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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1737147375798749623', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1079.8968369357965, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, 1]], [7, [1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '135240.1', 'coefficient_field': '1.1.1.1', 'conductor': 135240, 'conductor_radical': 4830, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 1], [1], [1, -2, 11], [1, 4, 13], [1, -1, 17], [1, 2, 19], [1, 1], [1, -2, 29], [1, 0, 31], [1, 6, 37], [1, -9, 41], [1, 13, 43], [1, -8, 47], [1, -3, 53], [1, 5, 59], [1, 2, 61], [1, -13, 67], [1, 13, 71], [1, 16, 73], [1, -14, 79], [1, -4, 83], [1, -2, 89], [1, -17, 97]], 'gamma_factors': [[], [0]], 'index': 15, 'label': '2-135240-1.1-c1-0-15', 'leading_term': '2.05285347073', '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/135240/cp', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.052853470733449, 1.247217632407454, -0.6832745271491866, -2.358606426709631, -2.262133916566212, -0.2439729906427063, 1.863112078628961, 1.917259144846908, 0.02535715079000402, -1.316138560598288, -0.3102543586685244, 1.611026956778312, 1.657003025429028, -0.2181981031009446, -1.071345914893237, 0.5206674019224918, 2.016518302313023, 0.9328960155985065, -0.7548103868404167, 0.3811846095959405, 2.972113560324499, 2.24470517376887, -1.93004231254503, -3.683695616106164, -0.1040658797366853, 3.756436112210963, 2.77635650544739, -0.2750485051954604, -0.147574322019895, 1.898353672177351, 1.386905460063107, -0.6218026328288933, 0.01896818452819954, 2.029779023543402, 1.125757706542663, -1.304226539472189, -0.8734043691039008, 0.7686561030547262, -0.8567256469235757, -3.50700723932813, -2.258513484219344, 0.1775871897370835, -1.487967647046504, -3.778574331671979, -0.5436303818317394, 4.360415699023113, 3.602177017339991, -0.06518829356261575, -0.1212751735180354, 0.9404043998028148, -1.491519809092446, -3.232305348373187, -0.2703200193689156, 1.748287777411428, -1.247553920125911, -3.259911464477588, -0.6578365636136827, 0.99458971225836, -0.5485724976166299, -0.5179743220918256, 0.810583896415122, -1.032118885788509, -3.04609480999221, -0.6979780009367847, 0.8891412588335149, -2.443111649377732, -3.887753444099602, -0.08395597995496092, 1.322069621423272, -1.246077166319374, 0.2616846286796704, 4.645859607811427, 2.852072740095112, -2.156228986433396, -1.141486090759788, 2.52888885582664, 1.664938976722767, -0.02210641316409565, 1.098388513763116, 0.7160912954602175, -0.9836373791211149, 0.4292375361501259, 1.203109281088885, -2.301143765712608, -3.205093746041065, 0.93291467336285, 1.808787649626133, -0.9241034991982274, 0.3353418089436372, 2.227706270451909, -1.453629539342663, -3.525153355506369, 0.6885921819610556, 2.136476473468573, -1.144784638230331, -0.1215842056595675, 3.490364796729357, 1.758715598032359, -0.9034760994980587, 0.4887977132434268, 0.2796811770577456, -1.669635195718807, 0.8708750529341398, 3.404974316343998, 0.1135941109537619, -2.191419867771055, -0.2261056563181577, -0.5320766031598135, -1.684789726945834, 1.303443306245595, 2.626781606160209, 0.003710503179120263, 0.6592871025959955, 1.301279343848876, -5.3844161144565, -9.75597214193755, -4.06685170581078, 0.2815124686860679, -1.807715706782564, -1.153759203674126, 1.140105134490527], 'positive_zeros': ['0.4184575519738328', '1.274508825565234', '2.003013133990856', '2.538289004933283', '3.222236221268968', '3.689474861163252', '4.361560070801012', '4.711052732969954', '5.390805016355301', '6.005215560626970', '6.718495017687787', '7.018538448591297', '7.655299199450050', '7.997752225892111', '8.603658436471592', '9.105694032301749', '9.425119816213279', '10.21015609479749', '10.35767800989949', '11.02394091206513', '11.74329169095537', '12.01776596115701', '12.38401380259769', '13.01745158458092', '13.42104008412103', '14.05313494007871', '14.42245698911718', '14.82638068542215', '15.16074505352314', '15.80356762202677', '16.09599009208516', '16.75520410723943', '17.12922097005523', '17.48500375519625', '18.12605652865255', '18.56660759439210', '19.22398351107503', '19.27766140948054', '19.83499678669839'], 'prelabel': '2-135240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.861783836788234, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1737147375798749623, 'z1': {'__RealLiteral__': 0, 'data': '0.4184575519738328', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.274508825565234', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.003013133990856', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1079.8968369357965, 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '1.1', 'conductor': 135240, 'conductor_radical': 4830, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 2, 0, -4, 0, -1, 0, 1, 0, -2, 0, 0, 0, -1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, -6, 0, -4, 0, 9, 0, -13, 0, -1, 0, 8, 0, 0, 0, 1, 0, 3, 0, -2, 0, -2, 0, -5, 0, -2, 0, 0, 0, 4, 0, 13, 0, -1, 0, -13, 0, -16, 0, 1, 0, 0, 0, 14, 0, 1, 0, 4, 0, -1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 17, 0, 2, 0], 'euler11': [1, -2, 11], 'euler13': [1, 4, 13], 'euler17': [1, -1, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, -2, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 6, 37], 'euler41': [1, -9, 41], 'euler43': [1, 13, 43], 'euler47': [1, -8, 47], 'euler5': [1, 1, 0], 'euler53': [1, -3, 53], 'euler59': [1, 5, 59], 'euler61': [1, 2, 61], 'euler67': [1, -13, 67], 'euler7': [1, 0, 0], 'euler71': [1, 13, 71], 'euler73': [1, 16, 73], 'euler79': [1, -14, 79], 'euler83': [1, -4, 83], 'euler89': [1, -2, 89], 'euler97': [1, -17, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 0], [1, 0, 0], [1, -2, 11], [1, 4, 13], [1, -1, 17], [1, 2, 19], [1, 1, 0], [1, -2, 29], [1, 0, 31], [1, 6, 37], [1, -9, 41], [1, 13, 43], [1, -8, 47], [1, -3, 53], [1, 5, 59], [1, 2, 61], [1, -13, 67], [1, 13, 71], [1, 16, 73], [1, -14, 79], [1, -4, 83], [1, -2, 89], [1, -17, 97]], 'index': 15, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/135240/cp'], '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': '2-135240-1.1-c1-0-15', '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': '2-135240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.861783836788234, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1737147375798749623, 'z1': {'__RealLiteral__': 0, 'data': '0.4184575519738328', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1737147375798749623', 'Lhash_array': ['1737147375798749623'], 'label': '2-135240-1.1-c1-0-15', 'type': 'ECQ', 'url': 'EllipticCurve/Q/135240/cp'}