-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': -2, 'A3': 0, 'A4': 3, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': -4, 'A9': -2, 'Lhash': '1270343409320887797,1459918945821948014', 'a10': [0.0, 0], 'a2': [-1.4142135623730951, 0], 'a3': [0.0, 0], 'a4': [1.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [-1.4142135623730951, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.611670552024722, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 1]], [7, [1, 0, -1]], [17, [1, -6, 17]]], 'bad_primes': [2, 7, 17], 'central_character': '56644.1', 'coefficient_field': '1.1.1.1', 'conductor': 56644, 'conductor_radical': 238, 'degree': 4, 'euler_factors': [[1, 2, 1], [1, 0, 2, 0, 9], [1, 0, 10, 0, 25], [1, 0, -1], [1, 0, 22, 0, 121], [1, 8, 42, 104, 169], [1, -6, 17], [1, -4, 42, -76, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, 0, 46, 0, 961], [1, 0, 70, 0, 1369], [1, 0, 46, 0, 1681], [1, -16, 150, -688, 1849], [1, 24, 238, 1128, 2209], [1, -12, 142, -636, 2809], [1, 12, 154, 708, 3481], [1, 0, 58, 0, 3721], [1, 8, 150, 536, 4489], [1, 0, 142, 0, 5041], [1, 0, 142, 0, 5329], [1, 0, 94, 0, 6241], [1, 12, 202, 996, 6889], [1, 12, 214, 1068, 7921], [1, 0, 94, 0, 9409], [1, 0, 202, 0, 10201], [1, 8, 222, 824, 10609], [1, 0, 70, 0, 11449], [1, 0, 214, 0, 11881], [1, 0, 190, 0, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 9, 'label': '4-238e2-1.1-c1e2-0-9', 'load_key': 'Costa', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/2.2.17.1/196.1/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.5047204462532152e-76, 0.06894443058409669, 0.13848765568595112, 0.20917432031229585, 0.28144143935463056, 0.3555663514228644, 0.4316170583511611, 0.509406161422447, 0.5884499171503579, 0.6679342704082497, 0.7466900460222391, 0.8231797519856878, 0.8954986251639636, 0.9613925893091504, 1.0182956520850306, 1.0633889034528363, 1.0936826606602295, 1.1061224151294002, 1.097718069073609, 1.065694519223966, 1.0076599887374564, 0.9217866883881859, 0.8069964930483624, 0.6631424636513895, 0.4911753660516803, 0.29328299264186447, 0.07298924739303878, -0.16480022183413465, -0.4138184118368651, -0.6665343381870668, -0.9143357117086874, -1.1478015097586367, -1.3570642739012264, -1.5322562921557263, -1.6640274541313878, -1.7441158118354467, -1.7659451387589429, -1.725217533656838, -1.6204638981533186, -1.4535114899090567, -1.229826264347295, -0.9586888595174297, -0.6531672361522752, -0.32985638798596034, -0.008366212972045832, 0.2894476303753604, 0.5404987483564309, 0.7217016619839222, 0.8113719114790188, 0.7907280011990153, 0.6454120226076857, 0.3669326535743876, -0.04607400640904106, -0.5868722956841789, -1.2400447438631752, -1.9813875974834019, -2.778350538353451, -3.591057886873783, -4.373912918047422, -5.077746525615274, -5.652428783911124, -6.049819927786371, -6.2268991949332975, -6.148879271516095, -5.792094027056102, -5.1464406588470135, -4.2171664011281536, -3.0258156999920045, -1.6101960992375344, -0.023278546153546045, 1.6689824795541774, 3.3908459103640562, 5.060854658175974, 6.596559523760708, 7.919609390834058, 8.96087030210203, 9.665207755647845, 9.995564743551718, 9.935995219855215, 9.49336914111569, 8.697548794121259, 7.599942096107826, 6.270459839706765, 4.793031415730553, 3.259957012801025, 1.7654827864714357, 0.39906857250194977, -0.7611336164585755, -1.6540644426864457, -2.2403163984694583, -2.5050591247466314, -2.4590433166667505, -2.137547476196261, -1.5973030291996917, -0.9116095488231792, -0.16401716005622188, 0.5589081919187371, 1.175123314580494, 1.614291474434226, 1.8239661477567604, 1.7742038728150358, 1.4601656056892542, 0.9024424416619655, 0.1450489657766181, -0.748753184886306, -1.702428884268962, -2.633387932934606, -3.4607660279946395, -4.113020436984438, -4.534600324567736, -4.691034451367638, -4.571930529514229, -4.191587185902601, -3.5871611568014266, -2.8145844031769895, -1.9426616492387525, -1.045972574293621, -0.19733241288528933, 0.5393857280120008, 1.1153013188286565, 1.5008070455396667, 1.6876332196177535, 1.6884982759366187, 1.5344216365868346, 1.2700433132086908, 0.9475255083108108, 0.6197772764425358, 0.3338230525722657, 0.12511827132071657, 0.013500522857403746, 0.0012646702272852838, 0.07358782050130988, 0.20123609685313315, 0.34519570350301726, 0.4626221998582047, 0.5133265145248692, 0.4659380222133392, 0.3029162804754532, 0.023722393021565306, -0.35430696449191523, -0.7975429739875394, -1.2599413163431499, -1.6887379585100697, -2.0312362045446304, -2.24179467405276, -2.2880790678807617, -2.155718976184138, -1.8507075366283985, -1.399173151115256, -0.8445016938616188, -0.24214849485720594, 0.347197506175379, 0.8651955010890883, 1.2631583361315397, 1.5080792301473898, 1.5865377736843487, 1.5059266744121644, 1.2928103013240357, 0.9886317657675728, 0.643369949886091, 0.3080553514006475, 0.027236716806833174, -0.16748167704182368, -0.26184894210410586, -0.260626445012639, -0.18620030889638176, -0.07430880939573989, 0.03250521502782251, 0.09273455831396604, 0.073821814242633, -0.041129744012552164, -0.24899011189109407, -0.5254047247000289, -0.8271278802057798, -1.0977116709961867, -1.2758364790706151, -1.3051143211908371, -1.1438993655906706, -0.7735547788630702, -0.20377600814832217, 0.5260530859177737, 1.3499392070127407, 2.1826029465820027, 2.9301901407491546, 3.502945185354967, 3.8280396655621494, 3.8606275192059973, 3.5913672115375554, 3.0491015824395067, 2.298062403120904, 1.4297762703304684, 0.5506723791247866, -0.232896765700106, -0.8300305838615284, -1.1786983759388685, -1.255045107344964, -1.0769771369685452, -0.7012484348859443, -0.21426228905320352, 0.28218412047822927, 0.6881139543542564, 0.9228620110215442, 0.9399744421044229, 0.7369103229401148, 0.35763393915160774, -0.11276986146680484, -0.5610788424038404, -0.8648742462764993, -0.914719585506665, -0.6361447770545618, -0.007791939754375384, 0.927565902218895, 2.0615222203159456, 3.2291032369892534, 4.227866307250931, 4.844884659089422, 4.888094201136988, 4.217558212585903, 2.7719136506028637, 0.5856791571991745, -2.2057955591135228, -5.375308869462757, -8.62630785380288, -11.626485539118097, -14.04829651200938, -15.611002190730895, -16.118396413393818, -15.48675154620263, -13.75873878300115, -11.100960013454914, -7.785020624699339, -4.1544395381111086, -0.581779427586499, 2.57813610649903, 5.03240916089802, 6.585462515288259, 7.160687694807945, 6.805383568249694, 5.678474656969384, 4.02303910388066, 2.127916669966716, 0.28425946108157196, -1.2564178830606563, -2.316447527398558, -2.813514727662701, -2.766539628290841, -2.2854944308247513, -1.5472428514940206, -0.76165855422754, -0.13374536093201178, 0.1719883209424335, 0.059135788640111535, -0.48536735460112784, -1.3906032830960502, -2.515415878356202, -3.6739372425242762, -4.668373883573807], 'positive_zeros': ['1.54182063036964932495656311077884', '2.57969057241224021562840012921274', '3.04116088637864497579983367989583', '4.04379426959865020166490254053975', '5.05791232432713970996781243182598', '5.57928681742950427486583645839251', '6.04516833074826431165424798565025', '6.87015167727116618005628901277482', '7.57571100088867902110310233811410', '7.61488245805577994602083893658164', '8.090068662745416752784621377031670', '8.812642335551285956694248042849818', '9.440338822267021662634471861951068', '9.765547119459919407856461234632429'], 'prelabel': '4-238e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.37856431409872, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 424419345929141860, 'z1': {'__RealLiteral__': 0, 'data': '1.54182063036964932495656311077884', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.57969057241224021562840012921274', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.04116088637864497579983367989583', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.611670552024722, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 56644, 'conductor_radical': 238, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, 3, 0, 0, 0, -4, -2, 0, 0, 0, -8, 0, 0, 5, 6, 4, 4, 0, 0, 0, 0, 0, -10, 16, 0, 0, 0, 0, 0, -6, 0, -12, 0, -6, 0, -8, 0, 0, 0, 0, 16, 0, 0, 0, -24, 0, 1, 20, 0, -24, 12, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 7, 0, 0, -8, 18, 0, 0, 0, 8, 0, 0, 0, 12, 0, 0, 0, 0, -5, 0, -12, 0, 0, -32, 0, 0, -12, 0, 0, 0, 0, 48, 0, 0, 0, -2, 0, -30], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 8, 42, 104, 169], 'euler17': [1, -6, 17, 0, 0], 'euler19': [1, -4, 42, -76, 361], 'euler2': [1, 2, 1, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, 2, 0, 9], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, -16, 150, -688, 1849], 'euler47': [1, 24, 238, 1128, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 12, 154, 708, 3481], 'euler61': [1, 0, 58, 0, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 0, -1, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, 142, 0, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 12, 202, 996, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 0, 94, 0, 9409], 'euler_factors': [[1, 2, 1, 0, 0], [1, 0, 2, 0, 9], [1, 0, 10, 0, 25], [1, 0, -1, 0, 0], [1, 0, 22, 0, 121], [1, 8, 42, 104, 169], [1, -6, 17, 0, 0], [1, -4, 42, -76, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, 0, 46, 0, 961], [1, 0, 70, 0, 1369], [1, 0, 46, 0, 1681], [1, -16, 150, -688, 1849], [1, 24, 238, 1128, 2209], [1, -12, 142, -636, 2809], [1, 12, 154, 708, 3481], [1, 0, 58, 0, 3721], [1, 8, 150, 536, 4489], [1, 0, 142, 0, 5041], [1, 0, 142, 0, 5329], [1, 0, 94, 0, 6241], [1, 12, 202, 996, 6889], [1, 12, 214, 1068, 7921], [1, 0, 94, 0, 9409]], 'index': 9, 'instance_types': ['ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.17.1/196.1/b', 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-196.1-b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-238e2-1.1-c1e2-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-238e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.37856431409872, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 424419345929141860, 'z1': {'__RealLiteral__': 0, 'data': '1.54182063036964932495656311077884', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9489367
{'Lhash': '1270343409320887797,1459918945821948014', 'Lhash_array': ['1270343409320887797', '1459918945821948014'], 'label': '4-238e2-1.1-c1e2-0-9', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-196.1-b'}
-
id: 9490039
{'Lhash': '1270343409320887797,1459918945821948014', 'Lhash_array': ['1270343409320887797', '1459918945821948014'], 'label': '4-238e2-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.17.1/196.1/b'}