-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '215443120620529753248532975567', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-10.0, -17.320508075688775], 'a4': [0, 0], 'a5': [37.0, -64.08587988004847], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-78.5, 135.96598839415688], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.87045736668842, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '392.177', 'coefficient_field': 'CDF', 'conductor': 392, 'conductor_radical': 14, 'conjugate': '1653140090389715052131572885444', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [10.0, 17.320508075688775], [-121.5, 210.4441731196186]], [[1.0, 0], [-37.0, 64.08587988004847], [-1562.5, -2706.329386826371]], [[1.0, 0], [0, 0]], [[1.0, 0], [62.0, 107.38715006927039], [-80525.5, 139474.25730488764]], [[1.0, 0], [-478.0, 0], [371293.0, 0]], [[1.0, 0], [-599.0, -1037.4984337337576], [-709928.5, 1229632.2317411618]], [[1.0, 0], [1522.0, -2636.1813291198314], [-1238049.5, -2144364.636285245]], [[1.0, 0], [92.0, -159.34867429633672], [-3218171.5, -5574036.5454701455]], [[1.0, 0], [3282.0, 0], [20511149.0, 0]], [[1.0, 0], [-2864.0, -4960.593512877264], [-14314575.5, 24793572.054780666]], [[1.0, 0], [5163.0, -8942.578319478114], [-34671978.5, -60053628.36093575]], [[1.0, 0], [8886.0, 0], [115856201.0, 0]], [[1.0, 0], [9188.0, 0], [147008443.0, 0]], [[1.0, 0], [11832.0, -20493.625155154958], [-114672503.5, -198618602.2931199]], [[1.0, 0], [5843.0, 10120.37286862495], [-209097746.5, 362167920.6861574]], [[1.0, 0], [8438.0, 14615.044714266187], [-357462149.5, 619142604.7167817]], [[1.0, 0], [-9241.0, 16005.881512743996], [-422298150.5, -731441852.6083683]], [[1.0, 0], [-7766.0, -13451.106571579901], [-675062553.5, 1169242640.9491835]], [[1.0, 0], [31960.0, 0], [1804229351.0, 0]], [[1.0, 0], [-2443.0, -4231.400122890767], [-1036535796.5, 1795332663.4018745]], [[1.0, 0], [22280.0, -38590.09199263459], [-1538528199.5, -2664809010.4114656]], [[1.0, 0], [-67364.0, 0], [3939040643.0, 0]], [[1.0, 0], [35997.0, -62348.63292005687], [-2792029724.5, -4835937339.076535]], [[1.0, 0], [-48866.0, 0], [8587340257.0, 0]], [[1.0, 0], [25803.0, 44692.10698769974], [-5255050250.5, 9102014030.193556]], [[1.0, 0], [90212.0, -156251.76745240355], [-5796370371.5, -10039607982.924889]], [[1.0, 0], [-32850.0, 56897.86902863762], [-7012758653.5, -12146454289.080307]], [[1.0, 0], [-56353.0, -97606.25915892894], [-7693119774.5, 13324874318.146824]], [[1.0, 0], [23502.0, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-392-7.2-c5-0-2', 'leading_term': '0.636375630949063246153957190342016326497811362037373331', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/392/6/i/b/177/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.6363756309490632, 0.42179189286292684, 0.1839546909602744, -0.07444248931134187, -0.35030697133141336, -0.6401856639947572, -0.9403088803450046, -1.2466390094123119, -1.5549238146507345, -1.860754077981531, -2.159625237363107, -2.4470025787346015, -2.7183894417139824, -2.969397785036542, -3.1958203356794797, -3.393703418961738, -3.559419440309258, -3.6897378680289767, -3.781893455910061, -3.833650350548825, -3.8433606567859844, -3.810015991200928, -3.7332905435143178, -3.613574193726035, -3.451994302806279, -3.250424909738227, -3.0114822294984327, -2.738505555647599, -2.435522926612261, -2.107201213909356, -1.7587806292892425, -1.3959940201546985, -1.0249717210999194, -0.6521331448674986, -0.284066717858662, 0.07259981828202877, 0.4113363193793298, 0.7258515797854368, 1.0102359951012032, 1.2591021784378644, 1.4677199730735946, 1.632142199825931, 1.7493174679390386, 1.8171864722504214, 1.8347584028132327, 1.8021644090143816, 1.7206854882252778, 1.592752705208598, 1.4219182851155008, 1.2127968482688305, 0.9709768534969351, 0.7029031693303488, 0.4157325763090374, 0.11716489349347854, -0.18474670971666873, -0.48180183843429186, -0.765870319850586, -1.0291152341563294, -1.2642153027430278, -1.4645800852393938, -1.6245513009920265, -1.7395836584950997, -1.8063988597918257, -1.823106951283699, -1.7892899157580262, -1.7060433331432459, -1.5759730619314904, -1.4031451838368367, -1.1929888779284064, -0.9521534070278663, -0.6883219623548437, -0.4099866711617275, -0.12619057200664796, 0.15375625262900205, 0.42057798210268627, 0.6653424065930311, 0.8797682055571684, 1.0565196375253991, 1.1894780660407218, 1.2739800593795267, 1.3070124947722612, 1.2873561681524166, 1.2156708407841053, 1.0945164127531248, 0.9283069543152528, 0.7231965901208646, 0.4868986470026216, 0.228441961904402, -0.04212928631440923, -0.31410350257241804, -0.576486492243208, -0.8184104537488984, -1.0295529689313532, -1.200550811661113, -1.323392918031379, -1.3917769543993952, -1.4014146085078165, -1.3502720180445649, -1.2387336209919968, -1.0696801196965702, -0.848474128836511, -0.582850337149224, -0.2827105447066518, 0.0401723841630432, 0.37253392584266365, 0.7000693852290528, 1.0079429282830423, 1.2813367874918218, 1.5060209975054166, 1.668922427432592, 1.758671060915766, 1.7661015032986425, 1.6846886037028108, 1.5108978708212224, 1.244434000464594, 0.8883742492685316, 0.44917747570458516, -0.06343571307673683, -0.6367312903355872, -1.2553330456499048, -1.901706043363188, -2.5567367543475026, -3.2003899103366527, -3.8124183946512558, -4.373099596609976, -4.863969773413601, -5.268527200177129, -5.5728753199136944, -5.766278755770961, -5.841607890842528, -5.795651676528513, -5.629283267008061, -5.347468815070505, -4.959116081338287, -4.47676614884399, -3.9161382181737165, -3.2955438929234773, -2.635193259512659, -1.9564201417193263, -1.280857917901769, -0.6296000165388719, -0.022380493024662003, 0.5231901627091092, 0.9923006654141293, 1.373496061442034, 1.659091173288969, 1.8454212270191142, 1.932917565927723, 1.9260040965973995, 1.8328182203019416, 1.6647681048926128, 1.43594586982501, 1.1624232161517571, 0.8614618848978639, 0.5506757641791699, 0.2471842391004379, -0.03320268719985732, -0.27672797046108405, -0.4723231999705111, -0.612104541919916, -0.6917035482239577, -0.7104152355149294, -0.6711546800311256, -0.5802228374782454, -0.4468919286442762, -0.28283005546182327, -0.10139325321423068, 0.08317950753741356, 0.25662718273746, 0.4055384870451361, 0.5181883045970973, 0.5852931330036799, 0.6006432286512263, 0.5615746030251119, 0.46925155183000294, 0.32873965130887906, 0.14885970072791682, -0.05817558204353498, -0.2773287583736009, -0.4914842351328461, -0.6823394704853352, -0.8313974146126626, -0.9210101316013227, -0.9354193339791372, -0.861738074245224, -0.6908192374803079, -0.4179607783895713, -0.043404705480353405, 0.4274036545738679, 0.9838180062619696, 1.6102638756047751, 2.286776753895433, 2.9897864530861065, 3.6931150762208906, 4.369143879140346, 4.990094179836921, 5.52935995218948, 5.962825293023192, 6.270098896997494, 6.43560016215027, 6.4494375441941685, 6.308029055189161, 6.014426955015775, 5.5783231395206725, 5.0157277752532545, 4.34833055052174, 3.6025706258611034, 2.808457076484333, 1.9981954586789705, 1.2046873146283261, 0.45997729363639994, -0.206273385634665, -0.7682084793996543, -1.2050188918709268, -1.5019394335411038, -1.6509461439310846, -1.6511152894412633, -1.508622621635858, -1.236380388322185, -0.8533289193161488, -0.3834183061975826, 0.14566728073811414, 0.7039757141481398, 1.2608656489418457, 1.7866133083199924, 2.253960585399108, 2.6395203514264103, 2.924962192570017, 3.097913495498513, 3.1525262716712974, 3.089678530190148, 2.9167993748798158, 2.647328179555489, 2.2998389864411606, 1.8968804783847688, 1.4635983690783745, 1.0262198483509986, 0.6104880217898394, 0.2401375542295746, -0.06449929084846098, -0.28767427915220417, -0.419122697615582, -0.4546272672879598, -0.396212705828457, -0.2519590280143671, -0.03544444660007365, 0.23514892442439084, 0.5382128009717762, 0.8501026079837248, 1.1466548318643373, 1.4047387834711798, 1.6037468978010438, 1.726930710087132, 1.7624983836332047, 1.7044036688083262, 1.5527746617393163, 1.3139526335559928], 'positive_zeros': ['0.16995465515635073577894450080293', '2.17455745708859994782932089885659', '3.33674395205035168783289064063329', '4.52794224933280397978147364900552', '5.49035294308262908639791900610273', '6.42987583563835415425886580191291', '7.30518112164259140487893381265123', '8.814920390660059116567004800770977', '9.742208080224699266486639568271446', '10.40915354379092878042248877332335'], 'prelabel': '2-392-7.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.929089315090883, 'root_angle': -0.2929874272254411, 'root_number': '0.6054643436493673635071294605077551469423497523567868621 - 0.7958724323465669471984178169629224157856347934855379281*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.14649371361272054', 'prec': 67}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.16995465515635073577894450080', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.17455745708859994782932089886', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33674395205035168783289064063', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 62.87045736668842, 'bad_primes': [2, 7], 'central_character': '7.2', 'conductor': 392, 'conductor_radical': 14, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/392/6/i/b/177/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-392-7.2-c5-0-2', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-392-7.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.929089315090883, 'root_angle': -0.14649371361272054, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.16995465515635073577894450080', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '215443120620529753248532975567', 'Lhash_array': ['215443120620529753248532975567'], 'label': '2-392-7.2-c5-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/392/6/i/b/177/1'}