-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1059830212502524700134058057969', 'a10': [0.0, 0.0], 'a2': [-8.575230645055953, 0.0], 'a3': [-9.0, 0.0], 'a4': [41.53458061590673, 0.0], 'a5': [0.0, 0.0], 'a6': [77.17707580550358, 0.0], 'a7': [-178.46239721276177, 0.0], 'a8': [-81.76122788527982, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 132.31665134570906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [9.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [8.575230645055953, 0], [32.0, 0]], [[1.0, 0], [9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [178.46239721276177, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [-361.97975231126577, 0], [371293.0, 0]], [[1.0, 0], [934.0035489334608, 0], [1419857.0, 0]], [[1.0, 0], [-753.9285307012748, 0], [2476099.0, 0]], [[1.0, 0], [3231.0135833415593, 0], [6436343.0, 0]], [[1.0, 0], [-2606.3405858617925, 0], [20511149.0, 0]], [[1.0, 0], [-662.2151728643877, 0], [28629151.0, 0]], [[1.0, 0], [-12924.192264092388, 0], [69343957.0, 0]], [[1.0, 0], [2538.5594570095536, 0], [115856201.0, 0]], [[1.0, 0], [22022.787315486214, 0], [147008443.0, 0]], [[1.0, 0], [20835.415073608536, 0], [229345007.0, 0]], [[1.0, 0], [-27450.464599671683, 0], [418195493.0, 0]], [[1.0, 0], [-7759.714620464504, 0], [714924299.0, 0]], [[1.0, 0], [-38469.206231967895, 0], [844596301.0, 0]], [[1.0, 0], [35521.33041031749, 0], [1350125107.0, 0]], [[1.0, 0], [62677.06705732678, 0], [1804229351.0, 0]], [[1.0, 0], [68950.18291029615, 0], [2073071593.0, 0]], [[1.0, 0], [17313.835496203486, 0], [3077056399.0, 0]], [[1.0, 0], [-89017.86244311304, 0], [3939040643.0, 0]], [[1.0, 0], [-129626.85615534242, 0], [5584059449.0, 0]], [[1.0, 0], [-136732.42018451597, 0], [8587340257.0, 0]], [[1.0, 0], [-51376.88514254514, 0], [10510100501.0, 0]], [[1.0, 0], [-94899.70978135937, 0], [11592740743.0, 0]], [[1.0, 0], [-52232.63464296166, 0], [14025517307.0, 0]], [[1.0, 0], [-138553.21240034504, 0], [15386239549.0, 0]], [[1.0, 0], [-136642.0571904332, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 68, 'label': '2-825-1.1-c5-0-68', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/825/6/a/v/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.5557538194652854e-61, 0.09105982819511706, 0.17860868366661856, 0.2592241164002104, 0.3296592064332992, 0.38692654581114094, 0.42837769678362836, 0.45177664766253306, 0.45536581833976836, 0.43792321211745827, 0.39880937294915875, 0.3380028913870621, 0.25612331238805547, 0.15444043726668477, 0.034869183535935155, -0.10005062765330369, -0.24718994516811632, -0.402881734324655, -0.5629875970465998, -0.7229792256051883, -0.8780337833914845, -1.0231419212700088, -1.1532267431682224, -1.2632716397546282, -1.348454525827793, -1.4042856579897243, -1.4267458877227321, -1.4124219349519578, -1.3586350623403805, -1.2635594041814895, -1.1263261680214671, -0.9471099926523572, -0.7271939213237035, -0.4690097397133549, -0.17615083702601508, 0.14664472536391387, 0.4935426148531476, 0.8576930333414289, 1.2313440307588015, 1.6059865242998903, 1.9725292647181103, 2.3215010081204586, 2.643276170734464, 2.9283192959070163, 3.167442779651216, 3.352071516631111, 3.474507475476784, 3.5281867221632437, 3.5079211115554396, 3.410116784854984, 3.232961764162796, 2.976575337996261, 2.6431125893901295, 2.2368183290844836, 1.7640258494723147, 1.2330972906118005, 0.6543039787914567, 0.03964682316634153, -0.5973813089976039, -1.2420874259515244, -1.8789187513591978, -2.4918440427101936, -3.0647666655794126, -3.5819587017133796, -4.028504128213402, -4.390738181350508, -4.656669462941233, -4.816371201338528, -4.862328372809139, -4.789728138592146, -4.596682259300623, -4.284371796337159, -3.8571064676795297, -3.3222934441082312, -2.6903130870887364, -1.974302061913072, -1.1898473176430564, -0.3545975073098976, 0.5121985805056731, 1.3902142053353161, 2.2586126035978715, 3.0966437058450844, 3.8842511046337505, 4.602669740485236, 5.234994428613611, 5.766699696403914, 6.1860924591134765, 6.484680820989678, 6.657444715820065, 6.702997132499607, 6.6236282189638, 6.42522850919967, 6.117091739619624, 5.71160206295854, 5.223814768794984, 4.670943713167288, 4.071772379989758, 3.446008686345625, 2.8136061591408694, 2.1940758301015117, 1.6058140248694848, 1.06547109744069, 0.5873850571169782, 0.18310196419836458, -0.13899801437401518, -0.3739538048853619, -0.5203452962158581, -0.5802783198486214, -0.559232546306079, -0.4657775940026122, -0.31116803770719215, -0.10883306807326404, 0.12621893061383502, 0.3780568556302183, 0.6305175570653173, 0.8679020988802427, 1.0756484355364218, 1.2409519976695271, 1.353307585421182, 1.40494905778789, 1.3911674737658055, 1.3104934280142346, 1.1647351262432808, 0.9588700214140756, 0.7007943105853464, 0.4009409863542418, 0.07178315454932643, -0.27275531155274074, -0.6179552708671703, -0.9489941630526719, -1.2516424273760198, -1.5129321819528339, -1.7217668205008012, -1.8694426360389245, -1.9500574344432828, -1.960786202307358, -1.902010026154607, -1.7772913513217905, -1.593196002485844, -1.3589698177172926, -1.086084914166626, -0.7876771495436246, -0.4779019341233167, -0.17123988625270462, 0.11821333218704418, 0.37743748938649685, 0.5951236448631978, 0.7622228393913916, 0.8723791093418494, 0.9222238994272907, 0.9115157987166997, 0.843117325383482, 0.7228088555306236, 0.558948310372208, 0.36199344456847254, 0.14391108009878756, -0.0824960059876424, -0.304308967869541, -0.5092209096284571, -0.686233326732933, -0.8262823020366732, -0.9227589368726712, -0.9718936402422523, -0.9729808108858107, -0.9284288022661009, -0.8436294456391167, -0.7266513395492822, -0.5877710687459895, -0.4388659474800729, -0.29270025842248026, -0.16214378663889753, -0.05936630452581248, 0.004945780956547668, 0.022304366727441974, -0.012977517996242896, -0.10333359398872663, -0.24767409271905477, -0.44131912945899604, -0.6761464483132874, -0.9409523452693198, -1.2220122792078483, -1.503815720000668, -1.7699388411620853, -2.004009393761091, -2.1907110806247605, -2.316770462841471, -2.3718682165841747, -2.349418600286454, -2.247166297514992, -2.067558194046227, -1.8178587733563667, -1.509991150834137, -1.1601006474595785, -0.7878534503153911, -0.4154984692487572, -0.06673509766539809, 0.23455763730531562, 0.4656648828537205, 0.6063801895069266, 0.6402745351787683, 0.5558155460438409, 0.34726756182054164, 0.015312525885862616, -0.43265526448476943, -0.9825913227766235, -1.614232288000852, -2.3018886801513023, -3.01557109626936, -3.7224023271468876, -4.388250239854634, -4.979501570490291, -5.464885927305453, -5.8172530564379565, -6.015205279906992, -6.044491220156867, -5.8990764291736175, -5.581820997967618, -5.104713001442588, -4.488628840377699, -3.7626160627975618, -2.9627198036484543, -2.130399199215414, -1.3106036126720184, -0.5495989058146732, 0.10734990245714855, 0.6183224459224137, 0.9469913821442755, 1.0646551241111923, 0.9519429829489725, 0.6000952834861704, 0.011741144489937247, -0.7988786058795312, -1.806267734050032, -2.974604379638199, -4.259208151958212, -5.608479328572872, -6.966218858593717, -8.274216261503417, -9.474976640845377, -10.514448874619337, -11.344615215065803, -11.925808243141983, -12.22863417008358, -12.235401236188858, -11.94097741345351, -11.353031425460465, -10.491643642007482, -9.388306898606817, -8.084369868315607, -6.629005442959765, -5.076811968387701, -3.485174667845541, -1.9115270486785132, -0.4106567856600355, 0.967802782522348, 2.1815656461248705, 3.1974591989548955], 'positive_zeros': ['0.836058620815318938427685584802695', '2.02476971779981580094426492904332', '3.34353758442410332535888394929932', '4.53587008193812360321373260284482', '6.06653297064713990704581704129286', '6.53181299650537164032019953421432', '7.39515500378832856808768694003232', '8.412970669236474084381010722675215', '9.119311963877995874049552096386254'], 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.836058620815318938427685584803', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.02476971779981580094426492904', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.34353758442410332535888394930', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 132.31665134570906, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 68, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/6/a/v/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': '2-825-1.1-c5-0-68', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.836058620815318938427685584803', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1059830212502524700134058057969', 'Lhash_array': ['1059830212502524700134058057969'], 'label': '2-825-1.1-c5-0-68', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/6/a/v/1/3'}