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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '2168220973155940975', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '369600.1', 'coefficient_field': '1.1.1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1, 1], [1, -1], [1, 5, 13], [1, -3, 17], [1, -3, 19], [1, 4, 23], [1, 0, 29], [1, -10, 31], [1, -1, 37], [1, 7, 41], [1, -10, 43], [1, 10, 47], [1, -1, 53], [1, -6, 59], [1, 1, 61], [1, 5, 67], [1, 9, 71], [1, -11, 73], [1, 14, 79], [1, -4, 83], [1, -6, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 111, 'label': '2-369600-1.1-c1-0-111', 'leading_term': '2.59753283961', '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/369600/on', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.597532839611996, 1.527740059720186, -0.8195604634328651, -2.305608040681215, -1.301054719792746, 1.17505476404946, 2.090987949852081, 0.1654474028666546, -2.083439152511787, -1.694019713800459, 0.3369939907531737, 0.7031491506199565, -0.6197802525313989, -0.3085727260138398, 2.096204850432237, 2.734493482995754, 0.371276258900858, -0.6229510538219829, 2.033707106669316, 3.783860137339962, 1.484011229952058, -0.05250302769177367, 3.209375994970925, 6.144642369388204, 3.473403524306249, -0.1232559388277645, 1.224289663440476, 3.548003452407299, 1.432049783922462, -1.334694915211784, -0.262111728804464, 0.731385071662969, -1.247086957092395, -1.34925240505055, 1.798396244393737, 1.997402105988013, -1.385549608936288, -1.799326900745628, 0.6428621611103383, 0.5004127214289066, -0.4838513450181568, 0.7020526531096417, -1.296029508496761, -7.6482033131978, -8.239497500174657, -0.8600249955092522, 3.010138847607588, 0.3241730145020629, -0.2050383483237027, 1.461385406169145, -0.7550031746326356, -2.448321435945696, 1.123500759925974, 2.885637334784269, -0.1775515335350924, -0.6023725351019614, 1.809046086072029, 0.9518631252626794, -0.1622081793325555, 1.756202242303164, 0.9740429478584895, -2.080910972819206, -0.2741934274118863, 2.446328963074201, 0.04145123458051474, -0.6231451865508154, 2.907819500396595, 1.734552998665411, -2.122014158523158, 0.1428965232510055, 2.479959294262538, -0.7824038578281142, -0.2833300140300484, 4.950852492068966, 3.932693183306505, -0.6660556161561454, -0.0574982680623975, 0.991275480667873, -0.672881280959656, 0.3504950932158886, 1.298520009000303, -1.172889466115593, -0.2227587516163086, 3.086541019474623, 0.9934148939744346, -0.7457225151616823, 2.648105627361849, 2.305548550620855, -1.214827982922489, 0.4395049493151925, 1.415099561255001, -1.671372698046217, 0.4142146124136067, 3.413691826521387, -2.492051353082366, -6.875770742758273, -2.331879769081471, 0.3822002617037228, 0.01907126863247141, 2.739310755647725, 2.725318367751365, -0.6085059104778703, 0.5740408768448498, 1.69794601468423, -1.035472310111429, -0.007649662110072153, 2.403446640365886, 0.4115558201734015, 0.6069678040635486, 1.939846093770316, -2.321098701635679, -3.475581009547725, 0.8063774420219219, -1.481470133786548, -5.135477538708215, -0.5591109140327389, 1.378417262169472, -1.998431763932463, -0.05747603276395294, 2.091411198440073, -0.4341317212738049], 'positive_zeros': ['0.4152647462078905', '1.131491372261151', '1.765075552548590', '2.453312748184026', '2.884966272373617', '3.289185304195719', '4.037960063712602', '4.336066296127704', '5.155433359446327', '5.262050807919402', '6.230667512406352', '6.382363838823954', '7.099299732716836', '7.531259855106902', '7.865549422556854', '8.364137781223687', '8.898416441107478', '9.425210904210859', '9.829455134941953', '10.12077512904793', '10.42414588598834', '11.27929614766359', '11.78008474258137', '12.02667298315235', '12.44585034934942', '12.93704465194974', '13.48553427506130', '13.81086257286816', '14.37143554869912', '14.53643658035216', '15.06971898436213', '15.51707758959421', '16.00322090220049', '16.30124231627497', '16.84201487330787', '17.24187056705212', '17.69658719355679', '18.01509058471687', '18.69669586412195', '19.00605097440077', '19.39389011578743', '19.71131752038362'], 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2168220973155940975, 'z1': {'__RealLiteral__': 0, 'data': '0.4152647462078905', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.131491372261151', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.765075552548590', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 1, 0, -5, 0, 0, 0, 3, 0, 3, 0, -1, 0, -4, 0, 0, 0, 1, 0, 0, 0, 10, 0, 1, 0, 0, 0, 1, 0, -5, 0, -7, 0, 10, 0, 0, 0, -10, 0, 1, 0, 3, 0, 1, 0, 0, 0, 3, 0, 6, 0, -1, 0, -1, 0, 0, 0, -5, 0, -4, 0, -9, 0, 11, 0, 0, 0, -1, 0, -14, 0, 1, 0, 4, 0, 0, 0, 0, 0, 6, 0, 5, 0, 10, 0, 0, 0, 6, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, 5, 13], 'euler17': [1, -3, 17], 'euler19': [1, -3, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, 0, 29], 'euler3': [1, -1, 0], 'euler31': [1, -10, 31], 'euler37': [1, -1, 37], 'euler41': [1, 7, 41], 'euler43': [1, -10, 43], 'euler47': [1, 10, 47], 'euler5': [1, 0, 0], 'euler53': [1, -1, 53], 'euler59': [1, -6, 59], 'euler61': [1, 1, 61], 'euler67': [1, 5, 67], 'euler7': [1, 1, 0], 'euler71': [1, 9, 71], 'euler73': [1, -11, 73], 'euler79': [1, 14, 79], 'euler83': [1, -4, 83], 'euler89': [1, -6, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, 1, 0], [1, -1, 0], [1, 5, 13], [1, -3, 17], [1, -3, 19], [1, 4, 23], [1, 0, 29], [1, -10, 31], [1, -1, 37], [1, 7, 41], [1, -10, 43], [1, 10, 47], [1, -1, 53], [1, -6, 59], [1, 1, 61], [1, 5, 67], [1, 9, 71], [1, -11, 73], [1, 14, 79], [1, -4, 83], [1, -6, 89], [1, -6, 97]], 'index': 111, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/on'], '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': '2-369600-1.1-c1-0-111', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2168220973155940975, 'z1': {'__RealLiteral__': 0, 'data': '0.4152647462078905', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2168220973155940975', 'Lhash_array': ['2168220973155940975'], 'label': '2-369600-1.1-c1-0-111', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/on'}