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lfunc_lfunctions • Show schema
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{'Lhash': '1751551485244168119701824636268', 'a10': 0, 'a2': -1, 'a3': 1, 'a4': 1, 'a5': 0, 'a6': -1, 'a7': -1, 'a8': -1, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.715214849384736, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [11, [1]], [19, [1, -1]]], 'bad_primes': [2, 11, 19], 'central_character': '4598.1', 'coefficient_field': '1.1.1.1', 'conductor': 4598, 'conductor_radical': 418, 'degree': 2, 'euler_factors': [[1, 1], [1, -1, 3], [1, 0, 5], [1, 1, 7], [1], [1, -2, 13], [1, -6, 17], [1, -1], [1, 9, 23], [1, -3, 29], [1, -8, 31], [1, 7, 37], [1, 0, 41], [1, 10, 43], [1, -9, 47], [1, 9, 53], [1, 9, 59], [1, -8, 61], [1, 4, 67], [1, -12, 71], [1, -2, 73], [1, -14, 79], [1, 12, 83], [1, -6, 89], [1, 16, 97], [1, 0, 101], [1, -14, 103], [1, 15, 107], [1, 19, 109], [1, -12, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, -1, 3], 1]], [[[1, 0, 5], 1]], [[[1, 1, 7], 1]], [1], [[[1, -2, 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3.022308748865623, 3.930920825653499, 4.839334345731215, 5.704695965244697, 6.48519333202993, 7.142400186220698, 7.643455995020301, 7.962950132355663, 8.084396568106024, 8.00120808556461], 'positive_zeros': ['1.38173049019092216490553795461494', '2.38132054649060130995470312920738', '3.28657802815929334491983585502551', '3.81940579301223498865955736204373', '5.15064908967874935587499015081451', '5.99964447663547060997519699177124', '6.45551106707916369319201081979954', '7.56119198074043944042548784342691', '8.184206734061753315129665023257099'], 'prelabel': '2-4598-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.059308116392889, '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': 1982333854437915618, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38173049019092216490553795461', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38132054649060130995470312921', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.28657802815929334491983585503', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.715214849384736, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 4598, 'conductor_radical': 418, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, 0, -1, -1, -1, -2, 0, 0, 1, 2, 1, 0, 1, 6, 2, 1, 0, -1, 0, -9, -1, -5, -2, -5, -1, 3, 0, 8, -1, 0, -6, 0, -2, -7, -1, 2, 0, 0, 1, -10, 0, 0, 9, 9, 1, -6, 5, 6, 2, -9, 5, 0, 1, 1, -3, -9, 0, 8, -8, 2, 1, 0, 0, -4, 6, -9, 0, 12, 2, 2, 7, -5, 1, 0, -2, 14, 0, 1, 0, -12, -1, 0, 10, 3, 0, 6, 0, -2, -9, 8, -9, 0, -1, -16, 6, 0, -5], 'euler11': [1, 0, 0], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, -1, 0], 'euler2': [1, 1, 0], 'euler23': [1, 9, 23], 'euler29': [1, -3, 29], 'euler3': [1, -1, 3], 'euler31': [1, -8, 31], 'euler37': [1, 7, 37], 'euler41': [1, 0, 41], 'euler43': [1, 10, 43], 'euler47': [1, -9, 47], 'euler5': [1, 0, 5], 'euler53': [1, 9, 53], 'euler59': [1, 9, 59], 'euler61': [1, -8, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 7], 'euler71': [1, -12, 71], 'euler73': [1, -2, 73], 'euler79': [1, -14, 79], 'euler83': [1, 12, 83], 'euler89': [1, -6, 89], 'euler97': [1, 16, 97], 'euler_factors': [[1, 1, 0], [1, -1, 3], [1, 0, 5], [1, 1, 7], [1, 0, 0], [1, -2, 13], [1, -6, 17], [1, -1, 0], [1, 9, 23], [1, -3, 29], [1, -8, 31], [1, 7, 37], [1, 0, 41], [1, 10, 43], [1, -9, 47], [1, 9, 53], [1, 9, 59], [1, -8, 61], [1, 4, 67], [1, -12, 71], [1, -2, 73], [1, -14, 79], [1, 12, 83], [1, -6, 89], [1, 16, 97]], 'index': 116, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4598/h', 'ModularForm/GL2/Q/holomorphic/4598/2/a/h/1/1', 'ModularForm/GL2/Q/holomorphic/4598/2/a/h'], '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': '2-4598-1.1-c1-0-116', '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': '2-4598-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.059308116392889, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1982333854437915618, 'z1': {'__RealLiteral__': 0, 'data': '1.38173049019092216490553795461', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20335606
{'Lhash': '1751551485244168119701824636268', 'Lhash_array': ['1751551485244168119701824636268'], 'label': '2-4598-1.1-c1-0-116', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4598/2/a/h'}
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id: 24566634
{'Lhash': '1751551485244168119701824636268', 'Lhash_array': ['1751551485244168119701824636268'], 'label': '2-4598-1.1-c1-0-116', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4598/2/a/h/1/1'}
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id: 100284
{'Lhash': '1982333854437915618', 'Lhash_array': ['1982333854437915618'], 'label': '2-4598-1.1-c1-0-116', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4598/h'}