-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_6025.5798', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.052335956242943835, -0.9986295347545738], 'a3': [-0.35836794954530027, -0.9335804264972017], 'a4': [-0.9945218953682733, -0.10452846326765347], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.9510565162951535, 0.30901699437494745], 'a7': [-0.958819734868193, -0.2840153447039226], 'a8': [-0.15643446504023087, 0.9876883405951378], 'a9': [-0.7431448254773942, 0.6691306063588582], 'algebraic': True, 'analytic_conductor': 27.979982369691584, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [241, [1]]], 'bad_primes': [5, 241], 'central_character': '6025.5798', 'coeff_info': ['x^240 - 1', '0.999657324975557 + 0.0261769483078731*I', '\\\\zeta_{240}'], 'conductor': 6025, 'conductor_radical': 1205, 'conjugate': 'dirichlet_L_6025.637', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^182', 'a^166', 'a^124', 0, 'a^108', 'a^131', 'a^66', 'a^92', 0, 'a^167', 'a^50', 'a^205', 'a^73', 0, 'a^8', 'a^117', 'a^34', 'a^131', 0, 'a^57', 'a^109', 'a^99', 'a^232', 0, 'a^147', 'a^18', 'a^15', 'a^158', 0, 'a^137', 'a^190', 'a^93', 'a^59', 0, 'a^216', 'a^11', 'a^73', 'a^131', 0, 'a^234', 'a^239', 'a^129', 'a^51', 0, 'a^41', 'a^18', 'a^174', 'a^22', 0, 'a^43', 'a^89', 'a^118', 'a^200', 0, 'a^197', 'a^57', 'a^100', 'a^146', 0, 'a^54', 'a^79', 'a^223', 'a^132', 0, 'a^35', 'a^62', 'a^1', 'a^25', 0, 'a^113', 'a^158', 'a^195', 'a^193', 0, 'a^15', 'a^58', 'a^73', 'a^42', 0, 'a^184', 'a^176', 'a^104', 'a^181', 0, 'a^71', 'a^84', 'a^233', 'a^17', 0, 'a^96', 'a^223', 'a^63', 'a^200', 0, 'a^116', 'a^88', 'a^204', 'a^19', 0], 'euler_factors': [[1, 'a^182'], [1, 'a^166'], [0], [1, 'a^131'], [1, 'a^167'], [1, 'a^205'], [1, 'a^117'], [1, 'a^131'], [1, 'a^99'], [1, 'a^158'], [1, 'a^137'], [1, 'a^11'], [1, 'a^234'], [1, 'a^129'], [1, 'a^18'], [1, 'a^118'], [1, 'a^146'], [1, 'a^54'], [1, 'a^62'], [1, 'a^113'], [1, 'a^195'], [1, 'a^42'], [1, 'a^104'], [1, 'a^17'], [1, 'a^88'], [1, 'a^129']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-6025-6025.5798-r0-0-0', 'leading_term': '0.225289725200385588349769910015-0.193225034999826101630023842564*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/6025/5798', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.2968019110982088, 0.2607464960935759, -0.39879157811277416, -0.9573080001138017, -0.43109467293421055, 0.9003106054820015, 1.512742768982804, 0.6293494016827514, -0.4742259867734272, -0.06233989392214365, 1.4136437976087062, 1.6062752359737709, -0.25547557731974757, -1.5804466781578823, 0.34468011953344224, 4.084285841141853, 5.2971156043650165, 2.594494252447557, -0.3138680619710336, 0.0733172123617437, 1.7757395015969681, 0.3516187245424397, -3.8851268194569086, -5.666076092472212, -2.5437200810142326, 1.1475221985653503, 0.6549319628017553, -2.1330919512677546, -2.0095095996269565, 1.1358834246471798, 2.273775967574493, -0.5527206435799518, -3.2202097489797863, -2.3117912572734594, -0.14318926294156892, -0.09875588958901871, -0.9937685209549773, -0.04254922604549301, 1.6691237027254018, 1.2901702370279944, -0.414314293380325, -0.6506681324948949, 0.12383145763285944, -0.23816819700382885, -0.21229006639620726, 2.892048643743541, 5.8138220419338555, 2.37536304125278, -5.408712411006496, -7.620000226718548, -0.9196043735334268, 5.496156121290538, 3.45249239011079, -2.383552497188205, -3.131847835213277, 0.48897832298622107, 1.5505133844182524, -0.7271674216686578, -1.3949533933888207, 0.3258128019803852, 0.7062849257700188, -0.512461516927099, -0.2543932663061486, 0.9538474794576598, 0.18621639000747758, -1.0040067952255718, 1.0307732607368778, 4.116612060795909, 3.092062501848646, -0.7660737994162679, -1.81806768285798, -0.1531172094787818, -0.4871830278836796, -2.4892821571594395, -1.941651576206119, -0.010165221276429314, -0.9748431509743138, -2.3891481318138883, 1.1861110880088384, 6.26709743721487, 4.682927611091371, -1.492689276586023, -2.5820456055041103, 1.7659636519512762, 2.444611422281376, -2.091430093893293, -3.353760177502436, 1.1924423224262695, 3.975816877579047, 1.4492109158236055, -0.8844502422161393, 0.0803699495505311, 0.6859269353844089, -0.6030303721405371, -0.8665892044794634, 0.04024894143733117, -0.28728868539982577, -0.485913466204499, 1.5710407135632318, 2.744602161705849, 0.46182590903452364, -0.9588082860973532, 1.3170565142200668, 1.9142823675320266, -1.7303005303005725, -1.993673428767642, 4.719498297257097, 8.396847409616903, 1.9440943855614332, -5.358597746303285, -3.4850258565285577, 2.0990041813680302, 2.3554173655040067, -0.07260628980317958, 0.43442016381887943, 1.1159517798745269, -1.0470816983438014, -2.004702049942972, 0.05306833236787823, 0.23712834270273198, -2.3802653606096027, -2.4091699915304705, 0.24435784688860213, -0.2255439580672004, -3.401734679430899, -3.399968240582642, -0.6699502854336074, -0.04052713066047636, -0.49777288196393377, 0.952584201283026, 1.349883182191099, -1.3945804978248715, -2.48338653342795, -0.10070050221118514, 0.2935233327114993, -1.7950669047134358, -0.45711411017369746, 1.2553489446866155, -6.499436196274096, -19.094639260194526, -19.935904445864956, -7.606600037224544, 1.6766194713322569, 0.7663646168638972, -1.4271443936407462, -0.058086324459555694, 0.04391443537209401, -1.7271975962621517, -1.0093961560602946, 0.8606349164582596, 0.18521676656099778, -0.7483753340625827, 0.4361879225602017, 0.8108264711835879, -0.2255405758902621, 0.6938615651081814, 1.9324093859096498, -0.437589339801834, -2.421861250497087, 0.7213921196682631, 3.0643460937321416, -0.9015252906040175, -4.008860585270533, -0.38723977926630865, 2.4209466586334987, -0.6604411626693296, -1.6592660829075152, 3.0820461005270365, 4.7900213673452905, 0.6984651297831808, -0.660584720657843, 1.985269884543023, 0.7126715971369376, -3.6977900869440843, -3.425660153703455, -0.26540409881026605, -0.8377349158146838, -2.3272108561568716, -0.15133473140995335, 1.100753792208306, -1.8522968982273094, -3.2842954665027007, -0.6668441021293735, 0.662732646742224, -0.5886538961340955, -0.5223711309885491, 0.216439266746735, -0.39767109788390337, 0.5527397347257157, 3.0014808406741933, 1.684087014244864, -1.4787657907822767, -0.10428452091686738, 0.24765335279270023, -9.157168761769091, -18.661274842801248, -13.517406916612197, -1.1136712175521344, 2.0595727610953136, -1.1274206148734476, 1.0368421860249954, 5.3233581326887, 3.5818384126326746, -0.10626031641993841, -0.06337261640597938, 0.4046022334817956, -0.6099734049961562, 0.025792589847104662, 1.0349428407044274, -0.354766676654154, -0.6448258007202454, 1.702175925297302, 1.418140704970816, -1.2937626440439902, 0.20990190092352334, 4.034087891662897, 2.7472523007636416, -0.9498270896417773, -0.7491075667129166, -0.1539696564978539, -2.347239075893948, -1.7582128533575236, 1.4231440283269436, -1.130785499004941, -6.7338767879515915, -4.597926225508355, 1.8684001863990876, 1.7791530750310904, -1.2192044104037887, 0.8412105202771996, 1.9166982064688056, -3.3260930242676086, -5.642078159713154, -0.06663441045533705, 3.7018223259405065, 1.0360724280185938, -0.8733842813403513, 0.1966973093086191, -0.12281859743188712, -0.87413042914349, 0.20399364126302671, 0.06284017003795034, -1.3776257561312537, -0.15707991752183575, 1.6285746506386547, 0.30345773680685867, -0.46154504482449477, 0.6400935364042987, -1.734412887487846, -4.315677909878568, 1.9341264079931075, 10.00265033712374, 6.206537943640688, -2.0682397801648853, 0.6765566380106551, 8.163861119300535, 6.37760866396489, 0.4515427220877995, 0.5628946361969588, 2.2539632390382813, 0.4151069678248075, -0.3452478434490035, 0.853503118059313, 0.08203028544482971, 0.2234783999995672, 3.866088568747307, 4.767178836810447, 0.9590660525217796, -0.5269423814821064, 0.9728068006147153, 0.03547862450505881, -0.9060166210511887, 1.8826759473503485, 2.8997620010400103, -0.39004729392100335, -1.4151738395148896, 0.6048087728756921, 0.20355155480580664, -0.5245576764484394, 1.428745441814262, 0.5851349231798626, -2.4682061990269313, 1.5487590575458468, 7.946699654121101, 2.5416442678033073, -8.596654851057233, -8.240041216917218, -0.5914667015119347, -0.3443259039987434, -3.8124901862794447, -1.3410624847856834, 2.0701218640676933, 0.7899260732245639, -0.18388321703383187, 0.8096285762810277, -0.16918304372616974, -1.1222471820807969, 0.6320707747329841, 1.2028829394723066, -0.236684343251524, -0.025361947333388247, 0.06971800985302538, -1.4737690549002729, 0.47076484073400804, 4.4442538553358695, 1.945469148994726, -2.8687297952437745, 0.5030049216419685, 5.698561789470094, 2.193715719765816, -2.2580427829757896, 0.3081204061945069, 0.8106153157633833, -4.59759095126055, -5.176072026843796, -0.20476519691752018, -0.1649477773769594, -3.31055553854751, -1.6732958669528446, 0.7062899749681798, -0.6472887749395515, -0.6444568511410452, 0.5702384209945123, -2.616203650240065, -5.601282149713804, -2.1558697332310204, 1.3823809101331987, -0.07929317579137674, -0.8243974960933347, 0.8465175080306816, 0.3532377478336604, -0.6564274744913112, 0.478419838586342, 0.20916061558397944, -0.8758433109932867, 0.9868136976244488, 0.7488116217220258, -4.307135599013392, -4.480924181290345, 0.8312402454915475, -1.9395065708750288, -10.080619702395222, -6.141997744809843, 5.5160970531774165, 5.677181355486836, -2.561672784103677, -3.6685663153226034, -0.05315925265704764, -0.23605296493499434, -0.44773593890407143, 1.776752933636672, 1.4914894429757912, -0.3186264036576258, 0.11713662458573534, 0.2609683915986545, -0.19712404044339887, 1.7763269198121971, 2.2211410698042333, -1.5457979279054845, -2.0484999945516535, 2.318551588824715, 2.7681239957657535, -0.33706382957544906, 0.21028057914551876, 0.9088076688162267, -1.4693854552032624, 1.1249811861439178, 8.019599510298018, 7.011706053820305, 0.27739490963878044, -0.4821523256589502, 0.8592438651395269, -2.6884499991186437, -3.2576623909788545, 1.9421253807845495, 2.4112906268685346, -1.2102848762343918, 1.083725063175622, 4.742080635922296, 1.3500795165351382, -2.2389324904712877, -0.2374494814584437, 0.7923611163489833, -0.8562450572923397, -0.14404048316063278, 0.9555233338681385, -0.2020111845787399, 0.1897505565667666, 1.5823493524682533, 0.2683475063705011, -0.4552921064184597, 0.6750896836692432, -1.3713213438378755, -3.5847906027430794, -0.5542196509011034, 0.3311890307767471, -3.14686061244588, 3.1223164936009895, 17.834712499733776, 18.306567728715876, 3.0058827148755425, -4.984814618406342, -0.764968178601192, 1.455283016992124, -0.061748136845365086, 0.11689755615115224, -1.4493310923772824, -4.63029640849495, -3.1980038157219393, -0.030658729097941942, -0.28087586128424097, -0.13332462277097407, 1.1942246710534095, -0.623027264641542, -1.7585088564924838, 1.4073014949252427, 1.8344564619773793, -1.9240100829951743, -1.7168579805606046, 1.0295958708620865, -0.29531073653900985, -1.277378536502937, 1.25596281176959, 1.0627525363057666, -0.7729924942431019, 1.0414709162341151, 0.37214070218948686, -4.549616450803096, -1.8674481426490985, 6.5604705166610255, 4.880158277210973, -2.6545126785382074, -0.3942548938773446, 5.312950134898324, 2.343577980016334, -1.5327826635911146, 0.6185030417457412, 1.1759496615057865, -1.158175878434351, -0.19817670712128857, 1.2011520591328435, -0.520696399429605, -0.9258450192530034, 0.23761140889620594, -0.4912918662034907, -0.5328205406533474, 0.6830272724787878, -0.45427410203237684, -0.679125248524982, 1.6479432458971297, -1.4680292330140046, -7.829417782188997, -4.74288252850948, 2.7622031454739364, 1.0937565197366717, -2.3125574647257805, 2.228596723625431, 3.538460455605221, -3.1713587281848046, -4.0551158677385875, 1.982989646617606, 2.347768828331648, -1.0482718558826423, -0.31226220500999036, 0.2670752942004845, -1.3649622395491996, -0.29615498975276966, 0.39136666544514737, -2.209839965663785, -0.9636162251798581, 3.8191610903084596, 2.925112337556887, -1.0554881971997732, -0.5817186388367833, 0.3441863164883265, -1.1974685892650965, -0.4120435557583815, 1.0425690673891401, -0.4607003817267172, -0.5086930023161191, 0.8107695810103603, -1.2766049790949343, -1.443935471484777, 2.5939603824908466, -0.3685966865939227, -8.557973831129543, -6.092037552722051, 1.3891456632228092, -3.0111213385342914, -9.963731553503289, -4.585179732678874, 1.820405570613869, -1.3788870268473388, -3.748855278159598, -0.5218688455424066, 0.49402354977066587, -0.6047439119861779, -0.05394724185907075, -0.3033371426989885, -0.4850344602922667, 1.4362956467765438, 0.644006148056222, -2.6778581782832873, -2.003003591813735, 0.09988533991170796, -0.4161944876832111, 1.764455650955218, 5.138400410280328, 1.5433391914814938, -2.4429603186385407, 1.6332196063207358, 4.089156508480622, 0.0686585538706253, 0.4246157619237644, 3.6145951026566046, -1.0371770180409192, -5.9154166463962135, -1.8250548124861727, 1.4458175802625006, -0.786165108118638, -0.17970442975445783, 0.9579544846781276, -2.823695446223699, -2.9115544898179486, 3.161331977389346, 4.11453618935342, -0.0005947799105949943, -0.31668803450868255, 0.328560632557365, -1.742776426907105, -1.4009286526375762, 0.6518997975067296, 0.08713978760777721, 0.4713972300277143, 2.4175017651268425, 1.005199638490342, -0.7301697794110881, 0.48462895061652705, -0.10622863025820034, -1.0066912558716616, 0.3358686747021997, -6.921927016581435, -21.963188682660153, -21.503559532374968, -3.782415807623427, 4.312000938652752, -1.779672420663128, -2.8276780969150743, 1.2802591482800212, -0.24261750265984366, -2.201039520729978, -0.1457537291954244, -0.2701621427930347, -1.4027985488784624, 0.5791890566439406, 1.124332781700181, -0.31304837656287715, 0.6284448780780097, 0.5929535820447611, -1.7594177086608123, -0.688350037738714, 0.8235595359109718, -2.261164362919566, -2.2999189052688633, 3.1114702138334174, 3.750817099485096, 0.17318079229039632, 0.49509156844965396, 0.8815131963070346, -0.8193268654324452, 1.9170881334439145, 4.177791303765412, -0.7279320872933082, -1.7883427818673108, 4.874230598399002, 4.7886407878838, -1.2398630764325262, 0.7834867313128926, 4.685051262222295, -0.09897303272736349, -3.7684250030338395, -0.6051188940650257, 0.19113010390323712, -0.7746745533897754, 2.667785103365852, 4.47672719193289, 1.2769559389712082, -0.2616345810437982, 0.19037192709972323, -0.4798054602978138, 0.18167301401835695, 1.0179055379057036, -0.09294911583064328, 1.5040385691276408, 3.8838683382816166, 0.26693284447352045, -2.327627366697442, 1.5787135931336538, 0.8950877252936076, -3.734425489909227, 2.6096172462644436, 12.062689177029766, 7.19470911805112, -1.0227802425378125, 1.584096844702052, 3.805651860938802, -0.8287274319340482, -1.9203362747496953, 0.48590333846533823, -0.1982624255394696, -0.1780927326737063, 1.1286133083960148, -0.9817254284543169, -1.9650806906213785, 0.6750868932298673, 0.3786078404454907, -0.32996914131792143, 4.449081591356624, 6.823151795475134, 2.265281964044765, -0.44548521594218304, 0.15604327366803988, -0.8298122138123043, -0.5947176911964918, 0.26003171279237236, -2.9638065030085126, -3.947912466103391, 0.569170025397027, 0.8398091272039663, -1.745247726838191, 1.7368431078274102, 2.555932242845949, -3.944851030631127, -1.1756624827363114, 10.471145138155876, 9.118332208259858, -2.593398578909423, -4.7313809521111905, -0.37014537368986755, -0.5859483586146734, -1.0498895028194475], 'positive_zeros': ['0.46221946395081033117072721192', '1.357156165678229817582827959285', '2.33621212878083407112545210168', '2.82758373928055790572576174987', '3.714289371439850657485339256450', '4.34296503671796439510196383992', '5.570004405957122727461885997035', '5.92476107009797040227016578044', '6.59273838174222289551314365133', '7.6862094220249265363677046593', '8.19844144333901825179654280712', '8.95484687296787161931016811808', '9.64056185695541770724749405218', '10.6625792016959728171892196660', '10.90429472015571565815746181204', '11.56955227483156870790622116030', '12.413843388157841393664622559081', '13.05264958684514659638243903961', '13.33855410130144915123067725156', '13.78919637742560547415078019215', '14.78493411504836747377156831271', '15.65837096478928599392341056713', '16.42324021383207298857030662825', '17.14377465799796871347965799653', '17.72011476016374463140136671388', '18.379316781817912039297545948815', '18.9273714161616691731488173009', '19.4332442684717580086710545780', '20.03345329074746723813779621966', '20.52380102791883145035585624380', '21.49432973053094031985662657524', '22.231523746139164090723440275971', '22.39266271577614124667843083931', '23.44133758587757741238438735840', '23.57028165535388233376818480286', '24.307954604911709930338467723717', '25.22992888882968409337598788026', '25.81653507995299448558671226038', '26.42920460401361495058721208505', '27.117135813110120715198988478308', '27.95216262025246538545484117787', '28.42149752366698655230547825625', '28.93163106055377241977989598358', '29.66513103911254258650960042518', '29.882708710882905721455963285140', '30.41758310161609321182973509565', '31.301430973684404529064959969744', '31.72855711112137598171301355028', '32.366608926232105584297452146730', '32.928823042830421369623718153647', '33.81494194782268416466610466837', '34.5521388893408447650449687169', '35.295738448399383983997480089472', '35.53200672208644092543646346378', '36.12510007997307314047234094296', '36.866942692467857603390261840694', '37.22328558583367028115305924318', '38.08873520752369058526348028987', '38.41029555812888804423856681015', '39.51875558366082962803380191037', '39.666698627731559968185598539954', '40.14802831665529909654229817538', '40.79883662252840286292652172184', '41.576167493796680851754154367413', '41.92238399419530582804453275860', '42.543364599028685927201304029', '42.91397784828220364146614779105', '44.27897419679923040707659706757', '44.75809474318221935326611685843', '45.3238659096952665092756373788', '45.63378310125066422076400641525', '46.39052191121035291652494359182', '46.91131290269999694112358109945', '47.409739325766822011252229830433', '48.03485279843435866064075306118', '48.307585632835640036428196427242', '49.0232647255524974715719915438', '49.63669766744871633759386644022', '50.260860287360737838900402863095', '50.96150721189243670429466788076', '51.51055001599186955654974484241', '52.00655095697286770678917411470', '52.86991482849007852631690842705', '53.21335558513975700165726285734', '53.800149542775396778081662266620', '54.75264427243222031897505043231', '54.84056749962324398196119321772', '55.641065984186975207224434868128', '56.085824084207988398896611943486', '56.953737840681856324543282702520', '57.36564035490304813543917313938', '57.9709449413260407459755026609', '58.27130275078863991461414691153', '58.668044912739069545429646285794', '59.51502220773036810211890097034', '60.01107015314139804053637527577', '60.32942242687815017792339371942', '61.602830092477819558968306832010', '62.0601275259385545339589476660', '62.43069398549921403314937629646', '63.4213948504726803202070665613', '63.76674476295416045509968604175', '64.19088357111416870173976696441', '64.68236113538743084451446637966', '65.25193699196583050743266827575', '65.72361812421929217883487579929', '66.39854211293045162940852330001', '66.85843838747151552790933043219', '67.70896725279303921818305184457', '68.31621286445276255345321065821', '68.37753828706500972671740808970', '69.21437116196899840535401573280', '69.62289880313490840816853396564', '70.51740619529193163105929549074', '71.08544615400805502005626522484', '71.48677113228132491146297665412', '72.01715622264799786710516448777', '72.81562164630522989020400758341', '73.53680802760142755691308028757', '74.00510195600680374471062552011', '74.34321536784595818886331854714', '74.94781401069169257858570520358', '75.32576874840188171922926383108', '75.95715208811119754125437349108', '76.61199799287245186920314995430', '76.99229223560904421878850001214', '77.34875028075523903736420514014', '78.061957461546143538499151329677', '78.95645244750903363670169582132', '79.34796208179536454771975045769', '80.36288367610153201721112339648', '80.54569000982881955437491000340', '81.31258274877825827774579384936', '81.6513265821648006858041711845', '82.20676140372368291221544866199', '82.46612949604041942171750130306', '83.530222903814334851102457132306', '83.863726862980782377671675303852', '84.38031665435954385097816494824', '84.8229673601244008250925559227', '85.58978129477418714737902085524', '86.14706900524321494104820535225', '86.601393932609451830357983673435', '86.98167258240123889258492975354', '87.55088968089687994338283937125', '88.05855961905946135822516960395', '88.81585643644404211501368536169', '89.72721367212997310379317392977', '89.97015924621241743824582027716', '90.7148528799815425218133650775', '91.38229901992094615721826839096', '91.62896126132386388912492763944', '92.15887791054179289532111793052', '92.71994067024202209566769463322', '93.37506537415855356610150536132', '93.75849315600470392740842044389', '94.07965398271911735440394824130', '94.65234530208049231369056936885', '95.41287270612087048761380926049', '95.91415373944696869346116189633', '96.6713881921930150622083598464', '97.162078048981282070259283356602', '97.559569498979496297516852310406', '98.45528741890712676934879977328', '98.73353746757670947357318219031', '99.53548460833192627038689584197', '99.892248863045976350394082200825', '100.42176065707760781598034531124', '100.734315358020069239304241392317', '101.70166760233607398246155962285', '102.17687486274212183375486127161', '102.65249527508682311258301284190', '103.19169792615537808004910718467', '103.63862015843331895246109900727', '104.103177910269773068282836895689', '104.56099465900675027166477809595', '105.05772750957245648505893790233', '105.874347501266719808499434971850', '106.164427367638215789050589416206', '107.02882113948282297297527929294', '107.706715884823919475096031163834', '108.44562543096920434876273657602', '108.69849159667801133877817461545', '109.13493946151467369884548765623', '109.915624592452732658460236120162', '110.27545006335038605029985800189', '110.719637464068345396802395885911', '110.99912036943864589093976471937', '111.75765648189548048548889233051', '112.34088758893721044149889831641', '113.07723697010886365085594103935', '113.404917530828460728177665594644', '113.87568182337400111854713139051', '114.31579864992912645248006449749', '115.3315048313287282184064780113', '115.68648474824151381164145205746', '116.048836767106190490883756812920', '116.76059351303244900099203343182', '117.37087944484317863617937916950', '117.74158473167888478754187620379', '118.51622640395326022462613139621', '119.08919386624273319343884212404', '119.52201975042071990421050910389', '120.02406793130486791913758425806', '120.57315086140792538906177988525', '120.90096493830287537976291513009', '121.606928705326763576553332830487', '121.98870653549410992677693358732', '122.36533693293153474805150353198', '123.17316321467900220169586027398', '123.470586227867358862365258256926', '123.98024508240669175636382214899', '125.06691647453128655426530393368', '125.67385383028300351055798277050', '126.22932943673203832656531159028', '126.4808133955651887064586142856', '126.677030789504564890265280808585', '127.81911036677992170662723313888', '128.04066168407413166830322354728', '128.46398349719576945359155964483', '128.99340615254398102518080021765', '129.56704572637475845556804296339', '130.153951483262474060975727916253', '130.78945420936273290502577851309', '131.214443574288296743219812809212', '131.7312040185161912075401905974', '132.321401274277166942392695613239', '132.68132275225651908060401629514', '133.1514394265398350217668689821', '133.81656429614180387313974606570', '134.554434561264827545865227586', '135.01743987675645092106765007489', '135.75806354156931274446650648674', '136.18653311628055370625432164899', '136.7077002790752693397352464813', '137.213142710781775376686646876354', '137.73456521246072614656093563188', '138.3390256551257530130635541452', '138.61817613988204899927232557004', '139.17752656670680588089207117495', '139.60983397438476957875409983879', '140.09034744565912591824564456674', '140.55056301664989390299968565673', '141.422068915044320077355884672248', '141.93718125478803512742306715647', '142.38287749996588457707667777224', '142.987258237493456571790675756799', '143.64231967318727823766538818280', '144.25237443575052113807927027542', '144.73974863602362283688649506050', '145.05531634446457411851137459108', '145.66951512130073638643591230226', '145.999463048836710235051686575793', '146.624202911331907877360752864657', '147.392500963619442924024334738796', '147.90709766959094717301544502553', '148.21061277984881264150505468950', '148.80761322989060676268940510915', '149.29911217220301976731910887403', '149.774746520817792211563791612130', '150.17077035105958114223692270044', '150.738309721874314745543387942393', '151.23552212421639955519065048581', '152.096772231154786494920806218313', '152.38710305386186720003758585926', '153.294929202250418368657062445371', '153.66702532808127293786526692856', '154.43119012848048282887265987848', '154.80514333151782225733870748759', '155.3409896949983471891935560787', '155.50550099607528450781488181369', '156.031932152861825213534330921872', '156.62153376568362742963186359438', '157.45965449589620283131008069820', '157.636795642086029851327076306791', '157.961148628528683653181713690013', '158.82870112089902200708186279253', '159.2870176231687619645312263551', '160.00614968534264676878421713704', '160.27615469402603171448632065715', '160.8938372427179513798002717272', '161.6661917008942119187111538243', '162.08777364918407070568096508814', '162.52196213420863572240214759597', '162.92100454254973547923788895391', '163.59328012474573379661086251912', '164.37493761168113033282784819607', '164.75051651898099114259351450621', '165.06778073175832562339268332689', '165.805997973905447040810197480288', '166.27836836598691076616396023518', '166.467092690968608695428073395040', '167.305980899574621176850434140980', '167.70605670253474250611675786071', '168.10740098362470320434199743186', '168.618272982868101009397579703827', '168.80934598288785625094959890361', '170.07697758618459088045178682447', '170.544776204888524692899695969293', '171.128004146092179574669977573303', '171.54129266137628234677765175641', '172.21354377534442639809720694025', '172.44854105717907618044701847061', '173.05089649268172510382038842426', '173.6504668572684200990467510007', '173.93524076554442766293753017883', '174.45457578772883280606338968387', '175.0773079512174367795697303078', '175.431848704063392624147077168996', '176.07723696321415410696842667', '176.90346755458495626526718829572', '177.09243078524198559777548089974', '177.63541054948692322841188342268', '177.97907881957617966605193276434', '178.71090292423261725418599792538', '179.15918071969829147553671319569', '179.91528081571522973056500411872', '180.26883944103705253000977456841', '180.93295936482907844040365477096', '181.62609782831195760452893822748', '181.91028527875771536636067714142', '182.29714529922598173963229777337', '183.28303623333218346547314980839', '183.57683588163634757154015709256', '183.87062176330137518746944894937', '184.337131893533379466509370582901', '184.96244725341847522396298191032', '185.12195240384588677388457901190', '185.95330742975167330115450052667', '186.45132874322453063467923249743', '186.92587263493056479107490529687', '187.42573829115422619238393794217', '188.36561648664362427551035905438', '188.65509052180357628358739892189', '189.32187241361506824159445975634', '189.91140932589705831449674700570', '190.27019359112219380812309397359', '190.6579095937103309355129637172', '191.14676412452377349799892640540', '191.79172313599954476713775998300', '192.24341850134762002925609245447', '192.53949137915854753279534153157', '193.62103767267721673371189081008', '193.95560624123018962713413684071', '194.171081189892842246388275019035', '194.79976016079303823852892397635', '195.05103584263109516643530242654', '195.89617683023526087201720577043', '196.326032233799020837021090525598', '196.764680347442281713333401316926', '197.31765980367252807045325775475', '197.84590004361765384739107816633', '198.6720054773188140214470186760', '199.43555081771292717514384862427', '199.56701105259497106425341384870'], 'prelabel': '1-6025-6025.5798-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.979982369691584, 'root_angle': -0.4513201998084598, 'root_number': '0.152336664250922618390569787582-0.988328660276985833156344867512*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(240)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.352396867637342916878881185295-0.455126445534621104531245499943*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.462219463951', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.35715616568', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.33621212878', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 27.979982369691584, 'bad_primes': [5, 241], 'central_character': '6025.5798', 'conductor': 6025, 'conductor_radical': 1205, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6025/5798'], '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': '1-6025-6025.5798-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': '1-6025-6025.5798-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.979982369691584, 'root_angle': -0.2256600999042299, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.462219463951', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_6025.5798', 'Lhash_array': ['dirichlet_L_6025.5798'], 'label': '1-6025-6025.5798-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6025/5798'}