-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 1, 'A5': 2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -2, 'Lhash': '566468870562368779', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.020618556701030927, 0.0], 'a4': [0.010309278350515464, 0.0], 'a5': [0.020618556701030927, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.020618556701030927, 0.0], 'algebraic': True, 'analytic_conductor': 0.13746842931581987, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1, 0, -1]], [7, [1, 0, -1]], [11, [1, 1, 11, 11]]], 'bad_primes': [2, 7, 11], 'central_character': '2156.1', 'coefficient_field': '1.1.1.1', 'conductor': 2156, 'conductor_radical': 154, 'degree': 4, 'euler_factors': [[1, 0, -1], [1, 2, 6, 6, 9], [1, -2, 10, -10, 25], [1, 0, -1], [1, 1, 11, 11], [1, 2, 18, 26, 169], [1, -8, 46, -136, 289], [1, -2, 38, -38, 361], [1, 8, 46, 184, 529], [1, 8, 70, 232, 841], [1, 12, 94, 372, 961], [1, 0, 70, 0, 1369], [1, -16, 142, -656, 1681], [1, -12, 118, -516, 1849], [1, 4, -2, 188, 2209], [1, -12, 142, -636, 2809], [1, 6, 118, 354, 3481], [1, -18, 202, -1098, 3721], [1, 16, 182, 1072, 4489], [1, -16, 142, -1136, 5041], [1, 12, 118, 876, 5329], [1, -8, 158, -632, 6241], [1, 6, 166, 498, 6889], [1, 12, 214, 1068, 7921], [1, 0, 94, 0, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 1, 'label': '4-2156-1.1-c1e2-0-1', 'leading_term': '0.557941943905', 'load_key': 'G2Q', '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': 0, 'origin': 'Genus2Curve/Q/2156/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.5579419439054731, 0.5779120653271707, 0.6373752069210272, 0.7344715845540134, 0.8644361194768949, 1.017346859721285, 1.175563407542686, 1.311622557176488, 1.387701057261703, 1.357979358782724, 1.175131113055365, 0.801490108238727, 0.224068528356644, -0.5293879452366986, -1.378260121084806, -2.187205487677871, -2.780576809347855, -2.975929935145856, -2.633350248128888, -1.709476719458111, -0.2982240975563768, 1.361949809237091, 2.928472745118303, 4.042151082915108, 4.440587823459356, 4.058080277371676, 3.06661521849095, 1.826849673152312, 0.7524226194380775, 0.134309377666883, 0.003583224662138904, 0.109418494556036, 0.0447723934293449, -0.5225843191652101, -1.626086732028108, -2.917600079014844, -3.806150323702041, -3.781173470140251, -2.759203611372596, -1.239810176275508, -0.1278970809787549, -0.2607766338679611, -1.877487839526132, -4.356143045621884, -6.437345792669912, -6.876965170270692, -5.181501724748669, -1.969860816505099, 1.313908817763522, 3.216661804848224, 3.13353917426673, 1.64565657294943, 0.09017633774662685, -0.3648739627599448, 0.4982657992667355, 1.871505024037498, 2.606144073292273, 2.134390207407104, 0.9023799146341415, -0.03744828404158353, 0.05779989672013031, 0.9751553040736699, 1.749047284163445, 1.568673981763042, 0.5883548554739543, -0.1418753114805311, 0.3438352847023209, 1.87735849797874, 3.060126473158632, 2.370223014948485, -0.3993412889266099, -3.689156319422379, -5.274125243038088, -4.090601941306216, -1.185545825110115, 1.160585883152631, 1.458546678469653, 0.3664780608622586, 0.06009400095479695, 2.104373293891, 5.784775568656038, 8.531859426027317, 8.143203634965737, 4.763732872714904, 0.7564448586217498, -1.405519054588652, -1.194650474879636, -0.1049246857248858, 0.1560540729408878, -0.6148009676547576, -1.239060144036758, -0.8011540891237567, 0.1694368823073687, 0.3666500036658386, -0.5945896563132689, -1.570095743585785, -1.272736907234974, -0.1127871397931563, -0.1485673427301072, -2.823245072947435, -6.887640633102532, -9.101794222643171, -7.389575516229342, -3.180956467414705, -0.2025430329231703, -0.7369304014165885, -3.300336331855519, -4.326366821585926, -2.069262003932307, 1.575171014763827, 3.316302792303979, 2.156327292136616, 0.2938359458710008, 0.3305097721245498, 2.204605386505783, 3.479935351091924, 2.472829177378796, 0.2731727108528585, -0.7871739428040934, -0.1450308766333356, 0.4094795766324189, -0.7173429791138762, -2.652713072941322, -3.142152058352417, -1.60915034021604, -0.06633537564135229, -0.4983642522094093, -2.117562246903638, -2.299848581815439, -0.1970874135813341, 1.767545385258973, 0.8007289193112744, -2.523892381701402, -4.668963688630162, -3.40366819023772, -0.4775232872265078, 0.8264887704307842, -0.01296503104263811, -0.4667038944677137, 0.8762839469907571, 1.542958122895233, -1.880453982944574, -8.578020066631634, -13.17372273650144, -11.39245538995543, -4.932647230901886, 0.5414640740723995, 1.715280599887759, 0.4112814222552342, 0.0003585885461733775, 0.8758248828917896, 0.8869958986874286, -0.7649421842650496, -2.202978592180005, -1.764784415569784, -0.3927529491523191, 0.06844791442088902, -0.2972874502842491, -0.1892541118176051, -0.1146341449122055, -2.283700675979771], 'positive_zeros': [2.309843635216443, 3.784763852357839, 5.579286817429504, 5.606179608230283, 6.026435913010643, 7.575711000888679, 7.581874794264126, 8.919520401542258, 9.765547119459919, 10.04454810525505, 11.04890213928127, 11.23136141438461, 12.12455900124815, 12.30526099005271, 13.10274413461999, 13.95416200626634, 14.5207401194821, 14.6077730656713, 15.79553155219393, 16.33708100139527, 16.55477397890272, 17.21285321618276, 17.52889711962058, 18.21205413166163, 18.34995373195942, 19.54606788612343, 19.58002701984274], 'prelabel': '4-2156-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.6089066857976458, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'G_{3,3}', 'trace_hash': 566468870562368779, 'z1': {'__RealLiteral__': 0, 'data': '2.30984363522', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.78476385236', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.57928681743', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.13746842931581987, 'bad_primes': [2, 7, 11], 'central_character': '1.1', 'conductor': 2156, 'conductor_radical': 154, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 1, 2, 0, 0, 0, -2, 0, -1, -2, -2, 0, -4, 1, 8, 0, 2, 2, 0, 0, -8, 0, -6, 0, 10, 0, -8, 0, -12, 0, 2, 0, 0, -2, 0, 0, 4, 0, 16, 0, 12, -1, -4, 0, -4, -2, 1, 0, -16, -2, 12, 0, -2, 0, -4, 0, -6, -4, 18, 0, 0, 1, -4, 0, -16, 8, 16, 0, 16, 0, -12, 0, 12, 2, 0, 0, 8, 2, -5, 0, -6, 0, 16, 0, 16, 0, -12, 0, 0, -8, 24, 0, 4, 0, 0, 0, 2, -6], 'euler11': [1, 1, 11, 11, 0], 'euler13': [1, 2, 18, 26, 169], 'euler17': [1, -8, 46, -136, 289], 'euler19': [1, -2, 38, -38, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 8, 46, 184, 529], 'euler29': [1, 8, 70, 232, 841], 'euler3': [1, 2, 6, 6, 9], 'euler31': [1, 12, 94, 372, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, -16, 142, -656, 1681], 'euler43': [1, -12, 118, -516, 1849], 'euler47': [1, 4, -2, 188, 2209], 'euler5': [1, -2, 10, -10, 25], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 6, 118, 354, 3481], 'euler61': [1, -18, 202, -1098, 3721], 'euler67': [1, 16, 182, 1072, 4489], 'euler7': [1, 0, -1, 0, 0], 'euler71': [1, -16, 142, -1136, 5041], 'euler73': [1, 12, 118, 876, 5329], 'euler79': [1, -8, 158, -632, 6241], 'euler83': [1, 6, 166, 498, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 0, 94, 0, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 2, 6, 6, 9], [1, -2, 10, -10, 25], [1, 0, -1, 0, 0], [1, 1, 11, 11, 0], [1, 2, 18, 26, 169], [1, -8, 46, -136, 289], [1, -2, 38, -38, 361], [1, 8, 46, 184, 529], [1, 8, 70, 232, 841], [1, 12, 94, 372, 961], [1, 0, 70, 0, 1369], [1, -16, 142, -656, 1681], [1, -12, 118, -516, 1849], [1, 4, -2, 188, 2209], [1, -12, 142, -636, 2809], [1, 6, 118, 354, 3481], [1, -18, 202, -1098, 3721], [1, 16, 182, 1072, 4489], [1, -16, 142, -1136, 5041], [1, 12, 118, 876, 5329], [1, -8, 158, -632, 6241], [1, 6, 166, 498, 6889], [1, 12, 214, 1068, 7921], [1, 0, 94, 0, 9409]], 'index': 1, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/2156/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-2156-1.1-c1e2-0-1', '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': 0, 'prelabel': '4-2156-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.6089066857976458, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 566468870562368779, 'z1': {'__RealLiteral__': 0, 'data': '2.30984363522', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9954428
{'Lhash': '566468870562368779', 'Lhash_array': ['566468870562368779'], 'label': '4-2156-1.1-c1e2-0-1', 'type': 'ECQP', 'url': 'EllipticCurve/Q/14/a|EllipticCurve/Q/154/c'}
-
id: 1223988
{'Lhash': '566468870562368779', 'Lhash_array': ['566468870562368779'], 'label': '4-2156-1.1-c1e2-0-1', 'type': 'G2Q', 'url': 'Genus2Curve/Q/2156/c'}