-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_667.249', 'a10': [-0.28173255684142967, 0.9594929736144974], 'a2': [0.7557495743542583, 0.6548607339452851], 'a3': [-0.5406408174555976, -0.8412535328311812], 'a4': [0.14231483827328514, 0.9898214418809327], 'a5': [0.41541501300188644, 0.9096319953545183], 'a6': [0.14231483827328514, -0.9898214418809327], 'a7': [0.9594929736144974, -0.28173255684142967], 'a8': [-0.5406408174555976, 0.8412535328311812], 'a9': [-0.41541501300188644, 0.9096319953545183], 'algebraic': True, 'analytic_conductor': 3.097534977690338, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]], [29, [1]]], 'bad_primes': [23, 29], 'central_character': '667.249', 'coeff_info': ['x^44 - 1', '0.989821441880933 + 0.142314838273285*I', '\\\\zeta_{44}'], 'conductor': 667, 'conductor_radical': 667, 'conjugate': 'dirichlet_L_667.592', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^29', 'a^10', 'a^8', 'a^34', 'a^42', 'a^15', 'a^14', 'a^13', 'a^39', 'a^39', 'a^2', 'a^3', 'a^37', 'a^20', 'a^23', 'a^19', 'a^43', 'a^18', 'a^27', 'a^0', 0, 'a^0', 'a^16', 'a^7', 'a^43', 'a^8', 0, 'a^42', 'a^37', 'a^25', 'a^24', 'a^28', 'a^6', 'a^24', 'a^25', 'a^4', 'a^31', 'a^23', 'a^19', 'a^32', 'a^7', 'a^5', 'a^22', 0, 'a^11', 'a^5', 'a^40', 'a^21', 'a^8', 'a^12', 'a^42', 'a^4', 'a^3', 'a^13', 'a^28', 0, 'a^24', 'a^3', 'a^15', 'a^42', 'a^12', 'a^30', 'a^10', 'a^29', 'a^16', 'a^33', 0, 'a^11', 'a^38', 'a^29', 'a^43', 'a^30', 'a^1', 'a^9', 'a^37', 'a^36', 'a^35', 'a^28', 'a^28', 'a^24', 'a^14', 'a^37', 'a^31', 'a^12', 0, 'a^10', 'a^7', 'a^27', 'a^0', 0, 'a^22', 'a^16', 'a^7', 'a^10', 'a^41', 'a^1', 'a^9', 'a^26'], 'euler_factors': [[1, 'a^5'], [1, 'a^29'], [1, 'a^8'], [1, 'a^42'], [1, 'a^39'], [1, 'a^2'], [1, 'a^23'], [1, 'a^43'], [0], [0], [1, 'a^37'], [1, 'a^25'], [1, 'a^19'], [1, 'a^7'], [1, 'a^11'], [1, 'a^42'], [1, 'a^24'], [1, 'a^15'], [1, 'a^16'], [1, 'a^38'], [1, 'a^43'], [1, 'a^35'], [1, 'a^14'], [1, 'a^7'], [1, 'a^41'], [1, 'a^25']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-667-667.249-r0-0-0', 'leading_term': '1.90069079252640439458099815312+1.17610780951706890240524376914*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/667/249', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.2351409504551807, 2.7286928355184488, 3.0729527384704123, 2.4994183848580738, 0.9117498983090437, -0.9938832850075537, -2.1345204710632553, -1.7611657689471476, -0.0624941021630797, 1.8315991885141272, 2.569449084977626, 1.5700912345962739, -0.4788098987761322, -2.0924413776598856, -2.136396052544318, -0.73050181099236, 0.8870902688624921, 1.45812758153286, 0.7945576189938898, -0.15685864544562864, -0.34804160531267736, 0.2650909495958965, 0.7100677526545383, 0.16074860819141346, -0.9387082909745362, -1.1292527458307744, 0.45020826807053155, 2.6899090556523224, 3.0380524347534004, -0.19088958142661405, -5.830182833540149, -10.337956903100306, -10.63751155424217, -6.789804799926281, -1.9032758946242059, 0.7134497141744398, 0.41041327329656313, -0.6942367962527073, -0.28675324558995774, 1.6966873355499483, 3.2853489436665066, 2.896006162146285, 1.1131081976413235, -0.15200119735107476, 0.0070194503647391885, 0.524412678434369, -0.08334079702350629, -1.603784008120005, -2.176373689366083, -0.5967177653836062, 1.9206233860135398, 2.8544268234219454, 1.2404492702641865, -1.1329905219261933, -1.7711011871825493, -0.3862319998539407, 0.9009082625715742, 0.4031888845695713, -0.7923414724940183, -0.12004550564445483, 2.896987191524042, 5.3080405691054064, 3.742482516017258, -1.4610881481534286, -6.003448354002732, -5.942078794256949, -1.8224343857142808, 2.0841736012331014, 2.4816924634572914, 0.22535833572322833, -1.4289988126186408, -0.9211391230778595, 0.2476837661478817, 0.09908650434142, -1.0906425217557172, -1.4770606767773131, -0.4576299745553884, 0.4964158207755106, 0.11921817348210556, -0.6457802917130129, 0.013700981355589658, 1.8662711382405983, 2.4917528140416874, 0.5920840838988307, -1.677186567223686, -1.0602506983955122, 2.297363398494774, 4.232240116167882, 1.3439822995388808, -4.473443706816564, -7.674305399163186, -5.261363926542691, -0.06930868570897593, 2.793410688094383, 1.7422582327957592, -0.3490302581976403, -0.5809658155758334, 0.46205540401872525, 0.5133857897577326, -0.4502678586685711, -0.04051182724245786, 2.757191576142507, 5.474489888311448, 5.036724664754783, 1.7917517318626117, -0.9092348635702322, -1.0052131532039479, 0.03543072088629431, -0.10927384967292225, -1.1847633524676644, -1.1661579955028094, 0.19595897932509673, 0.7594229065554546, -0.5026154131955818, -1.2718191502066274, 1.0636323050390222, 5.007727159017744, 5.981484060973283, 2.307432442909078, -1.8682581041734574, -1.3744509418089361, 3.279798897142199, 6.248737488857533, 3.596107163734665, -1.9186359380977458, -4.565583946054705, -2.635035317065534, 0.3851331742374876, 1.104867008021115, 0.18187002470527824, 0.0761131350548922, 0.9532051329986413, 0.965043698525332, -0.23452940109156722, -0.7635620448506312, 0.27010358409105634, 1.0503175854222113, -0.0023627905119257683, -1.174573696922953, 0.3611354897249782, 3.8392623522673803, 5.023748167041751, 1.8626129546890795, -2.2382945442821565, -2.707270285341023, 0.0480209500432121, 1.4518123014961168, -0.5161137408696903, -2.4200110526770997, -0.5704748836964875, 3.284284253962889, 4.211953760573846, 1.0935001599035306, -1.8243509284449744, -1.0171663951125942, 1.5233529209369645, 1.584499985434792, -1.069409987369517, -2.7036384881970665, -1.3309330789274547, 0.6779902355012246, 0.650414548165419, -0.3535245063835142, 0.3110117350220307, 2.330771936773162, 2.8496551290820205, 1.041438668917187, -0.5978389590262924, -0.2307432539308464, 0.6705946634599427, 0.30279665398106737, -0.11671740070719851, 1.171917026437195, 1.8945764287202664, -2.4331324980999716, -11.241997060173896, -17.014748786675447, -13.418916424193355, -3.4567138874466643, 3.7237278515471273, 3.5176603532760495, 0.005276845391127816, -0.990129282151476, 0.7063042626542195, 1.4668217300298616, 0.3434516401690475, -0.11431903779565639, 1.1909041289801467, 2.0238161127922623, 0.8776633050810713, -0.2648385607571552, 0.7081278675740992, 2.256139274079298, 1.5870549905326796, -0.5202119217316665, -0.6285738357347453, 1.8042172188124388, 3.2582641196570536, 1.5997003298996946, -0.5272647215075956, -0.05180044552258638, 1.355757354986392, -0.03094917859767023, -3.4363879771152455, -3.984357261217772, -0.17682971502384295, 3.174276352175768, 1.7439326862116005, -1.8585499719757266, -2.0304253943732853, 1.365861424019232, 2.9827039915251783, 0.34927332745489303, -2.3373151232965825, -0.6806350990945605, 3.327989024430643, 4.484515085449274, 1.9122836955328504, -0.4780426281718281, -0.28095334598517796, 0.6719407050929016, 0.41337798576939233, -0.09760129958866852, 0.2383118594604569, -0.007744648846987925, -1.9522460778906296, -3.263747278733531, -1.3629054758277332, 1.6366679092618561, 1.294018453729355, -2.023145809602351, -2.870273691810116, 0.9588267893311023, 4.1795859132884505, 1.3870219831761592, -4.4935650084144205, -5.813590819872287, -0.9398037288099867, 3.7591411300289552, 3.2242877417616564, 0.06859677575932388, -0.6943814240057355, 0.8552322170362855, 1.2001285419616317, -0.09538190142899064, -0.25547373009346824, 1.1691694482976576, 1.4026300271406187, -0.2376575248230181, -0.49466012805087123, 2.403681457380239, 5.1364310593902935, 4.035276294109619, 0.6797831608151065, -0.8049171060431785, -0.10917185558100653, -0.22900698863364063, -1.5419139384064176, -1.14637519187598, 1.3869987562228945, 2.4466142668149797, 0.5708707438033102, -0.313445972544666, 2.532162935045027, 4.501148605743776, -0.6109986456816917, -10.356292794077902, -15.103543074267145, -10.375638259537462, -2.313723960040619, 1.2699052032561884, 0.43185876957184843, 0.09907991504395598, 1.4687425984075775, 1.6282053077393748, -0.05640197778251869, -0.7290451563731676, 0.5903483079977186, 1.2613455032875323, -0.10085327202417446, -1.1922348910082392, -0.38013035642370824, 0.3231428337130681, -0.7155081464048062, -1.282448500836706, 0.5054171855043935, 1.5532023082911859, -1.8248663136842476, -6.633718436049504, -6.098067149263206, 0.090349516757058, 4.320554175529004, 1.7274113332467256, -3.119967778475894, -3.6392437821222527, -0.6879086526617993, 0.4356599334503122, -0.8004656909974066, -0.25178118344574807, 2.696589215662759, 3.5746698354840927, 0.5714100931567226, -2.001238120718019, -0.6055231684377904, 1.9807702700496457, 1.6410925586090537, -0.39733004276184686, -0.3109842747499612, 1.5754153039076824, 1.7837935196379522, -0.009507310163740639, -0.7827117149820249, 0.08100493627151589, -0.0390647226734717, -1.5352869652492336, -1.407677660772016, 0.9139181884628023, 1.7494746752610058, -0.11587765991168544, 0.012608592442578205, 5.080546262473243, 9.494296434464582, 6.1446449186773116, -2.245833991236137, -5.85197507367261, -1.5053002719476338, 3.3681823781092843, 2.208969833301564, -1.9638639333779782, -2.9068730414423523, -0.6717161676006934, 0.40506395749214485, -0.5023498673610066, -0.7102978415197575, 0.17779831853285571, 0.12785362739850537, -0.507507946494771, 0.5644506347000675, 2.3791941577710496, 1.3666918668390948, -2.028088009060814, -2.8107820368908185, 0.6857903760002321, 3.654353271144021, 2.3444433628324832, -0.26723513277203437, -0.23670556673277116, 0.5926168864649506, -1.033909512600058, -2.384286002373342, 1.388666747754046, 7.789380401512766, 8.911039113649576, 3.141388273536173, -2.250745541267992, -2.079449783966413, 0.060014401864090065, -0.5448878310027802, -1.7029631535442757, 0.7105283045900622, 4.504935451952143, 4.392603940079197, 0.7898269335527727, -1.0960879313900114, 0.23059449410158292, 1.2014982906465719, 0.15668121482068728, -0.3843563981862718, 0.7367578125884661, 1.1609816217806312, -0.026796850406733165, -0.43486942016391317, 0.5651622785508407, 0.23141616700136214, -1.474047086278428, 0.05251424423483067, 5.801571860044117, 8.52557726162895, 2.4740145355694656, -6.438200804022698, -7.644444256539617, -0.7859372479789875, 4.45723364472722, 2.829692501499042, -0.5691092430944856, -0.3227314870748108, 1.427880250712939, 0.8632136906884889, -0.515140682133092, 0.12125484846767726, 0.9938269506689844, -0.6409347496451697, -2.6556355901078503, -1.5367550318475705, 1.1098972605726516, 1.2652674096926444, -0.4625876506903728, -0.4380917316223447, 0.9543597752190685, 0.24465179841657372, -1.8760958966443584, -1.0114154050089514, 2.8417458316697766, 4.448982076862748, 1.9928144268672874, -0.19055347459595565, 0.17291805545959307, -0.6634414356988538, -4.488956139119859, -6.12779204457672, -2.049446953902088, 1.9573267456067933, -0.9769346612427142, -7.150284903137702, -7.190539990592715, -0.31417367098524857, 4.935852280607291, 3.7844180936790464, 0.6281858141043083, 0.1077722914660602, 0.6793797015735565, -0.09480201515256659, -0.6384272127712715, 0.5025482974805537, 1.1080770595238798, -0.2830471835516847, -1.143816527307266, 0.1368071477215707, 0.8263576101087026, -0.7359008623875599, -1.2166054246335014, 1.4850971519010319, 3.060851380368319, -0.15802762398045656, -3.4914945069420096, -0.7019946752871682, 4.870130085415103, 4.620170665695138, -1.510264285165014, -4.816151372156442, -1.7198156854576185, 1.4461103579341563, -0.20643795848872903, -2.7823410727583426, -1.663512831016905, 0.7352953672563376, 0.5119327148571975, -0.721852663545201, -0.19261111681835233, -0.06773680658587122, -2.9617362581323694, -5.626769254087521, -3.718063796825433, 0.41178518702229094, 1.2856652714972778, -0.8930640838060622, -1.614941064762231, -0.1760712497614238, 0.37307950837119086, -0.14411625779654277, 0.586588396019554, 1.4853916528863929, -0.10079235534981656, -1.4579100341324236, 2.422641472540406, 8.623341229134182, 8.223929706908878, 0.39772238020939804, -4.666992888114238, -0.7913369507513582, 5.058527176294205, 4.289358604047167, -0.5883787722941408, -2.082290860729437, -0.20618791887067361, -0.29769182525085897, -2.5914465343582136, -2.712720852712674, -0.31472021653325777, 0.7672239335023832, -0.20548983281216548, -0.5215632417715255, 0.04118662994769304, -0.3929150121591586, -0.5116318994519482, 2.224395836230559, 5.239071336966462, 3.7333263277243067, -0.5981643432192816, -1.4992548622689816, 1.2088071996114595, 1.3886388086168184, -2.073235977499683, -2.856282947889583, 1.3187677538287395, 4.011133864724951, 1.0738436649646173, -2.296687600556246, -1.0723380568546663, 0.9909636971948775, -0.9432226022782598, -3.464403483061629, -1.276142628007951, 2.6870078512466775, 2.141305670339688, -1.6022429516986916, -2.3135088397864085, 0.34679413823704713, 1.3087197793877028, -0.3849604109698541, -0.8843623928744153, 0.5435167774700033, 0.7880587586390061, -0.28274424708681056, 0.2804935435925553, 1.984410884115322, 1.4962864717438835, -0.44357692907553553, -0.04857275115902841, 1.8858692090702303, 1.248753299179414, -0.8135977645431872, 0.32850965453725445, 2.0033782347267173, -4.16209768554676, -17.12512766159687, -23.699929096262874, -16.21175966359387, -3.4745094332176945, 2.27279923537896, 0.9792787416361087, -0.0714118724455165, 0.8061110034205605, 0.48218179647613585, -0.6425710693187338, 0.01832241157974567, 0.9943595695494414, -0.4156668739449796, -2.0863909163129613, -0.8228873678855191, 1.0306311184669668, -0.2841556082157194, -2.4934653410434575, -1.2568837439322653, 1.5780805123330106, 1.345859210683608, -0.7480544592249283, -0.3748311297107694, 1.1942447048779634, -0.23508405361858353, -2.713175398570364, -1.1228467965193254, 2.4601322177762257, 1.4459288300828272, -3.0044845933712403, -3.073036826532708, 1.92757116721741, 3.93400221589025, 0.20151087394553216, -2.072019801821965, 1.3261976454496645, 4.606377269989357, 2.7937063485561735, 0.03947682194018469, 1.2039291705746467, 3.3809021597520337, 2.217718289351575, -0.25439472396355534, -0.38669840466885724, 0.45731008122314565, -0.1912492099146927, -0.8357950679787073, 0.017403012667942867, 0.2968113843589595, -0.7161092584743807, -0.07877951075672175, 1.7971788056652127, -0.8127731476701766, -8.469283622275743, -12.148950445823814, -6.296096337978723, 1.469945410988367, 1.9537754848610125, -1.671868936182805, -1.1544887007233369, 2.1633199099481346, 1.1427264025694783, -3.3412270073731287, -4.086093422754722, -0.4508246186491661, 1.4827396350163213, 0.1955956906049987, -0.08017624518985556, 1.4004965434465857, 1.1464293204374862, -0.5537000754364636, 0.0064487187551803705, 1.9509406737606476, 0.9716034736440442, -1.9609728314224317, -1.7736148395883564, 1.2281914748951694, 1.8193499342326713, -0.5376915989337296, -1.3382328143633506, 0.06270352883042281, 0.1213149499548481, -0.8049279990600506, 0.6347053896147726, 2.425931012755845, -0.050378153543634174, -3.3054386298190375, 0.7496022055710693, 9.85181020880573, 12.21679252704904, 4.72774458921171, -1.9729894082708772, -0.49149043245736956, 3.127350692001644, 1.6412555420475257, -1.9586657331939483, -2.0306592293783368, -0.05408484694855567, 0.20358521278871144, -0.2645956327872136, 0.2406023667529331, -0.2687874157932105, -2.467823046805091, -2.8248023269713003, -0.21162397858586743, 1.3170571282162291, 0.13775730731265123, -0.013838613362909718, 1.7948579601734318, 1.1532716963565985, -2.209335637367111, -1.905382896304432, 3.3699595216483065, 5.650079804298693, 1.2025125221478459, -2.010747114614714], 'positive_zeros': ['1.39545355585247156600932760283', '2.50957336905845907615743692982', '3.6797521970969627299615197559', '4.81690397062994040581363134095', '5.8737541814630182004168820814', '6.4495657037161784255308210440', '7.23464519659206356375546211909', '8.06024757527626482721375138672', '9.050176322446287338548933253697', '10.804799261395527981889168370', '11.35171140464806790921235399653', '11.93214718942600961839285717894', '13.369857612575998813848066456716', '13.74653196005610559055153947721', '14.3541973450721225806007200706', '15.38564583439535448071834570318', '16.40240168266872893288558182439', '17.25709975952564948572245408962', '17.90607927829984973802432546385', '18.45489109104658194613091428922', '19.60843552824464567707332474450', '20.7480556256679843024206306975', '21.59138988410904979326291799111', '22.41345987411173957629468652384', '22.84378659805969395712264086106', '23.863743154484723413918411610', '24.41513694167475027961531763742', '24.99722246749591694221436374367', '26.005661793865131069416782947417', '26.67545657410062923268583658177', '27.57638630399282803821664442103', '28.75459356806907723571235246919', '29.61998975543902693772374878277', '30.173522785243741941996241300134', '30.78977805350835975295983309624', '31.25714621705850247197627025285', '32.67490314085471689163312181330', '33.42207869001625940956024696180', '33.708969435272438386658890745725', '34.6445938277091325768168016596', '35.2152485035537318628834839253', '35.840970883902842803691269160917', '37.02338125809155917288484661747', '37.6076929260705611776827213704', '38.63804398227347172734538462883', '39.63611580139100546231144954763', '40.40006536787100358929386444051', '40.58099225389389913004970405809', '41.505396607650593265867522795023', '42.125082480765019301846294096666', '42.812054919134945953680181506223', '43.39863651667279063622641935807', '44.50160367651919006949334606020', '45.30728523135228440188880345878', '45.879222830056090749827563400041', '46.60952895143015182314342658947', '47.58967023523337712533319456111', '48.24382013255357404119354652011', '48.94902078262851246160007243973', '49.869907085061491247065163073339', '50.490769308301207746852791590943', '50.87508337187702476764012564747', '52.03347928984419125364632347406', '52.56462649291785283081192725123', '53.246758730186344661875639480621', '53.49868036215421247709678957543', '54.25341101921076455485515445820', '55.74184012015360125610245256545', '56.56307531158353827426214633717', '57.07288187048957706073550700473', '57.91071682864158383404420179040', '58.17319857362170630137530028233', '59.24817908112244224781013734604', '59.54207211097585202958465790651', '60.53888526946710396112220121287', '61.038253028634562730058336293661', '62.078908243856158219122781051131', '62.50984203564586052184454805975', '63.121826610702349928701573156550', '64.07435630457208109279639143729', '64.82941394727423558129562276541', '65.50961332800401079930990859314', '66.27952297696438493740084221645', '66.92941262503647483435389444375', '68.02889446807371334340010031930', '68.5143474593188871131802160784', '69.26020816040388958149877293074', '69.52925462423500684105696126775', '69.997939749590531468867550278611', '71.06418615384490867684634253180', '71.69313614099355369068495808180', '72.43772177051253600938991616981', '73.198290151725415322001034244681', '74.11092390512645318508488796196', '75.00870834895681688617948017299', '75.465911360797616887243878686870', '76.22566696623037131493542436055', '76.63215589039825892384773352569', '77.4563615965468785793041618662', '77.89249154120435864960893606671', '79.14402382173253085893435227402', '79.74086093380091515790752298355', '79.91297647356753144266375708917', '80.77721865036932962669419146116', '81.64981968250299303337099826326', '81.93819500327709441628259469122', '82.79020986612888175774859929841', '84.19802193907532272904555783280', '84.82749846938386474497808514244', '84.95450416310864200689918467784', '85.92722148720796268801776809844', '86.446858226397654160039022351273', '87.16968681903134071436675519301', '87.91195129391527097176635869224', '88.27013202387889163861988704049', '88.99415643564255249482953748823', '89.56612597806568057465442856879', '90.62078583688698399683510209162', '91.35148056112258794502648803210', '92.279041582313742484635786363880', '92.628237381864157033729134847047', '93.15794388714004262796227853195', '94.11068813725983665899334831980', '94.75119431365744017353485073252', '95.551586979677090446159255799211', '95.99513059046576181615923659087', '96.87332555488826754147949974561', '97.47088848445043333509486025985', '97.80159986227910596431932586580', '98.63497352034269173099168042261', '99.3564257364691773893660211950', '99.68608385358825588666581814635', '100.851352766964608888162742586399', '101.638056500030256413274477357636', '102.346265107005178011867872694078', '103.23363084377200061022878868395', '103.6062162561728983472352296946', '104.30653468170169362369211801683', '104.7386085482851266708516999242', '105.21385686409084127710881049391', '106.06680880004309133174774212553', '106.825364401791837373365091434316', '107.765391826659518281399583407809', '108.18441687129061020992926834749', '108.60745196645688239560037201034', '109.30073525568102443277218024649', '110.46180284282643094496248591987', '111.23352057653686170145443006197', '111.44998040788060637450163255056', '112.12999915575181627408110752873', '113.20094847373310210404563254551', '113.71124768840584503648262593267', '114.41356385405362094396356857197', '114.8247151847930570269587544173', '115.618388425419918869960093577813', '116.08475422565388914634559944408', '116.60595471206680768410593471751', '117.1836110795411678729547970943', '118.20478045017710067262022906614', '119.094494384379793215750314713249', '119.92529598809275155154173332365', '120.3637309984911173995898470775', '121.099046434098026498205753005204', '121.53518479675978592734052769187', '122.10573187048656822348406788344', '122.98076838697949804397332191677', '123.65819975418048872064006258904', '124.15623851708294843928546766580', '124.7227975355794344465950593176', '125.40389607684151571726816240652', '126.50275253736566327062165579415', '126.79904764159752767188674373411', '127.08653336362798111934776562180', '128.244060471778756753375596139215', '128.69700259052140226243079526424', '129.70042670250305975562737680672', '130.78882474552456224949576006795', '130.86994681209071822349456582201', '131.53689243555857262026810319242', '132.07888336093319377611036876740', '132.76203498578879060337418212510', '133.411620710892110647428437042447', '133.94153314436944992572402528786', '134.54373033520721753073127287865', '135.3018848737340338687156139494', '135.975161230034717777740238234693', '136.80271565363898746493084793102', '137.62510902302509484614539556126', '138.10499063953810933593495004794', '138.942103022487030607039766446476', '139.4809719958086901288173538553', '140.06157789741931782036426356658', '140.2959921947771079178952380766', '141.524242889631357204571466084674', '142.06860086794715180950656844837', '142.85310338085613434264440157092', '143.32296720737377833861101165497', '143.58748153409087596428049493248', '144.36220230353321981560237397758', '144.86245814908614011054884699368', '145.95237525932660117257042355063', '146.5984057714595241836643701369', '147.45752577242399322230629487642', '148.170683646424687411436814807830', '148.37657746548383617516229536243', '149.41973973110042920768793275460', '149.943010548078411912383444989344', '150.58454532931911507027239508639', '150.76260305723882462694749071401', '151.34386553351388210928298976491', '152.45031520333356800096187184552', '152.99334715844246823339640991015', '153.57616662177918702740482139720', '154.29146899537271695233747524742', '155.075065007999621110947551330200', '155.74352472540410079149027698151', '156.157443518676291104233971210540', '156.964077798772838924997602623786', '157.675679629405631168308165960590', '158.39757616832220715150798292242', '158.99762880688774360040169620447', '159.57525364738375905088696673326', '160.215511313427892348227597959257', '160.56726770243941518844496917769', '161.474693685431345186789136197364', '161.88307267729334597605713614851', '162.66378647696777365925162497625', '163.08620708286341780356956039391', '163.60428640516410415311921910687', '165.12538199952392203637186081923', '165.81766391519638921594676991993', '165.98180164913935372139007517267', '166.67502868047911549498642975956', '167.18351771161710675579500930634', '167.7540777988739188276510692151', '168.54380189061006986483945148556', '169.0281818785269276448222588856', '169.8125180898311360743560667314', '170.49730109678533501110177976436', '170.99957331190407083944446376972', '171.536753312011560402769111289387', '172.27591180932839165815279361488', '172.91475597781628285752580912718', '173.63736495514962676483776069985', '174.38913109220147344992503383336', '174.91126030710505149426886899045', '175.951400880449724813087118706393', '176.05226759729449558050883909416', '177.14223032589547309988698493485', '177.61386795683799332953866992779', '178.07200267714480970062275850549', '178.74482169079512715236379580773', '179.16407263681660142561883472003', '179.69980441061316784743428616547', '180.266808108612321135472722969027', '181.48369341424313281248250724371', '182.0341641242983967434313727252', '182.60206861259760406893143653057', '183.20789756594981013202309355049', '184.1016250328045361587171644082', '184.732327855214214776380882566156', '185.021902987018670195097939528003', '185.81915112150258563638187482188', '186.24897615824676864945896629274', '186.97449032647348317074038412392', '187.68475505734709122768300991594', '188.36914837504379019495490291215', '189.04703947988047655303426666152', '189.409638207223117832389196919460', '189.91675348470015720612520922034', '190.621342851528034608300192192688', '191.2204484667074973769920751260', '192.3668306627666494049634601037', '192.8474012865494697539550623756', '193.56539741868085386704468555491', '194.38745827795860832889525885675', '194.78161873311139346641330038250', '195.1911778956935062760620387471', '195.56827146757119402093827814512', '196.58605369292827026022070345754', '197.22041542986952582529735612849', '197.50327214231636918353688612811', '198.23587870087554828345598022750', '198.8785039777158919881473878898', '199.75670891537120296137974022886'], 'prelabel': '1-667-667.249-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.097534977690338, 'root_angle': 0.35275953003713517, 'root_number': '0.446249116250055260234932823123+0.894908780963760946309332084060*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.176379765019', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(44)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.52014547312718906982254557525+0.551133832101845490283577607061*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.39545355585', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.50957336906', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.6797521971', 'prec': 40}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.097534977690338, 'bad_primes': [23, 29], 'central_character': '667.249', 'conductor': 667, 'conductor_radical': 667, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/667/249'], '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': '1-667-667.249-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': '1-667-667.249-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.097534977690338, 'root_angle': 0.17637976501856759, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39545355585', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_667.249', 'Lhash_array': ['dirichlet_L_667.249'], 'label': '1-667-667.249-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/667/249'}