Lfunction data - 1-1800-1800.1429-r0-0-0

Formats: - HTML - YAML - JSON - 2026-01-27T21:28:52.889123

• 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_1800.1429', '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': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5, 0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 8.359164857335244, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '1800.1429', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 1800, 'conductor_radical': 30, 'conjugate': 'dirichlet_L_1800.1669', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 0, 0, 'a^5', 0, 0, 0, 'a^23', 0, 'a^22', 0, 0, 0, 'a^9', 0, 'a^39', 0, 0, 0, 'a^13', 0, 0, 0, 0, 0, 'a^41', 0, 'a^4', 0, 0, 0, 0, 0, 'a^42', 0, 0, 0, 'a^22', 0, 'a^20', 0, 0, 0, 'a^11', 0, 'a^10', 0, 0, 0, 'a^36', 0, 0, 0, 0, 0, 'a^37', 0, 'a^23', 0, 0, 0, 0, 0, 'a^34', 0, 0, 0, 'a^6', 0, 'a^3', 0, 0, 0, 'a^28', 0, 'a^26', 0, 0, 0, 'a^44', 0, 0, 0, 0, 0, 'a^18', 0, 'a^27', 0, 0, 0, 0, 0, 'a^11', 0, 0, 0], 'euler_factors': [[0], [0], [0], [1, 'a^5'], [1, 'a^23'], [1, 'a^22'], [1, 'a^9'], [1, 'a^39'], [1, 'a^13'], [1, 'a^41'], [1, 'a^4'], [1, 'a^42'], [1, 'a^22'], [1, 'a^20'], [1, 'a^11'], [1, 'a^36'], [1, 'a^37'], [1, 'a^23'], [1, 'a^34'], [1, 'a^6'], [1, 'a^3'], [1, 'a^26'], [1, 'a^44'], [1, 'a^18'], [1, 'a^11'], [1, 'a^35']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1800-1800.1429-r0-0-0', 'leading_term': '0.647447209955596407914007571800+0.865460548347976763438609577791*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/1800/1429', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.0808375689371956, 1.8677098098208729, 2.336193575147972, 1.7398118919852743, 0.15686399463834455, -1.2704486686353442, -1.2792803832637571, 0.24221370238319415, 1.9284524040332367, 2.1160755601699788, 0.5560240443366566, -1.1337218278934995, -1.0044900183944687, 1.111673179511786, 3.233844177107888, 3.2483382252444235, 1.2369727676394027, -0.5763599488451009, -0.3922780746818974, 0.9926906104946597, 1.1070571422987565, -1.0937909478094907, -3.6879313831058917, -3.8961809689167124, -1.4370979807858368, 1.0595801821256066, 1.2610667363076824, -0.01638033677026546, -0.029971563424060925, 2.086295207635764, 3.962712696554715, 3.0544799867355783, 0.16554448347288092, -1.3875014495490843, -0.061424820458159994, 1.8925698176809953, 1.5124729242470594, -0.819439982410702, -1.9702733811980702, -0.5407149319158273, 1.0705710384160279, 0.0717702529074396, -2.5919367071191295, -3.3786140523195614, -1.1318511978599433, 1.1854965333214549, 0.6191322223485763, -1.6471659201867728, -2.1589996586714033, -0.3463231912856364, 0.6637009726997564, -1.141010988534939, -3.397733149782208, -2.7085318843226225, 0.25077220630694413, 1.557892810185836, -0.2584859029681742, -2.1394241582101587, -1.1903360339459792, 0.9718436567074745, 0.8735679837551964, -1.2609288607182292, -1.7482261881229693, 0.7417641262856584, 2.835956495592315, 1.4432066936079286, -1.4944921947872913, -1.897479875312999, 0.33007967878888084, 1.4617115760514636, 0.04405215747487227, -0.8330013982988502, 1.22840200752209, 3.6256904887338757, 2.5354845065994454, -1.0108334212577028, -2.491194847403338, -0.7097521600953156, 0.6940794001379035, -0.6564029414942143, -2.11836399757667, -0.7031362303165886, 1.5958499309441945, 0.805804602443378, -2.4056119759307832, -3.426037774168016, -0.8502606164149358, 1.4453921321568093, 0.6598561719011069, -0.605017104614771, 0.8929939582156636, 3.2726965150218597, 2.557969634453969, -0.4901504455644665, -1.3210804306738209, 1.0156115362073745, 2.3355194225154743, 0.30888225938207814, -1.6747614302130234, -0.24904753264037194, 2.273109534805748, 1.8828061373986023, -0.3327576601978375, -0.23424197976813954, 1.9851082294589095, 1.8829872180708092, -1.5707463982339471, -3.8295990013035546, -2.0386596781983184, 0.44458543794457606, -0.13971757365759707, -1.853392349041905, -1.049245916522071, 0.7775235177205161, -0.48724802238696463, -3.926577001221249, -4.385011239875446, -0.8333806826469682, 1.897055028599946, 1.0062007726298468, -0.2834744289844617, 0.8036715835088083, 1.4323877335117012, -1.4351951627306418, -4.774624780269743, -3.9320427428136284, -0.4129582786975301, 0.6062157611571634, -1.1407578760049402, -1.201991592964527, 1.2413716294477484, 1.8375240875621082, -0.9703392139902651, -2.874859507011512, -1.2140523031578687, 0.3395863661957122, -1.5504325083658321, -3.710410646989123, -1.9594083439585959, 1.398321770528584, 1.476593675487611, -0.8390553743483491, -0.9482742149792254, 0.9544039848853336, 0.4742418159221682, -2.4225859863406316, -2.7444882053029964, 0.6752013349782557, 2.752351861175529, 0.8062843629546048, -1.0549837153340151, 0.4700114553401991, 2.1768141985758067, 0.7202912588047792, -0.9835791706689762, 0.6822100710517515, 2.8031416766215127, 0.7628467333623936, -3.269373173039642, -3.7140250532892667, -0.9523963747158445, 0.054291473846088886, -1.0392685905180716, 0.014881063858616227, 3.2066985490828372, 3.5463857374527072, 0.22797071605791794, -1.3716230816815949, 0.9763716158006743, 2.57270177992006, 0.4486444111774244, -1.4771024832184847, -0.03061040899984178, 1.2924984310468857, -0.8081367862352262, -2.8805055994807143, -1.0830074306572564, 1.3559492569726315, -0.17550763926089444, -3.155111799657955, -2.452519694181249, 0.4243508538659715, 0.4374710221179978, -1.6156295366723121, -1.1291574275319423, 1.0260292416457242, -0.05822411910719467, -3.6595074356935586, -4.041932981419997, -0.686736893278495, 0.8828116792625471, -0.7652545248917997, -0.8481504732754483, 2.0484630270845674, 3.1112558620815842, 0.553924857593489, -0.8980791339787746, 0.8815826017173836, 1.2286694756472685, -2.2469068973653363, -4.5102977263582655, -1.9670090264380564, 1.1263823152303623, 0.5921628646403595, -0.6070784729186975, 0.7464889814547567, 1.2596962576464152, -2.19843198438451, -5.251149573883014, -3.122199360970126, 0.7488772843403902, 0.8734889543467563, -0.8702703049385404, 0.00822024943260099, 1.5534052382624242, -0.3098611592891999, -2.8952649112984004, -1.2657305358376647, 2.163359631440506, 1.723788019298923, -1.1191995875918879, -0.8372144195887965, 1.6538978741146533, 1.2131723066943971, -1.2713681151963128, -0.7582255683499077, 1.7592816672499998, 1.0009724638384034, -2.114955334819272, -1.8900022923729165, 1.2731276964710396, 1.6463500588930586, -0.8101629721647773, -0.5683547032516312, 2.56798675417935, 3.1078998226106638, 0.5589333961323775, 0.02274362355484411, 1.7043787746564565, 0.4331984311673934, -3.5325613202562476, -3.9155561068033364, 0.09936321162221523, 2.289309223312399, 0.6862820589000731, -0.039756176615152385, 1.1099423100763774, -0.41224864747984186, -4.456731868566024, -4.94490025096276, -1.1286236862374046, 0.5499466385841294, -1.8721355452856951, -2.944436944939855, -0.739612379335041, 0.09946249798513677, -1.3950310053343142, -0.22116250120141412, 3.99872660289694, 5.064702992580858, 1.6107890979630077, -0.32471165324927254, 1.2488624271978148, 1.1946518963572754, -1.813429421237315, -2.4363487328564477, 0.5240649282523813, 1.5902929255808, -0.4598379808246003, -0.27969200204050965, 2.925405493483673, 3.299674651657468, -0.14460421877337296, -1.290304622646811, 1.3995016510708405, 2.3368518529926643, 0.09645578317377468, -0.27131953648605744, 1.8601989263228857, 1.202404021310396, -2.232292797248114, -2.234377818010095, 1.615501339241093, 2.837153817579269, 0.259296006393495, -0.4791467644547556, 1.4610735480768877, 1.0267336013180435, -1.6131089714237794, -1.030837757897186, 2.0377084279133815, 1.424062764347433, -2.329651359645753, -2.7249227457810115, 0.2668310178498975, 0.7045455110418745, -1.39458312823495, -0.8701587725694966, 1.3447298216084491, 0.12961345392720913, -2.6279593656711415, -1.0626406208338608, 2.832575400785584, 2.574373745456995, -0.5680811368677801, -0.7000660657286916, 1.000708959242785, -0.33362824618849235, -2.495827106539374, -0.7337346044327987, 1.7827813871218965, -0.2880274021824131, -3.64242591917598, -2.5989135281232363, -0.066481816220164, -1.2214429068480608, -3.068776510230936, -1.0812633303138868, 1.201577469369988, -0.42597143324909403, -1.9394599708924387, 0.562660045650076, 2.4173792022788705, -0.32895719936386064, -2.644392843531631, -0.30802030367871613, 2.0237308671078833, 0.6217887200267862, -0.1043678342914861, 2.441023951485996, 3.1548713165992597, -0.05435071024725161, -1.4333838405378367, 0.9611295357080762, 1.0414242223893035, -2.967957972517939, -4.632947251170286, -1.7491118757871444, 0.2007001269394697, -0.1991153036976765, 1.6172498987242143, 4.700373230993167, 2.9191524272331364, -2.342342375133253, -3.4596021902344836, -0.28652229758658854, 0.7701855322933187, -0.4017786607448701, 0.8112519697608261, 2.3986725546581935, -0.48567051849652576, -4.347144105266518, -3.053351050510118, 0.37488138094770196, 0.05243821448842909, -1.2580386855813703, 1.1448021995555964, 3.5032697517651266, 1.3666062297815258, -0.9728271388374772, 0.6794803659689869, 1.906515426657122, -0.5874847299559612, -1.6670145242882541, 1.3843776289574763, 2.5731598914649556, -0.891247253516151, -2.9319418286079695, -0.8449750541791498, -0.034508987290585255, -2.032871182693797, -1.59344278825, 1.2377582989434794, 0.4147593117143008, -3.203073914792359, -2.6864449956643774, 1.2440775964462882, 1.724372025433535, -0.7475980615506416, -0.5090073683254825, 1.0531244933494548, -0.5840620682726851, -2.1062901557180154, 1.194710533911603, 4.637618384308447, 2.5196887497750824, -0.8172051010325121, 0.12242488496503769, 1.6877704692870898, 0.0918371830930922, -0.41194009686724453, 2.3970130246916366, 2.717928365978862, -1.3775582349843423, -3.175979729444812, -0.4548597296922495, 0.556402503877569, -1.5663849859092585, -0.949512694661405, 2.4925941557116187, 2.5460931644293736, -0.2584766166053461, -0.05340285482145374, 1.6344293387400741, -0.6076740358129493, -3.671147708160855, -1.575463888698846, 2.134297438591196, 1.3668454481938435, -0.6700088410348211, 0.8218224547568969, 2.1412761673948424, 0.04438712284132817, -0.36350020110024583, 3.4127741904613176, 4.913041856595382, 1.4348831585593378, -0.5600355170753242, 1.2335331901964985, 0.9247264920777187, -2.3682838544732308, -2.6126397077048598, 0.08011731776957588, -0.01722209707359116, -1.3759801620638867, 1.6113966193962368, 5.683621345703842, 4.182124308971896, 0.2391626132419048, 0.19247257148130945, 1.3285026250235958, -0.7001670509004275, -1.9562163716545704, 0.5298271751823781, 1.163821379063625, -2.555753412318066, -3.895224986841211, -0.27473210203290166, 1.6015693853795954, -0.47243354874281207, -0.6675405027922088, 1.6151676504468697, 0.9164443115161978, -1.3796847527526703, 0.5844926928356731, 4.005509051215697, 2.3706091920136085, -1.233932635064387, -0.6515599186535102, 0.9284147788001081, -1.1603451820626867, -2.5864500895796887, 0.30545954141941, 2.0900938976376517, -0.2793955935576129, -1.078481913371908, 1.4436847475093892, 0.9959144600051343, -2.9025918514180633, -3.0984769482306636, 0.600728542315345, 1.4027052557632853, -0.3000287929662314, 0.9792905321777576, 3.0244188863558374, 1.0183988570947196, -0.8819349046020843, 2.137026279295294, 4.617673985221207, 1.446716970884067, -1.9015760466135259, -0.838397131782264, -0.01565018250581543, -1.6698501456531072, -0.749579859498734, 2.4699873240576835, 1.2183620596327736, -3.377608226419363, -3.491452650222678, 0.06551183484260302, 0.36599354416512575, -1.3542608652558712, -0.07158747765120428, 1.0712847211871213, -1.7817903989693014, -3.2527040529608886, 0.5536950421969472, 3.2963119388927615, 1.0806434103432032, -0.2609051985254255, 1.5389353112938617, 0.6198532932475336, -3.2390738185136394, -3.2444894511219613, 0.14189523564021478, 0.5618703968652061, -0.4361507419226077, 2.3072088850014554, 4.873586960256848, 1.9060452633983263, -1.485304789994338, 0.19236680929696745, 2.014031277559175, -0.17230175614092877, -1.483628899131801, 0.018174603410553596, -1.170424851980282, -4.638842737052903, -3.279279784250785, 1.6548156054393137, 2.2199049407335267, -0.660523737845442, -0.5055723427312642, 0.8153749821744871, -1.1872194844267694, -2.3735250571199993, 0.8692220301334105, 2.584445549894175, -0.5059845969269213, -1.7537521944916052, 1.338624948766496, 1.9835806573037251, -1.1812383515945204, -1.6626928569140091, 0.5340763332091454, -0.12668234872304612, -1.3346059799412926, 2.0232129555198135, 5.222261180711814, 2.41143649566685, -1.2825051122214377, -0.4980618500444746, 0.04718887835132391, -2.599749759485941, -2.7029732723907713, 0.9432949900731082, 1.7289461638778136, -0.41800645971957806, 0.8424052838437299, 3.6537703049295387, 1.59648921779291, -1.9518728278899289, -0.4829535401124096, 2.240406028344605, 0.9614533047915481, -0.11574077622463037, 1.9764182215090182, 1.654627691782268, -2.161235008836768, -2.2719098675186524, 1.6500221940249278, 2.067031805501286, -0.6443278943226144, 0.14158497292555097, 2.5212745061992363, 0.8805075647188435, -1.2290679432845455, 0.7404176627540602, 1.874384416691209, -0.9036572514218725, -1.1540249036210408, 3.044101835954617, 4.036751758305136, 0.2548546483161712, -1.1245056927979207, 0.5516552533560465, -0.00485258706126276, -0.6085888022778938, 3.0623509185077795, 5.518080009001561, 1.5328528808346733, -2.4734629247894078, -1.0325038357363419, 0.5364255875668568, -0.7778899056614422, 0.2637585528768369, 3.553169839300433, 2.6118701580487365, -0.8051421242041851, 0.17204835537813803, 2.6923035101975406, 0.5615845331680978, -2.147020293499763, -0.33300416106179836, 0.9424374523231551, -1.8055208182469555, -2.5182944940189427, 0.7273083322679834, 1.4059368219457817, -0.769296859411903, 0.3832775399560785, 2.6962460666833064, -0.18474343790632744, -4.180038544563104, -2.525550667006585, 0.6226917912889033, 0.06076880448000142, 0.09006115065007282, 2.867199017167942, 2.4920326182642314, -1.020038734097315, -0.2848478900671939, 3.4882677846141896, 2.4766580679368477, -1.4032340239095165, -1.1701718423982856, 0.6844593661391214, -0.40729903802624473, -0.26998417957245113, 3.097632243876535, 2.799415551461321, -2.252850511102615, -3.6382878733097774, -0.20100422557484587, 0.7205295785220636, -0.6773018180333974, 0.9842515985013559, 2.5506654443048156, -0.5299658326311837, -2.7302333525761218, 0.14471480361060413, 1.7408564679371923, -0.8062032246212969, -0.8530845647583014, 2.391503829790428, 1.9005898007587372, -1.3973729767492442, -0.7650683435164306, 1.416112063786384, -0.28146841261274086, -1.7033666565641004, 0.8765317160228698, 1.26356166818836, -2.9922110905842145, -4.236246060148178, -0.6793976027044195, 0.36165390097817635, -1.4578281256936283, -0.1838476984215522, 1.9551158027300293, 0.11013924675657179], 'positive_zeros': ['1.27812485997042618912416988521', '2.14764156900361466243790405741', '3.212222830746104557366737843945', '3.92114472450991931029610353029', '5.18115738635750924872538772728', '5.71828251976588479336379211506', '6.43737142443464622018414457677', '7.65534770923331856946534099488', '8.432756471003110516970891810322', '8.75753002672412386070518090058', '10.01896932765680509211407332948', '10.63352068847175074370676050360', '11.45743206195825928563474383136', '12.26720589037999455939451347275', '12.82192286181975952869062415680', '13.87305998912855220890421306524', '14.46306937931465011358484898249', '15.368393722446384455154486627046', '15.790773435927583835608776393302', '16.847540959626665583730754739', '17.46844648941233233469073081556', '18.28281731167104926833423673063', '18.88620242510448352140748432577', '19.61215402271998846143247822736', '20.45683653220508102038112740162', '21.20709496226031534210511457377', '21.882469248486409505043436281884', '22.36025808561573646605760328792', '23.34688093497139587818615486636', '24.16427188408735293325681541345', '24.586430285686521505596954859387', '25.39420132720224762432054554290', '26.02223984730111858544774053870', '26.95933191374597769547609666415', '27.616217330119250064398609872208', '28.00706820508862125566012951770', '29.00846097275962647493646887090', '29.57221840363196713308575595817', '30.34630425531260627994614041248', '30.96493731685238558882462915163', '31.81783250350880419194361576423', '32.22605722002185260910373087658', '32.99888677319458236542236315295', '33.97752640643832023425209342893', '34.351464721925951242740958134203', '35.15106989990140621914461242421', '35.57155888137727354057221533867', '36.628665841917214112438674135556', '37.371351703239565736242642036779', '37.64972552406541426456956956415', '38.31951692649185731740815765347', '39.42284267181671582022776399703', '39.814541911519566502207774758894', '40.47667551500516048709477376333', '41.15926308856382253847533761968', '42.047504254308562525342304567208', '42.30500842783930027330648622413', '43.29118809625138602958222109437', '43.943978227124253445667373585072', '44.52726135584883045086490249373', '45.05759203154889374079430950586', '45.88280908651715152256311237170', '46.65342895951745454072334589875', '47.12794057884336205974745242089', '47.90455122981763731984362717172', '48.35968049963508555920692288451', '49.11913698552508619869235593078', '50.16415499986611384028628904636', '50.33610351465464785936653994445', '50.93581887489247083324117442884', '51.89606314549872336244168932122', '52.39925553377819383847099216060', '53.17247724472695117137249324516', '53.75409963477000370131751818743', '54.290901113317616026524632503214', '55.10682951394553570440565057132', '55.60801342825404834602490194278', '56.50501003939693727091822647422', '56.94253668518296375482262717371', '57.64689076818674855408132878094', '58.11923181693176754354350314220', '59.13198989797195235502474979492', '59.56552486973229585885785672248', '60.10866484342650550678534277433', '60.99977935533491028121728932676', '61.437923027419262316156810905047', '62.01192110120685731295274326515', '62.97631852560792734197587396999', '63.54106757820467049054395226494', '63.93925800931662264767478839400', '64.52393185402302319111514016930', '65.54609984636166406680716854005', '66.07359532628753301505734021856', '66.56127908000273778344451752208', '67.15731350273943897004177489473', '67.91560094675704094137513535577', '68.614452025937622640609912238597', '69.16377290361311308157099340126', '69.82955654073827350761027713256', '70.401407184613557128344783524617', '71.035501242702583756626268903870', '71.74666743295926408642198365204', '72.39281046250440219381376286737', '72.8767984730142516296147013629', '73.844289967688032672974937894536', '74.05686707711349762647018834743', '74.72449485080954492373711496976', '75.617612502353124629004216614367', '76.38883428780975336077825145975', '76.57764106015917791793575999952', '77.14934961125795364579478229832', '78.23274099282617047843213523702', '78.54187779922963764321409177014', '79.49772256024544329647611223156', '79.71715185166229532968515601770', '80.33187939295365451537144535269', '81.42248163580475888845977563740', '81.667428907224896389633159928657', '82.322701097238450733385438687814', '83.07280556629956148907005679837', '83.681408148770958925546868171317', '84.096300555784070427177454808087', '84.98674225918919027241804343057', '85.4822421036506637166925634637', '86.26436555009620206937945735748', '86.609967926345926127015189650129', '87.29878789215093469114532196160', '87.9994449425259404005249647215', '88.78326550412756879238010854920', '89.15186580097323334038944333412', '89.80484450706770596107240940083', '90.41429779045400417434241668252', '91.0573201149075728272464479834', '91.84399915726850464511979578196', '92.294649750064155215280989174140', '92.92033686393347857472750658183', '93.45050877305850936142474742650', '94.14210165598327706040156221489', '94.933005272333595254517954764463', '95.422734327167365112652307844484', '95.898895838925649012266483765493', '96.630113806765838325910233486563', '97.164484016544798438674754449340', '98.15167022627952540204107535580', '98.22694789126899702448356244574', '99.16818486043872263155636289150', '99.63859720746925284485004256656', '100.26151363835070794402400285064', '100.91080344288835616492144062179', '101.58972788234667613720268431621', '102.29205878605479080193758374083', '102.52300632217892385192214667600', '103.4325627646516673506447177016', '103.95163506247001517677037626996', '104.47308811818037799357154086226', '105.53477956824565195734914085801', '105.79189179098254595603561284930', '106.04185225736139127223479250234', '107.04355442747006320292678180825', '107.84408742177849435939096473227', '108.30916428579221945206289291177', '108.63166869586904320578687720730', '109.34212461343106096890307351225', '110.2620973050690250500921608341', '110.63325366595757401536411575426', '111.14608799909355995327804673339', '112.00507387458942821662018149613', '112.41819242764904614956964873682', '113.06549761786039033984392566820', '113.629784676981420347425210963667', '114.307593603953940328349553989994', '115.139714765488709079467125925683', '115.3030535241283738456193971799', '116.10263996299910506947052656536', '116.59955639482895447067859944565', '117.39426877449584558367043595889', '118.020376588322176549287685576145', '118.51644090813998025890825495078', '118.995270326547068782434878041213', '119.607828901616064630792639152', '120.51324315920392937520521572945', '120.92155274665056429239375241120', '121.576317420346937371694333321079', '121.93831233019280833786570112932', '122.71700377744835105116272612667', '123.4888360601146284206761142709', '123.84686696198233005568540793983', '124.46349596244606347153389383776', '125.27540344867888723708669489933', '125.63313599450669926778136449974', '126.20051326686939666350321558503', '126.98630183895236992020127729587', '127.66258341841131245755096822451', '128.018909867299178876641252763821', '128.75573221379526931652522830177', '129.1068664407800960720467876053', '130.13436832637595451746292469748', '130.44339610478968902548142092765', '131.03154454876086724685263245074', '131.86271001435899177946612412378', '132.18454495605897863521657258852', '132.699749431706806190336913854936', '133.78480030355841144638107336798', '134.02476343051036317797034521278', '134.60931989334518421164176086700', '135.25644137935292314296732377904', '135.74496723305885204392688343989', '136.58429716311521880569593240301', '137.12405279414113662144109484059', '137.59331988009029893508229669036', '138.227171142755296306409609034714', '138.70264012481278636964844539831', '139.55458821113360897457370954098', '140.08567902749641968436845292126', '140.50124846062207929096015392704', '141.22395488605165370101217318406', '141.8442215792760778594270345041', '142.33227292051174959758001053483', '142.89810749791880269241197196121', '143.695648863818680280365640427857', '144.295980882026332693353289238767', '144.55779159326962619704355806823', '145.413551194574526306910877557697', '145.76794808604948639433199144848', '146.661529580770689614897778247269', '147.35206580582650160190313642292', '147.49444025077004992659537838957', '148.19486711526133462848781143408', '148.83243545220063999066455170477', '149.68005834062241313731153041394', '150.05827891318540143533898820096', '150.63443149517916376912074244176', '151.092835776816912083555843107309', '151.8390361400591118139588190599', '152.635253128969230788504826402754', '152.87853286765843325728993716422', '153.49069959651309072731297047638', '154.358655771539316028647344581056', '154.7996817177620390519546016282', '155.09904260714540327117659107588', '156.0695183762111800101161796328', '156.54325519230586965262412263468', '157.168932749146662220156239921798', '157.807288572581148540417057099833', '157.973687376959989106703711912544', '158.94840521615355334043133962633', '159.604202707588477381761150221045', '160.0812431296295336627987990952', '160.49098603678233279295845111917', '161.1820978039022156980124297043', '161.831961643648536011679766314972', '162.37941660857945753002713023538', '163.01194022944613362254638166951', '163.65820581084489010297853887491', '164.04365489582158813674752647660', '164.54636149450465312230270208749', '165.47786570916934295853352820993', '166.02710215836051534947081204087', '166.25944620952004700980924529565', '167.10635133725159934911887383102', '167.73441727556273745348698943152', '168.03356406708195704527874257598', '168.86385757241305252878855017109', '169.417406482603156390443505668233', '170.15125208296655254451144187127', '170.34465196761318601624441755125', '171.07710490179202849125050735364', '171.74318205623711407782855326258', '172.4103721936072690443178862382', '172.79637663994475155700299871158', '173.52517711212772588323598189037', '173.9822975173527719480725885153', '174.59765487998018557752612701778', '175.10088170932290316193488503366', '175.959771041829815648903712243441', '176.45211459504079811181564519784', '176.8741126911419916979743637199', '177.271556870091401162133048547040', '178.211551022341179599530829122281', '178.87645306760646984089976056003', '179.2149168698678205877924532910', '179.66020313561450403393414679465', '180.528616199813066684328733277090', '180.9201239253305516914552034903', '181.607821617222292892360404235891', '182.22407158497182202799392454244', '182.63731440909032379650715604487', '183.369282773216753714458607771475', '183.93739118610644845811903455970', '184.333942946186436541426949153731', '184.98845140962227055116643033593', '185.84207550475384969788481369385', '186.263681109871406872999454397428', '186.54761936766211760173841416878', '187.39709199132155299966315001790', '187.83636788727560858769799959529', '188.61938178141755490435904891373', '189.216864558367664985936910196083', '189.61299464196309453237973217021', '190.03225696614396708328067528000', '190.80333004556790255888240266557', '191.58283085588078362547493062192', '192.0110011460512811452983166039', '192.385302472432944246433106096580', '193.085293723723173309586466676253', '193.73776175393267481379279934319', '194.286008576986135235918374653678', '194.77424926124358692594526458235', '195.47730250441553971353257404262', '196.0216620158164860473941432206', '196.531983322651943094387105169622', '197.09945950949437532044775465233', '197.61032908735964467904905721121', '198.50859498397357080212975823948', '198.81596000777908955190535978536', '199.39449468400260674472677485092'], 'prelabel': '1-1800-1800.1429-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.359164857335244, 'root_angle': 0.29555555555555557, 'root_number': '-0.282341456842876456149884567910+0.959313974540057522024035493880*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.295555555556', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.960983208414786046175026500289+0.186707100288181961417458125731*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.27812485997', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.147641569', 'prec': 37}, 'z3': {'__RealLiteral__': 0, 'data': '3.21222283075', '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': 8.359164857335244, 'bad_primes': [2, 3, 5], 'central_character': '1800.1429', 'conductor': 1800, 'conductor_radical': 30, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1800/1429'], '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': '1-1800-1800.1429-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': '1-1800-1800.1429-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.359164857335244, 'root_angle': 0.29555555555555557, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27812485997', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_1800.1429', 'Lhash_array': ['dirichlet_L_1800.1429'], 'factors': ['1-1800-1800.1429-r0-0-0'], 'label': '1-1800-1800.1429-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1800/1429'}