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lfunc_lfunctions • Show schema
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{'A10': -4, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': 4, 'A6': 1, 'A7': -4, 'A8': -1, 'A9': 1, 'Lhash': '33206018265108246', 'a10': [-1.2649110640673518, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [1.7888543819998317, 0], 'a6': [0.4082482904638631, 0], 'a7': [-1.5118578920369088, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 102.86328788381344, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [19, [1, -1]], [113, [1, -1]]], 'bad_primes': [2, 3, 19, 113], 'central_character': '12882.1', 'coefficient_field': '1.1.1.1', 'conductor': 12882, 'conductor_radical': 12882, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, -4, 5], [1, 4, 7], [1, 0, 11], [1, 0, 13], [1, 6, 17], [1, -1], [1, -6, 23], [1, 6, 29], [1, -10, 31], [1, 12, 37], [1, -10, 41], [1, 4, 43], [1, 6, 47], [1, -2, 53], [1, 12, 59], [1, -6, 61], [1, 8, 67], [1, 0, 71], [1, 10, 73], [1, -10, 79], [1, -12, 83], [1, -6, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 7, 'label': '2-12882-1.1-c1-0-7', 'leading_term': '3.30034163647', '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/12882/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.77862204597929, 1.266834531381219, 1.178875333315251, 0.4181567516735561, -0.6929867027964477, -1.450533817321535, -1.220499660276211, -0.05105548507712643, 1.128282568319428, 1.13307935390324, -0.3241202556126496, -1.975991552539854, -1.746749966391656, 1.372852807352973, 5.934064215931547, 8.737468959330318, 7.456169084868739, 2.890431816587809, -1.513874875013852, -2.728253580800574, -0.8495230778342766, 1.359962217424247, 1.591977046912745, 0.2690649188309721, -0.5621471945193599, 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-1.243080908716891, 0.6137745155662414, 0.9118607517365589, -2.591149102355458, -5.330298787511892, -2.816560580490149, 1.666951271912944, 2.158047267885017, -0.3351998000349793, -0.2176414976197925, 2.635857317639793, 3.034400156885598, 0.177783484264638, -1.106609689026597, 0.2222240562171344, -0.5576779001322972, -3.945836137981208, -3.125603067261794, 4.533134695097694, 11.01925502159186, 8.966785717167365, 2.48411984996104, -0.3364113157319716, 0.3866513371311355, -0.4259974405222878, -2.509223940847922, -1.981200785923031, 0.2581836382721175, 0.4467373008178085, -0.5403274838851841, 0.2209471179081354, 0.446154763671294, -3.562202061541832, -8.418303007470154, -7.736985529810723, -2.697595655719006, 0.09093932176147901, -0.6563351532682375, -0.8328947297763076, 0.4205751929576005, 0.563482264731096, -0.02277176205804385, 0.2886136326578552, -0.496969091355742, -3.034310082561284], 'positive_zeros': ['1.095993255036032', '2.009209144097549', '2.706198156886974', '3.413360827621125', '4.649022605793482', '5.332607180305933', '6.050929062842574', '6.582336018165581', '6.728617772844334', '7.636579962842694', '8.924632692064198', '9.038728106102049', '9.599995787581816', '10.27649765417188', '10.51154304758590', '11.23111606754041', '12.00567540508149', '12.73292644138163', '13.21962386723922', '13.45882883913358', '14.19292412022844', '15.08259308484567', '15.59317270232023', '16.17062216510382', '16.71057692986472', '17.19405544370187', '17.60693548091608', '17.97925723321198', '18.69335888982539', '19.17723577011636', '19.58812139492975'], 'prelabel': '2-12882-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.142154006117904, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 33206018265108246, 'z1': {'__RealLiteral__': 0, 'data': '1.095993255036032', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.009209144097549', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.706198156886974', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 102.86328788381344, 'bad_primes': [2, 3, 19, 113], 'central_character': '1.1', 'conductor': 12882, 'conductor_radical': 12882, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 4, 1, -4, -1, 1, -4, 0, -1, 0, 4, -4, 1, -6, -1, 1, 4, 4, 0, 6, 1, 11, 0, -1, -4, -6, 4, 10, -1, 0, 6, -16, 1, -12, -1, 0, -4, 10, -4, -4, 0, 4, -6, -6, -1, 9, -11, 6, 0, 2, 1, 0, 4, -1, 6, -12, -4, 6, -10, -4, 1, 0, 0, -8, -6, -6, 16, 0, -1, -10, 12, -11, 1, 0, 0, 10, 4, 1, -10, 12, 4, -24, 4, 6, 0, 6, -4, 0, 6, -10, 6, 4, 1, 6, -9, 0, 11], 'euler11': [1, 0, 11], 'euler13': [1, 0, 13], 'euler17': [1, 6, 17], 'euler19': [1, -1, 0], 'euler2': [1, 1, 0], 'euler23': [1, -6, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -10, 31], 'euler37': [1, 12, 37], 'euler41': [1, -10, 41], 'euler43': [1, 4, 43], 'euler47': [1, 6, 47], 'euler5': [1, -4, 5], 'euler53': [1, -2, 53], 'euler59': [1, 12, 59], 'euler61': [1, -6, 61], 'euler67': [1, 8, 67], 'euler7': [1, 4, 7], 'euler71': [1, 0, 71], 'euler73': [1, 10, 73], 'euler79': [1, -10, 79], 'euler83': [1, -12, 83], 'euler89': [1, -6, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, -4, 5], [1, 4, 7], [1, 0, 11], [1, 0, 13], [1, 6, 17], [1, -1, 0], [1, -6, 23], [1, 6, 29], [1, -10, 31], [1, 12, 37], [1, -10, 41], [1, 4, 43], [1, 6, 47], [1, -2, 53], [1, 12, 59], [1, -6, 61], [1, 8, 67], [1, 0, 71], [1, 10, 73], [1, -10, 79], [1, -12, 83], [1, -6, 89], [1, -6, 97]], 'index': 7, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/12882/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': '2-12882-1.1-c1-0-7', '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': '2-12882-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.142154006117904, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 33206018265108246, 'z1': {'__RealLiteral__': 0, 'data': '1.095993255036032', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '33206018265108246', 'Lhash_array': ['33206018265108246'], 'label': '2-12882-1.1-c1-0-7', 'type': 'ECQ', 'url': 'EllipticCurve/Q/12882/e'}