-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_32.21', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.7071067811865476, -0.7071067811865476], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.7071067811865476, -0.7071067811865476], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-7.040766286173228e-31, 1.0], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [2.9010907910729803e-30, -1.0], 'algebraic': True, 'analytic_conductor': 0.14860737524151546, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]]], 'bad_primes': [2], 'central_character': '32.21', 'coeff_info': ['x^8 - 1', '0.707106781186548 + 0.707106781186547*I', '\\\\zeta_{8}'], 'conductor': 32, 'conductor_radical': 2, 'conjugate': 'dirichlet_L_32.29', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^7', 0, 'a^5', 0, 'a^2', 0, 'a^6', 0, 'a^1', 0, 'a^3', 0, 'a^4', 0, 'a^4', 0, 'a^3', 0, 'a^1', 0, 'a^6', 0, 'a^2', 0, 'a^5', 0, 'a^7', 0, 'a^0', 0, 'a^0', 0, 'a^7', 0, 'a^5', 0, 'a^2', 0, 'a^6', 0, 'a^1', 0, 'a^3', 0, 'a^4', 0, 'a^4', 0, 'a^3', 0, 'a^1', 0, 'a^6', 0, 'a^2', 0, 'a^5', 0, 'a^7', 0, 'a^0', 0, 'a^0', 0, 'a^7', 0, 'a^5', 0, 'a^2', 0, 'a^6', 0, 'a^1', 0, 'a^3', 0, 'a^4', 0, 'a^4', 0, 'a^3', 0, 'a^1', 0, 'a^6', 0, 'a^2', 0, 'a^5', 0, 'a^7', 0, 'a^0', 0, 'a^0', 0, 'a^7', 0], 'euler_factors': [[0], [1, 'a^7'], [1, 'a^5'], [1, 'a^2'], [1, 'a^1'], [1, 'a^3'], [1, 'a^4'], [1, 'a^3'], [1, 'a^6'], [1, 'a^7'], [1, 'a^0'], [1, 'a^5'], [1, 'a^6'], [1, 'a^1'], [1, 'a^4'], [1, 'a^1'], [1, 'a^5'], [1, 'a^7'], [1, 'a^7'], [1, 'a^2'], [1, 'a^6'], [1, 'a^4'], [1, 'a^3'], [1, 'a^2'], [1, 'a^0'], [1, 'a^5']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-2e5-32.21-r0-0-0', 'leading_term': '0.796968449432350553542544613468-0.241757736074989497478809367004*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/32/21', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.8328298219580695, 0.9115583999650673, 1.0996287377431684, 1.2234222011523321, 1.1903407080678405, 0.9573770970043948, 0.5221831736859633, -0.0731125400796813, -0.7405977023759867, -1.3550972522569729, -1.775018640695923, -1.8736253124309512, -1.5745684927771926, -0.8822489508448255, 0.10342254348795546, 1.1960831240250784, 2.158437879144377, 2.75897636112041, 2.8365396382306174, 2.3539639204710063, 1.4218409758276278, 0.27979480867094436, -0.7652431922276268, -1.4296360074599221, -1.546039631468065, -1.1272825272287774, -0.3751776033597466, 0.37565114797722804, 0.766584281591562, 0.5430929252958293, -0.3427488433284127, -1.696106833708384, -3.130005128930508, -4.192166655263008, -4.526825311300035, -4.0122560757825045, -2.818444218628074, -1.3558894712494376, -0.12779419827429608, 0.4616952021014187, 0.2680649821344358, -0.5322857420175667, -1.511578486122945, -2.169145271074847, -2.148501630288124, -1.400813960341396, -0.2196706365280309, 0.8759946559958678, 1.3675156303623153, 0.9753075979683119, -0.19694634066142988, -1.6844488768232717, -2.8495715466631477, -3.159126042742589, -2.427381191693939, -0.9104812689791436, 0.7984071613798996, 2.0321353729816107, 2.352283881780836, 1.7485477044992943, 0.6356839084765096, -0.35617524130234957, -0.7001046905982541, -0.24374641081033424, 0.7054823615561998, 1.5317626297033489, 1.6304568466831137, 0.7376811794815687, -0.9011728169172403, -2.619741792847089, -3.642542802295511, -3.468903455841173, -2.1329529805342125, -0.20019115488458372, 1.5060577164804465, 2.3129594648381273, 2.0302434714611683, 1.0295195228768426, 0.025226000663365743, -0.32813513190078747, 0.19534293941869182, 1.2631076686203635, 2.1707657526613477, 2.2479963612998795, 1.259751807732335, -0.42660029874738487, -2.0131881559653655, -2.698580283738286, -2.126976130896636, -0.6050724156579943, 1.0449522858762519, 1.9248496544335174, 1.5513868534436703, 0.1220447163075363, -1.5992500520251984, -2.715374508094321, -2.701448646100887, -1.6896144579539845, -0.3655060197473334, 0.4637619328284588, 0.37295634368087005, -0.41168327873938493, -1.1468256912161792, -1.0384585682020788, 0.2374671864005259, 2.2807949849719007, 4.147891437810825, 4.875230685138066, 4.040582658662939, 2.023580931994856, -0.1991192997697553, -1.609458992684484, -1.7237675824623522, -0.8410985699446515, 0.18589279844308038, 0.5132409499546642, -0.1520480314001984, -1.3729783988483013, -2.2825924630699213, -2.173304094493105, -0.9954847081492684, 0.5647601911012695, 1.494000048301047, 1.0968577085045879, -0.5332113744412221, -2.529571867053047, -3.761313580652074, -3.5239553505436114, -1.9754303999798632, -0.035539735427637144, 1.1921917379176141, 1.1085238348279067, -0.025579508371564533, -1.2934147164137575, -1.7495026495147847, -1.0518719508720369, 0.32289933347210426, 1.4273931564451932, 1.5202446886528587, 0.6107653280190113, -0.5094368743356685, -0.7865959852161288, 0.3620133431267747, 2.597478493825655, 4.810456502170254, 5.794667146821038, 5.007877039422888, 2.916750525387918, 0.6929415824262997, -0.5391361228698773, -0.3999607368737308, 0.5677900785569248, 1.352023673777289, 1.230212321492141, 0.29873896193431226, -0.6029582280998508, -0.5231792821142602, 0.8631588600852405, 2.9414615156564756, 4.513501186675528, 4.594814593793919, 3.103933103872152, 0.9534284720325348, -0.5391866416752967, -0.5268684277799534, 0.8071431614450767, 2.394587142233484, 3.0320156064677675, 2.2103154290748104, 0.4427420188817608, -1.1334488304656902, -1.5882481612921928, -0.8595103560029689, 0.23634959116774185, 0.6495156478042629, -0.0787579414006914, -1.4280847346372083, -2.250881690815139, -1.624957012962641, 0.41177599943454485, 2.7954964247150915, 4.115585813055747, 3.57177967389689, 1.5288343119793217, -0.7329698363529952, -1.8975106334575358, -1.493731075064653, -0.14968714893909355, 0.9479920143750903, 0.9732233464732241, 0.06659601990197749, -0.8233204208425404, -0.7356531895774582, 0.4849545171618355, 1.9886045958272802, 2.5160820418972922, 1.3598863094908484, -1.034558130145921, -3.3021588839661833, -4.083265771988097, -2.9735343026013528, -0.7985952763147612, 0.9936719007470003, 1.3758425473232552, 0.44688876365451663, -0.7158920842563871, -0.9311138330315738, 0.16221295651248346, 1.8384511275114406, 2.875302184302722, 2.533684833420475, 1.155534441257946, -0.0988380761905342, -0.18035761672920173, 0.9769236927486195, 2.3389905839021194, 2.5318448198824464, 0.9149362524487659, -1.857088160651711, -4.234883548532072, -4.856091029151502, -3.5008714939056826, -1.2042924472213616, 0.5480168968092687, 0.9134942986077241, 0.23462563975879694, -0.3696033564620067, -0.009520360614724041, 1.1954389943953334, 2.200425502908267, 1.9217754861152696, 0.20899802522210484, -1.9032175441397325, -2.906503915727814, -1.9645210621062694, 0.4041653043767437, 2.6621392415710274, 3.372455023116072, 2.2457927852554262, 0.3080702348825659, -0.9329700661293459, -0.6592706417393388, 0.6703377278251549, 1.7654788218953053, 1.6005272772899377, 0.260978872206843, -1.150021016005871, -1.4623792967798095, -0.45652979071944233, 0.9063994621445748, 1.2554646554859115, -0.032736686158586076, -2.242890674533082, -3.8090139093535567, -3.522781236659077, -1.5049181722824774, 0.847711020120274, 1.9143855256973876, 1.0749270608730586, -0.8608318275256173, -2.3444756512983087, -2.324050237873978, -1.0164578199970673, 0.3929553376365576, 0.8393242627912155, 0.3183375286244626, -0.12820110569804433, 0.6234068861774487, 2.684528115510866, 4.883389884022038, 5.598888497070635, 4.051960437076438, 0.99781912686406, -1.7742246650611422, -2.759610989652651, -1.8276933032658607, -0.21440555287204796, 0.5532899959135222, -0.09767128106203621, -1.3944918468680907, -1.975951922817548, -1.128685683088467, 0.5638687640333216, 1.7165128210884801, 1.3538800043265629, -0.21149273559530885, -1.6104171710769624, -1.5865579165374688, -0.11584250337817668, 1.4968619027378645, 1.6653883528377225, -0.13898633865332086, -2.880135398997167, -4.725886647043157, -4.474655922206434, -2.4685903555751993, -0.2508860376924069, 0.7229805253227612, 0.22555900478720775, -0.6971507189238645, -0.7700397413273405, 0.31911283819987096, 1.6374379554626002, 1.8852687201509115, 0.6550436848053833, -1.0645510549720254, -1.6340549507640214, -0.16030901502908607, 2.650704460172194, 4.95124319343013, 5.179931568947724, 3.284718254818079, 0.7232001013674225, -0.7490547657460954, -0.4712956341055401, 0.7153352891193353, 1.349255033522216, 0.7073203267236543, -0.5662557941062512, -1.104601433192144, -0.14120262397292999, 1.6941229714514983, 2.849767234417897, 2.2075381508536953, 0.12381347212764557, -1.7925677845412218, -2.017752994375182, -0.42575104250634, 1.5704739262520309, 2.1958703144660934, 0.8101491421799505, -1.5585735145303998, -3.095822798301252, -2.7261415687148807, -0.9623586756910818, 0.6314950963463254, 0.8487978814050179, -0.1504053978133462, -1.1187741265715603, -1.0038370590573962, -0.03309687612967572, 0.425111274869873, -0.8610932173547997, -3.7152826940283536, -6.471153162796259, -7.23202314370977, -5.421619791555339, -2.2838434586606033, 0.11734644721201844, 0.5458979680333875, -0.5204458519677444, -1.4944126507513842, -1.1859471089297884, 0.15383474483168386, 1.1663789849575132, 0.7468218784807366, -0.8512111883048512, -2.206276637728908, -2.0538822989614434, -0.5222570433587567, 0.8899746274921629, 0.6269793617204558, -1.4809919304853214, -3.9622012177863146, -4.910627847676755, -3.614901101016599, -1.1702424026612988, 0.4731209321890031, 0.1826981831836988, -1.440936112845832, -2.6937577203796943, -2.3381716801573362, -0.6773657250087063, 0.820868747445467, 0.9601228354103601, -0.05209143924835175, -0.8425733226681292, -0.25735713369455476, 1.4215495629363266, 2.6125669781591876, 1.8611317591523493, -0.7283828963511796, -3.3974094729376163, -4.130557725424791, -2.342435761966512, 0.635479315483509, 2.695368665753399, 2.6973173768082557, 1.2740980972172125, 0.03520643017685857, -0.024228846062445245, 0.595966822658671, 0.531171740156754, -0.9505034114303491, -3.0543279905592353, -4.071507548565633, -2.9641610364321362, -0.4331693172568899, 1.5818091772419998, 1.5746967457049974, -0.1900677610649068, -1.9122482503548972, -1.8721420489075307, 0.03169038242218778, 2.217197491907039, 2.8701105623357446, 1.568606496059328, -0.40161943892646623, -1.2930761680415255, -0.505202966724916, 0.9534449197331163, 1.5493834448958104, 0.7778656090117134, -0.3335138742884282, -0.27591057224816484, 1.34146398233875, 3.214153747457541, 3.4174350428486715, 1.189931559625913, -2.235219137914661, -4.573382352506603, -4.39491099718476, -2.2829899479173448, -0.21249767371539677, 0.24575119479761276, -0.7693022450074216, -1.756742876517405, -1.4410650183979774, -0.030938725503497817, 1.0602432938278847, 0.7256321981975549, -0.609237898219935, -1.2973714388330113, -0.07289055813931755, 2.5887197118584946, 4.711532938776975, 4.519297362220933, 2.0456066982180574, -0.855122350262424, -2.1307936690987037, -1.2987747830254945, 0.2629660842591097, 0.7279718000328059, -0.4310907676079002, -2.0112746324052098, -2.329813334208893, -0.9055941065309316, 1.07126227491993, 1.9238104646744454, 1.1450603569575877, -0.1202293944661933, -0.2642133955774908, 1.0837705147828167, 2.543616053004807, 2.231949846606218, -0.37394134329499235, -3.7483412394679423, -5.522762751484779, -4.512561279149107, -1.7003127842356756, 0.7145874214647175, 1.2773424481763933, 0.4081476450068722, -0.29500742975548033, 0.19951085177554184, 1.3278345251184456, 1.6205438026925396, 0.3773113935027088, -1.408585049306628, -1.8779940261830461, -0.13340699922304725, 2.731736264535002, 4.481910682482587, 3.7353412338797662, 1.2310875060809034, -0.8513662913564829, -0.8916502433904068, 0.7387507742324256, 2.1440369669602193, 1.7761865039795266, -0.11584504346933819, -1.834735356536859, -1.9768040362216757, -0.8088355188143829, 0.08218756127449545, -0.5147756202013204, -2.1281904751949035, -3.036358165413556, -2.0382353564651616, 0.21218413710213946, 1.6963314539386005, 0.9417297770489754, -1.4889056689241218, -3.4156362375141565, -3.0209882069670053, -0.5219623227953064, 2.0534235574038897, 2.7506195049968687, 1.4148738816754713, -0.36244386351233726, -0.9308210949945832, -0.16999219364162982, 0.5887924473472104, 0.1573607188773523, -1.0971393188978105, -1.5313638237274707, 0.03391597781356571, 2.879466105105858, 4.79230515421127, 4.034683176253249, 1.009634974473115, -2.0164246477175407, -2.9141722756968558, -1.5237636001554873, 0.40314451546260627, 1.0264642357724492, 0.17787980735341602, -0.6509601002758343, 0.0007381720552098738, 1.9596835615611468, 3.5433923707293546, 3.2715029263217232, 1.3944358342499874, -0.3493742273684247, -0.5252911605700625, 0.4847400481408046, 0.8321199576693503, -0.8772834324349672, -4.006044782482918, -6.282850605294973, -5.86342334367936, -3.072288730755978, -0.12399916616810445, 0.9072504871297818, -0.10309058792769679, -1.4589535061523358, -1.4832372387096209, -0.16515672041308613, 1.0195760617091973, 0.8394556141582585, -0.2803455654123278, -0.6800702894529392, 0.6939435484774611, 2.967091083311449, 3.995358890970726, 2.4498347169705093, -0.7398230501542791, -3.0866933145186524, -2.785458059287291, -0.3354369843853216, 2.0184624574261303, 2.4463925036953915, 1.1583583851193393, -0.05606178013457692, 0.19816529381882503, 1.5010858989794094, 2.1849634362337516, 1.2348078846082502, -0.5166370329890491, -1.1926228365722276, 0.13533869447154595, 2.3563247801772014, 3.3305104729892983, 2.034677597860181, -0.3402588599817993, -1.508207665872136, -0.34958831030125237, 1.9456952714249818, 3.0181056283506207, 1.6376072240647286, -1.1218431974504761, -2.9723367902193183, -2.6271536805657165, -0.9080025617687225, 0.299954950823269, 0.06571024402337561, -0.736832321604314, -0.6032081003451825, 0.7134708337082694, 1.6920159297999664, 0.559175768611403, -2.6927156883171968, -5.935308237068056, -6.706898292521057, -4.481659239301898, -1.160133766714981, 0.7214365551400924, 0.2966571116672248, -1.0621721832026503, -1.3771837979114678, -0.14585654838965761, 1.26659169247367, 1.2428772724924224, -0.24723665348538773, -1.5685218823690736, -1.1900391498473053, 0.5972891303527145, 1.891458768376445, 1.165193073059226, -1.037018885484867, -2.51910534917281, -1.6224500839223683, 1.0327850640479845, 3.067151388296216, 2.6423756140762578, 0.23558588489644441, -1.8892151606923644, -1.9413688394507749, -0.2816501727372132, 1.1439916512816806, 0.9318125261839145, -0.3606771341962589, -0.9604685693108369, 0.08181582762662594, 1.8026882024196178, 2.392955125846389, 1.2841794183851634, -0.03341360741244919, 0.5476090668755487, 3.4687725817790263, 6.774773598214981, 7.799138949143498, 5.649271097339535, 2.019153475454493, -0.46221904658400753, -0.6527091634399879, 0.32846040867564213, 0.6261998098783166, -0.2568073403418149, -1.0388807989778428, -0.2860149935412172, 1.7655506714442284, 3.2514435726735966, 2.6150844481484476, 0.3727804360305557, -1.2505602051032185, -0.5400367985294702, 1.9164686397022455, 3.7660402524337186, 3.2575942537870697, 1.012984712840851], 'positive_zeros': ['2.15208420554387225095307454879', '4.3448045258246410580413065085', '6.6398393015379132960083902410', '8.271598278038628119782902138912', '9.27675058392445512892036410164', '11.91882458571795196144177639340', '12.625353747572036786697191452355', '14.431147901555861288032844235250', '15.58119910909992541977281714715', '17.35029326376551831968410870985', '18.93307526224527398048631155899', '19.77656624005411640344479335117', '21.08941396553547631988238970952', '22.84467694102314894095181619414', '24.38551129533217145706266670991', '24.9254448069711538350572794677', '26.48799908497637749150262788891', '27.92052182446549550368239295172', '29.08440065835051747602932838639', '30.729521429612034795059730910646', '31.4171103920484692173867853411', '32.457015952033051194784995940441', '34.34387020947609737957986842652', '35.55755422315961523221760036174', '36.20350179842608913420178686591', '37.69545263612490646826413235739', '38.6638591137191720523820929362', '40.31888986845750240775179982322', '41.24420472721315267189157133333', '42.42934284438789647278477498342', '43.596031255526574957156758625019', '44.30842507741759847522404923805', '46.383715733757144421809899327004', '47.01843715207191168443231430535', '48.211765041117051094548541826692', '48.90090310989207780896656929894', '50.79189801890979418937771154633', '51.39993264826310090578279055551', '52.88784988785080334444195483755', '53.987407312686993368436228315785', '54.666607950194133839607129724342', '55.88408423835928870265657999929', '57.38927916634763845705469694129', '58.47087396387902164025713632928', '59.39411999773433853376753183772', '60.21111110142639356494177960630', '61.43703175518567944142695462015', '62.930767353805775285445940979982', '63.85876763216181628760600829394', '64.65465466998612698284174512302', '66.21377047459255861132937729214', '66.634723613566749262040977138703', '67.92261600627422364188460851528', '69.56413196986372149661474215692', '70.40260536133848720448142333561', '70.94079113021425005641793794830', '72.217453462203919001194860000216', '73.38904384303655409655244075385', '74.74270375280503942345684989801', '75.480737159272143836592747327158', '76.6133240172231090135796818260', '77.5980299389789815593974926610', '78.43229340665456555664844254885', '79.87747913207996789901822818405', '80.804531644770568769430049738824', '82.08487903387917073390432154397', '82.97037404683222842845836005557', '83.25447487699452083875405775466', '85.0988588171683396606801962189', '86.30088218552250525852226450405', '86.8487222074424665048320714630', '88.02309960719071092914759863244', '89.02482642250610914908170204364', '90.01972564761095630632559928951', '90.920315969178364567339109705234', '92.5474306410151232087951765670', '93.1963904692124288288798220583', '93.99081051672242899233599595129', '95.11370437190580917236233784331', '95.95803472580434897078760601351', '97.61239624170626117165985535635', '98.25569523050192506854782339686', '99.23417622001226290154901800118', '100.02661602004437579180477654912', '101.26675112420151612975290933930', '102.2495367461815668807079281763', '103.23457359813421166929782789229', '104.53954097775642110720712808870', '105.274101721266589458224661945175', '106.26060987918699214737454010890', '106.7260293283538997021455936041', '108.7265391201950448520719133266', '109.24801387568227214285750360250', '110.27931361033049440700465552675', '111.097750044296101191586254541050', '112.28145878931629223413709883293', '112.93006332254750828870094912901', '114.55838878569793902876993288725', '115.04420977495655774744830504355', '116.36904139904609591957121359856', '117.17360349597057425478354469999', '117.869022895786640645387079587593', '118.985882738851953115636900676476', '120.244840024340303828973721394469', '121.579173400158002895227350062788', '121.89017889967185459436235498587', '122.64666033200650139888623967737', '124.11526750147178696722858720613', '124.97173482499530654963410656974', '125.93335572418141128495920137985', '127.11737967526681202630473432587', '127.91916771176590449260923075396', '128.950424926661750696543500233', '129.451469912209826895606679384031', '130.735672856301206752010065126383', '132.240709328238323789150792791261', '132.608340118598063919271682373678', '133.75638065412289921728310707298', '134.55181089401481058255207060736', '135.32279277914178162770622112006', '136.77231780029944842870932544569', '137.75220796692821821629310643967', '138.35254093240606996033283949345', '139.51177886017866587585325157174', '140.58700214316273199739041447317', '141.02655016612150024417817241692', '142.15239735006308173811340851961', '143.634882817748154281239557870675', '144.50682333336629730964720294222', '144.93405356325396707361109718301', '146.00093225426018072930827673248', '146.89060616283987944591320999702', '148.28100621581603392061211303390', '148.9388230730637148237977293174', '149.98304105312338532537850843157', '151.184973612065790716653644435', '151.39801904757751666061730626320', '152.7832250935212052539672850134', '153.57106209318237441339787935008', '154.74302706834953482487918380349', '155.862183645612661033077962334786', '156.61430944373771272731058704475', '157.23157773572058995955815823625', '158.12074226041876353277560429014', '159.466982352962766356669281291', '160.54839916694595762939889364827', '161.298528574860227302098255385522', '161.874846118110051611661592030536', '163.35334642380325487886810440077', '163.92563331179027898594486612765', '164.57257606273752058455826181825', '166.268054865681779838406399098084', '166.853880473245098781529306726285', '167.84616666457413726990186242889', '168.67254545006045840068516949008', '169.26127528623964916687215894371', '170.554639639074323514313996632077', '171.599842935186744070381880797', '172.78552123341521786122727698493', '173.052921292640628054254303077261', '174.27793674887898505239189693583', '174.97965344023261653124300184722', '176.20210037620274275395244610150', '176.924986267126315701036050436465', '178.00023479144370082092269268636', '179.25604420164747960074618193738', '179.712935709394902517847876690064', '180.47535180330570428303259655907', '181.31632858498592402391598109530', '182.95714032841365387676432751894', '183.50660274437712667918614972717', '184.402590922049691397497295653648', '185.268368957127632431430777674', '186.154293794966108533155016634788', '187.0485826295147636177131045467', '188.011495707422443826135998448124', '189.09007536309785918478032234075', '190.04711558030517243643783690515', '190.852291896288914214785007760569', '191.54711350213505275678639132098', '192.797475153599486762519524398679', '192.99950833148285469172281470793', '194.91336421277303907416686999841', '195.52170168301121520054956523368', '196.178848143289479566192223993928', '196.92655817430379941285152553232', '198.17606078508423123581222090944', '198.82986727526211367414481417242'], 'prelabel': '1-2e5-32.21-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.14860737524151546, 'root_angle': -0.1875, 'root_number': '0.831469612302545237078788377618-0.555570233019602224742830813949*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.09375', 'prec': 27}, 'spectral_label': 'r0-0', 'st_group': 'mu(8)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.01297569186368451209669094112-0.213873333059611846694152233829*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.15208420554', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.34480452582', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.63983930154', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.14860737524151546, 'bad_primes': [2], 'central_character': '32.21', 'conductor': 32, 'conductor_radical': 2, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/32/21'], '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': '1-2e5-32.21-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': '1-2e5-32.21-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.14860737524151546, 'root_angle': -0.09375, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.15208420554', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_32.21', 'Lhash_array': ['dirichlet_L_32.21'], 'label': '1-2e5-32.21-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/32/21'}