-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2882583627460098048374307747856', 'a10': [-2.0, 1.0], 'a2': [1.0, 0.0], 'a3': [-1.7071067811865475, -0.2928932188134525], 'a4': [1.0, 0.0], 'a5': [-2.0, 1.0], 'a6': [-1.7071067811865475, -0.2928932188134525], 'a7': [0.12132034355964258, 0.2928932188134525], 'a8': [1.0, 0.0], 'a9': [2.8284271247461903, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.072370503085302, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [1.7071067811865475, 0.2928932188134525]]], [5, [[1.0, 0], [2.0, -1.0]]], [17, [[1.0, 0], [3.0, 2.8284271247461903]]]], 'bad_primes': [2, 3, 5, 17], 'central_character': '510.287', 'coefficient_field': 'CDF', 'conductor': 510, 'conductor_radical': 510, 'conjugate': '3036000580934271735283673199572', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.7071067811865475, 0.2928932188134525]], [[1.0, 0], [2.0, -1.0]], [[1.0, 0], [-0.12132034355964258, -0.2928932188134525], [-4.949747468305833, 4.949747468305833]], [[1.0, 0], [5.121320343559643, 2.1213203435596424], [7.7781745930520225, 7.7781745930520225]], [[1.0, 0], [1.5857864376269049, 1.5857864376269049], [0, 13.0]], [[1.0, 0], [3.0, 2.8284271247461903]], [[1.0, 0], [5.242640687119285, -5.242640687119285], [0, -19.0]], [[1.0, 0], [2.7071067811865475, -1.1213203435596426], [16.263455967290593, -16.263455967290593]], [[1.0, 0], [4.121320343559643, -1.7071067811865475], [20.506096654409877, -20.506096654409877]], [[1.0, 0], [-0.7071067811865476, -1.7071067811865475], [-21.920310216782973, 21.920310216782973]], [[1.0, 0], [-1.2928932188134525, 3.1213203435596424], [-26.16295090390226, -26.16295090390226]], [[1.0, 0], [3.1213203435596424, -7.535533905932738], [-28.991378028648448, -28.991378028648448]], [[1.0, 0], [0, -0.3431457505076198], [-43.0, 0]], [[1.0, 0], [0.1715728752538099, 0.1715728752538099], [0, 47.0]], [[1.0, 0], [0, 6.82842712474619], [-53.0, 0]], [[1.0, 0], [3.585786437626905, -3.585786437626905], [0, -59.0]], [[1.0, 0], [-10.949747468305832, -4.535533905932738], [43.1335136523794, 43.1335136523794]], [[1.0, 0], [1.5857864376269049, 1.5857864376269049], [0, 67.0]], [[1.0, 0], [-10.363961030678928, 4.292893218813452], [50.204581464244875, -50.204581464244875]], [[1.0, 0], [-3.3639610306789276, 8.121320343559642], [-51.61879502661797, -51.61879502661797]], [[1.0, 0], [10.121320343559642, 4.1923881554251174], [55.86143571373726, 55.86143571373726]], [[1.0, 0], [0, -0.3431457505076198], [-83.0, 0]], [[1.0, 0], [0, -14.142135623730951], [-89.0, 0]], [[1.0, 0], [8.535533905932738, 3.5355339059327378], [68.58935777509511, 68.58935777509511]], [[1.0, 0], [0, 5.17157287525381], [-101.0, 0]], [[1.0, 0], [12.65685424949238, -12.65685424949238], [0, -103.0]], [[1.0, 0], [-0.5355339059327376, 1.2928932188134525], [-75.66042558696059, -75.66042558696059]], [[1.0, 0], [5.292893218813452, -12.778174593052023], [-77.07463914933368, -77.07463914933368]], [[1.0, 0], [-11.363961030678928, 4.707106781186548], [79.90306627407988, -79.90306627407988]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 31, 'label': '2-510-255.32-c1-0-31', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/510/2/w/b/287/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-6.630223057204534e-60, -0.2565257587355987, -0.5186745668698064, -0.7910226896390133, -1.0749331315234683, -1.3676991170661574, -1.6622371275284322, -1.9472494968019771, -2.207775643320479, -2.4260870610166974, -2.582906204056122, -2.6589255644835514, -2.6365737645199183, -2.5019311116352534, -2.246649138016015, -1.8696872504792124, -1.3786534930426084, -0.7905329045096655, -0.13161145751154915, 0.5635412364139237, 1.2540823652333473, 1.8958421333628555, 2.4450246802357185, 2.862358589079904, 3.117284654580296, 3.1916964213937473, 3.0827287477283485, 2.8041338468399366, 2.385898381478881, 1.8719353266555223, 1.3159159385663433, 0.775565301257334, 0.3059960865939553, -0.047138942829990295, -0.25377245595397085, -0.30391477275444384, -0.20972666466991177, -0.004645887248471331, 0.2605864789021412, 0.5247089825907306, 0.7247842149855648, 0.8059585893573576, 0.7307236189905784, 0.4861884105330733, 0.08802605058926767, -0.41985590452401694, -0.9702819537868981, -1.482055526248743, -1.8723864551040557, -2.0707530335903175, -2.032024891303777, -1.7465635856142812, -1.245284303627108, -0.5983035190548958, 0.0932529911893711, 0.7115791504492723, 1.1408220055741964, 1.2872536501679033, 1.0976657673789374, 0.5726438871759624, -0.22806433566069634, -1.1897685258608752, -2.156814362069077, -2.9548071443600255, -3.4179891455128026, -3.417508398941015, -2.8858005815024814, -1.8325986128590346, -0.3492047619800212, 1.4005265462848835, 3.2018158449595377, 4.820245025170208, 6.037858097128747, 6.68809371158158, 6.683451507603258, 6.030792036836, 4.8311644357030135, 3.2637304225485324, 1.5562374752859909, -0.05295345703800932, -1.354570008101914, -2.20265090616792, -2.5369568877751116, -2.389374062198426, -1.8731366889882068, -1.157034569826787, -0.4297594154119704, 0.1384394616431883, 0.4290272971890558, 0.39662373584917554, 0.0742894647973618, -0.43825806272016915, -1.0007504941198024, -1.466903114093062, -1.719570392341993, -1.698492470041052, -1.4141783541794937, -0.9445523050084315, -0.4149290204447843, 0.034189525299106266, 0.2839934419148187, 0.27006198737208176, 0.002701190109309845, -0.4306092773453995, -0.8821187660600823, -1.176917619189106, -1.1550613778854446, -0.7129880159166725, 0.1658028821828628, 1.398761425129938, 2.8148570244446116, 4.186370238447732, 5.27544838717304, 5.885165717878462, 5.903329514928711, 5.328542228764135, 4.271879528661116, 2.9331474270946214, 1.5567416636882845, 0.37718140470038153, -0.4328562425689612, -0.7994841506276149, -0.7604317265048649, -0.4504259824611585, -0.06258633101305767, 0.20459507940002847, 0.2012486784973148, -0.13289265378094492, -0.7514919764590094, -1.5135823990892325, -2.2220415760125314, -2.6789939345136533, -2.7437149027258814, -2.377369508367888, -1.6617708959353052, -0.7857238740809096, -0.0009015183045558685, 0.44253396491501007, 0.3644040704350079, -0.29103359696196396, -1.4300113364529443, -2.8219523625936813, -4.1488171074173374, -5.08027106789268, -5.356541589311656, -4.857944874559334, -3.6425580906760935, -1.9409581276057908, -0.10759170203406482, 1.460493723435656, 2.4180595333852906, 2.5557442722105677, 1.852316923777536, 0.4812948288697262, -1.230452995078799, -2.882188528871416, -4.097002276277509, -4.612958859914618, -4.344467023183914, -3.3983240320630377, -2.0407228826561616, -0.6243883920729767, 0.5045303863633279, 1.0949835070905996, 1.0516314907698514, 0.4520317060980492, -0.4831162941761491, -1.4573120963268458, -2.1836572601445203, -2.4641586466142185, -2.2409571683042135, -1.6058713589543292, -0.7667797748761107, 0.018226375930994597, 0.5188937097228099, 0.5998808710963741, 0.2573647091607104, -0.3849006413454288, -1.1178307440367221, -1.7137937016337692, -1.9969008248472206, -1.8950011053126725, -1.4575341762969296, -0.8342787082438711, -0.22248522182568042, 0.1999861636300016, 0.33332282081214426, 0.18653377152386877, -0.13037060887002544, -0.45081617832614373, -0.6183202687481548, -0.5528446574861521, -0.29331376478856075, 0.0005018962310660996, 0.09088012327877823, -0.26081429577520465, -1.2058096744333908, -2.7367845599756433, -4.659137815878252, -6.618371107518367, -8.180595338276646, -8.94628912785646, -8.665638069581547, -7.32103292006129, -5.149951225710804, -2.5976799761069405, -0.20960820116688356, 1.5088676263772756, 2.2260740538260566, 1.8731152522138257, 0.6617935032915455, -0.9750037882813355, -2.5043952541485597, -3.4418722039321326, -3.4844570025788917, -2.5904285891996044, -0.9830863281338473, 0.9214657231858244, 2.6399848001116135, 3.762965894912148, 4.06844929919479, 3.5753718250802407, 2.522147583698389, 1.2794759207593713, 0.2266283762836088, -0.36869203328603967, -0.4287881983727309, -0.0786618766129193, 0.40941687714313596, 0.719607129904014, 0.6089950955377897, -0.0024857275733297947, -0.9990279753914679, -2.1040565091609973, -2.971880378768804, -3.305265195801226, -2.959384675903608, -1.9968456706542432, -0.6745521392879279, 0.6341878190568736, 1.5572097398642386, 1.8421026868475756, 1.4365971663238526, 0.5039011542346707, -0.6323107719438269, -1.595095087193361, -2.0779670103111627, -1.9439074880420135, -1.2666826119302317, -0.3009606104360256, 0.6081963604839126, 1.1453230340615643, 1.1328795256730086, 0.5908183502665865, -0.27291793737683795, -1.1374378872575506, -1.6832460922179213], 'positive_zeros': ['2.27395752973344080958453604511217', '4.10503141518493789751057548895605', '4.62736714202855921332598083702829', '5.52328304204547191191630977328700', '6.73285117076420804052892889609689', '7.46766135492449091093923773862523', '8.526047761184092982543663488264628', '9.870562083984329573685736395239581', '10.83916920615807432149305746024307'], 'prelabel': '2-510-255.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.018011522039778, 'root_angle': 0.9951059662490528, 'root_number': '-0.9998818060860164 + 0.015374454727431269*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.497552983125', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.27395752973344080958453604511', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.10503141518493789751057548896', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.62736714202855921332598083703', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.072370503085302, 'bad_primes': [2, 3, 5, 17], 'central_character': '255.32', 'conductor': 510, 'conductor_radical': 510, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/510/2/w/b/287/1'], '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': '2-510-255.32-c1-0-31', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-510-255.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.018011522039778, 'root_angle': 0.4975529831245264, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.27395752973344080958453604511', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2882583627460098048374307747856', 'Lhash_array': ['2882583627460098048374307747856'], 'label': '2-510-255.32-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/510/2/w/b/287/1'}