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lfunc_lfunctions • Show schema
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{'Lhash': '1071786728919402068823648598585', 'a10': -1, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': 1, 'a6': 0, 'a7': 2, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.27826216393724, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1, -1]], [31, [1, -1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '2790.1', 'coefficient_field': '1.1.1.1', 'conductor': 2790, 'conductor_radical': 930, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, -1], [1, -2, 7], [1, 0, 11], [1, 4, 13], [1, 6, 17], [1, -8, 19], [1, 0, 23], [1, 0, 29], [1, -1], [1, 4, 37], [1, -6, 41], [1, -8, 43], [1, -12, 47], [1, -6, 53], [1, -6, 59], [1, -2, 61], [1, -2, 67], [1, -6, 71], [1, -8, 73], [1, -8, 79], [1, 12, 83], [1, 0, 89], [1, 10, 97], [1, -6, 101], [1, 10, 103], [1, 0, 107], [1, -2, 109], [1, -18, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [[[1, -1], 1]], [[[1, -2, 7], 1]], [[[1, 0, 11], 1]], 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-2.0657298505524913, -2.5313885921627683, -2.8915813697812776, -3.122204523521, -3.2047727517721283, -3.127523413144244, -2.8861933022169297, -2.484419608671086, -1.9337360699066148, -1.253156596032369, -0.4683607541983925, 0.38948275248989217, 1.2851982917184543, 2.181317395502253], 'positive_zeros': ['0.845490649179226708045903681820310', '2.06128053911733423533178380013837', '2.73830314365781363876465257615474', '4.09880450289800587409359689726658', '5.06269933860006516679132716999830', '5.67746660566841356256437070473911', '6.79822391154486169782162796968047', '7.35265443309237049687362875941559', '8.038084838934107691702825582988224', '8.960813041623609009130793487464420'], 'prelabel': '2-2790-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.71998539869958, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 487803406692229645, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.845490649179226708045903681820', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.06128053911733423533178380014', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.73830314365781363876465257615', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.27826216393724, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 2790, 'conductor_radical': 930, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 1, 0, 2, -1, 0, -1, 0, 0, -4, -2, 0, 1, -6, 0, 8, 1, 0, 0, 0, 0, 1, 4, 0, 2, 0, 0, 1, -1, 0, 6, 2, 0, -4, -8, 0, -1, 6, 0, 8, 0, 0, 0, 12, 0, -3, -1, 0, -4, 6, 0, 0, -2, 0, 0, 6, 0, 2, -1, 0, 1, -4, 0, 2, -6, 0, -2, 6, 0, 8, 4, 0, 8, 0, 0, 8, 1, 0, -6, -12, 0, -6, -8, 0, 0, 0, 0, -8, 0, 0, -12, 8, 0, -10, 3, 0, 1], 'euler11': [1, 0, 11], 'euler13': [1, 4, 13], 'euler17': [1, 6, 17], 'euler19': [1, -8, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, -1, 0], 'euler37': [1, 4, 37], 'euler41': [1, -6, 41], 'euler43': [1, -8, 43], 'euler47': [1, -12, 47], 'euler5': [1, -1, 0], 'euler53': [1, -6, 53], 'euler59': [1, -6, 59], 'euler61': [1, -2, 61], 'euler67': [1, -2, 67], 'euler7': [1, -2, 7], 'euler71': [1, -6, 71], 'euler73': [1, -8, 73], 'euler79': [1, -8, 79], 'euler83': [1, 12, 83], 'euler89': [1, 0, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, -1, 0], [1, -2, 7], [1, 0, 11], [1, 4, 13], [1, 6, 17], [1, -8, 19], [1, 0, 23], [1, 0, 29], [1, -1, 0], [1, 4, 37], [1, -6, 41], [1, -8, 43], [1, -12, 47], [1, -6, 53], [1, -6, 59], [1, -2, 61], [1, -2, 67], [1, -6, 71], [1, -8, 73], [1, -8, 79], [1, 12, 83], [1, 0, 89], [1, 10, 97]], 'index': 9, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2790/k', 'ModularForm/GL2/Q/holomorphic/2790/2/a/k/1/1', 'ModularForm/GL2/Q/holomorphic/2790/2/a/k'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-2790-1.1-c1-0-9', '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': '2-2790-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.71998539869958, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 487803406692229645, 'z1': {'__RealLiteral__': 0, 'data': '0.845490649179226708045903681820', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20041976
{'Lhash': '1071786728919402068823648598585', 'Lhash_array': ['1071786728919402068823648598585'], 'label': '2-2790-1.1-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2790/2/a/k'}
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id: 24558779
{'Lhash': '1071786728919402068823648598585', 'Lhash_array': ['1071786728919402068823648598585'], 'label': '2-2790-1.1-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2790/2/a/k/1/1'}
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id: 98131
{'Lhash': '487803406692229645', 'Lhash_array': ['487803406692229645'], 'label': '2-2790-1.1-c1-0-9', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2790/k'}