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lfunc_lfunctions • Show schema
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{'Lhash': '1211377791803754501385491948110', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.12482701569341, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [5, [1]], [67, [1, 1]]], 'bad_primes': [3, 5, 67], 'central_character': '5025.1', 'coefficient_field': '1.1.1.1', 'conductor': 5025, 'conductor_radical': 1005, 'degree': 2, 'euler_factors': [[1, 0, 2], [1, 1], [1], [1, 2, 7], [1, 6, 11], [1, 2, 13], [1, -3, 17], [1, 1, 19], [1, -9, 23], [1, -3, 29], [1, 4, 31], [1, -7, 37], [1, -6, 41], [1, -10, 43], [1, 9, 47], [1, -12, 53], [1, 15, 59], [1, -8, 61], [1, 1], [1, 12, 71], [1, 11, 73], [1, 4, 79], [1, -12, 83], [1, -15, 89], [1, 2, 97], [1, 0, 101], [1, -4, 103], [1, 15, 107], [1, 10, 109], [1, -12, 113]], 'euler_factors_factorization': [[[[1, 0, 2], 1]], [[[1, 1], 1]], [1], [[[1, 2, 7], 1]], [[[1, 6, 11], 1]], [[[1, 2, 13], 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5.566530551207652, 5.35751754062961, 5.023074916237016, 4.5771535307858295, 4.038313607392917, 3.4288227282249957, 2.773573018416246, 2.0988725501833683, 1.431172853811176], 'positive_zeros': ['0.955608581406940151163003760419140', '2.61877696534424514656803719596812', '3.24045151746287150463892219547560', '4.36834495992243608195613218887349', '5.01221268972886890031762331213537', '5.54916654274818587466664159640353', '6.26254330997417014761252017282768', '7.40424067250842220186106599802885', '7.68396908547946760925076105443492'], 'prelabel': '2-5025-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.3344160753532295, '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': 1515977490317896506, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.955608581406940151163003760419', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.61877696534424514656803719597', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24045151746287150463892219548', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 40.12482701569341, 'bad_primes': [3, 5, 67], 'central_character': '1.1', 'conductor': 5025, 'conductor_radical': 1005, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, -2, 0, 0, -2, 0, 1, 0, -6, 2, -2, 0, 0, 4, 3, 0, -1, 0, 2, 0, 9, 0, 0, 0, -1, 4, 3, 0, -4, 0, 6, 0, 0, -2, 7, 0, 2, 0, 6, 0, 10, 12, 0, 0, -9, -4, -3, 0, -3, 4, 12, 0, 0, 0, 1, 0, -15, 0, 8, 0, -2, -8, 0, 0, -1, -6, -9, 0, -12, 0, -11, 0, 0, 2, 12, 0, -4, 0, 1, 0, 12, -4, 0, 0, -3, 0, 15, 0, 4, -18, 4, 0, 0, 0, -2, 0, -6, 0], 'euler11': [1, 6, 11], 'euler13': [1, 2, 13], 'euler17': [1, -3, 17], 'euler19': [1, 1, 19], 'euler2': [1, 0, 2], 'euler23': [1, -9, 23], 'euler29': [1, -3, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, -7, 37], 'euler41': [1, -6, 41], 'euler43': [1, -10, 43], 'euler47': [1, 9, 47], 'euler5': [1, 0, 0], 'euler53': [1, -12, 53], 'euler59': [1, 15, 59], 'euler61': [1, -8, 61], 'euler67': [1, 1, 0], 'euler7': [1, 2, 7], 'euler71': [1, 12, 71], 'euler73': [1, 11, 73], 'euler79': [1, 4, 79], 'euler83': [1, -12, 83], 'euler89': [1, -15, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 2], [1, 1, 0], [1, 0, 0], [1, 2, 7], [1, 6, 11], [1, 2, 13], [1, -3, 17], [1, 1, 19], [1, -9, 23], [1, -3, 29], [1, 4, 31], [1, -7, 37], [1, -6, 41], [1, -10, 43], [1, 9, 47], [1, -12, 53], [1, 15, 59], [1, -8, 61], [1, 1, 0], [1, 12, 71], [1, 11, 73], [1, 4, 79], [1, -12, 83], [1, -15, 89], [1, 2, 97]], 'index': 85, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5025/d', 'ModularForm/GL2/Q/holomorphic/5025/2/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/5025/2/a/d'], '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': '2-5025-1.1-c1-0-85', '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': '2-5025-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.3344160753532295, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1515977490317896506, 'z1': {'__RealLiteral__': 0, 'data': '0.955608581406940151163003760419', 'prec': 107}}
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lfunc_instances • Show schema
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id: 21327337
{'Lhash': '1211377791803754501385491948110', 'Lhash_array': ['1211377791803754501385491948110'], 'label': '2-5025-1.1-c1-0-85', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5025/2/a/d'}
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id: 24568548
{'Lhash': '1211377791803754501385491948110', 'Lhash_array': ['1211377791803754501385491948110'], 'label': '2-5025-1.1-c1-0-85', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5025/2/a/d/1/1'}
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id: 39343
{'Lhash': '1515977490317896506', 'Lhash_array': ['1515977490317896506'], 'label': '2-5025-1.1-c1-0-85', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5025/d'}