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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': -6, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 3, 'Lhash': '1883722513434514463,2179305512936749972', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792515, 0], 'a4': [0.0, 0], 'a5': [-2.6832815729997477, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.066245894480033, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 2, 1]], [11, [1, -1, 11]], [19, [1, 0, -1]]], 'bad_primes': [3, 11, 19], 'central_character': '393129.1', 'coefficient_field': '1.1.1.1', 'conductor': 393129, 'conductor_radical': 627, 'degree': 4, 'euler_factors': [[1, 0, 0, 0, 4], [1, 2, 1], [1, 6, 19, 30, 25], [1, 0, -11, 0, 49], [1, -1, 11], [1, 0, 22, 0, 169], [1, 0, 33, 0, 289], [1, 0, -1], [1, 8, 62, 184, 529], [1, 0, 54, 0, 841], [1, 12, 98, 372, 961], [1, 0, 74, 0, 1369], [1, 0, 82, 0, 1681], [1, 0, 85, 0, 1849], [1, 18, 175, 846, 2209], [1, 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'1.44645188395830487846696686993787', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.47849673392805399692938216212743', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.57553622245677274525627107283723', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.066245894480033, 'bad_primes': [3, 11, 19], 'central_character': '1.1', 'conductor': 393129, 'conductor_radical': 627, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, -6, 0, 0, 0, 3, 0, 1, 0, 0, 0, 12, -4, 0, 0, 0, 0, 0, 0, -8, 0, 17, 0, -4, 0, 0, 0, -12, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 0, -18, 8, 11, 0, 0, 0, 20, 0, -6, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 16, 0, 16, 0, -24, 0, 0, 0, -34, 0, 0, 0, 0, 24, 5, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 24, 0, 0, 0, -20, 0, 3, 0], 'euler11': [1, -1, 11, 0, 0], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 0, 33, 0, 289], 'euler19': [1, 0, -1, 0, 0], 'euler2': [1, 0, 0, 0, 4], 'euler23': [1, 8, 62, 184, 529], 'euler29': [1, 0, 54, 0, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 12, 98, 372, 961], 'euler37': [1, 0, 74, 0, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, 0, 85, 0, 1849], 'euler47': [1, 18, 175, 846, 2209], 'euler5': [1, 6, 19, 30, 25], 'euler53': [1, -20, 206, -1060, 2809], 'euler59': [1, 16, 182, 944, 3481], 'euler61': [1, 0, 121, 0, 3721], 'euler67': [1, -16, 198, -1072, 4489], 'euler7': [1, 0, -11, 0, 49], 'euler71': [1, 24, 286, 1704, 5041], 'euler73': [1, 0, 25, 0, 5329], 'euler79': [1, 0, -98, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 20, 294, 1940, 9409], 'euler_factors': [[1, 0, 0, 0, 4], [1, 2, 1, 0, 0], [1, 6, 19, 30, 25], [1, 0, -11, 0, 49], [1, -1, 11, 0, 0], [1, 0, 22, 0, 169], [1, 0, 33, 0, 289], [1, 0, -1, 0, 0], [1, 8, 62, 184, 529], [1, 0, 54, 0, 841], [1, 12, 98, 372, 961], [1, 0, 74, 0, 1369], [1, 0, 82, 0, 1681], [1, 0, 85, 0, 1849], [1, 18, 175, 846, 2209], [1, -20, 206, -1060, 2809], [1, 16, 182, 944, 3481], [1, 0, 121, 0, 3721], [1, -16, 198, -1072, 4489], [1, 24, 286, 1704, 5041], [1, 0, 25, 0, 5329], [1, 0, -98, 0, 6241], [1, 0, 22, 0, 6889], [1, 12, 214, 1068, 7921], [1, 20, 294, 1940, 9409]], 'index': 9, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.11.1/3249.2/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/3249.2/a'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, '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': '4-627e2-1.1-c1e2-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-627e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.237547811049919, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1757185017157570484, 'z1': {'__RealLiteral__': 0, 'data': '1.44645188395830487846696686993787', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9918804
{'Lhash': '1883722513434514463,2179305512936749972', 'Lhash_array': ['1883722513434514463', '2179305512936749972'], 'label': '4-627e2-1.1-c1e2-0-9', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/3249.2/a'}
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id: 9918525
{'Lhash': '1883722513434514463,2179305512936749972', 'Lhash_array': ['1883722513434514463', '2179305512936749972'], 'label': '4-627e2-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/3249.2/a'}