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lfunc_lfunctions • Show schema
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{'A10': 6, 'A2': -2, 'A3': -1, 'A4': 2, 'A5': -3, 'A6': 2, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1295265223762678770', 'a10': [1.8973665961010275, 0], 'a2': [-1.414213562373095, 0], 'a3': [-0.5773502691896258, 0], 'a4': [1.0, 0], 'a5': [-1.3416407864998738, 0], 'a6': [0.8164965809277261, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 259.4100010465337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [7, [1]], [13, [1, -1]], [17, [1, -1]]], 'bad_primes': [3, 7, 13, 17], 'central_character': '32487.1', 'coefficient_field': '1.1.1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'euler_factors': [[1, 2, 2], [1, 1], [1, 3, 5], [1], [1, 6, 11], [1, -1], [1, -1], [1, -1, 19], [1, 5, 23], [1, 1, 29], [1, 1, 31], [1, -2, 37], [1, -6, 41], [1, 5, 43], [1, 7, 47], [1, -5, 53], [1, 4, 59], [1, 10, 61], [1, 8, 67], [1, 10, 71], [1, 7, 73], [1, 11, 79], [1, -9, 83], [1, -5, 89], [1, -13, 97]], 'gamma_factors': [[], [0]], 'index': 12, 'label': '2-32487-1.1-c1-0-12', 'leading_term': '3.01250909837', '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': 2, 'origin': 'EllipticCurve/Q/32487/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, -0.1770723006969986, -0.5696080800908824, -0.7738086317606118, -0.3181436469663764, 0.847111515849139, 1.962137356458052, 1.806221417672909, -0.1430062643893937, -2.719007059207378, -3.592858274319801, -1.424770340192526, 2.284559952643065, 4.020680100892325, 1.669648188723924, -2.857224411700114, -5.174121209552448, -3.147256111943653, 0.4465750312406943, 0.9561442053453566, -2.496032902790088, -5.67276667683643, -4.340479037341887, 0.2842229152956175, 2.854320727923013, 0.5385740524288841, -3.593225607528288, -4.786189882129681, -2.512433733970358, -0.1943736355072118, 0.05821464283831163, -0.3181191360130942, 0.2468244863858966, 0.661926193762015, -0.3979537763958585, -1.423852893053038, -0.1891073036213475, 2.199125544943272, 2.514138965114806, 0.4425646492435565, -0.9195609701462024, -0.1333175789346513, 0.5536112333687376, -0.3463295293139585, -0.7753082135221318, 0.7101691118583628, 1.639019763453207, 0.204121153518737, -0.2840822807016415, 3.272141502161329, 6.809098423776379, 4.479164397623822, -0.5121227408584269, 0.7512663207828324, 7.765192703049782, 8.72462672529275, -1.861477719368036, -12.98995126308143, -12.01274147378631, -2.249011332922657, 3.474060348476651, 1.438676229720151, -1.289867368093, -0.5835702488980172, 0.404627262081009, -0.07221784322914789, 0.4940438082519391, 2.150363305849935, 1.572318418491186, -1.05631690573974, -1.799153171149215, -0.1421662373858083, 0.6321954722369661, 0.02720295958559639, 0.3152983505697447, 0.9275371394748586, -0.1047425667286488, -0.9770343240158607, 0.5116424413253016, 1.576730223825384, -0.1420705210735381, -0.6875193347805184, 2.425303011862231, 3.347695317379392, -1.33373744667231, -3.484039184254767, 2.911296406714702, 8.461303135486341, 2.989986490770702, -6.206885892594974, -6.497483324786249, -0.7347710264271309, 0.6534072741518427, -1.238118600319581, 0.3958427825886356, 2.764229558005234, 0.6510214898366218, -0.8908718357752873, 3.35519986977401, 6.479154036042728, 1.73073713965161, -4.167472562781223, -3.095478979054535, 0.843408190818983, 1.044397317472518, -0.3196679532376326, 0.1854435702241193, 0.3117633862645314, -1.000714398209507, -0.9092750013912355, 0.4317006142158593, 0.3756502240435931, -0.04326322766074764, 0.6616057241825405, 0.2038079283253948, -1.428250115135831, -0.6537234162671194, 0.7514490051726281, -1.802370038103235, -3.590058051880747, 2.290846251237017], 'positive_zeros': ['1.080735801420912', '1.986162454255755', '2.846412935957008', '3.593841546693942', '4.461806330055660', '4.842197090028969', '5.734487478914867', '6.281852625874201', '7.294944526577764', '7.528675018339403', '7.925355981593068', '8.432424025840526', '9.019834367780571', '9.801029338079363', '10.27703159103685', '10.67787434344670', '11.15325751537467', '11.77895139440794', '12.03746686739496', '12.96373407108660', '13.21223139474747', '13.96562928484541', '14.81356790008228', '15.34969801087034', '15.84889360574452', '16.21353462055323', '16.39569551601022', '17.14914317631190', '17.77131978897967', '18.26738712514121', '18.38046084986607', '18.98326666040063', '19.43787722476939', '19.98354520044152'], 'prelabel': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1295265223762678770, 'z1': {'__RealLiteral__': 0, 'data': '1.080735801420912', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.986162454255755', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.846412935957008', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 259.4100010465337, 'bad_primes': [3, 7, 13, 17], 'central_character': '1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'dirichlet_coefficients': [1, -2, -1, 2, -3, 2, 0, 0, 1, 6, -6, -2, 1, 0, 3, -4, 1, -2, 1, -6, 0, 12, -5, 0, 4, -2, -1, 0, -1, -6, -1, 8, 6, -2, 0, 2, 2, -2, -1, 0, 6, 0, -5, -12, -3, 10, -7, 4, 0, -8, -1, 2, 5, 2, 18, 0, -1, 2, -4, 6, -10, 2, 0, -8, -3, -12, -8, 2, 5, 0, -10, 0, -7, -4, -4, 2, 0, 2, -11, 12, 1, -12, 9, 0, -3, 10, 1, 0, 5, 6, 0, -10, 1, 14, -3, -8, 13, 0, -6, 8], 'euler11': [1, 6, 11], 'euler13': [1, -1, 0], 'euler17': [1, -1, 0], 'euler19': [1, -1, 19], 'euler2': [1, 2, 2], 'euler23': [1, 5, 23], 'euler29': [1, 1, 29], 'euler3': [1, 1, 0], 'euler31': [1, 1, 31], 'euler37': [1, -2, 37], 'euler41': [1, -6, 41], 'euler43': [1, 5, 43], 'euler47': [1, 7, 47], 'euler5': [1, 3, 5], 'euler53': [1, -5, 53], 'euler59': [1, 4, 59], 'euler61': [1, 10, 61], 'euler67': [1, 8, 67], 'euler7': [1, 0, 0], 'euler71': [1, 10, 71], 'euler73': [1, 7, 73], 'euler79': [1, 11, 79], 'euler83': [1, -9, 83], 'euler89': [1, -5, 89], 'euler97': [1, -13, 97], 'euler_factors': [[1, 2, 2], [1, 1, 0], [1, 3, 5], [1, 0, 0], [1, 6, 11], [1, -1, 0], [1, -1, 0], [1, -1, 19], [1, 5, 23], [1, 1, 29], [1, 1, 31], [1, -2, 37], [1, -6, 41], [1, 5, 43], [1, 7, 47], [1, -5, 53], [1, 4, 59], [1, 10, 61], [1, 8, 67], [1, 10, 71], [1, 7, 73], [1, 11, 79], [1, -9, 83], [1, -5, 89], [1, -13, 97]], 'index': 12, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32487/a'], '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': '2-32487-1.1-c1-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 2, 'prelabel': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1295265223762678770, 'z1': {'__RealLiteral__': 0, 'data': '1.080735801420912', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1295265223762678770', 'Lhash_array': ['1295265223762678770'], 'label': '2-32487-1.1-c1-0-12', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32487/a'}