Lfunction data - 1-384-384.101-r1-0-0

Formats: - HTML - YAML - JSON - 2024-04-25T15:00:17.705798

• 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_384.101', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.19509032201612828, -0.9807852804032304], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.3826834323650898, -0.9238795325112867], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 41.26653112113601, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '384.101', 'coeff_info': ['x^32 - 1', '0.980785280403230 + 0.195090322016128*I', '\\\\zeta_{32}'], 'conductor': 384, 'conductor_radical': 6, 'conjugate': 'dirichlet_L_384.365', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^25', 0, 'a^26', 0, 0, 0, 'a^45', 0, 'a^7', 0, 0, 0, 'a^44', 0, 'a^15', 0, 0, 0, 'a^46', 0, 'a^18', 0, 0, 0, 'a^35', 0, 'a^8', 0, 0, 0, 'a^19', 0, 'a^1', 0, 0, 0, 'a^30', 0, 'a^5', 0, 0, 0, 'a^28', 0, 'a^20', 0, 0, 0, 'a^29', 0, 'a^6', 0, 0, 0, 'a^41', 0, 'a^11', 0, 0, 0, 'a^0', 0, 'a^11', 0, 0, 0, 'a^26', 0, 'a^6', 0, 0, 0, 'a^39', 0, 'a^20', 0, 0, 0, 'a^47', 0, 'a^5', 0, 0, 0, 'a^18', 0, 'a^1', 0, 0, 0, 'a^40', 0, 'a^8', 0, 0, 0], 'euler_factors': [[0], [0], [1, 'a^25'], [1, 'a^26'], [1, 'a^45'], [1, 'a^7'], [1, 'a^44'], [1, 'a^15'], [1, 'a^46'], [1, 'a^35'], [1, 'a^8'], [1, 'a^1'], [1, 'a^30'], [1, 'a^5'], [1, 'a^28'], [1, 'a^29'], [1, 'a^41'], [1, 'a^11'], [1, 'a^11'], [1, 'a^26'], [1, 'a^6'], [1, 'a^20'], [1, 'a^47'], [1, 'a^18'], [1, 'a^8'], [1, 'a^33']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-384-384.101-r1-0-0', 'leading_term': '0.798291530782920823726678020783+0.688611010123661387604191487904*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/384/101', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.0542554203717756, 1.6834467955659804, 1.65094046978757, 0.9679395602303814, -0.08791768965791642, -0.9731635260335274, -1.091622437949753, -0.1503919961687244, 1.5689066541832846, 3.258159916901694, 4.005857789936496, 3.378448541265226, 1.7680327916377514, 0.20447122124343614, -0.3193923364375956, 0.42749164146867447, 1.6916531865814304, 2.2552890262436756, 1.3772670552118509, -0.5559331118221543, -2.23523669118786, -2.41296941217987, -0.9239945494831034, 1.1113567008629928, 2.144963091421044, 1.4680165040928055, -0.17842453798260005, -1.2244711128081653, -0.6465600985028639, 1.0945343656615127, 2.4297177596016226, 2.099350432438486, 0.35373752189310453, -1.2034293296674161, -1.0615683324126803, 0.7588271679249861, 2.6486784453048173, 2.860452859765511, 1.1445803838293163, -0.9974937518773563, -1.7359160946970051, -0.6680464678409297, 0.8190426966260431, 0.9778774395918781, -0.4745285023230222, -1.9938706972274096, -1.7454025981998067, 0.46521772665667116, 2.854712856844465, 3.3455684140613906, 1.6158116688801958, -0.5850217516038361, -1.2165856747366663, -0.003921833856461597, 1.383064796732274, 1.228056330844983, -0.28280817178006684, -1.198066931399473, 0.05468189041307271, 2.8106858334008935, 4.672664948962341, 3.9400678439809975, 1.3916331827835813, -0.5271640200020413, -0.2672091956236339, 1.2907509569620523, 2.0054770145965226, 1.0210199982120205, -0.20612589149407357, 0.38808262757719186, 2.940441033072374, 5.226259307793027, 4.942190318219495, 2.2129148991407113, -0.5172441252220196, -1.1358623919091462, -0.08108938783285188, 0.383580271314259, -1.0287081685454338, -3.0369737844816944, -3.3054158411911154, -1.2996805321216345, 0.9191405191464496, 0.9943852341522661, -0.9761282073176901, -2.5053698589287876, -1.5967063462218816, 0.9160149044609918, 2.343340582523909, 1.293898538163128, -0.7434691223557731, -1.2781345889498799, 0.12294318516825983, 1.3284199750565273, 0.33572637861215776, -2.124745262563102, -3.3265361050494784, -1.8177035626147091, 0.7469316536333785, 1.5134540762957736, -0.17996181348613646, -2.051528066558411, -1.6920358930500252, 0.509705292368614, 1.934453869427826, 1.0560212542589638, -0.6690923415355137, -0.7477331370800441, 1.0212500075714013, 2.1105060860089857, 0.3994414044969127, -2.9987484636442945, -4.832832566843081, -3.477420848499144, -0.7326747403926908, 0.5380854744921045, -0.09921483681442664, -0.447989454317987, 1.0693741030916075, 3.0284289952206676, 2.7048434554841156, -0.25331160527395336, -2.988115026571691, -2.6983911181862488, 0.020745706006876266, 1.9943617780069165, 1.4028659026480694, -0.17937726037659213, -0.1672898976890355, 1.4653796888167339, 2.182272330252642, 0.4488609004713655, -1.926065102717705, -1.928680039897507, 0.7207401405529984, 3.01782681070862, 2.361115752027857, -0.24330738840832233, -1.6010055584188363, -0.468350639725367, 1.0429542920815704, 0.5720820689927243, -1.137078494202167, -1.2187379819815993, 1.2865777063851398, 3.846515420576112, 3.579139648896792, 1.02008026617866, -0.5453769725931488, 0.6336227921560315, 2.560064626170522, 2.2853044957113466, -0.07725302290426121, -1.5427113021136358, -0.3522759799936701, 1.643523743391186, 1.589635774911438, -0.3673634420871247, -1.2359155654636214, 0.6344395814216186, 3.082717087452713, 2.883701596927089, 0.07642690764199908, -2.0154764932667817, -1.1437834028404597, 1.0215466715754373, 1.3664384533891167, -0.38747256981920297, -1.5392543024366285, -0.511433001057892, 0.6797890814217231, -0.7886023560406551, -4.310198766329174, -6.185094775166786, -4.309333971118426, -0.9029820600972671, 0.4422636848780691, -0.6633629864594963, -1.4280757153632813, -0.22814092552016418, 1.0092371933753554, -0.21573462990783077, -2.9733343295341736, -3.7885325329933175, -1.3986002688876447, 1.2835357692983826, 0.9268379630642745, -1.8175758023618913, -3.324267633873552, -1.9358764716185297, 0.07631203904179563, 0.1180790239435997, -0.9056966647529632, -0.11614448173357085, 2.7167580905353836, 4.304732585978145, 2.251867248616379, -1.4228676586871005, -2.769477322150191, -1.0557817828433564, 0.5761685651126172, -0.2537942210903714, -1.9171372026176376, -1.4832197643345293, 0.7114060428569284, 1.3988758365153529, -0.8077385522966559, -3.178806985238815, -2.611008475607684, -0.03397990713636273, 0.9222322863101432, -0.8526217476130944, -2.365932126500254, -0.8842053371163666, 2.061944008093464, 2.8164893890492873, 0.7403119915953054, -1.1144349504416593, -0.6715621745709787, 0.13985101070558997, -1.4824473613395925, -4.5872735300016, -5.366298946244391, -2.504098787461385, 0.7739580072474104, 1.0546245669038878, -0.7094278395567325, -0.9423872561717772, 1.2077422806824885, 2.7899447253580876, 1.6710943920183183, -0.1954453814319044, 0.18362748908196336, 2.076515792068324, 1.8628431379118204, -1.5263809540270998, -4.598801202570701, -3.9004027927311498, -0.6937716465165438, 0.9935410207957927, -0.028819598311819013, -1.053041771395328, -0.19023274929811548, 0.550022258634662, -1.405536970153618, -4.591654112362099, -4.93717500747818, -1.4964227537700068, 1.9489423093621236, 1.9643171423333219, -0.07408069188205033, -0.49539084113318493, 1.1444245411431424, 1.801679735539906, 0.07325479760361801, -1.3540119610462424, 0.179829390794611, 2.9232641439670877, 2.9671808653724465, -0.01011573107542549, -2.130203087832832, -0.8837321283916568, 1.3626583672868189, 1.0870964752903183, -1.1333824036900726, -1.7364421975811406, 0.20882631809191768, 1.5809249317275074, 0.15267130805217002, -1.7904707949737673, -0.8730385168043999, 2.0673227084745673, 3.008308352853432, 0.7084535516948267, -1.4138389828214268, -0.3879653575630715, 1.9336622870699387, 1.822491306939126, -0.6470194105642904, -1.872409187581175, -0.38924775807780926, 0.9404995357158812, -0.3903970905609483, -2.361953254019898, -1.4419485742669682, 1.7384613211191353, 2.9198003453224337, 0.4030881626666719, -2.428236043767152, -2.0813240618158284, 0.1341657088672832, 0.5714352581409974, -1.0232163991568684, -1.5014810916482988, 0.16756654180677003, 0.840224338113796, -1.8502618372599635, -5.214131406172136, -4.8950359833078725, -1.123843950606618, 1.5919276705464287, 0.8716376324793732, -0.7043132314170168, -0.27893360591921684, 0.7621992672178144, -0.47132419854230495, -3.0170337750940894, -2.9857027008091976, 0.3448268918107174, 2.877657177462586, 1.4503886804900015, -1.6216493846298154, -2.140443042802346, -0.19146235294080693, 0.525007577005784, -1.1748307215807046, -2.1731166666938435, -0.30904108226144084, 1.9116861988157319, 1.2603536403590638, -0.8492092383608512, -0.30341199226096716, 3.239317056654247, 5.479780789803417, 3.7338223775501103, 0.696770852622225, 0.016638084624810152, 0.795777235410934, -0.37770592065015635, -3.380490637966405, -4.378615216931608, -1.9067450673095112, 0.5825060466531957, -0.04674981927932242, -1.8251868977737535, -0.9948532677231974, 1.794388930031523, 2.311713532755972, -0.6135029937292173, -3.122155923427755, -2.1441655804887043, 0.18025252783097379, 0.2998997273862161, -1.0716398490576986, -0.5772834002039922, 1.6840252855932967, 1.7923270613682283, -1.6798930943539852, -4.789799629014432, -3.746890479692373, -0.44254424468355885, 0.5841792221933753, -1.1117513755853574, -1.9299855099695726, -0.5069009005498726, 0.1966834970219551, -1.7178717838365822, -3.3513111170207703, -1.428191117163875, 2.0969993251159282, 2.559510436045701, -0.37946693690847355, -2.2255544130554488, -0.5055637933784172, 1.7812346347208805, 1.2757870416854353, -0.5857297512250422, -0.5834587881533294, 0.4703074564179697, -0.9654861561872912, -4.732606172017499, -6.223644370296495, -3.130481289749657, 0.8446135658295626, 1.340416600710486, -0.5725293340548158, -0.9380234152304396, 0.4444325323713186, 0.1381215301379548, -2.5844803055334813, -3.9926907900973143, -1.8755906514728045, 0.5974874733789621, -0.2551513676946605, -2.7450037203241524, -2.5169341381849435, 0.43591420507762163, 1.773021558994217, -0.22473818886398636, -2.050481770558487, -0.838573325676004, 1.0366248863185195, 0.13276606845549854, -2.1645155254158377, -1.8880477375578155, 0.8275160439788496, 1.8154122343306436, -0.229146960060628, -1.395410878604698, 1.1674292164813134, 4.457598945897772, 4.1544541429567445, 1.1798175199016359, -0.20825423766869058, 0.6462907518134577, 0.3143614750300648, -2.26203596407344, -3.5244830882236737, -1.2683949223882904, 1.1770403132164555, -0.07740193631413166, -3.1800850440790276, -3.2733708112479274, -0.021098821710572306, 2.116032915886425, 1.0353724846206243, -0.2012547186058059, 0.8821976907599899, 1.932851188228274, 0.25395349384486254, -1.79484064518411, -0.11324495829036627, 4.1678075196948, 5.736984824019039, 2.9669272748045636, 0.1223246743477329, 0.5486325399630998, 2.001719757398181, 1.3099806585682237, -0.030818701529797037, 1.1251918628430024, 3.3618013445148964, 2.361888749587789, -1.8460711224999313, -4.215760525920925, -2.193750413781263, 0.6004504120217165, 0.3998293898633464, -0.9671369933993408, 0.14651802770745914, 2.6470586540413885, 2.5184165997559154, -0.2000277952875832, -1.2898183557780034, 0.5687373628436354, 1.53378659756545, -0.8308161241875045, -3.152764165054003, -1.5965696968137912, 1.7898860998638546, 2.289648413738738, -0.026546487143705853, -0.8949264052679222, 0.7889696966065947, 1.3675865044385653, -0.910594453433505, -2.5574567160493635, -0.7063052203565474, 1.8043691176314245, 0.983899721792456, -1.6260097955103285, -1.48142431251944, 1.3126172100246543, 2.0509939953592378, -0.8428790625761897, -3.26653828084106, -2.145469201391374, -0.006751426768964791, 0.00479470092347103, -0.320994271581188, 2.1102708909672154, 5.264548007850149, 4.357036123486566, -0.3088457938223159, -3.1582174545734034, -1.5442308185012474, 0.8490246861253105, 0.5474117072373659, -0.47606378458807913, 0.7195033227340119, 2.2690923878929885, 0.7777149152714584, -2.0955357233696223, -1.6415113449303074, 2.0964909368878564, 3.9149060278121737, 1.544846566098137, -0.985304392929754, -0.12280744878804213, 1.7490634390093838, 1.0005653279458135, -0.9249104908150219, -0.46763181294781786, 1.2924481785282367, 0.23885303005752284, -3.3046112468342956, -4.319424158348493, -1.0769205663947163, 1.9060258720273806, 1.021017804862768, -1.0473035439787495, -0.4435765428019565, 1.3109750281001862, 0.46711228604928523, -1.9594787860109344, -1.7733602857552668, 0.9221451970544327, 1.5229616587909554, -1.3191433668980095, -3.250224561882376, -1.4520287302150614, 0.7019961315077481, -0.486042640004897, -2.709773372716735, -1.676128866777616, 1.5101355924236866, 2.2534692980386763, 0.21069151763316948, -0.5428934826997119, 1.0203433534285462, 1.060622764876857, -1.9860464580507315, -3.9089973923278194, -1.4394779471072743, 2.057620080463797, 1.8060518097726157, -0.8664967265664161, -1.2192268064000826, 0.9240506158144125, 1.516309491083829, -0.22552371714411112, -0.6597584695651836, 1.1641974898989524, 1.0896379596675718, -2.977889484785811, -6.585282260291033, -5.204866133083149, -1.2077587626567838, 0.22856733948073993, -0.7992427666872146, -0.2994675651838998, 1.9454848352860952, 2.1436895737732966, -0.20073472796768088, -0.8704273360130537, 1.642969245171978, 2.9568037194025583, -0.004657119328481511, -3.490723604415009, -2.7273949848718, 0.5720639342445245, 1.4618394436836986, -0.19416577332598278, -0.6185135332217583, 0.38876785758719584, -0.868091630810395, -4.539379870440201, -5.6922881995786, -2.181718620116225, 1.4537274989601432, 1.110032878128483, -0.643303831443151, 0.3855127439031826, 2.701352144642471, 2.1627885098544013, -0.35032087783891463, -0.34898218247308355, 2.3020261626042435, 3.062163164312318, 0.6885485820799326, -0.6193739541035456, 1.207995373187752, 2.2231766367702472, -0.6525534269340396, -3.9132878842912318, -3.0730089915367884, -0.0474247690657272, 0.33433234044153515, -1.5819590244805788, -1.5881784430879176, 0.4946779466465997, 0.638049830747066, -1.649348947218555, -1.852266419084625, 1.6404835591237406, 4.155509793901076, 2.2723430790887207, -0.5121435665684277, 0.22225720402848562, 2.54206635615247, 1.9933160607377152, -0.5697564490206835, -0.8917640108845497, 0.9279790588083766, 0.9937613463605568, -0.633089360897931, 0.5928402610937842, 5.380005435911649, 8.109369190514183, 5.272595417664439, 0.8592637046354575, -0.25812388300141187, 0.5778260653692531, -0.12171950641726938, -1.0383889619222864, 1.0286413596487158, 4.08765339936143, 3.342313428412534, -0.47026516978053, -1.6926059254777535, 1.0819892215136548, 2.891465720091486, 0.9060268453494094, -1.2108416607312582, -0.23677863629415566, 1.080106758962313, -0.4489089402822008, -2.2842432312882806, -0.763261488174422, 1.841062102710731, 0.901088350403521, -2.321555855923875, -2.504362244103948, 0.7202034729109801, 2.2723669440112317, 0.4297885718388489, -0.5736191289352188, 1.5722195475237781, 3.190625085022975, 1.4992962313605571, -0.22374069409428338, 1.3619556423831418, 3.380142144982972, 1.745378998482739, -1.3590599462356103, -1.0906851461059626, 1.5391188523474828, 1.3843717970114777, -1.8247113798769636, -3.0647032056504266, -0.7848128580677317], 'positive_zeros': ['1.22461241183957933962548057533', '2.21945659927037203995387731527', '4.1231952157142948480819446951', '4.56065881477534540029255471996', '5.85378810275008022285279883453', '7.01238887009485818906646771920', '8.09104803902728023863833983491', '8.87749007165944945227502020420', '10.05692090166896334346938875292', '10.82667000331874374378815012277', '12.03074108733584926406209024309', '12.939657978308379205695983287910', '13.66775185561460084266571537676', '14.63305972263894870212875844217', '15.841233547107755041127088470028', '16.563235696443215197934567598026', '17.44599085072081867068508092571', '18.117578107378715686126854314019', '19.5653150879972378457507461411', '20.06105881561358832130989918875', '21.16995843033946258180620800207', '21.4809909743681406473829647248', '23.04883770464213544696960824872', '23.772485339762514263077182948302', '24.194076701447965132291186000903', '25.47368084686319298415446525082', '26.11424505740182252298545559701', '27.07611865665392319134761128014', '28.001904814600804362109804103075', '28.72833065247002524513974229624', '29.422229772977326520536301686226', '30.52481974536520738402707526512', '31.225474776353516135147784671374', '32.11973932300201109617943449226', '32.98992972425131757368058755754', '33.58955118891911901716868312993', '34.41474005141117520499997114559', '35.738991920355617755295339694', '36.21744752923510599604829315588', '36.699305881532941892334295270332', '37.7897155269760425297527593354', '38.74776695889505276952955022057', '39.64140081208409780536402768910', '40.04228023996383969790228809428', '40.99052881746198822806511161845', '41.80256309165428023063508922166', '42.7826165875577624396035907179', '43.51609556306643995298618048405', '44.16771293143384981451546087005', '44.86635368730942195015782730374', '46.07866916801484106018848622839', '46.459446345308869176796990804280', '47.49025979918113273874004572957', '48.17504017180924297965424389887', '49.00646513328918893357300451570', '49.612846552782385544593371459009', '50.63277128195054449576567999042', '51.40672888897359453948751334257', '52.127452970445121018768413629', '52.90878554056112934950714367553', '53.34134198108413595054702434313', '54.81139914554919253970586558229', '55.16927509189401742809322423259', '55.97814163078646654614580907303', '56.53449471427623600501528451325', '57.63765414143054753393486595689', '58.242204848819567100597797710427', '59.356541439750809599977816596999', '59.723555641364145315503208430', '60.32891221987197951881725004356', '61.43464839243219932373879697706', '62.34347246606602471292101764719', '62.766414200151527574317338144368', '63.64938919421104304608202892827', '64.28755953078134498414856787591', '65.31709048107197566996599943593', '65.82039701837482812909955391463', '66.65424649131133776299970180240', '67.59345587078145880740544626017', '68.31286159061507825380454834970', '68.51862176322118648712724460953', '69.90490326643425802389592324155', '70.500956958291525853979202566287', '71.09801430539808182014276740464', '72.137944944298140770926129336317', '72.46260387360696702712605460132', '73.31731843606131970364218328886', '74.45303873221484001608059426095', '74.99438157519832895606981885618', '75.668495704358890905755320812624', '76.08322386955834166038695277025', '77.30002636859749668955986162273', '78.11180734795117938559578579992', '78.55309704676559581746572396497', '79.38525991038954546051939064268', '79.97961673669967093802384478104', '80.9365438659207399886563825681', '81.670422328120856811661029359725', '82.34407127440007256237075741631', '83.097163862429126558408511626413', '83.76993893065031035021472612790', '84.47214909347113010921743097399', '85.38877770249314366510169949683', '85.98690426182450140846146456873', '86.79745243073117048408905132149', '87.55981403363278400909246194077', '88.070522517200188077294823969001', '88.89594116058716467314968107800', '89.72349316591432948073186726758', '90.60257593063580578716233906102', '91.06738462824266474247178746985', '91.84752513862954537613100465903', '92.32842837143025792905188298617', '93.53037301940165015737817616623', '94.20749659903271149183384492057', '94.75192541273748352369086012718', '95.24775613754957385141958249757', '96.22183631021921302303608191024', '97.01360069981312806267985179966', '97.84473451483449913729428024262', '98.25380296389471440397371238097', '99.09732440533101466137882287612', '99.85931892347347355082472175907', '100.347645575122067161369606935616', '101.714796047341671843148294532192', '101.86623934193859191515401402656', '102.45038549527647871547774767845', '103.641246562744907096449748836150', '104.054838035424446146699109181742', '104.80108597346071080471122629020', '105.57130060543252975579557558148', '106.529344543472264271090478590944', '106.945196754758691065007522267789', '107.58520647693191382198147548113', '108.31024445503943758150599157975', '109.43061774707257627437909170158', '109.823401425011719626614962344955', '110.73153755504797838182058820480', '110.99871586364865818916228176944', '111.99416241000146568054884803803', '112.776531476999856636273611171092', '113.493445926406224970526318880767', '114.26147958148165930050224954383', '114.83229721076367468310111028524', '115.19378965329284091321918933808', '116.47769239637217297456589754468', '117.09294572456273705391399172564', '117.70986380273862645099023952592', '118.146879311959533305284006837887', '119.26512140376839466236311839363', '119.65295661212852943167037158223', '120.57983750948250390057069581101', '121.224171039125479603249618826212', '121.987782915965629979717918703885', '122.51784057076582919035178647064', '123.34449953384462271382526349901', '124.03376883092585943341625372964', '124.585592789049946804998421455360', '125.806533024876094635991757773984', '126.0545844191044517078854725941', '126.612393769999094255690469817003', '127.62643885783507350668692062606', '128.116860625983287452917109240', '129.06438697526570550599868573127', '129.88980483812466684500808284145', '130.128613188833545169248434756586', '130.967026079384343654729350655405', '131.5718411129040223268346941489', '132.84820107848413670399287240481', '132.991750457773109404752498083379', '134.04167419430004014077548345741', '134.15568078737734113426685334967', '135.18332012659118575031107021883', '136.1568437608509578583554494900', '136.63906148167963244869241721557', '137.16852554867530317406929521334', '138.101694685222251586102070214948', '138.67265164563047244719212098271', '139.29337169863365360108074830987', '140.138915401070000159743944863', '140.933870681604804891545204367920', '141.437994577894127081738410685651', '142.08588047150925899389590471967', '142.88403236822640179753002777287', '143.54922595036564484731060922132', '144.233951406607055898658643522101', '144.92617131850291681800126710859', '145.93921150827301576963511690599', '146.25178789946891342901323804334', '146.64113421192199136480613053958', '147.79241373421545189896660279496', '148.60828504912367729961730377251', '149.18524765722047501436399468372', '149.566990603051592322099646358904', '150.39021616948119427969089783611', '151.0858280445471669431822529591', '152.02634590332510533015468614364', '152.51748867757484902447066781445', '153.26878871211790051189859927845', '153.82545437613642575876849772853', '154.39942617048281690537749016486', '155.396844374362215816853479392615', '156.0683718338944537483333040900', '156.631504836210474323339923625760', '157.246624277323400019372163611987', '158.01935724905895743987903794803', '158.62705962894183952074960131112', '159.54247182489166000432417819990', '159.936595686331563697822079871464', '160.78568581122197928230628848278', '161.59573470920143916998150623704', '162.00652031023394943881613377278', '162.632111295856499561938104058', '163.54818938827270250948596014321', '164.26751341360507118699925347061', '164.872693578980630375655040491396', '165.58635891778241281063539631329', '166.06798572609029817330502314089', '166.67257139919597654451964247057', '167.9699963108328764778564577990', '168.21935865102197609157342664117', '168.79637691437194722943961208044', '169.66083670412134861778774059818', '170.136051571929233057973529778328', '170.93716030634823522062676887445', '171.814634503078220154105121525046', '172.46375486680932866268865248479', '172.98839785138916243893595556791', '173.32576655052343747525494572664', '174.53056936553352380198969799752', '175.16699161904572392819318804999', '175.57213135037876140462252927181', '176.510315286692174158077237710785', '176.9259403518280269531855009574', '177.90145750595526438483657420534', '178.2734907268201833346914232299', '179.01166835490598463495891773102', '180.0066729368539616902305270492', '180.37590471805441291474938340897', '181.17233066532006057867415939526', '181.662622129453004222256464924467', '182.37401695372322423361806062237', '183.35178989056752763245220836179', '183.71951659825848854280568500109', '184.609637009538637903398185635262', '185.15698661175266613543961129335', '185.80303165789999021319900075500', '186.19110123682121859070164551651', '187.613145612697465531603822522398', '187.90968215450162874400115692784', '188.411171796131893588543089021073', '188.958851903347599886494262736627', '189.95906861031730438696839631602', '190.52444916817431575586679260842', '191.34836428477087576116139298734', '191.91242691568009066395226060039', '192.442765164907074252556842519905', '193.20286432010382493514519724893', '193.83729863447398103281823416711', '194.62195026575569215181989629322', '195.374914048273395018458198643823', '195.74767110395928958278954584793', '196.78002124100822782979088539718', '196.99206286794969641340622400193', '197.97020720210774330145803966958', '198.565316231166539574581315027623', '199.20788026708735302802178101906'], 'prelabel': '1-384-384.101-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 41.26653112113601, 'root_angle': 0.453125, 'root_number': '0.146730474455361751658850129647+0.989176509964780973451673738016*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2265625', 'prec': 30}, 'spectral_label': 'r1-0', 'st_group': 'mu(32)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.949276933565508990459178203814-0.0340153162198481992272744480629*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.22461241184', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.21945659927', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.12319521571', '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': 41.26653112113601, 'bad_primes': [2, 3], 'central_character': '384.101', 'conductor': 384, 'conductor_radical': 6, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/384/101'], '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': '1-384-384.101-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-384-384.101-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 41.26653112113601, 'root_angle': 0.2265625, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22461241184', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_384.101', 'Lhash_array': ['dirichlet_L_384.101'], 'label': '1-384-384.101-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/384/101'}