Lfunction data - 1-143-143.38-r0-0-0

Formats: - HTML - YAML - JSON - 2023-10-05T01:52:11.796893

• 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_143.38', 'a10': [1.0, 0.0], 'a2': [0.8090169943749475, -0.5877852522924731], 'a3': [0.30901699437494745, 0.9510565162951535], 'a4': [0.30901699437494745, -0.9510565162951535], 'a5': [0.8090169943749475, 0.5877852522924731], 'a6': [0.8090169943749475, 0.5877852522924731], 'a7': [-0.30901699437494745, 0.9510565162951535], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [-0.8090169943749475, 0.5877852522924731], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.38', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.64', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 'a^2', 'a^8', 'a^1', 'a^1', 'a^3', 'a^7', 'a^4', 'a^0', 0, 'a^0', 0, 'a^2', 'a^3', 'a^6', 'a^6', 'a^3', 'a^7', 'a^9', 'a^5', 0, 'a^0', 'a^9', 'a^2', 0, 'a^6', 'a^1', 'a^8', 'a^2', 'a^9', 'a^5', 0, 'a^5', 'a^4', 'a^2', 'a^3', 'a^6', 0, 'a^8', 'a^7', 'a^4', 'a^0', 0, 'a^5', 'a^9', 'a^7', 'a^8', 'a^6', 'a^1', 'a^8', 0, 'a^4', 'a^5', 0, 'a^0', 'a^9', 'a^7', 'a^3', 'a^1', 'a^6', 'a^8', 'a^7', 'a^4', 0, 0, 'a^5', 'a^4', 'a^2', 'a^3', 'a^1', 'a^1', 'a^3', 'a^2', 'a^4', 'a^5', 0, 0, 'a^4', 'a^7', 'a^8', 'a^6', 'a^1', 'a^3', 'a^7', 'a^9', 'a^0', 0, 'a^5', 'a^4', 0, 'a^8', 'a^1', 'a^6', 'a^8', 'a^7', 'a^9', 'a^5', 0, 'a^0'], 'euler_factors': [[1, 'a^9'], [1, 'a^2'], [1, 'a^1'], [1, 'a^3'], [0], [0], [1, 'a^6'], [1, 'a^7'], [1, 'a^0'], [1, 'a^8'], [1, 'a^9'], [1, 'a^3'], [1, 'a^7'], [1, 'a^0'], [1, 'a^7'], [1, 'a^4'], [1, 'a^3'], [1, 'a^6'], [1, 'a^5'], [1, 'a^1'], [1, 'a^3'], [1, 'a^4'], [1, 'a^1'], [1, 'a^5'], [1, 'a^9'], [1, 'a^4']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-143-143.38-r0-0-0', 'leading_term': '1.88622267819497501429577471878+0.254661368823389911396688722289*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/143/38', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.9033361249416842, 2.273510876570063, 2.8613148292795736, 3.1973788722030863, 3.0311150641979747, 2.349861166050029, 1.3545394173365344, 0.38771143573212524, -0.2011261442741753, -0.21510692873181658, 0.2788094109590533, 0.9567084207267228, 1.3837003172340614, 1.2443907924207365, 0.5404991737803604, -0.3685048855083454, -0.9375856097740889, -0.757708412676638, 0.14350121074107525, 1.2153939990646334, 1.6109437095550079, 0.6478067574533329, -1.7375862760701901, -4.824254288224651, -7.378452883527376, -8.263087610520873, -7.06098371014528, -4.3395241198420536, -1.3673720308261377, 0.5808632787158843, 0.9268065881463503, 0.06354200920315367, -0.9752291315741942, -1.2407319078744945, -0.5080820952631934, 0.6061848344715481, 1.131137752023971, 0.4895216648700894, -1.0353352042975277, -2.467812155605244, -2.838215845910716, -1.9025767343963136, -0.3374897419397056, 0.7577165829446435, 0.6897046655841998, -0.3073667118391854, -1.2834998434474583, -1.3771616575785712, -0.5796596764533289, 0.18623608284326865, -0.19702813516262696, -2.0296213281107667, -4.333172916692196, -5.399908250061741, -4.030248602505195, -0.5428936967772295, 3.2653454729829345, 5.2709702954242434, 4.481861143036287, 1.7165342258713197, -1.0195628555778822, -1.9929041361993107, -0.9249084444221886, 0.9820881876456686, 2.128570947969859, 1.7885125082227566, 0.5404399499352235, -0.41999602538282366, -0.4063154346878249, 0.21776710018725165, 0.540513366262525, 0.13259217827930048, -0.41125381499277947, 0.005664638892109803, 1.8306504294665165, 4.172928585382508, 5.330830765829422, 4.199321888776576, 1.3478538930769015, -1.265177888348687, -1.8248754068893218, -0.18240180113159943, 1.973864526318929, 2.5207369179657966, 0.7164438791964095, -2.1399584064530126, -3.8031773137263265, -2.9938418419438313, -0.46033156484126825, 1.7303859360136882, 2.0178370110976744, 0.6472047889070539, -0.697402791898991, -0.5327305710383319, 1.0555824320247822, 2.568920414295611, 2.5745048543345703, 1.0673987924713604, -0.5764783734780408, -0.966908594116157, -0.02060653091803115, 1.0560258278121275, 1.0678706993377922, 0.07016302253046063, -0.7367762396697036, -0.35911043999182035, 0.8135337091952202, 1.3213539855988803, 0.24975233491965143, -1.4715341638958341, -1.5660146975972007, 1.512697284426239, 6.798505752963483, 11.133568640728477, 11.540948469320082, 7.647124092495328, 1.9980221614795197, -2.024332767907774, -2.8188422508676223, -1.434532955364906, -0.11315379270037312, -0.08490663850488528, -0.7371585758783759, -0.7496394986275533, 0.20672895919132356, 1.0633814285577052, 0.6122753335373096, -1.0180057868957375, -2.346026115796681, -2.0652758136833844, -0.4855948223633209, 0.7194677450216513, 0.27780678357090416, -1.2605915642486456, -2.0354142874158994, -0.8886363606789051, 1.225264054140218, 2.02807515628496, 0.23664896114680042, -2.94992974774591, -4.833272079065563, -3.8051648844000647, -0.9556222838581936, 0.9852523628581495, 0.36641406609459376, -1.740614934404991, -2.6576486540658673, -0.8553192480255762, 2.4506953554935125, 4.4733697348502135, 3.577375279984606, 0.7869277348912633, -1.368384122872149, -1.3611492128889529, 0.07653806353510675, 1.0874747774178168, 0.788698616024515, 0.011969418120341907, 0.02681086628709698, 0.8870829893627745, 1.3909894557655114, 0.6816090399270862, -0.4891495703490489, -0.5040033289468226, 1.0534066823113948, 2.428505491963035, 1.245312866025306, -2.8079657631774344, -7.071011015541771, -8.073515660822283, -4.8299802605574085, 0.05915231668293037, 2.7409479166185164, 1.6301166546560149, -1.3608354479446731, -2.995665386437743, -1.9345366922478393, 0.28363875978417763, 1.2597978954207458, 0.3472127294494606, -0.9607872220160611, -1.0370788315529293, -0.033636305164538347, 0.5018321886950816, -0.2747088210173138, -1.287967509277545, -0.7402694846408275, 1.6422189671298937, 3.9978023322688427, 4.1991159019154605, 2.1506470049599185, -0.11675753165169354, -0.6948665114650374, 0.18680383747897622, 0.713929130537733, -0.06303826028161018, -0.8573374362205933, 0.34198532627208766, 3.4908174577265, 5.784876123976716, 4.232778891954588, -1.0402466386601779, -6.411867982488236, -7.9863761509398845, -5.210584141161132, -1.1685562842107786, 0.6513670415341961, -0.36075127099274323, -1.9323827036999102, -1.8135795549497638, -0.1712248461577404, 1.0369111044845538, 0.6118172370941254, -0.5691835899727562, -0.8829623103532167, -0.07956345605775803, 0.5112472427335847, -0.1281901500731286, -1.2255865084205269, -1.171987358837338, 0.2003246973404159, 0.9927637248780445, -0.6103577650998402, -3.7985726982416814, -5.4309119203824885, -3.2886439076095466, 1.2031354099920313, 4.031998808837507, 2.5819916423360887, -1.6840944138763647, -4.77614368844597, -4.262991427793748, -1.4508408301232567, 0.5376611000295577, 0.3495615845531923, -0.46904800198519203, 0.15679630363491046, 2.037777017239152, 2.906680994906737, 1.2714345252590544, -1.6017200883569194, -3.0050709439514334, -1.8228984324604511, 0.3354714371934646, 1.1607491378426782, 0.2747984241606749, -0.6908841202337059, -0.46456594129838746, 0.18553866379367273, -0.3772131732045683, -2.205262430206443, -3.3501210339779144, -2.249207417437292, 0.03724008456097834, 0.8064349452754765, -0.9320057313822342, -2.786766290555451, -1.410396021742698, 3.434954413920647, 7.919901553356242, 7.771042299519739, 2.703353908298324, -3.199825762640747, -5.5710349799258765, -3.82187192601625, -0.9578538685597291, 0.13983194316865827, -0.5070611668746008, -0.9690896071469532, -0.31532976069517377, 0.39782815927986587, 0.002239552976899896, -0.8844251898292937, -0.6329639884908154, 0.9867207937667, 2.129967490633248, 1.1132318218530426, -1.19808969506458, -2.098825491373958, -0.27256394826262964, 2.4153903346855037, 2.9907753075496504, 0.9642066770538308, -0.9865370664921467, -0.2600884171508891, 2.365904824344098, 3.5011277249529456, 1.221041388351252, -2.4326375095359847, -3.6487674407473274, -1.2172626661216295, 2.11224073328127, 2.8682648838625378, 0.7829223575806229, -1.2158269605064875, -0.7142554619689883, 1.405821071715719, 2.3692148656941003, 1.0902807905285292, -0.6038854331866766, -0.4623167447105331, 1.3331282989481255, 2.551495214927912, 1.8420349601918673, 0.31216003188199115, -0.17379861930439294, 0.49961386096674637, 0.8304239590739428, 0.18402679125116805, -0.02856608791499264, 1.5254666913555457, 3.3716814919412936, 1.9939242602433245, -4.018235744071843, -11.283289887129742, -14.201661355415903, -10.495646936307567, -3.5864821181242057, 0.9653164298213803, 0.9719174034806828, -0.99672462934257, -1.4134642803287867, 0.12241148123904108, 1.199788914678737, 0.2519585546470799, -1.4091114274238405, -1.5670401014277444, -0.12023999543075062, 0.948299432993398, 0.4437838322689568, -0.36676888415873554, 0.39793031233515697, 2.4122826000281394, 3.3093244667084805, 1.78542159419952, -0.4844560895395541, -0.8387785924227605, 0.9383774377772919, 2.2886013530800713, 1.2269885197399926, -0.9817945571195564, -1.4591793715318917, 0.3395004204209051, 1.6019800462904885, -0.3191385213570802, -4.216429406010688, -6.08491605634612, -3.9337530347413994, -0.4256743365248915, 0.10965043501226149, -3.207152453307393, -6.753591571277432, -6.637241920496223, -3.025374548389033, 0.4818791780058321, 1.2317760391523385, 0.10251073494317471, -0.4555157640391778, 0.22940708707633772, 0.7409486828210312, 0.17777011981444313, -0.38513909374545685, 0.3256326762526542, 1.5165072981753207, 1.1459449099654424, -1.0451491421095653, -2.6387337698972058, -1.50156884770858, 1.1218057065245652, 1.8288354686504005, -0.4749554959438938, -2.5938332663477537, -0.5858944786325746, 5.175067022501655, 9.77977347485682, 9.036812218916886, 4.044626573405276, -0.30428707417325, -0.8672031464800988, 0.8846935034388326, 1.6542334240877556, 0.6132488889929296, -0.28615588580798285, 0.2477034807013965, 0.7908719005781838, -0.6272157105571059, -3.3340171610273015, -4.447305309617214, -2.535597136196535, 0.4169570504457797, 1.447825200502895, 0.23139583202127156, -0.8934673975519947, -0.32173121961224277, 0.7669260923176667, 0.44376864181411524, -0.9251816449311789, -1.1529656368440124, 0.3123656662001452, 1.0248748253198543, -1.241969576307311, -4.7434669435794055, -4.963785412658067, -0.04209354451557899, 6.248214515715954, 8.16115868876923, 4.266090417943852, -1.1282751456430946, -3.0215042011324473, -1.0163138915450998, 1.266112256175561, 1.1856405423248322, -0.11632646337825128, -0.15018133958217622, 1.2246768614323358, 1.9002890483305435, 0.7821528566225259, -0.6915539063564545, -0.8036402558657376, -0.05651150174112564, -0.16520042097297646, -1.1098137801492491, -0.8630904135364933, 1.4190136825907167, 3.319207066350413, 1.752370929128459, -2.7102082909749816, -5.741086903030717, -4.165896732878267, 0.1348940677389541, 2.4658365780728437, 0.9975506758439243, -1.3404524828403446, -1.0615390459038718, 1.2359482204237018, 1.882521355767326, -0.7175362445428952, -3.792771985871364, -3.797989245021679, -1.0146918601140937, 0.9455562620406636, -0.09998401379257946, -2.309614387957834, -2.6248076253365937, -0.8779481733935817, 0.35049141088004304, -0.4381366446724881, -1.6842200598323411, -1.2549248257304835, 0.40755388475874943, 1.0294456418271443, -0.08431184367265676, -1.0706127544773527, -0.41353420207219416, 0.6605767203517594, 0.10080082626790887, -1.3822100469378733, -0.6710482444732804, 3.175756032591311, 6.336464575812416, 4.036365931556038, -3.330729116156829, -9.669673276723827, -9.558985476544132, -4.062918176917517, 0.9488452769595721, 1.6004229900569769, -0.4607462015554995, -1.4079637648612726, -0.25772677557733326, 0.8704041464540128, 0.5516778099869187, -0.024260093493048994, 0.5631839605037724, 1.392561114217342, 0.575800273003635, -1.4812159435976997, -2.0771261509135326, 0.08988573057919053, 2.7505357402975115, 2.8069849406930016, 0.40093321806003845, -1.3934627281942475, -0.8896554660880192, 0.007476093790402889, -1.0629836631060514, -2.9302799600571836, -2.056775051068729, 2.3352719148927212, 6.324325060441178, 5.741071045835129, 1.4270782465891694, -1.7517438480993681, -0.9869453339566919, 1.2757567995282404, 1.1006097052095913, -1.4861343518482693, -2.7012828574863357, -0.3462215857948052, 3.1233897032757314, 3.8292248462947307, 1.3879095350136859, -1.044640158902023, -1.1571055768630418, -0.0204705457154652, 0.2635393187060682, -0.24022328997884235, 0.033710888711306466, 1.1412086951318843, 1.327971076160408, 0.06061270750888993, -0.5375613015244389, 1.290245829138022, 3.5976481364098643, 2.588426868446368, -1.9916505018873467, -5.359604345255068, -3.049289645132135, 3.29923409057389, 7.424682012311965, 5.703424100104848, 1.0836076923044133, -1.0720620382857498, 0.48817304618511614, 2.3336204240761216, 1.6605659709538259, -0.1923704257172777, -0.40638615241279386, 0.9748916444381094, 1.3667722765611783, -0.24932234083954688, -1.7597633529273338, -1.1597918677229955, 0.3832577409615518, 0.30583544164749493, -1.3797943318153358, -1.9323809319858571, 0.06564437722679396, 2.401529174957986, 2.2113428964354584, 0.019114293961957553, -1.0729709992852707, 0.1010388631513473, 1.2082572860911203, 0.16316153539720651, -1.4574499430268049, -0.7706034103511834, 1.4057827174769741, 0.5539150565647333, -5.535602706675563, -12.656699949321784, -14.172115755386901, -8.61680374134007, -1.32511453178231, 1.8824766250722877, 0.788622523970119, -0.5977610757917604, 0.04835880322757635, 1.1399704092707, 0.6873511800283725, -0.4549049474780102, -0.2642923912258353, 1.0162798104766584, 1.2322995476568432, -0.19376175593530737, -1.2436769374319174, -0.4592164218893223, 0.6906547678810104, 0.18458165863514706, -0.9223881570812928, 0.4320016983950004, 4.459067890235757, 7.063948646652928, 4.805533513944601, -0.0820379267378917, -1.906099918685745, 1.3752638660739076, 5.518976407512605, 5.448074171034737, 1.5321743528125666, -1.5020496815247293, -1.0406526994186522, 0.5795677634313702, 0.20842802671003796, -1.513635791610647, -1.639125266090939, 0.2083446930334528, 1.0668137938045188, -0.8975817576258849, -3.4224324903962624, -3.162795471504091, -0.33447391384044867, 1.6891893804468876, 1.0559409842803562, -0.4491079810657654, -0.5565410269416589, 0.2043790326812398, -0.00606155874525746, -0.8492471780562141, -0.23303121890628864, 1.7860356913912578, 2.082756688218006, -1.100284855662454, -4.582027361483312, -3.6042857501528713, 1.5862119155775123, 5.137398305754615, 2.6337647592058064, -3.2233091685897652, -5.953435726885341, -3.3261166112839184, 0.41937449240706254, 0.5911511189566384, -2.188553392536005, -3.7886307325523587, -2.4631860826925456, -0.44247169601927794, 0.061655509518544975, -0.18921593648358678, 0.4188758711833087, 1.2953039850020875, 0.8076662146503413, -0.4096534832825016, 0.17063445890708737, 2.9131744713792314, 4.613331150863705, 2.6157556840930285, -1.1818018580398466, -2.5809453574392123, -0.7625129415803805, 0.7659839284708281, -0.5335969247762304, -2.40188094476387, -1.1936994069602282, 2.342497322399069, 3.5585340078677783, 0.3435051854833281, -3.6544204162684815, -3.8335383561798677, -0.8179452532335736, 0.6631938544862318], 'positive_zeros': ['2.35893887996558478099649173383', '2.97867548231672152663672141224', '4.557639638626947876015963048870', '5.58425473385700245338895090393', '6.6653256225338118016092549232', '8.94042141425790423504054578283', '9.70481427945259393806950526712', '10.76442034782587981517762021830', '11.675142305110714200529580662770', '13.19838285861419905611523847788', '13.9796666714458545311860303451', '15.203291644527540898314708397381', '15.56406987532350740389740381954', '17.229466198561090311988604620076', '18.61766597263153108968646225930', '19.5263136506946573413251884844', '20.768270068660098383698944656202', '21.45914909563681067343503407608', '22.25004071505372329824537034453', '22.81095985878247945016113593174', '24.51669145561170883530686484285', '25.33725907786765514275419549909', '26.329732580839071912328767641188', '27.55359342875669049627740574432', '28.562241347997928214835600274729', '29.18823812894415596128437728225', '30.49792780956311489622386877299', '31.25508237990067539186538246796', '32.206860361460653975437681645473', '32.91511851029071799666751972973', '33.79423708045202495558885955349', '34.57166858071993958472432124558', '36.3780744819909415238704862963', '37.56201355671236250799233246664', '37.75461419110501944403110123791', '38.69409898299694676423012161386', '39.50709859609664827420573847644', '40.718924911766257874954961065917', '41.31391887120784613991958575936', '42.31795455165428396088622465039', '43.15008332596600660044376601426', '44.48960232973992956229606470712', '45.06025083165897136783414866166', '46.022044641026841629673562359024', '47.276883310949368290069047487950', '48.10933084754669968958684931405', '49.06971342819661470944451253481', '49.35960725566959025521562265224', '50.48134201116415676395736122425', '51.06557664035286969733934904942', '51.99009687112880159060612706167', '53.43325594152839475117366980951', '54.23430528342058431397081734589', '55.268360803356706171755829039100', '56.010556890603958132907140026845', '56.88515588045517346061714790869', '57.42572026636538700758355383059', '58.24194700177055920058818784962', '59.665535576909198920552981648534', '60.25689666879068085456329771952', '60.92039667635999278429157948339', '61.51552965790076350319605784884', '62.75886272175108161700938678881', '64.19574772282792573829895256813', '64.621324832135400655820990742860', '65.6556450201929634993409663322', '66.406991207686778117342228962076', '67.213417346819820046153212834902', '67.776251849769765649227047125983', '68.70902341351383516302281640598', '69.30050035150435678972406540257', '70.54224008146617284480696319195', '71.44545358045311181269987007348', '72.68759304435151455851866878057', '73.23580535361431890756102975494', '73.71609154298055551227227518443', '74.82481513207121529648966887440', '75.88235067156821177677796691920', '76.63126535375775466136027376792', '77.379170026407407030779251404881', '77.70835061104185259288203269025', '79.0565839483989204603542510896', '79.55893662406495835168063871060', '80.42049024949311514999618272566', '81.694858355003122372215574009012', '83.00664729196878604654036875484', '83.2467730251413427068345326102', '84.16762307256538434991319496873', '84.68827365227625705234646739770', '85.45250086267358944745854332381', '86.401098401528285644249250127471', '87.217600179635820256624647028065', '88.24719006358545709657897326420', '88.78612219827452451694528454100', '89.78846998656492574895455556039', '90.729502079292571902922111165243', '91.658297482087672467046835882930', '92.29949766807004365991915589425', '93.30259346634267584680101122740', '93.84612923305804453505006564962', '95.09544485082275113876776722012', '95.42501642924262527808312580111', '96.33345728369854058027777935281', '96.57578262463861128744535766766', '97.6283451462840836097712654980', '99.27436704416006734669925862106', '99.839956933853634652452510169353', '100.6035827623369367560205569795', '101.294586614024597455999548661', '102.21081691684356926114229206493', '102.94655754977682689899068385633', '103.3529280994235191527846803100', '104.60750245520144470956455726587', '105.17132703847424167572969035574', '106.103873299646289535112851747641', '106.82630288634850528909551354550', '107.47034220549473718043477780748', '108.8087876848960392770463179512', '109.08132130864119317318812941809', '110.56638152346031667114689806815', '111.27787869992416667803980692731', '111.79531694169997522398170737941', '112.565537920281053030634868270934', '113.03772633596290288116197501393', '113.92886253074793005884474860171', '114.862256190177668267905369684359', '115.575321806197588821932540814277', '116.28904853615094323807979554304', '117.77874493615474604836948103778', '118.290592971837631644394262762509', '119.22048147995694129640204356490', '119.60239012700034904025340093405', '120.22371209321971122283223666551', '121.5108001811594197686815081866', '122.23251166073488838370183256516', '122.8921920852180591020105132023', '123.542528888811241304655406751252', '124.31733653682222107020151700602', '124.87685822793938905483256010125', '125.939484962934693786745934879136', '127.1114973159844626012084448887', '127.92687455954716634513330343167', '128.715342586630633362555468599096', '129.10790797698678262627774500349', '130.14585139123827043687599324488', '130.97437645496999159470380934539', '131.16449660547809226922360207718', '132.01731476548189129979914954847', '132.94560975200147679596833492714', '134.05214477016541224962920827826', '134.80270968835959406975797631794', '135.4626571873224701545775053775', '136.18532280578211553866211630673', '137.30252002470401963445056233533', '137.79810454051120024873720858218', '138.91454868225297272515755122401', '139.27180475139304830826104457445', '140.23405963699239630402395976051', '140.91954039842623802009298057942', '141.66125557432542959321137531016', '142.208644223675178947312785493497', '142.88398948828753676730077607432', '143.93384098701688053651852472442', '145.23092778944042543958502752832', '145.87041707028949235662010730195', '146.61441325865795559601116577194', '147.45471763130151706787217536313', '147.57364287041816475254545758776', '148.52906989212330570325190155860', '149.36567986496814396700543346494', '150.361024884340142244817546431049', '151.23392191701614497239729301510', '151.28848783899375032398274708258', '152.353166838154827889977769660909', '153.54168455594433486841890135026', '154.187873018234927279624084653659', '154.833257872600785128888822624766', '155.65435016902641703294532081691', '156.71286487921314387209532668238', '157.50690571290193230565066010973', '157.97434424509295051631549932910', '158.42553857081035433946766447388', '159.38855544508858154329373795611', '159.82724148637491121048518508706', '160.8148684553268992791687081300', '161.71970145509351813277374730545', '162.906535098875468544978084608713', '163.37332251412207336049500705700', '164.33437766849492353246544535547', '164.79451916714217408162553825815', '165.5872255705247496387034807985', '166.47000228529670104104724622955', '166.94351105049851191424490623866', '167.80505567132933400374641178032', '168.75278900743396829615951678656', '169.35629529608493814864724475272', '170.02669481617524049462569355744', '170.73188314547790046841271976106', '171.292995553961587908417466005409', '172.8917491329669439632635819223', '173.57102634482002014461609533828', '174.05111389736172310273136569771', '174.857629837350522628582819497006', '175.383495625033471997462970856840', '176.21411810754182008255239577814', '176.97553671143514379981568664687', '177.54314654866797776334852088162', '178.07749122921643767257708748833', '179.36898587585063003945606710709', '179.90487607934267633879914518057', '181.05822762035464664928989096233', '181.74068188851971600159584823490', '182.22816697327138898914869239850', '183.09224064202339473579141758226', '183.64657911317125821927500607061', '184.72278039945123370371506009779', '185.5138770723943308775509999863', '186.15127430258464489260453829544', '186.56023300166544939561379724857', '187.228698605454123397322929888094', '188.041022080838058139006713062830', '188.97515335564334708273488870800', '189.82904268843742571733801980349', '190.888798803394092123253915968564', '191.331210491765547964525398563703', '192.64447247922221938301211789927', '192.8805890789698565523685593568', '193.29002435311342587919369608320', '194.25063084314326305878665373184', '194.65845065982075299516122423771', '195.83376000886489319451249758356', '196.66857411587720738191145840492', '197.110516233131848537065034319546', '197.92287979529276329525401259861', '198.7734122563076742358099470309', '199.78225489344148800490555288722'], 'prelabel': '1-143-143.38-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.08543426013921358, 'root_number': '0.964196527258429889770384438615+0.265188719260046705618715810899*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0427171300696', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.74039779727039754937325407397+0.0847518232927868809741355846987*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.35893887997', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.97867548232', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.55763963863', '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': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.38', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/38'], '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': '1-143-143.38-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': '1-143-143.38-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.04271713006960679, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.35893887997', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_143.38', 'Lhash_array': ['dirichlet_L_143.38'], 'label': '1-143-143.38-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/38'}