-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '299417607625216116254265530642', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.7071067811865476, -0.7071067811865476], 'a4': [0, 0], 'a5': [-2.099893082641794, -0.7684068202932247], 'a6': [0, 0], 'a7': [-0.011728464688048097, -0.011728464688048097], 'a8': [0, 0], 'a9': [0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.0193554789367, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [2.099893082641794, 0.7684068202932247]]], [23, [[1.0, 0], [0.0541507190788387, -4.795525800120696]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '1380.1333', 'coefficient_field': 'CDF', 'conductor': 1380, 'conductor_radical': 690, 'conjugate': '1422069240013241233161020691657', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [2.099893082641794, 0.7684068202932247]], [[1.0, 0], [0.011728464688048097, 0.011728464688048097], [0, 7.0]], [[1.0, 0], [0, 1.727695800827426], [-11.0, 0]], [[1.0, 0], [2.3721866424697815, 2.3721866424697815], [0, 13.0]], [[1.0, 0], [-1.6658289514034152, -1.6658289514034152], [0, 17.0]], [[1.0, 0], [6.733668272018409, 0], [19.0, 0]], [[1.0, 0], [0.0541507190788387, -4.795525800120696]], [[1.0, 0], [0, -0.8944818131937846], [-29.0, 0]], [[1.0, 0], [-6.900639624831721, 0], [31.0, 0]], [[1.0, 0], [0.057519890872000004, 0.057519890872000004], [0, 37.0]], [[1.0, 0], [-0.27879426343993047, 0], [41.0, 0]], [[1.0, 0], [-4.318870763139055, 4.318870763139055], [0, -43.0]], [[1.0, 0], [7.614503956912382, -7.614503956912382], [0, -47.0]], [[1.0, 0], [9.646147800592425, -9.646147800592425], [0, -53.0]], [[1.0, 0], [0, -15.137067764997331], [-59.0, 0]], [[1.0, 0], [0, -5.916923447126914], [-61.0, 0]], [[1.0, 0], [1.9906006280440651, 1.9906006280440651], [0, 67.0]], [[1.0, 0], [-12.648773099279648, 0], [71.0, 0]], [[1.0, 0], [-7.554735469029549, -7.554735469029549], [0, 73.0]], [[1.0, 0], [-3.9152646470776946, 0], [79.0, 0]], [[1.0, 0], [12.296104940665543, -12.296104940665543], [0, -83.0]], [[1.0, 0], [6.611338054351849, 0], [89.0, 0]], [[1.0, 0], [-9.80226527213783, -9.80226527213783], [0, 97.0]], [[1.0, 0], [-8.420526272671887, 0], [101.0, 0]], [[1.0, 0], [11.357672710970256, -11.357672710970256], [0, -103.0]], [[1.0, 0], [7.9466319120557, 7.9466319120557], [0, 107.0]], [[1.0, 0], [-10.30029197639912, 0], [109.0, 0]], [[1.0, 0], [-6.536079670120245, 6.536079670120245], [0, -113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-1380-115.68-c1-0-0', 'leading_term': '0.481333373634778971592968003834914836326971021888442297', '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/1380/2/t/a/1333/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.48133337363477896, 0.3760852412658516, 0.26163591022526866, 0.1377853168458016, 0.004311241848917391, -0.13896509002431603, -0.2921125100928071, -0.4550261267586097, -0.62736932547145, -0.808523928196794, -0.9975502303253194, -1.1931580709314824, -1.3936896663292504, -1.5971146406323804, -1.8010374881814613, -2.002717558914297, -2.199101528590235, -2.386868169466709, -2.5624850529515784, -2.7222765841435304, -2.862502488407796, -2.979445548673569, -3.069507040567671, -3.129307945918125, -3.1557936609307577, -3.146339572094342, -3.098854569707442, -3.0118793247087443, -2.884675987193427, -2.7173058910051795, -2.510691882265086, -2.266662041888767, -1.9879718507514343, -1.6783022547276962, -1.342231624213788, -0.985180262688012, -0.6133268897629645, -0.23349738894936578, 0.1469729534475059, 0.5204015116908504, 0.8789414873449073, 1.2147820116266652, 1.5203601082808227, 1.788578635456818, 2.0130236588293364, 2.188174219691702, 2.309597185089953, 2.374119831257469, 2.3799730388715012, 2.3268984828669956, 2.216213984913376, 2.0508322566423183, 1.8352295782990362, 1.5753625009005914, 1.278532388851546, 0.9531994820039663, 0.6087500893621276, 0.2552224610540933, -0.09700125488971399, -0.4375278577772216, -0.7563001537954824, -1.0439464751902672, -1.2921201138555536, -1.4938157684780609, -1.64365022875341, -1.7380951531070656, -1.7756509473325028, -1.7569524091936604, -1.6847989348685553, -1.5641046313776439, -1.4017665675096502, -1.206452527055757, -0.9883128881340704, -0.7586245134242394, -0.5293776618986422, -0.31281978342171113, -0.12097249622776884, 0.034860054596555966, 0.14457201518854917, 0.19970587670601103, 0.1938521368812962, 0.1229800994158947, -0.014316656696132387, -0.21667379845489326, -0.4799188752333384, -0.7971490437612747, -1.1589252374249648, -1.553579228761839, -1.9676250394449277, -2.386261286672754, -2.793946542327195, -3.175025841882421, -3.514383320500521, -3.7980937565623214, -4.014044716496479, -4.15250112457792, -4.20658548224303, -4.172649632261225, -4.050517843471699, -3.8435859617128916, -3.558767254674729, -3.206282143250298, -2.799295986145904, -2.353416161367644, -1.886066540793934, -1.415763749837338, -0.9613250208937986, -0.541041690999122, -0.17185520721527411, 0.13142630908204167, 0.3568334531098746, 0.49582776335636103, 0.5437497950819371, 0.5000978209908488, 0.3686191363003487, 0.15720427889192493, -0.12241641484924005, -0.4551650260201873, -0.8232787653629382, -1.207116077368877, -1.5860712163006532, -1.9395559981449164, -2.2480028690912155, -2.4938409772194956, -2.6623967923006506, -2.742673082692327, -2.727964703440594, -2.6162765286476644, -2.410517706591912, -2.118456849232346, -1.7524343133750324, -1.3288398379418251, -0.8673758693491421, -0.3901383131560951, 0.07944341582983129, 0.5177568778674335, 0.9021914955916465, 1.2122984662919505, 1.4308660501754913, 1.5448534003734338, 1.5461319514871112, 1.4319920585095545, 1.2053837070673423, 0.8748731855746523, 0.45431198536295986, -0.03777084981138413, -0.5790269493597858, -1.1443576837905118, -1.707142349146397, -2.2405642091634963, -2.718966647360892, -3.119168671994238, -3.421669745816797, -3.6116784409496887, -3.6799076004239457, -3.6230901694604616, -3.4441840953583824, -3.152250970047789, -2.762010554753254, -2.2930910419393746, -1.7690118954337883, -1.2159513988275372, -0.6613637375743834, -0.13251976670058507, 0.3449490308322212, 0.7484229046158, 1.0595055630310903, 1.265006272336682, 1.3576353618158594, 1.3363716595453488, 1.20647852350438, 0.9791649308306836, 0.6709084317646277, 0.30247649231210044, -0.10229932332162507, -0.5179268305575307, -0.9187536362950988, -1.2804770963861856, -1.5815748208387646, -1.804570371704072, -1.9370575846299163, -1.9724204544775443, -1.9102030445909892, -1.7561044359828943, -1.521596147748715, -1.2231824135019234, -0.881345806296449, -0.5192406005482465, -0.16121268050910859, 0.16876332984939252, 0.44863255789867196, 0.6596962515695686, 0.7878437597372768, 0.8244991855940389, 0.7672183803903807, 0.6198929087411459, 0.3925417261085026, 0.10069712517017772, -0.2355825506251365, -0.5930164890264291, -0.946642986812615, -1.2715038574890818, -1.5443653037694436, -1.745364200407628, -1.859471004985269, -1.8776697695795546, -1.7977715441539492, -1.624798994806993, -1.3709060736295957, -1.054825522445123, -0.7008670949692702, -0.3375187475732785, 0.004270215561332619, 0.29302272368560767, 0.49876653066239096, 0.5950388296934108, 0.5607345255159046, 0.3816765831993581, 0.05180157915982004, -0.4261245513730307, -1.0403177838531594, -1.770339437520076, -2.5880025408879206, -3.458777367064687, -4.343619907857337, -5.201118782284648, -5.98983390436978, -6.670685719891481, -7.209248051145821, -7.57780110608138, -7.757013963427571, -7.737147185529221, -7.518694909134847, -7.112420090102889, -6.5387743981958595, -5.826733171098687, -5.012113325005119, -4.135475713602386, -3.2397408723522854, -2.367666492216866, -1.559344948058382, -0.8498789755947194, -0.2673830265800616, 0.1685624995408601, 0.4479058217275107, 0.5705044129697477, 0.5458690061506314, 0.39229010629043365, 0.1354070033173586, -0.19368359681973873, -0.560651357482161, -0.9303381270012998, -1.2691830094301737, -1.5475024994529623, -1.7414712510699235, -1.8346694248337785, -1.819092248820664], 'positive_zeros': ['0.23619884499033771232223467598893', '2.20386527233660480708669406181991', '3.38217917980610702315956763661591', '4.49712834437715595989820868637892', '4.79967919507124330572830754156073', '6.35958282302503131184248755149981', '6.77276534246747839898335906058145', '7.84145257362852156328670422739777', '8.491828226020649994753037663432662', '9.566307905753201643068059661263897'], 'prelabel': '2-1380-115.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3195414561256347, 'root_angle': -0.4585369689187959, 'root_number': '0.1298918985588560045860619888366940139992716078239668209 - 0.9915281613190700805002721741739553581539680479728565974*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.22926848445939796', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.23619884499033771232223467599', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.20386527233660480708669406182', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.38217917980610702315956763662', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 11.0193554789367, 'bad_primes': [2, 3, 5, 23], 'central_character': '115.68', 'conductor': 1380, 'conductor_radical': 690, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1380/2/t/a/1333/9'], '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': '2-1380-115.68-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': '2-1380-115.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3195414561256347, 'root_angle': -0.22926848445939796, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.23619884499033771232223467599', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '299417607625216116254265530642', 'Lhash_array': ['299417607625216116254265530642'], 'label': '2-1380-115.68-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1380/2/t/a/1333/9'}