-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '734004424684501191062861935556', 'a10': [98.56419590152758, 0.0], 'a2': [-4.0, 0.0], 'a3': [0.0, 0.0], 'a4': [16.0, 0.0], 'a5': [-24.641048975381896, 0.0], 'a6': [0.0, 0.0], 'a7': [103.17452629076806, 0.0], 'a8': [-64.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.398901402574, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [4.0, 0]]], [3, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [529.0, 0]]]], 'bad_primes': [2, 3, 23], 'central_character': '414.1', 'coefficient_field': 'CDF', 'conductor': 414, 'conductor_radical': 138, 'degree': 2, 'euler_factors': [[[1.0, 0], [4.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [24.641048975381896, 0], [3125.0, 0]], [[1.0, 0], [-103.17452629076806, 0], [16807.0, 0]], [[1.0, 0], [457.9322877387697, 0], [161051.0, 0]], [[1.0, 0], [1025.2730075522807, 0], [371293.0, 0]], [[1.0, 0], [-303.3302789522676, 0], [1419857.0, 0]], [[1.0, 0], [-2733.9555948184866, 0], [2476099.0, 0]], [[1.0, 0], [529.0, 0]], [[1.0, 0], [596.5922011734284, 0], [20511149.0, 0]], [[1.0, 0], [-7038.902641656651, 0], [28629151.0, 0]], [[1.0, 0], [5331.375746752371, 0], [69343957.0, 0]], [[1.0, 0], [-1268.2905228850702, 0], [115856201.0, 0]], [[1.0, 0], [2364.630791628988, 0], [147008443.0, 0]], [[1.0, 0], [13980.920041381993, 0], [229345007.0, 0]], [[1.0, 0], [12290.777944323292, 0], [418195493.0, 0]], [[1.0, 0], [-50678.94205978277, 0], [714924299.0, 0]], [[1.0, 0], [-16685.021338699466, 0], [844596301.0, 0]], [[1.0, 0], [-53625.7502784862, 0], [1350125107.0, 0]], [[1.0, 0], [-51442.97205515859, 0], [1804229351.0, 0]], [[1.0, 0], [83874.63000119779, 0], [2073071593.0, 0]], [[1.0, 0], [63387.033582868, 0], [3077056399.0, 0]], [[1.0, 0], [49106.2965084367, 0], [3939040643.0, 0]], [[1.0, 0], [-61671.668432427265, 0], [5584059449.0, 0]], [[1.0, 0], [-31190.63961903933, 0], [8587340257.0, 0]], [[1.0, 0], [-144638.54817342022, 0], [10510100501.0, 0]], [[1.0, 0], [-29695.641854704038, 0], [11592740743.0, 0]], [[1.0, 0], [-180340.40686027904, 0], [14025517307.0, 0]], [[1.0, 0], [138551.84911209607, 0], [15386239549.0, 0]], [[1.0, 0], [-180768.2053868621, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-414-1.1-c5-0-6', 'leading_term': '1.0383658470400859835735954949170', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/414/6/a/o/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.038365847040086, 1.0245535756685136, 0.9833683555750148, 0.9155616341936843, 0.8223747089572422, 0.7055220585098703, 0.5671680207729306, 0.4098968484043522, 0.2366762032025106, 0.050814197321492484, -0.14408984731960184, -0.34420066827046886, -0.5455080070686649, -0.743892757896828, -0.935197715664894, -1.115302172269245, -1.2801994540369888, -1.426076333051878, -1.5493930855978666, -1.646962818411229, -1.716028544350442, -1.7543363703185932, -1.7602030687356132, -1.7325762463429881, -1.6710853070303024, -1.576081434459123, -1.44866490038811, -1.290698139489999, -1.1048032234274863, -0.894342616749388, -0.6633824037181218, -0.4166375354815749, -0.15939905601179075, 0.10255628418275008, 0.3630731346064301, 0.6157399754720643, 0.8540249640820069, 1.0714227824658127, 1.261609588081723, 1.4186027245177613, 1.536921460232696, 1.6117447074116384, 1.639061446225364, 1.6158094571134818, 1.5399979581585146, 1.4108098666220967, 1.2286796605660348, 0.9953432117768978, 0.7138564943903934, 0.38858073958248757, 0.025132395600610615, -0.3697028504743344, -0.7880917470445477, -1.2213095558104214, -1.659928153759697, -2.0940326886745795, -2.513462256092708, -2.9080690704694487, -3.267989711293342, -3.5839212725249654, -3.8473946655148947, -4.051036952830819, -4.188814449916679, -4.256248444045152, -4.250595759329758, -4.17098704820497, -4.0185166103524885, -3.796278716592034, -3.509346825001562, -3.164693686995783, -2.771052110511138, -2.338718025615979, -1.8792994273533699, -1.4054166883438814, -0.9303615727954303, -0.46772397570287316, -0.030996888650402912, 0.36682870734532635, 0.7136664591586053, 0.9987217300250371, 1.2128500684680432, 1.3488743651031212, 1.4018488628564434, 1.369259498109338, 1.2511517928040397, 1.050179649948713, 0.7715708696896919, 0.4230079269174468, 0.01442544714589496, -0.44227121323522306, -0.9335589398138397, -1.4447112510943492, -1.9602614352716778, -2.4644995859827086, -2.941986977074721, -3.378070050849111, -3.7593757451807424, -4.074270000669418, -4.313262094058612, -4.469338937011311, -4.538215631031905, -4.518491323277723, -4.411702680829848, -4.2222709845408035, -3.9573428081123745, -3.6265283465275293, -3.241545531226919, -2.815781952286592, -2.3637901356811266, -1.9007347393693563, -1.4418125927783576, -1.001668088879578, -0.5938271524514459, -0.23017279102240712, 0.07951593802556643, 0.327941824424727, 0.510567544697393, 0.625780910057306, 0.6749388293588914, 0.662286421936192, 0.594752934414852, 0.4816314101731056, 0.3341542024952405, 0.16498118293968, -0.012378346548346103, -0.1841856789282629, -0.337107937190181, -0.4588405421429619, -0.538688897497918, -0.5680824910763199, -0.5409970632086551, -0.4542641123832067, -0.307751666636014, -0.10440576733515361, 0.14985173602344617, 0.446366959096575, 0.7741306007291109, 1.1202723043104468, 1.4706518120407195, 1.8105209327232659, 2.125226397285484, 2.4009210329938435, 2.625249513769424, 2.7879753424054368, 2.8815177214651735, 2.901370527906797, 2.8463806000743417, 2.718868778924645, 2.524584355503719, 2.272491444239041, 1.9743939637709242, 1.6444139738773182, 1.2983456896893366, 0.9529141844378393, 0.6249732411152337, 0.3306807124577236, 0.08469185468442128, -0.10058874838672187, -0.21565792756943178, -0.2544324620108177, -0.2146062620999657, -0.09782442673125197, 0.09033891773774054, 0.34060249027195105, 0.6403928749835566, 0.9744361035420088, 1.32549974687819, 1.6752510469518207, 2.0051897215613557, 2.297609098720699, 2.536536500019058, 2.7086035078733555, 2.8037990132799986, 2.81606271329628, 2.7436838440209526, 2.5894791004934796, 2.360734497886824, 2.068907857181214, 1.7291010653521994, 1.3593236289650863, 0.9795806585143793, 0.6108286539069671, 0.27385072583492925, -0.011891315535020392, -0.22936762924701115, -0.3649935500792739, -0.40948845939435957, -0.35852990717555006, -0.21316190269016186, 0.02007191307429805, 0.329285789082994, 0.6977006997389678, 1.104369670836888, 1.5251496515145058, 1.933876005877731, 2.303683637503185, 2.6084093243775306, 2.824003615171238, 2.929878049411498, 2.910114760374375, 2.7544707443103147, 2.4591180657975085, 2.027073640815809, 1.468287426183863, 0.7993751065139528, 0.042999833911708876, -0.7730737228942423, -1.6172118287062722, -2.4553732625748226, -3.252729161571425, -3.975360239857752, -4.591944584257029, -5.075347847587656, -5.404030996063934, -5.56319874633577, -5.545624122841266, -5.35210060249195, -4.991492296066753, -4.480373566873207, -3.842271298123492, -3.106544508848394, -2.306955993269437, -1.4800079878238592, -0.6631275443799838, 0.10720351819186084, 0.7972750904976957, 1.3778339526160948, 1.8255366135259181, 2.1240905734210282, 2.2650211271332967, 2.248020880251676, 2.080861827100047, 1.7788738984031998, 1.3640179825260224, 0.8636041888582967, 0.3087262401087294, -0.2675008322343154, -0.8318010401695526, -1.3525912465558965, -1.8017238313815258, -2.1560196260009197, -2.398504257755425, -2.519277888615482, -2.515969351762847, -2.393749701613097, -2.164905815098489, -1.8480004206613934, -1.4666692653506177, -1.0481276026555886, -0.6214754896490314, -0.21590345030348976, 0.14109387731103118, 0.4253888559393229, 0.6176762940825293, 0.7046257115001773, 0.6796612062639644, 0.5433222937819427], 'positive_zeros': ['0.57902739489284359213514593082078', '2.03807294423683682487089448855736', '3.12911848362504003587317056732257', '4.75463556327975743658448397164191', '5.50206991835791707143121802742517', '7.10777079026494475917091443180466', '7.74563021796323353024611678480827', '8.339590753238997898076642593816347', '9.775877017216362515823169102912812', '10.09773806823976174329026749635444'], 'prelabel': '2-414-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.148552104673197, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.57902739489284359213514593082', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.03807294423683682487089448856', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.12911848362504003587317056732', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 66.398901402574, 'bad_primes': [2, 3, 23], 'central_character': '1.1', 'conductor': 414, 'conductor_radical': 138, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/414/6/a/o/1/3'], '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': '2-414-1.1-c5-0-6', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-414-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.148552104673197, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.57902739489284359213514593082', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '734004424684501191062861935556', 'Lhash_array': ['734004424684501191062861935556'], 'label': '2-414-1.1-c5-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/414/6/a/o/1/3'}