Lfunction data - 1-837-837.238-r1-0-0

Formats: - HTML - YAML - JSON - 2024-04-24T10:38:06.220197

• 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_837.238', 'a10': [0.30901699437494745, 0.9510565162951535], 'a2': [0.9902680687415704, -0.13917310096006544], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9612616959383189, -0.27563735581699916], 'a5': [0.17364817766693036, 0.984807753012208], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9975640502598242, -0.0697564737441253], 'a8': [0.9135454576426009, -0.4067366430758002], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 89.94814205310114, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.238', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.313', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^88', 0, 'a^86', 'a^20', 0, 'a^46', 'a^84', 0, 'a^18', 'a^31', 0, 'a^77', 'a^44', 0, 'a^82', 'a^39', 0, 'a^18', 'a^16', 0, 'a^29', 'a^59', 0, 'a^40', 'a^75', 0, 'a^42', 'a^43', 0, 0, 'a^80', 0, 'a^37', 'a^66', 0, 'a^75', 'a^16', 0, 'a^14', 'a^68', 0, 'a^43', 'a^27', 0, 'a^57', 'a^22', 0, 'a^2', 'a^38', 0, 'a^73', 'a^39', 0, 'a^51', 'a^40', 0, 'a^41', 'a^32', 0, 'a^85', 0, 0, 'a^78', 'a^7', 0, 'a^50', 'a^35', 0, 'a^64', 'a^54', 0, 'a^51', 'a^73', 0, 'a^14', 'a^77', 0, 'a^49', 'a^12', 0, 'a^66', 'a^73', 0, 'a^59', 'a^41', 0, 'a^25', 'a^21', 0, 'a^33', 'a^55', 0, 'a^20', 'a^38', 0, 'a^46', 'a^0', 0, 'a^36'], 'euler_factors': [[1, 'a^88'], [0], [1, 'a^20'], [1, 'a^46'], [1, 'a^31'], [1, 'a^77'], [1, 'a^39'], [1, 'a^18'], [1, 'a^59'], [1, 'a^43'], [0], [1, 'a^75'], [1, 'a^68'], [1, 'a^43'], [1, 'a^22'], [1, 'a^39'], [1, 'a^32'], [1, 'a^85'], [1, 'a^50'], [1, 'a^54'], [1, 'a^51'], [1, 'a^49'], [1, 'a^73'], [1, 'a^21'], [1, 'a^46'], [1, 'a^4']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-837-837.238-r1-0-0', 'leading_term': '0.0145880679021520653975766397710+0.477264579372556676973942509211*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/837/238', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.47748747674549624, -2.7774043111629565, -4.389082699831184, -4.680402575207532, -3.4940095024383373, -1.4029436751923026, 0.4855220185108491, 1.2089465287080583, 0.6465965561729827, -0.37735405510090736, -0.7761944834707939, -0.16166191040945013, 0.7732709370311786, 0.8822234088417131, -0.2941679586190349, -1.9584047937419873, -2.709656261038641, -1.8952919750541815, -0.3283406912441971, 0.46647401496149626, -0.16288689149324692, -1.2252269115870316, -1.1088942395331138, 0.4941736731308616, 1.8329888481925225, 0.6158126168505809, -3.472145939358919, -7.8709254197796295, -9.126257652285913, -6.064137470396877, -1.0041131465269888, 2.3560667554899877, 2.352158132142945, 0.6126234507663737, -0.04896010389087355, 1.2622585893959253, 2.7986108374617436, 2.4638472753322094, 0.35013379582136933, -1.430025377851181, -1.30217177507344, -0.027842575232702584, 0.4135887217408337, -0.6101950990626854, -1.6333945702056099, -1.0984804797854169, 0.49975664453588264, 1.1973982752215075, 0.20093850712696243, -0.9265489999627239, -0.3318209020490677, 1.3410319658260024, 1.301018050348629, -1.8476221729299587, -5.696958801866378, -6.214183200465946, -2.3861963770990693, 2.2408492504968627, 3.3216438218315396, 0.5351458170637473, -2.2637883422898946, -1.723870830436522, 1.2034415156257325, 2.8575196033535475, 1.5875045748939538, -0.4287440423088363, -0.3229329193003416, 1.718579716330742, 2.9564123028933755, 1.8666977133526876, -0.03398440678161516, -0.5669599183650523, 0.12851358956926012, 0.23042094431227259, -0.6595157070933082, -0.7095446923095704, 1.261054706401627, 3.436812131401018, 3.0097339391933744, 0.10674430233981848, -1.9983196634191518, -1.146758801721471, 0.7198218045588216, 0.30594601382633063, -2.041053871085102, -2.196162075071215, 2.218404367971999, 7.893031075922693, 9.186069482207966, 4.872338329042677, -0.39563606697952275, -1.7957398571077483, 0.24357393280315406, 1.6443930241628024, 0.462722086062547, -1.1474929155195612, -0.8043445133217556, 0.5686613097130402, 0.5533664169868269, -0.817988103343911, -1.1522062175904528, 0.42434568390844746, 1.7067585257385098, 0.695520379421455, -1.2931663709936971, -1.5779247463575263, -0.2259949117473781, 0.09507199379865881, -1.5094013878110488, -2.3918514489559937, -0.38941907406195353, 2.267154093641675, 1.656215631977203, -1.763888541335206, -2.789388754185828, 1.6815323130293796, 7.7944659663126075, 9.076251256491574, 4.511043832136557, -0.4888121472206497, -1.2658427869127489, 0.7752073378311056, 1.4580082996268415, 0.05302205030938904, -0.6040313932079385, 0.7064418464755082, 1.6090277545650333, 0.1888813751095532, -1.6934609418668665, -1.1905739961234536, 1.0895165317010993, 2.0195317668005335, 0.705126097750896, -0.49508523854574155, -0.07460917925921713, 0.32860880702274037, -0.685460339655945, -1.0248653131346976, 1.903438506288147, 6.14260797786211, 6.705529453896514, 2.6379774560834233, -0.8189753245162417, 0.8873404776228554, 5.15500038908447, 5.780301716609125, 1.6528776412011048, -1.9597430845835964, -1.1851115016529998, 1.2334072803367246, 0.6469466256887395, -2.4530474989175364, -3.58976626740528, -1.256590506251329, 1.1842576154849371, 0.9717478172157824, -0.26099948612241664, 0.09043682103183383, 1.2377403144609902, 0.8390245502851887, -0.586443629655742, -0.4785644983319843, 1.0925212944614255, 1.148338154950249, -1.1671523941602406, -2.706105443645928, -1.2651277159746377, 0.5946121159113439, -0.3291391410154927, -2.093874631555628, -0.09574965817054694, 5.223255465454792, 7.770074166740314, 4.304204852404305, -0.5489594273360053, -0.8191469791084642, 2.2625342164598568, 2.514308966064267, -1.742243736457433, -5.368952072781349, -4.219098577478997, -0.7538686906887786, 0.4775253190674331, -0.5571971493403886, -0.7900300395372929, 0.18460473965772167, 0.011362775615337634, -1.4634660057046796, -1.4541991890176542, 0.8102840522151684, 2.2834465649716376, 1.021452447478348, -0.45206309852143656, 0.6523730108537794, 2.5911317301763983, 2.020239039589087, -0.22253371518394735, -0.6591556046890382, 0.2763585973402238, -1.6093993886598854, -6.4485697865173774, -7.8065255867192525, -1.3669170320561728, 7.64449443183493, 10.389418129507948, 5.755624642240338, 0.6989815614394819, -0.09077773891521475, 0.6981045616105434, -0.5462927349999378, -2.193244099549539, -1.1122210913538177, 1.259046050675361, 1.1853711099454145, -1.031305789509647, -1.6948728597196125, 0.010717346719388593, 1.0136889515068068, -0.02600967491900654, -0.6006927988161844, 0.7206633585878172, 1.4743262865865936, -0.1339076771251659, -1.592018006671195, -0.4438695624928346, 0.8547772096310535, -1.0494647611686725, -3.715525122117376, -1.8364613484511485, 3.6434630138806745, 5.453485900356288, 0.5987727082758497, -4.663762214774644, -3.8173527085149805, 0.6846919979241758, 2.023165146048128, -0.5290246661141076, -1.7934736449996698, 0.10486282972401306, 1.2219457483876888, -0.7570341490484774, -2.5114288681691908, -1.000610538168529, 1.4448399039915303, 1.3958956111833265, -0.05361396681289083, 0.05301754671526311, 1.1020355622586107, 0.6090537437512684, -0.6478838694214665, -0.09881291171091484, 1.1211326078755257, -0.5281592826909968, -4.213688237258777, -4.851746759930527, -1.2683561717624976, 1.3655714550725913, -0.128439680837152, -1.598504903257845, 1.160458099229917, 4.499283383802662, 2.393815326564434, -3.095153365664973, -4.036731324323536, 1.3141422207518554, 5.850015163982136, 4.36219420056095, 0.3697056153345777, -0.7527667650585458, 0.2904772407121708, 0.046158486994673606, -0.9047622486311726, 0.11040549245115641, 1.982888938734817, 1.4937750113200285, -0.6874293306089598, -1.0953624310392833, 0.20892197107158356, -0.13992431486214982, -2.308604616269741, -2.6241884156355493, -0.32608269833641473, 0.7468984244031972, -0.9138147305651895, -1.6527664292992987, 0.1751077881882797, -0.02328139710547558, -5.270317989066951, -9.929443349028935, -7.012896057375219, 0.6122695797024627, 3.7822374122143447, 0.4537348256633761, -2.247857599907253, 0.10887325785669012, 3.1839777231168602, 2.235387765271388, -0.43935613475133267, -0.712791951283202, 0.3035460520434629, -0.39444896523145273, -1.4874721601083813, -0.12883688537254007, 2.0011642845388713, 1.2376592579397827, -1.4091846828312238, -1.869620339784189, -0.0348234213331193, 0.6015996571359592, -0.43827882188122724, -0.4409886604819633, 0.20803126198613583, -1.7650450333842498, -5.084996280934142, -3.869265656278432, 2.4150899872480545, 5.976732370231757, 1.9621109936462247, -3.6579370507080187, -3.2161329066321507, 1.0291254397098049, 1.5950404806327694, -1.8199102950343535, -2.9928107251993312, -0.41170164420956057, 0.834431103852863, -1.2807282123004684, -2.339251909657244, 0.23064861725588026, 2.664700518612438, 1.721339630247515, -0.12342198125312238, 0.08809957914060106, 0.8058164609163964, 0.17155164972801543, 0.23059619722990707, 2.508052246785297, 3.881796214503001, 1.7627657097075973, -0.7060531229405291, 0.04384207777624122, 1.4433653837645846, -0.28842889896302026, -2.255696927199466, 0.5830701636533078, 5.491570002824385, 5.1587640323483726, 0.029213826797568787, -1.6732266897553636, 2.6824699137194377, 5.850652076853205, 2.788957879459334, -1.5391737909733103, -1.2384164510042999, 1.0721339950518325, 0.08320550629827257, -2.8082651393163407, -2.873824625495439, -0.5836880538219185, 0.2170457706353044, -0.3861452761802868, 0.3597995053129733, 1.6507569438625975, 0.8107528726221377, -0.613549988271347, 0.8872473320952442, 3.792739106788292, 3.5969091201238435, 0.8490995816188471, 0.08113896957885017, 1.3270490157458774, 0.3939303164154558, -2.3776818702480633, -2.1508275152069607, 0.34453805422905154, -2.0003732489278714, -10.169171763169544, -14.731218708047031, -9.35015845177127, -0.6868523429841605, 1.775656622634122, -0.9465681116794925, -1.7862940035866446, 0.17802580187171854, 0.6238210744897553, -0.658275709632039, -0.17984772092484225, 1.4498488591825225, 0.42732853313163244, -2.501124032824681, -2.831218746629346, -0.3663976913229918, 0.7133387745427794, -0.43237004257141975, -0.6414143778682269, 0.32106818405356274, -0.4898887198965117, -2.3165104937825776, -1.220800662079269, 1.8682917447143832, 1.7328062098082018, -1.2901645237341421, -0.8565051791348195, 3.6457246720466205, 4.326633644575289, -2.052183959090386, -7.354672518424882, -4.527110580166465, 1.437031617611104, 2.313953300125193, -0.6577430838095575, -1.292617319943869, 0.0758445951313281, -1.124453956728599, -3.906414135257072, -3.4549972859281444, -0.30524675888837954, 0.7558891242326811, -0.6098509090791471, -0.6306105876498627, 0.8104720157945653, 0.43711790668577655, -1.3844898422217122, -1.3406269162151474, 0.019310753272775386, -0.40708613038882707, -1.2599158495668592, 1.0363949783877604, 4.019498786919989, 1.9979409098473206, -3.2342101021054432, -4.004196409881292, 0.3599234428246888, 2.3467278233112463, -0.39235801605963583, -1.220228514486696, 2.614577853689196, 4.055725547078037, -1.3778699655502409, -7.005496381757021, -5.647385912839189, -0.6759593931976292, 0.9926688897296164, -0.07426951440046421, 0.45568723699683344, 1.8651072762347194, 1.1522473672658144, -0.14775778947149, 0.711650636378645, 1.7030305157174979, 0.1546442751620554, -1.3169875131242024, 0.3988137076552611, 2.521447560921837, 1.4566020230134187, -0.28626524593003705, 0.8111498337552392, 2.1070872843762936, 0.2649160078474265, -1.2016065268421872, 1.580393197320171, 3.8023069696075904, -0.6273041289782928, -6.834818629208666, -5.28482375413396, 2.43255575093313, 5.825040775506949, 2.194952608395349, -0.7717770438894078, 0.7714735727905001, 1.8195300507184369, -0.5449419971509117, -2.1561951741564624, -0.5864128646409005, 0.6420621057897211, -0.2950204405690756, -0.32221642064724776, 1.3109570247591225, 0.8721121671381645, -2.1624999747304092, -3.2615277714621174, -1.0873865100374658, 0.2971754257623731, -0.5116068686557568, -0.1846424041283083, 1.5865924677345717, 1.0833205959236651, -0.9105129552512826, 0.6984252311725334, 4.32564646016244, 1.7060761212125508, -7.524383528103393, -12.417889268395472, -7.040596388430661, 0.5511276905468802, 1.8412921356302243, -0.08161048319718164, 0.660881875657085, 1.70235600082224, -1.0637093706749954, -4.170507839564257, -2.835289764266885, 0.061520242376582, -0.3626907002192462, -2.2230470627255565, -1.495785881518547, 0.1810978711936715, -0.37030344241838153, -1.3423888772739243, -0.2763930261804121, 0.5920989603141475, -0.46966671328667037, -0.2107584586789172, 2.842744396315965, 3.9176057064491463, 0.5677885362086075, -1.6937755279028948, 0.9064470723181856, 3.1566802638563103, 0.950519667048224, 0.0021383662363187094, 5.323397127230599, 10.30444779621528, 6.905319966372959, -0.43295914493008936, -2.3042902700791283, 0.39122261220148946, 0.26743879113102625, -2.617483198661785, -2.4741965637101373, 0.38126958663074606, 0.728843755276906, -1.2595677520439685, -1.157475665521381, 0.7416800373149122, 0.7954913923741151, -0.35376217077546385, 0.024309280887558248, 0.21907291732766743, -2.1489057922030947, -3.7895234323355926, -1.2427571678005338, 1.8099423240867856, 0.8116623486227547, -1.3320750764169405, -0.49754147355995043, 0.22532817752519707, -2.4857649322274336, -3.532653059348017, 1.7594139413127747, 6.774448178645136, 3.363382814588674, -3.4240318506840635, -2.990010494308898, 3.319368093676756, 5.435819756818086, 1.5518882996105428, -1.1357781763178494, -0.09103314845017679, 0.5625779098606644, -0.04638554061170955, 0.9544664020409184, 2.215742478231557, 0.051741057174755106, -3.3659901947301716, -3.0872885888603587, -0.36320897073173075, 0.20120885869295224, -0.7008770595398881, 0.1910609441921887, 1.314544815516665, 0.14037471920882072, -0.3542145802997423, 2.367117898612418, 3.739390428994769, 0.3857714696811072, -1.7016407778712959, 2.683805407397814, 6.923908876937217, 3.1018277245933765, -3.484925838332454, -2.874304520787821, 2.767975316473784, 4.050586545289326, 0.7268303475974675, -0.1616235769415725, 1.7811107626522404, 1.2420777956813096, -1.247013889136106, -0.7899381854019738, 1.6682394134578757, 1.4950614805808562, -0.271216431423776, 0.4234717425525271, 2.14371162778459, 1.2019513609282, -0.6882682350425777, -0.324409408691261, 0.34287390178015703, -0.8384984868452245, -0.7144335399080306, 2.3182307387013497, 3.3052460001207873, 0.13241723705806938, -0.6711451815162968, 4.339000306244975, 7.561813533901623, 3.1957409373751555, -1.9645173728140717, -0.5697533509019804, 2.54420112885158, 0.5280303737810118, -2.3988402421583244, 0.2584920629238412, 4.306680059187251, 2.614018547891286, -1.9067762051963653, -2.341293845325238, 0.15581827956554972, 0.5706576163730267, -0.325694397619617, 0.33571218515451007, 0.7626002163651525, -0.709680390903215, -0.932829217837365, 1.3840421546666086, 1.8987466580956944, -0.9582029462939335, -2.295523337534294, -0.15663591302307311, 0.8830763370859689, -0.5296663620868081, 0.14646725900690322, 2.763924939657333, 1.2479456925607864, -3.5632496831104827, -3.0950270208842503, 3.025003962563407, 4.3787368223104055, -2.2034456693491427, -6.564740660965008], 'positive_zeros': ['1.77965455130521028406933388789', '2.69105542211913037334220815135', '3.48858782301111439475871833975', '4.317056916261168109810535589141', '5.70455308859953349573716475138', '6.202921344439254933002684178986', '7.1057838041345098732101694632', '7.87345808917156278250839211074', '9.44444113388374944325451023619', '10.47812527473338478111203253523', '10.65366385938860455332882288712', '11.92229328803481075547227242939', '12.82013387300472766040908117752', '13.289376867080714342477073099401', '14.27693336869003104996607923353', '15.04292951292508070719699558736', '15.68897203114510738181789642129', '16.41123884248725089537396206886', '17.6467030452309148823481414932', '18.48443532496652644526571937750', '19.252502208615620098948794290158', '20.22659534857176609978368343544', '20.6871681556062401603340824243', '21.86772833245231978780303635118', '22.44551169980825639092444000985', '22.91059093292348885152657982668', '23.58342431619439671250640567256', '24.69821027763402046725446555688', '25.48420852199476671497347139882', '25.984434702279245444230547915115', '26.75047150203511101695374512193', '28.094059649233678558886121570969', '28.718784866416249679155735246547', '29.44822534797336558390300649626', '30.17235421305098078985128418787', '30.76079484582627896325255239763', '31.494430648735473877805493791257', '32.29049867969163578823637938764', '33.1862269048426903595553522623', '33.46873222416863435822392762', '34.414339049235410034278448014308', '35.15820549223404852700038469655', '35.85119909271878817602771175073', '37.14417763766369393884839185410', '37.69959533955186442522226309708', '38.44830840654934639900924024779', '38.92794936061906340021594789221', '39.713762611129080306911044362758', '40.47906160691062677678818567686', '41.38752759130869601518414984055', '41.902829293630965742305807140500', '42.32877621269253329345219023138', '42.96678139388967746333545414479', '44.25706948117030317557303444708', '44.61025332210209522413889580590', '45.7350916611969516573010647343', '46.38650930166730785647364901768', '46.948011646011616229946855798248', '47.94334117162589278121284822962', '48.660433019959814853433243231331', '49.037705940185648877811630058149', '49.8611014021910843702332609749', '50.41504813175295049567495066371', '51.11231662186146724521857492309', '52.048846279149867026529324652399', '52.44927870523316703770624789518', '53.13175068427532241818935054631', '54.326172373871095705198411324736', '54.779160705835976777866989381995', '55.51684605347375663250505849544', '56.66194988048598103968818320711', '57.043960808044662512905401998212', '57.74794327158600738572395832584', '58.12804737583335744284876743914', '58.96427797104875125285607923472', '59.85543850144289561331283331293', '60.20674253747708397971555969744', '61.21339806228876945792030662309', '61.74938041173034918325539884435', '62.00929623283073901469712170916', '63.169989934332667191590439377248', '64.472062187699055766450887498820', '64.718067102806342835143102942555', '65.2263233077237593068739134461', '66.07225637299219835857302484499', '66.73433202446523124845310494373', '67.49826856656866807109790015291', '68.11900886617653774676620952713', '68.61221160177032714357335257232', '69.356001113173338133927344908244', '70.070078095645865159212138849723', '70.51236271490426817231740540994', '71.35968414697850415785562597265', '72.21590192731736133695407479752', '73.072738779082215715572665977820', '73.693318179282338791567146771649', '74.36108604206686349975485528299', '74.91096201639633220107373102902', '75.7363679517110669548652703692', '76.54601665361745057276187141224', '76.858480554960730119883416517433', '77.63073597825768861558424173050', '78.14535874106019914925166421054', '78.69737428657389587419528954278', '79.7902559932744320867662964440', '80.296935573557691575832153279354', '80.84772063256226944487165821296', '81.69627017427922289116426094822', '82.436372200831768584474337068419', '83.47875690532537162941330244583', '83.969869153284283514316014085155', '84.38788652939860113141311002732', '84.98266983448821306897247713607', '85.83274379571261596707475556550', '86.505246731347383083880314212876', '86.84794860971027892151427875751', '87.85705566261020481430323427255', '88.297464976531918904866822396199', '89.034305950741195385147078676654', '89.37248687127997987498229108542', '90.59744208794835892323021838605', '91.282426139243500817551451538571', '91.866238546561315302552788714826', '92.747294526603374531025423742265', '93.31470361331177959461246148160', '93.65955094846403906148290892773', '94.391291153147637685271008299377', '95.14275884369459038157872593303', '95.94373861059306858476828534366', '96.438356524322087216034298645414', '97.02313917881361160629420755115', '97.276148180369346062923404788171', '98.32640770848441268339346025684', '99.155491453406943133960972845340', '99.91688009198976742000692014206', '100.47036676402025911874230855085', '101.29749027178379348766722976315', '101.71941186614319115700257790637', '102.4789368915041369471946039764', '103.40201133846370633404005451640', '103.72174354438247045642786755660', '104.44955765707795164114803668500', '104.61481751664369060895704806425', '105.810954727812194120100878009251', '106.242983999251972361240804919956', '106.84355037650714965987863247471', '107.4631552411967126628920804998', '108.43941084262792600721292124580', '108.902047989279918512692691565849', '109.861874911818539015713321712817', '110.45850545931763910518604188595', '110.94670029416864248692380657003', '111.98830076154563774204903493166', '112.30025786737409214305411249537', '112.73261319460420535536923078224', '113.57499335354560288094042371131', '113.955524747682926311809587566055', '115.1750318840540282992127048815', '115.27549400530589940426182537140', '115.98287192029188939161128603605', '116.81216353367956217567874282453', '117.04804588288401751954736075615', '118.47301485373102174979379261055', '118.964572772601061564679410490343', '119.65840964382584869628437929846', '120.14944777313193611522412736929', '120.65713960776881180163333919506', '121.29727797041519376886567087354', '122.23804703687426960596863411559', '122.710235779895919341401759591938', '123.31428792354642489746266857583', '123.659634862959180132860927881220', '124.49345810926332296429120975644', '125.175567282974229787478913602849', '125.69467676884054194422841218444', '126.47963295156944767022964473423', '127.41017014022936138715453541449', '128.05257633357195454095109631285', '128.71883576183540217772503527220', '128.8857605779452919135590416613', '130.03666684824412703933171085825', '130.49641149363184083015292012005', '131.070690938346843768047164397453', '131.637851379775308537631928106', '132.49246777663003688015434111730', '132.69955334734488688357586135169', '133.3427999483960556139592741081', '134.1796533296501305686647910777', '134.975453540012078372465680424576', '135.586845211388872370128606428715', '136.062226471146112209156168746897', '136.81502652354390849812376391794', '137.87113632163072548480567164008', '138.409069225059684267563275277320', '138.6411492640385278586040935822', '139.61571975754443405632382232658', '139.83685682905687796148513666092', '140.64588902657974281591105443150', '141.20458281408462591972755665952', '142.09456093795331035206500346101', '142.361318842131175325876702495902', '143.155740048981400993034877441473', '143.618431741459259961069133739509', '144.34693320504836990600019535503', '145.21489399302675440843497629212', '146.10739082206239638640082219940', '146.46187972423006188153492951921', '147.13018747814808932083769075322', '147.90327431057736921428679908535', '148.360281432927709103767746827334', '148.82011102813834072244894769008', '149.47597777781839848045249470855', '150.48007557313223404816114553349', '150.7793121054118023420980362711', '151.284828842983230456633200987069', '152.02228466071612287171113653564', '152.43719058513446759080812590276', '153.19241656261485851977015982765', '154.34268642540151117603124004327', '154.977050812089422919121811371723', '155.18563632566618337775984658519', '155.85257631752809216516219386970', '156.86345387744976694867498318799', '157.124614092810198794177190548973', '158.06753163849314546530962643187', '158.348038948780706749399157624451', '159.11775619650694758734206401538', '159.5747547337719978358811625194', '160.03006757468071045064274068324', '160.98241244170271677347207455834', '161.4862023347304353781085682377', '162.30061628858758135493268312405', '162.4997060013651359177270643585', '163.72686349362211097654792094797', '164.32575568908727142422461792766', '164.7200110453679295657260365403', '165.577343414699596790703690091281', '166.055708416222225665764363783390', '166.74490477882785690561260578765', '167.37959848875526256031865336554', '167.80447012321793769241541806322', '168.17497378430764587401476220829', '169.16251274326461893976693870070', '169.78200068348242912074176938134', '170.40523247334738871656472748803', '170.67357486478131589846710238748', '171.48315674988278664551489345188', '172.32729661136491753956383713401', '172.96554106383662276898159859600', '173.87179019470719410399568536246', '174.393484422361608193921748503748', '174.95009621933491526154911669362', '175.083041507600440549419477945461', '175.941812875657048849883500447666', '176.93658853778097708606649335186', '177.25231451722271255483440771280', '177.77635865343640300785898797506', '178.464069787140288362948053147802', '178.815005460677332339491576284559', '179.716322977658775465547281953634', '180.167150232140753843441258844139', '181.067328041894142073149735029893', '181.720745246957905036598088082604', '182.589560625513755362843823214087', '182.845977758297306684258442215359', '183.58229107088530992069786451234', '184.15893543328058245516565212565', '184.93099018964927625548397006010', '185.23791793908844952483241475244', '186.10756882535890743770336716010', '186.64807038278239857803109327607', '187.00325687811739423612467512969', '187.59114366764705211591280176874', '188.44989587412930912977972207458', '188.81434963294847005899102041376', '189.84516504192115458611536229927', '190.35702432753086043775198346353', '190.97829200409696239687738049347', '191.545832154279329455711428253321', '192.355125845182870408017688561321', '193.10132047370117011022163171760', '193.60331354770149922667730397050', '193.96944110857528980602114609513', '194.55796123582475163372858319800', '195.14283929064921195840401553306', '195.8450578039669943969511916207', '196.58272329100699697198715951128', '197.0748546143515126240133591069', '197.48096182528153677107960975726', '198.206194231554273770861638757447', '198.91429403068248327768696727546', '199.59863156223227270593215876309'], 'prelabel': '1-837-837.238-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 89.94814205310114, 'root_angle': -0.9805471383123302, 'root_number': '-0.998133183732812753409113171795-0.0610749337404393608444118850850*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.490273569156', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.43259075112195126566086207840+0.159983846239884005911998391732*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.77965455131', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.69105542212', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.48858782301', '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': 89.94814205310114, 'bad_primes': [3, 31], 'central_character': '837.238', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/238'], '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': '1-837-837.238-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': '1-837-837.238-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 89.94814205310114, 'root_angle': -0.4902735691561651, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77965455131', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_837.238', 'Lhash_array': ['dirichlet_L_837.238'], 'label': '1-837-837.238-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/238'}