Lfunction data - 1-1625-1625.1152-r0-0-0

Formats: - HTML - YAML - JSON - 2026-06-29T11:26:48.804395

• 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_1625.1152', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9685831611286311, 0.2486898871648548], 'a3': [-0.9822872507286887, 0.18738131458572463], 'a4': [0.8763066800438636, -0.48175367410171527], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9048270524660196, -0.42577929156507266], 'a7': [-0.8090169943749475, -0.5877852522924731], 'a8': [-0.7289686274214116, 0.6845471059286887], 'a9': [0.9297764858882515, -0.368124552684678], 'algebraic': True, 'analytic_conductor': 7.546468273983207, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [13, [1]]], 'bad_primes': [5, 13], 'central_character': '1625.1152', 'coeff_info': ['x^100 - 1', '0.998026728428272 + 0.0627905195293134*I', '\\\\zeta_{100}'], 'conductor': 1625, 'conductor_radical': 65, 'conjugate': 'dirichlet_L_1625.213', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^46', 'a^47', 'a^92', 0, 'a^93', 'a^60', 'a^38', 'a^94', 0, 'a^71', 'a^39', 0, 'a^6', 0, 'a^84', 'a^83', 'a^40', 'a^3', 0, 'a^7', 'a^17', 'a^1', 'a^85', 0, 0, 'a^41', 'a^52', 'a^2', 0, 'a^33', 'a^30', 'a^18', 'a^29', 0, 'a^86', 'a^84', 'a^49', 0, 0, 'a^49', 'a^53', 'a^45', 'a^63', 0, 'a^47', 'a^12', 'a^31', 'a^20', 0, 'a^30', 0, 'a^7', 'a^87', 0, 'a^98', 'a^50', 'a^48', 'a^89', 0, 'a^76', 'a^79', 'a^54', 'a^76', 0, 'a^64', 'a^98', 'a^75', 'a^48', 0, 'a^37', 'a^32', 'a^86', 'a^30', 0, 'a^95', 'a^31', 0, 'a^22', 0, 'a^88', 'a^95', 'a^28', 'a^99', 0, 'a^91', 'a^49', 'a^9', 'a^61', 0, 0, 'a^93', 'a^80', 'a^58', 0, 'a^77', 'a^2', 'a^66', 'a^65', 0], 'euler_factors': [[1, 'a^46'], [1, 'a^47'], [0], [1, 'a^60'], [1, 'a^71'], [0], [1, 'a^83'], [1, 'a^3'], [1, 'a^1'], [1, 'a^2'], [1, 'a^33'], [1, 'a^84'], [1, 'a^49'], [1, 'a^45'], [1, 'a^12'], [1, 'a^7'], [1, 'a^89'], [1, 'a^76'], [1, 'a^98'], [1, 'a^37'], [1, 'a^86'], [1, 'a^22'], [1, 'a^28'], [1, 'a^61'], [1, 'a^2'], [1, 'a^10']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1625-1625.1152-r0-0-0', 'leading_term': '0.588945116191945813065017871763-0.217886825330920310079430960451*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/1625/1152', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.6279578158914267, 0.3995205511708777, -0.05755814480993996, -0.39494517343634794, 0.16860305355087918, 1.9631666994990093, 4.148433327871433, 5.033356671158861, 3.480374678002811, 0.26061638541886106, -2.1223235717345292, -1.418006491409241, 2.1853038457478338, 5.892018207810382, 6.663361863197077, 4.0234632336181, 0.4769773285146957, -1.0155707349070942, 0.06881321126945746, 1.6272439845428333, 1.5707677183328754, 0.19988788626306286, -0.45563872716796083, 0.5607694359227692, 1.7505672528753973, 1.0362926384908069, -1.425331869493446, -3.168665570727763, -2.3613031283619748, -0.07881647970408844, 1.0660492783740845, 0.20929081380023243, -0.8785589774399583, -0.45176170655283443, 0.7203443193257844, 0.5970355448030928, -0.8567881088537476, -1.2336675725144657, 0.8073898110856185, 2.893010886755644, 1.4907530227383692, -3.0505457943496412, -5.900178340646829, -3.3082880693983956, 2.357415869905181, 4.899559648630809, 1.5194386174264793, -3.994768118873859, -6.044051151141971, -3.6678268646428345, -0.6327818055085077, 0.054847564315717176, -0.6202151960523226, -0.4229301851281467, 0.40386577615835983, 0.04231229622126795, -1.4087595394454588, -1.8165810361626522, -0.535978268858981, 0.2930287699161421, -0.849691299764127, -2.070558979222641, -0.7907647095871755, 1.805025742008386, 1.8680090395243512, -1.3309525819506671, -3.6189309315534137, -1.6062695692089957, 2.0882284620530625, 2.156101247255544, -1.8360722743779427, -4.650054372277719, -2.7330043584102985, 0.9567330453873185, 1.6209779874529107, -0.399457328003036, -0.7491037961850165, 1.848569786784868, 3.6531908520813214, 1.9488117027278022, -0.5805459599214206, 0.021001210544193537, 2.930382780591814, 3.9686703190801347, 1.9567051310085706, -0.02658827300193715, 0.07962683939514023, 0.41784052176397674, -0.9393746610399352, -2.386729735389933, -1.6118802502537066, 0.23943597342790046, 0.4768495146340477, -0.4634170307128138, -0.10509860478326816, 0.7675639826179531, -1.4930403144082642, -6.377832975277393, -7.227616135651431, 0.16572812656659675, 10.09726135727267, 12.89298156488454, 7.084657239779569, 0.6400059546654648, -0.16831544255378797, 2.1103919646629183, 2.124249871174243, 0.010770564578651649, -0.4536145082695323, 1.109620382464453, 1.5910839261661398, 0.23478689687658416, -0.38373558028515375, 0.5346494851738227, 0.5462213765630227, -1.144002650278926, -1.6597089027883716, 0.413211986955039, 1.7811237172427699, -0.38119757227080586, -3.240413560870569, -2.49176136935254, 0.6022129063907175, 1.3301943039603827, -0.5842675489775955, -0.8839517138627965, 1.305256149558008, 1.5932700222608442, -1.6225786305034329, -3.133166082670473, 1.035858737246628, 6.33477724126827, 5.955403923949042, 1.186672592319067, -0.886583645375558, 1.489570393944433, 2.853851019038728, 0.19728639644119927, -2.349358727504689, -0.9569023094836342, 1.6605990389553127, 1.3204389025317458, -0.8501228809879442, -1.25023746011037, -0.046020804706176525, 0.25295319394588933, -0.0403747214900667, 0.9274728712345224, 1.9256650836061056, 0.5649166324612804, -1.4252231089271423, -0.5538091649898862, 1.4842336203659043, -0.2576990442056591, -4.628194674046008, -4.281050232204314, 2.602282101941174, 7.72811303649704, 4.440525826608863, -2.153597548701542, -3.060438968353274, 1.3850538557687027, 3.6705979899660237, 1.4659813966032889, -0.4091151690535013, 0.5302880122284642, 1.1147987221333187, -0.37706905191685236, -1.1709127632005059, -0.1502031977133706, -0.45802746404202177, -3.1045189378618376, -4.002856129596032, -0.9064139491269819, 2.1727626081924094, 1.5311010584438078, -0.2815138154874148, 0.3577567056031241, 1.760028193288947, 0.9775630751594786, -0.08376838912850872, 1.3764941591731927, 2.7478767977262275, 0.421223330061709, -2.6472242269601756, -1.3780497674537422, 1.8365847829550412, 0.652878817129891, -3.2563539847666476, -1.4936020509414156, 6.789794741002394, 11.769119419633318, 7.3938307269288455, 0.047145496084327596, -2.0446658108138127, -0.18423688736766303, 0.04036700867486772, -1.295525181784448, -0.8166690686854725, 0.7152864547035372, 0.4066789873112861, -0.7830105083415783, -0.4116973997591828, 0.15837669419333572, -1.2410781628148753, -2.4896814161514706, -1.0619843512083207, 0.4092024755188242, -1.0897856979415328, -2.252163178447618, 0.9750425115226697, 4.534992991273852, 1.8394001715166006, -4.224199382718329, -4.78090888510142, 0.5240572944738111, 3.0050436540746657, -0.49426833966307104, -3.219330010130993, -0.9607245128412624, 1.5306059189119603, 0.4291217990264233, -0.5196456056318349, 1.7063488043625865, 3.0894124708905633, 0.35807454131465644, -2.4509246019816526, -1.2803701726185355, 0.8427913649869581, 0.10578491637130104, -0.9897106037644796, 0.8453246059584043, 2.874122579576951, 1.5262115230338482, -0.8527151038956063, -0.7122039185391861, 0.3144657174702509, -0.2627822197199992, -0.42967117138821054, 1.343081938415568, 1.6663297230933465, -0.7568439142154386, -0.37771356206396456, 5.260006009788245, 7.901003371032189, 0.5202935459019659, -9.372319940128133, -9.531785529362967, -1.3384493546575986, 3.5262029684796747, 1.4313238381327158, -0.5904728813940242, 1.0234562034457952, 1.9890671669799773, 0.2843374122982676, -0.4681581035837473, 0.9328353017019451, 1.2521135557383065, -0.057706068058308, -0.10121154065293647, 0.8258716099420188, -0.05757424228558132, -1.2435593352597063, 0.7377617936904162, 3.3404311498885018, 1.3735839084086825, -2.9557042042618926, -3.014819267715928, 0.56789615083417, 1.4596562119891885, -0.46797503004405017, 0.05294105846613541, 1.9618036939475942, -0.8923797387218844, -6.79876021884138, -7.064774624515113, -0.9202566902707221, 2.8890329335266824, 1.042864475709228, -0.27775589452199406, 1.5420310737217409, 1.0557982344051595, -3.3606595947537947, -5.216711553472516, -1.647177159949068, 1.4880879280888548, 0.3491221352674523, -1.1316808577769788, 0.016419047081168855, 0.8550405870232463, -0.3223687980398279, -0.803508289521063, 0.03642692124743744, -0.4752269867772545, -1.686454509809996, -0.42635850641440326, 1.5615467431850032, 0.39679559085497906, -0.9161444289166774, 2.8530704329323555, 7.218197734334942, 3.540306322740359, -4.6312945644646195, -5.138104464429099, 2.7252071524468904, 6.728405613332784, 1.828601233194302, -3.18166674839272, -1.9787671667335038, 0.6145847231289032, 0.05666519576331696, -0.7487315238401042, 0.28439244618229104, 0.3565338053191472, -0.8250806493435665, 0.15640688127406366, 2.404597420888619, 1.3939707776873456, -1.7787783847374463, -1.8150523777386915, 0.6418278660066842, 0.5115721274557923, -1.5163434105744973, -0.8349585279397211, 1.2059583019296136, 0.08951816162173948, -2.0919355711372116, -0.6117337078105856, 1.880883024987678, 0.49578649184777224, -1.5619493118077412, 0.45652616350168196, 1.771415346481934, -3.5915040055775047, -9.560646617248915, -7.0393336000241185, -0.2960074699699658, 0.14790596828656338, -4.390351669396982, -4.486386994434541, 0.2647448759598025, 2.269645193206845, 0.2572864522085361, -0.6827455817404412, 0.05811936638199414, -0.6336850206432108, -1.6719429654182312, -0.5054936878094124, 0.6545039860923467, -0.5126087907943968, -1.2706624855129582, 0.0886293868487952, 0.4087012141065198, -0.7053195201256256, 1.1327458611958052, 4.8250676835815876, 3.1500292444472002, -2.9363344993307856, -2.8899125109251824, 5.2318605643262845, 9.828727977197765, 4.9726413574630675, -0.5999125730857624, -0.12884433533769127, 0.8783679453956217, -2.1152622628285953, -3.984796229291555, -1.4698819255854145, 0.2347695490735333, -1.5874112421855129, -2.2859118673245424, -0.21397922020456311, 0.28228480220527885, -1.0803805897645269, 0.3156974366617374, 3.533750518828953, 2.89546034267532, -0.8103861551151049, -1.6916967692536722, 0.16491993110824527, 0.294838335360202, -0.5096752865047732, 0.9538463982415647, 2.350235463571669, 0.8167497305290833, -0.4243518675436646, 0.3869533776067703, -1.6483690482485944, -6.760072553918347, -5.6736994523877335, 3.9515102216360956, 9.563605327764046, 3.2085383840290724, -4.930924675214347, -4.001643806630514, 0.6899859362704936, 0.20191015138980659, -2.453063180901067, -1.147366269603145, 1.3026815590012937, 0.557841142763176, -0.680353185213967, 0.31447499090241565, 0.8999332405073489, -0.026634604105206492, 0.24515784521081152, 1.2462261940689112, 0.3020484918456525, -0.05192220436833686, 3.5165256559263307, 6.3944360533893425, 3.229998960435837, -1.3143036274886786, -0.8923501667946451, 0.7959833198880296, -1.1325289356448642, -1.5699205848097593, 3.91273850539123, 7.856940490142827, 3.629974089454711, -1.9357061630316532, -1.2643688087930787, 0.7704646928029698, -1.7111298006435973, -3.899935011914149, -1.1969930662344965, 1.3298408570021547, 0.13141807650579768, 0.4748639454262149, 4.5364361022780395, 5.8076464452429635, 1.7814648047625992, -1.202157878500933, -0.19466118363684373, 0.34200313305919805, -1.0568342182758137, -1.011276376229367, 0.14895132525940546, -0.39922649153169854, -0.7716900216073681, 1.1860347114384007, 1.8441103061782629, -0.49847328283934556, -0.6438528246456886, 2.3962894120278673, 1.5897525904315593, -2.8862769070101386, -0.27918263970148804, 10.350704383760808, 14.239936741115883, 4.822627392998785, -4.873307408349111, -4.092414289602794, 0.6267286469681167, 0.9653375258656658, -0.2560971147398329, 0.6121863523771437, 0.7300128883379347, -0.611509388118493, 0.13366800670587506, 2.0157840031748577, 1.0906411293882667, -0.73174720652897, 0.18082081967493221, 0.935404557034626, -1.3026036029499422, -2.08543076650296, 1.1749250720150246, 2.8007739117866515, 0.03569069877533243, -1.352781758792362, 0.6457890809235006, 0.27508726776168096, -2.9485149561586317, -2.645421377528381, 0.31651802466363127, -1.1678247015161554, -4.972332757523719, -3.0753843706211446, 1.5624625883710777, 0.1405050946766512, -3.8459742980430587, -0.8102165108200499, 5.8766802891410945, 5.9546528867556585, 1.0663723386012758, -0.14003966376006438, 1.7004832019539458, 0.9541334247326466, -0.8110569669629569, -0.037064116712065276, 0.5663026183507397, -1.1551491587423914, -1.7379530306766782, -0.11656623022355875, 0.15260293660182594, -0.8132967372186402, -0.0897470948019976, 0.4378977238884231, -0.9176151784845116, 1.0874403743363832, 7.959711883705028, 10.024307079211365, 2.8603465599546043, -2.02848478765938, 3.277629090444436, 8.604943093145662, 4.577038784207999, -1.1857849215631355, -0.26620410911467607, 1.796167171181102, -0.8271635570082804, -3.018962581353571, -0.9570823773908332, 0.6514270573284526, -0.1254328623901272, 0.6976161436760909, 2.5241369173131156, 1.2344570283094358, -0.7249738949017207, 0.9191109717768929, 2.4860327746512905, -0.12110759334175757, -2.284065688893565, -0.1284031392131138, 1.515233226718725, -0.4798249715524313, -1.5819665698111844, -0.07812456075925159, 0.18465712378992422, -0.13499345270771887, 2.133705308622592, 2.4831072304664983, -3.4402642369198864, -7.730325913002367, -3.0705237529171057, 1.8200174064414474, -2.52888080520999, -8.040465293919548, -4.328878281441916, 2.0102273536725868, 1.0719401229960002, -2.4000599476557283, -0.7076053581149939, 2.2107750254033203, 1.0078138850576308, -0.8091205013975441, -0.07927021042695209, 0.3287952738319955, -0.30253618342153155, 0.4123113234485063, 0.8078943913938602, -1.1527784603222815, -1.7160059632571742, 0.9013917339713656, 1.5957745647400943, -0.5297199168614236, 0.8009544304876767, 4.902228396077994, 3.5520551791258717, -1.8130378713991318, -1.4617165116187278, 3.0811982062269254, 1.810072993697714, -3.115978915368965, -1.4527231412315786, 4.39785087993293, 4.305974265482333, -0.15635747626768487, -0.9889451054318548, 0.255604452809208, -1.0725627406248124, -1.521492713181156, 1.172148145779858, 0.983552058959346, -3.7191432895068823, -5.380832051575776, -1.8316587459541078, 0.21370904016140616, -0.9729815233248892, -0.6594054720949752, 0.8836083664557816, 0.23722801141225783, -0.38777808513199863, 1.2968475349995576, 1.5434229776851858, -0.680796266700512, -0.5608651867581032, 1.4701422792860281, 0.3832649602497634, -0.7896800342169289, 2.9708076661945118, 3.618602277826758, -7.507739844722543, -19.0545012284905, -14.957447492357739, -1.526554223026775, 4.013498711351316, 1.108259681521233, 0.09868897625321328, 1.3776884291617686, -0.02631325286141961, -1.5941003432699197, -0.19876860732713686, 0.655804951632247, -0.45438781836538467, -0.07592621838939886, 1.0458262115574237, -0.3502240712141107, -1.381779661057842, 0.9981898270494673, 2.2919552587597365, 0.03182748931625736, -0.2974135959659579, 2.2216321762013953, 0.68504864254836, -4.413408368612967, -4.5987687122090595, -0.4638087224904103, 0.07308247646637672, -1.3207008479439781, 1.6670725178455172, 4.387904229344249, 0.5248460245004836, -3.227145223731272, -0.3204575437778621, 1.780733725991423, -2.7582408001372376, -5.72536358294202, -1.7067082382965153, 1.5651621036771173, -0.2650021645588038, -0.9356760637353336, 1.3214760629990927, 0.7756027806035921, -2.1438165097528983, -1.9109729946250276, 0.1116121595036401, -0.3122383413924076, -1.138960750299191, -0.18515343306862794], 'positive_zeros': ['0.59014723199921590526093679671', '1.20243914477480521632678143909', '2.83758414858957258926771610743', '3.58081079328031698201531103574', '5.056041918916145090706647686492', '5.61287062272810427488908149977', '6.61107857179976219975192041224', '7.06178674122135273995190836388', '7.95629193110201097369994269330', '9.07436714899724735159082419617', '9.734360224789657124113474949703', '10.42542291958715249923830710122', '11.076585841654923102102548185973', '11.77936340292926907094349602125', '12.61418027264304374551293625076', '13.61896479064841327378561392732', '14.45806726359374767719466717399', '15.76817708892370532903217218414', '15.97161566954458630569556833725', '16.7077027689168233741282392449', '17.19849189753290650799048477078', '18.250099601420229276084464378467', '18.57414180170612395270006782920', '19.46653375626445672743780687568', '20.19981268701580799748248713008', '21.06289306025729622380398861837', '21.7480800308148947703475520986', '22.718232313682113001359545692538', '23.37650468586925987809421453294', '23.86584108983016608420315378381', '24.902459927446773455062840001024', '25.30972023829555808069267716550', '26.5538283917681261952343711292', '26.84035269186490596694879883400', '27.32846293164745842138033291048', '28.38710195077977181935653512758', '28.90090871482122721482409544921', '29.40242973461478331298779164404', '29.86628998510123011511588103193', '30.93249698428336295422289773741', '32.24820136441885164508944926929', '32.527658024930037463419321170', '33.43936110392669202425260393300', '33.85879412148063875768175918501', '34.74158620192823199860945713305', '35.15554570406375520758766127124', '35.743384093623823231893688094443', '36.511752842281457155208617879504', '37.151809651594226193978426257304', '38.05810202120151969943180155537', '38.65974180377672707315205998262', '39.20321651089377096653630921883', '39.86225652469188677659665164128', '40.570513564891521116683366211', '41.65782795994918546982212705119', '42.030422603144036257265531753044', '42.829521747221499240223774693263', '43.53659116020790071600300554269', '44.24586885517372186673771827458', '45.014186469027174642405181761788', '45.49629231122450798632740626423', '45.66634019476549225128673823745', '46.63545343281273619781927077873', '47.25885730776105906393277819956', '47.79201878987556374874889323245', '48.64720817515633196660193997076', '49.571684999295303086811543961193', '50.222862034474054521598999228199', '51.1220644689531841607947583079', '51.44823206125242205024466016613', '52.12174372646067414777300448285', '52.87049663167914204551613958483', '53.012590693410693640112398075054', '54.133079067733919098676306201920', '54.92413889160473054554847083552', '55.240974985985530723550593455478', '56.16411024579898872039921718602', '56.311638197763546423787413687273', '57.22220563777016093777649795834', '57.930601656888827811824202267014', '58.48813029699606058707811318171', '59.13077502657452194593547176014', '60.31523200014496802142851656440', '60.975170641608480403939781903691', '61.26069592101235915699627151284', '62.02371476901347340343709335711', '62.59253607316766631569325351315', '63.258528566425243105235065118787', '63.51256847415925247674179833616', '64.53773211027190336352323019194', '64.83920730548075720755672228356', '65.55900063154773977755663531998', '66.341533268917215933455858538084', '67.15790717320608072425922308402', '67.77877572912893391794514833252', '68.523966078582007842050699626169', '69.13186427277476857339788382174', '69.48719173633048868802656516486', '70.341566770779472848151487108102', '71.09141387073916725603975146925', '71.58115218796734453768453547330', '72.088421586720157755430757723618', '72.98804020026194252753059065132', '73.61254619678826401954971644095', '73.97896103294681376264509129778', '74.47261988355411287960420861444', '75.21915922468866511300679481529', '75.65555369227080049923157518888', '76.5771739309711890683601543875', '77.5527900333463299872305190336', '78.27448353949606981568126277609', '78.603775903637726403884528726382', '79.42401959579733881499886710750', '79.816432088500013922446149739709', '80.60899871681624144789777074452', '80.96935360474256486305881934815', '81.55217492938862411307444732908', '82.11406253312572232147478246917', '82.90577608063302233137282657864', '83.69715879423949392484526730031', '84.29108151740506849474019285191', '84.67996004885064885373186475134', '85.26001971007431699981794616536', '86.295978946936856965593197852129', '87.01307158864360345833079074663', '87.26200054985272359214343836297', '87.901617044233856035961223916123', '88.86978859736158766828634743163', '89.422994928041591191742469278875', '89.99698229382111150363195233362', '90.554777907176930827512772729270', '91.23064306311522609877401758568', '91.42894664385630830267256430366', '92.24075364455464754069335241795', '92.864245628234345103878972306877', '93.25381371511034778948517956320', '94.19123868636505547336663492270', '94.90072386227473101766221280438', '95.71021946489264341900676569770', '96.45263867505701340448947378645', '96.88695026408159777427036062279', '97.426614588910985211246558445370', '97.90297128510114789561102794336', '98.41623593170078261778825973354', '99.193199465223331841039209207556', '99.908481782545156113737408389500', '100.388261065649402290290956769277', '101.045689821804218385850704921765', '101.572998349559090425152675367011', '102.24796168218559406978410016296', '102.86502001620632072911041622892', '103.39276484346322913396848499702', '103.89788828616325533705546514667', '105.0206014440666647376790339562', '105.32512310440080404286808772528', '106.23199995389754904095095362092', '106.91300402376003288967427775488', '107.46088157738443304930365326869', '107.63739607900989701009265752055', '108.52512797637501504843482507491', '108.96637372753057245566293357530', '109.66911160596430720227835774713', '110.10478609662880442675558091413', '110.515527879825438818347847620695', '111.408411424519750756397562460786', '112.00442313159272157937382200657', '113.06671503271570165600036360271', '113.455567294558201549024451439525', '113.878111367109766917078688548419', '114.868028628350549475136938778253', '115.07877581064428753271730004068', '115.97285226454462676768036886552', '116.31675931017946442547022858984', '116.84303960085770617694925802931', '117.73845314442142008752226794695', '118.4056050620585017684680082230', '118.831262322586733360909023778414', '119.22998581430403328768939528606', '120.128591091124612313037871113626', '120.48298231394308393560346520977', '120.78490842942619980941075848983', '121.7592502528830231608094749759', '122.60094608632242256906622698502', '123.37347688885502229150181888408', '123.77070955636225236508202955593', '124.49291420356160038493061259286', '125.09545285708602944852429086521', '125.557013838194343644289080929500', '126.23908974267787013161797600402', '126.48750414133398982525525851631', '127.252283351184927500789202229077', '127.50958176508415964560807689981', '128.63129583857995723317709191969', '129.176720346405314922522409200314', '129.555259148884864581991486465361', '130.119467050411030818388200332783', '131.10952646783156971311650694668', '131.6975241909192099356859452111', '132.03234373413481124227391048519', '132.913508538079319726842774658053', '133.464868751774027181390138795951', '133.68428052886881185063504028301', '134.8194113359125617759551600578', '135.3512840321113489614939053180', '135.716859058290168076988272904512', '136.4977085889344952643027104997', '136.7586836193322799622791079232', '137.33837262051773295777119297148', '138.062126019782999937594759527050', '138.5122760646583897640247525229', '139.16968125154422662639190076337', '139.697899834279403577354335108421', '140.750252403811432599841753123523', '141.50588627993949069374071769410', '142.06843316468208860137411779332', '142.3421765556363144249543916647', '142.972571209404038025407316699892', '143.41672872167360060489069941513', '144.21234754954333307579170087425', '144.65539191337153694541145019849', '145.16180141227836674967742211192', '145.84189834935594669093266584484', '146.565951622812240945635037820279', '147.09362983515171948862188933456', '147.53020388785000423409981997255', '148.38738550249434544002379110683', '148.642606469953504909275613601588', '149.5578931388416568619486969205', '150.00956559229275683158275344356', '150.66134812043461290851518254149', '151.670103489156534834029278407807', '151.903474924818282772148600843937', '152.63478560221505417236377666245', '153.13274044563463273912676353593', '153.56907753566699625781535876028', '154.400847898774894025951527521413', '154.73458526143999854511958887444', '155.33358429352188351893240160460', '155.739557073167460554004369078973', '156.17458108361936810901738278463', '157.30272478812483856693745693899', '157.67418211447578455504238005482', '158.65415264567381520921293141358', '159.08821627812641961103902348379', '159.6187806293344020005567290528', '160.429926498659002652152624315610', '160.88489204104040615837056497057', '161.11820974450658676706411435280', '162.02324531427630217415119709930', '162.39064564879038932036527806710', '163.11463413387441263525513258743', '163.76309215313874845370769542931', '164.31693479886983519258600154473', '165.01749522474086144137732641827', '165.3821279999783132904852969015', '165.661921362511157101158797361038', '166.4103122015635252467266367704', '167.32893478556809147730866759781', '167.69692908644169362979995258975', '168.62271013755368578495236797927', '169.140988730255001071171975802086', '169.745778101461874342569820930226', '170.44041452718412939604213895139', '170.95889390542750174913824646401', '171.39317006968601875699121614317', '171.764696459730561030640511884606', '172.34306788814807650629888845103', '173.02768605832260151411834385781', '173.66144316539542121190366071293', '173.989799684118310259346186736196', '174.88236912380236723953144004236', '175.409212362135458665487546163013', '176.04196508199388203763457417465', '176.63765331139909981241942441443', '177.48619825918882232373331643040', '178.01200258752660478544917845317', '178.2525398291314189581999209609', '178.93644077388337095140222087765', '179.45417146610430553486344391874', '180.51364943819525949079328974405', '180.71916346261601408362062259078', '181.36423055455244716066990197584', '181.927777388379323260458449201968', '182.289082607363447297674575695250', '183.02708506052224395041500879088', '183.51670778637114239056325739454', '184.11117865531106465952582814855', '184.478203196186454341953929155505', '185.13753805427443577137661535516', '186.29429985895472547868059882125', '187.035169195124229717290027035378', '187.15616546977744790417209828467', '187.80915867599024596713663687473', '188.47043489345603119487170222369', '188.93976882441843108348472381463', '189.39105259625880128783793685016', '189.94962165666562796082672664730', '190.52158853680474795162269432670', '191.25423691107758482932321704645', '191.60487300407696253732676837409', '192.23155654912609120262356227944', '193.176270218164437570634054856629', '193.45007547462684658516415699490', '193.94030222042108890244401640563', '194.71607970747210170223793817036', '195.33505918481007795734768428920', '195.785162074183038470286875812363', '196.6700189614641587807730534743', '197.15524959291472478543347082679', '197.636011773689233184673311683216', '198.20605659060152941911129306624', '199.03342563511346658128366783566', '199.29918222776775181841208992587'], 'prelabel': '1-1625-1625.1152-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.546468273983207, 'root_angle': -0.1127917604527497, 'root_number': '0.759214130155597604099850135272-0.650840921095223775667616258401*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.112791760453', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(100)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.527356492708901666580275614421+0.0300681381017502892072463184732*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.590147231999', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.20243914477', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.83758414859', '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': 7.546468273983207, 'bad_primes': [5, 13], 'central_character': '1625.1152', 'conductor': 1625, 'conductor_radical': 65, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1625/1152'], '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': '1-1625-1625.1152-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': '1-1625-1625.1152-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.546468273983207, 'root_angle': -0.1127917604527497, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.590147231999', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_1625.1152', 'Lhash_array': ['dirichlet_L_1625.1152'], 'factors': ['1-1625-1625.1152-r0-0-0'], 'label': '1-1625-1625.1152-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1625/1152'}