Lfunction data - 1-79-79.29-r1-0-0

Formats: - HTML - YAML - JSON - 2024-05-05T16:33:29.926407

• 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_79.29', 'a10': [-0.3546048870425356, 0.9350162426854148], 'a2': [-0.9199794436588242, -0.3919666098600751], 'a3': [0.6324453755953773, 0.7746049618276546], 'a4': [0.6927243535095994, 0.7212024473438146], 'a5': [-0.040265940109415144, -0.9991889981715696], 'a6': [-0.27821746391645263, -0.9605181116313724], 'a7': [-0.9870502626379128, 0.16041128085776024], 'a8': [-0.3546048870425356, -0.9350162426854148], 'a9': [-0.20002569377604443, 0.9797906520422677], 'algebraic': True, 'analytic_conductor': 8.489729058775376, 'analytic_normalization': 0, 'bad_lfactors': [[79, [1]]], 'bad_primes': [79], 'central_character': '79.29', 'coeff_info': ['x^78 - 1', '0.996757308134210 + 0.0804665687167259*I', '\\\\zeta_{78}'], 'conductor': 79, 'conductor_radical': 79, 'conjugate': 'dirichlet_L_79.30', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^44', 'a^11', 'a^10', 'a^58', 'a^55', 'a^37', 'a^54', 'a^22', 'a^24', 'a^46', 'a^21', 'a^62', 'a^3', 'a^69', 'a^20', 'a^75', 'a^66', 'a^40', 'a^68', 'a^48', 'a^12', 'a^52', 'a^65', 'a^38', 'a^28', 'a^33', 'a^47', 'a^43', 'a^35', 'a^70', 'a^64', 'a^57', 'a^41', 'a^17', 'a^32', 'a^53', 'a^6', 'a^73', 'a^34', 'a^45', 'a^14', 'a^71', 'a^56', 'a^2', 'a^18', 'a^25', 'a^31', 'a^74', 'a^4', 'a^8', 'a^72', 'a^67', 'a^77', 'a^26', 'a^13', 'a^51', 'a^9', 'a^29', 'a^1', 'a^27', 'a^36', 'a^59', 'a^30', 'a^42', 'a^23', 'a^60', 'a^7', 'a^63', 'a^61', 'a^15', 'a^76', 'a^16', 'a^19', 'a^49', 'a^50', 'a^5', 'a^39', 0, 'a^0', 'a^44', 'a^11', 'a^10', 'a^58', 'a^55', 'a^37', 'a^54', 'a^22', 'a^24', 'a^46', 'a^21', 'a^62', 'a^3', 'a^69', 'a^20', 'a^75', 'a^66', 'a^40', 'a^68', 'a^48'], 'euler_factors': [[1, 'a^44'], [1, 'a^11'], [1, 'a^58'], [1, 'a^37'], [1, 'a^46'], [1, 'a^62'], [1, 'a^75'], [1, 'a^40'], [1, 'a^52'], [1, 'a^43'], [1, 'a^70'], [1, 'a^53'], [1, 'a^45'], [1, 'a^71'], [1, 'a^25'], [1, 'a^67'], [1, 'a^29'], [1, 'a^27'], [1, 'a^60'], [1, 'a^15'], [1, 'a^16'], [0], [1, 'a^10'], [1, 'a^24'], [1, 'a^66'], [1, 'a^12']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-79-79.29-r1-0-0', 'leading_term': '0.224045291865431186828919053827-0.501898187015071963911268095725*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/79/29', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.5496344994049069, -0.0066071581612133935, -0.6083435619993842, -1.1823127912842457, -1.6128185422900938, -1.7670245387076684, -1.5494691627445687, -0.9614250948068189, -0.13713779063797765, 0.6666013805422115, 1.1372389646829295, 1.01715179136392, 0.22227448173441738, -1.0813512405717474, -2.48772887403414, -3.4643506294886963, -3.5422511479096013, -2.514804483667186, -0.5592141534095546, 1.786108969535729, 3.799807985599976, 4.852047157877504, 4.661947809929225, 3.41855060479727, 1.6983488755184575, 0.20548323759969686, -0.5486464252698791, -0.4697776829076116, 0.1084348770832394, 0.6388926132905532, 0.6903336627678767, 0.20969630532368974, -0.43827936717192373, -0.691304556027047, -0.15464638810367867, 1.1025570287066604, 2.5131457567921216, 3.2927201559718813, 2.899111276028681, 1.4074200558032064, -0.44162607914254787, -1.589452829207061, -1.2381936596915653, 0.6632835450553809, 3.32415787847885, 5.494973743810212, 6.134916369870417, 4.984156489897293, 2.698978559251277, 0.45789463071715875, -0.7325246512117419, -0.6117849283423297, 0.23430324503324, 0.8070358509435311, 0.38058827267150985, -1.0076928902800746, -2.5858419552096983, -3.375313419500346, -2.861868065690692, -1.3508075371506278, 0.24033396342190422, 1.0098690933577013, 0.6801070500507946, -0.2487270130114273, -0.913596354768111, -0.7725544973077116, -0.045509959947908525, 0.4412718128070413, -0.0736822661566685, -1.5839165921997935, -3.1318741869915248, -3.354429649182239, -1.4354346649241296, 2.19356133579234, 5.9419587341484545, 7.951327670917008, 7.231681685891778, 4.2812180003852625, 0.7576345014832139, -1.5831440499896696, -1.9567970306324058, -0.9070314189054093, 0.2555330072938465, 0.4778132815275403, -0.31599047233526933, -1.3151140098512595, -1.5933969454226964, -0.9109398448030321, 0.1050941064939778, 0.5345545315170828, 0.0020559619552832447, -0.9412196571035494, -1.2468191640808375, -0.28850367688826617, 1.4886727813257281, 2.775832240273736, 2.372497530903177, 0.18343130383227216, -2.5796003887772256, -4.219936349650624, -3.813669665477575, -1.926619876254147, -0.196070529412736, -0.06351972093099577, -1.634122244138906, -3.5705823064704196, -4.130359827148528, -2.5462802026117246, 0.3375569027976101, 2.6835599712882376, 3.0472845910188253, 1.4382263393182142, -0.7691079381806241, -1.9651284191850722, -1.5365386037042568, -0.2114504110748125, 0.7045822451767247, 0.49588501532908213, -0.40614738603746076, -0.9232589615935383, -0.3932701085814693, 0.7912630875112568, 1.561803461923504, 1.2256739604310753, 0.2018147560402601, -0.302257364945205, 0.5387366691759888, 2.1864453534779216, 2.916887656828229, 1.163015954160277, -3.0313231637353533, -7.711077182839238, -10.246213010370113, -9.212370686340927, -5.436749572427061, -1.3628467640212405, 0.7599992115703639, 0.41444055030715105, -1.1029724431661148, -1.9998856094314834, -1.5033993673370534, -0.2920605555372762, 0.4099427186172429, 0.13447441031633067, -0.37555680788778817, 0.04072106101773627, 1.711845975992948, 3.6548959811706294, 4.371525698274529, 3.2085716350781928, 1.00669346350668, -0.6067054925720385, -0.6595215764736441, 0.32557041642210127, 0.9022688376566825, 0.17219457884442796, -1.2383871189618343, -1.6829455026231248, -0.09253713902691971, 2.8016225425905685, 4.8382103763945725, 4.188622924360458, 0.9984787397841292, -2.5886223468818095, -4.130211994466725, -2.873603411376592, -0.3136080993939807, 1.1522295194124454, 0.27043241874410456, -2.1080748147137593, -3.9266438083568596, -3.7791151511719376, -2.0242691331627736, -0.23666995416194098, 0.3495911346372217, -0.13141955249892667, -0.594654089630169, -0.31466000224600904, 0.28315589167774974, 0.17875127877411073, -0.942457771489472, -2.0758422102201806, -1.7523731687433879, 0.3759418380495275, 2.830585525797315, 3.3715197427286046, 1.0194751325711489, -2.827437103255176, -5.349378280609685, -4.618737287835013, -1.2425449686234098, 2.1617388652175538, 3.2065903501846735, 1.6818948591508576, -0.5052364128042336, -1.2392504387512566, -0.11018911500787856, 1.4249719824690488, 1.6574689197137615, 0.35418166980317745, -1.0897862720616156, -1.1443426105976764, 0.2764874921408274, 1.7466038842386096, 1.807155753522177, 0.4597230679353381, -0.8556150132437008, -0.7634288764728433, 0.6201630366529435, 1.8168500044436366, 1.5421813224592267, 0.06507960699658151, -1.0741601470793978, -0.7276293055623032, 0.5648985654056371, 1.097207068068015, -0.08144982708717993, -1.810802832162257, -1.5886299515847562, 2.0519072569274432, 7.786715278477027, 12.181894867925932, 12.37961419051031, 8.421233473804834, 3.1188822509101364, -0.35429177920423827, -0.9152019826224848, 0.08111289644650538, 0.6397678733225909, 0.11621269440700184, -0.5189488862965635, -0.1457331826130458, 1.0634894547854865, 1.8051522612251334, 1.1541621625311231, -0.3228393639115511, -1.147792288477399, -0.6108127229520266, 0.32207129447603233, -0.01973302166588237, -2.098640851341909, -4.389767552472436, -4.738236591577314, -2.6026455308264143, 0.1396957719757861, 0.8182861829037649, -1.4527933708608902, -4.800234200308313, -6.270562226156351, -4.578983773198608, -1.2462360123118836, 0.9691020633258767, 0.7436825057700014, -0.6981750272040013, -1.0661252515199613, 0.5302673947591031, 2.684304368780314, 3.2267645207326368, 1.5256057523882274, -0.8551541507744579, -1.769176711555501, -0.629157925928257, 1.1490430115375563, 1.7584044063936997, 0.8570995777665779, -0.29968876663046085, -0.45554302289612303, 0.21955884610102175, 0.5068728333575517, -0.1558227523911281, -0.7131051577655236, 0.4206058962051171, 3.2803191967450207, 5.669047900132318, 4.968097367597239, 0.8379546180279249, -3.993023149770357, -5.9213976218396285, -3.6969688309031685, 0.43616054726922715, 2.8347779682844627, 1.75961959762913, -1.2892087200966853, -3.341681555099827, -2.8764293478412144, -0.9579402596608276, 0.30024717797194383, 0.049075269047608304, -0.7007081024303586, -0.6117053579973686, 0.27573977486991275, 0.6748280683279081, -0.19978641165672062, -1.4108340861316502, -1.167735739369342, 1.0864532225615304, 3.757409739042469, 4.543993646386591, 2.7961315642068767, 0.2088055550634736, -0.9871399411783183, -0.41280709015631195, 0.1341266163915716, -1.1592977502483741, -3.835028039500916, -5.36698413384802, -3.8032534874856427, -0.06101691343976548, 2.692240933893854, 2.0916150475725392, -1.0559083190789729, -3.565038623819263, -3.025065319986721, -0.069422435934053, 2.489813311719353, 2.598767613479083, 0.8367658307578956, -0.5810246015761732, -0.333104092094402, 0.7908339294578848, 1.1492323186829698, 0.3111827702096827, -0.5267379871475286, -0.15170750442331085, 1.0697571200606564, 1.5987570253255088, 0.664843405587309, -0.665108093860843, -0.7538815237287072, 0.3614337513190289, 0.5047509066788997, -2.3980163633593743, -7.6081476134398, -11.512684628964527, -10.707113676474979, -5.288435735848066, 1.0316583632458185, 4.216373002457034, 3.3378495434585123, 0.8212918937105886, -0.4488751488593035, 0.06774118729291076, 0.6840510681708689, -0.01847197957541085, -1.3808673037961836, -1.5699468643146184, 0.03822470529553342, 1.9126423640038897, 2.0176805543676837, 0.135131626005951, -1.8639483146488753, -2.122948283960544, -0.8312258763360075, 0.1658084769582373, -0.3289378235298751, -1.4126282963528747, -1.23729323919212, 0.6013116178927872, 2.360102368649539, 2.114536714613332, 0.15423670283324162, -1.1249627381440233, 0.04354005840393112, 2.476631805848906, 2.966002428794192, -0.2787741470550654, -5.3614056992428605, -8.233594987902402, -6.595753052608099, -2.1137964354051753, 1.3356996372968697, 1.462475400905543, -0.5750245887070791, -1.9379215892346497, -1.2571877780489464, 0.303328460288255, 0.8837490395983103, 0.18355909030173945, -0.5130557036577145, -0.2740720731107896, 0.21741447815447462, -0.2887141973700752, -1.6511060772951138, -2.136218424977618, -0.49829149712955656, 2.120756574704913, 3.0184916617265407, 0.8881131546114887, -2.422738783227428, -3.6020166554386335, -1.3863702653312437, 1.9808704528249157, 3.1006195568595043, 1.085220008792303, -1.503051365071015, -1.4943212501248724, 1.4212605576953092, 4.4191426218652, 4.65999204233947, 2.2427296525471694, -0.22615997194082593, -0.7223731284972078, 0.11134978168994411, 0.1673140765137814, -1.2944592938967536, -2.6626344336669154, -1.971480940421268, 0.6044622277846262, 2.794324485268054, 2.752939066165093, 1.0351316661504995, -0.27721960716970534, -0.11641189013145178, 0.5083097781647129, 0.14148153990221532, -1.0035993567263526, -1.2946785323166898, -0.11853518309369354, 0.6557603069030746, -1.5410658203671272, -6.636624946905964, -11.00179936337532, -10.564878847619621, -4.961837306063714, 1.7681330194662899, 4.885381459660498, 3.253941964843975, -0.1566317236495032, -1.7801573579286392, -0.9488294334139236, 0.23426866289591555, -0.0722967048093135, -1.3354558347918921, -1.7366797517136792, -0.7140684492767828, 0.37033994159287065, 0.16428302384311355, -0.7777909162830338, -0.6749231274121364, 1.0538410327934304, 2.7871361647614243, 2.5783887536965095, 0.6756107442087845, -0.5609245069014722, 0.5184490542311528, 2.6503387986459126, 2.9255109005514983, 0.25154056233509614, -3.077340219602956, -3.749906792453401, -1.1519655450201503, 1.8911935129237238, 2.2808113213367354, 0.08018000307803969, -1.7630251726959405, -1.0377846434806808, 1.0592135368476163, 1.347706979118859, -1.5171291692956903, -5.325854945226306, -6.671520261660579, -4.590441039921487, -1.333704242883308, 0.3690543342633363, 0.14389324299414902, -0.29347808336188724, 0.2575430463624664, 1.0164255981648145, 0.6118971289280439, -0.7554624022396126, -1.4035733447796648, -0.46316163941787875, 0.7313924726340342, 0.2400852410852557, -1.750402618474432, -2.709767990323248, -0.7936579426172271, 2.3826065965429954, 2.9056516608456535, -1.1577675537019783, -7.131886420233118, -10.008846877198375, -7.403052715703421, -1.8330267665832984, 2.067394001857666, 2.1761922817304216, 0.3144209275059759, -0.6094820127681352, 0.023189096231208323, 0.5131718875718077, -0.36959975183268623, -1.6419658967027375, -1.5677314059159753, -0.18976666994846092, 0.5491711641402914, -0.6477398324680226, -2.536381907048978, -2.678239939360463, -0.47221910630611985, 1.9490720933635188, 2.187037395903985, 0.39394797712365803, -1.0732539050618959, -0.7011765629575943, 0.35001421941549804, 0.04138779967892693, -1.4120021925838981, -1.2811494186064438, 2.334626568790577, 7.537694168627038, 9.97190910976272, 7.3684916839747, 2.16071497199136, -0.9717770951845088, 0.051228791885307455, 2.8956913598474836, 3.859315037134705, 2.016154735272634, -0.2680328735767871, -0.6012912176282524, 0.632299026219475, 1.1824213059641786, 0.0038345366590990543, -1.545992641112024, -1.6931255948366917, -0.5632477325770531, 0.23659125434402253, 0.006865225264764268, -0.12872627620137073, 0.8430330787445939, 1.737126416852642, 0.16046978823932032, -4.192489207801372, -8.157188690188987, -7.977761685553079, -3.531921295036796, 1.1258602201151835, 1.9045071710391914, -1.051259919415983, -3.8180946629509287, -3.2637548246361487, -0.3675181906929423, 1.4013815147470086, 0.37504075307439083, -1.6084956845088807, -1.8777216760282114, -0.3460014148565247, 0.6156573386498763, -0.5428292046944397, -2.4714242527863353, -2.6812319853990783, -0.7783329538282451, 1.0299984759810545, 0.7545328902069379, -0.921976554143258, -1.6854431923076285, -0.6579478798423827, 0.5743878657726247, 0.26775884525442617, -1.0063577818950327, -1.1239767710047677, 0.5544761141784809, 2.0367286521146815, 1.2562485188672026, -0.8663106013302847, -1.1197337654607882, 1.9192591224536448, 5.419689569699909, 4.939997268705149, -0.4794279494117425, -6.731637991967524, -8.668985491335775, -5.308121250688149, -0.4332407589394996, 1.763022711926212, 0.7775034856624616, -0.7491710125701873, -0.779074002239931, 0.07682052167569914, 0.27374558388029163, -0.133235351888944, 0.2667132494754266, 1.7945469688784539, 2.750145875941593, 1.5715369746555954, -0.7794125939387493, -1.6640805690462503, -0.05208532717403557, 2.0279612510605114, 2.005187354293178, 0.1725654665119947, -0.5325525979405858, 1.6259093542305991, 4.5416923464851235, 4.443277357304823, 0.4850144771295216, -3.9064852254733657, -4.7770938869995865, -2.060361957163093, 0.6284792978883939, 0.4391250762534086, -1.5427423023946056, -2.1358343257480867, -0.31844454622218255, 1.5572500761355628, 0.9659629928966503, -1.4463212955101041, -2.6628608173300137, -1.0971645313071374, 1.5190945557120943, 2.4337849398428175, 1.2166297520201808, -0.11189369837907215, -0.0037501576115794456, 0.7411055076055, 0.540299324536407, -0.4190069983974553, -0.40490602089081784, 1.1203355081085542, 2.2958768440945567, 1.3663845568086654, -0.21491394158470867, 1.3292353148813496, 7.497310796457683, 14.667944341845939, 17.047058949818325, 12.568189315695058, 5.053197060110333, 0.11276442770583353, -0.4545424685344053, 0.5156075926343842, -0.16402921832516906, -2.2505878718890644, -3.135806754699785, -1.7160478074102024, 0.1920577444598231, 0.43748377868640226, -0.6820992747246672, -1.179506746369463, -0.373219832558548, 0.19973520825695185], 'positive_zeros': ['0.30898546586682104464500625590', '2.54971283596496024982127184848', '3.81048826503597000103626254713', '5.700782234257863227880996552816', '7.870642681763515302874401120649', '8.69780932428403701688834145613', '9.78494942273188896441817232531', '10.67277888180225591423109041140', '12.42127443733824031061475260068', '13.349014917555317218961801752159', '15.39804070309503314814008888612', '16.16890274728759033386371692009', '16.978751128723105275414836809682', '18.69506601402850364891367040220', '19.60689884626151795725917252345', '20.64374801142031887714347543873', '21.22830498316948477067568618387', '22.63534775371028283898610516638', '24.45403579160856096479175656987', '25.53922843262809031087462227219', '26.15340978277747899509512023358', '27.4631556321203814408411542868', '28.125714769132750197926930162415', '29.11843394879554617793219890136', '30.33312698682742850928070224920', '31.94396352795284241450249148788', '32.16147822994183645259727057947', '33.71443357415167312553975712147', '34.88495847578745383113612045059', '35.989123402354693282072771173187', '36.74068566932288422769336280145', '37.61026696036717907739026660034', '38.81965502653395171375037533159', '39.23709446170981701852711149401', '40.41451457656127976073971546053', '42.34014764945885431636828415918', '42.90515836817169606839452316938', '44.15039907025466556654992868575', '44.75590847275579180283435739591', '45.30069809020508891206640898875', '47.03777350420751313555365165201', '47.71768520187886542369009445828', '48.47739796900267865651112735272', '49.386330783812608363117722246159', '50.70564275293597920867679320236', '51.91781045038527566364981943544', '52.54159926390203106614341889122', '54.12687134333598138610032078787', '54.62579087400497281614232832848', '55.4642764134793870224512359036', '56.00746645387333905509067805985', '57.14279793531194370147036725950', '58.21092763656005625567769347105', '59.476114308972533168410801303917', '60.542242426779817446367932561394', '61.2705025436060833396491335001', '62.25319726245533381059794439211', '63.07526671701654406650258786633', '64.152429789655288927787842338120', '64.87698398860810576003203198239', '65.95030527564959705844070731011', '66.74156969373270490889807212789', '67.485920277477858277646465943378', '68.29645969843331128724205828160', '70.262489722075219504268132475566', '70.91367350990510075365362438130', '71.60671966073493278724143401201', '72.232326485234226029127228498021', '73.36830717370996642603213328525', '74.24499673743168556846643238915', '74.68273674759525915386214535059', '76.22972880894721599223818081405', '76.71756194815776647592298530811', '78.26212366923134149564709004769', '78.91144529593713848821737840785', '79.61059276180630628952073408438', '80.81581342612781951609880380236', '81.66736802203541907381651443067', '82.7126707338750696867516222322', '83.34438968128949016759202144929', '84.00802804335977758456305143048', '84.62121716555833731236392082072', '85.98817114663848840418445134620', '87.152652200154265929232361151534', '87.997431299513828110681102768132', '89.25616371842966864870210345354', '89.70704760579129802179364735486', '90.533269489503854311350178472291', '91.20178806342754390652026222867', '92.0619933283718507218964608231', '93.46875874457957530740232818628', '94.21329659742457631504045327568', '94.45881360023813697164452939295', '95.94249587900643850888834885792', '96.77967985739995235669596876377', '97.81915272344552743061948421007', '98.8967814018087649133144564965', '99.47121359441578330943321081915', '100.40187477237633478497412951612', '100.98165836948224428678452405896', '102.01630615247642628423549114797', '102.71788412078217474142015775549', '103.21736063386000342207367949232', '104.941845297812855163495483153176', '106.07660621927230295073844570684', '106.53940979027337981444266697648', '107.18309227121427853534206279812', '108.1193767546143392162066445882', '109.08050430092677693868331869442', '110.21626456687311665855984940031', '110.515693711868952911895234079224', '111.47620748743339594911016638750', '112.52352889126043933561067084276', '113.11894140615297564300222351067', '114.04401407613569593603089669525', '115.47226304259275456501201712390', '116.168899631631331256828440663031', '117.12029225864930123456116863339', '117.87332844882628781661726494450', '118.576903301503936010447286966718', '118.96863923489821992981348279365', '120.0593674439873314824330350733', '121.019212560985349701910297156847', '121.99737236558035204878389925645', '122.92766797209471180775112567350', '123.620765976798990300093346352987', '124.95976801801770897083950162800', '125.58275164357753771478124401803', '125.992541553295926432201227499897', '127.12124553488915490883714319776', '128.33451735189234110248089727580', '128.800632039345972053099054711215', '129.41793173176105162198278131532', '130.33820872403242549282226805032', '130.78374099986996307274577187288', '132.40848897386331035920102604170', '133.42114215408807751228901404036', '134.2839588585074108831459437909', '134.66550620685423212784793796224', '135.79891103086810404149753458166', '136.30649838521744604262857596268', '137.02326220707228719656759151858', '138.24114428871142130257413336428', '138.6624923257507106663100542195', '139.70917528402254875224105200989', '140.7289167466568453991173425139', '141.57219102476843659108769387716', '142.33884172963164779119296891972', '142.99360425470888842842898147143', '144.56997144633160419229250592653', '145.06732960267323015600331435488', '145.530739542181137180513426430200', '146.39675796173958738044389849595', '147.28736475053574109142307641433', '147.85805458447995198703661791628', '148.82589586311391147747291476777', '149.62239646947094898934064307329', '151.05245439722491895510220855774', '151.93519162586338889621023407502', '152.492064290367297375008450585382', '153.03658060113707167474496812123', '154.105589875260667358287538884654', '154.57126264937948456521202543144', '155.67738253285540366788327354095', '156.62382332008085969039594527346', '157.37491396905807636193604109073', '157.82313121828230668948787642239', '158.58421463558226250371301827202', '160.16580858553265156501548390782', '160.618791267956935253692906221078', '161.82533839948395218169999330710', '162.354796294022745106983198947024', '163.12569364731154374798897310113', '164.23069978228381720534619453633', '164.692191877434807675681530170382', '165.07245003505583590985734850354', '165.95267430637655226368431422463', '167.405771283282427545560675648299', '168.03360384354910739666954034240', '169.10353836531026066410138914348', '169.74340298916782238907427599965', '170.692369607531251883099139119166', '171.156087543563340436591484397922', '172.29572924716270049253109328894', '172.95981118102353064645077197959', '173.888269115799684842612915958605', '174.44406356419427443682764757767', '175.22744765315881362792538718520', '176.11779879605013803909128173267', '176.71169361527515485941411595985', '177.790377131439271765805145478556', '179.09793882265777647082237466468', '179.82426648233023585549245951602', '180.592756683414058009400279414249', '181.13554816634172760867333724764', '181.46945094468815658545158585926', '182.70469110898788744906375175028', '183.44436320637717554704521026242', '184.405965603887882585140730759015', '184.80952233127405314888889508332', '185.96787715834922173385435385302', '187.08579212105789452154349704909', '187.57647688722593191913567860425', '188.47897372015088384836856471756', '189.195792816671588134802130895802', '190.12526458013757028731464637982', '191.20595103416243482285585071744', '191.56410989342601045138925510643', '192.36027366543008459182433956043', '192.91929437045094667902096998629', '193.99304868209832489454905138564', '194.2266055921323841818347571697', '196.26424928183317793143974417615', '196.69343684507785028432152993887', '197.15653633720400860793775789352', '198.394745008312496342652471474253', '198.88784200274495913855690564923', '199.812871198371850160326404831415'], 'prelabel': '1-79-79.29-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489729058775376, 'root_angle': -0.7327134613982299, 'root_number': '-0.667682149325742487077522315757-0.744446470521391424582208815984*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.366356730699', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(78)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.622398894365524570058514870873-0.152408455285041257712811925505*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.308985465867', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.54971283596', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.81048826504', 'prec': 44}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 8.489729058775376, 'bad_primes': [79], 'central_character': '79.29', 'conductor': 79, 'conductor_radical': 79, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/79/29'], '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': '1-79-79.29-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': '1-79-79.29-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489729058775376, 'root_angle': -0.36635673069911495, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.308985465867', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_79.29', 'Lhash_array': ['dirichlet_L_79.29'], 'label': '1-79-79.29-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/79/29'}