-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1616098565722166538449283733017', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-3.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.2392888740866585, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 69.386246166751, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [3.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1176.1', 'coefficient_field': 'CDF', 'conductor': 1176, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [0.2392888740866585, 0], [125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-8.096912229261694, 0], [1331.0, 0]], [[1.0, 0], [43.7693144359584, 0], [2197.0, 0]], [[1.0, 0], [-60.814778851521666, 0], [4913.0, 0]], [[1.0, 0], [-98.88605319722011, 0], [6859.0, 0]], [[1.0, 0], [213.87482997526516, 0], [12167.0, 0]], [[1.0, 0], [-110.313183131695, 0], [24389.0, 0]], [[1.0, 0], [-80.01384313386487, 0], [29791.0, 0]], [[1.0, 0], [2.8806413268283846, 0], [50653.0, 0]], [[1.0, 0], [-242.30719973355986, 0], [68921.0, 0]], [[1.0, 0], [-367.0061554447071, 0], [79507.0, 0]], [[1.0, 0], [89.39101240327201, 0], [103823.0, 0]], [[1.0, 0], [-11.4127152728666, 0], [148877.0, 0]], [[1.0, 0], [400.0970842758336, 0], [205379.0, 0]], [[1.0, 0], [480.3812660377401, 0], [226981.0, 0]], [[1.0, 0], [240.99942847225657, 0], [300763.0, 0]], [[1.0, 0], [978.4963005079792, 0], [357911.0, 0]], [[1.0, 0], [-622.215310185726, 0], [389017.0, 0]], [[1.0, 0], [545.9569834497747, 0], [493039.0, 0]], [[1.0, 0], [-845.9945327415805, 0], [571787.0, 0]], [[1.0, 0], [-203.31860529429434, 0], [704969.0, 0]], [[1.0, 0], [-1199.1741699730953, 0], [912673.0, 0]], [[1.0, 0], [367.5850089083673, 0], [1030301.0, 0]], [[1.0, 0], [945.2276661709602, 0], [1092727.0, 0]], [[1.0, 0], [713.1567913064332, 0], [1225043.0, 0]], [[1.0, 0], [933.6218700138855, 0], [1295029.0, 0]], [[1.0, 0], [-1191.3834864684784, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 37, 'label': '2-1176-1.1-c3-0-37', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1176/4/a/x/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-7.389830642460106e-61, 0.20866649007090152, 0.4137696763498878, 0.6117811244018395, 0.7992428217691618, 0.9728040366550321, 1.1292599874550573, 1.2655926580338048, 1.3790138799863738, 1.4670105558213478, 1.5273916276736084, 1.55833611739334, 1.5584412886863457, 1.5267697233680597, 1.4628938742129507, 1.3669364679401081, 1.2396049940061395, 1.0822184370743193, 0.8967244006349356, 0.6857048317562708, 0.45236869580954947, 0.20053016649875158, -0.06542881044980502, -0.3406123555960434, -0.6196812389630684, -0.8969400601728162, -1.166440340306722, -1.4220982703913911, -1.6578252753775586, -1.8676689687519648, -2.045961511661538, -2.187471872992686, -2.287558035165543, -2.3423148262659663, -2.3487128034083007, -2.3047234839790898, -2.209426237073115, -2.0630923198757842, -1.8672418814698124, -1.624670262913154, -1.3394405950369135, -1.016840525576661, -0.6633018797640928, -0.2862831515514812, 0.1058840920055067, 0.5041825671840194, 0.8991268025395348, 1.281006014489029, 1.6401463372068645, 1.9671853668842703, 2.253351098936678, 2.490736666496169, 2.67256187033821, 2.793412358914926, 2.849447498975096, 2.83856848910619, 2.7605391159004804, 2.6170527283359295, 2.4117404901832757, 2.150117729144587, 1.8394671881306757, 1.4886601393542933, 1.107918575547892, 0.7085239654224993, 0.3024802668189814, -0.09785905825513846, -0.48018847657531005, -0.8326592390420455, -1.1442855661505842, -1.4053334806724442, -1.6076775425421024, -1.7451112420334647, -1.8135978855805872, -1.811450455385406, -1.7394311067408743, -1.600763629132814, -1.4010552586507543, -1.148127588476069, -0.8517598610118667, -0.5233515046173481, -0.1755142550370863, 0.17839257272157033, 0.5247672694609524, 0.8502926921785299, 1.1424646909895335, 1.390100831389093, 1.583808218701301, 1.7163900937739427, 1.7831726231434042, 1.7822359224007593, 1.714536758408482, 1.5839144659158277, 1.3969762426786405, 1.1628629786091522, 0.8929019276146455, 0.6001576267913424, 0.2988972789288038, 0.003991114380028492, -0.2697281776761915, -0.508120203635924, -0.6983774855661106, -0.8296232515118851, -0.8934385951642067, -0.8842933846220706, -0.7998587238699405, -0.6411833356262442, -0.41272178047019975, -0.12220874147695777, 0.21961957301230808, 0.5994488182828143, 1.0019396704205004, 1.4103892278607602, 1.8074733882437197, 2.176038243150163, 2.499905166366814, 2.764652439130917, 2.9583361075253927, 3.0721143776620754, 3.1007432168290703, 3.0429158517536448, 2.901425362508817, 2.6831373067098707, 2.3987679471879293, 2.0624728132359986, 1.6912595754330408, 1.3042481095659266, 0.9218087181520181, 0.5646163419704218, 0.2526638461533959, 0.004280788023998922, -0.16479476707830346, -0.24224495533225218, -0.21985838601537241, -0.09403670821882296, 0.1339080713512666, 0.4576856309118841, 0.8661981205776992, 1.3439475518892343, 1.8716658781606916, 2.4271424274209004, 2.9862128572010653, 3.5238648054267747, 4.015408420403286, 4.437655385693495, 4.770048221936544, 4.995682725422137, 5.102170425176615, 5.082294786675353, 4.934424289750099, 4.662657046884448, 4.276684766286036, 3.791377960923249, 3.226108648451893, 2.6038406308897217, 1.9500300440327474, 1.2913895257561583, 0.6545774532359872, 0.06487874443268687, -0.4550546386991825, -0.8863372830282814, -1.2147973091173019, -1.4316848976155176, -1.5341023191034218, -1.5251296323313295, -1.4136360945947668, -1.2137840565716902, -0.944248797462646, -0.627193478693767, -0.2870522689514155, 0.05081408728195776, 0.36151810128015943, 0.6220245772593612, 0.8124327772996788, 0.9170899898595792, 0.9254732144590614, 0.8327878058657787, 0.6402471379590258, 0.35501485208518896, -0.010189900922266765, -0.4378046792697091, -0.90641554379903, -1.3919740674962024, -1.869171580599667, -2.3128927467798546, -2.6996649879662167, -3.0090194550916713, -3.2246833221307067, -3.3355320203103225, -3.3362432043364434, -3.2276110637422155, -3.0164991395851066, -2.715430976635814, -2.341839509169696, -1.9170167679947063, -1.4648240541794495, -1.010237996787116, -0.5778189143065042, -0.19019388332354992, 0.13335258022413807, 0.37809244480612647, 0.5347954624234913, 0.600336066808701, 0.5779236086538332, 0.4769361341451928, 0.3123620225646787, 0.10387810558061773, -0.1253840941696234, -0.35031208877094644, -0.5454379649876419, -0.686616489886424, -0.7526513673437026, -0.7267664452904761, -0.5978263318426893, -0.3612246441938613, -0.01937726305508245, 0.41821857918773003, 0.9353721571296331, 1.510019096990113, 2.1154308620167055, 2.721746229901173, 3.2977355236565726, 3.81269191798951, 4.238333999312115, 4.5506006833922585, 4.731223935655675, 4.768976379813024, 4.660509240706196, 4.410720128268666, 4.032618528288578, 3.5466878154574966, 2.979774236204329, 2.36356362955645, 1.7327337110921635, 1.1228917521439588, 0.5684229431066501, 0.1003825232040029, -0.2554357553863637, -0.4801312084832404, -0.5629211913055758, -0.5018768519434151, -0.30411677216943434, 0.014560823972900264, 0.430591266754517, 0.9140511416906907, 1.4304774487128453, 1.9429878770177298, 2.4145712492551143, 2.81040471908562, 3.10005090746595, 3.2593941962855033, 3.272190613643715, 3.131129287947223, 2.838333902376645, 2.405268053938851, 1.8520466581520525, 1.2061940691595936, 0.5009258755504166], 'positive_zeros': ['1.27487697748196713581538036122320', '2.56245189213143256831813867092745', '3.79409470114957627242817844888474', '4.71654380598690842173171430880820', '5.68440970921007057891911347195865', '6.29139468570387542401879027736817', '7.55978656625242766255680469784247', '7.82033952730821386276673361685407', '9.206078632577996100120584076706270'], 'prelabel': '2-1176-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.329840704764466, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27487697748196713581538036122', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56245189213143256831813867093', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79409470114957627242817844888', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 69.386246166751, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1176, 'conductor_radical': 42, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1176/4/a/x/1/2'], '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': '2-1176-1.1-c3-0-37', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1176-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.329840704764466, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27487697748196713581538036122', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1616098565722166538449283733017', 'Lhash_array': ['1616098565722166538449283733017'], 'label': '2-1176-1.1-c3-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1176/4/a/x/1/2'}