Lfunction data - 1-260-260.223-r1-0-0

Formats: - HTML - YAML - JSON - 2025-03-17T07:43:25.198747

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': 'dirichlet_L_260.223', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.8660254037844386, 0.5], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5, 0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 27.940880446602506, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 5, 13], 'central_character': '260.223', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 260, 'conductor_radical': 130, 'conjugate': 'dirichlet_L_260.7', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^13', 0, 0, 0, 'a^14', 0, 'a^2', 0, 'a^13', 0, 0, 0, 0, 0, 'a^11', 0, 'a^17', 0, 'a^3', 0, 'a^7', 0, 0, 0, 'a^15', 0, 'a^10', 0, 'a^15', 0, 'a^2', 0, 0, 0, 'a^4', 0, 0, 0, 'a^1', 0, 'a^11', 0, 0, 0, 'a^6', 0, 'a^4', 0, 'a^0', 0, 'a^3', 0, 0, 0, 'a^6', 0, 'a^11', 0, 'a^8', 0, 'a^16', 0, 0, 0, 'a^16', 0, 'a^8', 0, 'a^11', 0, 'a^6', 0, 0, 0, 'a^3', 0, 'a^0', 0, 'a^4', 0, 'a^6', 0, 0, 0, 'a^11', 0, 'a^1', 0, 0, 0, 'a^4', 0, 0, 0, 'a^2', 0, 'a^15', 0], 'euler_factors': [[0], [1, 'a^13'], [0], [1, 'a^14'], [1, 'a^13'], [0], [1, 'a^11'], [1, 'a^17'], [1, 'a^7'], [1, 'a^10'], [1, 'a^15'], [1, 'a^4'], [1, 'a^1'], [1, 'a^11'], [1, 'a^6'], [1, 'a^3'], [1, 'a^11'], [1, 'a^8'], [1, 'a^16'], [1, 'a^11'], [1, 'a^6'], [1, 'a^0'], [1, 'a^6'], [1, 'a^1'], [1, 'a^2'], [1, 'a^10']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-260-260.223-r1-0-0', 'leading_term': '2.08210462916043386397775230402+1.96911585571886185069780382821*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/260/223', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.8657594002314166, 3.4129043290991925, 3.4147433723896246, 2.7864274918964207, 1.6171650633882506, 0.24021000166236234, -0.8419237687458744, -1.181568811284501, -0.6488302586074375, 0.4344909269961098, 1.413677623988497, 1.6550162255537615, 0.9507808449217653, -0.2879837879721931, -1.2247947049039167, -1.1154933544241634, 0.15454930105182713, 1.8906283375112733, 2.9525420713855164, 2.484756321037885, 0.5404863886314596, -1.8628255726476532, -3.360472263375736, -3.147231816445423, -1.5348579516516279, 0.2739877552982122, 1.0669037666086492, 0.5137765616113855, -0.6244570581270209, -1.1597915741995783, -0.5035349931227724, 0.7877544163242216, 1.440852012471417, 0.5654257231865869, -1.4834994955102938, -3.258880374628953, -3.350217453846688, -1.5906152293104145, 0.6985180903395094, 1.7088613466944556, 0.6121540618645214, -1.7401941830961793, -3.5125342800108106, -3.410661551738042, -1.7270266370362555, 0.008421986594274069, 0.45101760353991077, -0.36204083086651173, -1.1479984724452925, -0.719739088010692, 0.7518096105035186, 1.807565842275951, 1.10836022266841, -1.1351166315940897, -3.138297637373687, -3.068988031308078, -0.7592005940845926, 2.0322927462092246, 3.13497048162984, 1.8953604014603422, -0.28660576149207195, -1.3265542778095152, -0.41803268171548197, 1.3011643249977536, 1.9955493341475405, 1.0121896247883975, -0.5127005218114652, -0.926184117491784, 0.1271235858918581, 1.2783497471907959, 0.9065813645173387, -0.9930978335372375, -2.5587960590223338, -1.8340075289857478, 1.1622676120288555, 4.220285996460477, 4.918883601414553, 2.8862918154586463, 0.08001339041388308, -1.1926369206998784, -0.4866324269843927, 0.5814756864763516, 0.26742482932769895, -1.355970910618931, -2.5359773285727467, -1.8661547775576603, 0.07253043291206858, 1.3213691790221962, 0.7725182845877927, -0.47695501777405336, -0.2589762282905635, 2.174150651893251, 5.040005858762649, 5.654070739283369, 3.1845403164086563, -0.3948815946788396, -2.2290915913768434, -1.3787711908458642, 0.45685721932914003, 0.9782316689515538, -0.22689566434656058, -1.4759761631648505, -1.1718079990952956, 0.2272568185838476, 0.7594217041235048, -0.615403068542506, -2.6039192630809884, -2.9524773200846823, -1.1215204057081483, 0.8613479642971547, 0.520797733454793, -2.2484963355688232, -4.876495532366219, -4.792191903972424, -2.167029313186475, 0.32138900447783336, 0.42451485135737504, -1.349038874036839, -2.5681678751683887, -1.7745111277627006, -0.01733915282615848, 0.6833898015987502, -0.037664047544039125, -0.4421259167733469, 0.9989057309982212, 3.381470406113664, 4.1031854331500455, 1.8878563256589695, -1.4597475394582387, -2.8138070543191627, -1.1380202291678336, 1.3698848962077361, 1.7757133734767092, -0.3050892760020931, -2.409855982845583, -2.182669368454099, -0.045735552525140846, 1.5116005369327339, 1.0153375493969912, -0.3548140181702697, -0.5022469953156327, 0.7694261491449843, 1.4898705947592823, 0.20093840440024088, -1.8287360355813806, -1.8355225631791654, 1.0452459699757495, 4.370134666136252, 4.898510715246768, 2.2197835683948077, -0.7858191155220042, -1.2321653593962039, 0.6233854084768296, 2.0329757185080264, 1.2469547950577278, -0.49739097892699885, -0.8148454961022775, 0.6552507321718862, 1.826499215030491, 0.9748624513692794, -0.9245203406894749, -1.44526796900756, 0.005755057152477827, 1.1786316244796584, -0.2326217284871238, -3.4019347963061173, -4.93035324304159, -2.7383201376203754, 1.369569701954171, 3.650840031643173, 2.5823141093661466, 0.24970204716288366, -0.529266344268337, 0.40776175927499003, 0.8552156654126833, -0.4500474379510187, -1.9903345968419175, -1.524907277790461, 0.7551536352416192, 2.2834267031428364, 1.4575925133436742, -0.12209113341680092, 0.36533929126280046, 3.1436896707176105, 5.166416745969705, 3.7043773302975067, -0.19011384145784216, -2.746794325879462, -1.837777264778313, 0.7372414719189295, 1.7510777833893458, 0.5029676841934744, -0.7648879419159651, -0.21816561845742066, 1.0951216361356355, 0.9118891228308258, -0.8617494585265901, -1.822941488163772, -0.40140785070298307, 1.6627261871804322, 1.2821333605761376, -1.8958453876986439, -4.673324306952972, -4.079199073844837, -1.0461610167381294, 0.7418499079178256, -0.5939863181518265, -2.962107621831239, -3.1824824028451792, -1.0423337955585155, 0.707962139680577, 0.15822476486985787, -1.3809385447278457, -1.5012747734139023, -0.18572630267100668, 0.27986591036358827, -1.1406737050398423, -2.29048941463401, -0.5051642451657904, 3.481211896469169, 5.831145998571325, 4.118498736705764, 0.35031824757448304, -1.4884397144946986, -0.2642838124766094, 1.2818523232810901, 0.44995537964996124, -1.8813796570037518, -2.6869838874533314, -1.0026520675746526, 0.9000574525711309, 0.8207639893860984, -0.3474221011832749, -0.13221354026263032, 1.6866074573924659, 2.508676241269272, 0.640553967623114, -1.8533383349607404, -1.4564044670942322, 2.0977383784996797, 5.057173344054546, 4.123540757774305, 0.46110014349579226, -1.9385263634996455, -1.2742528697905604, 0.27103549989731274, 0.017930794535940757, -1.5055612383991885, -1.6819524949011673, 0.13744609670611407, 1.5753717042451014, 0.6937388816701737, -1.0620032529848316, -0.8261552149288626, 1.4668887256729395, 2.6965758026140403, 0.859545791455353, -1.819133284612235, -1.5207821443052731, 2.076634741842722, 5.112739350616265, 4.316792568869493, 0.9538230918826093, -1.1528809765583716, -0.5855179919688354, 0.4558127059684573, -0.08386638679701672, -1.0684153598981379, -0.17082767440567448, 2.2326427193420457, 3.2076567353318577, 1.446687560521114, -0.587390277725172, 0.047263967987681225, 2.4830528949458794, 2.950091752463474, -0.06367779009913414, -3.466862695634128, -3.4370162219957154, -0.3644303912777308, 1.8050481637742255, 0.8173588476762992, -1.2545566349333508, -1.3287411580779245, 0.38948086411754995, 1.1444171191889492, -0.04757080654681338, -1.0213445970524984, -0.009274426412126594, 1.332861275196467, 0.20531547115748494, -2.868921219235969, -4.096469456185381, -1.4297983617860648, 2.332083318429561, 2.9370236104265723, 0.1465025782501287, -2.1568948856807326, -1.2799176297654438, 0.9299447393300506, 1.1212611606357386, -0.7348919792266865, -1.5836665414883953, 0.06722678208628653, 2.0250701498278025, 1.7906155879760046, 0.22427697026637694, -0.04134863484287806, 0.9976138325207874, 0.34836811986021143, -3.3626907453702244, -7.007557000231278, -6.491571366505939, -2.197691450365391, 1.2735983147148309, 0.9178469549162878, -1.1979263558437414, -1.3543904020416804, 0.602153584428573, 1.5455235414694137, -0.009148572423003681, -1.767418542918049, -1.276774904437348, 0.3401817656413944, 0.20078700511491315, -1.7933315759061665, -2.7046564129256807, -1.158741743130735, 0.16735059249807815, -1.7228843675088328, -5.388937843047847, -6.334825486658867, -3.019953328065859, 0.8795035898617254, 1.2487120633927544, -1.2601284619507673, -2.6856509686383956, -1.418675503869117, 0.09679403587317675, -0.40836540169522545, -1.5859713713080266, -0.9225111274621174, 0.9703647007509448, 1.0693314552754247, -1.2751360617932233, -2.8975829722047, -1.2987993115561884, 1.459507985712931, 1.4952068659372224, -1.2029704067084017, -2.4715149783846533, 0.22473613905314582, 4.099072143274204, 4.767302894512726, 2.0757999621495697, -0.14544200480731762, 0.35222763388690514, 1.5902155068874897, 1.0726782195872007, -0.2608482429610443, 0.09678068556424102, 1.7295086426986097, 1.5257341833410125, -1.4142494266705214, -3.805132101939349, -2.6574776672313014, 0.15935170406158444, 0.27091216944085383, -2.9905010933095095, -5.490003261999758, -4.0219720767344915, -0.6628733866860412, 0.4030857528315377, -1.2438841364002846, -2.1908806140184423, -0.5868881573040888, 1.286055466598545, 0.8600874609834022, -0.7162073388962056, -0.6387611051734319, 0.8573801216440472, 0.7949015965467434, -1.4908743448999664, -2.548971855058963, 0.3459712417311773, 4.649223140617725, 5.415214643077316, 1.9111813739125072, -1.4526098275314832, -1.2028743935641446, 0.8735830558034117, 1.0901838406581013, -0.5436534114768571, -0.8254844234916809, 1.285835992570414, 2.9555325880843024, 1.9282218376333429, 0.017337872333197796, 0.12756407126114402, 1.5824657433619227, 1.304295635251385, -0.8363042388876321, -1.0823591269173563, 2.657766959834147, 6.944923037725472, 6.879268193162109, 2.6441213653256295, -0.8651611361192222, -0.7249888122685568, 0.6900515018704635, 0.09347613985727528, -1.7103041071774696, -1.6364967052032813, 0.43167673996059935, 1.4152090914296511, 0.050222685814117186, -1.0279809878333732, 0.39611698567241604, 2.2626625580184307, 1.2569724799383426, -1.727302616537088, -2.3917457722427615, 0.6017371462114461, 3.2546685311094383, 1.7695735868757956, -1.9827446578974457, -3.1276126852815285, -0.6060732225704931, 1.8170801248406656, 1.3689502130382252, -0.1307252450109181, 0.08427039009638569, 1.160784602392805, 0.42933057251618806, -1.6734920985423618, -1.8999731266874211, 0.45713389353585954, 1.8257178565587073, -0.43033497100375423, -3.6375876781011973, -3.3553832761978564, 0.1237131810523896, 2.121195499108608, 0.40485306999458504, -1.681568054736005, -0.37834704327909263, 2.9381562479856025, 4.025180674090532, 2.0212407223582667, 0.11333510029702647, 0.1699672172738154, 0.17723052104361423, -1.6775665541821025, -3.362441094918519, -2.1209111585365106, 0.5609771542236233, 0.5738165633771969, -2.485421697551626, -4.1258698546160195, -1.3336692661252274, 2.841724796667486, 3.5075793640216197, 0.7562556937317086, -0.9744826981319616, 0.323634782701442, 1.7254570396796058, 0.5052142878237477, -1.5465043003206769, -1.273893820420425, 0.6551241650330515, 0.9634558585071783, -0.7714425309404572, -1.4990809547419992, -0.04257277791577446, 0.469749783705049, -2.4264147425272857, -5.814233424032354, -4.90874786896806, -0.09333881955495762, 3.187187933963374, 1.8283651860485493, -1.091955395694927, -1.3829453873727369, 0.35605801073060145, 0.7143703542843053, -0.5826197928134802, -0.47129803054010433, 1.959279836371389, 3.58560911016249, 2.1829422379784913, 0.058916754085221054, 0.27014913949469527, 1.505445111131925, 0.22041183757667743, -3.069855153229448, -3.635415360098795, 0.514739045556745, 5.090672498612461, 5.169797693147782, 1.8082359286144776, -0.09705691589263779, 0.9515679516076525, 1.730590440737932, 0.15424495174045874, -1.4869080456860295, -0.7739859702589265, 0.6038001688553503, -0.21105203570802195, -2.1273870281278224, -1.6349339250162174, 1.1814755454724402, 2.1352575199141364, -0.6260170820632853, -3.3101017945096403, -1.9648703324860475, 1.4449732038352132, 1.8757250605881604, -1.2675250387416468, -3.4187392411144732, -1.8241940428484198, 0.6894095248592301, 0.5793182610756871, -1.0754019444742475, -1.0221249429937833, 0.5865373223276747, 0.8573102751719299, -0.3805000080780984, 0.06126454136273988, 3.043662365317194, 4.63081674477274, 1.7070999413314716, -2.7860453703157773, -3.647953662929935, -0.8819972135535696, 0.6002601268343118, -1.4476081474381597, -3.4791862121498243, -2.0333775885271814, 0.905944301734992, 1.318628015434304, -0.5614871040027255, -1.1315202718446549, 0.48834161981498025, 1.3862324460014455, 0.26600171446994886, -0.15013871293018008, 1.9594009531944823, 3.6235590340678723, 1.3909356173412606, -2.6198208523695286, -3.0762371028960755, 0.736873888990922, 3.662021632993911, 2.1513002416857474, -0.8974894444868621, -1.0614507092564427, 1.0305899608542484, 1.5607320898232118, 0.05692644460751635, -0.23626560583937184, 1.7167880354069702, 2.781624194977871, 0.9662793552823453, -1.0758469133593884, -0.4516996149275829, 0.999920313736878, -0.1853964039372468, -2.7404380145784972, -1.8836400130452648, 3.0783880150546383, 6.789529462064119, 5.178384045088166, 1.088728893966967, -0.25945833663808743, 1.3246701616485665, 1.9479077339801854, 0.44438380335206035, -0.29130108764580814, 1.035175965188156, 1.5930580379041959, -0.5833903218893247, -2.7711746482087833, -1.781113964623649, 0.6393985528428404, 0.5396285792142115, -1.515621128959186, -1.0057758881320757, 3.0597617837678825, 5.773625562914016, 3.3874615310393743, -1.0230939522370692, -2.134599930065801, 0.031124431955703795, 1.120753411938127, -0.30958643014018605, -1.1718409219385535, 0.27013789460491017, 1.4289571333102002, 0.18144156253892724, -1.2102891047236797, -0.103656864804234, 1.4151009282092146, -0.4447667448061796, -4.46899175568373, -5.412494940819069, -1.8884792743905214, 1.2677891429196135, 0.22389524415375853, -2.2871876435216048, -1.695957186334786, 1.1735910521925117, 1.816515872933878, -0.5635933049249282, -2.096516051779409, -0.7636935466369069, 0.7147905327741163, 0.03439517674789523, -0.7766343161781659, 0.5581964047680017, 1.857259279655569, -0.0939686587981628, -3.3505677025819467, -2.8102986590557366, 1.840872374394689, 4.949719176792451, 2.9507607101149995, -0.7038357363791026, -1.2588736519552077, 0.31133123721852474, -0.12841752407796095, -2.627260664091348, -3.2692204802528826, -0.9429849950196654, 0.8672216601762144, 0.021637193283918797, -0.9908104290537058, 0.05942942905590723, 0.8438579528817217, -1.411216800497147, -4.3363192612795345, -3.5084365969876545], 'positive_zeros': ['1.620829025734895824789997321', '2.69495797952331663077130901780', '3.99146479632547844758146398677', '4.97075667958247345723760919903', '6.31909051787402016574625971542', '7.75704344684916374978258363903', '8.57836567182475766041940261705', '9.49942807461727782656789491916', '10.40973544167008436044498981509', '11.77149336583541019828886085822', '12.58851817695515701670273623729', '14.06035159168539424278638175408', '14.57793898768292433121263961614', '15.47707507582957527131861744679', '16.41860063250843570475769480350', '17.5793800641801867498970742458', '18.70502914723781652937307914367', '19.451167818614300717044295689919', '20.508937689041147240214038765296', '21.2219261080870796770258535115', '22.040909057816395834514178876772', '23.01917832168750042161800621502', '24.3859201765798405849477434010', '25.12011073536699745688011991649', '25.6888165900975786166420230788', '26.863331640424666303451353095658', '27.67867162369764316320482235777', '28.175090409048735029636023067274', '29.64907282048581973430660901067', '30.53827651705578363536954251450', '31.20520031282260977239782676005', '32.13571869631145756622839369849', '32.71189771517823742285276543311', '33.90124348850058014354717488083', '34.4516518394064276402347195338', '35.87891393429908353235030420535', '36.34236189059009613879568127463', '37.50363476819678015939754914224', '38.112541303802290036924315807772', '38.5855422773918401371574960155', '39.85714792913699001884380715066', '40.755173450360629382548705109511', '41.52600057824738338967927980307', '42.506275992125463353989784810136', '43.345347395331465327154378499436', '43.8944149541005514482398516684', '44.71688623819168567956625654026', '45.533828274807376625400813893532', '46.77390275766363453509820440084', '47.41003688040945456102402204218', '48.33818336443863099889981256249', '48.9458087862391030878746608872', '49.84366832721867752164161658236', '50.62401676103738104805646096839', '51.22255855926410120865926740265', '52.39387383853807474459708336986', '53.482470348219513411381023323839', '53.95158417968977511288454049725', '54.60896758711063827208011838407', '55.529182904720422413638529760417', '56.52570977785697327690054944849', '56.804668212855823720740932733726', '58.1097788829166666170719386022', '58.96846904032001068899764785003', '59.78072563538553724386185008240', '60.3616760198404068452406036241', '61.11065701591211723528395039885', '61.928729173766032972128056744676', '62.64656444444830134568161969482', '63.87335104470586791439576121171', '64.29286359649666228608563719379', '65.45720044256589938899097859643', '65.9695848957927459341028229996', '66.92271850849282260101108204836', '67.28359074876024086023205575889', '68.16954491771411316263137948053', '69.408813869519802583743524924931', '70.04084083549906130062318715130', '70.689017876235045699626459681279', '71.701477707830899156614659245723', '72.39512873507354195620046081531', '72.842496210063978980867671229911', '73.81993944764632728294900529654', '74.52265802319568072397821398526', '75.66543376940596926432353049003', '76.48717985341931097174978893921', '76.879349795069023366373267112676', '77.79257815604563540861057315873', '78.549443967333432778131303281639', '79.19001734126060961869557129351', '80.08880603762108049545342144852', '80.77722271972122981987595965073', '81.97372422223475267519638575578', '82.63906792072947895651109584834', '83.10268433037690560974277029527', '83.77542130665727595840851364559', '84.8777137423597973396378671968', '85.30525702746763096755103867480', '86.24501118108435478436607918075', '87.22250134079385570712060201447', '87.92508074129332480930704564914', '88.68199557438516455441016684903', '89.36558144865419395927472716185', '90.00169104940987573377840745429', '90.64909172496533799159832879243', '91.67090470327709334676679196563', '92.5139345585503555895611760795', '93.29427975543741859026218938111', '93.949289261730437548038902043141', '94.678618079151479040661725296181', '95.689986297096005428407463973135', '95.95409677210840290583704714393', '96.60484677242108557772170603268', '97.97401815492942714268624159415', '98.568256928669509612085637401826', '99.28646088956059259883145050425', '99.99872092120519238933518566485', '100.85818408573601456485696104442', '101.290618970966566608223380957851', '102.3968039127482213295771849726', '102.58783494949812508031566421307', '103.972391070140550039051356642706', '104.54473693519588088003579785030', '105.584973408951030940553354618421', '105.823757402648844741605328798921', '106.710288874998819675502223121667', '107.35140532491621454144952257224', '108.25926195669751329277157469984', '108.93509686099122317352714923593', '109.67026128299262731470895846213', '110.894885004771026402725904540559', '111.16402182145751043619621273988', '112.106706449343016824597779677841', '112.47772371155593020443149759320', '113.307136802608774002056172020317', '114.35208481155428416237001169780', '114.72587305984883857908184314444', '116.027154239329208345681958113065', '116.35878310143040467514750816980', '117.26597355802036054849213256262', '117.97157220662892141942655675327', '118.573539311672390843793416757779', '119.18990821441570452353719461531', '119.97531262345667182533043170853', '121.08392185021061891135885872710', '121.736301163313042489380225331110', '122.39894971346983922111034021437', '122.9617356860935274311901298735', '124.06717395132085207421486964041', '124.34081083282616266265238318717', '125.19316319276021087727959876787', '125.74903749697022223431377862591', '127.076296028639042888938875563984', '127.638792441209350785314702383723', '128.14174059617078295149066457339', '129.0004372000930054442259646748', '129.69607271961510849356894435446', '130.25704387495924591796109266069', '131.0698578285994666488357869363', '131.824798062761739614159868826804', '132.64500888216700859735122216235', '133.49668137363676818576667279062', '134.33426016626273809369197374705', '134.66292719641669172837477695339', '135.378856155920755705936937661321', '136.19687734536419544272628984162', '136.83643932633082044414408079687', '137.80172876333877335746451137611', '138.48318310243454666709914898245', '139.10036009408495623444848836991', '140.36532973867172110044606800179', '140.5189083586566040198197348731', '140.98753696434627364199267686306', '142.10976562745533948923955378147', '142.57514916799277424134487900136', '143.5289010948389931747753462826', '144.46021642741040789545891167093', '144.95033589419493951740378382535', '145.69254044134571327157825135820', '146.45222681160663510614655423307', '147.062331299580994551461692044077', '147.82039324424697790478486380851', '148.2100412386566928933216296575', '149.38081179600641487686083711193', '150.179672154130640320854180087406', '150.8709118908948054766727976824', '151.42815507129697505561728367430', '151.95412795475668027814365185788', '153.14161140567903942181180397783', '153.36461833211224694353443149087', '154.08563776112907154054571465241', '154.97020640064556148916669485102', '156.189662501384677218385769100437', '156.34367775902248928529172775239', '157.20915984582985271300369555623', '157.956688336119908773545185613096', '158.40197800606799372819746780377', '159.24865599769189678675330812031', '159.946148651560116992912660333113', '160.796565295069285427456460487248', '161.45289683362765621756773603493', '162.39083745561915276928759653368', '162.92007885493199042083001067388', '163.63486317071648425808600578430', '164.27537155316979513902322433012', '164.67788570972381682875371861579', '165.73493134720912573317971475966', '166.667515537347654471483703294952', '167.01597694843406535946908040213', '168.015297477865981565941375497004', '168.6605464654697106780989183499', '169.29437931125340033774994037491', '170.06544254340482057808301167575', '170.35359886098188146815103929521', '171.35260432214279883659824108834', '172.135853562854459915109894117408', '173.01573944336432062738314334190', '173.60055299913972017321298829348', '174.3874024770169657221647081866', '174.74323005412880684158205865675', '175.742164863542849125901867989985', '176.32825907071370743071825968385', '176.852055114062110078208549942132', '177.6359781513969775341727924243', '178.885214416365787831277564121', '179.14189300400899263982823269933', '180.09294481070592301297997691912', '180.4163538273501705109206967669', '181.18686785457191466944961288390', '182.08886453918424792474138773894', '182.58538401493321545377352445514', '183.219923710111740844138667041760', '184.29149401903879317130791538990', '184.995850952226817658618309394270', '185.57197598823285367141720975262', '186.20647105219926476374303650282', '186.903694116267999410836264183791', '187.51566866126057345232495946519', '188.08555659101533016052950121384', '189.20873749472854796331126003039', '189.71290374483405978491109663591', '190.494996928746014317663190212171', '191.18632812329416483247855868595', '191.99551898989699085011273890620', '192.5079796094763619926631582137', '193.03529288098502619692953803524', '193.74140473892564345137617406383', '194.575466660256420562098630387276', '195.55022914461093258140323191254', '196.17776035715897498460222572429', '196.541285313286611161569079675015', '197.61520998866970004195682410245', '198.129297741442583734613582584710', '198.73843522927903762825826676713', '199.22955124241907436554264341424'], 'prelabel': '1-260-260.223-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.940880446602506, 'root_angle': 0.4822492393122839, 'root_number': '0.0557367604433135539761871572509+0.998445498530232584211066732109*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.241124619656', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.48961293407654772209608103713+0.592817704956371604144305263151*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.62082902573', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.69495797952', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.99146479633', 'prec': 44}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 27.940880446602506, 'bad_primes': [2, 5, 13], 'central_character': '260.223', 'conductor': 260, 'conductor_radical': 130, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/260/223'], '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': '1-260-260.223-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-260-260.223-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.940880446602506, 'root_angle': 0.24112461965614196, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.62082902573', 'prec': 44}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': 'dirichlet_L_260.223', 'Lhash_array': ['dirichlet_L_260.223'], 'label': '1-260-260.223-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/260/223'}