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lfunc_lfunctions • Show schema
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{'A10': -2, 'A2': 2, 'A3': 1, 'A4': 2, 'A5': -1, 'A6': 2, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '2059086730351255613', 'a10': [-0.6324555320336759, 0], 'a2': [1.414213562373095, 0], 'a3': [0.5773502691896258, 0], 'a4': [1.0, 0], 'a5': [-0.4472135954999579, 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, 1, 5], [1], [1, -2, 11], [1, 1], [1, 1], [1, -7, 19], [1, 9, 23], [1, -3, 29], [1, 3, 31], [1, 2, 37], [1, -10, 41], [1, -3, 43], [1, 9, 47], [1, -5, 53], [1, -12, 59], [1, -10, 61], [1, 8, 67], [1, -2, 71], [1, 13, 73], [1, -1, 79], [1, 1, 83], [1, -11, 89], [1, 17, 97]], 'gamma_factors': [[], [0]], 'index': 16, 'label': '2-32487-1.1-c1-0-16', 'leading_term': '12.8403352361', '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/32487/q', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 3.067145716457318, 5.232239170423535, 5.574677214993018, 3.703498784887796, 0.4150925028278217, -2.455965604040738, -3.241397303953039, -1.810162434608454, 0.2527161652611795, 1.072061705986602, 0.2431220275009388, -0.9251902410829725, -1.016341255817865, -0.1272637050054097, 0.4708022037937115, 0.1898135153312593, -0.02618761525608909, 0.8440053526121453, 2.131970282281975, 2.165919797660812, 0.7821933388327197, -0.03316513546555351, 1.152054336498144, 2.800316438077961, 2.264754009742773, -0.1584527318217693, -1.094917687480497, 1.11009632462633, 3.4821638292199, 2.471400701401643, -0.388052899729979, -0.188882983422269, 3.788958029689441, 6.056798722794711, 2.636522528112342, -2.509838042073979, -2.817673636215663, 0.9931383711485383, 1.786757060736108, -2.894087816199569, -6.431099564078409, -2.774708711337559, 4.35499280209549, 6.794225863584085, 3.337566895566127, -0.06597877614228538, -0.09775197562077749, 0.3928137607112577, -0.8822768456155472, -1.666581387051185, -0.157162354049628, 1.286031530628388, 0.5090644614804832, -0.6622555387286808, -0.2057277779027448, 0.4622246280209608, -0.1415860000866366, -0.4843155377858143, 0.3422263522148472, 0.0714985195630792, -2.068442044251195, -2.810274127294115, -0.8726127284118173, 0.1488570115414577, -0.3287922782141918, 3.760969102899013, 13.88781094193684, 19.75611290617301, 13.2045086307285, 2.332534836482263, -0.2280213484970582, 2.888438741884274, -0.07961367238147389, -8.552936552173813, -10.57656459596841, -3.695949619158857, 1.619853539277824, 0.2414631646205046, -1.444631047537378, 0.4178299587220895, 1.419550502021885, -0.2112985452141589, -0.096990559424294, 2.460624054299364, 2.805068288457628, 0.4534525677670781, -0.3178288907635915, 0.709962626298056, 0.242250238713309, -0.8913925889223634, -0.03433882333699637, 0.6933064824956462, -1.213634943455794, -2.658951758919303, -1.089662108981324, 0.1991497129551802, -0.6701350487055402, -0.4773737455937738, 0.7160795329288367, -1.2500321241659, -4.086379813669361, -1.412371330735648, 3.316479621710518, 1.416748680560853, -3.640778001442801, -1.996607364745755, 2.927733099968766, 1.234516426582436, -2.820399985738841, 0.446806525015791, 4.89296980802037, -0.06135579414482128, -6.726090125858169, -2.245103319013023, 6.827946413987992, 6.610133791984345, 0.2512550865256103, -1.186701586680449, 0.9646792169081185, 0.09444427443734568], 'positive_zeros': ['1.280584055195388', '2.214289509273674', '2.796065352426352', '3.534043100444259', '4.111205876761376', '4.270506538206435', '5.434538235427940', '5.527690842354169', '6.483106466391201', '6.904399562058139', '7.708091633158551', '8.017096735633975', '8.865640503983461', '9.435597453327073', '9.868359292124485', '10.59476406345872', '11.49042472320857', '11.77538696832965', '12.10898108768541', '12.76889878816532', '13.33414529042622', '13.80128122002895', '14.21015160906822', '14.65619003777378', '15.01153499221865', '15.88007797270302', '16.06352298320583', '16.31139759330158', '17.60166013861858', '17.77270925534592', '18.24728702802517', '19.13353720425795', '19.52059058179411', '19.95741057992160'], 'prelabel': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2059086730351255613, 'z1': {'__RealLiteral__': 0, 'data': '1.280584055195388', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.214289509273674', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.796065352426352', '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, -1, 2, 0, 0, 1, -2, 2, 2, -1, 0, -1, -4, -1, 2, 7, -2, 0, 4, -9, 0, -4, -2, 1, 0, 3, -2, -3, -8, 2, -2, 0, 2, -2, 14, -1, 0, 10, 0, 3, 4, -1, -18, -9, -4, 0, -8, -1, -2, 5, 2, -2, 0, 7, 6, 12, -2, 10, -6, 0, -8, 1, 4, -8, -2, -9, 0, 2, 0, -13, -4, -4, 14, 0, -2, 1, 4, 1, 20, -1, 0, 1, 6, 3, 0, 11, -2, 0, -18, -3, -18, -7, -8, -17, 0, 2, -8], 'euler11': [1, -2, 11], 'euler13': [1, 1, 0], 'euler17': [1, 1, 0], 'euler19': [1, -7, 19], 'euler2': [1, -2, 2], 'euler23': [1, 9, 23], 'euler29': [1, -3, 29], 'euler3': [1, -1, 0], 'euler31': [1, 3, 31], 'euler37': [1, 2, 37], 'euler41': [1, -10, 41], 'euler43': [1, -3, 43], 'euler47': [1, 9, 47], 'euler5': [1, 1, 5], 'euler53': [1, -5, 53], 'euler59': [1, -12, 59], 'euler61': [1, -10, 61], 'euler67': [1, 8, 67], 'euler7': [1, 0, 0], 'euler71': [1, -2, 71], 'euler73': [1, 13, 73], 'euler79': [1, -1, 79], 'euler83': [1, 1, 83], 'euler89': [1, -11, 89], 'euler97': [1, 17, 97], 'euler_factors': [[1, -2, 2], [1, -1, 0], [1, 1, 5], [1, 0, 0], [1, -2, 11], [1, 1, 0], [1, 1, 0], [1, -7, 19], [1, 9, 23], [1, -3, 29], [1, 3, 31], [1, 2, 37], [1, -10, 41], [1, -3, 43], [1, 9, 47], [1, -5, 53], [1, -12, 59], [1, -10, 61], [1, 8, 67], [1, -2, 71], [1, 13, 73], [1, -1, 79], [1, 1, 83], [1, -11, 89], [1, 17, 97]], 'index': 16, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32487/q'], '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-c1-0-16', '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': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2059086730351255613, 'z1': {'__RealLiteral__': 0, 'data': '1.280584055195388', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '2059086730351255613', 'Lhash_array': ['2059086730351255613'], 'label': '2-32487-1.1-c1-0-16', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32487/q'}