Lfunction data - 1-373-373.210-r0-0-0

Formats: - HTML - YAML - JSON - 2024-05-15T02:44:11.560587

• 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_373.210', 'a10': [0.9189578116202306, -0.39435585511331855], 'a2': [-0.6889669190756865, -0.72479278722912], 'a3': [-0.25065253225872053, -0.9680771188662043], 'a4': [-0.05064916883871271, 0.9987165071710528], 'a5': [-0.3473052528448203, 0.9377521321470804], 'a6': [-0.5289640103269625, 0.8486442574947509], 'a7': [-0.9541392564000488, -0.29936312297335793], 'a8': [0.7587581226927909, -0.6513724827222223], 'a9': [-0.8743466161445821, 0.48530196253108104], 'algebraic': True, 'analytic_conductor': 1.7322047176589146, 'analytic_normalization': 0, 'bad_lfactors': [[373, [1]]], 'bad_primes': [373], 'central_character': '373.210', 'coeff_info': ['x^62 - 1', '0.994869323391895 + 0.101168321987432*I', '\\\\zeta_{62}'], 'conductor': 373, 'conductor_radical': 373, 'conjugate': 'dirichlet_L_373.254', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^39', 'a^44', 'a^16', 'a^19', 'a^21', 'a^34', 'a^55', 'a^26', 'a^58', 'a^7', 'a^60', 'a^38', 'a^11', 'a^1', 'a^32', 'a^16', 'a^3', 'a^61', 'a^35', 'a^16', 'a^46', 'a^49', 'a^37', 'a^38', 'a^15', 'a^8', 'a^50', 'a^40', 'a^40', 'a^2', 'a^9', 'a^51', 'a^55', 'a^53', 'a^42', 'a^48', 'a^38', 'a^20', 'a^12', 'a^52', 'a^55', 'a^47', 'a^23', 'a^45', 'a^26', 'a^51', 'a^14', 'a^6', 'a^15', 'a^60', 'a^54', 'a^5', 'a^47', 'a^26', 'a^27', 'a^43', 'a^17', 'a^40', 'a^17', 'a^13', 'a^41', 'a^60', 'a^48', 'a^57', 'a^28', 'a^19', 'a^32', 'a^31', 'a^30', 'a^46', 'a^19', 'a^36', 'a^25', 'a^20', 'a^15', 'a^41', 'a^59', 'a^27', 'a^51', 'a^52', 'a^29', 'a^36', 'a^32', 'a^35', 'a^24', 'a^22', 'a^0', 'a^0', 'a^22', 'a^10', 'a^3', 'a^46', 'a^28', 'a^18', 'a^53', 'a^47', 'a^45', 'a^33', 'a^54'], 'euler_factors': [[1, 'a^39'], [1, 'a^44'], [1, 'a^19'], [1, 'a^34'], [1, 'a^7'], [1, 'a^38'], [1, 'a^16'], [1, 'a^61'], [1, 'a^49'], [1, 'a^40'], [1, 'a^2'], [1, 'a^48'], [1, 'a^52'], [1, 'a^47'], [1, 'a^51'], [1, 'a^5'], [1, 'a^40'], [1, 'a^13'], [1, 'a^19'], [1, 'a^46'], [1, 'a^36'], [1, 'a^27'], [1, 'a^36'], [1, 'a^0'], [1, 'a^47'], [1, 'a^48']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-373-373.210-r0-0-0', 'leading_term': '0.309693340383968176970647169222-0.459977006462250950040442617217*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/373/210', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.554516736945021, 0.3203348542508585, -0.1174297210870252, -0.7455252550127949, -1.2504591651433838, -1.2737273846814066, -0.7010752304795369, 0.17648069475574385, 0.768528319352743, 0.5593775168658585, -0.4540703476782595, -1.5844362490488493, -1.757695505416552, -0.20657380040801987, 2.871580883927109, 6.201369704177932, 8.068309103895743, 7.382636617740454, 4.453414589188694, 0.865667963727696, -1.540628050699311, -1.8983292151156173, -0.8334552232992133, 0.14272376741126366, -0.09126701905637435, -1.3530095453424085, -2.369343630852575, -1.9481401413380042, -0.09871685312208386, 1.9021028142650724, 2.5926235979640926, 1.609597021671858, 0.0019256266289136978, -0.7380228678233597, -0.044337705541069375, 1.2418245751320898, 1.752523878098615, 0.9849313950350449, -0.18858744117924456, -0.45245432201578917, 0.483313275716695, 1.4233741641891768, 0.8559917774044723, -1.3113249021348492, -3.2632747280177723, -2.77487990729494, 0.5526635448161688, 4.505382660351453, 5.9083561089866325, 3.378988625150289, -1.3527603704631246, -4.868774044729632, -4.972162442295186, -2.397396357522132, 0.195027924238181, 0.8222315919359267, -0.2056016421106926, -1.0916815357542151, -0.6814572954488204, 0.4369390601921367, 0.91126975071223, 0.3685723647193195, -0.18769093539472553, 0.21049615702713592, 1.0159263303517885, 0.5451378167071164, -2.0068893981273908, -5.2059084685817725, -6.460532685694399, -4.632872978346693, -1.3539960269346691, 0.5753745077946552, 0.1287445609323969, -0.8729194976000035, 0.1378851503547941, 3.41824846153276, 6.325627594415077, 6.003553157925687, 2.4950628560465433, -1.1535390093915459, -1.9829705577845376, -0.06130283846236871, 1.8976472475463735, 1.6947952571301048, -0.021565134705183467, -0.7986849687292017, 0.5773591193929454, 2.648029130782464, 3.0623119445938727, 1.3561548689155887, -0.5839160533030163, -0.8248988194139811, 0.4089202177041954, 1.2609624352628233, 0.6831540588356543, -0.3668040390976592, -0.4494553113440105, 0.2187073328342401, 0.004638995428095178, -1.6328216436530694, -2.697465377940426, -0.649299665283846, 4.11127519430272, 7.60907606174299, 5.955587106990913, -0.3726038628337721, -6.519629553317497, -7.852557302606533, -4.325923302828095, 0.01829837614180795, 1.5639274766971496, 0.4564120801415799, -0.643704579689397, -0.2584483797868532, 0.4400203358368366, -0.19326197040790635, -1.727945714153571, -2.198971573997502, -0.8909613399756962, 0.5115120772387387, 0.07359044791714325, -1.761739518459818, -2.6464229137433377, -1.3993808475262473, 0.3830715687852141, 0.4411953064096106, -1.0069937062678735, -1.3569308982475765, 0.9338791273951623, 3.9867007475208878, 4.544669264935427, 2.0575749665713556, -0.45061731105886804, -0.080704780737199, 2.253944598320816, 2.956718317808491, 0.44470965523323636, -2.5383604648387013, -2.11476855253869, 1.865166054892802, 5.367102177681952, 4.769451182127366, 0.9060338080534085, -2.233266684525211, -2.2225530972469474, -0.44561926354505804, 0.42731947699981976, -0.10215861610871094, -0.4481389702759433, 0.1723662541828084, 0.5054179412807405, -0.6157279484908074, -2.1330024508587253, -2.025749996017195, -0.33117810177274126, 0.6102158706901178, -0.5099421132830286, -1.6203693023997026, 0.30135377473762004, 4.7312691442659585, 7.20573762132654, 4.341556341203846, -1.7003586644461215, -5.189112084486708, -3.206861270183079, 1.2716058878683993, 3.2582976275494895, 1.5688931079748927, -0.5573142551833308, -0.19518325319666513, 1.7105781267817317, 2.2996518602321205, 0.9482149222637749, -0.2599406057789955, -0.0035635535206055826, 0.20238276649345843, -1.581568955148724, -4.398826509442075, -5.191874667855175, -2.856414513010783, 0.10433069360118581, 0.7560307422604632, -0.6004755948136036, -1.2929325114164774, -0.2526197913658274, 0.6841384622452286, -0.09039682650927269, -1.2596480577469007, -0.6784280506627018, 0.6183007315750388, -1.1661039844464847, -7.320179088790019, -13.486047910641215, -13.723348361310903, -7.3885719283231195, -0.14607321960993744, 2.4056092809498195, 0.6002991945359574, -0.9636826316410839, 0.22689298468722316, 2.027713416823633, 1.510815451261489, -0.7594629212253607, -1.857127915886431, -0.7724159074934331, 0.5246980492549624, 0.3459250534189526, -0.3776787191128592, -0.0762200926681725, 0.6193477578918947, -0.09464349531450253, -1.824965754217233, -1.8838913499371246, 0.6734081329252255, 2.777763932753685, 0.9605737490788473, -3.578497679061634, -5.803385209318442, -3.164670858052581, 0.9471314292532129, 1.5346163374851505, -1.558091006315831, -3.7527603243658656, -2.0794605205246013, 1.059092403955022, 1.6497718304310292, -0.2975541886066143, -1.2028724167639255, 0.5731396468068057, 2.340777889903299, 1.1669953242977167, -1.7031278729831854, -2.5448524087817552, -0.3858135529735612, 1.824009736640832, 1.5418447408992857, -0.057351891424726284, -0.38512711030767743, 0.5711974562382942, 0.6910645784013675, -0.45559503346747526, -0.7293126669286026, 0.9777976857164385, 2.476083926239279, 1.3755008859852849, -0.9759499539707298, -1.205379063363495, 0.660642258152532, 0.39336072751119433, -4.372982836336223, -9.459975731794273, -8.30413027963127, -0.3305582728780294, 7.588565468151755, 8.90018238561672, 4.430825244509165, 0.08972099346771346, -0.7577069553181472, 0.02185585286933225, -0.23700238606251392, -1.0672848522088743, -0.776358455832616, 0.028487856618406898, -0.5975262281450713, -2.28399542307661, -2.4136462067679862, -0.2616150606220554, 1.3872752471941403, 0.18053516380981127, -2.099370852096042, -1.9916025618519928, 0.4549089489530306, 1.695978731838266, 0.10212274773883653, -1.4932150911157775, -0.2728506699465261, 1.7676134415378328, 0.3906972797677523, -4.29008653935184, -7.112827630622487, -4.679827193150639, -0.05753131823018734, 1.5249205421891636, -0.16731430674962966, -0.631649957351332, 2.3566839988637, 5.398517967516909, 4.500474616501198, 0.7987511796853909, -1.325783934054102, -0.49580803234038706, 0.38496502461806803, -0.8821002147213309, -2.5620541604934464, -2.1158617121430794, -0.22799254853620968, 0.5766161158970187, -0.005730388305664255, -0.10746161397253115, 0.5967089134426058, 0.27743044142776024, -1.128152577395416, -0.40002184604165725, 4.159042058498889, 8.394345687537793, 6.323016602329356, -1.655730391810226, -8.028503310218571, -7.0162085038298665, -1.4205297647110595, 1.7117918940188979, 0.26176357453878396, -1.540027804678351, -0.2944305483688026, 1.9317804881866203, 1.6686169924345595, -0.3988350499422467, -0.9239388390460473, 0.6179532205421597, 1.3877663904483808, 0.034986339128461524, -1.22696411024982, -0.5659183028094608, 0.28543431258546953, -0.9328678511072672, -2.734360965626479, -1.7335204612556783, 1.9041855955861888, 4.1449288408956955, 2.785138795111645, 0.40938551435196, 0.04117957776738531, 0.5456117313338178, -0.7834828100964846, -2.8231656631425235, -1.768866199162096, 2.290785559926599, 4.0572911421301745, 0.2954827301003603, -4.710773524290434, -4.356363123768801, 1.2138175727142677, 5.1650271509426116, 3.141003878978783, -1.4901426548628105, -3.116639291032866, -1.3292526467138457, 0.06737812331935861, -0.5521665752953938, -1.06288489892041, -0.08796710803827489, 0.7091575374268091, 0.004353227225951221, -0.6141473358331759, 0.40850262142955335, 1.3887540625694483, -0.004852745821986476, -2.3958710300422505, -2.3604226340208303, -0.09488286762788385, 0.3700539480574668, -2.316898848787723, -3.810832195242142, -0.3337680479309514, 4.735006083951074, 4.626500908910018, -1.318607852426711, -6.290966823243407, -5.0547242804812775, -0.41098463691343406, 1.7010038771322613, 0.37506994468052873, -0.6679522721804225, 0.14152642720192432, 0.43786285761337623, -0.8522688356344523, -0.90608716183598, 2.2464183325350437, 5.608673798910736, 5.0249302104429425, 1.2579500763483682, -1.194812036282447, -0.5691044972526648, 0.49961255025611123, -0.011151730447356043, -0.5764300449431906, 0.27392582900228335, 0.7700520613936811, -0.8993491660434029, -2.6432627531273765, -1.409684669654785, 1.2236774279993174, 0.7737452487003352, -2.5981911911497453, -2.901247989602815, 3.077241739889323, 9.799058591751832, 9.508114854025242, 2.6054433681401648, -3.0587264677013914, -2.7663167158084105, -0.05506869079407675, -0.053958693342235534, -2.1558001342047737, -2.468877001416541, -0.5300645385212664, 0.645944417469323, -0.0014754608713679574, -0.3523743333432434, 0.5168154363178226, 0.664283124845256, -0.7737852446460662, -1.5070534834075893, -0.17039075953098962, 0.5206070363502449, -2.103726460887565, -5.519210321197146, -5.056398251387063, -1.2549063094273833, 0.3431469775967065, -2.5797560740191963, -5.552008653944049, -4.18977789695205, -0.7170555989148945, 0.15022363597581512, -0.9141001307648151, 0.8403630101547805, 5.799597057879092, 8.309132577714383, 4.931045054344141, -0.24022737023436588, -1.5306404843446362, 0.4776746795530669, 1.0672330743110212, -0.8142536731025892, -1.6633329737836509, 0.08668904809936384, 1.4998264216946176, 0.3459109128804733, -1.2196594195869361, -0.5981030277811985, 0.8285875661612176, 0.3644011225969142, -1.2207090659819846, -1.2545502098126167, -0.06446945819199187, -0.19294301011706147, -1.2671878966043857, -0.37113387798993497, 1.612382963573955, -0.886437720200429, -9.619061358664153, -17.201462435691305, -15.131286673409166, -5.128503532843414, 2.7112418588984717, 2.686243937890297, -0.8482137551500244, -1.639840478677541, -0.0024467377660884406, 0.14584918663267013, -1.3989535179627017, -1.6388054063322395, -0.2644920933054826, -0.0014732895430153515, -1.3411117707757227, -1.5970295838593633, -0.08475726717895024, 0.09191879620668628, -2.62129468289976, -4.903489427232982, -3.4973079402349665, -0.4520282907861266, 0.23048926318258336, -1.0420692568969752, -0.8425897091325849, 0.7553561001962517, 0.20001003758573238, -2.6444734389752025, -2.9834277778037537, 1.3002007668968194, 5.238687662859944, 3.7839797013418903, -0.3382176347142386, -0.7454997318994655, 2.74619564052582, 4.234574178198781, 1.500673289550756, -0.43139805536974946, 2.441225706509072, 6.514222505626776, 6.076742855926826, 1.764540194846591, -1.1211168270246443, -0.6452689093771192, 0.3305569040498759, -0.006383046123449183, -0.1090011822448263, 0.807264494422065, 0.9075679973003896, -0.38915058566985394, -0.7483124050423163, 0.5443732723280342, 0.19215532937518762, -3.6409145957186455, -6.783214362455349, -4.529300090856117, 0.5603356821553374, 1.85417005178428, -1.0450012035281315, -1.3355472566184, 4.276522568313215, 9.851185489258057, 8.721886070020387, 3.062017949540043, -0.0017244794270362164, 1.2200908013126608, 2.2666839288013816, 0.892479966006732, -0.04807600634458209, 1.1989985320324248, 1.9071356802318034, 0.0688975964498311, -1.6689166741156953, -0.6192885271460752, 1.0316994469356693, -0.04976553588185303, -2.3895824676711954, -2.0766814225690977, 0.5153230004118037, 1.3300767822585113, -0.5216660795879648, -1.5760551305219679, -0.281418385981037, 0.6172974896727906, -0.3424184841661475, -0.4200616139776608, 1.5935978851607762, 1.459973101933144, -3.817808128247686, -8.876694516577661, -5.947742028481219, 3.3402561276435896, 8.799343411234657, 5.142741358578977, -1.6068382981383005, -3.551066800639697, -1.0802885654097871, 0.4773209659476998, -0.16096610219081958, -0.2041693658532133, 0.7415634289188693, 0.1672860475560071, -1.882684361616163, -2.255594997159098, -0.22752121074168044, 1.1434298907037685, 0.36443617417503144, -0.32632170307414715, 0.12615535597124722, -0.8123764732697965, -3.8880182654323754, -4.748635320220803, -0.36166655176674867, 4.764519438707097, 4.279089737395381, -0.2308184066344265, -1.4041657605426674, 2.539402086165004, 5.327190190949901, 2.8449074055559316, -0.732591831973795, -0.35542841122954705, 1.9638217072571937, 1.6023275503248555, -0.4110982385561024, 0.30481932804189943, 3.1973586815496224, 3.3326692354557865, -0.14951653579901325, -2.3936232624942413, -0.7590262924588952, 1.2728168403430733, 0.3766811800264704, -1.430555902449959, -1.1000345332371404, 0.14895424234761498, -0.20944930282402646, -1.0785007307688215, -0.20438500245831887, 1.031993463588116, 0.18161274053399373, -0.8898077734378921, 1.2107362289477286, 4.298883740036407, 2.761980363695425, -2.6611177976400375, -4.138050295898196, 1.5952010418759575, 7.237768737043892, 5.202540395682944, -1.2578871793797286, -3.3301890461831625, 0.3720976352140273, 3.1930304010820594, 1.4828166448035183, -1.0320252680953104, -0.7440368325938866, 0.564940872864434, 0.34347492596152396, -0.29650822474328276, 0.02627268717453481, -0.33730222734551285, -2.2641966727989047, -2.6422489613359277, 0.7421426711750179, 4.285548194621683, 3.4004607315383635, -0.1508449060358213, -1.1039575829826562, 0.8086033495902583, 1.2082198602535734, -0.7307840650548811, -1.1094295068182238, 0.7447948814589467, 0.06577652465000045, -4.754263657558989, -7.722867341226187, -4.0506462759656205, 1.7526324181663537, 2.472783476366622, -0.8837004482782516, -1.5911326374802095, 1.5476162678737155, 2.9962223740838403, 0.4103188842564621, -1.6851096609100946, -0.04084882021378235, 2.0441598781110812, 0.9008864535650691, -1.4173685550378516], 'positive_zeros': ['0.557210967768810547856239610108', '2.12393325578444879346144234049', '3.00514626464784862679864007102', '4.088194672073139861636146743159', '6.02599086779164699915737071142', '7.11473714475966254321903001221', '7.46578692168829687994411359110', '8.76398773432760525115374146209', '10.00043492841882118772767514955', '10.63623441388310873103577787522', '11.81511700726105269770967032034', '12.370529717737820671215755071855', '13.266472096773226171460074788949', '14.3330983233312773953368631465', '15.53742691572701726018269958565', '16.84251117870865559676505817178', '17.449833101255007941538487556145', '18.31344389983955427451891768777', '19.22276089080682680509440033882', '19.59942081316311418628568107173', '20.40303665401234013240118905191', '22.0452563015271453656689753496', '22.53271369281697564443558843499', '23.106359370687782813393403277350', '24.57004007722973762428481470130', '25.32025525449576566215899796376', '26.24593771807544791156560135290', '26.78452500330465988205268660950', '28.010282031834341794563999375123', '28.65912380622005271269340551613', '29.56183337078552554800313154706', '30.20488610680397122407064711468', '30.6263721809145907915843474480', '31.61244811426671027747385183897', '32.7963855132856190294340409001', '34.06075826453639439946623872712', '34.78258514209378826970728148459', '35.40132398857091052876175289126', '35.89018116692097620708933933022', '37.041128088440976246805983210110', '37.5154372524148468496521427829', '38.66511922123283765153712907696', '39.171127221678801278861493403584', '39.90419908566736948196439787864', '41.16745683882472485353184802846', '41.575723842270938548980965540500', '42.539622280977678441285928654539', '43.308863988590318029793116801831', '44.44477781619904075304475959374', '45.407877688807667798710331417739', '45.89485353737606815345884732462', '46.495297029927262192309214723003', '47.06072226092059683979190464162', '48.18747894434210131457945026034', '48.651874353686240347313598893614', '49.34857305702396097615510003379', '50.536711968832644995107134079576', '51.46907789612168223440469429633', '52.38826633203051044193617492996', '52.8485048441431716165835095885', '53.95461857588123969579292419457', '54.37668708408509070161831416396', '54.75736295276604946836120870621', '56.23486775500345640851234663183', '56.75396076807126911363633725745', '57.55659174720481890711458496195', '58.104710709885078306526531768821', '58.88493198599173833819375358249', '59.266434494608390537203020931232', '60.94602691110726538844820178830', '61.6416624017570498914654474853', '62.15326240973084985224564120989', '63.022265769431369697534784695419', '63.904195762747781915035011463064', '64.5026822724152846726212336970', '65.02853889671979567153127198439', '65.605660200779065374497587075705', '66.49432199414003136941998958000', '67.25933157159433859876900979633', '68.351226805492664721290082946490', '68.92581410136727083784081404268', '69.88183262826666215242140304951', '70.58129548490252276652182329077', '71.17555284718532461847683838967', '72.00119157388087532958145448428', '72.855313805026237109270491991829', '73.73621451239496879658039083333', '74.20152169933918220630924311283', '74.88588016715343447498141344272', '75.477509400686799153756987559293', '76.42216113121058129928129933799', '77.07893311679403718781608515234', '77.541247212787321549487089722492', '78.76098434081701446734329563756', '80.01083584927237770217758185797', '80.611591756792708877541590857', '80.83491718107255640496852165949', '81.85159768613460068698153557756', '82.00593318813610326937944708064', '83.15790896643269706834492453587', '83.77338910066937679962809418919', '84.63235118869625788084149435364', '85.32639529467218563557152074634', '85.97269306629246261740160755941', '86.59461150485103217400517668751', '87.81736455101655846564015270335', '88.41067141653668121088338056716', '88.84799432122500208831630652851', '90.07550531607054199093103267515', '90.73601549130005422087964980212', '91.09227717535901731788522469547', '92.23255597865437845369551745552', '92.80973660838421303814098764102', '93.18115576300696175771484558344', '93.81531896359915173186840762885', '94.41530591961463568243013146748', '95.56596854387437343039705560607', '96.65400614863967739736333799150', '97.21954325246930187914390599527', '97.84931031496925363173878557238', '98.68568894739647153199518583549', '99.26618445014126702635604666942', '100.00596955184591898621892277553', '100.77086910107078987272565666029', '101.080060742310274016939271239761', '102.03358836984226835106685723115', '103.24052690660802143858028463345', '103.414359046414296264549030635654', '103.93992691119357095681395935304', '104.832675121413542360049702718291', '105.64128567755092675066871891037', '106.50102232656562706266964243743', '107.39166104640005159329400513292', '108.38987352277331732272778763307', '108.557709756897531313221930430444', '109.396303276868803287415923949223', '110.00124524796334589526837651012', '110.53820320125442594265287992711', '111.24938765519546464632170142827', '112.202235060958826734313318411629', '112.56429325596896118139340625958', '113.45648701337534363902732401140', '114.315213875038954586285882607391', '115.34493873872576814525388871396', '116.00439823929471875728823395559', '116.521764499284382330697717611531', '117.003813470108969473474983354718', '117.62189952786993307261487298160', '118.86418829587300033480134148516', '119.50083739444652946416886473329', '119.99643167651078352859126157805', '120.55233362474840929067785238511', '121.12247767579658862970808156106', '122.02783048058590510769335384494', '122.58067249214776787706853684800', '123.30738055151366465239811061447', '124.48754080314920003050887840448', '125.32214381629561169826806423603', '125.61466611962451770099653081271', '126.6501523923028697457594656275', '127.186999034931895222503157254354', '127.651590320363993575149349127579', '128.29097860783341940088011799099', '129.09447621209961157072101631974', '129.4806330469371956295102049312', '130.75844233467754936872313561588', '131.00883807666450804942049849980', '132.29565327625305623133492850065', '132.54851135754520502678634668212', '133.04903827426156427839309224735', '134.35588527071421749914534657751', '134.93087386838756294239341621110', '135.506808820097164299792968391746', '136.23799448784463834799898500553', '136.92903616046879509055567698068', '137.61276844845568932610973952648', '138.195561283431750699634529325410', '139.08814438351001138419403859206', '139.307199863135335238621999802717', '140.05136367375194345687525280880', '140.574960992595944933883375278550', '142.044417875053577746845315164959', '142.72911005296419067870744834324', '143.43804655874079710905329911579', '143.78695252739529483601917944738', '144.765350625042885980017922873736', '144.9994495177298848323473921012', '145.95614193994196370705359147396', '146.268516485655852305412053763106', '147.57280815086423519575553871671', '147.88109759829801888644982154276', '148.594603561161648976768407923974', '149.08907176363271452587702585730', '149.92312056253125642030000117516', '150.90525477442137826671309839662', '151.33276738183617619067848900637', '152.34819047337090050876564620589', '152.60192356442507694311300480045', '153.89314953396335366597537955447', '154.53500895999144535062759348184', '154.99661997645231271211384269679', '155.3640206600935825882059746299', '156.16288696607007688481635322765', '156.75306454153263265106794406673', '157.21201954253185383918250819067', '158.39718781657998926671103597470', '158.960082812831160158793168069023', '159.47840153486307164507205741201', '160.936377993340232585240708396989', '161.00137886893839700268889394401', '162.08691769294864794139990188514', '162.22183197832347006265347882180', '163.1336393484303783644417103151', '163.84174707716112986298191846669', '164.36848428179057406463785522823', '165.248543586957716846564988587185', '165.86294350022051867909255317277', '166.61666138164563529152144517043', '167.09936222346457323873535152544', '167.582208416873265665558200637795', '168.24128032073609139922015278883', '169.2669755523360323957585890633', '170.22636099143370358348587807909', '171.08442283474249272358566250735', '171.50391138865766539592963739353', '171.94527157246830836278083394425', '172.5290493416562550635853841159', '173.46924643869806868471425738963', '174.16300041740040341602965280511', '174.6002987162902647404151780869', '174.84514390368456695331079965551', '175.95609685565423235584531218928', '176.85726118362481991750142159658', '177.32744387723776368124517144942', '178.348425421792765946048932365055', '178.796462900948516563453866066', '179.605306406130081921060870055861', '179.95887861897173639326800496089', '180.925293364401584107722962919742', '181.65091836537938257997479310089', '182.24337221734517139010215438381', '183.06751259395452882445773978945', '183.37312560187460942427848857858', '184.10184337253737338455853600246', '184.72130040462679429386985771610', '185.19175567431434991574079042767', '186.09942233618742967361355069759', '186.80749058132512642892783544664', '187.746297949666745583981647296008', '188.4119426024862146413164451986', '189.21689083913184039235345264814', '189.8408950464142459203943098755', '190.43770096866650373978672658494', '190.91819607679060140851116539789', '191.144731769565387673701030644375', '192.13492920856235677866784045359', '193.10932303192239572151636589382', '193.62929879088920325841948173011', '194.26453433638399441206395564036', '194.876220318530280532121034508351', '195.31880227020481709297599316935', '196.45151094204305727658408833911', '197.10536925183388825361038088259', '197.67557831416187827235073178497', '198.47645907346296745368396488183', '199.06708721984091466941893036521', '199.795220107122057914597550708'], 'prelabel': '1-373-373.210-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7322047176589146, 'root_angle': -0.6227600465750489, 'root_number': '-0.376172651004488204735760880917-0.926549586712041828458392101851*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.311380023288', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(62)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.507864457726670074282786864084-0.283743716853063541698826996935*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.557210967769', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.12393325578', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.00514626465', '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': 1.7322047176589146, 'bad_primes': [373], 'central_character': '373.210', 'conductor': 373, 'conductor_radical': 373, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/373/210'], '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': '1-373-373.210-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': '1-373-373.210-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7322047176589146, 'root_angle': -0.31138002328752445, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.557210967769', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_373.210', 'Lhash_array': ['dirichlet_L_373.210'], 'label': '1-373-373.210-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/373/210'}