Lfunction data - 1-1037-1037.112-r0-0-0

Formats: - HTML - YAML - JSON - 2024-12-28T07:27:53.544769

• 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_1037.112', 'a10': [0.7253743710122876, -0.688354575693754], 'a2': [-0.9986295347545738, -0.052335956242943835], 'a3': [-0.996917333733128, 0.07845909572784494], 'a4': [0.9945218953682733, 0.10452846326765347], 'a5': [-0.688354575693754, 0.7253743710122876], 'a6': [0.9996573249755573, -0.026176948307873153], 'a7': [-0.5664062369248328, 0.8241261886220157], 'a8': [-0.9876883405951378, -0.15643446504023087], 'a9': [0.9876883405951378, -0.15643446504023087], 'algebraic': True, 'analytic_conductor': 4.81580775392036, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]], [61, [1]]], 'bad_primes': [17, 61], 'central_character': '1037.112', 'coeff_info': ['x^240 - 1', '0.999657324975557 + 0.0261769483078731*I', '\\\\zeta_{240}'], 'conductor': 1037, 'conductor_radical': 1037, 'conjugate': 'dirichlet_L_1037.250', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^122', 'a^117', 'a^4', 'a^89', 'a^239', 'a^83', 'a^126', 'a^234', 'a^211', 'a^135', 'a^121', 'a^20', 'a^205', 'a^206', 'a^8', 0, 'a^116', 'a^142', 'a^93', 'a^200', 'a^17', 'a^39', 'a^3', 'a^178', 'a^142', 'a^111', 'a^87', 'a^85', 'a^88', 'a^193', 'a^130', 'a^12', 0, 'a^172', 'a^238', 'a^153', 'a^24', 'a^137', 'a^215', 'a^183', 'a^82', 'a^86', 'a^139', 'a^83', 'a^161', 'a^100', 'a^125', 'a^166', 'a^60', 0, 'a^24', 'a^186', 'a^233', 'a^224', 'a^209', 'a^19', 'a^207', 'a^62', 'a^210', 0, 'a^75', 'a^77', 'a^12', 'a^109', 'a^134', 'a^164', 0, 'a^156', 'a^54', 'a^121', 'a^120', 'a^1', 'a^35', 'a^55', 'a^146', 'a^218', 'a^19', 'a^191', 'a^97', 'a^228', 'a^65', 'a^62', 'a^204', 0, 'a^208', 'a^202', 'a^21', 'a^72', 'a^205', 'a^103', 'a^43', 'a^70', 'a^222', 'a^231', 'a^7', 'a^193', 'a^48', 'a^129', 'a^182'], 'euler_factors': [[1, 'a^122'], [1, 'a^117'], [1, 'a^89'], [1, 'a^83'], [1, 'a^135'], [1, 'a^20'], [0], [1, 'a^142'], [1, 'a^39'], [1, 'a^85'], [1, 'a^193'], [1, 'a^153'], [1, 'a^183'], [1, 'a^86'], [1, 'a^100'], [1, 'a^186'], [1, 'a^62'], [0], [1, 'a^164'], [1, 'a^121'], [1, 'a^1'], [1, 'a^191'], [1, 'a^62'], [1, 'a^72'], [1, 'a^193'], [1, 'a^140']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1037-1037.112-r0-0-0', 'leading_term': '0.247000453063356285046185646130-0.0670608327692953016326806490302*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/1037/112', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.2559421401512743, -0.046514121946075015, -0.7394160509215613, -1.637097461406358, -2.062437421774041, -1.3823723398750516, 0.3130916386237683, 2.0006216885872563, 2.3513342253504894, 0.8728186202212768, -1.3877228226820337, -2.401532856033924, -0.7833473508454027, 2.8211842590050704, 5.9606167205888205, 6.285345743433608, 3.5732914937961904, -0.02580612140313812, -1.8905408343875165, -1.248212148436376, 0.33164380856803544, 0.7538585125259762, -0.37174600265244356, -1.4531106741155608, -0.8718993984679927, 1.030869068611367, 2.23535396398377, 1.3394235767297875, -0.7542640919650958, -1.7819626529914254, -0.6759570246074319, 1.243934473640678, 1.8716592164043173, 0.7865372139854175, -0.4217046610477972, -0.34560560279902686, 0.3796274909521543, 0.0624150988316654, -1.4131277269086426, -1.9451306861627975, 0.0887263764305787, 2.9541392953184054, 2.57829008745324, -2.924327684609131, -10.313161955904256, -13.790414865040526, -10.727198717532309, -4.228659347241183, 0.348130361615142, 0.8444690120586924, -0.43947516966912237, -0.5245857402431433, 0.5754637958210103, 0.6908617474023945, -0.9291690142738164, -2.4295241645641754, -1.9986329998584023, -0.39542138163640955, 0.2536704762428551, -0.46708426392220065, -0.8864175511675916, -0.15083833034100147, 0.021785772304907806, -2.2538235732428715, -5.65471081108523, -6.511032382729258, -3.4525958152795595, 0.35719232562554826, 0.9253658966034621, -1.483758519671398, -2.7629675208046134, -0.540454532287713, 2.583400497263077, 2.6299601481919295, -0.2459040183541214, -2.001973623238418, -0.41669650804065267, 1.7369197974846482, 0.5698387040812102, -3.3803663670952813, -5.703667897923727, -3.9732764644110983, -0.7484152348293093, 0.2176541921998919, -1.068654152287656, -1.5773917017664534, -0.026911261275109136, 1.5204408874542215, 1.183378047768243, 0.10957249242192961, 0.32826807573166844, 1.3387509678177665, 1.075863930129299, -0.33173268288818436, -0.41516154101785147, 1.4222062182437203, 2.118523677838085, -0.6527398887373741, -4.057337961986864, -3.1296767534928196, 1.9488980111072838, 4.853081471576588, 0.9495680672122757, -6.263343717150921, -9.188442181308261, -5.452217275361312, -0.11927005662639084, 1.4898355775957912, -0.0456906024374219, -0.8648599920489968, 0.09171206101761395, 0.6737729196345856, 0.03329143899689382, -0.04336431595930994, 1.127498906470365, 1.246807616575006, -1.2291126980798301, -3.768126468891823, -2.894251915124509, 0.5531338325504764, 2.3463293069316213, 0.8886009314990514, -0.8762581179639822, -0.4555494193146884, 0.4739471089283036, -0.40233429474886495, -1.3555229034533873, 0.8757796207387076, 4.926349726427508, 5.4607096888774755, 0.8972915313975134, -3.4304219444064303, -2.3391235150362313, 1.9082908284718467, 3.0420037972297553, -0.07790667120589373, -2.251210543725343, -0.11430076705205916, 2.953248635984134, 2.292543943933986, -1.1169434083031742, -2.687895254945012, -1.1991495345738206, 0.27826892676866166, -0.10097407227126819, -0.5791084684606994, 0.24713843492935078, 0.7858407509558243, -0.2987871587004016, -1.2310859707175978, -0.2372034796821551, 0.9069380399281759, -0.041330025992380615, -0.8386618471703617, 2.557974468993902, 8.48172554624271, 9.76019676910644, 3.3956105220100152, -4.243496793934341, -5.398091462386507, -0.9890336433643476, 1.781409009339376, 0.06197119002076957, -1.8843040381175664, -0.6901709920192157, 0.9940742020398203, -0.1665918845656675, -2.285049389662968, -1.6626031283794698, 0.8118045455565734, 1.2931944166168545, -0.4264860304458367, -0.7747144058563225, 1.2577181762411966, 2.3782047327868674, 0.7504900180817913, -0.9087678990626246, -0.26353673841194375, 0.46907690879035524, -1.4106454845080438, -3.890694578698959, -3.2800958523967267, -0.42559151524525873, 0.7599824845117902, -0.1129862130491234, -0.05700909309000009, 0.5079280066443818, -2.8247678729912193, -9.995332379589462, -13.1967079794095, -6.701946296176414, 3.917620848190615, 8.111571858060397, 3.8475757051754433, -1.2157735746108151, -1.4168951319751466, 0.5400549420592397, 0.31477708405862276, -1.114242389688737, -0.7735291854966159, 0.5664944159720003, 0.46923515815397965, -0.29995004449565044, 0.4271914407559073, 1.5420585627391512, 0.4623542893568221, -1.6714143562108048, -1.5492051617150802, 0.11568951576072163, -0.7020896071162013, -4.006849435928058, -4.887660143562704, -1.766399185401872, 0.215025004965349, -2.497282810299814, -5.41609785643884, -3.0092034465776725, 1.8900316415083311, 2.187984026309036, -2.18596694614271, -4.302843641443831, -1.2784479482476112, 1.9209886871970068, 1.283771649443803, -0.42387944883970313, 0.11391366075144055, 0.6644682559904602, -1.6647960923599618, -4.023975901287168, -2.0505369684591885, 2.418771840300638, 3.798264773363794, 1.3049691456882062, -0.727106564118537, -0.32242381938406856, 0.1590220293409889, -0.38761852075139225, -0.05955500152199787, 1.256028109573054, 1.0417876563748014, -0.2421426486064336, 1.4139136263462977, 5.9058306119577395, 6.899191360948002, 1.6249154925409104, -2.937362895114209, 0.273043831500879, 7.0642612527616375, 7.835749260479054, 2.013616164713977, -1.7719158203880325, 0.6658507500073382, 3.8625027216524095, 2.7808451018771465, 0.1272504586242973, 0.0438557848370909, 1.106377294493658, 0.3005098191034036, -1.1180420324129978, -0.7321994643291185, 0.10489854773957095, -0.5727195702362048, -0.7846829254493379, 1.5736043093139855, 3.5107253867319255, 1.3139243476804925, -2.422725759449677, -2.448696635209823, 0.35111962917008865, 0.6852787216523926, -1.7106365687936282, -1.930586609638445, 0.6881269809357015, 1.061529564708378, -2.041909439423283, -2.9898828129374997, 0.8026274512599736, 3.6757364525525946, 1.3591381579723867, -1.211143622699978, 1.7628819541458352, 6.520959327674863, 5.492772356240356, -0.43991657875432355, -3.72650477693528, -2.0047322993016414, 0.046282401492514794, -0.13723408011525384, -0.0426269592077661, 1.2596706711828571, 1.0027381072765986, -1.2428145965262276, -2.0432407341860275, -0.3929996136464635, 0.5512788809892978, -0.27748945627702515, -0.076499672474777, 1.5323879263732003, 1.1688281464488943, -0.9420036837093929, 0.22815658921928278, 4.601618558725202, 3.8757580979393578, -5.735287971982338, -14.847618587128867, -12.856632505889333, -3.045615165835893, 2.9491448481126823, 1.6826216300963839, -0.5296953428863171, -0.03255697253620141, 0.2744829395657788, -0.8505965340445275, -0.41742369098264154, 1.7721206681935984, 1.7677332073719598, -0.9483895587816014, -1.9450904236097482, 0.08800925497785661, 0.9718170513022337, -0.9631114151576581, -1.727532042694981, 0.604026764550485, 2.09209339806864, 0.2990899019231072, -1.3570835227196754, -0.4428147103257128, 0.06302025041186038, -1.5700845446475997, -1.7120875222191771, 1.0303788665849392, 1.2478634540737623, -3.970201897164743, -8.077633826605332, -5.050033106186967, -0.08350549589420651, -1.3538642194410837, -6.228684404903489, -5.903902226751731, -0.3514589262339627, 2.226274433695333, -0.5883168190311575, -2.6495962363745766, -0.7575622143072989, 0.9889840983843592, -0.11230143102144514, -1.1419162301807122, -0.18902540579228652, 0.45488341163989565, -0.22092504879553682, -0.20073466354248123, 0.3618920669493974, -0.8191300938484476, -1.9669798861925316, 1.1855441249869936, 6.511948295110173, 6.764039299044437, 1.5404976501127006, -1.2240487484088751, 1.5552071254413888, 3.259070125115069, -0.050383757523720894, -2.532081825964414, 0.23903901897274318, 2.5733425182651013, -1.2412725204398376, -6.417557284687951, -5.753841565241368, -1.3975581339680154, 0.22485743057675794, -0.588571228600397, 0.2265361438139563, 1.5079392988796, -0.15025940165160906, -2.4245700813645708, -1.035040868878196, 1.8359461963201869, 1.2389021520214742, -1.5008831703929917, -1.5518605212072443, 0.5494980370504627, 0.7990801609100918, -0.34558306076708145, 0.16293895462893004, 1.0744285079361198, -0.32582291123074103, -1.7513385237109498, -0.3232342044961407, 0.5192530359161311, -2.4206388680631887, -3.0294662415141174, 5.563013244252959, 16.715349489833464, 17.107464389866294, 6.498338419524151, -2.0240860408393493, -1.643363732277722, 1.0140150942507626, -0.14393058038486503, -2.004398119070576, -1.023142006413542, 0.2522909770278827, -0.2831625619060621, -0.2367925494377702, 1.1409670563680632, 0.8231265346166355, -1.2209008338279996, -1.0153721564766716, 1.5743640683078262, 2.0438280978656125, -0.17585421181547733, -0.8673099347899844, 0.14188920398789207, -1.3255876955169665, -4.130365762342343, -2.211708986425984, 3.5734600479836627, 4.986127661130083, 0.35947324563564714, -2.247595262636721, 0.8601715253746238, 3.316093259601651, 1.2451574777984513, -0.13735495400885692, 2.2999843137085394, 3.1724523165556717, -0.5305818733440892, -2.818978726410173, 0.26871372592760867, 2.945259974568462, 0.09560749534710947, -3.7126024966712614, -2.8361121854666593, 0.12935884742355513, 0.5849839468582279, -0.13322322506879364, 0.5371628560615602, 0.8761702971610518, -0.28299008142036686, -0.17290338174362269, 1.822996055461785, 2.021085191282437, 0.015065439121878474, 0.1321261176842328, 2.3489532407451206, 1.5776203402285711, -0.9029606580332401, 3.054388571799673, 13.090824249887778, 17.006635125111202, 9.076112228797532, -0.5221051906196069, -1.9785104783291427, 0.3018413124389805, -1.3869587070520366, -4.477827441255469, -3.1948661880468188, 0.1525680547188011, 0.5666993975400637, -0.5459447392251158, 0.023450109624775093, 0.5916508298311095, -0.5675478439746386, -0.7963845604884003, 0.6968098300606301, -0.14622326476629752, -3.8500349846794246, -4.496333185261738, -0.08419755781826567, 3.163206252019683, 1.5222218571374877, -0.5822773367841811, -0.0018855298835244476, 0.019316018308113348, -1.7165659041545476, -1.3960775805897603, 0.4031680843611932, -2.1938606869386197, -7.846167508852217, -7.0671111861266525, 1.436399332452514, 6.502552925266098, 2.2344750193500853, -3.049267357523311, -1.9515282123497721, 0.796772584520238, -0.49817636669325627, -2.2455043108327004, -0.32063602061019275, 1.6227893815073924, 0.044976438112652735, -1.6475511700880452, -0.4452481088718271, 0.7555637976572234, -0.11912375715385697, -0.5015056179922264, 0.46634304512015184, 0.23907727445056248, -0.6350546798674863, 0.6532874963254116, 1.6367940685303388, -1.8548689945503987, -5.519684257830232, -1.9667156681957387, 4.9972622384289735, 5.0643465226690445, -0.5640992051683484, -0.7824115616017593, 5.88848126475126, 8.976436241210763, 4.4033526276089985, -0.13345450360799518, -0.04680220317758074, 0.3417614697400172, -0.9836573199312061, -0.2652068405052487, 2.3112250883287877, 1.891954273273738, -0.8168048200698703, -0.2193692483960702, 3.1319417117000725, 3.4255954826754884, 0.7033687844546352, 0.07829875114973779, 1.4740893854902628, 0.8183853337281349, -0.9729891652728847, -0.4228818390470842, 0.564068306865301, -1.1050170803330706, -2.344539463328644, -0.1149687831619139, 1.2469448036054231, -1.6846204010596466, -3.6060339184827006, -0.6551043451933259, 0.9924249564161826, -2.6718793254965623, -3.312701456436684, 5.424175591064717, 13.959465715298876, 10.73681215158676, 0.7379974182115148, -3.520536418721677, -1.0276032194174645, 0.7136629015181842, 0.010827857745062062, 0.07576357844056174, 0.3732258777315052, -0.7771943725819014, -1.0272958485007695, 0.8402361594466282, 1.3976236041982146, -0.3261702025657454, -0.4954561266615363, 0.9559131297893617, -0.6918583922987682, -4.586280696730229, -4.285161268934896, -0.18920547292956663, 0.4946114338921912, -2.4569391269088108, -2.223250569409457, 0.5865772994012077, -1.5920219927892225, -7.5249246177784785, -7.641644944460469, -1.3266962667187605, 1.9561904893543298, -0.29488598169840774, -1.0232450468874437, 1.4225982368522416, 1.1361373528423626, -2.1691386422928356, -2.5190258757928214, -0.09063201108947369, -0.5681061703794391, -3.2047972492608454, -2.4492048668806436, 0.6209176176462562, 0.6425584240277215, -1.3297599499956563, -0.6663033833423266, 1.365346886735238, 1.0184121610379235, -0.20473624463481047, 0.1806311542484517, 0.25115534980577936, -0.5897134997966171, 0.7060962035799088, 1.9337913375699516, -3.7995478595509145, -13.237120317802761, -13.106349021520952, -1.4634179846641975, 6.778799092918907, 2.84820731341769, -3.607234088976225, -2.958573665728605, 0.12888593341538304, -0.6672435318764172, -1.8889029246426976, -0.03369433455626894, 0.8787682575604729, -1.3846830958249812, -2.428177713357013, -0.5159415955239764, 0.4824400093595511, -0.2598168350045335, 0.18969343814037126, 0.6886615314008042, -1.679155889314054, -3.7373738477365404, -1.51545355895554, 0.8836242898510247, -1.3993655022160423, -4.000797384798037, -1.6405674951283822, 1.4147735199014189, 0.08361237454144384, -1.5878297003678508, 0.22420362949157288, 0.5489497227909692, -3.354873084452539, -4.481312014432883, 0.43751087677897704, 3.091259488975261, -1.1359383833695205, -4.105902678200621, -0.44496871010786665, 2.496012138870752, -0.7342352840568762, -3.6292115281665094, -0.8394161485224736, 2.4351001647833277, 1.5252459364360895, -0.022393809165710765, 0.6362203174150305, 0.8687300366315975, -0.053537662564984594, 0.23786961795964245], 'positive_zeros': ['0.28071766763155849603283873793', '1.82387965406517806981336923027', '2.93169913896629137975732790532', '3.827504583343122640575962979849', '5.30988379926281800205591406168', '6.17611851453107809561907280321', '6.79423006669419753578875330268', '7.65260036716748420064493860749', '8.636881232796431924143890617928', '9.48093447559694357423898818286', '10.48700979451076050249329246150', '11.07531627802898748470526211593', '11.5795924777520127063431262351', '12.4908646994228325407160102680', '13.301941923670083231287400247827', '14.96041166245723695415391291028', '15.51196196303814541738266064592', '16.09277310276087700387236838525', '16.72325634761669083272585363315', '17.91496185146638626599012474962', '18.27466396684358355356506347225', '19.11928551631994571766765633321', '19.38203623437922971543765199190', '20.8981411959712929331595364906', '21.390657142356820802991993036666', '22.23576878058890097294869649438', '23.10019672633723005379169110151', '23.798536167147032770268811470340', '24.42776142554872311316539967487', '25.74558199065581472587768496829', '26.01749209879271910887245495932', '26.87912451913290566669792706760', '27.90365296081379433305127271890', '27.94662701134594377801658135545', '28.98396128732731681602074016364', '29.4649807139754284940098261500', '30.259930819179924564666625201655', '31.13897513771478392523146422180', '31.917245316561747701574872438707', '33.13463849008115576805146468884', '33.74184910565233929532188945977', '34.35092070736571261412672335636', '35.01480278819757135199463784176', '35.33012895508234845780048326968', '36.124633398244562262508161448356', '37.13725906982766669107711353214', '37.93736774945372905644203856626', '38.55143423373657401621794411155', '38.97672074412211748957534573112', '39.61099320559706837127540448221', '40.67487733965699990165911711252', '41.419724808862839446076399703211', '42.18091589555958021453587832436', '42.822418740271404330062552479790', '43.64862439924971816276056546261', '44.58684120647155133217491532713', '44.963507561454261553504899360268', '45.55552294683347714399812973559', '46.18704807854619828792391274212', '46.920679956177789104197501645618', '47.492163727346057880299105041281', '47.94543605386352382291063573344', '49.18549934475147680024389327551', '50.069303074270118661843559995687', '50.63189932379196992255161141955', '51.346296558406819372918648801270', '51.85260578817385844854934319189', '52.70380112950918433744103296841', '53.36304839226352795519619075028', '53.89229232545057390021995212761', '54.792767643981218486105181932262', '55.37414903741018228698945490312', '55.75636026674695762620295790560', '56.93152561750830924871505510154', '57.46136767784159157055346964336', '57.83162169455124314164936768794', '58.23030399143530191711791245750', '59.564915586972774106013620260537', '60.523319107034859581698545950424', '61.1461396687080687212598571832', '61.62670071055371715439622400209', '62.35226820789805229750009453262', '62.9673311348694876077694302584', '63.33250510342037071954703454052', '64.1255226038037094157486032910', '64.96814221591229988149814910959', '65.20698770983701130144551558264', '66.446264350270400671087107337', '66.628187634444665584076917693360', '67.679049516417878013644968171447', '68.29436099429729838026952032183', '69.15904699130654576650729084274', '69.88827356299266062654785202362', '70.28467688434337526137814565937', '70.7580932143199682617049342681', '71.702799302790942790516082247071', '72.65253772329063576499886756720', '73.243681618065970371406991779779', '73.554757876900928161141551878823', '74.07817217130316003838570954169', '74.91062251940672963853328077478', '75.14927662260682284198237341112', '76.3290748375057575909478469727', '76.86202532102090691924731051655', '77.92278672433128341381081166245', '78.38617889872576337043241057162', '79.401230205890503369895969470326', '79.675286852185819755918281593205', '80.36749336995161607428353360277', '81.16330028443074621622977375949', '81.37237630894715744030605964909', '82.01350231616093421536107985921', '82.91184101590899439627211685706', '83.70597449484991710089346089090', '84.16327925732338204498353823662', '84.91902599271744369578447328862', '85.43796858645624134832008808069', '86.19645613071979415348154853863', '86.98984742337690939595822404598', '87.38187108394714782358583697595', '88.4141913707991886803694104230', '89.35849932965668575918089861770', '89.61725109759428305866216119339', '90.01314729565932191181601026474', '90.77418503217052022414853561812', '91.632723025314113118126599107', '92.09679258758891051249715268957', '92.51743946634386221912203958048', '93.28645055923117319946103939018', '93.72988714186951250536130902071', '94.52679441256679535237289076195', '95.73634263100569391543361825416', '96.44443597547707509635770940885', '96.88466559360301894700630728913', '97.27752405749454645722128946105', '97.87733806752512793480783388940', '98.6469666632414033421490811338', '99.36299855442434195842702105248', '99.86911253265298841213576516678', '100.55857774339312371930109326498', '101.287166425517759124672020919120', '101.98758131537919228381622447697', '102.20925810559424864722108343480', '103.01605175119060466898736137844', '103.53880994218032616274446651804', '104.69824193149401356567845732187', '104.8794030157157774718026934986', '105.95836455880882449474203559638', '106.51278703933192649786568638802', '107.27806389878564329155931872483', '107.79256371125074502504733562147', '108.48476502599469296882284114360', '108.97236741394696377765123681466', '109.45780034495436532195648723439', '109.84926434623653282901595548375', '110.55034357605994701735601868594', '111.66333422015691104762915060260', '112.05484362747417888183750748305', '112.8088514741909274197094483228', '113.419199659776329167748017359552', '113.99553798593323304488964438551', '115.16784165528811181603951873683', '115.41386704931106441873415785071', '115.89597021748358848287577405538', '116.54601555747093024146496266956', '117.28663140985040928012142192069', '117.94711651188720073642887803220', '118.66118889850045464777748379762', '119.26000462116963635362716539050', '119.64787612957768621627108847537', '120.26539523833535015109858752877', '120.98626616791617764557354792444', '121.33697950761737066259387264024', '122.02565366024620544181817410011', '123.32643533669811548570163600331', '123.90673207108660799757652368322', '124.35690630433395302018882610422', '125.19873845009380202016023998546', '125.51901296575479094918076248552', '125.99882654834730836003176262769', '126.68848377157095463205854067641', '127.31648819657151328798669533083', '128.09982175736857791112162829436', '128.679937897402728475373080001680', '128.87287241582804627481479620550', '129.80926692650206309956769519139', '130.64725111002831941572618779505', '131.18618021349355133810001059237', '132.04211937712036863785574394118', '132.22536172188229123813767096731', '133.08765053973519998333436115330', '133.73068480527864285321598737631', '134.38135958349801601445413956283', '135.29358697587593766064799729772', '135.832883806147220087398540555673', '136.07186792412808133973699722639', '136.80246226324134449213643695988', '137.22153503135071630982932842258', '138.12792031329590052328062272799', '138.41428043773870149394856286852', '139.22398218138694905366225743981', '139.53748873063495319630883552765', '140.91204777088377397290357648874', '141.49450063167244446540564275219', '141.727255155047194118986169827974', '142.792606444846733042366289475410', '143.2612655703548629947576849347', '143.74370360448141526727287229581', '144.24847473612318833426334632349', '144.854391630374588199173428298869', '145.29629052836453882019979439652', '146.25514610207297325199652172934', '147.0541685834210100488121810831', '147.50056759597326150270649006660', '147.817178310258743971355265214389', '148.642566682066892031495428079635', '148.89014665789879493493446175453', '149.951149911398619735184335970602', '150.72905798545037987421532747941', '151.43177865309753981322969886303', '151.8147113647436718295247929899', '152.53379315114122517576097378617', '153.13048824592313292404034417074', '153.823863679352949318759004939', '154.34418639566118511392146856762', '154.854058168597796703074368620499', '155.37668347684288048375289197698', '155.83451788032142949735617019211', '156.44007991376556230576212372217', '157.26997086320549565990677523555', '158.08917779292769354905619809937', '158.486041709153483528428792992697', '159.66857970058731141436786791129', '160.01214950669546563709248465877', '160.40530993125000687531507032913', '160.97087235632002975804358918451', '161.767015136920032996278342292532', '162.210492144143770785585979052543', '163.25597140865986851378367073865', '163.41179695711248756154372914921', '164.18557905131775522041796336729', '164.7717198663828493101453858495', '165.1582794528057011152503622526', '165.94982199194448347292479302930', '166.42053334048486947436357005653', '167.24403712855343790802173714492', '167.618672539363379277069816385241', '168.27658306148663014647489692765', '169.40274948028240801980335847485', '170.1149882663023642745704218771', '170.629921921462972489761722035836', '170.89975799538428961597766448751', '171.384025808994372784007718006631', '172.061228976784154633121599049519', '172.75424116098607614364047923872', '173.22389742909955201812955687770', '173.68620439202285039359408178989', '174.70538111142358605215126610682', '175.06177335683548717906621357700', '175.84847086194225440285371148232', '176.13780744169077953404588589174', '177.25864773053355638705662551126', '177.77971582884122466747843270', '178.265323020900210749232473232659', '178.86180274297366175947327981645', '179.70530618309489308647276541700', '179.91251736297599237255292779385', '180.86146309284212861847825299543', '181.34529862656161077164499699129', '181.96598168861875665782389159660', '182.72593665391599024560714096686', '183.05113088654298183829998384222', '183.521982028504097706156994625473', '183.96232435748423333944311316584', '184.537605331201069705138043760375', '185.661331215262473558664936658475', '186.364372413493897236759693347490', '187.16190292702854059067791689306', '187.39077929464870688171968649892', '188.12949240118845851544143215494', '188.58732366859457769457339540790', '189.45917896210959471998103845732', '189.88926368935463069770425140942', '190.25850570530089430094323096810', '190.75910325521988647082800693523', '191.70382900493485788041185454540', '192.06184125440893690428741853779', '192.941995626178438340883395497804', '193.447090817010566207921887859621', '194.032878831799025639233647652375', '194.43627016209446531574342374122', '195.28839588995549697590653290929', '195.87342591510247735267100111292', '196.59014673779812382409343199571', '197.13871410546508091686328296249', '197.87224583536203499118764223129', '198.7328903108555992647429664957', '198.84317652267136296917002466226', '199.66146988328200536443845346992', '199.90806942755857651162173259909'], 'prelabel': '1-1037-1037.112-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.81580775392036, 'root_angle': -0.1687743804767626, 'root_number': '0.862695653365661522560799546266-0.505723451763900681083524646381*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0843871902384', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(240)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.368752279875425778853312469274+0.0660707013098237295012120144670*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.280717667632', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.82387965407', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.93169913897', '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': 4.81580775392036, 'bad_primes': [17, 61], 'central_character': '1037.112', 'conductor': 1037, 'conductor_radical': 1037, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1037/112'], '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': '1-1037-1037.112-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': '1-1037-1037.112-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.81580775392036, 'root_angle': -0.0843871902383813, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.280717667632', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_1037.112', 'Lhash_array': ['dirichlet_L_1037.112'], 'label': '1-1037-1037.112-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1037/112'}