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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': '1963975111581066483', '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, 0, 23], [1, -6, 29], [1, 0, 31], [1, 2, 37], [1, 2, 41], [1, -12, 43], [1, 0, 47], [1, 10, 53], [1, 12, 59], [1, -10, 61], [1, -4, 67], [1, -8, 71], [1, 10, 73], [1, 8, 79], [1, 4, 83], [1, 10, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 11, 'label': '2-32487-1.1-c1-0-11', 'leading_term': '4.67981462941', '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/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.08409088323368, 1.658484561473262, 1.336086119232629, 0.1964226432973435, -1.001960522803255, -1.242351734110061, -0.1888867149333053, 1.247003636384506, 1.578280351591684, 0.3302337951196317, -1.093596478611567, -0.6200130829137682, 2.060886646238013, 4.581001125228041, 4.115008991502025, 0.7006649995517251, -2.350768303007195, -2.04743842919575, 0.6751800561512283, 2.040686836586868, 0.3167272242655668, -1.716829438839883, -0.3830125283278067, 3.619485574963894, 5.568089508533427, 2.750982741555789, -1.814120406561498, 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0.2103937028349449, -1.389530421765835, 0.5363240988375707, 3.085417529610934, 1.458380873700974, -1.333528789082238, -0.08577821509605801, 2.096433177005386, 0.02382224018145838, -2.676020217517061, -0.7689948309789556, 1.399369900758934, -1.401060463831212, -3.520022757420899, 1.083520105842197, 5.756039157205943, 2.922868352105871, -1.070661039362224, 2.171168479836548, 7.017152131637692, 4.758652020333416, -0.2194414340723668, 0.1351227573768527, 2.816790960379137, 1.717681722679787, -0.6048720841753168, -0.1754325737164205, 0.4063625909387367, -0.6877789178441733, -0.4801081023363074, 0.9374490570270143, 0.2315510524385797, -0.7228422422296216, 1.600269237448312, 3.420322778683449, 0.5654545632519454, -2.224928205911131, -0.5570887595747668, 1.027981569462148, -0.2714149460862988, 0.2901140963300999, 2.417684983369286, -0.8561153734226625, -7.128665112187417], 'positive_zeros': ['1.036476819782694', '1.781188984827314', '2.548229768256813', '3.073361872050615', '4.045358493863419', '4.690200434917036', '5.280026946003790', '5.777918444714075', '6.642767526082611', '7.339006318445019', '7.850384262366776', '8.250708236089537', '8.955033827211197', '9.383658786203668', '9.897186998237679', '10.24987852121666', '10.78017607433212', '11.42855211466595', '12.34508315647145', '12.79825323494695', '13.26889710379173', '13.86944574627533', '14.06821297054201', '14.55642282054943', '15.58958538878767', '15.73013259687924', '16.28923128676458', '17.20280871440041', '17.30397552065263', '18.01499756487380', '18.19434156735612', '18.78228952754428', '19.27297451634715', '19.70818146032447'], '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': 1963975111581066483, 'z1': {'__RealLiteral__': 0, 'data': '1.036476819782694', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.781188984827314', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.548229768256813', '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, 0, 3, -1, 1, 1, 0, 6, -2, 0, -5, -4, 1, 0, -1, -2, -4, -1, 6, -2, 0, 12, 4, 2, 0, 0, -1, 0, 1, -1, 1, -10, -1, -8, 0, 4, -6, -12, -2, 10, 0, 0, 7, -2, 4, 4, 1, 0, 0, 8, 3, -10, 2, -1, -4, 0, 1, -8, -2, 1, 2, -4, 0, -2, -12, 6, -12, -10, -2, 0, 0, 0, 0, 8, -5, -2, 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, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 2, 37], 'euler41': [1, 2, 41], 'euler43': [1, -12, 43], 'euler47': [1, 0, 47], 'euler5': [1, -2, 5], 'euler53': [1, 10, 53], 'euler59': [1, 12, 59], 'euler61': [1, -10, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, -8, 71], 'euler73': [1, 10, 73], 'euler79': [1, 8, 79], 'euler83': [1, 4, 83], 'euler89': [1, 10, 89], 'euler97': [1, 2, 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, 0, 23], [1, -6, 29], [1, 0, 31], [1, 2, 37], [1, 2, 41], [1, -12, 43], [1, 0, 47], [1, 10, 53], [1, 12, 59], [1, -10, 61], [1, -4, 67], [1, -8, 71], [1, 10, 73], [1, 8, 79], [1, 4, 83], [1, 10, 89], [1, 2, 97]], 'index': 11, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32487/e'], '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-c1-0-11', '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': 1963975111581066483, 'z1': {'__RealLiteral__': 0, 'data': '1.036476819782694', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1963975111581066483', 'Lhash_array': ['1963975111581066483'], 'label': '2-32487-1.1-c1-0-11', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32487/e'}