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lfunc_lfunctions • Show schema
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{'A10': 3, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': -3, 'A6': 0, 'A7': 1, 'A8': -1, 'A9': 0, 'Lhash': '1130813537957583751', 'a10': [0.9486832980505138, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-1.3416407864998738, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 228.10065841398966, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [23, [1]]], 'bad_primes': [2, 3, 23], 'central_character': '28566.1', 'coefficient_field': '1.1.1.1', 'conductor': 28566, 'conductor_radical': 138, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 3, 5], [1, -1, 7], [1, -3, 11], [1, 4, 13], [1, 0, 17], [1, 2, 19], [1], [1, -6, 29], [1, -5, 31], [1, 2, 37], [1, 6, 41], [1, -10, 43], [1, -6, 47], [1, 9, 53], [1, -12, 59], [1, 8, 61], [1, 14, 67], [1, 0, 71], [1, 7, 73], [1, 8, 79], [1, -3, 83], [1, -18, 89], [1, -1, 97]], 'gamma_factors': [[], [0]], 'index': 10, 'label': '2-28566-1.1-c1-0-10', 'leading_term': '3.10208004036', '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/28566/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.6990819861086754, 0.951244145394387, 0.4468325887121968, -0.6713690490831214, -1.631031023154626, -1.44393325608876, 0.1779890209334356, 2.221023550923537, 2.955151738123365, 1.540426569288896, -0.8376456278870676, -1.800928777582496, -0.1775550705520808, 2.499483718270254, 3.4233435318519, 1.708023175327233, -0.3524058340812471, 0.06713972873497309, 2.560082061462302, 3.446695819480285, 0.1721551629785264, -5.024476026023809, -7.178845393357779, -4.381709558945776, -0.06762698904287406, 1.27801254996588, -0.5408444992581476, -1.996852234225128, -1.099177975547969, 0.2732434825543711, -0.07286259694557592, -1.108415783311279, -0.5965456049486979, 0.8816911131004058, 0.7836219797126074, -0.8621609649356006, -0.994118824442484, 1.493591744422406, 3.40271773083882, 1.998755312562264, -0.4693326270770176, -0.1865167544992916, 2.09925653944752, 2.391304235410185, 0.1108913418203773, -1.201211113770224, -0.2554024261158383, 0.03998815441369225, -1.183537527985342, -0.04995940395389639, 4.725867732007253, 6.8782276093888, 0.9547375920322109, -7.876575254034247, -9.710717551415964, -3.913604802618615, 0.693287713848546, -0.4584444674802674, -2.356001774541208, -0.6590866634788023, 1.350076285767774, 0.1534834045426034, -1.301337107389463, 0.2362918377672959, 1.847894981743319, 0.1719259849635262, -1.946325043934557, -0.8272795557944064, 1.133482546438933, 0.4992214541794667, -0.1960416608647425, 2.48819479880645, 5.45935969404571, 4.122211710732429, 0.5870229673734595, -0.4844163388097717, 0.1115976987411963, -0.5042732840104902, -0.7975321471468457, 0.9200320282519062, 1.298687015999978, -1.391572834213582, -1.980839470932313, 2.147269080430282, 4.13261078049256, -0.7352966305674123, -5.270445892331453, -2.603064222022065, 1.315200275658227, -1.033219799487903, -4.75257711808003, -2.410177055257782, 1.775426399512116, 0.6661025192862589, -2.314547488430237, -1.142479449848023, 0.9425464334722538, -0.5157167840867762, -1.374085833675951, 1.871223297569982, 3.805886835232421, 0.937995541383402, -0.6829628671105389, 2.7195003628685, 5.278317676808281, 2.976665258180885, 0.2419577038933274, 0.06858581246572928, -0.2143124405927281, -0.9373553219136976, 0.1241874236201367, 0.6818896750889758, -1.781041497894311, -2.966598160404523, -0.09081832647763191, 0.829897754474274, -3.345462064138685, -5.408007732374915, -1.774708575225347, 0.4004051914825585], 'positive_zeros': ['0.8595831211664469', '1.728618804938094', '2.658009140212916', '3.266758360267214', '4.188660563979319', '4.490901924937799', '5.258525174349598', '6.255131964865060', '6.691302078715823', '7.426786857726018', '7.733331211376820', '8.346078210322909', '8.873315899420236', '9.370297569176822', '10.18677451939172', '10.52339100895060', '11.26155004513572', '11.81059881045570', '12.01154234475471', '12.50361610202890', '13.27570413810657', '14.18036486154823', '14.45711489610508', '15.05887791208402', '15.51731793770337', '15.97581519434323', '16.51529085806788', '17.08501035533523', '17.58666368500860', '17.79012347738132', '18.81300324675129', '19.17943048912894', '19.36364699231217', '19.88469191007811'], 'prelabel': '2-28566-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.103001635899721, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1130813537957583751, 'z1': {'__RealLiteral__': 0, 'data': '0.8595831211664469', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.728618804938094', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.658009140212916', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 228.10065841398966, 'bad_primes': [2, 3, 23], 'central_character': '1.1', 'conductor': 28566, 'conductor_radical': 138, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, -3, 0, 1, -1, 0, 3, 3, 0, -4, -1, 0, 1, 0, 0, -2, -3, 0, -3, 0, 0, 4, 4, 0, 1, 6, 0, 5, -1, 0, 0, -3, 0, -2, 2, 0, 3, -6, 0, 10, 3, 0, 0, 6, 0, -6, -4, 0, -4, -9, 0, -9, -1, 0, -6, 12, 0, -8, -5, 0, 1, 12, 0, -14, 0, 0, 3, 0, 0, -7, 2, 0, -2, 3, 0, -8, -3, 0, 6, 3, 0, 0, -10, 0, -3, 18, 0, -4, 0, 0, -6, 6, 0, 1, 6, 0, 4], 'euler11': [1, -3, 11], 'euler13': [1, 4, 13], 'euler17': [1, 0, 17], 'euler19': [1, 2, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 0], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -5, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, -10, 43], 'euler47': [1, -6, 47], 'euler5': [1, 3, 5], 'euler53': [1, 9, 53], 'euler59': [1, -12, 59], 'euler61': [1, 8, 61], 'euler67': [1, 14, 67], 'euler7': [1, -1, 7], 'euler71': [1, 0, 71], 'euler73': [1, 7, 73], 'euler79': [1, 8, 79], 'euler83': [1, -3, 83], 'euler89': [1, -18, 89], 'euler97': [1, -1, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 3, 5], [1, -1, 7], [1, -3, 11], [1, 4, 13], [1, 0, 17], [1, 2, 19], [1, 0, 0], [1, -6, 29], [1, -5, 31], [1, 2, 37], [1, 6, 41], [1, -10, 43], [1, -6, 47], [1, 9, 53], [1, -12, 59], [1, 8, 61], [1, 14, 67], [1, 0, 71], [1, 7, 73], [1, 8, 79], [1, -3, 83], [1, -18, 89], [1, -1, 97]], 'index': 10, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/28566/d'], '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': '2-28566-1.1-c1-0-10', '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': '2-28566-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.103001635899721, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1130813537957583751, 'z1': {'__RealLiteral__': 0, 'data': '0.8595831211664469', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1130813537957583751', 'Lhash_array': ['1130813537957583751'], 'label': '2-28566-1.1-c1-0-10', 'type': 'ECQ', 'url': 'EllipticCurve/Q/28566/d'}