-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_113.52', 'a10': [0.9937122098932426, 0.11196447610330786], 'a2': [0.9009688679024191, -0.4338837391175581], 'a3': [-0.8467241992282841, 0.5320320765153366], 'a4': [0.6234898018587335, -0.7818314824680298], 'a5': [0.8467241992282841, 0.5320320765153366], 'a6': [-0.5320320765153366, 0.8467241992282841], 'a7': [-0.2225209339563144, 0.9749279121818236], 'a8': [0.2225209339563144, -0.9749279121818236], 'a9': [0.4338837391175581, -0.9009688679024191], 'algebraic': True, 'analytic_conductor': 0.5247697938216015, 'analytic_normalization': 0, 'bad_lfactors': [[113, [1]]], 'bad_primes': [113], 'central_character': '113.52', 'coeff_info': ['x^56 - 1', '0.993712209893243 + 0.111964476103308*I', '\\\\zeta_{56}'], 'conductor': 113, 'conductor_radical': 113, 'conjugate': 'dirichlet_L_113.50', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^52', 'a^23', 'a^48', 'a^5', 'a^19', 'a^16', 'a^44', 'a^46', 'a^1', 'a^22', 'a^15', 'a^2', 'a^12', 'a^28', 'a^40', 'a^3', 'a^42', 'a^37', 'a^53', 'a^39', 'a^18', 'a^47', 'a^11', 'a^10', 'a^54', 'a^13', 'a^8', 'a^31', 'a^24', 'a^30', 'a^36', 'a^45', 'a^55', 'a^21', 'a^38', 'a^29', 'a^33', 'a^25', 'a^49', 'a^34', 'a^35', 'a^17', 'a^14', 'a^51', 'a^43', 'a^41', 'a^7', 'a^32', 'a^6', 'a^26', 'a^50', 'a^20', 'a^9', 'a^27', 'a^4', 'a^4', 'a^27', 'a^9', 'a^20', 'a^50', 'a^26', 'a^6', 'a^32', 'a^7', 'a^41', 'a^43', 'a^51', 'a^14', 'a^17', 'a^35', 'a^34', 'a^49', 'a^25', 'a^33', 'a^29', 'a^38', 'a^21', 'a^55', 'a^45', 'a^36', 'a^30', 'a^24', 'a^31', 'a^8', 'a^13', 'a^54', 'a^10', 'a^11', 'a^47', 'a^18', 'a^39', 'a^53', 'a^37', 'a^42', 'a^3', 'a^40', 'a^28', 'a^12', 'a^2'], 'euler_factors': [[1, 'a^52'], [1, 'a^23'], [1, 'a^5'], [1, 'a^16'], [1, 'a^22'], [1, 'a^2'], [1, 'a^3'], [1, 'a^37'], [1, 'a^47'], [1, 'a^31'], [1, 'a^30'], [1, 'a^29'], [1, 'a^34'], [1, 'a^17'], [1, 'a^41'], [1, 'a^20'], [1, 'a^9'], [1, 'a^50'], [1, 'a^43'], [1, 'a^35'], [1, 'a^49'], [1, 'a^55'], [1, 'a^24'], [1, 'a^11'], [1, 'a^40'], [1, 'a^15']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-113-113.52-r0-0-0', 'leading_term': '1.47903500609473592897330535889+0.117522361580865891784839302806*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/113/52', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.4836967529536484, 1.747091180497644, 2.156917679805372, 2.3367499902922324, 2.0830168668270783, 1.3790104998211072, 0.384369209199651, -0.6073612953339016, -1.2637178190952933, -1.3429951903266397, -0.8094562238264081, 0.12444216865030433, 1.065571367510519, 1.6054904016089553, 1.5166481863234886, 0.8809541695169196, 0.06880560659935728, -0.44620296820563116, -0.36095981400796556, 0.23731021195202406, 0.8441714890767221, 0.7573783764637823, -0.538903810538573, -3.0190379372292058, -6.0020203412458635, -8.385730352975125, -9.150087734981268, -7.88198886599873, -5.030259740792151, -1.7224192710559851, 0.7865991768301099, 1.7431786797448419, 1.2464119900225776, 0.11483477812376952, -0.6536805495169894, -0.4985797321339347, 0.3952860827262031, 1.291381363265116, 1.4632026527424242, 0.7396225281922091, -0.34897049684549963, -0.9387221841654189, -0.4668823739219398, 0.8803627571844589, 2.249770509348159, 2.7068747368026687, 1.923869608160468, 0.4615842680687465, -0.5975146031987435, -0.43961916509482035, 0.830439658473271, 2.1844562007989645, 2.371058760059982, 0.8523966104270593, -1.7093388108523826, -3.819399816493028, -4.166081690133184, -2.578480829846896, -0.21632936513652953, 1.190099331552851, 0.5384354075052216, -1.8645368882510505, -4.512274218304819, -5.752804039665885, -4.9181842271970115, -2.7081403612965294, -0.5773150717057424, 0.3668799346012538, 0.09377154627821324, -0.5283398920873614, -0.6050027923742434, -0.011649190097696263, 0.5694114286663794, 0.38429526185792356, -0.5596454106779297, -1.350573610604366, -0.9195533319466985, 0.9258421112702035, 3.111904195849094, 4.004132091517768, 2.7311955379764803, 0.051800981461076374, -2.032281998626782, -1.7253838458835342, 1.1476952851180584, 4.906378156843715, 7.20036877889586, 6.717511600550961, 4.076770241187804, 1.2220526291430607, -0.14950739063216523, 0.17860400905870943, 1.0236507332289229, 1.0373725060915822, -0.042798215049514046, -1.2258309393613909, -1.2845242762296685, 0.010823646918078599, 1.59655343226645, 2.0439587468348046, 0.8640016974430037, -1.0210716328410538, -2.092874426481272, -1.6006981252705743, -0.21103015217303134, 0.6693752283016446, 0.26251730160678494, -0.83396645521544, -1.2791064884876244, -0.44054907654742836, 0.7431767351310521, 0.4355039903211233, -2.3636205703736497, -6.577271219903312, -9.553457202210607, -9.053252922702777, -5.0933727719701825, -0.0402980533457003, 3.177673279935752, 3.24891887478889, 1.2343059162430166, -0.6370727392853156, -0.9547889346980503, -0.11792427862071075, 0.4250664929111563, -0.20799733454822428, -1.4768862750757048, -2.0866745468444776, -1.3985586504044887, -0.09262614516851184, 0.5976533659607216, 0.2582946838493845, -0.20754727615669044, 0.43887008976089203, 2.2683828535247765, 3.765526171732001, 3.106618295379095, 0.02187309601440749, -3.6018305909807595, -5.138000801343121, -3.482345636392724, -0.0719027630613878, 2.3532396477826976, 2.1563654705225033, 0.16230251184498232, -1.2784645919679847, -0.5941093338808585, 1.5488077415475254, 2.9964472984300765, 2.2789633524568385, 0.05204935273459753, -1.5805616033785113, -1.1442387358072086, 0.8071583389893491, 2.320733380975179, 2.003718547107981, 0.31666735364172605, -1.0488959579568053, -0.9704004278703668, 0.03706704383902167, 0.5542514363952784, -0.0763982973513926, -1.0072520236092295, -0.8959728385549843, 0.4477828108126679, 1.668531388731222, 1.3106299679235849, -0.36349713302119924, -1.2407263071209913, 0.6649747548031378, 4.965430955049687, 8.738897737995899, 8.894187980224197, 4.965027128424654, -0.33061182151688673, -3.3732164120673795, -2.6651990305858684, 0.1841540180348452, 2.2732484826482264, 2.104342650352501, 0.5670598836385041, -0.4791656815027646, -0.2753628323260039, 0.3225513803453744, 0.2231618041675707, -0.38550031300090265, -0.19747613936524144, 1.5457036533853548, 3.840783676742942, 4.683086464543356, 3.118391150574004, 0.36336646510344806, -1.3314054530198223, -0.9615352658378438, 0.2486300814743202, 0.2820774738846398, -1.3211469871658208, -2.7901319932648754, -1.9857075493370246, 1.1102246807882759, 4.003621649631468, 3.9957605241113336, 0.9051626197657194, -2.63607497480076, -3.7013442683587643, -1.8696101987980855, 0.533701721584758, 0.936674154108287, -0.879479270053541, -2.739900976202251, -2.497167889598315, -0.2620579918882646, 1.8640854157258149, 2.0947176060576274, 0.7109274941305608, -0.5497192568496964, -0.5757966658820016, 0.015459761691628573, -0.07538547825316079, -1.0350025385493802, -1.6496862849768967, -0.9236479922433508, 0.3929049436402346, 0.42251826571228346, -1.507801292783463, -3.4835244060123274, -2.4918689741654623, 2.416586839310744, 8.59704274783516, 11.797683913127681, 9.928268056373417, 4.894771030040532, 0.6707729259966876, -0.3955241082702395, 0.6760238752350093, 1.231327101310949, 0.04650977621655201, -1.6156625757338767, -1.848925368992121, -0.4961471305492063, 0.6894845367516295, 0.17569858696181348, -1.5236154919363847, -2.486455916253286, -1.6925209203554445, -0.23849759634219161, -0.0002687286054941772, -1.3270927797892345, -2.5379098098992, -1.8849044921195794, 0.30075023622963915, 1.8636961880589396, 1.275925216282395, -0.563699685509649, -1.3690492621214032, -0.21882552890945003, 1.232832589443988, 0.6826992751945994, -1.838500149840274, -3.4557553519487056, -1.321594137446833, 4.089338527542646, 8.93911466603641, 9.516690004063918, 5.708473960846774, 0.8876101797070346, -1.510622638327015, -1.03105744700711, 0.14780783313485912, 0.0991480604598257, -0.8778138820813768, -1.1995160129022784, -0.3086537910364518, 0.6197139813099962, 0.32644286879950357, -0.7833566144514065, -1.1252560848819206, -0.08883171632738547, 0.9419765101991782, 0.2087777802444753, -1.9994608398620985, -3.22358142145804, -1.5278253056183881, 1.9771327768809663, 3.9188859040218587, 2.2237364571622216, -1.428985016965168, -3.1560867264875876, -0.91099781619022, 3.3590663445793676, 5.7908144918359294, 4.591573905756357, 1.5791144809082636, -0.1999086678279341, 0.16563760089918225, 0.922861896240686, 0.2650682537350674, -1.278448053694131, -1.56139858956565, 0.3489437970155398, 2.7838355855386148, 3.2740641873411427, 1.382672618312148, -0.8295239142807456, -1.217774353563125, 0.09567008689967, 1.1913751143598788, 0.8683789304052358, -0.04604306602700767, -0.1942261625220645, 0.09357010172664601, -1.0191786835923122, -4.2335951040900275, -7.354954248066492, -7.08349200638163, -2.770610513427535, 2.209575251478825, 3.4890933244865403, 0.1411516830817617, -4.324389633941695, -5.588143666702587, -2.8498216770949476, 0.764982312823651, 1.8729283689091094, 0.2850290668619515, -1.4327457213243913, -1.278511614138989, 0.11177150522289782, 0.816789063435714, 0.2816066910620023, -0.18787986577381638, 0.509627210824343, 1.60296202422135, 1.506026731388302, 0.20794219586730175, -0.3208016718197199, 1.4548215038637973, 4.3476239447267675, 5.4056986411061825, 3.2905044752594406, 0.03872598133471685, -1.1335633613597522, 0.4469976973349059, 2.120094070353953, 1.0997101344966376, -2.0936988537025423, -4.134334017829298, -2.8036457458605004, 0.35033736906248053, 1.820786970731993, 0.2777727770699484, -1.90468934199772, -1.5246491778695432, 1.6398616810775484, 4.594514981667159, 4.608011037118046, 2.171572961069007, 0.05615764728701468, -0.0787497631959892, 0.7137039710942907, 0.5561256810072936, -0.6154714909392711, -1.1171897008391891, -0.012258430196333625, 1.4427788570021653, 1.4016387327689157, -0.07397064811656062, -1.0743206388621425, -0.5223639950043935, 0.14090651554480413, -1.1493408434303813, -3.7453482634922404, -4.009413848346449, 0.814009566061678, 8.79180373369148, 14.313334112254708, 13.341235797878898, 7.300572143377412, 1.3760670920665874, -0.7415415693706767, 0.17486099468641098, 1.0101354231344284, 0.3498312003819033, -0.4549977322449784, 0.11551010671126206, 1.3743274543421216, 1.4225249197999816, -0.04886928790484499, -1.1116257634228535, -0.1003484593559853, 2.048194600777771, 2.819875649909423, 1.2995277424001512, -0.6308160487782504, -0.7049422609609741, 0.8011821724130431, 1.482067611127009, 0.07348444349601504, -1.7306445521630904, -1.4505167709766273, 0.7317349281989024, 1.8635276043760511, -0.07844958298517588, -3.2616163667366274, -3.793343639755445, -0.37005653121643894, 3.8637607314216664, 4.707186069524178, 1.6281666919027191, -1.7805008423594797, -2.0722307611845583, 0.2378267273780164, 1.7320390351191275, 0.3978514594866763, -2.1863224675079396, -3.1542465826056754, -1.869204306406326, -0.25236187991795417, 0.0329738737651432, -0.4649095171365819, -0.31624008139481696, 0.4223744945272408, 0.355978474508768, -0.7887952346521179, -1.1286732534207775, 1.0133016350918775, 4.257340951218843, 5.014874094748006, 1.6744114248947481, -2.9281257211136045, -4.248551636162266, -1.1295594099657622, 2.8178044677376386, 3.35496888450336, 0.4042697954243672, -2.1850219532964554, -1.4191117741862982, 1.4306333259760997, 2.7551922025241375, 1.128948799373751, -1.2749343586325366, -1.7891808084639398, -0.5420188570870659, 0.25503589560623247, -0.30744709561832256, -0.5508845148676492, 1.2643780314400102, 4.15808613192396, 5.315981620067895, 3.5828959154885367, 0.9315032126248142, -0.05851979502225625, 0.645438045320502, 0.8991894874498212, -0.3762631965965551, -1.6369037278305756, -1.0386261844614342, 0.6430070727262818, 0.8355598205901441, -1.0110047436648113, -1.8443282223023565, 1.555518056596242, 7.9923458460440076, 12.120345425912193, 9.926069310897036, 3.210921631103931, -2.2602708406408447, -2.803697645038019, -0.06458935027273457, 1.843132453182546, 1.2462016004989507, -0.05098792811277769, -0.04780271608242059, 0.7490321317852985, 0.5923285930877052, -0.6038936086588724, -1.0729998612169749, 0.0956272105682596, 1.4078553788583448, 0.9824499200377164, -0.6487825606623925, -1.0762859721915488, 0.6006747621888868, 2.2476979884475994, 1.4908153686237988, -0.7025706327292001, -0.7314772025480923, 3.0268559879247534, 7.53919122328916, 8.187638245454433, 4.126313445890173, -0.6846005407001231, -2.092276315225899, -0.2864209773733578, 1.2185184256112962, 0.4559153899008356, -0.7153506830214016, 0.343796897569419, 3.05128206719161, 4.107611398804336, 1.8062371317791148, -1.6249446793340945, -2.731849118949129, -0.9822203044744937, 0.9816831155992684, 0.9873785721266862, -0.1590392326886644, -0.4015079855240957, 0.4323829243603731, 0.6041235370627596, -0.6391981785999703, -1.6930338973368992, -0.9348627343361275, 0.6135771174431827, 0.494556581107092, -1.3807684890666332, -1.7873949975346086, 1.8327265739205103, 7.2857979641683395, 9.204013593171025, 5.098577099123458, -1.378960266623579, -4.235561087491382, -1.6323331681779265, 2.6028205679464738, 3.890015921435916, 1.9195992337869008, -0.0600490762882866, 0.07677381559329635, 1.0615793921078038, 0.7796872655253342, -0.5427373969230884, -0.9814749897477144, -0.023939238625993734, 0.6656020860419777, -0.0326456795675302, -0.6407873868394824, 0.9644636741181195, 4.1300266224555635, 5.569182898299025, 3.3703770145968965, -0.37609271687405676, -2.041707700699251, -0.8851919798185345, 0.4660873005101772, 0.06394039270912849, -0.4723562171832101, 1.5876991954967241, 5.559279773040658, 7.227052932266511, 3.886701177507031, -1.8647331184439573, -4.78400966391373, -3.0001746520196746, 0.1257661619311433, 0.486286074663832, -1.8383224583966293, -3.331946820118352, -1.975198097728409, 0.35075851244556516, 0.811289133684103, -0.5319185591757182, -1.1900267429077322, 0.040139078118627755, 1.5269239652883642, 1.3751941718015688, 0.12175578581315938, -0.3509186255586119, 0.1763338572906004, 0.06004769722960987, -1.1761993921745852, -1.3496906332078202, 1.4157468790704444, 5.055130548142059, 4.9336251419437565, -0.5124898334687389, -6.958218873903736, -8.465544284856279, -4.12940124086811, 1.0217294021170085, 1.9711540408826003, -0.8761349739685347, -3.1742704691130497, -2.408435945998627, -0.3462010780831059, 0.3193273323107726, -0.18317365640872335, 0.3530919392481151, 2.2825545232192224, 3.2583065325284077, 1.6335425711939056, -0.9018073468914135, -1.3976758917312955, 0.4105245057365777, 1.8576838998213907, 1.1231817202484031, -0.3642610330983678, -0.255493545425415, 1.1429806690399906, 1.336484789752569, -0.4770616559710715, -1.8823800757985065, -0.6132592477782358, 1.860499498894294, 1.9484343785059937, -1.0509772714390648, -3.541293176835282, -2.2698330922508836, 0.97433445058513, 1.205686995385399, -3.33342889937532, -8.47788891860233, -8.866516951371025, -4.185042196609714, 0.8282171373839553, 2.183901290942217, 0.6613681996355993, -0.46239424719410716, -0.0016116219048131777, 0.47097993429669266, -0.14908861005764898, -0.7451789368984033, -0.14950838919716947, 0.560393319035503, -0.4495834659225931, -2.625622773913889, -3.280360683866975, -1.3982426571348177, 0.5022555822878212, -0.3435053454707099, -2.779995277003418, -2.831532701997049, 0.8530588060608858, 4.566049901289994, 3.89605213755135, -0.5531533165885584, -3.714519975263034, -2.3400903329346088, 1.1584302041562116, 2.182688030666694, -0.12862994108825604], 'positive_zeros': ['1.99031384178781645899981583226', '3.39897012523929083162643275997', '5.02977581576993120325609856493', '5.83106627987470704654654504547', '6.77893284618080555484874878653', '9.257269037057166222722057879206', '10.34589821725579863765209970043', '11.12839699268784232911111949865', '12.39617295281868692819124347948', '13.24897116460739545278116259862', '14.79416467268607119529427248923', '15.44335517077756317358706682193', '16.67274256052644161756351984107', '18.15712461026876958476172607338', '18.83647171038274299175807235483', '20.75839693232100177648276857647', '21.29508166443725374671221535791', '22.192423299700012313995946647289', '22.95796928251021479178212528552', '23.9277947311262812664027293449', '25.318386950238768693210006839688', '26.14788970314307103764185783048', '28.05138712761911470587963774076', '28.36528513304234510278000160974', '29.36517508817686320722688685880', '30.310502888341298699483523669164', '31.39223166449714305974779336349', '32.55034810605863275261067592530', '33.203980495610689181428104112032', '34.1660406925129983914666071661', '34.76077163307051574396716728884', '36.56527422795770879695094298083', '37.68165461104718218140546164390', '38.47803886497593242222934176252', '39.001909737484751693624264320579', '40.337735400177168693923779941088', '41.06670652137458685850617667763', '41.43632910984959702204824659638', '42.814294953456710196539920695965', '44.069209196480201744776367544518', '45.02419361407622474070633796560', '45.7214006407828355422394157845', '46.88209038332962360382406503543', '47.693521817710918367265863779223', '48.80562446221703035393395140819', '49.675898036395756239221338552263', '50.28878940008292473142327169425', '51.16126323177601559425842874306', '52.123332636406787513635359980835', '52.746080338193122844459576027447', '54.353300170878052086462397448940', '55.2929155879023523595583260253', '56.37663247482783016262076083942', '57.00304972000333685588806004109', '57.614876037218806512793781222230', '58.17984113359377388350533852072', '59.733416148303333730599735622779', '60.55004430677259016138117596346', '61.01493736833487548452014543350', '62.08857222504749218303549885215', '63.197240306826249073237647610073', '64.29030630957957894591503323510', '64.87591880822709065460344676588', '65.96922484703347409750063435290', '67.02130744877114444313301535253', '67.80141057920129721213603988945', '68.08380883138580673332228804855', '69.26978857908097254578363775295', '69.783334350420175698281472057148', '70.80785461155029677236731078254', '72.59435931973680675496192102831', '72.958439860505442516467636992900', '73.75812139708167297064929575070', '74.78667265689981361616350961442', '75.3503171065587969375565190900', '76.64570893970420150783353837165', '76.87487775719299843849998157741', '78.084378513181585780524903835735', '78.96580735051212053052765736711', '79.72646352445572821153176683338', '80.41176555337567968516179325762', '81.33835297825967405398671752996', '82.88879852945123889991365880580', '83.695113065604429700081870120282', '84.100886162082163641547830090817', '85.081947100362019789198062553415', '85.7222825804446120553349564396', '86.58252044758336609751819228984', '87.222846712190183093696185663344', '88.26482962081324614661973575328', '89.25183637847110328800932304563', '90.069644970823523537466987807547', '91.490620347020106120534974471758', '91.81888392497363938906414032232', '92.55566995521669145630543587399', '93.39510676330600998170627811820', '94.55144095060921547662104201357', '95.29333761328270495685887240311', '96.22937425569282831823846496577', '96.71906216001183339467491262287', '96.96249346368651048573967582028', '98.59713341246359136146773776786', '99.38428706674476651336645950020', '100.54661158386341806196048566275', '101.291449102295767050186859063159', '102.161769878041331346102119237228', '102.93319983750629388896931054120', '103.27366621355037588272491690711', '104.427654476321241138268240625908', '104.78945529063159921586285890819', '106.254616543361294047713460646638', '106.81129131650912515028170773649', '107.61777680352758666016846779472', '108.71285460733287420379146202341', '109.40958775093116940831052329214', '110.17009830276298281067024406228', '111.57834191461567732573739796871', '111.90873311998341573259503453293', '112.6582934270142665466768101445', '113.43984010792105829161149930358', '114.36058277088026570880775704811', '115.17619569185575528572317527349', '115.40772409184393092588319726393', '116.52587791543882101200916319718', '118.25204731624182194793236276125', '118.710215390691740540773305959297', '119.4767896043794672376139326759', '119.9693803319485924552003370538', '120.928443449605358853938570374003', '121.57821086847204243585683666813', '122.68921517369678383944751534006', '123.28426395002374554052084004789', '124.07347537716763065854100075501', '124.90235624039953515806005445870', '125.61725524616906369686039572951', '126.58734903407714018048086973524', '127.62917768828579667799237766406', '128.40824379762691648476412557804', '129.111088991934672761040743301005', '130.410844486769994978591912237345', '130.65092993824624052482894437291', '131.383030096704691572785209123077', '131.98897203704707904864095466251', '132.704230039827767127017707909433', '133.85666771423184560137344765292', '134.76696717671874894009725916774', '135.66121307852309572699123099723', '136.40920069837591633567932650020', '137.32142547377762711746559726187', '138.2683419471076112197504295635', '138.63139518829829393690708351498', '139.20398591435255002534287477812', '140.84286475508314612775148017204', '140.99911214928751635134511616545', '141.80382742135562081778772678277', '142.68640093724896307973565590486', '143.28785680187776982499865545372', '143.96502309611862464545543209931', '145.46724144210188151953764423988', '146.25690519420248697636154963061', '147.16866842790107235343491996440', '147.52069737707584648171710459442', '148.28892737770017441168992896854', '149.0441786001513214719843409262', '149.875056036423760074860574257253', '150.537422840146658589043845599852', '151.45494748287657767649668513070', '151.96376725343766662554119685581', '153.38184607968805429396498009347', '154.10251557667341872859873939940', '154.780694460235305579162528646579', '155.26264915109134783565410530056', '156.405144087801571732688731279624', '157.31894593690173854825420122396', '158.076901624044960472716152411224', '158.60259941848539226849685878682', '159.24216282548469308738206552488', '160.17419042539154799679320992061', '160.721143724764890588092730946287', '161.44345942919518463782863587200', '162.739684887212443287763257865908', '163.5502921032771755272291582437', '164.669591298053551602875958077033', '164.97455682170188079779975134539', '165.81015829290670506198597192926', '166.568885151260954903897982330191', '167.17807185170927220395528773138', '167.68534433192260974612742369871', '169.02703408669042231488641995259', '169.85240900381296408353354482122', '170.33240385669030216798822160858', '170.75541676754424159617651620689', '172.08236384423436882311577628563', '173.10759925268826064915282939056', '173.52230831837441488452463239356', '174.62950891552246946355771393256', '175.20303065998951743802564673930', '175.93044879615724952668413964870', '176.91085766887611653259397888566', '177.405469883444056047421430899616', '177.83353323817994386693721997599', '178.62641673114547895317043035975', '179.66461488698402210018679884740', '180.85920056673021426197072302010', '181.48133209992697159304796850507', '182.57678695964969106416478836907', '183.00775659312653472552524879864', '183.34524662882940458493229143740', '184.56351510704824546226287012627', '185.25345522383811457339143985208', '186.15463083565591345262647249436', '186.62721184875436069542968185908', '187.43176831381631016095473669868', '188.19922338332843716943849413577', '188.96972832424606736991773540970', '189.89731296285003913915264622250', '190.42583560150893212452188384871', '191.80872225796014002347517863864', '192.62888263814304470895929765650', '193.12561842643940943731315995905', '193.6986661526324299608069719920', '194.42090668206780951373437592198', '194.91997799911550200296333107049', '196.129426331942056476029742828717', '196.509980198597676415770751655778', '197.44161752660070644393605688866', '198.401525528532793600357400395748', '199.26468651630384539248869008835', '199.986493113540587649945037278934'], 'prelabel': '1-113-113.52-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5247697938216015, 'root_angle': 0.02523949569363915, 'root_number': '0.987451820488650658141682673140+0.157920556653178107738469927118*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0252394956936', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(56)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.44413517713038913449703750955+0.0200970325711120568682711980517*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.99031384179', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.39897012524', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.02977581577', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.5247697938216015, 'bad_primes': [113], 'central_character': '113.52', 'conductor': 113, 'conductor_radical': 113, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/113/52'], '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': '1-113-113.52-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': '1-113-113.52-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5247697938216015, 'root_angle': 0.02523949569363915, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.99031384179', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_113.52', 'Lhash_array': ['dirichlet_L_113.52'], 'factors': ['1-113-113.52-r0-0-0'], 'label': '1-113-113.52-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/113/52'}