-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '129777511624955418314062576925', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-43.840620433565945, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 119.0821974725887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.449', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '1320144848599257144331622557533', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [43.840620433565945, 0], [625.0, 0]], [[1.0, 0], [0, 0], [2401.0, 0]], [[1.0, 0], [0, 0], [14641.0, 0]], [[1.0, 0], [0, -238.0], [-28561.0, 0]], [[1.0, 0], [0, 111.72287142747452], [-83521.0, 0]], [[1.0, 0], [0, 0], [-130321.0, 0]], [[1.0, 0], [0, 0], [-279841.0, 0]], [[1.0, 0], [-1129.956636336103, 0], [707281.0, 0]], [[1.0, 0], [0, 0], [923521.0, 0]], [[1.0, 0], [0, -1680.0], [-1874161.0, 0]], [[1.0, 0], [0, 3166.4241661533597], [-2825761.0, 0]], [[1.0, 0], [0, 0], [-3418801.0, 0]], [[1.0, 0], [0, 0], [-4879681.0, 0]], [[1.0, 0], [-5318.857208085211, 0], [7890481.0, 0]], [[1.0, 0], [0, 0], [12117361.0, 0]], [[1.0, 0], [0, -2640.0], [-13845841.0, 0]], [[1.0, 0], [0, 0], [-20151121.0, 0]], [[1.0, 0], [0, 0], [-25411681.0, 0]], [[1.0, 0], [-10560.0, 0], [28398241.0, 0]], [[1.0, 0], [0, 0], [38950081.0, 0]], [[1.0, 0], [0, 0], [47458321.0, 0]], [[1.0, 0], [0, -15724.640600026443], [-62742241.0, 0]], [[1.0, 0], [18720.0, 0], [88529281.0, 0]], [[1.0, 0], [18895.307406866923, 0], [104060401.0, 0]], [[1.0, 0], [0, 0], [112550881.0, 0]], [[1.0, 0], [0, 0], [131079601.0, 0]], [[1.0, 0], [0, -9362.0], [-141158161.0, 0]], [[1.0, 0], [0, 12669.939305300559], [-163047361.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-1152-24.5-c4-0-6', 'leading_term': '0.353869196116995394929182021014208944923279297537953383', 'load_key': 'CMFs-workshop', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1152/5/h/b/449/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.3538691961169954, 0.17765663046052263, 0.0027732329540800936, -0.16733239664860058, -0.32926550186714715, -0.4797290934483614, -0.6155674020245988, -0.7338085479034947, -0.8317060858407298, -0.9067790471630406, -0.9568500631807393, -0.9800811147100773, -0.9750064151787625, -0.9405619018027066, -0.8761107833272749, -0.78146457639863, -0.6568990582045199, -0.5031645728028071, -0.3214901544297439, -0.11358097454666444, 0.11839131851878824, 0.3718057172343905, 0.6436166793796473, 0.9303867901756844, 1.2283272568260566, 1.5333460790449205, 1.8411035752022207, 2.1470747701745734, 2.446617971543522, 2.735048679615121, 3.0077177984523753, 3.2600929446485343, 3.487841493076761, 3.6869138595775586, 3.853625404695948, 3.9847352551751873, 4.077520285632106, 4.129842485863393, 4.140207963091574, 4.107815895878668, 4.032595869192569, 3.9152321789100957, 3.757173898403387, 3.5606297480390756, 3.3285470973580864, 3.064574754991511, 2.7730095572708655, 2.458727146002604, 2.1270977208131896, 1.7838879526091471, 1.4351506419527857, 1.0871040888037682, 0.7460034970081683, 0.4180070569196862, 0.10903962161530238, -0.17534289413249318, -0.43008511720955306, -0.6507564774523593, -0.8336647960884864, -0.9759559721156166, -1.0756967297443523, -1.1319376735116684, -1.1447542701343778, -1.1152638327753255, -1.0456171165810635, -0.9389637338779461, -0.7993912504804445, -0.6318385160109952, -0.4419844937309934, -0.23611457022675922, -0.020967022239195957, 0.1964370238799066, 0.40897620613588365, 0.6096196620746756, 0.7916210142460327, 0.9487104333318784, 1.0752794367510876, 1.1665530550676022, 1.21874412549181, 1.2291847554271447, 1.1964304391415492, 1.1203329022570017, 1.0020784819961939, 0.8441897112963875, 0.6504887426112222, 0.4260222987453488, 0.17694894583267523, -0.08960938318958413, -0.36574856071099127, -0.6429919950821379, -0.912523776921621, -1.1654392044931723, -1.3930059024656085, -1.5869281737845773, -1.7396068500905881, -1.8443867528280684, -1.8957839596103918, -1.889685396439911, -1.8235138465231442, -1.6963522733555982, -1.5090223841998642, -1.2641135869019355, -0.9659598875465906, -0.6205638012516872, -0.2354679600037782, 0.18042324838968765, 0.6170680390634941, 1.063552044896006, 1.5083865953969782, 1.9398321896892479, 2.3462378363015195, 2.7163861391807713, 3.039833516240946, 3.307234771577146, 3.5106414230004845, 3.6437637196664467, 3.7021871655055536, 3.683535576145821, 3.587574211324143, 3.4162483012346985, 3.173654273111791, 2.8659431236052226, 2.5011576056565854, 2.0890071326203388, 1.640586471147037, 1.168046321124208, 0.6842256911242615, 0.20225750154753133, -0.2648399773025018, -0.7045724708511556, -1.1053661149615681, -1.4569373583803782, -1.750623381428937, -1.9796611391848642, -2.1394046632759527, -2.2274721878203554, -2.243816945367255, -2.190718036741005, -2.0726905308014363, -1.896316802759721, -1.6700039724973523, -1.4036750536582452, -1.1084039668438896, -0.7960068070056798, -0.47860359515134737, -0.16816610859377543, 0.12393179183936831, 0.38734468085750706, 0.6131506501608036, 0.7941956559405039, 0.9253734184447193, 1.0038292940848341, 1.0290791620834538, 1.0030373907483376, 0.9299512696712708, 0.8162427955240071, 0.6702622521930631, 0.5019614964187743, 0.3224981126620813, 0.14378450473419893, -0.02200157452217091, -0.16292669722008618, -0.2678120870306286, -0.32672458295554796, -0.33142852642712567, -0.2757799342194525, -0.15604614930796395, 0.02886330684307724, 0.2772658048209495, 0.5846820593023417, 0.9439233733292199, 1.3452888051427894, 1.776867038296144, 2.224933487627607, 2.6744291983391046, 3.109504558056472, 3.514107894508751, 3.872596806965958, 4.17034868494897, 4.394346379526225, 4.533715452721841, 4.580190843881497, 4.5284931244412405, 4.376597692336451, 4.1258841758157265, 3.781157832290494, 3.350539671622632, 2.845227213672709, 2.2791330012257824, 1.6684130194129636, 1.030901811526927, 0.3854751297880561, -0.24863576113605163, -0.8525516518994198, -1.408447031506463, -1.9002178040926154, -2.3140880188155597, -2.639130623954037, -2.8676803956687094, -2.995621289298542, -3.0225353641692374, -2.951705951890568, -2.7899736529789263, -2.547449815719039, -2.2370981210387924, -1.8742005131593948, -1.4757287329352515, -1.059646904613769, -0.6441738033567918, -0.24703543613683757, 0.11526070424621128, 0.42809895701745143, 0.6793475618400435, 0.8598438584526601, 0.9637513512830829, 0.9887727072431168, 0.936208854653714, 0.8108609623604784, 0.6207789191686034, 0.3768667076900019, 0.09236147365776372, -0.2177911577483673, -0.5376381389430903, -0.850965375075706, -1.1420560218385971, -1.3964264326868099, -1.6015061304745974, -1.7472303492908365, -1.8265173133728605, -1.8356073523812082, -1.7742469950478257, -1.6457080811187528, -1.4566393857200306, -1.2167559308489724, -0.9383787190337951, -0.6358447165342864, -0.3248132047112593, -0.02149980560931371, 0.2581266865406886, 0.4991472725431343, 0.688457549344561, 0.8154575613973419, 0.8726328272510178, 0.8559971986135274, 0.7653741840718374, 0.6045005358136099, 0.3809439433433107, 0.1058352446788056, -0.2065757369936176, -0.5395231981819798, -0.8744619142905, -1.1919053573866694, -1.4723280465472965, -1.6970911274582847, -1.8493483555396402, -1.914889808059221, -1.8828828034773857], 'positive_zeros': ['0.10237640529779271402195796737312', '0.990332650397682746876906820316427', '2.76109493493058694139961458587680', '3.55958149660570249200866395434712', '4.40117607063412088941936224305587', '5.31038513283702210577144103362300', '6.47092876856752099201233419164937', '7.39200500761098460435510144464492', '8.117883939327408123880364887083221', '8.473582296978988089374742020766666'], 'prelabel': '2-1152-24.5-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.912478979250714, 'root_angle': -0.4729566380076518, 'root_number': '-0.98559855965348878087536279295293935430859299804623856409 - 0.1691019787257627481429347680509755569866105044940151880*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.47295663800765186', 'prec': 67}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.10237640529779271402195796737', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.990332650397682746876906820316', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '2.76109493493058694139961458588', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 119.0821974725887, 'bad_primes': [2, 3], 'central_character': '24.5', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/5/h/b/449/2'], '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': '2-1152-24.5-c4-0-6', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-1152-24.5-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.912478979250714, 'root_angle': -0.4729566380076518, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.10237640529779271402195796737', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '129777511624955418314062576925', 'Lhash_array': ['129777511624955418314062576925'], 'factors': ['2-1152-24.5-c4-0-6'], 'label': '2-1152-24.5-c4-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/5/h/b/449/2'}