Lfunction data - 1-273-273.83-r1-0-0

Formats: - HTML - YAML - JSON - 2023-12-03T14:21:41.332682

• 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_273.83', 'a10': [1.0, 0.0], 'a2': [-7.040766286173228e-31, 1.0], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [2.9010907910729803e-30, -1.0], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [2.9010907910729803e-30, -1.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 29.33792446893263, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [13, [1]]], 'bad_primes': [3, 7, 13], 'central_character': '273.83', 'coeff_info': ['x^4 - 1', '6.12323399573677e-17 + 1.00000000000000*I', '\\\\zeta_{4}'], 'conductor': 273, 'conductor_radical': 273, 'conjugate': 'dirichlet_L_273.125', 'degree': 1, 'dirichlet_coefficients': [1, 'I', 0, -1, '-I', 0, 0, '-I', 0, 1, '-I', 0, 0, 0, 0, 1, -1, 0, 'I', 'I', 0, 1, 1, 0, -1, 0, 0, 0, -1, 0, 'I', 'I', 0, '-I', 0, 0, 'I', -1, 0, -1, '-I', 0, -1, 'I', 0, 'I', 'I', 0, 0, '-I', 0, 0, -1, 0, -1, 0, 0, '-I', 'I', 0, -1, -1, 0, -1, 0, 0, '-I', 1, 0, 0, 'I', 0, '-I', -1, 0, '-I', 0, 0, 1, '-I', 0, 1, '-I', 0, 'I', '-I', 0, -1, 'I', 0, 0, -1, 0, -1, 1, 0, 'I', 0, 0, 1], 'euler_factors': [[1, 0], [0], [1, 'I'], [0], [1, -1], [0], [1, 0], [1, 0], [1, '-I'], [1, 0], [1, 1], [1, '-I'], [1, 0], [1, 0], [1, 0], [1, 0], [1, 1], [1, -1], [1, 0], [1, 'I'], [1, 'I'], [1, 0], [1, 1], [1, 1], [1, 0], [1, -1]], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-273-273.83-r1-0-0', 'leading_term': '0.0238252633624778542734489879596+0.160906775497375043607143607858*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/273/83', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.16266110037514836, -1.0435176582081649, -1.5544597235264774, -1.3925363828527644, -0.357537034002087, 1.467187070777584, 3.6113534428259233, 5.314918396476207, 5.836569359738107, 4.842097797765006, 2.65132390993413, 0.15767016939234385, -1.5948411858056382, -1.9707197960875997, -1.1042823854100514, 0.19129568394718147, 0.9490892773661788, 0.6867655458635482, -0.2772046061725959, -1.07422534904852, -0.9507336622829783, 0.13142887002487671, 1.4295069125517321, 1.9770675475065247, 1.3574570275621654, 0.07147110993112363, -0.8446306605800055, -0.6938309042113875, 0.22459913656140312, 0.7822740953429863, -0.026565345410337237, -2.0870547464118148, -4.003765530564044, -4.052615645157347, -1.5855490020464003, 2.2507055493072543, 5.171791446191716, 5.386368368195381, 2.9437305581018554, -0.31081392100316785, -2.179504680243746, -1.7938930858861655, -0.1535412026321793, 0.8966532164059067, 0.32683311467263365, -1.243753128454625, -2.2405602174247856, -1.663410357461694, -0.0084746883787854, 1.2634203698468478, 1.161574372894194, 0.08577127719651266, -0.6705585465675191, -0.31860962690441497, 0.5705899207142031, 0.6772683835969114, -0.5714931553042608, -2.1893773051202468, -2.4707610692732747, -0.772048024712279, 1.566629045961779, 2.261987819642277, 0.26568868912666394, -3.014674064169213, -4.787055281353157, -3.388917323388677, 0.10631174497905081, 2.791152766832143, 2.5574902381038487, -0.020072221208898202, -2.338342872980714, -2.2833574871800946, -0.14007605507658005, 1.9115585641987698, 2.0721515103691517, 0.5994763486049244, -0.743463417129186, -0.7125440485852619, 0.17176828399768962, 0.4475888996482358, -0.4344572758225268, -1.3941512512862178, -0.9889322714430363, 0.7881186492148788, 2.3118889089765737, 2.08342845640818, 0.5053331742794136, -0.4326198869056112, 0.6220508239916664, 2.690568666416928, 3.3501283472557044, 1.4494468118312578, -1.290046360088686, -1.7526594850868902, 1.3334883879229258, 5.787114893762682, 7.849205188515745, 5.758755839128796, 1.3875198576645649, -1.712756551416307, -1.7494867548649162, -0.050675692649464574, 0.8482807917290975, 0.0527713420047815, -1.0555429962765317, -0.8456949041589962, 0.45839457367078096, 1.0961961320616678, 0.019673898169425344, -1.7304534136423453, -2.2271664293408797, -0.9816295652379778, 0.4673086091135806, 0.461362570046051, -0.6993027415287808, -1.1320364511220604, 0.15786840171903516, 1.7749413596643397, 1.4798414857241018, -0.8404654077482078, -2.418846693138578, -0.3840494660246029, 4.807446634780506, 9.270693124159017, 9.3752761750873, 5.363190009645052, 0.9715343244674953, -0.4929762046481158, 0.7106218483581698, 1.7120197492919922, 0.6597821345283987, -1.2833243755293529, -1.6989218656475593, -0.027099564564858344, 1.7953800414933976, 1.7903302947928332, 0.30904232748606353, -0.5973258374906749, 0.13123192396040723, 1.3007175684803696, 1.1856916581329158, -0.10177914185196207, -0.7758788622796224, 0.08833904591908126, 1.045188823498195, 0.024370164899842523, -2.703004237869907, -4.281512832589077, -2.516691155147869, 1.1545675149974521, 2.829567522956171, 0.4631525686411424, -3.646128468124287, -5.302373251272113, -3.095817749560681, 0.11192038877527044, 0.6052126275089097, -1.9423098818929545, -4.343773621717292, -3.808956008954997, -1.0601127785096085, 0.922557189741888, 0.6274197463243151, -0.504020575097628, -0.3890054197400806, 0.8967986212188724, 1.48158527509291, 0.48670742410835044, -0.6968209832482647, -0.40814593202403393, 0.8022055311193953, 0.7584315384148467, -1.2987567360442718, -3.342422855007345, -2.972297849282073, -0.621728152688946, 0.8022435808297472, -0.30082764412907015, -1.8640564675379685, -0.5901053020398145, 3.568430184041596, 6.62709553295735, 4.9100922255316615, -0.5216572554524015, -4.790480491977233, -4.508764411578343, -1.2076923074303676, 0.9797010303671412, 0.2248586019987548, -1.492182714150944, -1.6062850848977572, -0.3202108243263605, 0.1591668843702745, -0.9984420153955293, -2.0813633113878165, -1.3831268788371747, 0.2516155118767203, 0.5263917741304753, -1.0708460487757794, -2.45003022739406, -1.7461334208098456, 0.11469156623838125, 0.7617060550735459, -0.1714749527645117, -0.44088802125533494, 1.4188618198043463, 3.3271436880233, 1.7902483411001244, -3.294565675855765, -7.496427930947274, -6.490240507206389, -1.1212396684654369, 3.415922581500358, 3.4303332790405396, 0.5289773814275401, -1.0330408850602266, 0.28439147580371366, 2.0149532253754776, 1.5673006025821292, -0.2850089269098266, -0.830069994446919, 0.6128335702398994, 1.8011208866917383, 0.8161861999722471, -1.2581188417959877, -1.9355359235910123, -0.7845210737578637, 0.20668985506681098, -0.2605470219038484, -0.8758646251617852, 0.10987907962728219, 1.8261756130249214, 1.6146574284383932, -1.007256130698581, -2.9285014440813475, -1.195721511508669, 2.735414180659494, 4.261544972391977, 1.3360979714556613, -2.6823009260694204, -3.0041808257635068, 0.6989680916759304, 4.027560248440441, 3.4748974548609293, 0.5993676139040027, -0.45923566844854335, 1.5179232104115477, 3.6137879938388955, 3.0275703685603377, 0.7036850977051947, -0.38758402720024115, 0.5610139453085985, 1.4945244655818781, 0.8632880203940493, -0.1617178292886447, 0.19384834473330603, 1.2758603279869336, 0.8319490026804142, -1.3972962185744429, -2.808110401253581, -1.460594267020322, 0.961094839022983, 1.318737948453388, -0.45372583073591116, -1.039298127095241, 1.4645171705937032, 4.253301534148081, 3.099899931159359, -1.764425917295185, -5.2366944928012495, -3.4562857903646007, 1.3582710668335833, 3.6931348365404864, 1.484570833377765, -1.8779702494881076, -2.41025776464758, -0.37529362784042786, 1.038507460724648, 0.5317894759607484, -0.010580125807819725, 0.9714767048142215, 2.1039166648161913, 1.2836517357601909, -0.8465424698132576, -1.590795937804989, -0.12473564864307203, 1.2651938529525009, 0.5854164495341865, -0.8909564092669191, -0.6295669463741286, 1.1482129857697145, 1.6805890025104144, 0.12488893205618659, -0.4739281868069185, 2.675663314155936, 7.331850238546627, 8.07202882801432, 3.1478165418832815, -2.718127479404293, -3.7493518642167754, 0.07196220147528366, 3.5519174850815642, 3.08058507487109, 0.49971892525167805, -0.5130426047442085, 0.27262032570038386, 0.07583471595385423, -2.111054638280386, -3.812000224686048, -2.7903292718214945, -0.39825880896342747, 0.4361084039662684, -0.606492253448491, -1.1733820086182458, -0.14238391428943498, 0.6808113461883872, -0.3394568198755956, -1.7814365215202868, -1.2879323918304826, 0.42160134788707326, 0.19225749205811926, -2.5916013204888997, -4.145641511204189, -1.13041200629057, 4.1665584931377255, 6.043330206068092, 2.639143966312922, -1.571697820558867, -1.6367527338281318, 1.5815265220967123, 3.137290934251661, 1.001247293346794, -1.5032464994535426, -0.7997009941925011, 1.9529459147509867, 2.891175106347543, 1.0132746330825317, -0.8715035255671644, -0.6283688653111038, 0.35474745325688095, -0.08088005874896254, -1.2920409270798512, -1.106208605543848, 0.3316079649488996, 0.5382793210835777, -1.26773038824706, -2.5577944751635613, -1.2721335577721384, 0.6746165492227713, -0.04980836931698983, -2.996270443181705, -4.113237171588163, -1.6376771181736027, 0.8999638316600359, -0.470668064433546, -4.059452582280674, -4.247172548082309, 0.8243573085071157, 6.279494328772186, 6.592454373163829, 2.4373586107689977, -0.8583465239567953, -0.5192814517871909, 0.966732112632171, 0.5494831730671574, -0.9420192545830879, -0.8665144183266754, 0.6954064246636198, 1.2264166693954934, 0.06082614539626728, -0.4540468220022889, 1.164927432279821, 2.908219845886517, 2.2697106769901216, 0.224872685502437, -0.2103117407953249, 1.2841794673195952, 1.8468326599593474, 0.17460785941991427, -1.078340608243994, 0.43539023981411673, 2.1720129648613953, -0.4329765529289606, -6.890110357410361, -10.838561194318624, -7.701951139804098, -0.6750786983586389, 3.304988438180877, 2.096269968279356, -0.1315049724444968, 0.37640617161643886, 2.1250335142292207, 1.7587819676875902, -0.4116671802813697, -1.200373300643754, 0.21317468410339888, 1.0893314140201686, -0.3656686943189027, -2.1447660972349416, -1.6884643891253404, 0.1030838393608248, 0.47345295536422066, -0.7325018098624436, -1.0482706043457293, 0.261032214429827, 0.8404062891469148, -0.5576440433245577, -1.2099867024802577, 1.6799668232576868, 5.806310278245433, 5.913416525959425, 1.1937462180331424, -2.85026257889996, -1.5414400081777355, 2.644320660665908, 3.6597721959937126, 0.27972171631764275, -2.6515935894718567, -1.4789855923390756, 1.3563013564446604, 1.5259779357151086, -0.7579404631494763, -1.6312302604837758, 0.2672034775860652, 2.029345409047342, 1.2886903940286372, -0.3500508817853641, -0.3554771807592544, 0.6447869374451345, 0.3707309941461986, -0.9059471783764693, -0.7641235336873452, 0.934623727002148, 1.2292737074486104, -1.209536234764089, -3.3548659102196448, -2.0984336320162593, 0.7630411673108942, 1.0080827518527344, -1.3510406258187413, -1.679169765519545, 2.106759488482698, 5.533847908602009, 3.432835012449137, -2.4560227462429247, -5.411365888502246, -2.693167004212553, 1.2311018543220402, 1.4043302133588933, -1.1108864326637156, -1.9168457329315447, -0.09476413520942073, 1.2160084521998595, 0.3064584525629262, -0.7881071779007679, -0.3148108319555269, 0.1096371452697481, -1.457498117781149, -3.468188028896793, -3.0087519184665306, -0.5766305111525613, 0.47131170525033833, -0.8458722635723556, -1.7327728362467798, -0.4562650883292153, 0.5981637939593345, -0.9324182372778302, -2.674328333535179, -0.6342755590994171, 3.879509362111341, 4.727607669046175, -0.5632215140516791, -6.473478004763025, -6.326157350611643, -0.9662953913933028, 2.922781844914455, 1.997894913069312, -0.34963258759928434, -0.23485775413627397, 1.170707728692028, 0.6920697438279644, -1.2035347991182335, -1.424102633760071, 0.3156980878003539, 0.914754285169245, -0.9740326920129415, -2.6835916756814804, -1.8186574939569253, 0.07903893186236106, 0.4154313844712523, -0.12989549417619428, 0.75599232186555, 2.336297539209445, 1.5431706800552818, -1.5194966971858321, -2.7195067987644626, -0.23183012950089354, 1.6967847894904375, -1.4790770881877608, -7.242540626151708, -8.61739672046934, -3.7081494482550146, 1.6833752220142906, 2.211091282367498, -0.16797356297142924, -0.31071489599223845, 2.0716152030740185, 2.693649417931913, -0.014157079954167368, -2.441504819321645, -1.5741606327866775, 0.607491305429651, 0.7677622244181468, -0.5895093838064718, -0.6666315006102542, 0.6310950756789386, 0.8674966714889032, -0.27245059904176516, -0.26760228039370454, 1.5850957951447273, 2.3631755293365098, 0.26783903266907655, -1.8462801275512484, -0.6814661690774452, 1.9130184238777634, 1.5029788226854297, -1.6029134881706038, -2.1281301251268907, 2.0810271521939936, 6.073948363421556, 4.742099816504414, 0.5240853343574936, -0.013268224081705176, 4.2254485049751995, 7.436753266418415, 5.463116579214976, 1.2545163483229358, -0.2775374611426005, 0.793660800688385, 1.0015664809671794, -0.31168762922477256, -0.5933846849902635, 0.7876228435578884, 1.24762812810332, -0.34353111397710795, -1.416201418211397, -0.01803339963373043, 1.6769076308635085, 0.9098596742216101, -0.9175992753458907, -0.5231169777151503, 1.581784463726751, 1.7907971566200986, -0.33855099798170807, -0.9984689060087983, 1.1756192118730735, 1.6004210724882952, -3.6178651775464585, -10.488310725119875, -11.313871080357599, -5.137230137048037, 0.8481490121442951, 1.0698590381279187, -1.8121615756988605, -2.3318148000602736, -0.28659811957592535, 0.5605872505015203, -0.5421769321273303, -0.5315816437000177, 1.6194614099684346, 2.8875522973737144, 1.3317892104321363, -0.6043680180503155, -0.21985242995789783, 1.048401986978349, 0.39182597963110266, -1.4063471110250434, -1.4384920754981398, 0.10698536822913081, 0.301860054705792, -1.0414044066727421, -0.6653215642845123, 2.026165182368553, 2.5012454875633106, -2.16304199276568, -7.419494171068712, -6.611157788507624, -0.5469205548240093, 3.3071288412822146, 1.2574844670512488, -2.0894486861478927, -1.532214178504619, 1.1529030352038547, 1.0380190847653075, -1.783489326210939, -2.7804307652049554, -0.552408415183111, 1.251249557204108, 0.18928939806093642, -1.3318956720887185, -0.619506055316193, 0.841992133516377, 0.41187426252005355, -1.0058790356415406, -0.864276531895822, 0.23249938950008148, -0.3060277597605986, -1.8755261418563083, -1.0885620265446165, 2.148211227925788, 3.4463142925814854, 0.7066139124816909, -2.025427340103614, -0.7443542664669521, 1.792156587258117, 0.1818709952589599, -4.6090786803668795, -5.952871352529334, -1.577446225920558, 2.643231139745443, 1.252728159888106, -3.0195105024870044, -3.9187807689274106, -0.8933846725527677, 1.2276512559048358, 0.29938937957643275, -0.6841985753830644, 0.4434063121183056, 1.5322171676235115, 0.4943590056010876, -0.8816224251499315, -0.3953307031693042, 0.39037799034736737, -0.9815053822022715, -2.983463386933974, -2.2131624718023657, 0.7259275499714232, 1.8648529659146362, 0.3199674434194534, -0.5224367458593825, 0.6391572747897524], 'positive_zeros': ['1.321310702307152130356659560457', '3.45937081918149033217150622572', '4.63803969999198709349943608809', '5.54269628248608801508828876273', '6.53198342878171541275833661373', '7.83015757518690776364432203410', '8.67879826021385943341259351508', '9.36969026470641986659225403767', '10.75781044901782137691608222776', '12.15444585583765830944463380651', '13.15496503508294944517184413481', '13.822311254289219815171801524107', '15.00154285378326264972459518355', '15.96137493573433953343484462595', '16.672794734679533381579087922316', '17.388240118630382632416417671083', '18.5354516714829838071962547813', '19.40161490192325601573450712580', '20.61581082121237451264689421171', '21.560363202167245146901362883405', '22.51745037979409859187800203621', '23.550830297380229706167683411335', '24.31291832360959219782968431928', '24.880400419873621399933691037508', '25.813400827508082578814768997419', '26.98341355427915100220571099918', '27.38252666458423416788570550820', '28.59216179080468050311428446969', '29.27249766650960910632624123837', '30.7343810495777228681960406468', '31.57213006079062901776163011110', '32.20015953914657119118979129522', '33.02057021969185258038367285449', '33.75352361320485732621081729737', '34.87535587277242097372758235370', '35.448595049953408241631553922428', '36.22312693656882187006925244430', '37.086709733223616820532009709', '37.8410346332403976142956652624', '39.4929643293585287868949056826', '39.85894092395915526893076339864', '40.72684609164292483520044426357', '41.56637587477395819306350086364', '42.566334965403682313806933706829', '43.09241610064946210763542430502', '44.03853820335877747247716862379', '44.66633245405739191377224157366', '45.31594689159275999980909278710', '46.46220000788616224356390062233', '47.223341504684103225483593049661', '48.422649501272158010212733285560', '48.85162002758700845394372203991', '50.12803242335579214070691868442', '50.783431061182494188795429670171', '51.356910036470462031124704566880', '52.29291946041965757256354256873', '52.918392989542730244302087503404', '53.58021447542675705146667380348', '54.775154570038714201310770622225', '55.26231946219427603208944562193', '55.99184853814878412949068195714', '57.15932593741873024994471028780', '58.25029640402224912229919213638', '58.788551757744802283446535740715', '59.78119474950602108688572342864', '60.074665738280019348237518760643', '61.194317331428100516534291926278', '61.69437505461836502055502000668', '62.79051178624595182002046374020', '63.38895618429576552190881334564', '63.86004644602117384101458082121', '64.81291359541086419731136749175', '65.99814093431653393774849408827', '66.93670074976491643017459000635', '67.45725938224217549646631739331', '68.38544308949485271570262274513', '68.95565898405098818582165217022', '69.808000781311095532940400548566', '70.82345606074300604983521709862', '71.155047967693761141190103530343', '71.855112715296406212444472232059', '72.70756692590071213652441020580', '73.535423474156918329210239061482', '74.46829865232908632629494678459', '75.263023779342166473545477289965', '76.33355272550157493569718229115', '76.67603229451958854765592302607', '77.93568735561895949000194364820', '78.30324657485092353977991254588', '79.29967685241254511524486284027', '79.624691316764205543811203114497', '80.44426338814187540860078941339', '81.426208595162884383462144550688', '82.1139199259118949829550312636', '82.6682020314126791544636063536', '83.64599336284239585923224591282', '84.59787997975548758677080840945', '85.43707509306162382046014334110', '86.30444336016994204805823138813', '87.10551372092025955582615512971', '87.20142651510302747981829686982', '88.31139290189066419431002640199', '89.08262248722960438452285328693', '89.79879700536336736562661918946', '90.43122126280077016171608563523', '91.27242527356091766417720879122', '91.64778261071147350033349483535', '92.96346519238987836008024975871', '93.74514951178231884023504095993', '94.767221525571978301834627059803', '95.21764676716911568983485009487', '95.641578061188350870676706173410', '96.94567672746960272372131884422', '97.35054528206954706046059711154', '98.15794910773761433616424255617', '98.68465387877743312774256755149', '99.59922613924977565515237359670', '100.03040312945988896049160797321', '101.0044104107046855970765734583', '102.04803620085789488390984602753', '102.669194442799298494149785285580', '103.53808706745271399716731043783', '104.157695627206321337692257067153', '105.13513291416344500469358108086', '105.79715717749475382595013504904', '106.2281535683615738062952119100', '107.11253802332321173471360326302', '107.61953050148913796842265832708', '108.614361839060806682653416504915', '109.05580868486378009888481647328', '110.161389636661520932444918962109', '110.57740820943553248998552735115', '111.52216796646528093807921525845', '112.692515675957279991781011996658', '113.21979379163598236432474068246', '113.859307182732991950334666935675', '114.55397219481706500699537172449', '115.32702084791964875950005026999', '115.75413802573910103948207888220', '116.92180890893202438036232360094', '117.24959579252144911713183889118', '118.15122909062450107992566626653', '118.69293549945713242317308548239', '119.34825584958828088382572348715', '120.65853156420841428788779435908', '121.52942415248923340369690041396', '121.79900446721805068833749074729', '122.75165157874733996154246543736', '123.39923013980118983188478046013', '124.00893745116184139356345324720', '124.97846490731508241516695827932', '125.45206251846621590483853540065', '126.1951944361022563789066749221', '126.775530495972970349536663656185', '127.36427381536169522696415094175', '128.506444159126160108311574398710', '129.17746806754249578064344793212', '130.021133704160344404705155963666', '130.775889673336067103871300358641', '131.46394957176369671496231929002', '132.15385999762115695614400600669', '133.040294456378425599371727239314', '133.54420935020976402347801740648', '134.153566306437770608068529207480', '134.83635966487607755485296352456', '135.49730999125127603864848409529', '136.4669052561267855711015078373', '137.01990578400539525666452792785', '137.66771522507797915151047256692', '138.62170544992514401204802234086', '139.567821419147547533939871435168', '140.17855808336732955199100323124', '140.95125649263493717121539841282', '141.6263830686714097548393374355', '142.30259528778570154896298504089', '142.550195976054356948401188261', '143.840476244966550366868365199898', '144.215152542965608105345110262919', '145.08310404971283196601067016290', '145.491631465900076660247320451003', '146.296015325849527189024887285602', '147.1621774233826684078528681518', '148.17926003571399309468546087741', '148.99778231587625759393853880673', '149.42538053494279898578632996334', '150.11426482228858429768751725773', '150.883561494536039773594482840892', '151.43322289107930645467375849072', '152.48237219633176162984987391462', '153.01006515511301731946986790575', '153.252194691482102858918337192883', '154.22611476182664316166137248487', '155.02234912378615629995089816158', '155.53266493449089897675540704457', '156.75323372497841233442047868851', '157.47390330683815257789609746619', '157.864018443121557865470205546800', '158.74869147231771549770627022112', '159.58490963791987266521769999187', '160.17521319660820153940122962112', '160.79087018408395284878770551953', '161.48807534106224153859145995772', '161.93519256349631463619416395888', '162.84169953650265862163003408419', '163.51332239141637206380645816090', '164.218404514707893623016494628047', '164.873255402687873701601711921440', '165.99462150173424377307982718610', '166.25169959488082343809158410199', '167.65850680156557634285224658054', '167.92942092288766375882334585422', '168.67801590864716987844770508626', '169.21543012810000752668715946174', '169.944934216716376555306672321068', '170.62758684037588689865704910414', '171.38930440543816616039398574580', '171.95674481101343432133247341025', '172.7646434841544159191450674006', '173.29195966330167995055916926105', '173.88523237200256324826172965926', '175.24689545409996278858685402635', '175.74340574130952800246984050275', '176.609923642318678042722707049594', '177.05354945779300766130847415554', '177.59751862208461788186718533450', '178.620173218691202448401276653978', '179.109811215031772103745633607401', '179.75412403013461806643298380766', '180.60052994554665060910194696887', '181.01736266441086002579392309921', '181.65199180343842360163454084581', '182.38599842010371823529116469938', '183.46537884543694856075556653689', '184.16118447481860142882268111575', '184.8551710606728379703116075799', '185.43780171049801850121239722129', '186.31420874892498906564156396737', '186.90495931993665281809793345727', '187.61272945480453923792504911696', '188.20988361352429106367967977190', '188.9750239935343208656908709969', '189.3056229739867950823989848511', '190.11485591254813447083470350808', '190.99718778871380451723532728504', '191.638940711561481636863723171828', '192.201096230311897008175792894775', '193.21458070580630252723595103485', '193.84102815896570766160045355810', '194.77531695055332597026687877218', '195.370749876665440063142713745228', '195.85344367830536822502413061750', '196.650374694303739347201075542182', '197.29205243278720910185188652821', '197.65425737143328068615504049333', '198.67107927831314745231688181004', '199.43299401915248681881042228416', '199.85350644666363654986150480551'], 'prelabel': '1-273-273.83-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 29.33792446893263, 'root_angle': -0.9064164790945007, 'root_number': '-0.957092026489052849592220722565-0.289784148688430089716825558519*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.453208239547', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(4)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.727917631052768959767454215396+0.220395724958364911474398990780*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.32131070231', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.45937081918', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.63803969999', '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': 29.33792446893263, 'bad_primes': [3, 7, 13], 'central_character': '273.83', 'conductor': 273, 'conductor_radical': 273, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/273/83'], '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': '1-273-273.83-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': '1-273-273.83-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 29.33792446893263, 'root_angle': -0.45320823954725037, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32131070231', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_273.83', 'Lhash_array': ['dirichlet_L_273.83'], 'label': '1-273-273.83-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/273/83'}