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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 1, 'A9': 0, 'Lhash': '45324902891984509', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 176.07013645692334, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '22050.1', 'coefficient_field': '1.1.1.1', 'conductor': 22050, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1, -1], [1], [1], [1], [1, 2, 11], [1, 6, 13], [1, -2, 17], [1, 0, 19], [1, -4, 23], [1, 0, 29], [1, -8, 31], [1, -2, 37], [1, -2, 41], [1, 4, 43], [1, 8, 47], [1, 6, 53], [1, -10, 59], [1, 2, 61], [1, 8, 67], [1, 12, 71], [1, -4, 73], [1, 0, 79], [1, 4, 83], [1, 10, 89], [1, -8, 97]], 'gamma_factors': [[], [0]], 'index': 114, 'label': '2-22050-1.1-c1-0-114', 'leading_term': '7.58363378147', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/22050/dm', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.802512702425992, 3.016730553918837, 3.044411534246224, 1.635060207501982, -0.6666482457773778, -2.586070659207146, -2.920726609186755, -1.550750874920227, 0.3096481458611223, 1.096801907944387, 0.3819851141351186, -0.6371084772744439, -0.3574289336483127, 1.409926132911878, 3.058794065703618, 2.899159006485802, 1.137759745241246, -0.3005268663128945, -0.09604617869212277, 0.8243835077253931, 0.5806769644975339, -0.9433588999788456, -1.672545295895512, -0.1354638930506835, 2.168546784194181, 2.426546223257419, 0.3620446770592386, -1.131504360795218, 0.03668721244899731, 1.974071023127777, 1.401568914304783, -1.177719218928406, -1.472306446708222, 2.521783538963046, 6.792376474994856, 6.043225475840797, 0.9248976847071037, -2.625288176762923, -1.423869703270842, 0.9947418304215336, 0.1878605072471052, -2.469802854906158, -2.290466759637534, 1.154702742271613, 3.340971449317411, 1.857287190853889, -0.1834558036283189, 0.4245005942093069, 1.973757230148854, 1.353033819706722, -0.4104706246283955, -0.2177813312026735, 1.318600669913517, 0.849532280649486, -1.581889238236763, -2.309412857288208, -0.3865157592799645, 0.8225572551313989, -0.2193918984014096, -0.5631523923583615, 1.334087076850893, 2.155588645854054, -0.2027672609339377, -1.962891822681071, 0.2798001336887674, 3.039680031996411, 1.72378087278732, -0.9272601755808789, 0.4212318470450095, 3.479677902091209, 1.699645265292378, -3.551209803157618, -4.034683519400898, 1.590206237606425, 5.16612256018681, 2.507604532124239, -0.5566564090260304, 0.5314411950562948, 1.501622256665633, -1.567236122973323, -4.460057786587585, -2.795416599571977, 0.00939447745420032, -0.3955978993405561, -1.522827138879191, 0.01196615360219441, 1.506780571955882, -0.04166802717148658, -1.658726164592799, -0.4745399721650225, 0.4590401380449499, -1.342635640357615, -2.427691814348963, -0.4769400446527609, 0.7211163343311413, -0.9950587198406613, -1.597979748961406, 0.7081426896107812, 1.578419127716557, -0.1253548271612423, 0.6371654323800501, 4.144715642305132, 3.636959697581215, -1.534132218609923, -3.336570695490944, 0.04499023087064372, 0.9009532951073665, -2.293985907232734, -1.484382193232303, 4.293540507635464, 5.430860625415424, -0.4031702326236741, -3.692417727307676, -0.6800608499788259, 1.153152546856383, -1.263816305533906, -1.960810800153385, 0.5665618072979877, 1.055628853631931, -0.3823781992677383], 'positive_zeros': ['1.180200956639165', '2.202705037592629', '2.830381416305905', '3.315063518187133', '4.420779064646366', '4.775890226275020', '5.356029576944658', '6.013926517238104', '6.789322369642588', '7.245756480113507', '7.886394049132306', '8.368140847215170', '9.294585912850502', '9.875062416219078', '10.26827260156112', '10.92403241304703', '11.70935116312820', '11.93013673657478', '12.67824910124685', '13.03640401459112', '13.59306201601649', '14.29573078834552', '14.71035818241066', '15.09558050350882', '15.73325490934321', '16.23018829012138', '16.88739050608364', '17.21697124891506', '17.83104190467287', '18.43746079084064', '19.17074217668696', '19.43781525627191', '19.90176990756380'], 'prelabel': '2-22050-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 13.269142265305748, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 45324902891984509, 'z1': {'__RealLiteral__': 0, 'data': '1.180200956639165', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.202705037592629', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.830381416305905', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 176.07013645692334, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 22050, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, 0, 1, 0, 0, -2, 0, -6, 0, 0, 1, 2, 0, 0, 0, 0, -2, 4, 0, 0, -6, 0, 0, 0, 0, 8, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, -4, -2, 0, 4, -8, 0, 0, 0, 0, -6, -6, 0, 0, 0, 0, 0, 10, 0, -2, 8, 0, 1, 0, 0, -8, 2, 0, 0, -12, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, -4, 0, -2, -10, 0, 0, 4, 0, -8, 0, 0, 8, 0, 0, 0], 'euler11': [1, 2, 11], 'euler13': [1, 6, 13], 'euler17': [1, -2, 17], 'euler19': [1, 0, 19], 'euler2': [1, -1, 0], 'euler23': [1, -4, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, -2, 37], 'euler41': [1, -2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, -10, 59], 'euler61': [1, 2, 61], 'euler67': [1, 8, 67], 'euler7': [1, 0, 0], 'euler71': [1, 12, 71], 'euler73': [1, -4, 73], 'euler79': [1, 0, 79], 'euler83': [1, 4, 83], 'euler89': [1, 10, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 2, 11], [1, 6, 13], [1, -2, 17], [1, 0, 19], [1, -4, 23], [1, 0, 29], [1, -8, 31], [1, -2, 37], [1, -2, 41], [1, 4, 43], [1, 8, 47], [1, 6, 53], [1, -10, 59], [1, 2, 61], [1, 8, 67], [1, 12, 71], [1, -4, 73], [1, 0, 79], [1, 4, 83], [1, 10, 89], [1, -8, 97]], 'index': 114, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/22050/dm'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-22050-1.1-c1-0-114', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-22050-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 13.269142265305748, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 45324902891984509, 'z1': {'__RealLiteral__': 0, 'data': '1.180200956639165', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '45324902891984509', 'Lhash_array': ['45324902891984509'], 'label': '2-22050-1.1-c1-0-114', 'type': 'ECQ', 'url': 'EllipticCurve/Q/22050/dm'}