-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_136.101', 'a10': [1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [1.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 0.6315813447764407, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [17, [1]]], 'bad_primes': [2, 17], 'central_character': '136.101', 'coeff_info': ['x^2 - 1', -1, '\\\\zeta_{2}'], 'conductor': 136, 'conductor_radical': 34, 'conjugate': 'dirichlet_L_136.101', 'degree': 1, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 0, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1, 0, 1, 0], 'euler_factors': [[0], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [0], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, 1], [1, -1], [1, -1]], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-136-136.101-r0-0-0', 'leading_term': '1.56595980254979054194385538111', '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/136/101', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.565959802549791, 1.7610880786747547, 2.0584338778115616, 2.0702799334468343, 1.6398110291394656, 0.8356510151179538, -0.08953390992986607, -0.7872413526915572, -0.9552053688553671, -0.4902303682844333, 0.4208406346550503, 1.3359932325150412, 1.732133935156094, 1.257950147863756, -0.054099750140643894, -1.7410729762180308, -3.085727233074349, -3.457560430235014, -2.6549151209423814, -1.0551700304742861, 0.5389436671974395, 1.3063560608691602, 0.8597036515910296, -0.5192001060284154, -2.0204399329569283, -2.768366916587674, -2.343574656301797, -1.0407091487216764, 0.3198629318191444, 0.931760997434393, 0.5570108883691284, -0.28025623781694703, -0.622345571778474, 0.25625314870466, 2.2827603533293073, 4.526661023476071, 5.73462760683159, 5.137001263636633, 2.985914105045907, 0.4348460931207651, -1.1906623343036187, -1.2470695379961738, -0.1562305476342498, 0.9611363793345248, 1.1434543539725046, 0.307896851985858, -0.71321480783997, -0.8603098696831161, 0.2599665588922451, 1.979295010682976, 3.016097118352901, 2.4613015522914155, 0.5461693993172819, -1.4376502716525659, -2.05906398721446, -0.8325052898576232, 1.3777911364794295, 2.9798260128629153, 2.847515830512723, 1.1614601455690172, -0.770661765061567, -1.5757668991669334, -0.9047686937380569, 0.33762007258453275, 0.8089912970859672, -0.09572935436235393, -1.7123064545343263, -2.6895447108717554, -2.203870561507552, -0.7534220673875843, 0.19732212144531283, -0.5259052275946617, -2.705900958364512, -4.767830352483818, -4.989953396619904, -2.9136066655120283, 0.23805854245991365, 2.510612510693242, 2.7522592110262947, 1.4383010168486965, 0.10517571945738702, -0.07275717118183601, 0.7184637756851427, 1.246611779772457, 0.5459719303530365, -1.0152946939904326, -1.9533687542066223, -1.0307000022679302, 1.4748232164614405, 3.8116692121657207, 4.164247056685095, 2.216902366683681, -0.5412431185952635, -2.0853509823737575, -1.5873469241689386, -0.06051680659742634, 0.6568667164907025, -0.36772759572429514, -2.318059248611724, -3.441675515155659, -2.7283126964992155, -0.8487224759160594, 0.5395793086967262, 0.4362162626736872, -0.5244960092687851, -0.7470682107143496, 0.6315871276681259, 2.7013051921100524, 3.4861651669812295, 1.8096696172711046, -1.4501664607768943, -3.975173745434827, -3.9928464669319426, -1.804245792536754, 0.5732128548751168, 1.2936928427366892, 0.2967802042446218, -0.8619474628838248, -0.712960724176088, 0.6378826705907311, 1.724994761299489, 1.3838434206659773, 0.10496254925455531, -0.3793676627880065, 1.0760458573574314, 3.6455414921546434, 5.093211204098261, 3.8481457468593314, 0.5884051180682026, -2.2703578183512434, -2.7477180391756852, -1.0432553307475487, 0.8284673152097279, 1.1030650785158145, -0.057086386685907015, -0.9286828111383069, -0.1818563584110539, 1.6522641309180244, 2.7396129826030005, 1.9242604758386324, 0.015105059279187295, -1.0253923995951637, -0.17196583293199907, 1.5123746442103054, 1.9506930799698314, 0.2967056619617634, -2.0053246266406792, -2.542598283723285, -0.36721390076623284, 2.94069616467746, 4.709579671998812, 3.690182729083742, 1.1216167122836862, -0.6662594531014757, -0.5854674332042671, 0.378688674664578, 0.6005968730910072, -0.17542083652076204, -0.5238888592749128, 0.9088549490047588, 3.559269523093527, 5.1712894833099945, 4.0282417375466375, 0.869104679452682, -1.6356316137727405, -1.4394223495348224, 0.8934011335594569, 2.834332905436902, 2.4901797178594065, 0.43175033697247667, -1.1168742974148356, -0.7604374303491194, 0.6373939958869894, 1.0812589807244968, -0.2057703023236176, -1.8758256325818574, -2.0151865905887623, -0.395963668135642, 1.1693292323199058, 0.8502768381743783, -1.0338851755320813, -2.1934107609546167, -0.8262119922977067, 2.292832506125708, 4.440585301516627, 3.7129714728083325, 0.9871437409290151, -1.0326113427424328, -0.6426907986855728, 1.2143458262495714, 2.1967252390052714, 1.2133028834033466, -0.4999766415836759, -0.9899059368634807, 0.08166767308289848, 1.1330299073067418, 0.7361013404403749, -0.4094272532078693, -0.04999907886040503, 2.977709683560622, 7.012888392047034, 8.87557918762387, 6.984377462675647, 2.9582474683491, -0.048409902766299216, -0.4744474859167938, 0.4201286295405061, 0.4113919177431009, -1.0078512436516947, -2.1967518504464354, -1.5561870916644358, 0.3525339415275383, 1.329837993017411, 0.11903413042780772, -2.0209725202606177, -2.6933207713810647, -1.1640979615042932, 0.6963864862602263, 0.5319729711103469, -1.694100850975679, -3.4793344248904376, -2.5150608424164687, 0.6739150043312225, 3.1940517259415704, 2.8629341572180818, 0.45420911414909115, -1.3546919190342939, -1.0116347614879047, 0.41343163428663476, 0.8592195323444156, -0.08775487743387603, -0.7820347529760868, 0.20558184172536775, 1.9940165207031342, 2.1958751141604886, -0.173456704413893, -3.157528258276219, -3.725790484785078, -1.0957467560202325, 2.27846237112516, 3.2701023147681347, 1.3562954405651988, -1.0480815372354375, -1.454103331478982, 0.02413408443859854, 1.1961275449237896, 0.672475879981347, -0.4921129199836358, -0.3396838865182513, 1.283107097538571, 2.320669374715922, 1.0304577479164372, -1.6340524399156477, -2.8271634372790753, -1.0398554861679907, 2.039966037691491, 3.3421527746604816, 1.8743048232856099, -0.21346400779500171, -0.2153456185422982, 1.9446626088035002, 3.6737354244824125, 2.804299679639139, 0.10431461608987146, -1.7324554958135232, -1.2796014697299622, 0.14763140907571667, 0.4171823073536441, -0.6413540065018485, -1.1539202172324012, 0.09029556882197148, 1.655841709823728, 0.9315333034974138, -2.5320253412169405, -5.931628544240474, -5.972132643825436, -2.452126089286731, 1.480438031283556, 2.7180584056170263, 1.3028951272210145, -0.22298958872126307, -0.15561528674988878, 0.5171051358204481, -0.1406358994878164, -2.120302396855281, -3.246231976972945, -1.9515818343416447, 0.5296204772633024, 1.4937642432796319, 0.1058083463145699, -1.4417142881614742, -0.5574894001524016, 2.44984185851068, 4.498960235455122, 3.274590941025572, -0.038592762885030406, -2.1273881754990516, -1.3627617728782264, 0.5353816918060994, 0.871311811245431, -0.6777472515228847, -1.8711366574881612, -0.9427131668419297, 1.102567516180739, 1.8487677058110228, 0.6523848832136645, -0.5437110114490582, 0.11075473886853754, 1.6704933610728125, 1.3236778288649262, -1.9841368527031376, -5.764539327402547, -6.502061621333468, -3.6307092124750584, -0.20236127246548144, 0.5802847210559945, -1.187695476053375, -2.701170025456604, -2.063725800401332, -0.33402959649158004, 0.3499606408332405, -0.17543540510492678, 0.00295386486867939, 1.9290718268817553, 3.832348201997349, 3.0345824223796534, -0.5156119169885088, -3.673430149672592, -3.520329817960332, -0.7173528729776868, 1.3597852864074795, 0.680514132783681, -1.1752664943139135, -1.2673252106717792, 0.8765090376547188, 2.6913361737481667, 1.8840089035371226, -0.6764491754136475, -2.13727979005951, -1.2714158451203228, 0.18774317301538013, 0.11228229768125216, -1.0783377869703135, -1.0847010315557568, 0.8603007106992674, 2.4810644213912765, 1.141424823013809, -2.54262059873432, -4.916146250930748, -3.3812198748023663, 0.5540303237308593, 3.0400141059635066, 2.292081539662844, 0.2639438004010839, -0.22443401623067616, 0.9865162259635024, 1.6632847513469633, 0.5538329346734702, -0.8345854533432859, -0.4372943477055887, 1.277929486033233, 1.7059594924483477, -0.32751894607227366, -2.576598757910327, -1.885754318822541, 1.7661850615489298, 4.893640115050303, 4.489509110413994, 1.4907970385527944, -0.5533412467253328, 0.16507216056919927, 1.844571915561072, 1.843779758178755, 0.24477864208390468, -0.46645643261135983, 1.0094998935308948, 2.871616262864567, 2.5895204388573854, 0.3449992963747534, -1.151639253897664, -0.28816195374039943, 1.2719909344480658, 0.9067621281752203, -1.1625442866761744, -1.774295334307823, 1.1443769906117018, 5.545328148148052, 7.290750732819355, 4.877555868499823, 1.0076174051715874, -0.8197172643602425, -0.24237700101645981, 0.342945562501567, -0.5083066989868553, -1.451431627174554, -0.7175004523925073, 0.8973494048661168, 0.847914595638144, -1.471927306957175, -3.3255395504615466, -1.8338098764409168, 2.162261814779485, 4.742826191360719, 3.5125122368334316, 0.400717347344095, -0.8786995597807847, 0.6093656433114353, 2.258373608195025, 1.6907525401311072, -0.10020846954906185, -0.33218312194439586, 1.6110212140048228, 3.3060371305131793, 2.620408053054147, 0.5875639719595177, -0.164086437859312, 0.7669797195761169, 0.8738461425974928, -1.6763585236420226, -5.052956395386034, -5.670400838136004, -2.75085931541187, 0.4677311017104084, 0.642479159187765, -1.614734262392295, -2.7440606637126788, -0.902972914297646, 1.8205437020172313, 2.3484917651672745, 0.5702499852781624, -0.9159836898668903, -0.58475983279617, 0.13483173600677165, -0.5877965698508238, -1.835647996327542, -0.9577407427595863, 2.4028503070080567, 4.9598191452016565, 3.4803767560835404, -1.0148376676512343, -4.1446972313026444, -3.246750172599186, -0.2493308902004565, 1.1653958597904128, 0.17909944950616313, -0.7596360965068982, 0.15808199527155858, 1.5262066808901815, 0.971701525536972, -1.1460814634520118, -1.9634349703597604, -0.060934236172301766, 2.4096982290461346, 2.5323693264447957, 0.580845902224848, -0.4096822610041011, 1.010436039048926, 2.440037590219188, 0.7633130940341014, -3.397810927401992, -6.000280111549142, -4.461382398913355, -0.7694705550316541, 1.169072542330713, 0.3050560975925869, -0.8937413015327451, -0.33598614229010254, 0.8995029043724343, 0.6063474414233007, -0.9361550354727619, -1.2102565468040574, 0.6811213694165218, 2.2061052547218325, 0.6333240373384885, -2.9117959535868327, -4.349668550619997, -1.722698094990873, 2.1770399776483256, 3.2055579970445036, 0.8947625607949601, -1.3933661031170737, -1.0972530249074999, 0.489881183837807, 0.5994195183448476, -0.9258957896998743, -1.6636033143515092, -0.4841599101421351, 0.5394872274271768, -0.8961747459194787, -3.7030360439425856, -4.5166338371708745, -2.28483709794224, 0.054822151730963865, -0.6169082011527238, -3.3668398502894874, -4.393851685629544, -2.126023052484795, 0.6779248862913327, 0.6666765703592195, -1.6506664333466774, -2.753210810247529, -0.9334489274175243, 1.5763338453552211, 1.891930260135267, 0.34779545723689814, -0.42192311130169163, 0.4557163085705484, 0.9873605076264046, -0.20742817901584376, -1.1072154461859043, 1.2742614666307226, 6.258271125756891, 9.337857994525793, 7.332402683518201, 2.2993493328148813, -0.9823918406178066, -0.654513869222756, 0.7662538928060936, 0.5463346689705497, -0.5901579174640492, -0.18580522360014015, 1.7957026589980831, 2.6504550940677705, 0.9051536009719326, -1.3453672823237073, -1.3389225542088967, 0.2993004883652843, 0.32704722173225337, -2.3746416182890573, -4.818339373797948, -3.7567123192489214, -0.1920237795760424, 1.77587247502165, 0.327271126226013, -1.7991495643406912, -1.1842450376110083, 1.6607426059563837, 3.2249803454884245, 1.9078791966382533, -0.0593660362356409, -0.12988240031352627, 0.9337184605878862, 0.5530735307137921, -1.4676138733546842, -2.43733881726529, -0.8675946848369407, 0.9097097253887426, -0.20597129431231714, -3.4198561601592443, -4.559526158149112, -1.5147927777401509, 2.7182636567337872, 3.6715060393398726, 0.9171578898731771, -1.827771531997781, -1.7785203534505558, -0.21070032590553797, 0.25661706069669876, -0.2936420741939419, 0.29430033816622725, 2.2179310629134545, 2.728900510419869, 0.061608647612310566, -3.4292310157882167, -3.910108723588805, -1.1853062793525098, 0.9153910384639522, -0.33869517257873233, -2.9603143041097035, -3.1467463359095014, -0.5986298079678987, 1.18803877304941, -0.06761996038877897, -2.2897839065411776, -2.123473597953919, 0.32223931546511875, 1.8172539657903544, 0.7099508466377371, -0.9393985847188712, -0.717013791326113, 0.5224545734183212, 0.27351909866575375, -1.2430935047439797, -0.797959724197536, 3.1015859320836494, 7.213101873775131, 7.107956973319663, 2.8384375013881282, -1.0190898913201254, -1.1036137228276963, 0.943661931879601, 1.471489342262701, -0.041931535873963775, -0.8997881810860895, 0.3041347705133767, 1.5606163502793793, 0.7461248000893956, -0.892769624283831, -0.5610761835950224, 1.5916657751047592, 2.246143356250376, -0.26779185746387935, -3.036550384053336, -2.1475238246647748, 1.9122843471759983, 4.647818600575857, 3.3537446503108024, 0.35415496082531145, -0.6035239658770544, 0.550063484380209, 0.7624707243482763, -1.1703428981450452, -2.724032185065049, -1.516217870962146, 0.9989204767485635, 1.5764226746018832, -0.10817575010477923, -1.1536616949043026, 0.016670796043288343, 1.1698026809995523, -0.22312819849624282, -2.6228761196872665, -2.002196509712095, 2.410759671368644, 6.40117431150264, 5.870177284707773, 1.9450006796633748, -0.8117375796237545, -0.37002839769868034, 0.8902085127797266, 0.400187288584416, -0.9343133444284264, -0.8191958892462352, 0.34750754323943456, 0.027183575514942753, -2.03895252775563, -2.607077451122272, 0.594077123453987, 5.0031427949831935, 6.002454647442782, 2.889475637328675], 'positive_zeros': ['1.84328295784507981166774605058', '2.99116446940677859873639032969', '4.364436884900257673752153440121', '6.132983694125622366769591600344', '7.08348898872446162809741343739', '8.66583580329093748214223264764', '9.580925209380395515540201289', '10.25659748416673504034794408536', '12.25011670105187166229263472295', '13.162365431062265257246167860300', '14.14757675383255549272809575764', '14.947593972311764276615303434739', '16.32724646566848456202196144949', '17.309927217566412297723478339090', '18.61377781551928162778894894257', '19.59641076495500690070427874899', '20.29170332121643428566157855807', '21.75914128983445403914986864357', '22.05829635263788718136904356299', '23.72564304014311803863331319866', '25.04316994067640521704661576259', '25.35546175131352008928231632289', '26.36621626418345757090190646875', '27.33023854636295342534610583217', '28.68404081445512164791737876591', '29.70113999369881493774862089352', '30.24179323251327382754513247191', '31.7180093023511137599146648004', '32.33385084035704958637177070025', '33.01823650588163773076016034676', '34.24147547660703945493945476746', '35.53468779359271912711334460507', '36.31629644488062475377098209368', '37.05554370328965527244971586772', '38.15354764280977424281302895285', '38.57016117601710535376135430939', '40.05318987375800220656327234016', '41.09132720380912591300915253431', '41.86179009405806624852723377719', '42.535347158928998876943335958027', '43.75263676799736021479271530836', '44.40764047887884953414127729789', '45.350837270683290232292373217332', '46.28537232036466446839644110647', '47.658150129169266220966560438634', '48.31134022251563722670382753103', '49.0017779826847135525542013520', '49.54180916752879728463053345306', '51.02270528059931366516640404240', '51.76845452863911051121356781276', '52.876354445975810040900825969639', '53.60738811842777187006532509576', '54.33936873203926469975920889616', '55.37543927992920716472021416185', '56.09130404898773429238596382446', '56.96545118748630643952310633966', '58.24279151963753133591297092316', '58.8663968368782044370476241384', '59.8988790648612087982012437089', '60.60681310384516910800685812026', '61.43802173672445451359700378182', '61.88385276111556272922972311069', '63.741427960076432982830760874457', '64.23106876260011167014186401063', '64.80207313475569390419666344351', '65.87967213265757932897236736450', '66.58020452298261213383624861957', '67.67238965204686298258028726347', '68.21870725598568446482279690795', '69.313866211980416628018623433375', '70.3697306731048405378966037571', '71.15470786304556075215878612157', '71.85185937413402299909928152895', '72.46173293563567801933938128056', '73.42048088951726599861070328065', '74.4685578760500306711480379919', '75.47108739746568159376070851408', '76.245636807019264130023633513467', '77.03960608983722327058327325027', '77.58177735227680522350428555204', '78.56045155854822689386720289802', '79.47906164363163561401539108068', '80.580760891576640707435182059372', '80.98167868901384017679185512733', '82.19958678896823058534117681658', '83.08610660731183861826914036049', '83.58284316373280398823288276185', '84.35964761632883729705300620808', '85.10392026577502097469762403728', '86.42897769844673207096441548418', '87.429876956341535470419776505048', '87.875110274965489952051966221154', '88.407886284098714331690019670010', '89.61535493899156365063213256534', '90.32899568686177373124689636015', '91.00575680977139706488061761052', '92.18378253013936238628341875559', '93.02625040639626018335738176990', '93.63461569913645515659090186628', '94.51720266521930219294553392150', '95.44374122929154563103803979765', '95.91410461478828470374944471647', '96.71484670832140591286336854229', '98.15258068150894175456846910289', '98.57105441536336478327145377657', '99.7681849801867466685029975108', '100.22350463940270484661656883243', '100.62416524275964993978556158796', '101.83499615401261330849353334212', '102.89008862263591122091742303336', '103.546931523079206594576653919914', '104.26622940155972925156864313527', '105.23105865175522105203168042659', '106.193716854504164413022902057752', '106.5967988608793283673960798158', '107.38355606473945071004266946699', '108.23136622496222958555007508495', '109.33084666656153167882211930630', '110.37155692012129776947082800021', '110.70698489281433482113365165192', '111.66564286091384292450452199319', '112.273681038777547495134067419415', '113.087279093904908221803465106500', '113.9272863742048605398765462180', '115.17920580308943316505203264843', '115.59393795955274017816693936936', '116.61328256299505361570126492384', '117.021664226891054305284800898642', '118.172048399373181403449249848012', '118.801076524941769681850175296821', '119.52001515809706395594473099424', '120.223852992718918402359771329548', '121.676121935915971481262000308032', '122.263846467441947896448381411131', '122.67813041457712875334780507650', '123.56908349667038707400778554368', '124.20062267332477551433822522521', '125.150989182628714303190971196118', '126.2996236717008136265830845408', '126.78313036531651659378147413057', '127.79116391653152927300520970122', '128.20162720029012370287646909162', '129.5093417155823779116101637669', '129.77494725980487953172331173107', '130.457454422363974213661942561620', '131.81216616085812492033406829244', '132.29230384112227979790061006256', '133.22018457411351224052127940315', '134.15099732238192539136219582929', '134.89450066196104128283367964622', '135.145526896545175159666321171523', '136.04248058286342382918074249361', '137.12015464267189001955143122737', '138.15496113065071150061174221580', '138.78841911997035103158660273569', '139.34353273322102017984945784942', '140.14913314077857419436261075495', '140.94435797966512521176942166999', '141.97822954120258070888826793809', '142.32868583916176338434996315420', '143.18954563756486744951624784220', '144.45354956379603548067873351398', '145.06042822287825080818133271551', '145.70110697016730951857626620009', '146.377504594850087147255185629215', '147.0954713728526033426396187960', '147.87204597945121082460976526523', '148.87868517275341863532394878414', '149.78430445639431751387884635252', '150.51862968575347494434328627095', '151.07678813718317243290581742363', '151.97253704788963595221791194370', '152.374003240762438794847482976442', '153.73535020067066636845728572353', '153.95408771745346136361037124968', '155.21522500693781243646420011565', '155.72872587170085706028075055191', '156.66606046140912644191015040367', '157.57579101879647061636736219729', '158.00071854354198945359443378073', '158.71032988715468900117804240866', '159.265627314912981467452129059102', '160.80083180635895631988762112870', '161.37682588162264564630321002673', '162.01299276937053767615908029238', '162.53609929876919531842975034140', '163.54646673241923211235399684133', '164.31335022191828199144638624183', '164.74393779578621117246442533197', '165.9552178308831556094375075513', '166.60279458769860022773189612865', '167.32676855838429794988520858472', '168.42288960565900494354329266544', '168.79077924999164983894692311390', '169.47294529799751877557986835593', '170.43218361498680557127645525841', '170.91290201739638803485947449078', '171.97798154326917985276530696275', '172.89644842505910901441628454702', '173.80597065165335355096936514896', '174.20778019933555473992850373950', '174.619042139245233983714611432776', '175.6300842860457891724194102389', '176.69090199687770173952232370402', '177.1451499374922745209913298845', '178.19398202751942730426704786748', '178.74106656995588190542298852596', '179.64881384509233542386352055945', '180.42623405872661747671677990091', '181.105404954564882453631649723020', '181.623035292866554988041291030881', '182.27476910714538286172673686520', '183.63862447545314146621656385955', '184.23189880998792040436305405070', '184.99229712460481245688011395363', '185.56982306810012493470436004913', '186.37753722895563175946191214522', '186.96655545962580165954335770399', '187.78792142879035872625071895471', '188.61322714782951867896337298415', '189.73789803234717155557303571165', '190.18401923157643971501003558416', '190.77647329972892561965659688469', '191.74223368253197284406039341448', '192.48252044959369533586069406707', '193.12202893517441883014839871681', '193.72178344603560899725960066643', '194.53716414992458837019440979563', '195.80121862094832015170237413499', '196.32610689464099959268668836477', '196.96195487842357005264638637574', '197.70804019944353198941347749012', '198.13053730986996809307771651768', '199.02126213535898110755961530549'], 'prelabel': '1-136-136.101-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.6315813447764407, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(2)', 'symmetry_type': 'orthogonal', 'types': ['DIR'], 'values': [[1, '1.45715182513166627518814388312']], 'z1': {'__RealLiteral__': 0, 'data': '1.84328295785', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.99116446941', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.3644368849', 'prec': 40}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.6315813447764407, 'bad_primes': [2, 17], 'central_character': '136.101', 'conductor': 136, 'conductor_radical': 34, 'degree': 1, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0], 'euler11': [1, 1], 'euler13': [1, -1], 'euler17': [1, 0], 'euler19': [1, -1], 'euler2': [1, 0], 'euler23': [1, -1], 'euler29': [1, 1], 'euler3': [1, 1], 'euler31': [1, -1], 'euler37': [1, 1], 'euler41': [1, -1], 'euler43': [1, -1], 'euler47': [1, 1], 'euler5': [1, 1], 'euler53': [1, -1], 'euler59': [1, -1], 'euler61': [1, 1], 'euler67': [1, -1], 'euler7': [1, -1], 'euler71': [1, -1], 'euler73': [1, -1], 'euler79': [1, -1], 'euler83': [1, -1], 'euler89': [1, 1], 'euler97': [1, -1], 'euler_factors': [[1, 0], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 0], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, 1], [1, -1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/136/101'], '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': '1-136-136.101-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': '1-136-136.101-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.6315813447764407, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84328295785', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_136.101', 'Lhash_array': ['dirichlet_L_136.101'], 'label': '1-136-136.101-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/136/101'}