-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_4560.3197', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8660254037844386, 0.5], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 21.176550971915955, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [19, [1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '4560.3197', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 4560, 'conductor_radical': 570, 'conjugate': 'dirichlet_L_4560.1733', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 0, 0, 'a^39', 0, 0, 0, 'a^33', 0, 'a^16', 0, 0, 0, 'a^23', 0, 0, 0, 0, 0, 'a^19', 0, 0, 0, 0, 0, 'a^13', 0, 'a^12', 0, 0, 0, 0, 0, 'a^0', 0, 0, 0, 'a^20', 0, 'a^62', 0, 0, 0, 'a^31', 0, 'a^6', 0, 0, 0, 'a^28', 0, 0, 0, 0, 0, 'a^59', 0, 'a^37', 0, 0, 0, 0, 0, 'a^22', 0, 0, 0, 'a^44', 0, 'a^29', 0, 0, 0, 'a^0', 0, 'a^2', 0, 0, 0, 'a^30', 0, 0, 0, 0, 0, 'a^34', 0, 'a^55', 0, 0, 0, 0, 0, 'a^5', 0, 0, 0], 'euler_factors': [[0], [0], [0], [1, 'a^39'], [1, 'a^33'], [1, 'a^16'], [1, 'a^23'], [0], [1, 'a^19'], [1, 'a^13'], [1, 'a^12'], [1, 'a^0'], [1, 'a^20'], [1, 'a^62'], [1, 'a^31'], [1, 'a^28'], [1, 'a^59'], [1, 'a^37'], [1, 'a^22'], [1, 'a^44'], [1, 'a^29'], [1, 'a^2'], [1, 'a^30'], [1, 'a^34'], [1, 'a^5'], [1, 'a^61']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-4560-4560.3197-r0-0-0', 'leading_term': '1.41242804132216944135617846502-0.712688205284457761506784870710*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/4560/3197', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.582048497949656, 0.740777073172467, -0.8603623508059386, -2.4820123025289873, -2.6235597888480213, -1.0851306548030593, 0.37804141241591177, -0.08457290595641112, -2.0287690088498316, -2.922250518647929, -1.1949537997126862, 1.5142327833358844, 2.130008248163036, 0.05609660797725607, -1.9356496733975916, -1.3745200024003177, 0.5066886971922535, 0.5427475376136882, -1.6732164645151781, -2.9721681331477066, -1.187694579639279, 1.4424206023954738, 1.3606509709051196, -1.0213067773743265, -1.8332496096761242, 0.43940562651647797, 2.6352505274991347, 1.809118886785578, -0.20908504618880178, 0.12320688922978085, 2.151140328692668, 1.913603527006335, -1.2799387492090548, -3.234884823998456, -1.2323297414410783, 1.697169445386406, 1.6057448226680147, -0.2635516733958094, -0.1296188346273768, 1.5066324205915453, 0.6424307982640743, -2.9464561113078407, -4.49859634448004, -1.7546282940887503, 1.279977079442461, 0.8256531090432493, -0.8206008527469238, 0.0640736485583124, 1.803804150101545, 0.4478629668725749, -2.6804188295339078, -2.707167390945547, 0.38655858768082313, 1.5235460476859128, -0.7870195483836223, -2.035735812300118, 0.16164880771575527, 1.9294603578264198, 0.3635862794147995, -1.0986192778172956, 0.9114849545767768, 3.2067004132754025, 1.6219215331088022, -1.3241711023715572, -0.868959356158439, 1.3495335667363908, 0.33530012667285003, -2.9972193075586597, -3.377024235251043, -0.6476966145270574, 0.42769658032919416, -0.5566520337181833, 0.9529011286034259, 5.056104013866966, 6.026812418500338, 2.3164277066278793, -0.4432488019480523, 0.7940635668303109, 1.9375516710396332, 0.39519033024010713, -0.06871556448980806, 2.476132211793708, 3.2367828007658668, -0.5978065827951727, -3.891683152083515, -2.263081133456124, 0.5020244145014319, 0.06019528439647068, -0.6740965488988142, 1.7260772886035451, 3.6812902879588614, 1.4788326162771934, -0.9421296851899039, 0.9030169542856865, 3.460662772364048, 1.9284588657398254, -0.585052214382093, 0.6904715487607173, 2.8740618859622376, 1.3195698831748075, -1.1409068204853252, -0.006046829796714737, 1.766802990910939, -0.18268498165200517, -2.3932978538293903, -0.028493560229432145, 3.385011057049206, 2.3690788690764717, -0.3561264992111075, 0.1921144841110984, 1.4741686982584956, -0.6464577395938403, -2.779304469909266, -0.7045688858364217, 1.5872351489175118, -0.6127700969619628, -3.2844900336743548, -1.4100476676763198, 1.3468947795507589, 0.19977934880974632, -1.501153940466131, 0.16098079901616227, 1.3829328607336266, -1.034069639070203, -2.1739707103989265, 1.400962411561567, 4.108355800876425, 1.7023814604183418, -0.8918069734879521, 0.2853098093090212, 1.0349439263924294, -1.0879580219496583, -1.1765433470214073, 2.3292260015635295, 3.3523993280321136, 0.1527713775098713, -0.8660531977394392, 2.167502603256124, 3.105292693037508, 0.38796888087011405, -0.3124487843279685, 1.696888783330618, 1.076329402844335, -1.445301304223658, 0.00453202599092207, 3.784134546139825, 3.13524374435143, -0.5575820805462213, -0.8584336626596494, 0.81935611102416, -0.830612801291448, -3.2131437895011, -1.4177829372792468, 0.9314497733418264, -0.9143814371743849, -2.6883183239347668, -0.07153320347528558, 1.9747055299664396, -0.5172726409298894, -2.14294075222931, 0.6290479919712543, 2.2717589374126894, -0.05608429709562664, -1.1122697234080041, 0.3800371181582404, -1.1127992735424002, -5.031021155496525, -4.351990254276387, 0.17981653622323734, 1.033041062967262, -1.535015922703262, -1.3152585860407244, 0.6676615110710261, -0.06448639866721526, -0.2250805111446289, 4.130694834259613, 7.253103316094732, 3.83146829882768, -0.5203173392992626, -0.4109340998698711, -0.11495600014976651, -2.4412672608559314, -2.346234171832008, 0.9613178047061437, 0.9196393091576276, -2.642476327940061, -2.7512578584047276, 0.14472007037794785, -0.5288338788294465, -3.164421770656478, -1.6182585243074505, 1.3372192381522554, 0.07868268704577289, -1.7934237966356663, 0.1840102302502641, 1.275753278547, -1.7588113712104874, -2.9030822243635903, 0.24078926383857172, 0.9128484147672493, -2.4403967644507727, -2.8652102197019618, 0.2981071945761193, 0.6605802823559861, -1.0940236538083392, 0.27303333857770135, 1.700000162043068, -1.6700899508376612, -4.534350664198949, -1.4448410439971004, 1.8657874672579162, 0.2906260563548908, -1.0970088017482036, 0.6430376854407008, 0.46143879151382206, -1.687896009941685, 0.3563185360737402, 4.534722685382862, 3.2277261098147387, -1.1983724205826833, -1.4182719036048053, 0.17328143668400783, -1.487342542529532, -2.351926959865501, 0.8391572461901958, 2.14729997157976, -0.6783214738028129, -0.9083157193960438, 2.2779652274237323, 1.7222059962842629, -1.9717164567052083, -1.688751681016839, 0.8350649889443567, -0.4319918554319993, -2.185172595355615, 0.22756523934076364, 1.860657594437538, -0.4786661246985479, -0.4747765966489307, 3.478697959456901, 3.8182969982463053, -0.15228107965405574, -0.9178129903880178, 1.2603588362664269, 0.4815287045832896, -0.6656523755414426, 2.3358343141738094, 4.213909246828272, 0.9407999593225347, -0.8937932394183756, 1.7834674963073442, 2.0774871149964707, -1.2595372325533336, -1.2022027905377861, 1.7074223890176166, 0.9688904947267596, -1.1983721025665635, 0.09567427179798878, 0.21788447068742342, -4.1985231597255295, -5.8095469274376885, -1.3382428662132804, 1.4170422527817919, -0.19121764214934872, -0.06439468533819723, 1.3995822275291716, -0.9070090983937656, -3.1074974916152796, -0.10682768590975261, 2.0980535888459673, -1.2194223808908955, -3.2564306407842842, -0.5476623828679625, 0.279826211048102, -1.9430055966678037, -1.2025643227895142, 0.6344305925057243, -2.041580377208776, -4.608737138378667, -1.7044034647640185, 0.633712234517509, -1.7997523936935491, -2.4821891356302, 0.5271297825780838, 0.3914148012206897, -2.423982264932563, -1.2995284227616828, 1.1065672886615736, -0.7161001789697654, -1.9013038624963865, 1.5570980865159516, 2.9790679567844545, -0.038747248988797986, 0.020579299405650252, 3.646120309443627, 3.294666976594381, 0.13081506030287715, 0.18133585131365665, 0.22554786698122614, -3.0739776662447396, -3.192765088335121, 1.7651283216506157, 3.0203986632583923, -0.9711786590585303, -2.03027378462263, 0.05488380282662859, -0.4081136192353766, -0.5322050668142618, 3.040856873852187, 3.798496956787793, -0.516138788657648, -1.3815115484240754, 2.659435506195887, 3.2751123894522998, 0.3595991799283783, 0.01912134403846061, -0.5339279386667868, -4.879606536882066, -6.313841016845322, -1.8164925308877689, 0.7637613085987088, -0.2929068277010571, 1.7068379817886257, 4.7726958434976545, 2.2713310822822503, -1.2396112269838035, 0.3378508085281313, 1.7778195833228467, -0.19978582140256979, 0.3859591576276653, 3.1860438732151994, 1.2095498097721167, -2.3289805569459983, -0.16922037132366533, 2.8516248505569197, 0.7993266678345691, -0.6715328109986959, 1.5425213705439251, 1.272305270157636, -1.1519716569416518, 0.4959918951889718, 2.440638315930426, -1.247659420714386, -4.1603982896752445, -0.978404309445349, 1.2542544409361531, -0.6887268914205211, -0.5265593968554941, 1.1849970656167923, -1.0879406809141994, -2.9117774894762154, 0.6043652601591998, 2.427798141124249, -1.171573297533928, -2.2718990086708635, 0.780669299505462, 0.661956127419835, -1.4244081337319836, 0.19361413261059188, 1.1024922677713647, -2.3299090361983104, -3.0037332620474535, 0.7321649519397587, 0.6657697409093876, -2.6503893306138977, -1.5756464886637054, 0.8834371611907496, -1.1282161685866736, -2.4079328812338088, 0.31194132114996853, 0.5349942503559848, -1.6245531596115794, 0.9584488284181607, 4.814873548318669, 2.6990021600666467, -0.1471439830759523, 1.7074090031600613, 2.108192987841145, -1.002442954289067, -0.8516307707367068, 1.2189573157550773, -0.9887369645711054, -2.7402788050803415, 0.927454529793838, 2.871741729098721, -0.04179858542129085, -0.04772829712421076, 3.043234195102711, 1.8422236837358166, -0.9330898618653469, 0.5426655130354998, 1.48862316915115, -0.497637390520873, 1.5425300119195242, 6.291326700086091, 4.606329868444293, -0.6415387724775989, -0.921851361293926, 0.508684202641665, -0.6291160565205148, 0.5800429600148396, 3.424238136817083, 0.556593569880419, -4.130670657213048, -2.4026473791728526, 0.6585334089464443, -1.0371485263113003, -1.6597882255611194, 0.8552446636487913, -0.08643149687332646, -2.581650321012235, -0.19873958654470697, 1.9705867729154178, -1.0568093152754388, -2.1867695210430336, 0.9313130107553287, 0.5414262772540417, -2.3702228242127132, -0.58768992606311, 1.8117432076875422, -0.6382845821245406, -1.8390847777876296, 0.6602333632626726, 0.06324594084664482, -1.9973425389435557, 1.2529935814094029, 4.365361323513286, 1.0412088033349762, -1.632947989217557, 0.44764845311111173, 0.5025972464439025, -1.5386288508659232, -0.06087096502655015, 0.5213217614997422, -3.748000819313131, -4.701261703346404, 0.15164624082100714, 1.43730538465159, -1.4739627799873407, -0.9754434574130976, 0.5639866492101165, -1.1598969567651691, -0.511172071026067, 3.0459000350031444, 1.2141310260194096, -3.620235435527308, -2.485699657113834, 0.6524808610838825, -0.7189594126664053, -1.387882654570671, 0.5806781557011391, -1.4358931051376191, -4.936804145656843, -2.6464036345710507, 0.3071142561026078, -1.524890028077853, -1.561008914818491, 1.6048949891563433, 0.04293648260623097, -3.995553108211918, -2.5696183998059072, 0.10513271815887697, -0.9297158318010488, 0.023200709287863375, 3.107948757654863, 1.0800539313664843, -2.159165707923573, 0.7987958963347687, 3.627342317116505, 0.8320875637762051, -0.5406525270865025, 1.2493260911270856, -0.11020937421126255, -1.570440884350243, 1.8229664767407725, 3.09492203811466, -0.7561570233190376, -1.1012509222194018, 2.072914500645503, 0.5372551348594454, -2.4064656777055333, -0.4384806541388823, 1.0382265870090013, -0.4246941398690488, 1.5757132303302108, 4.393482511164761, 0.8784713426461547, -2.7962537822138156, -0.3804294658122037, 0.7895152904513525, -2.051687303409452, -1.4931448121095594, 1.1673259190801673, 0.13408481359113894, 0.46119083225981217, 4.649660570863084, 4.161866994915867, -0.8234681397424526, -1.0264877939215582, 1.0821325741682337, -1.0894752888940669, -2.102062402879363, 0.9856555030103873, 1.0121462627920428, -0.9519268228066704, 1.8690555678302956, 4.227894728606642, 0.8524355672918349, -0.6720758799173177, 1.7481532222284066, 0.05446883618131261, -3.678028181680805, -2.0688959911430875, 0.11400447637189727, -1.2507330659903442, 0.22291759020504073, 3.6362665208982476, 1.3748495882181286, -1.809423713885484, 0.8155905006354699, 2.3079390787281815, -0.7803864458140506, -0.5570678111134625, 2.4150438405835506, 1.0754409187076222, -0.7832107346045437, 0.26524587378539355, -2.6188156936435503, -8.000173634192675, -5.953759955465478, -0.09255317588197744, 0.3503200261844302, -0.6376661668567318, 0.7380456765762795, -0.8771774293038723, -3.1457653084339623, 0.4339807476406505, 3.1868135634491317, -0.7282399728021363, -2.8088646508164494, 0.02817393029221249, 0.0685785124175295, -1.2332848327033579, 1.5459966946242203, 2.359592747454661, -1.4426120538813687, -1.4122221119107237, 1.8801302494568999, 0.648591363191722, -0.8798575849325431, 2.119572150903716, 2.0395971968515845, -2.448195815969342, -2.406341503337308, 0.46276688152929224, -0.6506934567531468, -1.067854847363069, 1.4864659365313513, -0.32442407465975354, -4.054627470204162, -1.2781011532983897, 2.3134128706809283, -0.10305186989691764, -1.4883968893588075, 0.9459501157522843, 0.6760764634505586, 0.12764732439245155, 3.717914813835572, 4.011649133697118, -0.8965926807730525, -1.0227732808578665, 2.935805313760529, 2.0689410688956213, -0.15182404050395093, 1.1713327329353587, 0.07093783693224362, -3.151722057295104, -1.23272265262843, 1.1459627887286872, -2.0166276144267448, -2.8568606462225987, 1.5647825986531667, 2.2242426698693802, -0.40736783915627783, 0.4532410430720545, 0.3068824782440219, -3.5201100123792948, -3.0028293238130335, 0.8749280205457681, -0.23499081963211071, -2.0035448375001383, 0.9314940225936816, 1.0708163266148643, -2.922849942061139, -2.2395257775928155, 0.8941087829356655, -0.41372145209555977, -1.2205059126839997, 0.41987505023327243, -2.6733171518640337, -6.936985768725478, -3.9059968507132607, 0.029381537438408416, -1.3952715410004808, -1.187733166405954, 1.5517169705374498, -0.008731146565324062, -1.7685289337244352, 1.020389228935439, 1.0281139141915152, -2.407260256694485, -0.5913398993715736, 2.86845231723534, 0.2966408793752316, -1.8569528868324428, 0.5513415257967752, 0.31040071262930097, -1.6391219052786083, 0.6427920203672294, 1.4037021122448872, -2.1743623943725376, -1.0724259419845652, 3.7470079621543046, 2.6257050395603803, -0.5752190695673965, 0.8423070128530699, 1.233444897549079, -0.5504571431044362, 1.6476181364934692, 2.90241615974271, -2.230246266567117, -4.732915669398788, -1.0991348194790564, -0.3383110501665738, -1.7625799476069177, 0.9187479570878828, 2.0617616165627055, -1.21816416974917, -0.8557765381332053, 1.809385897036038, -0.5363406001549363], 'positive_zeros': ['0.47409442800158142471971549696', '1.76081809026083799495933944703', '2.16953468926915632740530801885', '3.25488686200932670874497133618', '4.069148748002776275943519744454', '4.90513108308468422068486141479', '5.408170244860286293641191825282', '6.3749569138774513707996128366', '7.059604194686983708451743251617', '7.76629642813887988007255002253', '8.70378728639360869733141150849', '9.03951087516604473572648773046', '9.88738310290524696526811535990', '10.73856878589244393451054017973', '11.50778332520305491523801142310', '11.90117663034371643527175080327', '12.56522270286687016845505777306', '13.58605039303449664315294704148', '14.19259653817347970063025888156', '14.67775312482063787530728998352', '15.35671143576715977454506009407', '16.21098328725428051758079357310', '16.78687713179552999767372984489', '17.4826385711735941354680340191', '18.1721563968878329826190519867', '18.65413048423816616486285638330', '19.52565569296800361184909935581', '20.109597651821141287979717749397', '20.65839548492462740579834959247', '21.6525847506378749979410659053', '22.012007832601750733623441608815', '22.3974902187789500379060569483', '23.64738311264758661360298933497', '23.93998361115168442798564522669', '24.76196894166406076278560721372', '25.01464516392418425965802067536', '25.89881876593600338968366098622', '26.789622949643620256941972863039', '27.19967412835743679809313870168', '27.63017388825955907312222116452', '28.57877336708367463671496031868', '28.97237195957132871070318605826', '29.889093742104908091505463476132', '30.22856620027579144167961004088', '31.07151971071044481373826097880', '31.5632498861130558932569466769', '32.16982986131004089831506000437', '32.8146565984053661332075584025', '33.68809188871458851448765093805', '34.03041884457767720132202922306', '34.62382392813584957930627216812', '35.377569786086947918742144888228', '35.884516722092032113974035569113', '36.68818674531561013270134917027', '37.21213643517770007696762961505', '37.79259005109482132093451191635', '38.33247778849708659739218120867', '38.96544202295203559356730821520', '39.84181910370910116806329463548', '40.2684395083911017861453311737', '40.79662387231858438396079192117', '41.370485430231822577583607063386', '42.20233039505021912097735299789', '42.61170208020328007914462370825', '43.48772338002992940579249686201', '43.808140693341580426859467022891', '44.49328110036503401081605020424', '44.99962581093909265532517129749', '45.88039094895524382298184219187', '46.382121786572536966375262150237', '46.785941892437135107722809419446', '47.63871179303615757797195071176', '48.02870543091885565401851652209', '48.7561278700221676756381496659', '49.32778076876439896554988136627', '49.94427074668550378395323353222', '50.618589877848963243771756401585', '51.15853230250988567399404772705', '51.4476989242662587261492758976', '52.48516486323448641789782192605', '52.941293829506075952894924309902', '53.61671154443601019415030681659', '54.05005701517624016963215209405', '54.40346721616392559962911839545', '55.56431418235107447247009717229', '56.04377951621584015723795920510', '56.2206196303965275284885562290', '57.09269468517955066823642424143', '57.58678552363448011990783252459', '58.41513278441716877560172754436', '58.6846965159895777891267459155', '59.51450178301294948538225216436', '60.00863588925090731768738949682', '60.60468740557629681088831916899', '61.096495074742143968436233106714', '61.85198907623779140464256586739', '62.287401654220719889533300630713', '63.09169782167259394054470628473', '63.54014766853958964880268055873', '64.03004248444892671221242613707', '64.5724531467662276260028963951', '65.41009696201498795484150645292', '65.97109927007283701410535735367', '66.461267147576674816187729886206', '66.93686663672712201498852295767', '67.474468622068110202314595883796', '68.3372074925314857931968118010', '68.98036888384708551159358185415', '69.158033950782961480670675955807', '69.929561667584469500710195010849', '70.55470453941987475111678010861', '71.03217003706048189511770027178', '71.701014631805732028585301760013', '72.3669261978405905798132622095', '72.762926095906038055176338381508', '73.41641138293623377211560350271', '74.00630243851910758553932945670', '74.42141431099805310845968133828', '75.29891696540053535853067843611', '75.750464557578079688740657108147', '76.31898036900413460535974143345', '76.67355134907386758872949486679', '77.57964220290460550550970177810', '77.94614351828529029245805415882', '78.63015862230828241087495458854', '79.18354903775932718360534220772', '79.795391441298115060838628602018', '80.298184988739552170510209126010', '80.64889615198907954547410651573', '81.65252190290416965737629339788', '82.15418834614432124791099997236', '82.51095198122398764923464930279', '83.04549059056607017411250864524', '83.757898523486063314734218411368', '84.28711050597856029267515313098', '85.06398563034672183537716483411', '85.35977816431047794382359321736', '86.08358000534397526854332263823', '86.38770231688182856276234251995', '87.33340230468129397353432005488', '87.62610464666504047521981081037', '88.37892085306205511648377312936', '88.79292828458039012802924953995', '89.50231932737166197874150727684', '89.924264841403673643118420966885', '90.50713780588597007941801167814', '91.24563384542423100576473547244', '91.56032255232878357789417342169', '92.52276734469510558849246030723', '92.767073536020806678939310379704', '93.156392854420794241253682979271', '93.956329365534405919513408223392', '94.61365323305285236009907980377', '95.2996726614815290672222821606', '95.53445798312828760066195729189', '96.00209902696247257939895746508', '96.837772689949789961339727070451', '97.306535529763986032188882107451', '98.1898135673800696288778192614', '98.429831052734684974927680404329', '98.6716418505616864196135680615', '99.82550685180397666092126690677', '100.21306655953515882927547678258', '100.44907201507054737659421736266', '101.40844195995074955711666550009', '101.83910264972184441643958836446', '102.4672630597846993848287931273', '102.766386251311688675654169433527', '103.52108153111613897286735443058', '104.07477198515570260728911020185', '104.771443074346153504476412300857', '105.11916878446573872918823620069', '105.76493244380965703892143432046', '106.202821638078067611117454803175', '106.798478095736953734906931341', '107.576015967950480152296987163515', '108.02830037372219668160424259711', '108.51081864853974309137269197041', '108.96471914811698052696232166283', '109.64531428150242709100164519317', '110.22460977528224515979613962750', '110.85392143058236357734570194186', '111.330127639726367506908900343629', '111.85265401328646262184807384088', '112.312433921339878214293948029752', '113.059688203820328440002095297822', '113.49880150506844679142268560038', '114.21265692698498189611230037017', '114.57191306606444156876382526671', '115.27755088055349241584135351721', '115.69296495740708939507758911016', '116.18549512751397563128997708191', '117.13198321363682229358811972126', '117.27328797810300614543414972902', '118.02091599450460441476390773386', '118.5372151716258489749564692858', '118.974494262515838156202934924788', '119.62461964183429853879695934607', '120.30782351986048186498539554325', '120.630300733095011932686347302905', '121.41530502162075620585174419833', '121.80907532231669367154982637732', '122.408298146616340584037669374', '122.691876257923117039304522189717', '123.698556199844861296963228088464', '124.20298404947905387350177396370', '124.54375340083577102282702430530', '124.93918750532330522450025796576', '125.65543114843106361202547037387', '126.44408188664805510771669127547', '126.75068113011053892267436618703', '127.38585740686172417271596278698', '127.803803698959598289339436152973', '128.45323583602291777642785026164', '128.97683034949736863791310446329', '129.59285063425894035273497344110', '130.051511162276705450150734946174', '130.67427292385686990421825131125', '131.19134907864609637376479495159', '131.789188008024008171504166497832', '132.19458202155409040491661819752', '132.73284720434429187126638348565', '133.5089871361329809009214298903', '134.005581308183414625796120400752', '134.44196562949003727847880827872', '135.00750287620081704026390005249', '135.3683349490579812216449466671', '136.23982446671589382465176409022', '136.71468344340804250078443820422', '137.318097929150545011761653847979', '137.6418883469951644745300535021', '138.17001988134471907438522682349', '138.8200470253284265444907148478', '139.581118934720357154868115947907', '139.90659996582311458473407580794', '140.512197181558154867471258251445', '140.81535495891862952103163926354', '141.7911169836677367715372357829', '141.99239670422914224400102729747', '142.64531597933428386310858103579', '143.128003882723740116793035291828', '144.02475029394602070453306851401', '144.175332689955400386759943455118', '144.6852369115773616671498626620', '145.38699394582191114069119491717', '145.885099094072660790005939935854', '146.64465422453584804065687428714', '146.974024787599337402410533540885', '147.48801274234316236376081269342', '147.989572316030825944769226395247', '148.68954732902451697803236278338', '149.1642904223902852834474543763', '149.72962597370511456522493206561', '150.3572307369235254607371773823', '150.83003051718412914953621507271', '151.10098130806544482636693931411', '151.924571882772998802140239911240', '152.53547777566260591151463625129', '152.91260816412521903833681184867', '153.58239680777389233386847843871', '154.086466000077650152039151953658', '154.32052709346366697616596029032', '155.25104065564291832461264220751', '155.738114894537946506190442978856', '156.14255678341881722027345466244', '156.777978040291507009353259374924', '157.30711292165014750635896003971', '157.668273388537602480251124914123', '158.50938898421295576135487008914', '158.84579708112719830601712344622', '159.378915509117023818363034859', '160.24113531762777774468853361099', '160.37585414428483584332700815724', '160.919076138065263083021482038859', '161.655924430592245953508809212116', '162.12227849518983303737734086339', '162.73490330075627379838396718375', '163.1787424049427102373370585526', '163.866175931117027628705308989018', '164.28054194429899530469031476083', '164.4850884460713271104688974073', '165.632983254115028207002950614462', '165.996974719058779612170124099167', '166.399034027262060810194556930935', '166.78792586648898205758069103701', '167.47399017947861823149050481909', '168.07945160852822139388532037034', '168.746504604047900220249097334406', '169.07295621943599686425648381425', '169.551054442036457793905136671720', '170.19715359025438151130148883681', '170.74525546625712514907672470654', '171.31735366308087279353456893172', '171.68475875286981692711205162413', '172.32959306102701986054658698797', '173.04506054278018260916642174737', '173.34442218139604324997109175235', '173.87817507956205841253900643924', '174.35206995819504138724745756478', '175.076727410761329314059036930336', '175.61604225082245746513577838900', '176.12972186754073915489273757680', '176.69107368766895749206633636948', '176.85041039233491791509207771586', '177.75084002379884121397893292271', '178.203324295091949887974531300475', '178.99456379745419445629841716087', '179.15205363014325681981233167578', '179.69380796797371558058602049492', '180.411692750767624526945804908342', '180.78080924514862420940760360441', '181.45529244541020930215802561363', '182.11593827186436562396094987654', '182.42455613543093465071078965223', '182.843718603624009706369517825174', '183.65690849254411820734728342387', '184.03935480748774354050102405965', '184.60389623046414434083149801642', '185.087371136978643753110329968870', '185.81233982322801343304323590979', '186.1984385812866260900233848553', '186.75771744773413241793357376714', '186.99316784405502882171650093145', '188.11598334576218581596662147384', '188.21999429646753962883892502201', '188.86942003193159920932358446713', '189.37417393757470745908119197159', '189.90286283267970596009434708997', '190.40162470006735849703273019503', '190.97717619670585919641058014104', '191.58476575663989112838318521880', '192.12061739765186416730376159098', '192.537446240365025652782701023880', '193.06355167338772910116820774799', '193.56814605996225830277663218107', '194.12801822040786751742918625731', '194.90143774287499975086884125385', '195.20015456341162691769279338094', '195.80242911800126624064993592173', '196.09079106097345615139635518647', '196.761261322634355595483475204810', '197.654535090110945037169095521705', '197.730287516714914077335858071894', '198.35877957127967522243819706146', '198.94898077772165136855220069002', '199.45451137023065728602160540535', '199.95645436532770079206834838420'], 'prelabel': '1-4560-4560.3197-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.176550971915955, 'root_angle': -0.2974974255115995, 'root_number': '0.594127568667793767769585751953-0.804370829996274791076794811291*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.09426099859563371198965504333-0.0668023496614766206702955146398*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.474094428002', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.76081809026', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.16953468927', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 21.176550971915955, 'bad_primes': [2, 3, 5, 19], 'central_character': '4560.3197', 'conductor': 4560, 'conductor_radical': 570, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4560/3197'], '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': '1-4560-4560.3197-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': '1-4560-4560.3197-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.176550971915955, 'root_angle': -0.14874871275579976, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.474094428002', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_4560.3197', 'Lhash_array': ['dirichlet_L_4560.3197'], 'label': '1-4560-4560.3197-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4560/3197'}