Lfunction data - 1-1480-1480.909-r0-0-0

Formats: - HTML - YAML - JSON - 2024-04-25T04:25:55.969372

• 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_1480.909', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.766044443118978, -0.6427876096865394], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9396926207859084, 0.3420201433256687], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.17364817766693036, -0.984807753012208], 'algebraic': True, 'analytic_conductor': 6.87309110492009, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 5, 37], 'central_character': '1480.909', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 1480, 'conductor_radical': 370, 'conjugate': 'dirichlet_L_1480.1029', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^16', 0, 0, 0, 'a^1', 0, 'a^14', 0, 'a^15', 0, 'a^13', 0, 0, 0, 'a^14', 0, 'a^16', 0, 'a^17', 0, 'a^12', 0, 0, 0, 'a^12', 0, 'a^24', 0, 'a^9', 0, 'a^13', 0, 0, 0, 0, 0, 'a^11', 0, 'a^4', 0, 'a^9', 0, 0, 0, 'a^3', 0, 'a^2', 0, 'a^12', 0, 'a^26', 0, 0, 0, 'a^14', 0, 'a^26', 0, 'a^22', 0, 'a^15', 0, 0, 0, 'a^10', 0, 'a^10', 0, 'a^16', 0, 'a^9', 0, 0, 0, 'a^16', 0, 'a^1', 0, 'a^10', 0, 'a^14', 0, 0, 0, 'a^4', 0, 'a^17', 0, 'a^14', 0, 'a^25', 0, 0, 0, 'a^12', 0, 'a^11', 0], 'euler_factors': [[0], [1, 'a^16'], [0], [1, 'a^1'], [1, 'a^15'], [1, 'a^13'], [1, 'a^14'], [1, 'a^16'], [1, 'a^12'], [1, 'a^24'], [1, 'a^9'], [0], [1, 'a^4'], [1, 'a^9'], [1, 'a^3'], [1, 'a^26'], [1, 'a^26'], [1, 'a^22'], [1, 'a^10'], [1, 'a^16'], [1, 'a^9'], [1, 'a^1'], [1, 'a^14'], [1, 'a^17'], [1, 'a^12'], [1, 'a^21']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1480-1480.909-r0-0-0', 'leading_term': '1.47803323590177645908353144970-1.74671353041672024183339503941*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/1480/909', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.2881412552050007, 1.6019750996663837, 0.579367380363847, -0.6288021875052093, -1.1368759342827113, -0.43776546226847274, 0.9226662808388286, 1.7096187972829835, 1.1635123004076557, -0.11700976765981909, -0.59785629341563, 0.643707820084326, 2.7364319747259636, 3.6054777368084414, 2.027479795152324, -0.8876188955643549, -2.5462633094783196, -1.449989378221439, 1.1501648455220457, 2.4567888704146656, 1.0690985175622816, -1.532114462783941, -2.683922551929225, -1.534700721955543, 0.14376551885264763, 0.2677253249355455, -0.9837945398002094, -1.576768308777554, -0.5158016201845665, 0.5785762223827522, -0.49979573909383196, -3.335151973836618, -4.822054931376409, -2.778571101501517, 1.1309623753976568, 3.0757008209850083, 1.5400964125040977, -0.9580342274446842, -1.1439592897865216, 0.9203194789786489, 2.1915153561604512, 0.8536206430739111, -1.318814595999552, -1.5554678211691204, 0.07896819623196745, 1.002102314923474, 0.03968683037585134, -0.8072060018172619, 0.5221262028942655, 2.634333136335029, 2.2067446353024462, -1.1552583979779734, -3.656761482429168, -1.9751883304665856, 2.2423039019548394, 4.337613490051412, 2.561330328148144, -0.08364403483439813, -0.3868059674268414, 0.7763340666415804, 0.3803900784165651, -1.8426473678962378, -2.9950748805449665, -1.580319109777667, 0.1093892791357666, -0.4175662636548181, -1.824886570217537, -0.9513372307520969, 1.9740227696422625, 3.0998970454251786, 0.6236949214922732, -2.0165777942094274, -0.674237964084883, 3.506193512594864, 5.463920487783348, 3.1340628813344873, -0.08052429151855656, -0.5524104260649272, 0.7423513636623633, 0.7642037336717563, -0.3490581603702807, 0.14408920514271284, 2.4240279602341075, 3.1672832360394203, 0.7649002953356266, -1.7158650834261606, -1.07315893758671, 0.8862950169718604, 0.05316674621995394, -3.253940891710958, -4.20722616238169, -0.6737407441903499, 3.2506247600492113, 2.987043730422906, -0.17319367563016314, -1.605543869739749, -0.37519316687624565, 0.23149461247809205, -1.2461946748662436, -2.150741312027515, -0.6855473553024312, 0.6860390987818498, -0.521253350925832, -2.1521429630736013, -0.7464667948249026, 2.193005162463744, 1.7758342235026192, -2.5509351706969903, -5.454603427220931, -3.378137502247484, 0.37105415969933575, 1.0185016744274362, -0.5316294535904666, -0.015045347407943659, 2.7718924099654814, 3.769333069010176, 1.558733846696421, -0.44749630333671453, 0.08312713617241428, 0.8307402143328582, -0.3929470847322955, -1.3068211335919444, 0.6084495418123357, 2.555930360366059, 0.039412107005912286, -5.378955593124406, -7.320093683107114, -3.807602904851281, 0.010047783954036523, -0.0554092623712138, -1.4328563067013798, -0.16159621929276982, 2.241928968037959, 1.8409226620719754, -0.6636842980978401, -1.245190783999601, 0.4219658351286084, 0.7648873120645028, -0.9225841683351371, -1.1399445467619782, 1.1173889207390624, 1.8395292539007402, -1.0437785764133503, -3.173226507707085, -0.4383061219636655, 3.7868211713450433, 3.4102592095925974, -0.923251542239903, -3.1068159607549513, -1.1861072324150113, 0.5797315466077542, -0.3624484870009282, -1.1815657457919138, 0.1580786559042016, 0.8827293523771382, -1.0882250081079037, -2.6166811699879013, -0.6573945941924249, 2.0033413479323485, 1.4355128433058622, -0.2862493516515746, 1.3643844098287512, 4.809014583369046, 4.193329501528842, -0.7299210586527323, -3.580112822452459, -1.3561185015638282, 1.2594947069468203, 0.13332975400619332, -2.0082134644608325, -1.3264223466201568, 0.508607584865673, 0.33725210691908875, -0.3009362626490741, 1.3418431566481936, 3.014590027938479, 1.0575770700767535, -2.221313957933682, -1.570878890776846, 2.117237141717857, 2.95496190673141, 0.16832996046690457, -0.48903701229800034, 3.1796603178626284, 5.79409183348312, 3.4548604407877885, -0.0002576859687488184, -0.0314220615013846, 1.2900429264494704, 0.18785886325301354, -1.6742397221708027, -0.9013381442664303, 0.858970885353846, 0.2609314919641579, -0.898451418564777, 0.9245330112529082, 3.313569779550245, 1.1672742966235528, -3.7210483629915414, -4.411705813723597, -0.08402387708135854, 2.5854033418652564, 0.4897413071058256, -1.5566806186506357, -0.00923897130625189, 1.683289001416028, 0.3641127474836341, -0.9329724553851729, 0.7755299160288308, 2.4731002925635788, 0.8756403655431074, -1.3128977188782214, -0.6550595200800462, 0.5611880959168959, -0.5290078098621507, -0.5401952219705652, 4.401423023740221, 9.936127607883996, 8.82237865711236, 2.504689707724733, -1.1489927072307973, -0.11672235935005676, 0.49988750679477323, -1.1573759266482795, -1.1871233577702158, 1.3867943742069693, 2.2256281289958326, -0.047938278442520646, -1.2835342362645128, 0.09103249329081507, 0.26082527134529043, -1.901191085413404, -1.957598242384872, 1.3353912660031289, 2.4228117956322044, -1.3437111780635584, -4.184604849330312, -1.6323394036587384, 1.5492022232681744, -0.2722927780235037, -3.941154323628913, -3.578202970327553, -0.6188830582911617, 0.012874009124121821, -1.0430809665099028, -0.34428165105932396, 0.6972256348094269, -0.9468965384480047, -2.6628178662866957, -0.45184323822704137, 2.8198909550568096, 1.9525568083831408, -0.8135258895611834, 0.3852594943493871, 3.993410861063708, 3.5651595447869306, -0.326345669607125, -0.9132801679828852, 2.5772522999650898, 3.783456816501155, 0.7357671290596302, -1.3953892919729523, -0.26580503934463534, 0.46636722865349256, -0.47900438460919587, 0.25114142029788433, 2.645661435568821, 2.2748355209695617, -0.6925910696902806, -0.7151613167094325, 2.564938236360298, 2.6516922872165636, -1.9999527872907257, -4.424891404906162, -1.185245497317116, 1.8472126734329863, 0.3270250422711784, -1.4873430910990653, 0.2146094352739667, 1.753676884012571, -0.16684320655413729, -1.9575561198820808, -0.501378469612357, 0.8674703410761236, -0.49659700971686754, -1.2738446139776003, 0.3442937418782334, 0.1001557386740464, -3.513041223896362, -4.41982109659026, 0.48832381783264894, 4.487468078104587, 1.917893271234554, -2.2977164213225385, -1.714647095151342, 1.0121154982318838, 0.699867505671191, -0.6938787906732269, 0.563613346248764, 1.8564937977867488, -0.15056884618631908, -2.1994272716114676, -0.7207779293072692, 1.0189183315642993, -0.3646320980577748, -1.4287810087353514, 0.693320024449809, 1.4340895819588875, -2.4728071719512186, -5.088282794598881, -1.0145841509102906, 4.3470789121482385, 3.603203572257076, -0.5518883179020189, -1.4647880795047232, 0.015383761452247222, -0.3041382732292099, -0.786783696102939, 1.5923654742818008, 3.663280547582976, 1.8575145947505847, -0.44808858075154273, 0.3631648943069613, 0.8496496062113605, -1.927672579705515, -3.092400679143931, 1.1385339934006011, 5.045188195084035, 3.0077070588628767, -0.3120477630579472, 1.2274481237069352, 4.094130534221541, 2.4425717847381967, -0.8974229003224212, -0.5516969470169208, 1.3443702608688264, 0.5062894171181465, -1.012946972726052, -0.2605146265379476, -0.04299900296550872, -2.1910883159094356, -2.1161527694296094, 2.1909227487054537, 4.366936259847655, 0.5983354482898465, -2.868285715152667, -0.9361867738585146, 1.3413147227479978, -0.9394877456302297, -3.2037822985012667, -0.8424585548958993, 1.7311599836269111, -0.08293504157850476, -2.464467251818082, -1.2671230294210483, 0.39760653946148206, -0.3472344962219864, -0.42121621145463123, 1.3632622900495577, 0.6714016455135298, -2.753404129510489, -2.5597447179906125, 2.2072120425210677, 4.029972653587989, 0.5507253562978144, -0.8722085043989332, 3.0096689901343403, 5.47260508677036, 2.6737959102997326, -0.029463628828563525, 0.7015779537163813, 0.7608985650738026, -1.4758200606480965, -1.6576908670900867, 0.7342995101612859, 0.6705226206893065, -2.0681534375564823, -2.31809276361417, -0.17181315380983822, -0.23521274521349445, -0.6851468851481577, 3.994172394624501, 10.3039310224994, 9.40895201825858, 2.510638172274688, -1.038935700281438, 0.48141353942490317, 0.7608024060956942, -1.1957156959695805, -0.8092886138735284, 1.1747389118956786, 0.3186138884006364, -1.7216945053287633, -0.7589268923490139, 0.6246396344701233, -1.6109166440040954, -3.866945082963174, -1.8359065667626366, 0.3947149493637979, -1.2651852667467796, -1.6931713402809385, 3.4677246054960214, 7.723552451818285, 4.604909150828761, -0.70892667469496, -1.1707333651015102, 0.3872566028798614, -0.8666824683017313, -2.138880709729542, -0.34696107723434466, 0.9599729607918488, -0.29444471080088686, -0.06571599264592923, 2.4227837703217174, 1.965370712759173, -1.4825232474490275, -1.3889321451844083, 2.280263989288414, 2.0431737106271264, -2.553008808092354, -3.6415835287791705, -0.12915437257747486, 0.6195310442426702, -2.5664327779533567, -3.0332047677763656, 0.09247257820729335, 0.9172784683622683, -0.9652721443209633, -0.7072644738628123, 1.0491986452201756, 0.28463556748953284, -1.0267942497970837, 0.4558244284662896, 0.9687445700204258, -2.6644565923063865, -4.336479443236175, 0.7899641631215839, 5.8692303942753945, 3.9060597174195624, -0.15589899393361006, 0.22451246033688962, 1.5768653514315456, -0.44424999312076546, -1.6686312928108276, 1.2013856644180223, 3.1847846106489985, 1.0909154249942503, -0.5009891556200272, 0.7202739200562673, 0.8748797626237214, -0.2200092164226773, 1.768793990767721, 4.795961153088792, 2.630655495306579, -1.9312672690822419, -0.7192801688960289, 4.312080629900132, 4.454599073545111, 0.5112269538669796, 0.2521254104274132, 3.1617616735281517, 2.7979538481580914, -0.013758977578746986, -0.32097089035345444, 0.23507646595979675, -1.6518148438428724, -2.486464423447009, 0.5650789043944396, 2.5716620012588924, 0.541156280656311, -0.39225457923102464, 1.835271640049681, 1.460507873999284, -2.2235990402927763, -1.5700901251561896, 4.235074100776087, 5.963442596923613, 0.960411928515016, -2.540434547253084, -0.9578365567925433, 0.21134939214729387, -0.9113385519841025, -0.5128581161062719, 0.5135710936934361, -1.6733470142070304, -4.107515467740165, -2.1906225187841835, 0.3762942209747271, -0.9252930668268128, -1.7800988855750286, 1.4686910410196685, 2.8520681411551925, -1.4346739482949808, -4.147253839713681, -0.44635832530723907, 2.8008641620393586, 0.5443034471307813, -1.5256304527069404, 0.5006284220632354, 1.6324647070919003, -0.5004684408524519, -1.2636571451818819, 0.13761168842685614, -0.543267488020294, -2.1522511653848184, -0.413403455872518, 1.6210815756404835, -0.6249755774625082, -2.188439948050485, 2.543281287380405, 7.4302118504009815, 5.0937797275472825, 0.4789518113248275, 0.6319551174334277, 1.9087809935263944, -0.3749367282196892, -1.7244857925981458, 1.2660455071455696, 3.178701337424033, 0.8743480971633322, -0.8023324007596959, 0.013388853936314215, -0.6818369497445812, -2.237900650537959, -0.38266282223779924, 1.838113185546304, -0.9059793011267363, -3.844286907698006, -0.12124517639861027, 4.933474082585345, 3.021540963328985, -1.7271549283589378, -1.442716764276473, 1.1145453759164123, 0.47144589825072036, -0.3537950804108727, 1.6739097107951182, 2.042535998899259, -1.1310432508969332, -2.2976398838429115, 0.02134455412022712, 0.7349893061768287, -0.14771636320840073, 1.8120276000546884, 3.7748030021498318, 0.34952911602661685, -3.4526340654044008, -0.1682882419328444, 5.19054589673858, 4.11054158869362, 0.25399657214096877, 0.9565307778487547, 3.097761981552039, 1.3354634336972255, -0.8146734422771263, 0.30969294905603767, 1.022809922021599, -0.1228646807462845, 1.2312861621556572, 4.280270643847034, 3.177469386879921, -0.32681508491480366, 0.19188373327236993, 2.2074144967223615, -0.43367009183032873, -3.709817082062095, -1.2481169050588046, 1.7992586843889211, -1.4099215362278448, -5.503876299019461, -3.4533795196444683, 0.4013743627307905, 0.3777926216277777, -0.2789210632962466, 1.154728672099418, 0.9939932798785678, -0.9552570226907399, -0.16530971221794907, 1.50430841568304, -1.2948052357397661, -4.887395416477719, -2.7399586642663745, 0.9276428606390265, -0.4879387077896437, -2.303499170481936, 1.317578944355313, 4.4706269858298056, 1.1871902477200065, -2.630483479754898, -1.309093872530454, 0.5389528732309765, -0.48932651076364986, -0.12333331448951987, 2.3170131083303014, 1.738982139936406, -1.0587687157898107, -0.8485743058517072, 0.6360687762521623, -0.2687476660695951, 1.0166802785534463, 7.584009547428914, 11.011072753244571, 5.417772020408617, -0.8737377247892408, -0.36814780878603964, 1.584826121725847, 0.15890880921717307, -0.010618263059110128, 2.757469166299977, 2.7849374348314626, -0.1286974168354046, -0.008898557630930545, 2.3562927372734888, 1.6326911807690647, -0.3330900242838758, 0.2595394525849366, -0.18309901870661222, -3.555606878300958, -3.1726935849034077, 2.5120535400528308, 4.1054754578928065, -1.3372105939797072, -4.21992598789851, -0.6678334034737664, 1.6023477743987171, -0.17880319266483474, -0.25281707341538584, 1.6263529104437704, 0.5572276473638568, -1.4672233344664867, -0.016587286972317553, 1.493140407941562, -0.31721822548168566, -0.7503107693387996, 2.122585743358331, 2.1717257920077406, -1.2713359045122188, -1.0238710249083414, 2.1657761141830143, 0.013642721137800837, -5.6805193767745], 'positive_zeros': ['0.7681677841651879720771695607', '1.6670218902528996258894211331', '2.78161332543105372157888707699', '3.32248544928385014229444574666', '4.5913414616274042371674952390', '5.487721624859161686256888388763', '6.3769498907766088628603541068', '7.46295075749810930056291325196', '7.89532488686296988565996221747', '8.8592125734384826106542330308', '9.299176917099874756660636354610', '10.53161306410811157014800924119', '11.42579063287448896774018049055', '12.06311034560618997771420921246', '12.92458114757337932669909879546', '13.73589990896037032436918172490', '14.38383329573653778906424742348', '14.922569653996067814507804672709', '15.842448806534358278260664972063', '16.71123657581682983523828431959', '17.7978670352889015177899218937', '18.23049973363763130577547711258', '18.81456288577342800786229273718', '19.96162466347239762832484657035', '20.21104427316301545431848446101', '21.046586749527947234187188846939', '21.93170855897883197646720326998', '22.55625293692964182951358011945', '23.73842108876056040460396185273', '24.19941784767607654305916816508', '24.889473634495230918031641728039', '25.28533927232048929023992478304', '26.325309795565873282628202761774', '27.02659728484855913904133604215', '27.50614864272843869676237734231', '28.48171100132840866361568796308', '29.35699150736897495487976827263', '30.08565097556668965623371991127', '30.3914861564135131403778704738', '31.35886464959394518218967437335', '31.793956859174836910895680243869', '32.57485781435218805003653899748', '33.27040431622494579459101245450', '34.33460777942636239248382082547', '34.88551979844873080753859803586', '35.31467256140505265025652813603', '36.45014449689039434784877140815', '36.85434009816406228704609803398', '37.42892397907080692873803045670', '38.05606869255130739936216379483', '38.75251176723216068394213893013', '39.99844805363719736379370192014', '40.30143565398291676314789301106', '40.956858837126571662910785085853', '41.78769099364738811635153865115', '42.42448231629730113173007142057', '42.96759996004776908159938511329', '43.610790401106842648872023095464', '44.284137368374924680789076499688', '45.029090894018739321287543794902', '45.87271129213807808424085582403', '46.715966103958881103965793328952', '47.11474241653115309797275549610', '47.78422064311236642077785677152', '48.30134023471154315979875325133', '49.125961575385892470251207056820', '49.9107326930144520679561090594', '50.15244317283797845208637867986', '51.20605646617694831549922850099', '51.999136316753640339726816141753', '52.51633468547338126350597939197', '53.327819543618690353559016991323', '53.84873685911969915737374669709', '54.170286719063176516546486400673', '55.08883925542821028608467654199', '55.760860841707959413878489758553', '56.58211315281775280737000673617', '56.93841123137490750624408367277', '58.124959754784636072620451759109', '58.44408413806062645625556936787', '59.088657694404147460815975349435', '59.82286104596107871899182268300', '60.36107107227463591576649530935', '60.83522905723343482937785977639', '61.636772749479667719610503042298', '62.505578880587962254816823051306', '63.17389853936628141161845115506', '63.75113423268516894750164782413', '64.42838961020669595911197294896', '64.9021459416304732818959412615', '65.72428777056114879232421368067', '66.36976839785614600281693019865', '66.771794176209879764042497923025', '67.24512184805758340927234189831', '68.591598031793155333186876628010', '69.083649685675692118759066228737', '69.49045092001809138559902737583', '70.15655341881288538740211123465', '70.93165666011204964649721778888', '71.5441802249514304410948977975', '71.92428185241453269430835733014', '72.69637303675059408994388575982', '73.3476468523867661367564339804', '74.18583469487324384483750353262', '74.66550034492507472604993592333', '75.73716226839906389528413468112', '75.942025122759649114258098580271', '76.63048451958951713543077800962', '77.06374020860901064999893098679', '77.848913169453822995426896843121', '78.632940501232847494207427399122', '79.0258177838180526312986261557', '79.97015407713885411721964980590', '80.411298813471390599235139136035', '81.317640567665248183319035975482', '81.92759223808525100404681744229', '82.35032462417158994289831343970', '82.77352729592394165809278085066', '83.67072630586179346028899955956', '84.14056742145554644859654606880', '84.879189953612419533638894522785', '85.71064591297685317371680593375', '86.28650558624436713887800635571', '86.84948105274351842774143306941', '87.481478102566875351775819596926', '88.195608482669180121473775467306', '88.668646995587802487717237540192', '89.31363273592972383223956376941', '89.69987641449579230084659819716', '90.59990386981050478957540143908', '91.370137824685763150756126595926', '92.05086826423171070176306164465', '92.61933493009703585450217109006', '93.04026268934802179180044347712', '93.73430400797298481847842155141', '94.46408742526433413007860378492', '94.94783147047516594953977585832', '95.54420000889963271090758176631', '96.08412734860208296066838206779', '96.924249888632509535084456776608', '97.76326986071598063863084375650', '98.43239101619796149724753214993', '98.65978558256772731517074155643', '99.20662569274205270282699125871', '100.21152353090939540281835751463', '100.55482688721304972948750933878', '101.06327740963260897657147734835', '101.81078328036936094289916098567', '102.756126234489404088900035342', '102.99491968647558250833461878344', '103.95477893038949697043890507652', '104.45214594730219443788531920220', '105.078197661815385265918758008500', '105.695952607000535265703362648270', '105.92649244706271960450565912475', '106.73366654112141689633594764208', '107.53670629708045901401164245116', '108.21022557601477355555134286996', '108.66562331833647299388986558326', '109.44642046521679283256709012341', '109.99196581873916887500891433381', '110.81192898814478408418697677466', '111.15951941098277600557471775872', '111.64548929663791854783807676178', '112.2539991669719645234584171244', '112.98992550312380135703661974832', '113.79683004599408847396274424178', '114.16363275370683609221534734965', '115.30146869023435914699797869784', '115.444642397222192130991435314292', '116.05610274329387476812993671992', '116.77627221689325768838991747172', '117.27122139072773277142207275792', '118.164615180137873301250686510888', '118.375599366923216763678921197366', '118.83512985707230401744926741987', '120.14784313074231819046609624156', '120.55166014344856554590984708835', '121.06100326414948112873446874218', '121.67596407342162062462861504433', '122.22859153777090931968863588697', '122.92354226907638346438167282704', '123.27039772716384007186348244112', '124.26157556368835537728534039880', '124.51769468499154197133826142795', '125.13451278768281648927895416705', '126.192487122571425928452814006378', '126.75564080476684155267687526350', '127.05250811665364171782011360314', '127.85835294960020868870506544523', '128.374579131111062666241350532998', '128.76015328699867077977261768789', '129.54965147322168237815638046147', '130.12181863769764545143294660825', '130.77064648271223388101099444414', '131.57493101328088260468963105437', '131.9502806365171968488091018416', '132.802547321210304001593315342561', '133.280371942255766351637323362717', '133.86073424109086705722775128996', '134.42078376508548345021904763212', '134.93340702416774974590192748622', '135.42468764398681305824487561894', '136.214292299275075310001420834762', '137.166566201915073264493539376407', '137.46522235316132392614611729583', '138.075618587742025849515328946914', '138.64686842437672030764778651663', '139.51267922943468298858218524676', '139.85466769703177946803530502907', '140.5164645998796137534029301637', '140.73105751236273874176020433447', '141.72226732644758421289430359445', '142.233511604263128451823062620111', '143.18727360349660147863801943619', '143.40099861506042639798441953343', '144.37286645580943919010752743494', '144.78281343028321210073360793884', '145.07217693994544917816529496073', '145.89051638740002381606530866828', '146.634137743222732040109096567682', '146.949616272223686069748347787828', '147.62618107019202970050037188769', '148.22032312658958581087093395438', '149.11628352895035309410747969006', '149.83963993495185590012623015285', '150.08296410759445136732035251149', '150.72784562981084612185908501825', '151.070007267953779201182651372', '152.100116633188246971566807358525', '152.36714550065136364783380492854', '153.008039668596597644148567725584', '153.665339368273560577781101152950', '154.4023953048731334635935033933', '155.04875850108419029066914620568', '155.5683343586166433444620176494', '156.1859070520597902372482933184', '156.83470188830504005810786277103', '157.08817765967213678310350048863', '157.85466755508700539483712272665', '158.3804406675210068544892142218', '158.93543908181657729868037082603', '160.08648785356984719527771303912', '160.18402420103291647133928451412', '160.89960977659351837993469725258', '161.457254225172131772058323159004', '162.28796222668601668997292228339', '162.806444147018973507520040364485', '162.97648896741526907502915753104', '163.786281737094261058633425509091', '164.30984463888322892469836750687', '165.00604656452922531962087630130', '165.802717652286735985297441105389', '166.401367265342547284453220195033', '166.96149792969878650315045294021', '167.272231021155176306329757456805', '168.02350824777567553583780804122', '168.74712304405854755727331099732', '169.267010346792319619895167306654', '169.45031742088005954264863309612', '170.332918683871166572451640520', '170.94596451801509838844274791557', '171.92461792970064097248969933513', '172.04117548225003719770342347956', '172.95605049275101419420979728729', '173.38456469569071572367207956186', '174.01423765483640072558393918491', '174.205151450897943766131612804978', '175.27042340885575380569629168575', '175.60105481217307180266735836061', '176.21943214478243441650647385812', '176.96298010272925991600219945557', '177.41374904133825657174831188886', '178.38707830886568779485294696625', '178.8387677381307642117721928580', '179.14920172900270227380766790653', '179.8349265273470413576777144670', '180.33441880803072881854404122544', '180.84428665125696138108604191901', '181.75966089992778493311598818108', '182.138642109768799615761779832908', '182.73065947167360463045445707918', '183.50946326335522789306930341338', '184.22181412167198163346411582228', '184.57746677746210897793107946315', '185.017740052783777423052157137604', '185.80478956204343281927443851660', '186.38769086004863251328497644025', '186.808535719597031792854402451690', '187.09459160138013062183807937932', '188.367576390834502953022374964307', '188.79070649329709958181309523684', '189.40267400188850693921811745379', '189.689213611417217132880262190653', '190.607359756030588211731101811511', '190.93874843581723064436316151223', '191.788400937539633222365273138169', '192.1175865873001882354246597867', '192.47527222716369764267762476403', '193.30720283609632646545003133564', '193.99566725134289718703290565562', '194.73723580741858672074872631115', '195.28398965028450047801249800287', '195.66688594466637565249505617752', '196.31534651729982047549865858527', '196.87700408140304598184960064978', '197.457145810699918745330627943834', '197.90981308644636627527570626151', '198.63064178641815394669938612901', '199.155229591632600901130377038969', '199.68827498743285092038772310771'], 'prelabel': '1-1480-1480.909-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': -0.552919823285637, 'root_number': '-0.165487718498088086079207748238-0.986211850986540089394674985661*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.276459911643', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.38405315672655775996165025159-0.610647717702433474896440788189*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.768167784165', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.66702189025', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.78161332543', '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': 6.87309110492009, 'bad_primes': [2, 5, 37], 'central_character': '1480.909', 'conductor': 1480, 'conductor_radical': 370, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1480/909'], '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': '1-1480-1480.909-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': '1-1480-1480.909-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': -0.2764599116428185, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.768167784165', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_1480.909', 'Lhash_array': ['dirichlet_L_1480.909'], 'label': '1-1480-1480.909-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1480/909'}