Lfunction data - 1-1480-1480.1059-r0-0-0

Formats: - HTML - YAML - JSON - 2024-04-25T19:10:25.364373

• 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_1480.1059', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.5, 0.8660254037844386], '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': 6.87309110492009, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 5, 37], 'central_character': '1480.1059', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 1480, 'conductor_radical': 370, 'conjugate': 'dirichlet_L_1480.1139', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^4', 0, 0, 0, 'a^16', 0, 'a^8', 0, 'a^6', 0, 'a^7', 0, 0, 0, 'a^5', 0, 'a^7', 0, 'a^8', 0, 'a^15', 0, 0, 0, 'a^0', 0, 'a^15', 0, 'a^15', 0, 'a^10', 0, 0, 0, 0, 0, 'a^11', 0, 'a^10', 0, 'a^9', 0, 0, 0, 'a^0', 0, 'a^8', 0, 'a^9', 0, 'a^8', 0, 0, 0, 'a^11', 0, 'a^11', 0, 'a^7', 0, 'a^0', 0, 0, 0, 'a^4', 0, 'a^7', 0, 'a^10', 0, 'a^0', 0, 0, 0, 'a^10', 0, 'a^13', 0, 'a^4', 0, 'a^2', 0, 0, 0, 'a^7', 0, 'a^5', 0, 'a^11', 0, 'a^7', 0, 0, 0, 'a^9', 0, 'a^2', 0], 'euler_factors': [[0], [1, 'a^4'], [0], [1, 'a^16'], [1, 'a^6'], [1, 'a^7'], [1, 'a^5'], [1, 'a^7'], [1, 'a^15'], [1, 'a^15'], [1, 'a^15'], [0], [1, 'a^10'], [1, 'a^9'], [1, 'a^0'], [1, 'a^8'], [1, 'a^11'], [1, 'a^7'], [1, 'a^4'], [1, 'a^10'], [1, 'a^0'], [1, 'a^13'], [1, 'a^2'], [1, 'a^5'], [1, 'a^9'], [1, 'a^0']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1480-1480.1059-r0-0-0', 'leading_term': '0.385580369577209069203916300628-0.109982830690534754122737204662*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/1480/1059', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.400959404990081, -0.2630080965543294, -1.688060939188635, -3.566858795666916, -4.759992219417557, -4.2082582684195025, -1.9695267631153084, 0.5605512171179863, 1.6419726077839647, 0.6920721408373236, -1.0966677176586757, -1.7879707716607307, -0.5542578079277073, 1.4792191537153012, 2.3830570840976044, 1.4736342994537461, 0.04746948806581951, -0.1269856754301503, 1.0530357607654508, 1.793623868817381, 0.5699153735663528, -1.7384289767972578, -2.458008173977271, -0.125490319875138, 3.509694050307708, 5.069737003639851, 3.1873539015283794, 0.025333416650681943, -1.2110752859308793, 0.10964889314069627, 1.6183226075884014, 1.1340721020770257, -0.6204538836002303, -1.2270899713069563, -0.014914972062232539, 0.9456447642153175, -0.26914905117615606, -2.578792742250094, -3.160080357683247, -1.3525106531620403, 0.16260645445171082, -1.1226583078660513, -3.8563278452309744, -4.162299202871707, -0.6258659208634542, 3.5909334770232975, 4.486627250313146, 2.009233990268035, -0.35059531121675586, -0.364440440506788, 0.4174931220579474, -0.3461815487895856, -1.9762300926373872, -1.8278885330313848, 0.4388131058168995, 1.9645213539036992, 0.8290500644393572, -0.8481737904592437, 0.2048541010350713, 3.412086581235195, 4.691607819908767, 2.1151610893184376, -1.120597650603723, -0.9294560699741834, 2.0591032195276524, 3.5022795298601994, 1.457530354858486, -1.2074634296823987, -1.3027508617685803, 0.2536620264235741, 0.5275795698275653, -0.5268670110738604, -0.21770430556291454, 2.0435440096806983, 3.2431448659635342, 1.4611335367840805, -0.541687532911443, 0.9599739286055411, 4.78576928339835, 5.9738828305933405, 2.7761387707281577, -0.7742350014838566, -0.6637823140384547, 1.564895923358503, 1.6870285418484783, -0.6542419230025316, -1.8132886409035058, -0.19043416211828504, 1.3554290779830467, 0.35115052697364374, -1.3379668544798, -0.8959519485972058, 0.5480522253378981, -0.050231608464095, -1.8983439047903512, -0.854216663669574, 3.7739965158904, 6.957129147912067, 4.670562316820517, -0.22914665917863755, -2.0815791739718015, -0.2996067758456592, 0.843029363582212, -0.5134790581552796, -1.3378764371178062, 0.5338305241915404, 2.4671894437552373, 1.4592449486898753, -0.7837506375086178, -0.807530351482343, 0.7235909476513571, 0.45236144510134524, -1.3135308929705054, -0.5672713131521478, 3.330557334495889, 5.362008043045603, 2.11349188722889, -2.607659013643657, -3.1364508796174637, -0.14141010459221057, 1.1110634644553368, -0.83223426065766, -2.127148556913226, -0.6551124375564311, 0.7297712141907288, -0.26328989125329716, -1.2941163490889944, 0.015369645007865763, 1.271019418586935, -0.6851533587115577, -3.6874144885139533, -3.2057463154637693, 0.02429442459567315, 0.8750752758443341, -1.6358996176213036, -2.4510018346494498, 1.1494865493928195, 4.67645137637109, 3.324503596840873, -0.6387875913770836, -1.8773215582315967, -0.18759975895388895, 0.5659684428000851, -0.2630140323264987, 0.23849030572434196, 2.0975693960199546, 1.7410241496302201, -1.2358727492711905, -2.377529001263307, 0.22044386790067755, 2.1651565263756685, -0.0032240597829976845, -2.597060958611039, -0.6778905988206085, 3.5195327185115515, 4.002234572512623, 0.6387927700587492, -1.1321566480344334, 0.4858852156584854, 1.407532329071538, -0.5211929827085837, -1.941077078008677, -0.49083237840485133, 0.9670756992304447, -0.014069835488326366, -0.8495780473362798, 0.754095608976995, 1.5341432794416054, -1.8431408954965633, -5.7323801413401565, -4.35947304272141, 0.609183937984347, 2.27173385895742, -0.714570172088792, -2.736811326262425, -1.0065966688068917, 0.5706458636476374, -0.7485088293348293, -1.7687066503279536, 0.14554906583917557, 1.8893270441779655, 0.3580784755820878, -1.7984288460131739, -1.1736287254759548, 0.19301134671825393, -0.6952750981907885, -1.1169586493362418, 2.8018528472342847, 7.766609675916011, 7.142949454919499, 1.7041899345333853, -1.2186783297436856, 0.7955775568138309, 2.4725060310685487, 0.6198603911159003, -1.1494426751253513, -0.027639820814372346, 1.0001954690518127, -0.44014687357031984, -1.2671755606527815, 0.9197411783753127, 2.688603892169442, 0.916946843928112, -1.2292746990587844, -0.24091789645528489, 0.7506105388906372, -2.3088773084682597, -5.904603759368649, -3.9733492783261632, 1.4972475569198371, 3.1876878172863536, 0.1483683432197273, -1.6716596980668994, -0.09191152328890956, 0.6947726118715978, -1.0749842634424913, -1.7254803827916658, 0.19597754976660706, 1.1308232723082945, -0.09374255867822925, 0.3098358844164945, 3.1617542352089822, 3.412608995037723, -0.8312043395679947, -3.777220014697525, -1.3866987158115596, 1.6905293416200287, 0.48978281827215253, -1.5748154745708096, 0.6223109987124158, 4.29281216696077, 3.6619101778062513, 0.04989198576929937, -1.103337740216417, 0.1979539628863773, 0.05021956315653109, -1.1294845804247726, -0.21611942735524625, 1.1311930665365677, -0.8942477512697866, -3.9170072547761765, -2.4972167620770866, 1.6515318555782632, 1.7710625220896514, -2.107918675132223, -3.0503374396590877, 0.576845985574916, 2.593042448599193, 0.3220664171412553, -1.2464851109516522, 0.7007885929407818, 2.0195053187373877, 0.15310187142283052, -1.1731851818857046, 0.27422742304901654, 0.9441348395333057, -0.9017895242092091, -1.3229374640537708, 1.225472309757717, 2.0930627738553755, -0.46981664437800286, -0.7639042386063809, 4.096031893017543, 7.573151374617068, 4.082389606131765, -1.5855641189718896, -2.4986932177227246, -0.26072071764211885, 0.22848392739221435, 0.12428046678871382, 2.477454267460158, 4.493287869137786, 2.4085756961016913, -0.8469759779237525, -0.8998211497531325, 0.07237119682122564, -1.5209006051675498, -2.8672562540614197, -0.5401715300954943, 1.2513871163382442, -2.495588355132683, -7.348518138696243, -5.92659103002594, -0.4316276402167405, 1.4288873461430311, -0.6002852507108806, -0.7842448669491453, 1.2523281175459335, 1.109043818533599, -0.8129348486006567, -0.4775285026296602, 1.055978351644442, -0.1979175569864099, -2.436781399678606, -1.2123628463122662, 1.176572053484097, -0.5413863916072833, -4.005802056905749, -2.958205183671468, 0.8001333055585423, 0.30116285274117094, -3.6418712266387496, -3.8587344022853145, 0.04567694445757996, 1.4780623578323853, -0.8698133753829306, -1.7426017553474094, 0.003510979662709057, 0.2534641558392305, -1.1472545360655113, -0.4738609561302552, 1.1930253546749392, -0.2844144756696456, -2.750195771360016, -0.8132727790302385, 3.1086372286362165, 2.0007696435140176, -2.7999800248237476, -3.5108478055612053, 0.30898678411239355, 1.8185376231522747, -0.005407791547094724, 0.5305793049648684, 3.8744782740138155, 4.30919603398074, 1.1606028832215942, -0.3510739122507386, 0.602198585047354, 0.08866594306986109, -1.400173455295144, -0.1343468337162651, 1.8653056150500138, 0.009658017680725293, -2.5995733292926944, 0.41533808292669433, 6.169663026553319, 6.381797169283766, 1.7015330034743865, -0.07565319762231465, 1.8883031165044322, 1.607258034626759, -1.2685075794250111, -1.4977700290091789, 0.7318273538305381, 0.6052671380574092, -1.1955509158009665, -0.296819029974857, 1.8236775919505064, 0.8717181353914871, -0.9390270986665004, 0.6910804061327598, 2.5912144773209267, 0.014510689698227098, -2.8238244385569806, 0.2883773449642219, 5.208336171570384, 4.063872047936341, -0.8480752248406979, -1.8028515195164665, 0.746840135960232, 1.053512083959713, -0.5344984991243249, -0.34023106854553875, -0.2106733301078976, -2.9738838374285277, -4.781064521141754, -1.8693158985119307, 1.4749353240234562, 0.813319135622633, -0.25204196701737713, 1.4257500386509026, 0.8721706978322108, -4.908156637385417, -8.749895553189264, -4.906288822085602, 0.697457038647974, 1.1081417488415157, -0.47099334941960236, 0.9351166281086953, 2.457297221133427, 0.7779346827051191, -0.5890234873671878, 0.9039905375113467, 1.4658490174266388, -0.3889840788538572, -0.2202449792269825, 2.3263189628928234, 1.3331064298995117, -3.3274058935293738, -4.119919203566305, 0.2277860207587468, 1.998672133605396, -1.0025609262853248, -1.8267024099560114, 1.6884504037692896, 3.1677416687032007, 0.6598728016405793, -0.16816438081624394, 2.029752496910163, 2.1472456550823384, -0.39931732254283125, -0.9860391553303667, 0.21430651217057634, -0.41215383878762835, -0.6589848026326324, 3.15318427455316, 6.204924762964888, 2.2800293115702086, -3.7970952206961934, -3.6970216442414556, 0.027532688999050932, -0.0024730928950356967, -2.023786363943242, -0.2589692833428466, 2.7935407427319654, 1.8279882033409072, -0.4580101107258885, 0.5345555152641083, 1.9587828080452536, 0.32765855805599214, -0.8952588881868027, 0.7883973905546939, 1.135192452189373, -1.3449891435466175, -1.267875846133665, 1.9679660946474162, 1.0364155034153966, -5.0996759037432, -7.464880389310194, -2.8069487993075297, 0.9987362540773348, -0.24918146761792392, -1.1475093324438004, 0.8522669373636682, 1.2689273012805544, -0.5225451892070713, 0.10395089187092982, 2.4535468134314233, 1.572370937380957, -1.0727867614940376, -0.6569202635314241, 0.41326661909565576, -2.3426519392951834, -4.882788904900366, -2.066634399819677, 1.0899627174726274, -1.4821919727243125, -4.60128956958785, -1.4830217513521184, 3.2328917211567814, 2.490564143234813, -0.597709506018808, -0.4728627343755396, 0.5569944502829216, -0.5143048884083361, -0.5534246892708614, 1.4602229605232844, 0.7690478558462344, -2.722074697530898, -2.7488987506690092, 0.8076521706702978, 1.2952021704465788, -0.9740005637594531, 0.8206572099626364, 5.378699611438104, 4.806174831354541, 0.18090178469973642, -0.26304789284778496, 3.1759744431753707, 3.2668897151468324, 0.19897577496241747, -0.3411780081590243, 0.841974656310337, -0.18254836604192884, -1.0142622950626212, 1.2695861006731535, 2.6048210475679245, 0.4692245726648343, 0.0037437342452015174, 2.886295192986908, 2.273196367533787, -3.4100462318368927, -5.51413747162664, -0.8644102120423192, 2.404135863355148, 0.30973478359532935, -1.0828847113633457, 0.6314381224380656, 0.2663627410474717, -2.513084807703458, -2.071693488765529, 1.0533854050672962, 1.2231203453415622, -0.7458081192914839, -0.4704101946435727, 0.06847456972718213, -1.8547347881019383, -1.527332856300581, 3.550201495560998, 5.5924017989058745, -0.13144855023580485, -5.395522714043569, -3.3196595169366074, 0.33890494588932873, -0.18383068219916884, -0.7939759436154611, 1.3778898894808564, 1.5283016961414315, -1.618329764081365, -2.4316418769313533, -0.127123696564448, 0.15823232397589454, -1.1912723844440696, 0.10516486198126508, 1.4560841451964333, -1.5063495611905746, -4.143320906712426, -1.1944126039162133, 1.7425769508403899, -1.144628357082604, -3.7274370811287847, 0.26990896891995997, 4.82695618454999, 3.2915025699389746, 0.07940483356830354, 0.2602036799512193, 0.6131131584939793, -0.8471267182767128, -0.17202342219101932, 2.3956303440412263, 1.692832146517875, -0.9071266321887896, 0.24908115248007073, 2.718580080609809, 0.7499175412856388, -1.9701212106667025, 0.45410572529785637, 3.1936551044707375, 0.051086054292346667, -3.438754896760136, -0.6610261493969299, 3.149586587985437, 1.6716840597872304, -0.8787318779474008, 0.11954689764201717, 0.957148817477682, -0.6580135571130712, -0.8103310260257945, 0.552067719574888, -0.9436015434658405, -3.0504879081866414, -0.2752656838592468, 3.6202387269561633, 1.9582263990363307, -1.0942269736878965, 1.2705641720881067, 4.369647481348474, 1.4817766743907848, -2.4951376402439855, -1.1976289251242092, 0.9316723659337366, -0.9628231032801675, -2.3681026579720603, -0.10565290048455067, 0.9906604041723618, -0.8400174565307097, -0.8922476262425887, 0.8939902186879043, 0.27462211105267714, -0.32984503775533774, 3.464278365858225, 6.498687895146523, 2.8564303695462425, -1.1981161130247195, 1.6181530902141805, 5.540408787235036, 3.3184013792139524, -0.28859052758804193, 0.4765789680437704, 1.4485242091283541, -0.7463804989929608, -1.5797909414080111, 0.2192559913121897, -0.5001151249102914, -3.345058744490209, -2.61307840680493, 0.37018348526347455, 0.3146203212568631, -0.5999491374478491, 0.8719508908878205, -0.7264360728993339, -8.352549987205125, -12.670954534954603, -7.249220721066803, -0.33454463515570254, 0.3119598722101748, -0.7681959430686099, 0.6000601492113831, 0.2729245037082363, -2.6012411169872296, -2.5476805754369725, 0.15715958145526052, 0.16446057084125235, -1.0637456070547895, 0.7720335025542807, 2.1232958151416814, -0.7553652401421582, -2.4626982768753765, 0.2859718688032243, 0.550635450485826, -4.451958578161024, -6.23880014578979, -1.5879875206254785, 1.0695084789927285, -1.4469533629364166, -1.9848459665187514, 1.2164075281029718, 1.9215470357732531, -0.2143983749050127, -0.19888859404933557, 0.7973093649170757, -0.3437173714765697, -0.00244801317312914, 3.6163034452504297, 4.156760835262513, -0.03371941270907724, -0.9908898185329683, 3.049116365510561, 3.8799773025070756, 0.3277487099980676, 0.20934727005697817, 3.2695703947275954, 1.730076074298679, -2.976507203313712, -3.026256320179798, 0.13984810487535024, 0.1976873760144315, -1.1505956117555278, -0.2538934358002971, -0.2333379225988746, -2.3059691908513544], 'positive_zeros': ['0.22003203272803682752313057993', '2.10873638807366402671713618318', '2.931774335543905711024748564044', '3.834495628938095273045881052928', '5.01520146953331800143635437013', '5.36199726646740404677214438322', '6.32837449451264779788916109580', '7.1985447901931358182729100030', '8.44054563375828708170577649003', '9.04468630926865737595958514825', '9.887752268364864593372980780374', '10.62799791176041756658814892377', '11.2103153362051251522801750103', '12.42231854687999273701169741845', '12.62793893705029614924646088134', '13.79154277571384599030094781009', '14.92866906279857131404240597251', '15.43073678606550815601254956954', '15.86312383602141372512362555179', '16.82074472246602840784764421771', '17.62538146846000089705903151133', '18.09994397119574901384513445549', '19.24302515472753756992374474204', '19.79713606832715536778370982459', '20.7739943174966125464393882649', '21.5064313911746846713085322792', '22.0341449061440776943788377271', '22.53982966778268071511134985661', '23.6224553525410958130250522586', '23.956502461387848825813807202892', '25.219078863153990344213532994', '25.72027572392945505538531775095', '26.48185752060638816909930149092', '27.21398025008917948376376297476', '27.867251867543543727838518820', '28.60910791115714022023177124667', '29.05373512011102001350537949027', '29.75871753622011796424761601087', '30.92036951102222926717235910398', '31.606221477090091672873319749083', '32.09870606813758748244171440504', '32.747871176555262229237330509466', '33.624206650094465768020522410253', '34.220703135301993427714655507139', '34.76780330463642627244286052344', '35.36919825024476000794725529272', '36.37581362478861137972409853545', '37.20285219818368123578544084917', '37.7054724686617933475089533557', '38.539090327030070059645101533766', '39.01243918103426989267500814748', '39.68512023533495557475670065934', '40.24404816214491332056534049272', '41.247326868293650638996428655859', '41.69503499381399877458166293744', '42.422545009114199465041587293246', '43.38070792419764974792326622394', '44.09654756755988316095071065195', '44.58765100377210855062313576774', '44.94984788345978108548686718408', '45.81521259574420313873390924123', '46.54165642512048425076948519894', '47.187210265222728191961568941907', '47.86209195761388473267268977861', '48.81168111455805954798262376601', '49.304565619878828058536859991610', '49.93428939246172294177086895449', '50.69661888530091478810094636368', '51.24728405649704202841574111926', '51.76285683143221629282836403636', '52.36995523515658490099839960244', '53.3957742914186729459080168038', '54.001273107624354370128907809434', '54.82370300549173181416695391313', '55.19057467347268429670340070672', '55.92048923214154784282194443515', '56.60396017971882903158393488655', '57.4156702690715709514436725572', '57.65778406140052111502133241639', '58.25682171791232461024855462688', '59.48958754496101083750856392639', '59.91515006786320252605701470697', '60.69884114708407077800266605956', '61.2546748879795118428383922019', '61.804495850199889292165754811604', '62.39875708610735411900080950536', '63.22576881422756603736885195592', '63.78810055354782159973468839887', '64.1883631670139233909198437521', '65.221538425997497403736412453051', '65.95103673634690597441849650131', '66.576970766607039496637292316931', '67.02500946372129048022707413643', '67.7843105525360735598100460219', '68.41289223102271331885497145003', '68.698007408304326649511454687696', '69.63502967367926744728011655465', '70.42193622379080031373431566927', '70.99119747888786091865419458601', '71.51254203659422187587039982645', '72.505157713178257421058300858004', '73.07359361979426622610292656653', '73.44988749195733881173483677144', '74.09742289540227278449638368894', '74.60219463642267635432729540525', '75.49078456314418144969782664742', '76.08841889672016531638711634965', '76.83107691659936135928857566658', '77.53451898833428112408230866463', '78.041050415076400972204984059170', '78.769732354673836516925867642271', '79.32986972010226158077482019079', '79.86800747557633019536261295043', '80.49151386016522654064951863607', '81.19755428026961461649206069654', '81.633683129125520267746767181663', '82.70779106981901493513339739402', '83.4887084411626137152625128479', '83.88094873919875099452778897692', '84.01167675949324403942711646611', '85.208157578651306158041417046020', '85.85150862058954695310016621210', '85.98817068169443308046247698775', '86.9271480102117473921730359092', '87.34644215093772629800170413499', '88.46804281425303769604323689574', '88.976415818935998709003299475852', '89.49791761358059199841866486946', '90.16868046234600868361133417823', '90.70661749793487329066775193231', '91.22604407510711864867857783906', '92.0030722270799441808880000450', '92.4524254451560444263155323575', '93.35604807229949073353180433347', '93.777103342978826297828377755992', '94.68366648482374585367987693786', '95.21154802904064200704002200137', '95.936828393712427920603207055642', '96.30958274873333960707466929381', '96.94721984812204050875316608648', '97.4696221577481272974900515988', '98.183385114382182563766128693515', '98.87972095833157619468862973491', '99.662283812815443152204271234326', '100.3113985242742212111554479258', '100.55072611083451123368878471999', '101.70944541778933006592961203859', '102.01399376584773009264857510613', '102.51622223685918532654389306660', '103.141107580005145136889385959778', '103.75086182924458512034512908412', '104.35219147618211439466165135517', '105.492710352881425429216560960239', '105.64720952165446611748763021757', '106.422126791095755577585852776822', '107.07759087993209173963756086665', '107.5957577810404729673647790749', '108.16279735887975762611283110624', '108.8632619056916634277928927244', '109.29714637958249031975958627721', '110.00109749482486489885428931866', '110.608717883592260673948613715872', '111.50041035133445824953687321313', '112.09349748299554076484949649402', '112.692279466708537203123166522445', '113.25901710092820336454812637719', '113.36787025124180892775708596039', '114.51496798483336518030651552321', '115.14478796599429134380933593131', '115.39371569979464189944391573978', '116.00204134400290686721302958585', '117.13191007937246130706039609853', '117.67545291712994178494283970439', '117.99319136098257727247739910098', '118.85797495143194893626986959797', '119.22837700192841421899794243593', '119.93457826788424515484141405919', '120.34315813836728138750721321094', '121.03292572462380349280172606694', '121.8591497237800809859486578740', '122.40944614391666158293734815194', '122.99173369642134936642676449983', '123.84118402340187475054651835551', '124.0977331496617345796843963788', '124.94806277110134922819753328704', '125.54828551009005514461593452378', '125.837807785200671195371560209660', '126.33488119602107331605894166836', '127.2903040525066076777696912911', '128.121667268799074305381212467881', '128.43714706548177172745314508204', '129.0848741887441481035150282262', '129.90275608174098055071375089868', '130.231266849415512244765983723374', '130.98184062381328550791622720500', '131.4447278993016591617334473491', '132.02852498820605397141259664604', '132.625390816703986834999735852918', '133.18824998910321955350087886181', '134.2396797707867494831768000068', '134.65301883772337817646762674096', '135.19510060212771297687363435691', '135.83706708789623575918542462273', '136.23574277144954952469475438989', '137.040625906289348789051586953061', '137.61327377319834611729690425439', '137.904736924988974867274608121589', '138.90193229175499426260112918949', '139.26328481616802122216186355842', '140.08204749921601131868437506765', '140.85683587085182072927904132707', '141.346568180942845266311998673146', '141.76209024230686289356136226325', '142.28069222301217390791179091655', '142.8856842069374444143113099662', '143.67505887933931233085885738572', '144.2251402590599042285661859379', '144.62388573421866610166271456934', '145.64131577838690101261409850556', '145.96658215165397611096547242839', '146.90192267301970539471379184711', '147.26649939160822025839974490889', '147.78107021371675921851916728931', '148.29833320906505176743208522127', '149.13227993356630661017638770240', '149.37437448609660314016648891312', '150.13732066604340083356142516971', '150.98755240227011776296172543439', '151.595817608729888616903817642397', '152.082939685680228694547967428789', '152.532919483988981582932697826427', '153.32324487432354342954948009737', '153.928596481917773675993571048148', '154.499253466584817732245458736082', '154.70933810882002702312688467209', '155.42549244391749291021975085940', '156.24452357887539737784172781733', '157.13612718959023659354102485483', '157.46609412916719510989250878753', '157.949086187349562876025071693289', '158.599086866791001226919019930285', '159.39572189641388166340782005032', '159.72186040491922458138574569851', '160.29882863097719239239825910147', '160.8215168057765999228727874041', '161.64627482667375767500337412686', '162.10614000601409855186570298342', '162.79847850324601959883382795198', '163.76672498401350480603887135819', '163.989928776173336284900925491516', '164.514637503875503391294451137941', '165.02152431879209596190065896072', '165.80340074134042244442718652520', '166.22370733026660627338264708521', '166.93657386095796076007158983814', '167.46570320299855121561066556716', '168.12816492150194959648083100745', '168.791466638546742977191414015762', '169.53679626128557373667962643639', '169.98041300907958941488753834095', '170.51224876582760117504289251876', '171.09581480030667902769338705378', '171.44870731382446061919673364521', '172.20521865039566823526225806611', '172.9685484827202442425814132977', '173.33966282499098533317316379489', '174.1535376289608316519014652998', '174.81038422565726623442341008520', '175.20513064193612071616384413324', '175.94986961149390666947860950936', '176.43288244346981532005219399583', '177.01828419557924726744441096937', '177.55075475497742376846097336372', '177.86447095518099315767857156653', '178.919473948576362260839122190927', '179.26883181731373704103438125694', '180.26579145244574271333392067286', '180.55006661267407502196762863133', '181.16150080416391926006542907809', '181.8304682840928363526750152380', '182.121303161155669281441443744634', '183.07279203228416678163214273299', '183.50134917913382211823685109005', '183.90528085047370660003714428742', '184.32624011430097960473229589179', '185.653987610906555268908216264787', '185.99535598563607147582844645169', '186.44992252696553814283704401666', '186.9094832269157277757963861237', '187.78883421669473457743595704701', '188.15609550547111747498490306688', '188.66129641498472152007900227696', '189.31159702160079834328887377447', '189.97133821406187327657704612071', '190.360316521521155534420486159104', '191.35704052209636221654074594684', '191.72912774509196415181659387387', '192.386262712327518372500589171245', '193.08731590965962246464476546962', '193.48202179768972778810564968969', '193.99093623380006566573684453739', '194.37530237475840537588336006854', '195.30987917583502414493642130171', '195.71886702359160415413765082341', '196.60046459371596905770026800874', '196.84893571904562243512527010586', '197.60890709500333169012305334769', '198.41851410958272003259030616995', '198.78656921149639579600306694310', '199.44600851129306521025515920863', '199.63123815894227657461412606799'], 'prelabel': '1-1480-1480.1059-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': -0.1768917048924255, 'root_number': '0.849519934237283267589274312792-0.527556519563052990141496739417*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0884458524462', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.593932749781944877969553632412+0.192189288590012695845472933813*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.220032032728', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.10873638807', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.93177433554', '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': '1480.1059', 'conductor': 1480, 'conductor_radical': 370, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1480/1059'], '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': '1-1480-1480.1059-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': '1-1480-1480.1059-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': -0.08844585244621275, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.220032032728', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_1480.1059', 'Lhash_array': ['dirichlet_L_1480.1059'], 'label': '1-1480-1480.1059-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1480/1059'}