-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1142911533318320222529463940161', 'a10': [0.0, 0.0], 'a2': [-0.9555728057861407, 0.2947551744109042], 'a3': [0.6801727377709194, 1.7330518718298262], 'a4': [0.8262387743159949, -0.5633200580636221], 'a5': [0.0, 0.0], 'a6': [-1.1607805781953429, -1.4555728057861408], 'a7': [0.7818314824680298, 0.6234898018587335], 'a8': [-0.6234898018587335, 0.7818314824680298], 'a9': [-1.8077819654162506, 1.6773765349520995], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9555728057861407, -0.2947551744109042]]], [7, [[1.0, 0], [-0.7818314824680298, -0.6234898018587335]]], [17, [[1.0, 0], [-0.07473009358642425, 0.9972037971811801]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.1495', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '1993854704949051656296302492260', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9555728057861407, -0.2947551744109042]], [[1.0, 0], [-0.6801727377709194, -1.7330518718298262], [-0.7330518718298263, 0.6801727377709194]], [[1.0, 0], [0, 0], [-0.9555728057861407, -0.2947551744109042]], [[1.0, 0], [-0.7818314824680298, -0.6234898018587335]], [[1.0, 0], [-0.43214166466688053, -0.40096886790241915], [0.07473009358642425, 0.9972037971811801]], [[1.0, 0], [-0.42526990641357576, 1.8632292009656188], [-0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [-0.07473009358642425, 0.9972037971811801]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.14571290823472977, -1.9444036320112692], [-0.9888308262251285, 0.14904226617617444]], [[1.0, 0], [0, 0], [-0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [0.7818314824680298, -1.3541718505915235], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.36534102436639504, -0.9308737486442042]], [[1.0, 0], [0, 0], [0.2225209339563144, 0.9749279121818236]], [[1.0, 0], [0, 0], [0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [0, 0], [-0.8262387743159949, 0.5633200580636221]], [[1.0, 0], [1.6340207397322455, -1.1140564768884775], [0.36534102436639504, -0.9308737486442042]], [[1.0, 0], [0, 0], [-0.9555728057861407, 0.2947551744109042]], [[1.0, 0], [0, 0], [-0.36534102436639504, -0.9308737486442042]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.2685648836527178, 0.12933403147014585], [0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [0, 0], [-0.8262387743159949, -0.5633200580636221]], [[1.0, 0], [0.6801727377709194, 1.1780937397424551], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [-0.5356278435360241, 0.4969900095266461], [0.07473009358642425, -0.9972037971811801]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.16259205190913367, -0.41427779188744757], [-0.7330518718298263, 0.6801727377709194]], [[1.0, 0], [0, 0], [-0.9555728057861407, -0.2947551744109042]], [[1.0, 0], [-0.8258856460056492, 0.7663098922688142], [0.07473009358642425, -0.9972037971811801]], [[1.0, 0], [0, 0], [-0.07473009358642425, -0.9972037971811801]], [[1.0, 0], [0, 0], [0.9009688679024191, -0.4338837391175581]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-3332-3332.1495-c0-0-0', 'leading_term': '1.129785126802218170165599435734', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3332/1/cc/c/1495/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.129785126802218, 1.0724855326720892, 1.0220415038179258, 0.9764202621885927, 0.9334227100159495, 0.8908831928925802, 0.846833853531136, 0.7996197545470966, 0.7479657323075309, 0.6910044597632033, 0.6282774408745283, 0.5597190487333772, 0.48563071213751086, 0.40664946638385385, 0.3237129212206774, 0.23802133096344943, 0.15099672705472258, 0.06423879850020137, -0.02052278248812838, -0.10147971098977762, -0.17679992454505314, -0.24468553721011208, -0.3034330430661627, -0.3514946883259096, -0.38753962749896975, -0.4105132353220935, -0.4196927525931966, -0.41473730965169897, -0.3957303038814944, -0.3632121139016932, -0.31820121817924374, -0.26220195293867, -0.19719739456717672, -0.1256261838196909, -0.05034251883808467, 0.025440975845884544, 0.09822725678917157, 0.16432491078960745, 0.21995279295505626, 0.2613571712056205, 0.2849386743784407, 0.2873857530287445, 0.26581083017830587, 0.21788486792123124, 0.14196572867032645, 0.03721548914741781, -0.09629820922490179, -0.25752160170923377, -0.4443595987923275, -0.6536500629787065, -0.8811710583119781, -1.1216837637582564, -1.3690127741060332, -1.6161644000722781, -1.8554823495114197, -2.0788388572914958, -2.2778579718010215, -2.4441663454941716, -2.569665563510684, -2.64681882871818, -2.6689437546868096, -2.6305021501001633, -2.5273770557547826, -2.3571269602517453, -2.1192071072270857, -1.8151481409604473, -1.4486830331905411, -1.025814294588393, -0.5548148890769274, -0.04615801374688444, 0.4876270566934243, 1.0321735858926513, 1.5715685254628615, 2.0887117193516063, 2.565736116038407, 2.9844794483062738, 3.3269955160185773, 3.576091146330967, 3.7158731989448373, 3.732288715045812, 3.613640550298984, 3.351060643169735, 2.9389234908537456, 2.375183456956955, 1.6616212161906148, 0.803986926534731, -0.1879694407343327, -1.3005868610264584, -2.5165036459943337, -3.814988022391873, -5.172383340176778, -6.56265823397033, -7.9580481014205695, -9.329770609900246, -10.648794748473902, -11.886640344251008, -13.016183084051677, -14.012439024895091, -14.853302414416747, -15.520211417975148, -15.998718071542575, -16.27894142069295, -16.355886301296508, -16.229614465988444, -15.90525962750286, -15.39288331123459, -14.707173996235865, -13.866997669886937, -12.89481341029084, -11.815972724059934, -10.657925894954396, -9.449362346497196, -8.219314819937567, -6.996258881485054, -5.807239803238755, -4.677058159772015, -3.627543545185319, -2.6769426929002607, -1.8394440725006367, -1.124855892628495, -0.5384485477986821, -0.0809661380639883, 0.251194980299003, 0.4656493138739546, 0.5735420889746536, 0.5889467156272888, 0.528165707184716, 0.4089648347800889, 0.24977299233798453, 0.06888157466710519, -0.11632294965693786, -0.2900611725648469, -0.4387684864950598, -0.5515836238673214, -0.6206986080261204, -0.6415570389437797, -0.6128945658763209, -0.5366226364689622, -0.4175638280557261, -0.2630539272889794, -0.08243210422901326, 0.11355427207809758, 0.31339966574853945, 0.5055122206173251, 0.6788734456055441, 0.8236524669498108, 0.9317439122837672, 0.9972023695216629, 1.0165516131277457, 0.9889531716324673, 0.9162260225306784, 0.8027168960573643, 0.6550284686930113, 0.4816202384385932, 0.29230371096471824, 0.0976593284725333, -0.09159297414318421, -0.2652348524388557, -0.41416647443911875, -0.5309642863683752, -0.6103473009403131, -0.649524029664169, -0.6483981977773854, -0.6096186914940442, -0.5384674372553309, -0.44258768849769253, -0.3315640457930671, -0.21637399392460308, -0.10873834551736525, -0.0204043085816551, 0.03760042626081677, 0.05570144825561452, 0.02645751656482715, -0.05485350051333199, -0.18977886049865209, -0.376395654823315, -0.6091985514288071, -0.8791839424498464, -1.1741336716661537, -1.4790908302775065, -1.7770094896135487, -2.049550255163596, -2.277984730513084, -2.444164878280732, -2.531508288564493, -2.5259478437350085, -2.416794410364972, -2.19746406718607, -1.866026920577599, -1.4255425498789485, -0.8841572100216244, -0.2549496223001872, 0.44447507132354275, 1.192630478538499, 1.9650077004938173, 2.7351102485592644, 3.4756175330729278, 4.159621360608292, 4.761874636607617, 5.259989305025187, 5.63552166151653, 5.874887576288968, 5.970057704486524, 5.918993119737838, 5.725794493424761, 5.400552333065517, 4.958901154666784, 4.42129599189885, 3.812044506745905, 3.1581413453722265, 2.4879625242754453, 1.8298858848389676, 1.2109085115696592, 0.6553331375329652, 0.18359282388303882, -0.1887233274483808, -0.4515907037797265, -0.600976288476642, -0.6389480985455701, -0.5734596824962178, -0.41782002929070805, -0.18987654212376415, 0.08904525099213785, 0.3953877583500935, 0.7047248542522656, 0.9931674267114055, 1.2387324722995479, 1.422598613394501, 1.5301766224190163, 1.5519333596767264, 1.4839209769003334, 1.3279796026165556, 1.091600122645737, 0.7874530808341335, 0.4326090550061375, 0.04749399826328518, -0.3453610893219972, -0.7227041343956139, -1.0619989296812988, -1.3428302785587485, -1.548193394790439, -1.665589346613507, -1.6878587536006535, -1.6137005163468088, -1.447840302122983, -1.200833829796247, -0.8885115405874999, -0.5310927584295835, -0.1520176618269536, 0.22343691400322124, 0.569677748472565, 0.8623619326273728, 1.0799159751256904, 1.2049144770662734, 1.2252322981501564, 1.1348961940972604, 0.9345786444794226], 'positive_zeros': ['0.901598226761024685228963230807812', '1.76019175476058300336264675459845', '2.30045149430903191123798031707709', '3.50837463558891699031874525459457', '4.35804365274743997184255202044060', '6.15533549906213736285507990164326', '6.56956408363180701341923435469661', '7.13104975852026777013565685220325', '7.896939969046150724403692092551020', '8.596760137954628440600572882078452'], 'prelabel': '2-3332-3332.1495-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.3979591836734694, 'root_number': '-0.80141362186795665978698328953346 - 0.59811053049121596205926635490525*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3979591836734694', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.901598226761024685228963230808', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.76019175476058300336264675460', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.30045149430903191123798031708', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '3332.1495', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/cc/c/1495/2'], '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': '2-3332-3332.1495-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3332-3332.1495-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.3979591836734694, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.901598226761024685228963230808', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1142911533318320222529463940161', 'Lhash_array': ['1142911533318320222529463940161'], 'factors': ['2-3332-3332.1495-c0-0-0'], 'label': '2-3332-3332.1495-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/cc/c/1495/2'}