Lfunction data - 1-1480-1480.1003-r0-0-0

Formats: - HTML - YAML - JSON - 2026-06-12T18:12:27.578012

• 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
  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_1480.1003', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.3420201433256687, -0.9396926207859084], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.984807753012208, 0.17364817766693036], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.766044443118978, 0.6427876096865394], 'algebraic': True, 'analytic_conductor': 6.87309110492009, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 5, 37], 'central_character': '1480.1003', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 1480, 'conductor_radical': 370, 'conjugate': 'dirichlet_L_1480.1027', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^25', 0, 0, 0, 'a^37', 0, 'a^14', 0, 'a^24', 0, 'a^49', 0, 0, 0, 'a^5', 0, 'a^16', 0, 'a^26', 0, 'a^21', 0, 0, 0, 'a^3', 0, 'a^42', 0, 'a^0', 0, 'a^13', 0, 0, 0, 0, 0, 'a^38', 0, 'a^4', 0, 'a^27', 0, 0, 0, 'a^21', 0, 'a^2', 0, 'a^30', 0, 'a^35', 0, 0, 0, 'a^5', 0, 'a^8', 0, 'a^40', 0, 'a^51', 0, 0, 0, 'a^19', 0, 'a^46', 0, 'a^34', 0, 'a^9', 0, 0, 0, 'a^25', 0, 'a^46', 0, 'a^28', 0, 'a^5', 0, 0, 0, 'a^31', 0, 'a^8', 0, 'a^14', 0, 'a^25', 0, 0, 0, 'a^21', 0, 'a^2', 0], 'euler_factors': [[0], [1, 'a^25'], [0], [1, 'a^37'], [1, 'a^24'], [1, 'a^49'], [1, 'a^5'], [1, 'a^16'], [1, 'a^21'], [1, 'a^42'], [1, 'a^0'], [0], [1, 'a^4'], [1, 'a^27'], [1, 'a^21'], [1, 'a^35'], [1, 'a^8'], [1, 'a^40'], [1, 'a^19'], [1, 'a^34'], [1, 'a^9'], [1, 'a^46'], [1, 'a^5'], [1, 'a^8'], [1, 'a^21'], [1, 'a^30']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1480-1480.1003-r0-0-0', 'leading_term': '1.24732951836782833393011057633+0.0396048060129871112391696087595*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/1480/1003', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.2479581195100435, 1.4060930491889811, 1.0940486201203472, 0.10043632646221319, -0.9599743621055024, -1.16523209211362, -0.2716364120067766, 0.8092182908505599, 0.6675365538754998, -1.212633741926513, -3.637752794811191, -4.500988635475682, -2.7167820323481138, 0.5338037614564395, 2.687605073064771, 2.1811046285634506, -0.026266752723476713, -1.4775680433670249, -0.8241859577401678, 0.7968541956269171, 1.1923347175151118, -0.24892038510857242, -1.8114975254326668, -1.556170756507286, 0.24808627909952413, 1.442717829152048, 0.8045824629285341, -0.16385218984451144, 1.0037382183185344, 4.360002505858512, 6.868608112711009, 5.69038776542841, 1.652050528484826, -1.470758833912468, -1.2049869098933208, 0.9767293753169968, 1.8426245374829158, 0.5223021890411371, -0.7594977986296143, -0.09682324869628808, 1.3375559031823043, 1.019615585704077, -1.1694389183713552, -2.5695668314587436, -1.468926363208714, 0.3143801858878805, -0.08223315295468818, -2.256833417535165, -2.6319176018614026, 0.7112274152859615, 4.969350771648636, 5.835285342820178, 2.9305995164459393, 0.13149574585195664, 0.38037790386573583, 2.144158166311569, 2.197369421134353, 0.3939705933835771, -0.49400163654209917, 0.7160317210921371, 1.805549073496078, 0.840088746328801, -0.4334598952546114, 0.9362220007802301, 4.203508951179064, 5.261761603083736, 2.340282254568936, -1.1718567960538855, -1.2810484191049647, 1.0308905533296284, 1.36853587339882, -1.5844050567469068, -4.155127435859651, -3.0637029727362433, -0.008647003754491133, 1.1810822043572078, 0.11771498423102866, -0.366120952506362, 0.6512714914319738, 0.7076117927111434, -1.46264790325399, -3.0262050129531928, -1.163165774884546, 1.9911123709240046, 1.8701271775105868, -1.707867795873116, -3.8828241105194254, -1.7155061812498036, 1.5819197162414447, 1.5519625009017866, -1.0081620245255098, -1.774993809429162, 0.24572004232217207, 1.5743762404177246, 0.18017596262639463, -1.4079079102706773, -0.6591379137096695, 0.6315561823056915, -0.421425267228605, -2.554948237189934, -2.292431001588367, -0.15373214713675293, -0.46350958091769545, -4.236271659633928, -6.562011762147116, -3.485519022220878, 1.8933241292484684, 3.702029086760389, 1.4346687727680751, -0.4267492408784449, 0.08643680673800595, 0.14637949245025905, -1.9599236969893006, -3.37395810952728, -1.5770641976019266, 1.013206751733367, 0.9080215126078071, -0.6915426151435243, -0.30266678849330503, 1.3049319215595159, 0.0682747444990591, -3.9254094769115286, -5.285559910931074, -1.4123150052628994, 2.964495710411185, 2.5675204919278602, -0.8329726453511701, -1.8561027320122037, 0.0986946814760776, 1.0385643622833913, -0.24083646986159146, -0.5838114669640019, 1.216081543117277, 1.9903544529495547, 0.08430880089397402, -1.2118765119792283, 0.6561159091786348, 2.5567112649916983, 0.7449722880252854, -2.313204964267628, -1.547262287807266, 2.135411481773072, 2.899488294559232, -0.5978953387462563, -3.000897228419676, -0.917005909135487, 2.007482111632724, 1.5953346425823673, -0.34182935756825755, -0.14379524582652042, 1.1121870756857863, 0.2756926096957008, -1.527560810323311, -0.9646167179437358, 0.7827700897727088, -0.41587186193944586, -3.7467235709398654, -3.6304334190828413, 1.090452928674836, 4.502053608446373, 2.7201019421071635, -0.24976054348679028, 0.36495655344678285, 2.339409301506965, 1.0517566419962647, -2.176719531335107, -2.5683059591179287, -0.2326755933259817, 0.5108967566379323, -1.0379320405966403, -1.413817814557793, -0.11363798326978808, -0.5038698523562942, -2.5919378087622054, -1.7443641155275553, 2.9512437753684746, 5.584669104729369, 2.4711623678337435, -1.5545701166034718, -0.7999876078991675, 2.390894180412526, 2.3668690294112205, -0.24410858893360482, -0.5851858644391743, 1.4265479571463568, 1.5286192134719534, -0.6319864599470312, -1.0484545528226443, 0.8430927786128432, 1.1380281299921775, -0.830327861172341, -0.9354251443584152, 1.7195477400759367, 2.4140299539549748, -0.5239016665738593, -1.7009858536771936, 2.2859401328738684, 6.206746349841646, 4.279361739966485, -0.5118186461345131, -1.6924851778914054, 0.4681254617250902, 1.129668754751655, -0.059243385603796495, 0.245427119808851, 1.384160821120167, -0.28057904910042347, -3.6026243158617057, -3.7185153931595094, -0.7261938063933566, 0.4352175782660382, -0.8270422569673963, 0.16405864056592107, 3.712141486946288, 3.7085133645562793, -1.7969304864692284, -6.09870464880582, -4.168016995939483, -0.14523336982190688, 0.544665254958957, -0.2380052089734001, 1.3675572221728136, 3.400334389691234, 2.3069797249585977, 0.04619104404932226, 0.017340005947868994, 0.20585428992258334, -2.444185838460324, -4.804426534380347, -2.485033933165944, 1.4109002162780695, 0.8332529529537818, -2.535114329390415, -2.058866478871001, 2.0982160707778594, 3.3964013620047355, 0.5585891190798241, -0.7605645211794794, 1.38098548851058, 2.2443716583640576, -0.19302669071668468, -1.7504390093438733, -0.37553456429848886, 0.42092437906758573, -0.8089945463453679, -0.6508168964874461, 1.2863410385567942, 0.1472202041306204, -4.70511129982145, -6.492656699684777, -2.0068736682238373, 2.414393570206107, 1.3556457799442105, -1.17097721058394, 0.030754609570353256, 2.1585213625000943, 0.717489295060117, -1.6944579036786807, -0.6995800620735204, 1.4854919239488162, 0.7723458727424605, -0.8694661610736549, 0.1007200890221854, 1.3684461564010157, -0.36568728119681226, -2.072093969801406, -0.17396050568347288, 1.291284228653879, -2.7298118933835935, -8.020664360749345, -7.0629529281816845, -1.6112094851618084, 0.6350359887189927, -1.103395646481765, -1.3287020018135742, 0.5981597577442525, 0.35519999104846367, -1.7968503803622382, -1.471457873485273, 0.8032554119244566, 0.6310529826785638, -1.174887706198599, -0.12740617499590443, 2.4939802577274794, 1.6580202495198, -1.0750398623430693, 0.31691964716825094, 4.5832648116166546, 4.556745356571154, 0.17451656543339078, -1.068225782484204, 2.601838122503858, 4.627808763084933, 2.170916463827514, -0.012028558900243135, 0.5247424990593632, 0.5430556843819083, -0.5225377965080792, 0.9760407502100057, 4.275258091615889, 4.067667798590742, 0.5992643895648884, -0.21685118821105587, 1.932340798959879, 1.0853797417501259, -2.98823164293313, -3.476989960305283, 0.6876982949915532, 2.2687520070459133, -1.2867814223429093, -3.6075337315708915, -1.322323054764605, 0.7554956975976521, -0.2760583061991404, -0.7416913030038931, 0.8740719025457364, 0.8068456714276783, -1.3752022313400514, -1.1684084892053468, 1.414182571411231, 1.2006330793879185, -1.3449214884228122, 0.18612621290880274, 5.5732802211885595, 6.773334888230408, 1.8373036551297877, -1.751599467964264, -0.43094318624731076, 0.5613269002819212, -1.3625041976481334, -1.6196522610937318, 1.276375326176958, 2.2490686555348876, -0.27799443985938543, -1.529700048179429, -0.10646190363588476, -0.023337867056282935, -1.4369109126127613, -0.3272384196494021, 1.5903442831329777, -1.6152906277084926, -7.7891452245928035, -8.178294288038405, -2.2364022749708603, 1.4579845647654779, 0.010098218256617551, -0.6765884249757572, 1.461596969603681, 1.6594779349327906, -0.772267224598125, -0.8306881315019956, 1.7555725560231665, 2.0064185763048363, -0.11379352376048185, -0.15704802645233196, 0.9657150457858873, -1.0408148872388896, -3.7793336664000434, -1.8431757015809427, 1.825705386850093, 0.5245458040579226, -3.1219332164514575, -1.4317110728370697, 3.9354716727463437, 4.859665404246495, 1.189245685168175, -0.46384817945498946, 0.6168493303155067, 0.08739268125555334, -1.270510329562755, 0.08644888012763806, 1.722606583694343, -0.20291511149851946, -2.3603827899289263, -0.5732012475845785, 1.307544491308713, -0.9747822037956745, -2.8269639508808235, 0.4150755671993582, 3.509669918921185, 0.8127670285990243, -2.712512533800653, -0.7659447206323413, 2.654351355233403, 1.4571062842432738, -1.3680100397903585, -0.770645404557279, 0.8642274897864846, 0.233952065321448, 0.13099753988797863, 2.1552080137790752, 2.0783221051925342, -0.8988645929910808, -0.8677584120877944, 3.1752803354192998, 4.123493223632686, 0.12327976839372404, -1.5399666381109371, 1.523466192847209, 2.3070577684738884, -1.6967865096675423, -3.770573709334511, -1.1976435599165172, 0.2532557822384859, -1.5738704206895096, -1.761649954220656, 0.7064029467283172, 1.2150441288402487, -0.2614899681895333, 0.4672495644341922, 1.9869763001662402, 0.16410016976052072, -1.705089212228243, 1.6126671949875522, 5.598411277298916, 3.0103421454902524, -2.3248929618160044, -2.181785967853859, 1.3011383557995428, 0.9107397019176425, -1.8717636564396738, -1.3961572673334246, 0.5715985702102724, -0.1069407217741465, -0.6177989315420663, 2.218717988213844, 4.174574530646396, 1.8836740966081265, -0.2733017435268204, 0.6334676377007685, 0.6889102295021712, -0.6050034626921923, 2.783100926892937, 10.295487069556605, 12.223636555102066, 5.877757804640172, 0.3849956172199769, 0.7727290356470107, 1.5921493824459527, -0.06901513099104162, 0.11126436712985835, 2.599541735626822, 2.3434025716545976, -0.3437800763915988, -0.4258405271476142, 1.0688845143644252, -0.33544070860002495, -2.2157066477447582, -0.2389468508201658, 1.6051119442153492, -1.5151411598245377, -4.453879182480605, -1.4472600933014714, 2.0847982763139696, -0.34368978115916443, -3.8282653844188705, -1.8735612058352464, 1.511340914129474, 0.7583378597631297, -0.8465195624058082, 0.5071408585798266, 1.4699535337697074, 0.02250447878080113, -0.01156890978040475, 1.5123008798753768, -0.3524651018620138, -4.2004296697112675, -3.151035047272261, 1.4145704833772843, 1.6305621613385104, -1.7155331592098557, -1.2148119495830751, 1.9110047198923754, 0.49990532226917095, -3.603369447985921, -2.9946429731743023, 0.8691042465786754, 1.3922389110162772, -0.31262458167649326, 0.39290867283062997, 1.5056824354182348, 0.0855466942792629, -0.41868295897990526, 1.6346788951130178, 1.0401146142394673, -3.1078845103979758, -3.748160673631408, 0.2156265718674945, 0.624028839820878, -4.127978177877765, -5.554074143754789, -1.3398349415828275, 0.9684677946654089, -0.8594027667375839, -0.9741048066313451, 1.1848633495096292, 0.4214042708099398, -2.1621442676971294, -1.321165020279805, 1.1261238790702985, 0.5787715164763152, -0.4990605552287811, 0.9490087110045056, 0.6834769590898901, -3.2460507902496287, -3.989218061675464, 0.9525192324649827, 3.0372428283608155, -1.7865410514465152, -5.2744160664859585, -2.4393970453350833, 0.36240655542702876, -0.8276331117919096, -1.3315013451150257, 0.29987160385948197, -0.44489652377910127, -2.8866604244001515, -2.0229442890469542, 0.29354155511579044, -0.9178885630310893, -2.816899357195034, -0.9040199596204934, 0.8720793428711097, -1.1226614158011272, -1.1821744686255422, 3.9045868340664858, 6.109217215912171, 0.6313517914535824, -4.4000451324826075, -2.682778389471656, 0.23316114168569146, -0.3119020110717909, -0.42767775667244023, 1.40899463331853, 0.9350762682315541, -1.2249213911457044, -0.16895017348271443, 2.156884299406107, 0.7190147627636029, -1.4438925760162495, 0.17744738985956035, 0.8669246095105995, -3.659261413069607, -6.687760643765639, -2.765762605027421, 1.322575900964565, -0.246642103724488, -1.7459114762380572, 1.1817721478913683, 2.811740617685496, -0.013779473113826518, -1.6688928657428774, 0.042154710400679994, 0.4712655304580945, -0.687020152492823, 0.35496614556570183, 1.3036973041076727, -1.5452063960431945, -3.360971086105113, 0.2670596840232386, 2.694803608735057, -1.7267275155747424, -5.977607703621236, -3.520673395580341, 0.008239909235381891, -0.5124191032293537, -0.13589693442787917, 3.6358513793121263, 4.497504235918128, 0.5771195834520755, -1.6257004292854593, -0.3180500205592814, -0.08283833471062581, -0.5505453020486327, 1.5037402893957206, 2.524218682945609, -0.9085336733002503, -2.8782337953478767, 0.7563909880573092, 2.8715737805260138, -1.0503464540766398, -3.27511759714258, 0.9655924312142732, 4.188795134344379, 1.7652222038994088, -0.1903474451978045, 1.3683550365852581, 1.5006024354280656, -0.35108701357815264, 0.4356171494641148, 2.1120346304660282, -0.11987571228232256, -2.9616236820731103, -1.535036301605712, 0.48297728134821266, -0.1357087209189292, 1.5893595081803813, 6.6096086367681615, 6.462995499381835, -0.4758675839942258, -3.976511960655607, -0.3276287703400754, 2.067473587317109, -0.14974174231658488, -0.8883330029730809, 1.0305231738550398, 0.8576070632664804, -0.23397048296361708, 1.6023542199389433, 2.9322033421595783, 0.36659092330200477, -1.050995600660457, 1.558567995652936, 2.289811987686459, -0.5838479632756639, -0.43688968013925755, 2.7076963903407556, 0.7847262588898223, -5.181626501089499, -5.5850963484082365, -0.626140433633213, 0.876956982214273, -1.2462318549407378, -0.668982244592597, 1.3215453868582139, 0.2903807918871693, -0.8221597533175722, 0.8996849794012568, 1.3096101284429222, -0.6925231091182131, 0.18053094914710222, 2.92469572026873, 0.5803779077367528, -4.504873664412602, -3.780372827331765, 0.46765137254943157, -0.11062664550621423, -2.930909996692935, -0.7847899391890012, 2.6673778648799256, 0.9488710049725787], 'positive_zeros': ['0.963878217054549540250672393075', '1.94366541005629782850514988433', '2.64136714138803090416125497659', '4.01063742457112351419931979303', '4.99633387347823200740389081635', '5.77932405172074527949656527473', '6.521394616689693076703555473684', '7.45975854603066953466408168309', '8.34181446242416829081290773069', '8.57546103847899252391406899791', '10.131858329784192926436072437224', '10.79984413360759706311989794206', '11.6566364173340270586764325773', '12.20745891078863046611609874375', '12.972132297533040941780069535644', '13.986227130013512686246385256745', '14.35967884015780515997415794887', '15.26299901318107739774348142757', '16.5963132320468839346584608324', '16.7826234118326455391393763843', '17.88586853138196038451929647038', '18.29703117165099462015847534349', '19.222910474141518290065122155143', '19.561957180700835029673308046534', '20.81029980341337683606555634790', '21.42572482323853280077251495569', '22.04606477769181311919927470130', '23.12603902000736868814920712874', '23.780286766024552492719621397701', '24.20051082687155812932208793620', '24.816207234936758531210178244603', '25.73012915699054960882849735955', '26.42762158664857110938995854977', '27.33122270381115816755175291308', '28.004263339367787565962130687357', '28.718047872377402303604954136246', '29.401177059033917715292388957727', '30.124295710771814781058494316053', '30.56028788618633530903434260526', '31.595414368793960213596740345777', '31.80102725796218379368078108582', '33.00609504428784770269155871496', '33.939328133065327597933333685082', '34.34619385810491281093532707387', '34.72248783400457609336613077486', '35.7922049758282507730657198092', '36.413625432100736926972057957402', '36.929482197381858014685022080736', '37.50651381187572243837732449465', '38.52066525026734872409983896712', '39.29451681339413304343551104997', '39.9856279105827368697648584967', '40.57456660258886140270708771677', '41.06292898724650407144771267327', '41.88613667974881469283632044280', '42.424170309243051429994570830542', '43.191571682133953324510262870996', '43.88392801628088147947695775631', '44.642014555860731712422723878803', '45.39336165482253623076427269870', '46.177517118192386131758714711787', '46.59467614873444583538490542233', '47.23036476028486250019896412448', '47.9613383189209649629864481457', '48.39145214811516830698229027900', '49.311613238725119068966525831071', '50.26834225780795768470955594097', '50.569156635551223562385406615990', '51.3484753058596876933543268329', '52.22271287170308880993600153250', '52.62422069866930329196612704522', '53.47982374647649997073630523075', '53.62836384550381958223870089437', '54.505960921711522078565170952625', '55.47479859100980515123144105653', '56.01337263931201249292638304901', '56.84126842633728992438385203216', '57.28824073589401749018534313180', '58.033952073382335196789716219505', '58.61922396634555612302676799956', '59.24922667672538071329599257162', '59.81274971934962676943551046455', '60.575992504649031119357220251196', '61.10800064335490167883125481284', '62.147237246244522208097168557122', '62.74724668838454505847997826967', '63.417457608306206644902534204570', '63.68533380872286955451094766873', '64.34730625913791455281936986820', '65.406597917845438427295414377892', '65.74773356763223461279339519759', '66.23219112954735330215568911322', '67.10013528283155785483904687902', '68.14241872036999673617418714289', '68.596309661865294609675777770752', '68.85600936805451274872885625302', '70.01120498581557542337975460393', '70.30604923564206986386703265897', '70.67057917616417872430776219435', '71.73927562975106079490899183888', '72.264147761002885197942341116869', '72.97213351521071077497362949337', '73.81109522255711338178860946054', '74.20522671614141191591258971152', '74.979145104671091647886556487057', '75.69475840362998669450842474869', '76.06950023882906083559213334958', '76.66766877478889275808662868816', '77.19964456050708895924216604121', '78.234587002524754151288467347448', '78.88543071232328730800523537708', '79.3714465592678011722332130834', '80.0751060834080948885259264202', '80.708946349745602226075957093313', '81.36654646478797462699163366205', '81.858788843862989914078176219791', '82.45697010052181858383735530834', '83.143749783049811766347719812108', '83.5897404102582191833546593329', '84.81694270484420688446512393862', '85.14545697086742735326227959005', '85.83435668284582216540707389460', '86.30390606645662695079563370955', '87.0660861056570519847653754115', '87.59904326607506869360771363534', '88.13941322096409189503624047842', '88.91734115359214641283607800609', '89.348731068817920650236333005444', '90.326347298493075360630665830198', '90.74197064473302095984760517809', '91.86887264174430067784526426586', '92.00040585328301150614059192670', '92.63815454602418903281342417670', '93.01002897500237825285399997330', '94.13483354638647990344658400440', '94.41530436870829551282297298831', '95.088853845717338579324530972423', '95.888465536084792405110619816583', '96.46983008084207957366830143507', '97.3289708098934446777112250293', '97.758272562159252369572782397423', '98.281817547498638645733351950503', '98.86966459663380043340779592017', '99.51536883833638557166782355743', '100.13715304469036716539632620232', '100.61175679930697815230813116789', '101.673192919563606038874958671738', '102.249902003369698547472954389499', '102.62016970260887811415724110698', '103.311422794705324586598670717778', '104.03183942170778521229357057649', '104.71247461781454137812551524932', '104.994218656048864450814439059045', '105.664254755612693250660503925694', '106.155710573855420485791914790598', '107.31630609797228417875736705817', '107.81394959510358304853114616925', '108.24282140317313968421032530410', '108.961612575581446664541228275879', '109.48254023168820946388012501975', '110.29178269404146789456789856611', '110.659533453396073565128690523336', '111.14697327800287144602298183878', '112.00897348289559998909173368324', '112.540696503728188971452722566733', '113.20904591175978667720857959605', '114.191142880277756168087332496669', '114.52496831954446605633682666093', '115.01608710174012717461532105620', '115.61384674689413228599301150676', '116.22963931170544311868016127250', '116.93500273159770546976243038309', '117.40845700674800724072810871398', '118.09719580823103984598797820350', '118.8041578020563596706529394767', '119.432032690681619606008780199655', '120.136807780390472465262419532903', '120.74028488717701169115097548143', '121.322764164236179387051441259405', '121.52670231748309985910128576331', '122.404318151590142320784778741411', '122.89237224504223143516488070515', '123.75930645483146895467817439988', '124.24168829243070256445259681205', '124.88424417342712159555307543622', '125.774555972422822141100833672818', '126.00900617156850701214793117488', '126.78587184092473422006422712433', '127.42836553651719152122493230119', '127.730492676176352844211075272626', '128.45418169617876846702988618834', '128.959232865385777812417465775816', '129.846412295725995881452911937480', '130.49464453496432910180959744554', '131.03241931949418731132105956143', '131.75269243001051358656198441143', '132.16600967833611874629609997284', '132.60070469868694217026050814943', '133.66103312387397020573816115552', '133.91748900612681027030238763470', '134.50640070382062756912426309443', '134.82113013684848838342129673690', '136.3498153921778512596071292086', '136.37316209035058012602704331997', '137.1739649827803568153661838496', '137.482007764716699684425054671528', '138.38916164237819966438568584280', '138.82555210686141215197119588767', '139.33498427747743845880160151308', '140.02335295582900120268570343460', '140.516936460561619597849638782363', '141.343057589395317509521664014632', '141.85113815815565653627946113924', '142.643140483946263245172653527641', '143.22861943661124117608400773092', '143.672538103282077373635696052808', '144.37990108809424995944776264557', '144.68997945256933292092158311103', '145.28381505494044913445587248248', '146.1433494979614610111639120507', '146.71005642945151385202414308701', '147.29761764613950593291676862739', '147.849267354006006416576226322280', '148.66965889561697393430083518270', '149.29514784595889025610327246245', '149.61306216834788267056926782786', '150.32728492390607683719700234603', '150.70503862691882915681266958560', '151.337363899460841373349057266470', '152.169303689301022300694875920731', '152.55370293315144469054163549429', '153.54147315484656356518549698610', '153.94091996039231616295396419159', '154.51057759554136621422669440268', '155.047247367747149488300995094324', '155.77070842177250159173060120182', '156.35429760195776695594118342520', '156.71106713341410912702121373307', '157.25534399192920868175553794753', '158.07074262097822480181902413924', '158.65737499588538750645685828034', '159.5977339220786953441570499484', '159.858721958939960666288030695019', '160.557733426245923116559855370979', '160.87419397740103669499085119703', '161.807352189389540147245471780142', '162.06390186604600710877006841403', '162.910141315790681199043275597', '163.30183304739230350767965701266', '163.84346178984303684435947080984', '164.71514616384505510840104094366', '165.57490024806413873444644847919', '165.86123936105756308396022103923', '166.3307637623573248004143933164', '166.99503997842881279009257826603', '167.51886835521374677981560423780', '168.19948644715760176574270474111', '168.72838033220879352734537385018', '169.151660220284973151836998928127', '170.16429600206939185722544978542', '170.59964400723775400713219083805', '171.15043529568244787867135849125', '171.87372843432419327233060389159', '172.49292816161872233706109634806', '172.926385455835794837383644197676', '173.38006924597449347424398190855', '173.93051617791548844477730009455', '174.67011087961926069418640941139', '175.22369097586866190460897024516', '176.24817663066237127414542534338', '176.44037915889396614007167933717', '176.890550464660200846103065260333', '177.85741328247069560940270948963', '178.525396185213781842917039720556', '178.71623184830937516005835799912', '179.18832136651628037316121363337', '179.93371269261998530635647360776', '180.57429363960547096471969746556', '181.1841096375309320563032447488', '181.82012114327940493313714145742', '182.70631175316548121073811261161', '182.89068906434778776863756977310', '183.67352519173945884789166071471', '183.996749700609439749486548970812', '184.67750444493436824328951027570', '185.498200509390001991615441590784', '185.88048657499590783102973394367', '186.07581995375601618590859908273', '187.16690460082683091211151370521', '187.83494803514307739368102411521', '188.419585557255656823173672398048', '188.89872377950389397493016659776', '189.5507659738753686562878343240', '189.77897171292522169928889398029', '190.66174120176079991524848777638', '191.09275870753980994200796183060', '191.80974340585864910128319109282', '192.23226059569347586372547556518', '192.855413688227808123000358058093', '193.798487277233156953210796568322', '194.19604379798389784917336390004', '194.77335939461040278584403121536', '195.35684132694895870120846552586', '195.805714403515094124188280997809', '196.44754093556403212974819583635', '196.85525155719772026033175790402', '197.5335866794628308700240990845', '198.39009174503524869646530504935', '198.739042822522908944296361025523', '199.43055199254606738539785717936'], 'prelabel': '1-1480-1480.1003-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': 0.010103478784855936, 'root_number': '0.997985692570847943887481080447+0.0634393996179422796677977004866*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0101034787849', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.954075477688404232468953800369-0.153588102738806114766548243013*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.963878217055', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.94366541006', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.64136714139', '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': '1480.1003', 'conductor': 1480, 'conductor_radical': 370, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1480/1003'], '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': '1-1480-1480.1003-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': '1-1480-1480.1003-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': 0.010103478784855936, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.963878217055', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_1480.1003', 'Lhash_array': ['dirichlet_L_1480.1003'], 'factors': ['1-1480-1480.1003-r0-0-0'], 'label': '1-1480-1480.1003-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1480/1003'}