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lfunc_lfunctions • Show schema
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{'Lhash': '1563613186280558739096783445332', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 61.70839068204551, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [7, [1, -1]], [23, [1, 1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '7728.1', 'coefficient_field': '1.1.1.1', 'conductor': 7728, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 3, 5], [1, -1], [1, 0, 11], [1, 1, 13], [1, 4, 17], [1, 0, 19], [1, 1], [1, -5, 29], [1, -10, 31], [1, 3, 37], [1, 11, 41], [1, -9, 43], [1, -3, 47], [1, -12, 53], [1, 10, 59], [1, 10, 61], [1, -12, 67], [1, 6, 71], [1, 4, 73], [1, 12, 79], [1, 12, 83], [1, -6, 89], [1, -9, 97], [1, 18, 101], [1, 13, 103], [1, 0, 107], [1, -1, 109], [1, 3, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, 3, 5], 1]], [[[1, -1], 1]], [[[1, 0, 11], 1]], [[[1, 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0.03798314313441002, -0.16851185505718658, -0.2793333750926715, -0.2932627343048713, -0.21536224988930128, -0.05667794568995155, 0.16641402264483632, 0.43318188739935004, 0.7197794753489267], 'positive_zeros': ['1.23347331354479212409499920845446', '2.43378750100698839758206508133683', '3.08400932814634790744861853224274', '4.10721408376758978447161596512518', '4.38789318063603582788983743598966', '5.21569438121451725456142195156018', '6.33582082496062884460268580844442', '7.00217750434419845410448942993055', '7.59965267583394120895466385026051'], 'prelabel': '2-7728-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.855468839098371, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 833543271268843873, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23347331354479212409499920845', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.43378750100698839758206508134', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.08400932814634790744861853224', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 61.70839068204551, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 7728, 'conductor_radical': 966, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -3, 0, 1, 0, 1, 0, 0, 0, -1, 0, -3, 0, -4, 0, 0, 0, 1, 0, -1, 0, 4, 0, 1, 0, 5, 0, 10, 0, 0, 0, -3, 0, -3, 0, -1, 0, -11, 0, 9, 0, -3, 0, 3, 0, 1, 0, -4, 0, 12, 0, 0, 0, 0, 0, -10, 0, -10, 0, 1, 0, 3, 0, 12, 0, -1, 0, -6, 0, -4, 0, 4, 0, 0, 0, -12, 0, 1, 0, -12, 0, 12, 0, 5, 0, 6, 0, -1, 0, 10, 0, 0, 0, 9, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 1, 13], 'euler17': [1, 4, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, -5, 29], 'euler3': [1, -1, 0], 'euler31': [1, -10, 31], 'euler37': [1, 3, 37], 'euler41': [1, 11, 41], 'euler43': [1, -9, 43], 'euler47': [1, -3, 47], 'euler5': [1, 3, 5], 'euler53': [1, -12, 53], 'euler59': [1, 10, 59], 'euler61': [1, 10, 61], 'euler67': [1, -12, 67], 'euler7': [1, -1, 0], 'euler71': [1, 6, 71], 'euler73': [1, 4, 73], 'euler79': [1, 12, 79], 'euler83': [1, 12, 83], 'euler89': [1, -6, 89], 'euler97': [1, -9, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 3, 5], [1, -1, 0], [1, 0, 11], [1, 1, 13], [1, 4, 17], [1, 0, 19], [1, 1, 0], [1, -5, 29], [1, -10, 31], [1, 3, 37], [1, 11, 41], [1, -9, 43], [1, -3, 47], [1, -12, 53], [1, 10, 59], [1, 10, 61], [1, -12, 67], [1, 6, 71], [1, 4, 73], [1, 12, 79], [1, 12, 83], [1, -6, 89], [1, -9, 97]], 'index': 95, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/7728/n', 'ModularForm/GL2/Q/holomorphic/7728/2/a/n/1/1', 'ModularForm/GL2/Q/holomorphic/7728/2/a/n'], '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': '2-7728-1.1-c1-0-95', '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': '2-7728-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.855468839098371, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 833543271268843873, 'z1': {'__RealLiteral__': 0, 'data': '1.23347331354479212409499920845', 'prec': 103}}
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lfunc_instances • Show schema
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id: 22163888
{'Lhash': '1563613186280558739096783445332', 'Lhash_array': ['1563613186280558739096783445332'], 'label': '2-7728-1.1-c1-0-95', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7728/2/a/n'}
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id: 24580871
{'Lhash': '1563613186280558739096783445332', 'Lhash_array': ['1563613186280558739096783445332'], 'label': '2-7728-1.1-c1-0-95', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7728/2/a/n/1/1'}
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id: 40765
{'Lhash': '833543271268843873', 'Lhash_array': ['833543271268843873'], 'label': '2-7728-1.1-c1-0-95', 'type': 'ECQ', 'url': 'EllipticCurve/Q/7728/n'}