-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2094589585703328016218449130790', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.5, -0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [-1.2426406871192852, 0.7174389352143008], 'a6': [0.0, 0.0], 'a7': [-1.7426406871192852, 6.7796167617053715], 'a8': [0.0, 0.0], 'a9': [1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.155336882505978, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.5, 0.8660254037844386]]], [7, [[1.0, 0], [1.7426406871192852, -6.7796167617053715]]]], 'bad_primes': [2, 3, 7], 'central_character': '336.241', 'coefficient_field': 'CDF', 'conductor': 336, 'conductor_radical': 42, 'conjugate': '389095826610725102490376410236', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.5, 0.8660254037844386]], [[1.0, 0], [1.2426406871192852, -0.7174389352143008], [12.5, -21.650635094610966]], [[1.0, 0], [1.7426406871192852, -6.7796167617053715]], [[1.0, 0], [-3.0, 5.196152422706632], [-60.5, -104.78907385791707]], [[1.0, 0], [0, 21.3279687498343], [-169.0, 0]], [[1.0, 0], [7.757359312880715, 4.478713487492331], [144.5, 250.28134169370276]], [[1.0, 0], [-6.257359312880715, 3.6126880837078925], [180.5, -312.63517076618234]], [[1.0, 0], [18.727922061357855, 32.437712530461866], [-264.5, 458.12743860196804]], [[1.0, 0], [33.94112549695428, 0], [841.0, 0]], [[1.0, 0], [38.22792206135786, 22.07090109268499], [480.5, 832.2504130368455]], [[1.0, 0], [-13.98528137423857, -24.223217898327892], [-684.5, 1185.5887777808964]], [[1.0, 0], [0, 54.83127996792352], [-1681.0, 0]], [[1.0, 0], [-1.4852813742385702, 0], [1849.0, 0]], [[1.0, 0], [-37.242640687119284, 21.50204862604083], [1104.5, -1913.050116959825]], [[1.0, 0], [-42.72792206135786, 74.00693191211492], [-1404.5, -2432.6653592304883]], [[1.0, 0], [-35.698484809834994, -20.61052981462], [1740.5, 3014.634430573631]], [[1.0, 0], [1.0294372515228594, -0.5943458742805514], [1860.5, -3222.4805274818964]], [[1.0, 0], [-2.198484809834996, 3.8078873903026147], [-2244.5, -3887.5880375883453]], [[1.0, 0], [137.39696961967, 0], [5041.0, 0]], [[1.0, 0], [-68.3528137423857, -39.46351541403474], [2664.5, 4615.049376767273]], [[1.0, 0], [-49.16904755831214, -85.16328853076708], [-3120.5, 5404.864545018681]], [[1.0, 0], [0, 110.40111830144954], [-6889.0, 0]], [[1.0, 0], [18.0, -10.392304845413264], [3960.5, -6859.787223376538]], [[1.0, 0], [0, 10.986650719693815], [-9409.0, 0]], [[1.0, 0], [92.82337649086284, 53.591601404089644], [5100.5, 8834.325144005059]], [[1.0, 0], [91.11017305526642, -52.602482939371455], [5304.5, -9187.66350874911]], [[1.0, 0], [-59.27207793864214, -102.66225045991057], [-5724.5, 9915.124847928038]], [[1.0, 0], [55.52943725152286, -96.17980663534547], [-5940.5, -10289.247822362915]], [[1.0, 0], [-101.39696961966999, 0], [12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-336-7.3-c2-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/336/3/bh/e/241/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6273865095508673, 0.852824183402756, 1.0564539234521517, 1.234150432775281, 1.3804782440878773, 1.4886401049090288, 1.5507017712317126, 1.558082041496782, 1.5022734966860551, 1.3757417109289145, 1.1729360248415968, 0.8913312920527172, 0.5324071452418736, 0.10246099239773707, -0.38685394666614353, -0.918370483564608, -1.4697188768799243, -2.0141691118716607, -2.522023592516015, -2.9625264090283583, -3.3061940422796408, -3.5274088251221163, -3.6070579935141147, -3.534956013628561, -3.311764442868369, -2.950129226007947, -2.4747951458697526, -1.9215328138840282, -1.3348223880398986, -0.7643725123784983, -0.2607002852785749, 0.1298582170058996, 0.3702164003750478, 0.43711557449084637, 0.32462543298652247, 0.04603164144359601, -0.3662952911535473, -0.86325585692476, -1.3835537991945972, -1.8600741022221035, -2.227500188069397, -2.430333325430522, -2.430330480780679, -2.2123456564817725, -1.787663953815053, -1.1941600558840408, -0.49297657199919537, 0.23813445005921485, 0.9141861728040758, 1.453986415765444, 1.7914256677804192, 1.885460223283982, 1.7272713857609485, 1.3433544784796432, 0.7937761927659241, 0.1654843487269299, -0.43872175721378454, -0.914253338994733, -1.1699568054145857, -1.1423067089494698, -0.8063595239595444, -0.1815910625704041, 0.6686071914771309, 1.6440985212254993, 2.6211417990019297, 3.469816788809971, 4.0732558111391395, 4.345755571455973, 4.2468410983364375, 3.7888336211552134, 3.0363923363668537, 2.097734062021634, 1.108597850311516, 0.21128927850755796, -0.46791419577587473, -0.8392763996006235, -0.8644933461485474, -0.5632284860185507, -0.009891276650604078, 0.6790896381639626, 1.3655527209113894, 1.9140712373580215, 2.216332012657358, 2.210998639919817, 1.8952842742466347, 1.3258439753066718, 0.6084962479985506, -0.12163214062099864, -0.7260612697517798, -1.0902272991276591, -1.1468289873338917, -0.8905564517014077, -0.3809906449205986, 0.2673522772348061, 0.9063625761128878, 1.3832692649469867, 1.5716833804340118, 1.3986016206697436, 0.8617521981838132, 0.03335719388914788, -0.9510435627774096, -1.917090350866483, -2.6850204499111614, -3.1055826163274713, -3.0912313709183064, -2.6360359902133728, -1.8197778191710672, -0.7947782873268806, 0.2424920401660463, 1.0897398592095882, 1.5795613171922904, 1.6142131506229136, 1.187058363442293, 0.38583865090467945, -0.623416535292716, -1.6289917414062645, -2.416170428199544, -2.8112564868592953, -2.7176722658350694, -2.1363424595624694, -1.1657751269271797, 0.018457111528818862, 1.2006603219275325, 2.1705432300271226, 2.767455783098763, 2.9136030665170836, 2.628808061600193, 2.0234371420905735, 1.27100192133566, 0.5666141554832147, 0.08081707328985828, -0.0804660199944485, 0.0996174775107462, 0.5459708314558365, 1.111204787002754, 1.6134262290406831, 1.8832927773161554, 1.8090031400837445, 1.368082616649034, 0.6377099975327922, -0.21968774126561505, -0.9929050518250686, -1.4723283430770675, -1.50234695909167, -1.0230116011225983, -0.09030759549145563, 1.1307516319115056, 2.399577292679594, 3.4528709463032143, 4.06479220194856, 4.10013900109851, 3.5475050077636947, 2.5238718155998265, 1.2488233954272485, -0.0060564455912704976, -0.9808330558132194, -1.4886768035463094, -1.4601012857516278, -0.9589088110640346, -0.16556597776148044, 0.6682513278910704, 1.2829542872503703, 1.4765541093216403, 1.1559810002365265, 0.36115070875401595, -0.7445508242842834, -1.9152347292834415, -2.8847412869664217, -3.4343767402800105, -3.448795172267809, -2.9455323677607104, -2.0703717123725864, -1.0595315961125125, -0.17834063173493986, 0.34767360581314355, 0.3912113812535077, -0.04431607702892781, -0.8269473319814807, -1.7325006652329529, -2.505425329897949, -2.927825824795674, -2.877941377139641, -2.362050368008072, -1.5108807742300239, -0.5412866736148431, 0.30640685958067254, 0.8380410821061894, 0.9626248299403031, 0.7202320547175923, 0.27215782741467415, -0.1448560634897101, -0.2882929170706825, 0.01573358075761307, 0.8144603802857314, 2.0040440864803024, 3.3470506115717176, 4.528714340772524, 5.237854677733072, 5.250982735341553, 4.496543760554691, 3.0810282087059786, 1.2686819809148748, -0.5809032542972339, -2.1013788639393574, -3.010976444192023, -3.1820280261173264, -2.669770623962636, -1.6925427792996655, -0.5688271395340915, 0.3714400590384412, 0.8766805704530539, 0.8396759067862813, 0.32155320542783217, -0.47252291205177566, -1.2584598420785649, -1.7599802692852313, -1.7916397265144939, -1.3138931391953128, -0.44418071782780855, 0.579070086504484, 1.4687218708027077, 1.9758785330423971, 1.965440459266694, 1.457461996138923, 0.6216297699171061, -0.2737864494054764, -0.943369711582345, -1.1718470687785985, -0.8806144814469041, -0.1528387564056692, 0.7911683613365768, 1.6615060625368587, 2.1890643705472446, 2.211204538360117, 1.7260798006660396, 0.8979984284274215, 0.010903659641670409, -0.617035692719275, -0.7324132876924347, -0.22898926047194898, 0.8123704982570285, 2.1397738398568182, 3.3991652223542523, 4.236520430631976, 4.403258878700344, 3.8330428724510184, 2.6660896312597937, 1.2125260597363177, -0.13538992582177667, -1.0167134644363123, -1.2072942021058857, -0.6856169095343274, 0.3610546321574203, 1.5924137966628944, 2.6161900934081075, 3.1042079497843242, 2.8884383127684146], 'positive_zeros': ['1.65233983664443142631883754336087', '3.82836960282743377088542992835582', '4.39094462496383554117165315713086', '5.83396232702134959754649287497757', '6.90785231855669327180410414564177', '7.65419972440289389774311525835236', '9.159062715593132092511158498251318', '9.751919295857267957583741724112937', '10.85326984065199690400081492159947', '11.57492397230277680847894361117319'], 'prelabel': '2-336-7.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0257787233216473, 'root_angle': 0.7064058083209576, 'root_number': '-0.6039461471509299 + 0.7970251259160827*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.35320290416', 'prec': 44}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65233983664443142631883754336', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.82836960282743377088542992836', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.39094462496383554117165315713', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.155336882505978, 'bad_primes': [2, 3, 7], 'central_character': '7.3', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/3/bh/e/241/1'], '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': '2-336-7.3-c2-0-10', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-336-7.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0257787233216473, 'root_angle': 0.3532029041604788, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65233983664443142631883754336', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2094589585703328016218449130790', 'Lhash_array': ['2094589585703328016218449130790'], 'label': '2-336-7.3-c2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/3/bh/e/241/1'}