-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '736948564919571364316647195715', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.4682131924621356, -1.6675660126077214], 'a4': [0, 0], 'a5': [0, -3.0204479180442196], 'a6': [0, 0], 'a7': [0, 3.622582728609198], 'a8': [0, 0], 'a9': [-2.5615528128088303, 1.5615528128088303], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.265021750468673, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.4682131924621356, 1.6675660126077214]]]], 'bad_primes': [2, 3], 'central_character': '1536.1535', 'coefficient_field': 'CDF', 'conductor': 1536, 'conductor_radical': 6, 'conjugate': '1652798265692227962810423499411', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.4682131924621356, 1.6675660126077214]], [[1.0, 0], [0, 3.0204479180442196], [-5.0, 0]], [[1.0, 0], [0, -3.622582728609198], [-7.0, 0]], [[1.0, 0], [-3.335132025215443, 0], [11.0, 0]], [[1.0, 0], [1.3243068937239129, 0], [13.0, 0]], [[1.0, 0], [0, -7.123105625617661], [-17.0, 0]], [[1.0, 0], [0, -5.207984795063985], [-19.0, 0]], [[1.0, 0], [-4.416738332472206, 0], [23.0, 0]], [[1.0, 0], [0, -6.412729966684833], [-29.0, 0]], [[1.0, 0], [0, 0.7941556038630077], [-31.0, 0]], [[1.0, 0], [8.10887099100514, 0], [37.0, 0]], [[1.0, 0], [0, -4.0], [-41.0, 0]], [[1.0, 0], [0, 1.4622792553669002], [-43.0, 0]], [[1.0, 0], [-5.656854249492381, 0], [47.0, 0]], [[1.0, 0], [0, 3.7641161792370075], [-53.0, 0]], [[1.0, 0], [-5.733837665506615, 0], [59.0, 0]], [[1.0, 0], [13.406098565900791, 0], [61.0, 0]], [[1.0, 0], [0, -7.080837564912528], [-67.0, 0]], [[1.0, 0], [10.073592581964586, 0], [71.0, 0]], [[1.0, 0], [-10.246211251235321, 0], [73.0, 0]], [[1.0, 0], [0, 4.862698645629372], [-79.0, 0]], [[1.0, 0], [0.4105735144816423, 0], [83.0, 0]], [[1.0, 0], [0, -4.876894374382339], [-89.0, 0]], [[1.0, 0], [-1.1231056256176606, 0], [97.0, 0]], [[1.0, 0], [0, 17.750853377668925], [-101.0, 0]], [[1.0, 0], [0, -2.0342715208831823], [-103.0, 0]], [[1.0, 0], [-16.149807255634585, 0], [107.0, 0]], [[1.0, 0], [-8.10887099100514, 0], [109.0, 0]], [[1.0, 0], [0, 12.492422502470642], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-1536-12.11-c1-0-13', 'leading_term': '1.312099797821039001166016065791707375426699816520582205', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1536/2/c/m/1535/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.312099797821039, 1.2410301231981358, 1.1584650577083468, 1.0636745126558254, 0.9557875608672075, 0.8338513783329111, 0.6969000266823844, 0.5440290746527455, 0.37447218111830116, 0.18767617289266275, -0.016628300773575508, -0.23836289768708535, -0.47704637648683196, -0.7317495683525834, -1.001061784157482, -1.2830697405159859, -1.5753499572001826, -1.874975451758106, -2.1785374027969073, -2.48218224863375, -2.7816644199541223, -3.072414569647053, -3.3496227634152316, -3.608335640379479, -3.843566057739108, -4.050413215317264, -4.22419073499291, -4.360559669038608, -4.455662953857291, -4.50625743551621, -4.509839294296128, -4.464758509295983, -4.370317950702639, -4.226852783089137, -4.035786120223777, -3.799657297387821, -3.5221197222031115, -3.2079060239726545, -2.8627591320203853, -2.493328955731039, -2.1070354860239715, -1.7119003561450694, -1.3163501491386853, -0.9289959753159162, -0.5583950169015659, -0.21280079818304895, 0.10009016291245428, 0.3733869807170648, 0.6012395361282163, 0.7790512178442384, 0.9036605619880145, 0.9734836190030226, 0.9886097653616489, 0.9508449104431008, 0.863697604110906, 0.7323053911294531, 0.563300832829715, 0.3646188586632653, 0.14524944246701543, -0.08505806759271371, -0.31613039533948983, -0.537734939602422, -0.7399611544655783, -0.9136049502505093, -1.0505414485474867, -1.1440710516197585, -1.189224003222477, -1.1830094552980153, -1.1245965195767418, -1.0154168545651474, -0.8591809686593964, -0.6618035333469567, -0.4312364944064219, -0.17721251768765095, 0.08909483634597536, 0.35548400903177235, 0.6091976248228078, 0.837436976135185, 1.0278991892828535, 1.1693155116969198, 1.2519680543320788, 1.2681621457807526, 1.2126322679982444, 1.082861368289977, 0.8792961540027749, 0.6054447041608012, 0.2678472586545682, -0.12408379076714682, -0.5583530828728093, -1.020793212705767, -1.4955842163805644, -1.9658629946805286, -2.4143992057434587, -2.8243101495151213, -3.1797842308638407, -3.4667809161687546, -3.6736748321479613, -3.7918128786866325, -3.815955955697569, -3.7445810824686223, -3.5800251886828205, -3.3284584809726043, -2.9996827744246577, -2.6067582065184043, -2.1654699605974375, -1.6936546291601136, -1.210413246841293, -0.7352444318694951, -0.28713613591034626, 0.11634209216388701, 0.4599029132257646, 0.7313182036043145, 0.9220690465237811, 1.0278332300676098, 1.0487814345772566, 0.989661632448935, 0.8596608949872933, 0.6720443751750969, 0.44358221803897435, 0.19378600548052555, -0.056013482919078185, -0.2837064592650502, -0.46751430491777746, -0.5871167046633278, -0.6247401355983955, -0.5661522634512708, -0.40150977193104204, -0.1260128924020379, 0.25967178398914037, 0.7492480794652179, 1.3309021382669508, 1.9876915146907552, 2.6981994521135433, 3.4374285214493248, 4.177894864592353, 4.890872994259192, 5.547732083033829, 6.121298479120137, 6.587176229643253, 6.924957929674406, 7.119262322046499, 7.160542634562455, 7.045620351416458, 6.777912487581205, 6.367335821084298, 5.829888160768998, 5.186923717011234, 4.464156084373235, 3.6904373260400565, 2.8963743123356345, 2.112853056349578, 1.3695477057214571, 0.6934926771006008, 0.10779396350568116, -0.36945105395926814, -0.7259666171025958, -0.9557998544355589, -1.0594825501171394, -1.0438443124220547, -0.9214874708831113, -0.7099531604064838, -0.4306257662725472, -0.10743815317855995, 0.2345480500305315, 0.5706051480698712, 0.8777600963733726, 1.136090229036506, 1.3298178771691826, 1.448139263558199, 1.485738584028932, 1.4429568732711415, 1.3256060367969693, 1.144440092478102, 0.9143169036325544, 0.6531031942999429, 0.38039218381304624, 0.11611568158062179, -0.1208599137636962, -0.31406214024702905, -0.45057755426095425, -0.5219746292220707, -0.5249201392128235, -0.4614434912291217, -0.33882557053366197, -0.1691127501298137, 0.03171869215790793, 0.2448989583096087, 0.45023215082126444, 0.6276079667932304, 0.7585590750940202, 0.8277598241019898, 0.8243627653289535, 0.7430770447086495, 0.5849067111200709, 0.35748670381902686, 0.07497860369228945, -0.24248426256383096, -0.5697837663657083, -0.8781886748890891, -1.1370372796468597, -1.3156345385985522, -1.3852502186378186, -1.321094185066297, -1.1041422583512779, -0.7226913394136855, -0.173535682447328, 0.5373233526300852, 1.3944951143041164, 2.3735748301843103, 3.4420719076385797, 4.560852462363153, 5.68602403875502, 6.771161050464848, 7.769745706779455, 8.637682758088276, 9.335738516690181, 9.831755989384916, 10.1025087153482, 10.135075552152939, 9.92764612272412, 9.489700323735699, 8.841543160309243, 8.013215857176577, 7.042843180257764, 5.9745126579774075, 4.855811553749075, 3.7351699667227667, 2.659171747470674, 1.6699980068174285, 0.8031605232880192, 0.08566466304340838, -0.46528545708439095, -0.8429612545782514, -1.0511248856419824, -1.1033894094303032, -1.0219705165664799, -0.8359161525798777, -0.5789345738675122, -0.2869677162286251, 0.0043266104520488825, 0.26201447280630785, 0.45808396687668584, 0.5712550263630654, 0.5882809915042165, 0.504657194561019, 0.3246929165726515, 0.06094732741760795, -0.2669256039438166, -0.6338368348086852, -1.0113046895552809, -1.3697309880166748, -1.680745119053993, -1.9194452629663257, -2.0663730314807562, -2.1090765843848676, -2.043146566220466, -1.8726469915689028], 'positive_zeros': ['0.58134991202377865149537193575293', '2.67580577977176634928150530970779', '3.43555195173422361824347182171182', '4.31647237278174974603064563824833', '5.07986422576135130656966121827931', '6.36899953771180856436691709129168', '7.01784185841199525898999161532111', '7.46244497366679321485024384567131', '8.976927615104274652863163995035330', '9.510739108048224811632859566922670'], 'prelabel': '2-1536-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5021453068752977, 'root_angle': -0.08713049381842664, 'root_number': '0.9627696862705388027827489388706805560479672876970928268 - 0.270323012706148063739829563749182129514397989863472316*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.043565246909213325', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58134991202377865149537193575', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.67580577977176634928150530971', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43555195173422361824347182171', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 12.265021750468673, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 1536, 'conductor_radical': 6, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1536/2/c/m/1535/5'], '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': '2-1536-12.11-c1-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1536-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5021453068752977, 'root_angle': -0.04356524690921332, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58134991202377865149537193575', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '736948564919571364316647195715', 'Lhash_array': ['736948564919571364316647195715'], 'label': '2-1536-12.11-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1536/2/c/m/1535/5'}