Formats: - HTML - YAML - JSON - 2026-07-02T18:49:29.764711
Query: /api/lfunc_lfunctions/?_offset=0
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{'A10': 1, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 1, 'A6': 0, 'A7': 1, 'A8': 1, 'A9': 0, 'Lhash': '1639352003099371819', 'a10': [0.31622776601683794, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1087.8978472183287, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [29, [1]]], 'bad_primes': [2, 3, 29], 'central_character': '136242.1', 'coefficient_field': '1.1.1.1', 'conductor': 136242, 'conductor_radical': 174, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, -1, 5], [1, -1, 7], [1, 2, 11], [1, 6, 13], [1, -6, 17], [1, 2, 19], [1, -7, 23], [1], [1, 4, 31], [1, 0, 37], [1, -2, 41], [1, -6, 43], [1, 4, 47], [1, -5, 53], [1, 3, 59], [1, -12, 61], [1, -3, 67], [1, -5, 71], [1, 2, 73], [1, -14, 79], [1, 9, 83], [1, 0, 89], [1, -18, 97]], 'gamma_factors': [[], [0]], 'id': 8253152, 'index': 10, 'label': '2-136242-1.1-c1-0-10', 'leading_term': '4.24087902511', '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': 0, 'origin': 'EllipticCurve/Q/136242/bm', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [4.240879025112788, 3.153852010961743, 0.4399799672957035, -2.267013852025415, -2.97363382323805, -1.067639725537674, 1.686598482347645, 2.684903971557223, 1.373121412579256, -0.05983161468696966, 0.4523463748133444, 1.966240560874325, 1.872688902893005, -0.04523215589129497, -0.8967267497098957, 1.050864039069121, 3.392276301093684, 2.926974392764511, 0.4877070953820009, -0.5172025311752109, 0.4185957834331983, 0.6331991080446684, -0.391863263053884, 0.04071733191007212, 2.231955695930588, 2.333195027433288, -1.021861083278008, -3.350632272853565, 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'3.649156278562473', '4.562440939702443', '4.907129084679559', '5.402929977280725', '5.744006099029200', '6.434537876044075', '7.153674534541231', '7.396447472407776', '7.942742451048277', '8.413321464976790', '9.327324132581465', '9.538240929009850', '10.17841015030831', '10.52239346064709', '11.09722887283332', '11.66720620269130', '12.02417574630493', '12.64970459106987', '12.95051967409261', '13.25849114264835', '14.17110546953022', '14.34462244106870', '14.64193799359625', '15.21137139966768', '15.60630405503052', '16.21574702178356', '16.82747580667097', '16.97530715631165', '17.47808649100280', '17.97758093658170', '18.52312104452289', '19.03881615234350', '19.54510518043145', '19.64264092110777'], 'prelabel': '2-136242-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.98329648804572, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1639352003099371819, 'z1': {'__RealLiteral__': 0, 'data': '0.5360086706146842', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.342192087288448', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.228414204648202', 'prec': 57}}