-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1480.147', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [2.9010907910729803e-30, -1.0], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [2.9010907910729803e-30, -1.0], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-1.0, -1.4081532572346456e-30], 'algebraic': True, 'analytic_conductor': 6.87309110492009, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 5, 37], 'central_character': '1480.147', 'coeff_info': ['x^4 - 1', '6.12323399573677e-17 + 1.00000000000000*I', '\\\\zeta_{4}'], 'conductor': 1480, 'conductor_radical': 370, 'conjugate': 'dirichlet_L_1480.443', 'degree': 1, 'dirichlet_coefficients': [1, 0, '-I', 0, 0, 0, '-I', 0, -1, 0, 1, 0, '-I', 0, 0, 0, '-I', 0, 1, 0, -1, 0, '-I', 0, 0, 0, 'I', 0, -1, 0, 1, 0, '-I', 0, 0, 0, 0, 0, -1, 0, 1, 0, 'I', 0, 0, 0, '-I', 0, -1, 0, -1, 0, 'I', 0, 0, 0, '-I', 0, 1, 0, 1, 0, 'I', 0, 0, 0, 'I', 0, -1, 0, -1, 0, '-I', 0, 0, 0, '-I', 0, -1, 0, 1, 0, '-I', 0, 0, 0, 'I', 0, 1, 0, -1, 0, '-I', 0, 0, 0, '-I', 0, -1, 0], 'euler_factors': [[0], [1, 1], [0], [1, '-I'], [1, 0], [1, 0], [1, 0], [1, '-I'], [1, 0], [1, -1], [1, 0], [0], [1, 0], [1, '-I'], [1, 0], [1, 0], [1, 0], [1, '-I'], [1, 0], [1, 1], [1, 0], [1, -1], [1, 0], [1, '-I'], [1, 0], [1, 0]], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1480-1480.147-r0-0-0', 'leading_term': '0.416127395153950604396868241339-1.46482961054923642538797176322*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/1480/147', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.5227894788641798, 0.8251803205274953, 0.04013230159451065, -0.4615062782758055, -0.04781039726933165, 1.1957476311893078, 2.2631943126745266, 2.0335179065610745, 0.4297652712900121, -1.2361225887951237, -1.3228122327497123, 0.4822262001363451, 2.5750502105038025, 2.7816235819712567, 0.5368931731587757, -2.330207856055811, -3.247971742752164, -1.474979779850206, 1.116817146712909, 2.0098979500241074, 0.6897653461331773, -0.9804102420683403, -1.0887539804527462, 0.05455123538804292, 0.4760484352445899, -0.7350949171507533, -2.0107218383369885, -1.2042401386854173, 1.4181152773068029, 3.02796879240594, 1.5180635970116885, -1.688205208205388, -3.0168913589674937, -0.9314242649982652, 2.186128283977628, 2.921290020082378, 0.9455652138658207, -0.8200608396878662, -0.12369355818284175, 1.7931271092486218, 2.127188579198131, 0.43796382616614166, -0.8683650302361049, -0.09478423896850993, 1.282702407095686, 0.8923772130413388, -0.7154793766150087, -0.4365856885743096, 2.8934011232373194, 6.142138551887895, 5.454807175976314, 1.3137159974321957, -1.8506522502647786, -1.207073111332624, 1.1871681828866059, 1.6769097511255964, 0.05762390079598599, -0.6919735303905744, 0.7736421315110499, 2.1057229647336477, 0.9543418792407856, -1.3033019170701774, -1.5701400838350312, 0.25273913041244983, 1.1849871795389204, 0.05853827966505233, -0.1950293801353873, 3.118905043235065, 7.6789937800973975, 8.452165716643862, 4.371841928334621, -0.12218345103805385, -1.0245349763774922, 0.3088395845013625, 0.08581281205591208, -1.9954102775441052, -2.7606961843617333, -0.9577271013243127, 0.754004851860671, 0.26416787273036185, -0.49307575653890423, 1.130975832866809, 3.6840435496237127, 3.444345558979318, 0.45029951415874575, -0.9670116148115114, 1.3847418644147544, 3.946087184840053, 2.5744641005711273, -1.1303399034621786, -2.086711044393663, 0.7794842690865806, 3.1970628417335694, 2.1038187426801795, -0.25543829052617884, -0.6110635579805574, 0.19299125806204467, -0.519623250060138, -1.9937780147016064, -1.1603584158088176, 1.5731539641268304, 2.029050564098312, -1.1976555320518922, -3.9118145550678673, -2.474141629527169, 0.46751169212250476, 0.03102865137069897, -3.2166586077486428, -4.145873060276833, -1.1223399509445147, 1.591543041421322, 0.6549574283471138, -1.5137596385793093, -1.314944977952191, 0.20706238616414926, -0.10217275098148146, -1.5933771200572318, -1.056932210567915, 1.1544306539368356, 1.2770021774735598, -1.1030800502807974, -1.4718396952403252, 2.330444631360311, 5.72816515343292, 3.8739268527552113, -0.8917827165403469, -2.599362563912467, -0.5420932680975686, 0.6336817813605251, -0.9663807338002192, -1.9405968332329961, -0.21018034995390045, 1.1830059818573238, -0.42941519390155974, -2.5255533485454054, -1.8117152222021005, 0.08741851358580016, -0.06956758742033121, -0.7888558752261092, 1.6888495291644934, 5.818770506803567, 5.79156828344235, 0.714161535134096, -3.1924978529624553, -1.696843495297238, 1.5104043476586608, 1.3474895507904672, -0.9149690654541475, -1.0967350849471076, 0.3390460088534183, -0.11781951098021337, -1.987458029917628, -1.5028900006994137, 1.2814312271786066, 2.219218338960651, 0.4738852317303448, 0.09970801837092297, 2.485589285173977, 3.263776769836456, -0.013410848845308168, -2.653129672395289, -0.00011422075755392863, 4.593513925180687, 4.747598831824092, 0.9067132934452806, -1.1692153452448504, 0.04290880473202689, 0.6132673790573896, -0.8953450570865192, -1.2332921026901644, 0.6685690039558676, 1.2592458851579231, -0.8884239961362675, -2.0389549502254596, -0.27341098599201286, 0.28978257919699507, -3.329272358576757, -6.778107109075959, -4.964390525176674, -0.6495129277135524, 0.06441918490649391, -2.202702792574357, -1.8197399145480266, 1.7318558931035355, 3.1464434085327637, 0.6804463764435624, -1.2670490469068765, -0.23996395876338888, 0.6997679694311658, -0.3035380985920324, -0.41234556229876135, 1.5005694874125237, 1.4898859201620145, -2.181778550919203, -4.43092404246583, -1.3071149418967476, 2.7550210505184793, 1.8420266313484936, -1.7719899935735297, -1.9430496224097678, 0.8335718070490047, 1.1108872237391898, -1.415784804833784, -1.7734169194141107, 0.9402379689008099, 2.175724072365759, 0.4310644529976118, -0.6259612577974178, 0.18809748296262646, -0.5528987749830147, -3.3040346645056378, -3.48966814640866, -0.0357737621251248, 1.5500412328089188, -1.3303828641275695, -3.0605716043893856, 0.7899262244450348, 5.444697929837718, 4.62562576629921, 0.5438379319472768, -0.8555769725586068, 0.1907159664187696, -0.26679847970829373, -1.3993543852608803, 0.28919792294637037, 3.1036236651556393, 2.5691055189750855, -0.18392634659630908, -0.4329495295798267, 1.3157960429640512, 0.8326799810277166, -0.6862242760668924, 1.9374237092964735, 7.337208817118112, 7.991399008431836, 2.4778994822408817, -1.8499690231341805, -0.7502285066000369, 1.2545551956535765, 0.24822697330131635, -0.7757235301937497, 0.8369600863292925, 1.953236616138705, 0.3479374217922192, -0.512606095933699, 1.510536317386935, 2.4675040361007543, -0.07341097551907491, -1.6808981860804266, 0.7832012444687544, 2.659452466218283, -0.13347224334576685, -2.942878399261244, -0.28433246369622894, 4.145738198692831, 3.7765852173195182, 0.31173812688824537, -0.25945527685492087, 1.5447434481273168, 0.9730790301445982, -1.4045882227448354, -1.4745486060566997, -0.030502077287917997, -0.6134146132552342, -1.6124344405170985, 0.5557642946961576, 3.0217712938600885, 0.6027284228019658, -3.9263418517838407, -3.543859400447692, 0.8042918158047115, 1.930636690378337, -0.8312579109511181, -1.2355132532853639, 1.8106886033844765, 2.581627923054489, -0.36943172232006327, -1.8782181254448966, -0.2650715976283085, 0.165315863085578, -1.748808117116007, -2.010268997395082, -0.07767837902270694, 0.07103066677503189, -1.1406563718013105, 1.128312147899922, 5.658365419145234, 5.164971657685822, -0.9718098721996786, -4.559146033001873, -2.0058730954569546, 0.676773383986914, -0.4191202775145103, -1.0496582494860727, 1.4698815800369895, 2.821039129527911, 0.5987009579685562, -0.8885025157298475, 0.7259217723023426, 1.5557683587471036, -0.07187854785989808, -0.1184767342187328, 2.3080145448570404, 2.2702839960285663, -0.8854100517378944, -0.8804664134026179, 3.7315780685673205, 5.635435213010984, 1.4736150611869316, -2.006298833095579, 0.05289369716774038, 2.760347062083222, 1.4177890567152422, -0.6003113335403403, 0.14122359932006615, 0.7331957080503259, -0.6998266737820623, -0.4469682835475648, 2.566293590527585, 3.2341485151341436, -0.08833208249845236, -1.901641177435855, -0.06096059625966031, 0.23027561950099684, -2.515581911451062, -1.976325814323576, 3.782035393771565, 7.091173134036538, 3.4876948593470276, -0.9315085574833094, -0.7887232490456428, 0.39404580539638706, -0.9776304242397617, -1.8696685538142315, -0.3752840106056331, -0.2298287216229831, -2.496437858854088, -2.572654755638678, 0.2573901998464957, 0.5682618088974852, -2.2926601172795453, -2.1073726611089887, 1.9258618171772905, 2.5841430034268766, -1.99654353073341, -4.415229905763223, -1.41704205741985, 0.8944022043554646, -0.7502137870706009, -1.4051345848456454, 1.2694894381358395, 2.4873004879554603, 0.3839163540968426, -0.5641874935490739, 0.9197632346468636, 0.8941712176152361, -0.5217010999310157, 0.8237445400551049, 2.9927783750992822, -0.0578330640968142, -5.9832370263456305, -6.2055348998649, -0.7846952907904983, 1.7823858476214829, -0.43986361042241134, -1.2259604451534445, 0.6405115007860287, -0.028815730811284433, -3.127490811393784, -3.0544975484414376, 0.05526167930385281, 0.9039404671480051, -0.4037790833454621, 0.1822455335898658, 1.1670846067933318, -1.1416986994795122, -3.4963748498269993, -1.4253526983570388, 0.6800514519725661, -2.9664259119720158, -7.56137260873661, -5.454218166343282, 0.04525646495965942, 0.9413922780787634, -1.5075975602796494, -1.2256285371180058, 0.6944694194467044, 0.09979100139632816, -0.7022257610448884, 1.640482849892235, 3.534605586732512, 1.5166686528333173, -0.46615008807475533, 0.6816919266304318, 0.7756540019849126, -2.083940638173613, -2.0321704856462475, 2.965201302904313, 5.501781576519098, 2.036456467352128, -0.27830189299975666, 2.9000854873892976, 5.289374403236611, 2.4175491264519184, -0.6172486524879999, 0.07142743449257681, 0.8170883863839994, -0.260800592821133, 0.32321802206787564, 2.2288607029060734, 0.7157198111466299, -2.8823323018324007, -2.55201532419598, 0.3646785854686261, -0.44967446918913156, -3.197606251629413, -1.0861083406231977, 3.727904802427186, 3.6636967638891154, 0.30666110814374264, 1.070471034194885, 4.731106141009446, 4.377882648458851, 0.8201798912215509, -0.20673254568718452, 0.573151972545642, -0.5306066522922323, -1.3322082606847012, 0.6588443503187318, 1.2918430298573909, -1.8120681098993665, -2.999603767368385, 0.4290225239381988, 1.787167148783678, -2.186353763974894, -4.2956411241481405, -0.5677746557732581, 2.089135494414815, -0.6896227071825264, -3.0456786388634187, -1.1804019299594422, 0.1667118573210952, -1.165484540613512, -0.5994666839421271, 2.394974810666232, 2.54982586746359, -0.18621446357437602, -0.7549545983080063, 0.2919802215932733, -0.8269987179335754, -0.8751662378648688, 4.548852091973497, 9.441510776263682, 5.920767387288879, -1.2578540951759913, -2.6765707202561027, 0.06853093312314833, 0.15821367093168898, -1.019226497144449, 0.7234553766445506, 2.168878555787712, -0.22541487976525243, -2.155209227002276, -0.22600050509228423, 1.251391969367125, -0.13887866959753867, -0.10344774006956844, 1.9244728461586122, 0.6277313327590992, -2.9929046111689868, -1.69542554760065, 3.2852857377669356, 3.036327329919354, -2.373345047428029, -3.992336118133269, -0.6469166551944519, 0.4729909289882209, -1.4669034668726444, -1.1046479523351072, 0.908877133218563, 0.186213120078187, -1.2396418894342425, 0.19757463226128827, 1.060868960136189, -1.453097377967851, -2.215026796812599, 1.4602890285001981, 3.161383545538368, -0.08144725399881782, -1.5380917713752258, 1.3225550657119978, 1.2409603620998575, -3.879861013630512, -5.889832340750924, -1.8017956386401581, 1.2364528246925914, 0.18485937461163782, 0.02367381452266904, 1.70773569141179, 1.0459094437499665, -0.928172228693752, -0.3962251957684233, -0.21626945360229932, -3.83772770909789, -6.084621023734092, -2.5963125903145685, 0.4311565094197629, -2.1131273980116667, -4.0176522346955785, -0.3649152114355737, 2.4882638099213312, -0.1417153553336269, -2.2230289483024808, 0.2077993488651459, 1.639231271053355, -0.6284192695610484, -1.408978591776437, 0.6496379404106656, 0.7650802853508581, -0.9259927309010796, -0.24399544220573832, 0.7065284249136176, -1.8396447178484125, -3.19145354313057, 1.237161368038153, 4.862314073428108, 1.2677943136869896, -3.2376824830405937, -1.5672793470616608, 1.317805747102747, -0.3564842064718026, -2.0908792679296018, 0.1460342901760808, 1.7228580685045713, 0.16748910859287328, 0.1466748151402132, 2.2965565172886278, 1.5119588279671947, -1.412899523770276, -1.041402082273141, 0.9595335830831984, -0.08980772071230482, -0.7117283664318509, 3.085958003022196, 4.732591548525384, -1.5121921285215523, -7.913944054327576, -6.087960797395769, -1.0507698958712797, -0.04470922199700605, -0.31634558683347924, 1.4358198218077294, 1.4231060324209852, -1.2591322454219607, -1.2981074560904187, 1.337733851255259, 1.0580468522394024, -1.1415088616404903, -0.013618121904467477, 2.0114147498600916, 0.33428978538764154, -0.38012767713448914, 4.64208630008326, 8.557561053751492, 4.902442100329653, 0.21681430448455302, 1.3732747280866062, 3.270267595240607, 0.7605612383747492, -1.4017931393607586, 0.13039409515881417, 0.8318777349100361, -0.6503248565107194, 0.055942259051911435, 2.121161581383336, 1.0660024094278973, -0.31562298622430096, 2.413927528958954, 4.224656694960991, -0.011873703185302037, -3.807487311281296, -0.9206530355806664, 2.5658918026754294, 0.9188563543533823, -0.33565307148650847, 2.6147758587623837, 3.430033579631007, -0.720310381105042, -3.047521638314513, -0.8618317091967287, 0.49434906718998245, -0.1940524254648995, 0.4573625595681467, 0.4103104637645067, -3.1849548387593543, -4.925881104369114, -0.8164319956340883, 2.333954654906691, -0.10536118327295393, -1.0516397670847097, 3.525344512347166, 5.816510433831102, 1.8403382318366548, -1.0032264391301906, 0.7369941291838737, 1.1631194514773338, -0.9595961131448603, -0.28884533996362866, 2.244510936087592, 1.3050952571301426, -1.0041166859663018, -0.1610158234049094, 0.7482654534284566, -0.9985441673630924, -0.5331063335747299, 3.043371751296376, 2.1305542607199697, -3.791031500275225, -4.949029299718395, 0.28152078449622875, 2.2656867489362718, -1.2402179005955083, -2.48212271072782, -0.17566600403102728, 0.053684807418177966, -0.9722058370468926, 0.7991307001583073, 2.0771178592874477, -0.5504067333788706, -2.200190146738362, -0.03651638547526296, 0.5612649712225791, -1.7356064783204936, -1.2355971462679647, 0.9806763199734365, -1.936870670780359, -6.7568648928824775, -4.439947400894912, 1.8758581521714608, 2.37758771616746, -1.2086039328001068], 'positive_zeros': ['0.641540535522301554039404838474', '1.265664950819015169510394845458', '2.569505594509637274348755125759', '3.371492035733630982685071123461', '4.42985207460449764473382160949', '5.480699863912272524984003202384', '6.36229328751180785633903847193', '7.1725234005608543825851073362', '7.66289119856724833105724416385', '8.59096545611020577260402540031', '9.5226615979570096523259202653', '10.39942240919467652877705081856', '11.37859430419103030237364501832', '11.89614871479613752595773313635', '12.884301554474505245333541071589', '13.45644221085132164971819444667', '14.22973070801913416824123152045', '14.7465064955624874926274212202', '16.035112051907190658723969538982', '16.7145702376677028954230802290', '17.51061691462599265980480116819', '17.99776191662624484327956226007', '18.87406518245815372685538039150', '19.6473266470308427147394076373', '20.32591123182763270841016501368', '20.66148873665920479565466041138', '22.174961857803887955489318829944', '22.73496895739676968894677968409', '23.14183685328066182700828342724', '24.19801169626820420501174920296', '24.75497444183181174177420470544', '25.15700283613125129094825797034', '26.29954712456456400874309939983', '26.73684419313270622196102184030', '27.71118754872463929489310987689', '28.368656565237199584366335080559', '29.33056660035277736899142518435', '29.89789827009068897097006418353', '30.18901611733474380137771445257', '31.072021279269470568221165362221', '31.779400011213100837991145043398', '32.74551705996956248723187843182', '33.128779697949336882388106198325', '34.158777153355263449780654944675', '34.77110656586948428443121616304', '35.567945306975778824549563979493', '35.91410961575169551095304543380', '36.71014711347739107695428641265', '37.36426322225911385669514060867', '37.963642400395259415927871279567', '38.99847535958365945487216693622', '39.76301834138769025655148153823', '40.16295234835241915028223565368', '40.96611897712673147933148045556', '41.50975850136143299525355312017', '42.47766927690007760169573089826', '42.793006879165628652689153528669', '43.2850690689693442143325364887', '44.41456711894395713135972618240', '45.146470463374581332420170024613', '45.80338408355732143552094672066', '46.47462286337674948059576814833', '46.85294814990737635894115387601', '47.67251752281089149414246918209', '48.53902217554734645814613106785', '48.72461389129901684590700906233', '49.686487423554517610549062507958', '50.31250740054053307288911907009', '51.331155508422562676381973886155', '51.86676529170462052728103862257', '52.33698429442907760025490584876', '53.02583399244667828019446873853', '53.640484564850314803101276005646', '54.417383476587027090644475280242', '54.732828163167581137355320505038', '56.01517882361556284065542364517', '56.261929566861473108753780481249', '57.043154378138232883094201684687', '57.884275422014138883923969466997', '58.48278793074592209984276626552', '58.9876475437872067481967238378', '59.45810489379124490776998554597', '60.14918180068576827306508359886', '61.02012916434096981659695522306', '61.71327389450804267601010342898', '62.40259899264590367481709828373', '62.95819303467689833533272784702', '63.65118625713924017843046544964', '64.44421931023168567594323424097', '64.92896116340640566713247667722', '65.21779916898604736238997469868', '66.2531067588872583601812536906', '66.761211747588318986451394343023', '67.45554307899790356912528046687', '68.49259630891947017871498953492', '68.99795686379126986601445940832', '69.31218456618153152830705808216', '69.9698563308174066009121889022', '70.91130085137998316250345912817', '71.32929621373504900154267896931', '72.005393312032768988047286145703', '72.34941913542912959643987641983', '73.57213308085328546448438367066', '74.14910270529837520829102945139', '74.72965381965799466894881597447', '75.19010075298087828018974760214', '75.99342432745300140324825062571', '76.36368461405339697967168083888', '77.180194599509073040962063076473', '77.73982531195715994008023121336', '78.42742512349599611030045160291', '79.08048705832179263810096114977', '80.03965704094677686561616638546', '80.36270978435180320806107278024', '81.0601449015969310530946442644', '81.88889922928985936833886295521', '82.02561503946118636980379247934', '82.76003463136422082137411104329', '83.47620480698430083312926475252', '84.31368070169385561119718713205', '84.91057246961793927805653421035', '85.45283863504023842350072711521', '86.214529273016682951054006900390', '86.924879613097077045057021841120', '87.22554105632282096597920451691', '88.140501596675008941081621217762', '88.454398661480579293308872819364', '88.97288740250071813296417532278', '89.95357520610987850181008505861', '90.80684143989893966726408467862', '91.18113500248228658395026809983', '91.72063593808733045939285450546', '92.57097800340008403413250467835', '93.0178586949496229811781330917', '93.73638415400765271085592496312', '94.08267839999527902879646870603', '94.91073276861212146211022259942', '95.38782141607650408746403636476', '96.34078498401301758103630986328', '96.87051908291000626990553763652', '97.67572985480290755072607357561', '98.09453830038312969580210720990', '98.61455461026736190536484393013', '99.119815583984397082191297368770', '99.99246076730323363893048614497', '100.63428981217073312276360667922', '100.97240456679801784943967235143', '101.68755741332123877920481939067', '102.71753177718239063225294166840', '103.26973360649950832846117063657', '103.58366904999470001469497264512', '104.46783714150514263713618585755', '104.62974559044752630067601095974', '105.594286189315924282783334813494', '106.01036401778286434876648088418', '106.73155801158297123653756604267', '107.37960319398769648105868987222', '108.250955968431755757934967616956', '108.6478404744890483561336356326', '109.246490207547456916961062691778', '110.05455665693663768600752781895', '110.45091982981574050924648858901', '111.107534657111056867472849419957', '111.45909354294794007372427779256', '112.1844102625543361231147605126', '113.17396471204249634125766217644', '113.698723696418552098132104571453', '114.264762558393368508242038284', '114.68414785605964694224496848405', '115.61863673272213804707648721610', '116.14044647840766898200627653566', '116.52603040770511466135161003254', '117.07816840740271773070958460008', '117.949863680027769429891621669242', '118.240737699052046028175882777893', '119.37150001602226005144356868783', '119.8082796097019874831536786026', '120.48686321063612564373585302600', '120.95689548022193359261620838839', '121.38732633280328783582966104294', '122.36688028918286636364197878415', '122.68551345420928371113937201903', '123.224927669187821628085427469153', '123.89526902145670691574114231765', '124.86994447182714932955374500760', '125.06241505049476128515977597376', '126.14500301342057512928123226104', '126.54848687833878972107024347874', '127.110470298916596099608912682804', '127.44310977764609740819967666872', '128.18425276771422333909216107422', '129.00871962674007588495653819697', '129.32407286541164925035347520102', '130.06665423648975984353037272656', '130.99634287646336169564645700019', '131.10697042064244722007222222229', '132.30137063541805748478715305173', '132.575062613113030053732877044882', '133.02820925699350219910992700725', '133.6659301334055837984177599855', '134.21657604622144820282530130193', '134.965910382430917741988343266922', '135.480628116399596192093237585453', '136.28822133846176721085017474589', '136.820408261825874294482562305139', '137.67805868766770416649407535102', '137.88005675773244889755269039042', '138.505108160841988978810859863070', '139.35082237165944343492807999955', '139.873889400231175932689361017078', '140.15683208493217683547431979797', '140.70299314536437767715718135986', '141.80845655950083987794475455790', '142.48996698987513100129866971475', '142.84365055291755030268801385022', '143.35034769862202278913731628630', '144.04121799788732099134153225518', '144.7137525861756954285833342604', '145.28502089034846010795736427615', '145.642893313862339637782234679448', '146.30172581619557707200517428946', '146.97953547640791489018441242816', '147.67894221640998526738397945779', '148.506416820244151951299495496200', '148.83912328995224583004190609205', '149.52588568632143351133131611226', '150.02878365456871375274449380095', '150.59665542024552707442959916238', '151.09815661462140037490764471313', '151.768127410114393154705239303691', '152.49320620567776664343871785779', '152.99670699412799274354872835620', '153.529061549752196859280241754219', '154.503364222907451770591663189423', '155.04140292461221958436862866149', '155.30698052304538141771381191275', '156.07959536572580724370881039401', '156.66464450306251905855315154338', '156.829237600451704393933454717872', '158.018081604030275691890598337342', '158.242408156043646722252463873843', '159.08629747373554754688785537518', '159.67590495202745185491192167752', '160.29216503778519661973939667846', '160.864215771673634714522832045240', '161.466528461862975531190122409226', '162.00459890400031042520594540586', '162.5422989555149534457792602678', '162.942981341464750903771346003454', '163.68351768252477724770999338379', '164.44199641684698857604355171916', '165.12827757654303500916274775297', '165.58779208311504786519754645011', '166.23494047587131581031592400040', '166.90913943194066385519742803747', '167.159339831853632926682015418245', '167.96146565842009417212056402910', '168.57220551930294107175594434545', '169.04887400880938837105397845678', '169.46279303589445612244518749042', '170.25592532810909739003807577353', '171.408365324394408043339726299574', '171.54097370659346396892409157357', '171.95445649318585522493553551504', '172.66816359242630687956565948913', '173.2755354401227591205246620433', '173.881104783924016615587351924713', '174.37656758899075731673301607613', '175.040998306675447631048856621814', '175.355218029626160582699153548791', '176.61547697193399830773690951200', '176.6759120632222056166660782946', '177.56890119590294193286131401254', '178.10551755308178322955417213367', '178.61182165967368836279560028161', '179.05463794657610377820409395478', '179.84023433626473711999770953313', '180.07748172431775100032132050437', '180.936860946128482189822840040722', '181.621462371723088617724160050511', '182.29824315828361971734460471768', '182.56031260013387156168565240903', '183.38975373469848499239900103336', '184.17808921832397364632558740523', '184.58853082753529742784723326342', '184.8739537787036892322390425491', '185.36629533744655161982417016534', '186.29963096599522558262979516704', '186.865237181654791026950354993194', '187.28564688699218272572561751607', '188.2584617204895523557762007206', '188.651988495868543490396185191489', '189.229810451436046741277578053355', '189.72090644239509320187754241119', '190.45828303195979785954555331274', '190.964279591344385050253683447906', '191.40778056216667861190663124710', '191.92699821959017603908582237944', '192.61922714452888040247411953253', '193.4209912722448282230614355984', '193.96467531372214764599630014576', '194.71742946464131284644517356008', '195.01266543128795288763881440995', '195.5276923169904367403488705400', '196.19930900997934739162189625364', '196.87968049769956714567026377019', '197.27457680885495130809162824034', '197.95079249208024562924677141652', '198.309645438861989649633869805924', '199.26852539050830541829820368410', '199.88386862631678211887162839418'], 'prelabel': '1-1480-1480.147-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': -0.8237918088252166, 'root_number': '-0.850650808352039932181540497063-0.525731112119133606025669084848*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.411895904413', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(4)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.903145231404156042328057436755-0.641235644915019670278894748797*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.641540535522', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.26566495082', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.56950559451', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.87309110492009, 'bad_primes': [2, 5, 37], 'central_character': '1480.147', 'conductor': 1480, 'conductor_radical': 370, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1480/147'], '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': '1-1480-1480.147-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': '1-1480-1480.147-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': -0.4118959044126083, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.641540535522', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1480.147', 'Lhash_array': ['dirichlet_L_1480.147'], 'label': '1-1480-1480.147-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1480/147'}