-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '91210265618195888191904553267', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-2.685543932670793, 2.685543932670793], 'a6': [0, 0], 'a7': [0, 2.1589416510366775], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.198766312851504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.289', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '2925162202315792037220264737492', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.685543932670793, -2.685543932670793], [0, -5.0]], [[1.0, 0], [0, -2.1589416510366775], [-7.0, 0]], [[1.0, 0], [1.7979326519318135, -1.7979326519318135], [0, -11.0]], [[1.0, 0], [1.3837190895587184, 1.3837190895587184], [0, 13.0]], [[1.0, 0], [-0.22477743852204093, 0], [17.0, 0]], [[1.0, 0], [-0.15894165103667743, -0.15894165103667743], [0, 19.0]], [[1.0, 0], [0, 2.8284271247461903], [-23.0, 0]], [[1.0, 0], [1.8571168079246028, 1.8571168079246028], [0, 29.0]], [[1.0, 0], [1.8410583489633225, 0], [31.0, 0]], [[1.0, 0], [-3.669485473709513, 3.669485473709513], [0, -37.0]], [[1.0, 0], [0, 5.881631688014421], [-41.0, 0]], [[1.0, 0], [7.754806954900304, -7.754806954900304], [0, -43.0]], [[1.0, 0], [2.8284271247461903, 0], [47.0, 0]], [[1.0, 0], [-7.513971057416983, 7.513971057416983], [0, -53.0]], [[1.0, 0], [4.0, -4.0], [0, -59.0]], [[1.0, 0], [5.987368775782867, 5.987368775782867], [0, 61.0]], [[1.0, 0], [10.424292428609817, 10.424292428609817], [0, 67.0]], [[1.0, 0], [0, -4.317883302073355], [-71.0, 0]], [[1.0, 0], [0, -5.9747375515657355], [-73.0, 0]], [[1.0, 0], [15.007526508256312, 0], [79.0, 0]], [[1.0, 0], [-10.115815954005168, -10.115815954005168], [0, 83.0]], [[1.0, 0], [0, 1.4284672316984113], [-89.0, 0]], [[1.0, 0], [16.399029980175552, 0], [97.0, 0]], [[1.0, 0], [-0.08189424644664377, 0.08189424644664377], [0, -101.0]], [[1.0, 0], [0, -13.35067225876393], [-103.0, 0]], [[1.0, 0], [-7.277982001790272, 7.277982001790272], [0, -107.0]], [[1.0, 0], [-7.0405733390510985, -7.0405733390510985], [0, 109.0]], [[1.0, 0], [18.848584857219635, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-1152-16.13-c1-0-0', 'leading_term': '0.158906510844015386889024162052159428793439520910405427', '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/1152/2/k/f/289/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.1589065108440154, 0.028880120290725498, -0.09571357661479213, -0.21490715490338302, -0.32856843020203297, -0.4363621910930313, -0.5377245003596204, -0.63185044555138, -0.7176953413183593, -0.7939886983591505, -0.8592598173407534, -0.9118736238907592, -0.9500752793371193, -0.972042115235116, -0.9759414877857249, -0.9599931871296508, -0.9225350412433185, -0.8620903165756547, -0.7774354418678543, -0.6676664798267486, -0.5322626594887403, -0.37114517744108827, -0.18472939521038031, 0.026031481899913157, 0.2596131496447219, 0.5138992069932043, 0.7861741083792583, 1.0731315438984736, 1.3708994346749865, 1.6750823657287677, 1.980821844136157, 2.2828742739266326, 2.575705992009271, 2.853604125543784, 3.110801427465592, 3.3416126427314157, 3.540579374679242, 3.7026198815278626, 3.823179761025333, 3.8983791000417924, 3.925151397940407, 3.9013694383456263, 3.82595330101772, 3.698955887586743, 3.521621690723515, 3.296415069111723, 3.0270149971924543, 2.7182741291201276, 2.3761410336463133, 2.0075455965800146, 1.6202488190711137, 1.2226595259792994, 0.8236217963983694, 0.4321781911880966, 0.05731503058281721, -0.29230298194776194, -0.6086006350461522, -0.8843538025226485, -1.113435618625764, -1.291038053375163, -1.413859991647192, -1.4802535522264482, -1.4903213639375497, -1.4459588333595155, -1.3508370663930611, -1.2103240036816938, -1.0313434433565176, -0.8221738868743634, -0.5921914770097982, -0.35156361492961985, -0.11090205364669935, 0.11911372633513777, 0.3281303395897178, 0.5065176653190655, 0.6457546410595677, 0.7387886105677701, 0.7803533804300907, 0.7672319629499261, 0.698451408191775, 0.5753991347631863, 0.4018527104485166, 0.1839180382555366, -0.07012572514295594, -0.3500725706518242, -0.6441216746480437, -0.9392856897673051, -1.2218623946701361, -1.4779536468112853, -1.6940129203101038, -1.8574006888057917, -1.956925650864957, -1.9833493873846166, -1.929832549144892, -1.7923021245000315, -1.5697217187274222, -1.2642500328728177, -0.8812767646553509, -0.42932983118236984, 0.08014703880124158, 0.6331418783276705, 1.2135372945589438, 1.803673324471513, 2.3849903038601243, 2.938727553833364, 3.446650407407399, 3.891775887763369, 4.259066355942324, 4.536060767500549, 4.713414857701433, 4.785324595555752, 4.749811528174901, 4.608854036164891, 4.368354837415593, 4.037942058033003, 3.630608540309916, 3.1622014530768956, 2.6507813676895555, 2.115876420668985, 1.577662674629201, 1.0561060177264152, 0.5701036614388376, 0.13666432205854476, -0.22983460826876387, -0.5182772082960205, -0.7212951871887988, -0.8355847660227986, -0.8620363982753478, -0.8056679371328984, -0.6753610553993621, -0.4834102035945994, -0.2449026978744439, 0.02304280266384341, 0.3021445900228159, 0.5738920545598727, 0.8205005419933438, 1.0258396773523655, 1.1762881148001536, 1.261470239976419, 1.2748352321862984, 1.2140459145417437, 1.0811536925073728, 0.8825462114159449, 0.628665668647445, 0.33350744626280193, 0.013920293687910704, -0.3112599155939386, -0.6222013883533798, -0.8991435574828734, -1.1234859346985264, -1.2788419043666872, -1.3520010614247784, -1.3337470341916382, -1.2194839544423692, -1.0096336011749687, -0.7097763611932753, -0.3305219962404278, 0.1128898492704334, 0.6012451353010859, 1.1122386814994452, 1.6215441301846891, 2.1040185722864995, 2.5349813019958765, 2.891500700321838, 3.1536211873974223, 3.30546373557314, 3.336138616369325, 3.2404176823441033, 3.0191251834232324, 2.679220329800503, 2.2335608288632267, 1.700353610228192, 1.1023160017504186, 0.46558679187880603, -0.18155900606672182, -0.8101261258228716, -1.3918717995833565, -1.9007568380298894, -2.314296339815728, -2.6147354439359023, -2.789983884043429, -2.8342553116055194, -2.748372825352201, -2.5397200773669057, -2.2218367603468696, -1.8136771450392637, -1.3385695093962329, -0.8229316715053654, -0.2948123735313249, 0.2176609307239878, 0.6878409563243302, 1.092037720612122, 1.4108291017769972, 1.6301285498953755, 1.7419468006728447, 1.7448014557616414, 1.64374827633904, 1.4500298709665773, 1.1803598922220886, 0.8558825732263398, 0.5008671323123752, 0.1412130406092914, -0.19714566141689194, -0.4898417077015653, -0.7155848249822291, -0.8574883519274294, -0.9041297534042897, -0.850277653533514, -0.6972374813981264, -0.4527905325284974, -0.1307258741171743, 0.25001040698154503, 0.6665001255471815, 1.0933021891920034, 1.504078694893291, 1.87329820253254, 2.1779100596034677, 2.3988837340157443, 2.5225137979854537, 2.541404210497945, 2.455064184151002, 2.2700711433668452, 1.9997827248363893, 1.663607846294118, 1.2858748483342972, 0.8943608368332215, 0.5185689404367895, 0.18785775506955343, -0.0704614324928249, -0.23293980687713725, -0.2816019806246871, -0.20524682739422148, -0.0003498499252995371, 0.3284977602832271, 0.768650168055541, 1.2999739402621016, 1.8958951438385503, 2.524869769373556, 3.1521930227663875, 3.7420401704095054, 4.25961518966677, 4.673274633521183, 4.956493568007961, 5.089548364655511, 5.060807165777442, 4.867542095555601, 4.516206388459084, 4.022152769111, 3.4088045690960933, 2.7063259653135416, 1.9498701076165996, 1.1775116321583572, 0.4279912605076959, -0.26158661145556256, -0.8579582008965482, -1.3336665120928508, -1.6686637160921731, -1.8514467089305138], 'positive_zeros': ['0.07195221270101893830270542545874', '1.34075838627652567919648085986199', '3.17334972197940613648439364282337', '4.12931082824143592239418979028507', '4.78919801505605139650791820306800', '5.73333367201342376509700211969412', '7.11037201055097159930185319385631', '7.67089171703012738716026983739971', '8.440003844067960334781880224638914', '9.126359101408692396621965726192679'], 'prelabel': '2-1152-16.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': 0.7733918281059706, 'root_number': '-0.75711511984860209823630756760962525490746412927713980046 + 0.6532814824381882639283215867135935767918805941746347638*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3866959140529853', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.07195221270101893830270542546', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.34075838627652567919648085986', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17334972197940613648439364282', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.198766312851504, 'bad_primes': [2, 3], 'central_character': '16.13', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/2/k/f/289/1'], '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': '2-1152-16.13-c1-0-0', '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': '2-1152-16.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': 0.3866959140529853, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.07195221270101893830270542546', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '91210265618195888191904553267', 'Lhash_array': ['91210265618195888191904553267'], 'label': '2-1152-16.13-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/k/f/289/1'}