -0.6848740506694104, 1.1720207287486728, -2.683651081879297, -4.87076554691254, -2.058917081295627, 0.38243734666011303, -1.111707616332889, -2.6467110483792378, -1.093406449998801, 0.4918453294509503, -0.36256062885993184, -0.9124078804083867, 0.5803340236518397, 1.017630546279587, -1.098674975941256, -2.1790862398082687, -0.43002222505789234, 0.5955430188745141, -0.8359917479508789, -1.1193127565486882, 1.1234918961690072, 1.767585345688689, -0.24167042603809286, 0.33730333100118975, 4.55601267404537, 4.923821527929296, -1.8460544957967762, -7.168410911425799, -3.765396450115985, 2.4108855037933736, 2.6431736923837685, -0.5066878758188034, 0.08578664486093601, 2.7279920582518127, 1.3965123535713995, -2.246239511863933, -2.3453019637634, 0.23018970013131315, 0.6109390043137168, -0.6050195219720745, 0.08759197113166789, 1.295774474717943, 0.09387198724539476, -1.3008374560252354, -0.14163416534311188, 0.6764139270008134, -1.5236007308530202, -3.1395392711878576, -1.2272517539776389, 0.41189399395258475, -0.9930820977633401, -1.48080751074754, 0.4987496468686092, -1.1165979790675205, -8.063113511561781, -11.205123829041634, -5.141536717642365, 1.4345017620860643, 0.027469362680800614, -3.860658726420056, -2.0200568057828425, 2.004357556690568, 1.2308043648150404, -1.696180924097422, -1.1152029485833863, 0.739921535593718, -0.17427220076741667, -1.029435457626457, 1.3147269419757233, 3.256633909260565, 1.670006154594619, -0.15760702870703266, 0.17759532335131348, -0.08605400828372449, -1.4396639070795314, -0.24569023360819903, 2.620761891862143, 1.9563193664156113, -1.3028328230578718, -1.3100522856482915, 0.9994910040623484, 0.1316266177517002, -1.652262732404717, 1.4283603189975587, 4.734600235212659, -0.45743919088596474, -9.432648363049292, -9.815377802681734, -2.2196004229162383, 1.9151728198774454, 0.17030939035447012, -0.1404190864885321, 2.0368879531552415, 1.2825717003753172, -1.5382704527406086, -1.1841853494354424, 0.8863919652749936, 0.11733658316320973, -1.5061765788125183, -0.3793579010740111, 0.7985308519171465, -0.7008848008610837, -1.534858502514191, 0.12709448205944848, 0.46610439739622744, -1.209475017760621, -0.6203367094034028, 1.418222497780808, -0.22552513625897325, -3.191851786640666, -0.9074528421982306, 3.411730013995455, 1.8461828336166537, -2.1481446721077573, 0.012332701139827472, 4.301649808097581, 1.08069875516248, -5.632289135047666, -4.802312679760789, 1.6191363978258086, 3.498653210681282, 0.7379310874936136, -0.011873532452681348, 0.6436859325333643, -1.0914291112023462, -2.445818704547682, -0.5776072371736861, 0.46713744907171895, -1.616362892171783, -2.402838761926356, -0.39802038648992316, 0.0890468556076566, -1.2554078454584001, -0.5832072805670898, 0.6460241015570645, -1.1657591265535143, -2.656130221164922, -0.3185436057007349, 0.7186565801146041, -2.74117273808425, -3.378720592492304, 2.2985000532309243, 4.968132813216529, -0.1065063726735569, -3.131969891756931, 1.3844807026298172, 4.120561293543789, -0.36036211878671487, -3.54660334554504, -0.4947264549028342, 1.6591035336397408, -0.6769700575135936, -1.6973447392022778, 0.3121435144835904, 0.5871889137635735, -0.6466498710079366, 0.4741357117918041, 1.8224976363727146, 0.14454481074833625, -1.0613599700102927, 0.7782739291617483, 1.437206502819948, -0.47608876359013164, -0.22780625040335567, 2.1493003501969823, 1.6922716398168713, -0.15095548771390077, 0.6799214590459102, -0.3510170135338276, -7.1689836147528725, -10.82331055778681, -3.9950791549579714, 3.739309934780742, 2.4637192046687537, -0.8841503552718672, 1.7750975350043754, 3.9849011566374433, -0.1250799933809381, -3.356429416768565, -0.669049067892768, 1.4545895058281566, -0.4217261446738332, -0.8455626840794809, 1.3847050398760556, 1.4476342700065499, -0.08050504872318151, 0.5453902396190189, 0.9774117929506608, -1.2585353711518767, -1.9870342074359726, 0.4767533173509048, 1.1563447354388972, -0.5204865503460787, 0.2545466437892591, 1.9601965234424545, -0.042587535320797246, -1.8335153980812011, 1.0391144679666953, 2.335674082444927, -1.749333248218761, -1.9799047382921333, 5.594143461983683, 8.749256114335173, 1.1990448094401311, -5.186175457819793, -2.5214154634725063, 1.010357616918576, -0.03902456070007602, -0.23613324451319667, 1.287476217124151, -1.0004102500109489, -4.929166336163006, -3.972206783792706, -0.5300091035499118, -0.02721669279927136, -0.4126503859691937, 0.5743470589164565, -0.14802911678303543, -2.01077837950944, -0.5570506292393032, 1.8778379854994118, 0.33914848133765707, -1.7312253408033669, -0.22356195037449378, 0.4268113078398958, -1.574347771097437, 0.13317289521873926, 4.843350150141017, 3.6510692274636685, -0.9359757109573019, 2.328511001790624, 9.948017623049745, 8.690324067836137, 1.1025775003896798, -0.14601876094680016, 3.5719355933321757, 2.844132253545663, -0.2675521348291554, 0.2818106823410254, 1.082420387032778, -0.8972856915297711, -0.8204166798709223, 2.112318058460489, 2.25003071621087, 0.06322112334915883, 0.3807094136333607, 1.2378690308871334, -0.5985320685252858, -1.5899502745877991, -0.16827485536994977, -0.4323503808436058, -1.1461727233500736, 2.424567697048193, 5.797756728667014, 2.7412091320203302, -1.1116499138228821, -0.16764694810240108, -0.9015470136404548, -5.5257062689269425, -3.5762400423760132, 6.096466529439429, 9.292431953204051, 2.638058427950642, -0.9226321498470632, 2.1851498021212623, 2.41456799379902, -1.2341498250825804, -1.5308910133486913, 0.2502012036946883, -0.6780064394688494, -1.082776632374364, 1.3018416042881313, 1.549058409562516, -0.785877974052702, -0.36473314503673304, 1.6285038722625014, 0.6188169661742353, -0.7774334162056445, 0.179381205413938, -0.3501492488641179, -2.311384611953321, -0.4551172298984348, 2.5070015925293347, 0.5412925514900087, -1.3086162249576887, 2.348237520398631, 3.3183236826776117, -3.253380562589979, -6.23943269098926, -0.5374713315225116, 1.9940914332890967, -3.0132096162085436, -4.4010465633283244, 0.3059528317717012, 1.1601048961341167, -2.161232439427554, -1.4434226874227791, 1.6872250951143581, 1.1777006509437233, -0.14368736134765964, 0.8331616242096125, 0.47842447853915837, -0.9989562115399957, 0.7592052049394907, 2.895796035583749, 0.8410959359584845, -1.2264509849802772, 0.1948773520396527, 0.7710248312842254, -0.34874010015048806, 0.683197317751301, 0.6172298514462117, -4.213582784831974, -6.152984747720433, -0.8784897635886052, 1.4095474691411587, -3.2293388389419473, -3.342308717725975, 3.177218244825422, 3.548705633698845, -3.1961742856335125, -4.599590675395691, -0.5456420136698289, -0.8425194908093696, -3.492054425178987, -1.5619836135908391, 0.8213506267701041, -0.7325974155489596, -1.1755326702823456, 1.1081115778647164, 1.0379392295325776, -0.5561748013304324, 0.26390449026778345, 0.6013471898674024, -1.2621621788251927, -0.5147946283069659, 2.2610807132737505, 1.1534181096426974, -1.4608309691445318, -0.30391390961120796, 0.7202813754952996, -1.0357673505700709, 0.01480280574454464, 1.950058526160431, -4.058714589206381, -11.82145731496652, -7.602363035826773, 2.476132941933138, 3.184017855100881, -1.6779594528887174, -1.0091939930800233, 0.9736619387595826, -1.6106524354479301, -2.179843394005419, 1.8065764322374127, 2.5148727233671564, -0.6651058704888907, -1.0104798592959099, 0.2952071018406053, -0.6670666299844329, -0.5138098872576224, 1.882807781599987, 1.6245137215671408, -0.3094914913197982, 0.57916144988672, 1.2601972918211366, -0.7136251558293176, -0.04720027750835602, 3.1585885036291304, 1.895551696700364, -1.5679788484739872, -0.5820967008216088, 0.14921638246775062, -2.977647413716786, -0.24032319366100957, 9.894829325615149, 11.935498155287194, 2.375319708617809, -3.1262562495921595, -0.11173997328762979, 0.3125573904774696, -2.7457435179850584, -1.5982636952128428, 0.8580981040959528, -0.6177131481758338, -1.364486706314855, 0.5726756294957303, -0.3890044028380438, -3.127305475922535, -1.9528199562096422, 0.36070479056100735, -0.15845047926473732, -0.12605034015114516, 0.961189696851559, -0.6892773982353426, -1.8894037002016557, 0.9960487054294798, 1.8931399748072522, -1.6266130562200876, -1.8940977853268155, 1.1604964229357182, 0.13332852107947146, -0.5656651797986939, 5.983378576591691, 9.781645339454084, 2.602135552763007, -3.05221631785954, 1.393371410456847, 4.155242585456628, -0.9229456833598708, -3.5631780545427914, -0.7497176701063588, 0.04841569462205442, -0.41893895752752247, 2.090618045168832, 3.0742497923454573, 0.4072271828274219, -0.08379329421946145, 1.5034302245594717, 0.20786277369754091, -1.2477972676962243, 0.3088280187985509, 0.35563970999409616, -1.722231587962093, -0.8513098532147655, 0.8881079365373911, -0.14449487372220635, 1.1721107833428952, 5.4352273357847976, 3.9456320046054523, -1.094589426467082, 1.2904606408546182, 6.380930184374725, 2.897902005774452, -2.353610639725733, -0.2014949300843746, 0.22010593421748897, -6.906601223630325, -9.537931042269697, -3.089185210413152, 1.0957632898330143, -0.2229286312069812, -0.14926601438223064, 0.590592260251356, -0.9891722545405066, -0.5010545970985023, 2.256815033131561, 1.343520692910633, -1.3569483841861734, -0.7076899641431051, -0.0354227529236273, -1.5004809576790001, -0.4286330770747817, 1.9979483449911246, 0.8274881177798248, -0.09690501443862717, 2.123666466171786, 1.1187577168236003, -2.279706493719348, 0.6058234133808564, 4.696085483043237, -0.27667093002929766, -5.461563697185933, 0.18089576215282588, 6.091642190597443, 2.3049179027839033, -1.4810351047775525, 0.3918888252626868, -0.6124206597304939, -4.417301876725855, -2.5385759820021887, 1.6275250402657613, 0.8967566615784756, -0.6369197789117128, 0.44697133530572036, 0.05854113821594495, -1.0115382354523985, 0.5138649128691808, 0.48778252333109556, -2.527254334239972, -2.26114861607474, 0.7647822210498042, 0.519904496414716, -0.42202545103445355, 1.1974484194002457, 0.5200867073579196, -1.4508976030648575, 2.007617902704429, 5.080896511393217, 0.13598020102578726, -2.478403305980191, 4.856171901826566, 8.60024695213494, 1.6438376276550455, -2.515895877824247, 0.8921986869429549, 1.125592321071526, -1.7826530636128404, 0.3085371053341217, 3.145453386027035, 0.9949170599968313, -0.3214941118926253, 1.3442283805408093, 0.21598928120432104, -2.1268580279791034, -0.8835062590943497, 0.40276143501118167, -0.33390565868786554, 0.7654504729791831, 1.5203798053000128, -1.7480281710150587, -3.347586068971561, -0.5328308470888442, 0.05184793288715568, -1.3755003859129489, 0.6890083445831953, 1.2021620230394534, -3.4528894789084266, -3.64585443234568, 1.3493160930890435, -1.7180767686117373, -10.093139786841641, -7.547888931476428, 2.042047019702068, 3.17535873495929, -0.7317184831738328, 0.2305228500466741, 1.597865738174875, -0.08519610134338153, 0.974057706286012, 3.1040964628802095, 0.3881804765046062, -2.374839201897409, -0.5854562699332017, 0.4957623600690309, -0.5517634100701246, 0.3364228295182658, 0.8442445596078458, -0.8596787681152318, 0.3123758131318315, 3.1848779742267137, 1.5236404760145252, -0.7466649534962558, 1.20109770819362, 1.3681933347037754, -0.7555176352559849, 2.917539634038355, 7.513715775479044], 'positive_zeros': ['0.84528094378542188582066724797', '2.5210326218551182797575672589', '2.8915079778059503722517230661', '3.82901112290799856438212496144', '4.79239967965170498338128612179', '5.309477278950491295370574261920', '6.162099802549193017079458371659', '6.80002541600786771919224282299', '7.477689106204116819964988442942', '8.28791409012641594125713275116', '8.995942700195205445607744170359', '9.73803651935894474015288448779', '10.46339361233492454877460358800', '11.583348453670601599369308298824', '12.36606326722121908395865102537', '12.76088377674250550072522023215', '13.38032480178713241841288873763', '14.237030887356301516339115411135', '15.008271288031320478078190505475', '15.55916630388607282828508085814', '15.90924863865041362789021742669', '16.940418422134335948194738461141', '17.39165657858562766362655959725', '18.174665961985693502926876824864', '18.79334802025469653776228750793', '19.65493146864305970978825703685', '20.46382361514333177526471328328', '21.1521726155476403012815536803', '21.755264417985016983559036060800', '22.59847612017055706540468910221', '23.017448743430280626825932922534', '23.38912806821401663967873235399', '24.41722412413271117775777950355', '25.21318022149041895870742491224', '25.37960844377558515009657835016', '25.96179716986960666856199573422', '26.79326060165155209235912483234', '27.701777700113953535144199825799', '27.90904805104838261967092050639', '29.106809459439700502946349991746', '29.49899299414608076813783095500', '30.52072703413818549013905230938', '30.7822538993176212898163561054', '31.72301665030869083862670256320', '32.10562874168046543684223419656', '32.709818721955228739462907797456', '33.297890275463095554148999545446', '34.12929597156202218289474630817', '34.53702095504438305412153997342', '35.17095043100321337408598032803', '35.89695059273118681054990794134', '36.212993446949286670574405180547', '37.11639261470812033691241471742', '37.98336236401427814123699210343', '38.68462423469349708774607280678', '39.05260231111660865176185397206', '39.79995514797641473849293393958', '40.59179412139731595774170246495', '41.078427804783528979988052004449', '41.545509172304793360546069163868', '42.20177268302548780025004320271', '42.83707460081144014760447549223', '43.26123534593888095676568557290', '44.22481581563271677786247819785', '44.52097346382254430078790103623', '45.22741699686002359565436450864', '45.54076886023709386869597134116', '46.7728485400196774754549062770', '47.189395661519884570636166116', '47.9479143877271643241811519027', '48.55273910010331412725287292139', '49.21471431834726399604173493288', '49.65728551441614519543871875467', '50.175810354883865658110998751156', '51.1928471224251216222658729787', '51.48176118169681226739937230642', '51.85298352598943373102579736849', '52.52616024583836808516697067644', '53.30342421551804375925653580375', '53.91102683237982905563740336005', '54.39101964361451958447079486146', '54.90475729061798600675824808881', '55.609314358699980075641671418660', '56.66717249700574526507603162863', '57.21309822307669918897084850140', '57.52384510687281487671807653556', '58.256024721109900721529294453235', '58.905568217224198639192667305558', '59.39240683829843591797958808149', '60.05990669462762536377365422441', '60.51639968123072668817028936344', '61.22782874294080315488216319195', '61.65616673855650058866221655619', '62.26892711225570877962878513796', '62.79233429191570421778982429327', '63.493877382727407343022890160399', '64.18328700004012327622588221870', '64.68674817265730210364701360680', '65.358987689916346921216625670785', '66.16643317063729056363009416399', '67.00158482048396053747321711047', '67.19206823684311051112793283647', '67.6659848021026845152766951367', '68.51868382522102039208712334020', '68.85154186456066758513906154882', '69.76163223237291705643674367079', '70.02463278175662848931844651017', '70.72535371192145847248611490810', '71.10673231555837949928060063963', '71.90936693301210816080187131354', '72.27867195905647036171489879182', '73.01451084198697544256396202353', '73.7446481865071773666452343296', '74.30096458991940281206700681707', '74.980511103500916875490934063417', '75.663308153291608142287545996168', '76.17802510900050702352411416411', '76.826414357831884085454356654475', '77.31371387131844222046597951026', '77.73919469348924549310257835895', '78.456457436678702010302057677717', '78.95615268386353138999532239942', '79.60869768661649500867205902195', '80.03188994462823346942697024157', '80.885370736619125422189443289693', '81.09415781797253120936585788099', '81.53510716616738444107626216883', '82.63009364507470052631235377387', '83.30214678393895622918154920996', '83.61234476305451169496454146356', '84.36785185292470554565775186438', '85.05607579015485722443276166347', '85.56821598373953119958401971595', '86.06354119045645216799770485003', '86.84436018943015360723549224613', '87.0487674009554124809255782439', '87.66113953264240929069910710273', '88.38073518242462436977774472936', '88.95395224370706717368813534295', '89.3381409894120971046690703630', '89.99588429032789606326970628501', '90.53957168623272536674560698676', '91.13277360208900013127905530566', '91.66419018906321412772620395754', '92.539581911464367464595100682276', '93.29779060231698041703169692569', '93.74294550395335559992836010415', '94.10702035921037617644928711449', '94.6099316735885172803889311964', '95.72342455500861753785145495324', '95.926123724603469321189617258278', '96.39288799936745927623619762365', '96.85183419820150350513122807647', '97.55558496254649441424622005060', '98.16001311952411794592396010416', '98.78305537697788477328436679622', '99.1389161712267880980610168169', '99.67824221689113649158579279062', '100.532838200747274714177399024016', '100.82460504123018196292206203170', '101.9455014873140197956075921790', '102.202206797886950246064011724441', '103.08096550227099331421975446544', '103.3879070424646351100950489692', '103.937285067338063389544726334083', '104.46900159257839801344277035651', '105.32807936775071093929082560295', '105.53513319860770482367642543165', '106.17109211970262708237740872810', '106.93017749460311069028496255358', '107.06958699016333740184320361070', '107.646362416425003366729667392904', '108.61629304183057492706523059137', '109.096707300459202425330289195799', '109.2723108702405735833291352708', '110.12382370479822781863395155891', '111.075110004299415264171964015531', '111.37607193772328695560340240699', '112.07609191882895618369727143097', '112.73750572831789129940456890866', '112.99308078615667569317040017722', '113.59395970524488550660409054630', '114.260822335560219295997641630789', '114.73694984318787119723126975587', '115.40371526148784130045191046044', '115.88739528744774628480464372590', '116.190766615688937816527999040875', '116.91202828183149324696051479198', '117.54763974351108671679048284739', '117.96230194848356747153536785606', '118.615759388694938126550272470387', '119.401696342789888581861388655506', '119.83618987635595015593163626695', '120.60349534330675621198307556345', '121.04814318430989422293632801824', '121.68926164686892744424934653122', '122.403447391463883971116497954138', '122.593442304078520559898843352129', '123.20571106521439002832523149549', '123.66967545211394143494761354260', '124.45790964920669390307645945553', '124.968822687492392717726754932449', '125.49991185698489137814602959222', '125.80985931360985005896579103062', '126.30779985871803128265904032856', '127.23661404302965852632136247265', '127.61877418955876785981719977782', '128.28912899736847123577857976458', '128.91828638011265535221011293853', '129.7666637118539227194772853343', '129.88241874761488592059957239362', '130.77127235698995174061189812006', '131.14741729988789006841850066611', '131.72619056374235093102096730352', '132.35735459458344020885780683955', '132.75748391952805739582001332838', '133.23569853946955698420786545822', '133.8041801061377630031184836795', '134.48556931747662564934887427812', '135.04227258991247708498494594187', '135.45382360542554834296772095775', '135.93599334017190454207676557203', '136.40904850881293099818760645837', '137.40749063272174215553184522168', '137.999306682563057094377848014559', '138.53782721712454135822890989603', '138.91002614410431666192870136876', '139.55411534858226634440768554187', '140.24138449649960245715981416032', '140.81978477699565477272652713428', '141.09890727980208634648700862999', '141.63535930838664271244045472849', '142.42087644341916561676711446278', '142.70768721016409535226023721980', '143.3293416331792025284965787732', '143.7548473721870455780471258322', '144.51998378403133594548755370518', '145.07997697944843504105355727894', '145.33455588450811624519125970150', '145.946554961701444232499026338682', '146.95412021824339811409784836100', '147.51034442861246353409417166749', '147.84629715394193808281255283972', '148.59319910738567467554575487885', '148.98036249192174398462391843107', '149.58745073874664409918934034905', '149.95630129066640864220594986198', '150.854076999684525847997972174247', '151.20415954030951247475592580512', '151.59294586380821823831650700035', '152.10307753269277476318855420076', '152.723992742821308353099098825710', '153.30295198485713668726119410398', '153.92716980793254122859754884182', '154.389996723129525258201960414029', '154.734555497812002812641073793497', '155.71639761800181604780045415775', '156.18174815963563512435988121977', '156.82712396586962325993157556495', '157.609811580281817999823209556311', '157.82820330750586201669368381842', '158.20835447848079800190957893812', '159.12001699265518534742023533712', '159.391824557674130826372481573286', '160.02647576325199213347926763720', '160.573636438995358032604804644297', '160.99232336931940129635440779992', '161.67211763923332930556665003503', '162.14957935224296527128496701445', '162.37493146527728328865881069007', '163.344180858196885515068555791376', '163.67835761836566691930584750185', '164.50767666891198004047631984166', '165.01712210854908775205450978046', '165.32785610735476575273004089708', '166.412281105508149246872491447646', '166.83272132585916584616561470845', '167.221239820151157006834929497459', '167.642644090541429184546145330939', '168.18133267859474799442055822004', '168.881211605705531800890806997287', '169.53799526901966838513522104601', '169.67386884546779916996928375612', '170.35833366305436026541930476400', '171.06774707913078896915780276091', '171.27261828741514629574223433301', '171.96204810972455882940036675898', '172.4667938340546915207641599317', '173.1142466423504228061258397770', '173.74359430395896431767457860628', '174.50277812832201233646602834715', '174.9445784816418591280047967875', '175.257701256589086012329086363379', '176.09959770600373331153594399458', '176.681676530404521459180772715319', '177.0785103132660769824755217775', '177.5114310756572308452297977919', '178.04316692717123380514180827939', '178.49633552709051816070435324646', '179.27956370472299074853583288033', '179.78121111662963637098119847377', '180.107988978413484948852615077868', '180.68418729100172319924565740378', '181.12577651839758717302855245654', '181.88149166436809116035947808673', '182.32580793806085775813451954448', '183.19184552683403703657386224910', '183.67838205032126370422426282459', '184.16704468054728782194577609', '184.66418646643409414079618747925', '185.43030321462644724251303447075', '185.69937798646514095113822651344', '186.27300098751689764225720108272', '187.00997726023795061190004950323', '187.35842965882555556540986445870', '187.68070787604614222241817037076', '188.29935677891087311773796922854', '189.13211670051171861208481936233', '189.3851194669067107960319951975', '189.92816250042387833934156254623', '190.41101962739018011114461943908', '191.14878464273204092634060171591', '191.49082949574981674830540727624', '192.421215255496354332231600898255', '193.043392541396209513076021185098', '193.410693847892528507541226465423', '194.041938256168393512645167851900', '194.24471245864529118127866314875', '195.02848597856479320231323779602', '195.70413328530248334080472305075', '196.07840036989455223781048717340', '196.49706976917177884449652622863', '197.03125209251686805393072642798', '197.4684305720900289870478785266', '198.27041998080153943835657620272', '198.60464609788473801832861082924', '199.22236490460845198096557282418', '199.51405445480186753639290743979'], 'prelabel': '1-3525-3525.128-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 16.37003117894819, 'root_angle': 0.6772857119416587, 'root_number': '-0.528607659114321794995649381933+0.848866269046942968547894211918*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(460)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.02336268406960147720864868557+0.725490890672873538358181604218*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.845280943785', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.52103262186', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.89150797781', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 16.37003117894819, 'bad_primes': [3, 5, 47], 'central_character': '3525.128', 'conductor': 3525, 'conductor_radical': 705, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3525/128'], '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': '1-3525-3525.128-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': '1-3525-3525.128-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 16.37003117894819, 'root_angle': 0.3386428559708293, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.845280943785', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3525.128', 'Lhash_array': ['dirichlet_L_3525.128'], 'label': '1-3525-3525.128-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3525/128'}
Lfunction data - 1-3525-3525.128-r0-0-0