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lfunc_lfunctions • Show schema
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{'A10': 2, 'A2': -1, 'A3': 1, 'A4': -1, 'A5': -2, 'A6': -1, 'A7': 0, 'A8': 3, 'A9': 1, 'Lhash': '1395961218557726007', 'a10': [0.6324555320336759, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [-0.5, 0], 'a5': [-0.8944271909999159, 0], 'a6': [-0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [1.0606601717798212, 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, 1, 2], [1, -1], [1, 2, 5], [1], [1, -4, 11], [1, 1], [1, 1], [1, 4, 19], [1, 8, 23], [1, 6, 29], [1, -8, 31], [1, -2, 37], [1, 6, 41], [1, 4, 43], [1, -12, 47], [1, -6, 53], [1, 0, 59], [1, -14, 61], [1, -8, 67], [1, 8, 71], [1, 2, 73], [1, -8, 79], [1, 0, 83], [1, -14, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 8, 'label': '2-32487-1.1-c1-0-8', 'leading_term': '3.38921937692', '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/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.7626883743615727, 1.031913748983448, 0.4699710672326416, -0.7649609085578477, -1.850810086396816, -1.786031272083524, -0.3775036009690563, 1.198781249847215, 1.15782456048683, -1.145894022279032, -4.184773711265547, -5.395969791289308, -3.731604638667022, -0.8867853002859204, 0.5295097649420075, 0.05944525549944188, -0.1104386887323667, 1.724854744113364, 3.841721292107291, 2.664823535560833, -2.360815670896978, -6.883476820957191, -6.111440006343169, -0.6911658854850063, 3.683707696774855, 2.973582342634218, -0.6511382170871969, -2.242919144321368, -0.5706753984449906, 1.168337738691223, 0.6290507501911576, -0.6625912329433161, -0.5646652232586657, 0.1162625721761205, -0.431076130728063, -1.412457943076783, -0.789332494061054, 0.7345340802677114, 0.6013015197538787, -0.8089000445546387, -0.2311099385614489, 2.597629532505132, 3.340173946868844, -0.1554622894963779, -3.500206072687326, -2.178679624494484, 1.071983049190326, 0.7214149683136395, -2.05935203761424, -1.17859736857963, 3.708977502151968, 5.942843569133777, 2.728577451790655, -0.3733039249729405, 0.8830594101413043, 2.579927559549712, 0.4033877765537022, -2.428685946335098, -1.464664619566488, 0.4720491539075179, -1.338676045410748, -4.281837298540411, -2.948242958666937, 0.712148600324567, 0.7130318514791207, -2.175892995153906, -2.226030997747242, 0.5798511736888216, 1.182319454977537, -0.5025888258990056, 0.2094151771813876, 3.176808026132588, 3.515568523086277, 0.9078871172634442, -0.2482147542957654, 0.6296363101896608, 0.3982389437759832, -0.5382676831538316, 0.2775113588149279, 1.05216083781981, -0.2159296119592243, 0.5667296282101033, 6.11473221514545, 9.481708890575103, 4.349599232828489, -2.793398235450645, -2.923804793805585, 0.4257731850941066, -0.4626212749457624, -2.395397299691153, 1.001205301487899, 5.161748586830862, 3.228413420831252, -0.1066516334346594, 1.872879307293033, 4.25652616662318, 0.6661515786200843, -3.511164849074112, -1.693223534211591, 1.285521182227384, -0.4608945461023406, -2.670299661270274, -0.7970774062467753, 1.105963256513891, -0.1658147846355227, -0.9302747972413818, 0.410368209672474, 0.5513631258493219, -0.4268397709296731, 0.2605258622821295, 0.8723505507511395, -0.4652974561570426, -0.2656848067424662, 1.561406631792317, -1.707699883932892, -9.36244039805193, -10.54138866792977, -3.436843833736379, 0.7493514057620717, -1.524793179906698], 'positive_zeros': ['0.8548692494929604', '1.802433492934002', '2.399606992831752', '3.607663926435165', '4.019301747726851', '4.279593592685560', '5.146170514380349', '6.029371079418115', '6.703361331226486', '7.311370453378898', '7.856607693604781', '8.429636231141922', '8.634241767125698', '9.369898431090872', '9.852950240710379', '10.27516392441236', '10.99140580344956', '11.65261097274765', '12.06425819404636', '12.56933198350827', '13.43972213510813', '13.65536449899501', '14.27807071094766', '14.90149806434437', '15.13391120157892', '15.94055246513326', '16.31551201738035', '16.94585299103991', '17.41827727801681', '17.72829236250738', '18.61513621708176', '18.84056579320872', '19.33449058970157', '19.70105442237944'], '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': 1395961218557726007, 'z1': {'__RealLiteral__': 0, 'data': '0.8548692494929604', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.802433492934002', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.399606992831752', '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, -1, 1, -1, -2, -1, 0, 3, 1, 2, 4, -1, -1, 0, -2, -1, -1, -1, -4, 2, 0, -4, -8, 3, -1, 1, 1, 0, -6, 2, 8, -5, 4, 1, 0, -1, 2, 4, -1, -6, -6, 0, -4, -4, -2, 8, 12, -1, 0, 1, -1, 1, 6, -1, -8, 0, -4, 6, 0, 2, 14, -8, 0, 7, 2, -4, 8, 1, -8, 0, -8, 3, -2, -2, -1, 4, 0, 1, 8, 2, 1, 6, 0, 0, 2, 4, -6, 12, 14, 2, 0, 8, 8, -12, 8, -5, -10, 0, 4, 1], 'euler11': [1, -4, 11], 'euler13': [1, 1, 0], 'euler17': [1, 1, 0], 'euler19': [1, 4, 19], 'euler2': [1, 1, 2], 'euler23': [1, 8, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, -12, 47], 'euler5': [1, 2, 5], 'euler53': [1, -6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -14, 61], 'euler67': [1, -8, 67], 'euler7': [1, 0, 0], 'euler71': [1, 8, 71], 'euler73': [1, 2, 73], 'euler79': [1, -8, 79], 'euler83': [1, 0, 83], 'euler89': [1, -14, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 1, 2], [1, -1, 0], [1, 2, 5], [1, 0, 0], [1, -4, 11], [1, 1, 0], [1, 1, 0], [1, 4, 19], [1, 8, 23], [1, 6, 29], [1, -8, 31], [1, -2, 37], [1, 6, 41], [1, 4, 43], [1, -12, 47], [1, -6, 53], [1, 0, 59], [1, -14, 61], [1, -8, 67], [1, 8, 71], [1, 2, 73], [1, -8, 79], [1, 0, 83], [1, -14, 89], [1, 10, 97]], 'index': 8, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32487/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': '2-32487-1.1-c1-0-8', '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': 1395961218557726007, 'z1': {'__RealLiteral__': 0, 'data': '0.8548692494929604', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1395961218557726007', 'Lhash_array': ['1395961218557726007'], 'label': '2-32487-1.1-c1-0-8', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32487/d'}