-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1045.118', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.5299192642332049, 0.848048096156426], 'a3': [0.8290375725550417, 0.5591929034707468], 'a4': [-0.4383711467890774, 0.898794046299167], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.03489949670250097, 0.9993908270190958], 'a7': [-0.9945218953682733, -0.10452846326765347], 'a8': [-0.9945218953682733, 0.10452846326765347], 'a9': [0.374606593415912, 0.9271838545667874], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.118', 'coeff_info': ['x^180 - 1', '0.999390827019096 + 0.0348994967025010*I', '\\\\zeta_{180}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.62', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^29', 'a^17', 'a^58', 0, 'a^46', 'a^93', 'a^87', 'a^34', 0, 0, 'a^75', 'a^19', 'a^122', 0, 'a^116', 'a^101', 'a^63', 0, 0, 'a^110', 0, 'a^85', 'a^104', 0, 'a^48', 'a^51', 'a^151', 'a^88', 0, 'a^84', 'a^145', 0, 'a^130', 0, 'a^92', 'a^63', 0, 'a^36', 0, 'a^62', 'a^139', 'a^95', 0, 0, 'a^114', 'a^7', 'a^133', 'a^6', 0, 'a^118', 'a^77', 'a^49', 'a^80', 0, 'a^0', 0, 'a^117', 'a^38', 0, 'a^166', 'a^113', 'a^127', 'a^174', 0, 0, 'a^115', 'a^159', 'a^102', 0, 'a^176', 'a^121', 'a^143', 'a^92', 0, 0, 0, 'a^65', 'a^44', 0, 'a^68', 'a^91', 'a^111', 'a^168', 0, 'a^124', 'a^105', 0, 'a^10', 0, 'a^112', 'a^143', 'a^101', 'a^36', 0, 'a^162', 'a^119', 'a^35', 0, 0], 'euler_factors': [[1, 'a^29'], [1, 'a^17'], [0], [1, 'a^93'], [0], [1, 'a^19'], [1, 'a^101'], [0], [1, 'a^85'], [1, 'a^88'], [1, 'a^84'], [1, 'a^63'], [1, 'a^62'], [1, 'a^95'], [1, 'a^7'], [1, 'a^49'], [1, 'a^38'], [1, 'a^166'], [1, 'a^115'], [1, 'a^176'], [1, 'a^143'], [1, 'a^44'], [1, 'a^111'], [1, 'a^10'], [1, 'a^119'], [1, 'a^154']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1045-1045.118-r0-0-0', 'leading_term': '-0.462359877676338251701855684829+1.20343650741957986640260026617*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/1045/118', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-1.2891997843139424, -2.8586937795645193, -5.0730512651480275, -6.874303183016044, -6.969384064108941, -4.883168015776766, -1.4564751010574273, 1.5677485733559173, 2.708672483612619, 1.8271726911452466, 0.19227472950244073, -0.6261596660738891, -0.12765835813962548, 0.7510423395981682, 0.675946150470325, -0.6167257274762913, -1.9367421319826645, -1.8349560218163494, -0.20258652893196744, 1.4658989473412092, 1.5713574874154066, 0.1489223936137943, -1.1002285729594459, -0.6598305746188746, 1.056595728083884, 2.108615651191661, 1.2572382019579589, -0.5217174343799802, -1.1461788624531084, -0.021766517794534753, 1.0013900568726672, -0.24268253047342075, -3.2899532775403424, -4.928075062565602, -2.552868069432304, 2.5642566997192993, 6.031878615393107, 4.696690917132745, -0.06850125780298628, -3.846878959352614, -3.788250793232016, -1.1826349958992055, 0.662152040610682, 0.36563773432839497, -0.49253342321742766, -0.049627232692598035, 1.279816013748936, 1.648914369468378, 0.5557573494477955, -0.4538840469423968, -0.10028001067971179, 0.7268726423535656, 0.3911173124138812, -0.6808058068404883, -0.1009381393214477, 3.040439434722929, 6.046004209706817, 5.355177375394243, 1.2114489129488428, -1.9580743046164957, -0.6045702367203325, 3.54375624342286, 5.502512139429556, 3.1317049971380375, -0.41132232335585955, -0.9293968776478541, 1.522075003978712, 3.1641034826315644, 1.77218026025418, -0.6068951172864743, -0.9420730054430142, 0.4494523407306493, 0.6637590418665968, -1.281698304463092, -2.882382228331148, -1.8046670371092324, 0.6176389223480704, 1.188004189619853, -0.6717540449879505, -2.267492899021153, -1.6171105673454678, -0.09165848807718238, 0.054343664949259976, -0.7944977667625508, -0.5989038734765977, 0.5033575479303618, -0.02239415677089577, -2.749439978848513, -4.147088170441181, -1.0417541606589724, 3.9972941200626697, 4.7300541558482525, -0.8111099213166093, -7.080161470672422, -7.477347258806784, -2.3317861246853577, 2.043317524992522, 1.560684717310076, -1.336411376986716, -2.245153588501467, -0.8207541402870142, 0.02604672664362272, -0.7652723064365674, -1.2323503251752024, -0.22029752286604165, 0.6500277206719681, 0.06191736171202797, -0.3901313332896287, 1.135956732943567, 3.0318616172736665, 2.083911227177044, -1.3911227795361218, -3.3482082789724643, -1.7574148954902433, 0.3645001666426671, -0.325654170888185, -2.0884933155373986, -0.6835031404448689, 3.6269951974613837, 5.60264961874649, 2.4295261676339397, -1.9740328514335248, -2.4739752892574565, 0.0659483237789089, 0.6484677638481278, -1.9940584593750268, -3.670170905192138, -1.5621740829623467, 1.2112832711085508, 0.36008610723049717, -3.0414690519174385, -4.30361011673034, -2.099556097379148, 0.14790111699326497, -0.06382014860817105, -1.011666718042787, -0.48848079803449335, 0.4090793569775022, -0.26242107301721584, -1.4249986888058261, -0.8133718977453172, 0.700058659966801, 0.31231914568005603, -1.569137103395764, -1.535942843407476, 0.529883467116858, -0.26782800464999695, -6.361162989142722, -11.955337114594155, -9.363579369182792, 0.28154121894313927, 7.620721591095329, 6.774862283316634, 1.7583065725481482, -0.606054306559609, 0.2701537291821836, 0.43068778075726605, -1.0730059826224885, -1.3979531173260118, 0.2621436322344812, 1.1177822711843823, -0.1126132355291126, -0.8876182878436468, 0.4810090213760177, 1.5669502584502708, 0.04224077482503158, -1.8830430418038082, -0.8903369476861118, 1.669714653056876, 1.7266642037657438, -0.7680286088996361, -1.7550405629621904, 0.027366087499334533, 0.9363550046368662, -1.1208770196304747, -2.8433799695104502, -1.3459288083574552, 0.2517612824189861, -2.1774971468805977, -5.872172960459996, -4.279566357402642, 2.541128918069883, 6.836532866964562, 3.980853413064888, -1.2300089677831478, -2.220737201607891, 0.1520247815218267, 0.6216810645431505, -1.5649289466188703, -2.407931105800584, -0.5130310052114259, 1.0125025288609764, 0.3849766740754138, -0.24408558927254, 0.5972730475854794, 1.0120621636146259, -0.2115875931789209, -0.9611915912574115, 0.020026530094769856, 0.1804749686646202, -1.964426049053348, -2.573250418814065, 1.9176608359852756, 7.481851818190236, 6.966674800022363, 1.0280730370147269, -2.0706606300345336, 1.4011984667849091, 5.367978317113713, 3.769626389409516, -0.4016730304242831, -0.7944879257061813, 2.161126723733212, 3.0496242780228, 0.7681760668250743, -0.6715459183807613, 0.17314067148369044, 0.27872548886716536, -1.3366948884154248, -1.3959666582480654, 1.297499109283883, 2.8183097334578098, 0.5037616964780971, -2.313002572409093, -1.727484984563962, 0.5601107283194331, 0.8401434393650853, -0.2070548971686919, 0.2881477345087117, 1.4265680875432927, 0.4271637697881351, -1.3098269549215542, -0.26705140337667405, 1.8818365895336284, -0.01719573710342445, -4.9716886886452825, -5.404345538859411, 1.0078153192571435, 6.224112906092676, 3.2802366906744016, -3.1948917367595833, -4.203827185638921, 0.3401211490996627, 2.989456156865006, 0.8925819364420605, -1.3737995888084913, -0.6863798001428406, 0.4458549141532637, -0.13100450473338127, -0.62605909872306, 0.07496873436337323, -0.1291904712995432, -1.842608799647547, -2.073233632666501, 0.23502033400611314, 1.5656728667105166, 0.09933257176866359, -0.4520937128528675, 2.439315644581597, 4.551906087856652, 1.650595298864374, -2.5543852950662878, -2.0581853804849084, 1.0563682973011908, -0.12684144599559088, -5.3501414790810475, -7.103387203240878, -2.879562862021393, 1.1129661946035099, 0.574603353141333, -0.7524785636378909, 0.7559246730002414, 1.851731349538965, -0.8986560376238597, -3.905941446799999, -2.3762108500072685, 1.3211959210558932, 1.7388075733939388, -0.6680350560354668, -1.372811090093698, -0.023742193190538545, 0.004557581121279356, -1.33802100042267, -0.9944431847569799, 0.7739943656323797, 0.76604029652327, -0.7794987512010109, -0.7040347599326602, 0.4746553819788142, -0.509431844134167, -2.155926621655143, 0.3014416779917972, 4.702058621500655, 2.3377774293837277, -8.029187671468401, -15.35020472433111, -11.119394996352197, -1.454056811660978, 2.577014425566454, 0.2795598289984169, -1.1873052290518047, 0.2899810910730866, 0.7011699715509754, -0.8810232081380448, -1.1059800215333355, 0.3578586785089598, 0.29339643226998857, -1.333942102484631, -1.2636784059587387, 0.4048176314185617, 0.3918430164032509, -0.8400861065381899, 0.4574299185702563, 3.499415896394126, 3.1877327649906175, -0.7190498459020573, -2.4397439776744227, -0.024926522496571714, 1.574807327243084, -0.11819710826208588, -0.9481720871520428, 0.969577871186983, 0.6542347771795652, -4.2025238353407826, -7.162338148236485, -3.2049178226666037, 2.178427991769013, 1.841515000505664, -1.2440395102929156, 0.11053396018079738, 4.559070312700425, 5.043828697447053, 1.1831405927010823, -0.9465375361027262, 0.19962113611578694, 0.22951235271017978, -2.0497827165547493, -2.827907070263678, -1.0146755441140671, 0.09579484035135963, -0.5128888915668111, -0.44166332910956696, 0.30454777769715297, -0.5391624993525355, -1.608358390167497, 0.2818992342553544, 2.6907336607906287, 0.42211051947749784, -4.063702769684108, -2.8315072823625176, 3.6804908330070054, 5.6209614875899, -0.40804901518523884, -5.237161880390736, -1.8922432579095878, 3.7213779577344357, 3.597647308267505, 0.056815928462878675, -0.537025489323855, 1.0257439758199696, 0.40384348284108323, -1.392273862133568, -1.0208440291692429, 0.04136589274132885, -0.9086142361495334, -1.4534492500708183, 1.287491972264502, 3.9340639209970183, 2.1891221712150983, -1.183741928058433, -1.1275550853478662, 0.982285447141512, 0.8630848126186041, -0.4832862731430198, 0.13028630524589033, 0.8274964149665828, -1.362203078194091, -3.337772070869079, -1.3208394994538106, 0.7300300324411046, -2.4721792092015282, -6.767759308400981, -4.840207215894152, 0.07537655661682716, -1.3023313801709615, -7.976118137365926, -9.472486180649991, -2.9715998675212205, 2.7585193066645064, 2.1482957758920413, -0.0963588224126126, 0.5560607453325014, 1.584608277996664, 0.5537788772610154, -0.12156004618737914, 0.8598953304365894, 0.9185738577663369, -0.44063346862237707, -0.36251178329928924, 0.8856357701523176, -0.10015043702533599, -2.344683883001536, -1.366345065416289, 1.768282531431961, 1.6417519069375563, -0.6111079383099349, 1.7299157367617293, 7.686136335005212, 7.992586807581169, 0.6724983462873176, -4.713680771039432, -2.5595291251578307, 0.7349053894151513, -0.6054046752336658, -2.4412800236513554, -0.4059669525943202, 1.6712982210574905, 0.12299523537371879, -1.1661207235551374, 1.1571664093868184, 3.0099502267142526, 0.9265643449450004, -1.0778916200798143, 0.6596249331430513, 2.5084097020985485, 0.8286822431801185, -1.2920672801728028, -0.6486469622989779, 0.08066645987127295, -1.4069406140099336, -2.127018287623748, -0.31986290814923896, 0.6484963063028268, -0.5925745624972308, -0.5444547547054248, 1.0408423914385132, -0.2802574653083582, -2.9398730522369094, 1.4952936351832404, 12.913211524855956, 18.377178360517522, 10.737789624742485, 0.11865264234249699, -1.7713707600856492, 2.0112639487366613, 2.52260602061484, 0.1481595687091419, 0.30324051531055934, 2.031012529749235, 1.356023413651158, -0.22720264086482783, 0.42870798057263526, 1.4438366562327465, 0.3650548689356737, -0.6234941864858743, -0.0045344016275228344, -0.7055263338967276, -3.272105466110416, -3.018821090783364, 0.9497390822147648, 2.5226246326454818, -0.5995175245645946, -2.346817414427696, 0.32696890565999387, 1.7989172206278319, -0.948386038825852, -2.3747806668823186, 0.18311005233651725, 0.5348273352998082, -4.069909247360059, -6.1957694763548545, -1.3375222135001088, 3.446349190000478, 1.9591732726844409, -0.9805263023875747, 0.05578341259910986, 1.2327225812585823, -1.5161040557379561, -3.6320777043706647, -0.7174036224374952, 2.8654197703874273, 2.146057551292441, -0.05258779159651574, 0.1895089551708695, 0.9156351583345176, -0.029358240889794454, -0.3568815677914688, 0.8341683612889137, 0.6680799915965165, -0.7597503264371995, 0.007278285836881719, 1.6255040484628036, -0.4252861444861949, -3.2321990734086157, 0.3982062118971573, 7.345848812687967, 6.694828323090053, -1.4252049499591057, -4.577022381914884, 1.427109157843828, 6.119893132797483, 2.7968472111491987, -1.6880712410180916, -0.8906416313616561, 1.328604754086265, 0.6220084192919064, -0.41157708987932895, 0.22385127770956986, -0.17639746955918545, -1.761100019758489, -0.9117731006920984, 1.5169748858503154, 0.791139291082564, -2.1144219519669214, -1.8292205519343936, 0.9034230499491112, 0.6882418494823171, -1.8493678707374634, -1.7569903738730381, 0.04302828016440996, -0.6860491833973085, -1.858200054405253, 0.7047511960500183, 3.5211803183291055, 1.5745691108766997, -0.9547670510188584, 1.7021025956119282, 4.659643486696254, 0.9192185983642869, -4.3654499523261165, -2.3486220513942655, 3.0536129894605435, 1.941907837217315, -3.9417598894032486, -5.108126179028396, -1.0312158429230112, 1.0469177256904287, -0.18869857045798522, -0.35836799999482644, 0.6898337366715372, 0.27503609436978166, -0.08271512053206849, 1.737317724183093, 2.945258466070326, 1.3633159230275238, -0.005174920937000971, 0.23599125402907378, -1.2158569691940966, -3.9927758906519193, -2.933629277921684, 0.5507356857116908, -1.6234649740886031, -8.749658140187574, -9.844495974084577, -2.407059287753028, 2.4308632889924966, -1.0233965612356375, -4.30897918677446, -1.2492168492984543, 2.2064934373929868, 1.0297253125174457, -0.45582267246528696, 0.6930312740702975, 0.3150540341448071, -2.7214598810607358, -3.2549274193852185, -0.42284343780140976, 0.49171247989661354, -1.1436468543380294, -0.5334490080859111, 1.9735785519774107, 1.4161671791643557, -1.2835847914115295, -0.961180303402228, 1.4395438691800853, 1.2294926273097648, -0.48365902214461176, -0.04839842139904997, 0.7361632505699217, -0.36229607109296186, 0.20725357859351778, 3.6531936649073233, 3.6262661061670944, -1.3193584662704938, -1.4066385907920849, 7.591650213064476, 13.903672633760733, 7.9761033321085755, -1.6470045455767515, -3.1396468384542824, 0.457840166101843, 0.5512540787621967, -1.4467109841085726, -0.3139793338971571, 1.6931369693705371, 0.7175868410429423, -0.7282042207625393, -0.005744000182991547, 0.36617354064684504, -0.7330532761251131, -0.4836825451088088, 0.8175323966678893, 0.08580455568585023, -0.6050140726534554, 2.66370939854711, 5.943015246310297, 3.0765153589546554, -2.0825116196805773, -1.9610982572931306, 0.9657799578464064, 0.28950782675062925, -0.7125463125836311, 3.806704989653294, 8.548805631070257, 5.6684697979202845, -0.16917052428596205, -0.18274945753505725, 2.894779017850124, 1.8461296133740626, -0.8966390430799069, 0.1563372319073127, 1.7524649165659103, -0.5842207180867698, -2.4904274557194754, 0.3888307813445817, 3.1590032909180548, 1.1605301782419495, -1.364517352471358, -0.29795470673924274, 1.03554653015311, -0.03661774465524238, -0.6243235545199263, 0.2883394862122522, 0.042686270791587794, -0.3861043446954121, 1.8856112571139285, 3.719401040654392, 1.1405977197123693, -1.506250046365017, 0.1278086839667122, -0.19016394340191672], 'positive_zeros': ['2.009300968031747144106019084032', '3.16894863583427396787572180838', '3.791801779437890607372166554850', '4.56140152760788243993197937821', '5.6570175374641511915724190927', '6.590339070442056788279398801163', '7.31816729339571685181379602164', '8.34017135195034435965353722852', '9.06697276420081506684219739257', '9.65603769047697674657545725655', '10.78671908196632251120233619935', '11.87075487199106105382631517976', '12.96858227592325977075194840628', '13.54790493607429317389523122481', '14.07559082459467904241405095571', '15.133433908619187331999806491813', '15.65870607250867231608499437154', '16.35749845739814243923404476568', '16.89012703040321768920694497777', '18.212679838197518127086199469388', '18.80068293300909880105176582712', '19.95297020008471143095465528162', '20.45329608496169285964914811945', '21.467485151096047923218709405906', '22.08982580015619651924390983366', '22.63484946564967571260113944354', '23.66203037752941145830340250239', '24.282852756310383666451233198811', '25.341864935550880173324998599029', '25.64857751109626541231699852118', '26.41090377483217598535725288995', '26.87131527888329069664046804571', '27.87481737749924075763998375092', '28.71473970538146340690671226615', '29.8201734306170264577148811167', '30.478047310729025645329768739310', '31.489315699389908937234376494011', '31.5973513019039131908491567016', '32.552425467705176943810818758114', '33.1449801806581553664446575218', '33.56632551410471261546601069337', '34.56850177805858400156821301456', '35.54095764458473741069486550173', '35.88149440775556757373812180242', '36.61914705523774781443165422350', '37.6547421689835415142944099001', '38.42874921932588159842779669258', '38.85258366885854445012286660758', '39.83510602357143132965212018299', '40.35007460656912252658631790986', '41.52503900479097562570485295184', '41.856617206461340780398307063616', '42.632759569725033149523761547385', '43.06090920124985405419207711724', '43.901691849940937523415430023993', '44.43046824062068346650362621137', '45.22656349494744492268586709304', '45.600925049221483804986869321970', '46.86640094852852596346455914820', '47.97140453735708280858642824634', '48.36814237274516295299170272754', '48.85492855052503218080786405401', '49.64341542537737052539246210889', '50.29036290041709603849471027514', '50.85615768616852680661373149287', '51.567923226478868098882477085078', '52.291369812251745178015723024788', '53.03349352617399570010255288453', '53.74594469172291919431590918844', '54.24165915252599150067271648684', '55.19537053356933831709330308347', '55.40321060241887601780528889094', '56.45398100505418940092035282657', '57.411944917536664782624166261482', '58.10367187511806414666453996292', '58.54511846358938675283513344766', '59.44624250469364365845603687881', '60.11485285133017366710820603662', '60.449145337474587237345412307189', '61.20610197155337976937017710907', '61.86966791409840798785359539130', '62.22830530023775642995582862189', '63.02465267887901881524255245504', '64.11981343244806282278973859460', '64.600268103923678121297269428559', '65.58634223407464434892226682334', '66.03370022916077561281786442651', '66.9793335757615077289066385481', '67.45156474686532720891665179642', '67.880376701110316474706289006734', '68.61763975951350070391528411740', '69.41997036621910346272644946695', '70.223424993837648986831689630575', '70.85578434918168293668558776951', '71.176172231776310494237158699633', '71.9383840095309927374828317161', '72.533035639966946903243211094442', '73.12378114264970758525949725305', '74.02147247443089827189455866232', '74.83626484216895208979734505037', '75.603337524142319192431248074739', '76.340739561878093661749847292035', '77.01727012169931110804937805004', '77.45902184064210640118397397146', '78.093078292225338948850695536268', '78.401866487441232727953712606621', '79.34674455161798642536709320480', '80.01684961862845519183414924844', '80.389794780336079640578711472', '81.35535835512336397661822350577', '82.06407314976914689594583337952', '82.49032698014990945799751015509', '83.624361135546621018450909658396', '84.15338924909497812190277449099', '84.57984795744180399464297000866', '85.23971324977465710546878167325', '86.12558872363720777620016050777', '86.78857435310727390360317972784', '87.506459402178426541371692763290', '87.81377877255237110479146204074', '88.606462784921927436196369557899', '89.214201152316210373043035439515', '89.8482257028469151858595891840', '90.23055564442307328154587549151', '90.91695732014182894331586466037', '91.64759055505793454556028259307', '92.8737910567395680611513006873', '93.467406706681133904186527988321', '94.01036911054265931212563515466', '94.525644573247733227180366881061', '95.23160360247426396308524829862', '95.68683531194948890905267446019', '96.47858198887654825568358880221', '96.96381905333885566682002103680', '97.44704749684145162823356300901', '98.38155335657660700134383711398', '99.065090710057861685294077923823', '99.670620742732010074280407503', '100.17297032763522461927775761968', '100.68315513580594227727377847104', '101.723453020196647259149399174793', '102.353308757822719182314557469374', '102.80381328684346327492661262373', '103.85673571964151868188124334182', '104.33183122357575933954781829008', '104.72928649190564040168576832817', '105.84373306144704795281303459024', '106.03355534223637662731678293236', '106.71502280996031221027311938842', '107.06833161917119625483965783563', '107.7840198756773166529368149425', '108.46514819007241774423638537563', '109.20476856632865167570117329371', '109.98295648155360364023286335367', '110.716592441454521367111195773341', '111.56915029565670578537509587845', '111.97941078578491911479391822466', '112.56296619875623386215572945030', '113.39614424939744520493794445018', '113.512091561644677273291401200852', '114.262134488041368172788184083014', '115.18305792851818228267841589502', '115.781663981663545314072936925529', '116.422552430049858811472609726927', '116.845543286353015347442758413689', '117.35035755484983102018550893688', '118.259284603754866911319864105769', '118.57218091931163710209532871426', '119.67960202689626505648625971683', '119.90752895884702212184472866742', '121.06377755431930040058528981360', '121.84692066329457393216625794224', '122.06444194297526553308540976929', '122.958408804393551394624171892502', '123.19039867309997702169317211317', '123.957556787016859817662546321971', '124.45875396146246046663386704075', '124.98646856712095111743255700658', '125.75425041783650011169564564660', '126.44894951009165183350631086660', '126.74882072171890479359333497692', '127.83830911452074173642694325134', '128.63855894863030646882855538329', '128.992439578456877495640235306213', '129.72801200145142513839581332997', '130.32813510005237811716509352179', '130.82050581617810644000591331034', '131.65957086993883068245323671555', '132.112084320822180827896460832308', '132.90569623739138993306392397649', '133.603229880372017778498808197233', '133.78807146484631401735112058373', '134.73760307647903100101915955961', '135.18364254856652558146182244098', '135.72619734382413631948303243336', '136.22147003592301011358943620638', '136.82049491016067339527852304857', '138.13026458749260647282224611445', '138.58829566150443540536809414629', '139.40565478716627226703223648155', '139.62465615599088149905771428011', '140.55036605528086050857838595420', '140.83969841950121797618248858136', '141.63444317386821708058442354622', '142.19003358371705499071866462088', '142.345614770049904712957589713367', '143.36639815169796249680453047152', '144.01307875064746675352821534928', '144.657112921184960262402377611124', '145.225663668482851762302143440209', '145.91734871335422628665709841651', '146.30258185532204527236676800418', '147.25217213354662971015030027286', '147.98289079110540113863405347735', '148.42991147724483272565258124718', '148.9301479656825762626290643225', '149.73697998995370169958647876812', '150.61148438750116846750457351505', '150.883361340760224461523087640517', '151.55478430007813593309498314107', '151.98320468166896578261305261619', '152.63350410525759378840112543709', '153.12387885577818212546256198927', '153.71364028675513988914395267145', '154.35693750886587156412603249689', '155.258145350627405369670781304786', '155.879005703817287137178140780050', '156.72288805727327201962126487606', '157.287183351200972879622728736930', '157.93944750773874800865917525882', '158.34823194550886895487319195252', '158.71026987982214898993662695244', '159.4825777389692876832381341611', '160.08306413717988491197871413209', '160.82344709666981417908207412726', '161.33538656415782762300709782190', '162.17359786372753559156727761243', '162.36173230791860366412832758528', '163.06726138303698684770371414569', '163.890374737994264037623876508618', '164.24257834610022079480654057695', '165.04432057706725685397226723853', '165.74706802944539881275581462476', '166.355221204832624117518671161277', '167.275105443176090645869410542266', '167.7706787565024017881163639598', '168.22405492323703405857744051705', '168.84125993680752530600802034203', '169.09102784301524011543476048276', '170.30652578955554414441689072341', '170.397961053031508702739455435606', '170.75493019864406653889423299032', '171.80504775932530674622704788447', '172.08422146617900786342606509309', '173.22440098886049470939550149492', '173.68957277210836864329213514511', '174.45785215247651305904990352834', '175.145647433188199543419282607661', '175.47696698404510011141990264962', '175.977168498419684712561342761883', '176.9281828179292497402395806764', '177.29295385980992096506359143491', '177.87766527882974771292892540196', '178.59061962075535498228586551323', '179.181043998594023844587007729', '179.887562596470875713519011819927', '180.32382450028551926941123748142', '180.850056108626388645425778077049', '181.22333238800354092821591158379', '182.10539627807507194718568641143', '182.5686884106713247019794980550', '183.68139599619638170371950213191', '184.327131742764713512544942688948', '184.76301478663842511282377066799', '185.35059988675269138479614523348', '186.05073320818601026576145448914', '186.56405108336107576603661582786', '186.99257594229131864576631674313', '187.60187795532054524395816409005', '188.14167300788157853652180986036', '188.536860996299743422120717684048', '189.541663672773831733732965225563', '190.187800315992584136645471103181', '190.66528869911488390018190778227', '191.02618157763164991165040034270', '192.17365449450036330560881922502', '192.51841000225063764894672044994', '193.30317385479988375026274140920', '193.73042614441312914502663056401', '194.321270438101681909612749285949', '194.970803239801135240834261928134', '195.73226484608092264054857716454', '196.29436693541530181178932288780', '196.8672357323526895415179922623', '197.39941569717976422997118726410', '197.826034173356204232879749928251', '198.21669383890106558710197927112', '199.15623067354292970910352628203', '199.67078856458839389158842592159', '199.984925793555606512612301793333'], 'prelabel': '1-1045-1045.118-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.38324023576719085, 'root_number': '-0.742753290907561785944590493448-0.669565193872849766428363456250*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.383240235767', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(180)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.806085907540532516135072223563+0.974048023496277815763913822249*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.00930096803', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.16894863583', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.79180177944', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.118', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/118'], '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': '1-1045-1045.118-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': '1-1045-1045.118-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.38324023576719085, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.00930096803', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1045.118', 'Lhash_array': ['dirichlet_L_1045.118'], 'factors': ['1-1045-1045.118-r0-0-0'], 'label': '1-1045-1045.118-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/118'}