-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1132266800564761502119837930709', 'a10': [0.38196601125010515, 0.0], 'a2': [-0.6180339887498949, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.6180339887498949, 0.0], 'a5': [-0.6180339887498949, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0734888421735882, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [239, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 239], 'central_character': '2151.955', 'coefficient_field': 'CDF', 'conductor': 2151, 'conductor_radical': 717, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [2.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-2.0, 0], [1.0, 0]], [[1.0, 0], [-2.0, 0], [1.0, 0]], [[1.0, 0], [-1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [-1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-2151-239.238-c0-0-2', 'leading_term': '0.65613765244475929523169709039139', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2151/1/d/c/955/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.6561376524447593, 0.6574346144382216, 0.6609008884022589, 0.6653246624116752, 0.6688707687914535, 0.6692941915460577, 0.6641510189476859, 0.6509755047403181, 0.6274152490075892, 0.5913310416365583, 0.5408726418311668, 0.47454055042890814, 0.3912404733068682, 0.2903338178020568, 0.1716849816674664, 0.03570445780204691, -0.11661427721741069, -0.28366668562919795, -0.46322071215597266, -0.6524147218704904, -0.8477723735588112, -1.045236578289456, -1.2402241638125682, -1.4277022161687185, -1.6022863173378066, -1.7583600610000905, -1.8902143303255587, -1.992203889304506, -2.0589179039663548, -2.085360107233592, -2.067133489398578, -2.0006236752800834, -1.8831745791950587, -1.7132495486068975, -1.4905710518889494, -1.2162320648817504, -0.8927726872953875, -0.5242161868126172, -0.11605962848724662, 0.32478450989438357, 0.7900978320163309, 1.270516993799682, 1.7557446137228216, 2.2348065678760736, 2.6963500559902225, 3.128974806149133, 3.5215878954605344, 3.8637709921308225, 4.14614746074723, 4.3607358016476665, 4.501275392263427, 4.56351052486516, 4.545419335191439, 4.44737541268429, 4.272231673945642, 4.025318438647798, 3.7143505161204415, 3.34924140850031, 2.9418263540395335, 2.5054997401174446, 2.054776258795374, 1.6047888937726866, 1.1707402444685264, 0.7673266389113427, 0.4081567985276597, 0.10518834753836837, -0.13179391517379627, -0.2956344335907312, -0.38217586939455056, -0.39052097145223336, -0.32317115908182836, -0.18603004169231002, 0.011734717220371208, 0.2579720020886504, 0.5379649717839635, 0.8349743053910844, 1.130889267088355, 1.4069632546821516, 1.644605608381774, 1.826197586160933, 1.935897798312689, 1.9604012300086051, 1.8896164025227573, 1.7172272988860169, 1.4411103999823163, 1.063582454331386, 0.5914612702670969, 0.03592962705317488, -0.5877989636615085, -1.2610048259173692, -1.9621600699593702, -2.667774252567958, -3.353354193305369, -3.9944377795456805, -4.567656630115328, -5.051779493281335, -5.428687465358365, -5.684233667443332, -5.808943934000617, -5.7985212536520905, -5.6541249450303726, -5.382405519533612, -4.995287445520883, -4.509504066404544, -3.9459011570825293, -3.3285374130797973, -2.6836209344757123, -2.0383299007315148, -1.4195726029711841, -0.8527463698005064, -0.3605563742481731, 0.038046331735370066, 0.3287529591121179, 0.5025644141586922, 0.5562014923655829, 0.49223383998290493, 0.3189178005174473, 0.0497482409895344, -0.29725548498134197, -0.7004949462090401, -1.1359221187151314, -1.5782951156843203, -2.002494709681895, -2.384831982661092, -2.704276962344918, -2.943541485081975, -3.0899566748742164, -3.136096038902751, -3.0801087378245344, -2.925743396459724, -2.6820600292062218, -2.362845310682694, -1.9857635180540971, -1.5712910031516758, -1.1414950786261429, -0.7187279023319224, -0.32431167059691157, 0.022707245783088352, 0.3066608484727538, 0.5161521193945495, 0.6446829500700139, 0.6909780446213946, 0.6589834971311082, 0.5575384129587471, 0.3997380683538486, 0.20202645862218285, -0.016926539011483967, -0.23749388824693246, -0.4404262927058655, -0.6081681498249887, -0.7260692802663802, -0.7834123874467436, -0.7741866308087166, -0.6975527896862396, -0.5579644104569269, -0.3649309593400418, -0.1324320328257305, 0.12198533424426745, 0.3783727574659241, 0.6157379667216, 0.8135073345667871, 0.9529981406715016, 1.0188022292672965, 0.9999860699775593, 0.8910219147377479, 0.6923803014133628, 0.41073473677045413, 0.058753790894671865, -0.3455174425168985, -0.7796572137810327, -1.2181928126509416, -1.6341733217663135, -2.000891940961246, -2.2936476073739365, -2.491429804894545, -2.578412178518331, -2.545149957781706, -2.3893928545966423, -2.1164481429367394, -1.7390567053206287, -1.2767762194080687, -0.7548983572550488, -0.20295872964813794, 0.3470728322644357, 0.8628102321984319, 1.3135488180510684, 1.6723054303239877, 1.9176634085910689, 2.0352944368605237, 2.0190472446767522, 1.8715192258270685, 1.6040594606891088, 1.2361884232877565, 0.7944584551991828, 0.310817324382679, -0.17942775049549958, -0.6399188090452244, -1.0356801667524824, -1.3355151752968322, -1.5142045860707214, -1.5543537645091163, -1.4477560042424127, -1.196168721912039, -0.8114366077738733, -0.3149385141939855, 0.2636198020211523, 0.8880000483612498, 1.5177044306010636, 2.1105839368435153, 2.6256124923216, 3.0256426535581884, 3.2799558650928335, 3.366430436775218, 3.273172912027875, 2.9994921140875754, 2.5561378003398305, 1.964774767429764, 1.2567151717230418, 0.47098321409508603, -0.3481664060951614, -1.1541151189963288, -1.9009417452025588, -2.5464713468610185, -3.0551021561320244, -3.4002131737429737, -3.5659811436433797, -3.5484741602077112, -3.3559376680800037, -3.008243830963691, -2.5355333918302483, -1.9761361572716432, -1.3739080489463262, -0.7751655043846037, -0.225428677075276, 0.23379900695650313, 0.5679872201080042, 0.7520593729759251, 0.7722172429516497, 0.6269739974398485, 0.3273150008210858, -0.10403272988596306, -0.6341779257931395, -1.222383610087781, -1.8229667287875873, -2.3885753779520007, -2.8736109133030796, -3.237549528651813, -3.4479228539909825, -3.4827396151452126, -3.3321689888933155, -2.999358351322573, -2.5003199954265374, -1.862888655877078, -1.1248194373436613, -0.3311590105249098, 0.4689230001793867, 1.225614753555753], 'positive_zeros': ['0.893201013245216599471994312764306', '2.24237372544536865240578055502882', '3.83251471585125388032081975924395', '4.21566624381821295087942567330259', '5.10119724032208083074151577128832', '6.49758097879193600084400970858291', '6.86465073720404434702563489460261', '8.023186007479946412827564376961684', '8.550239327567276490040822434967490', '9.171472081492781686708045463320014'], 'prelabel': '2-2151-239.238-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.036093066366911, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.893201013245216599471994312764', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.24237372544536865240578055503', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83251471585125388032081975924', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.0734888421735882, 'bad_primes': [3, 239], 'central_character': '239.238', 'conductor': 2151, 'conductor_radical': 717, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2151/1/d/c/955/1'], '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': '2-2151-239.238-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2151-239.238-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.036093066366911, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.893201013245216599471994312764', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1132266800564761502119837930709', 'Lhash_array': ['1132266800564761502119837930709'], 'label': '2-2151-239.238-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2151/1/d/c/955/1'}