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lfunc_lfunctions • Show schema
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{'A10': -2, 'A2': 1, 'A3': 1, 'A4': 1, 'A5': -2, 'A6': 1, 'A7': 0, 'A8': 1, 'A9': -2, 'Lhash': '2991953154106534405953928726056', 'a10': [-0.632455532033676, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.5773502691896257, 0], 'a4': [0.5, 0], 'a5': [-0.894427190999916, 0], 'a6': [0.40824829046386296, 0], 'a7': [0.0, 0], 'a8': [0.3535533905932738, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3672625940905021, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1, 3]], [5, [1, 2, 2, -5]]], 'bad_primes': [2, 3, 5], 'central_character': '5760.1', 'coefficient_field': '1.1.1.1', 'conductor': 5760, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, -1], [1, -1, 3], [1, 2, 2, -5], [1, 0, 4, 0, 49], [1, 0, 4, 0, 121], [1, 0, 19, 0, 169], [1, 0, -2, 0, 289], [1, 5, 24, 95, 361], [1, -3, 28, -69, 529], [1, 3, 40, 87, 841], [1, 0, -17, 0, 961], [1, 0, -74, 0, 1369], [1, 0, 1, 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'symplectic', 'trace_hash': 255634874438691172, 'z1': {'__RealLiteral__': 0, 'data': '2.36023487352734216619085451403010', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.33988096585002869805307011925726', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.05913985275459354094038282359196', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3672625940905021, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 5760, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 1, 1, 1, -2, 1, 0, 1, -2, -2, 0, 1, 0, 0, -2, 1, 0, -2, -5, -2, 0, 0, 3, 1, 2, 0, -5, 0, -3, -2, 0, 1, 0, 0, 0, -2, 0, -5, 0, -2, 0, 0, 7, 0, 4, 3, 15, 1, -4, 2, 0, 0, -18, -5, 0, 0, -5, -3, 0, -2, 0, 0, 0, 1, 0, 0, 10, 0, 3, 0, 9, -2, -5, 0, 2, -5, 0, 0, 0, -2, 1, 0, 0, 0, 0, 7, -3, 0, 0, 4, 0, 3, 0, 15, 10, 1, 7, -4, 0, 2], 'euler11': [1, 0, 4, 0, 121], 'euler13': [1, 0, 19, 0, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 5, 24, 95, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, -3, 28, -69, 529], 'euler29': [1, 3, 40, 87, 841], 'euler3': [1, -1, 3, 0, 0], 'euler31': [1, 0, -17, 0, 961], 'euler37': [1, 0, -74, 0, 1369], 'euler41': [1, 0, 1, 0, 1681], 'euler43': [1, -7, 78, -301, 1849], 'euler47': [1, -15, 130, -705, 2209], 'euler5': [1, 2, 2, -5, 0], 'euler53': [1, 18, 187, 954, 2809], 'euler59': [1, 0, -80, 0, 3481], 'euler61': [1, 0, 58, 0, 3721], 'euler67': [1, -10, 78, -670, 4489], 'euler7': [1, 0, 4, 0, 49], 'euler71': [1, -9, 142, -639, 5041], 'euler73': [1, 5, -30, 365, 5329], 'euler79': [1, 0, 103, 0, 6241], 'euler83': [1, 0, -113, 0, 6889], 'euler89': [1, 0, 43, 0, 7921], 'euler97': [1, -7, 186, -679, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, -1, 3, 0, 0], [1, 2, 2, -5, 0], [1, 0, 4, 0, 49], [1, 0, 4, 0, 121], [1, 0, 19, 0, 169], [1, 0, -2, 0, 289], [1, 5, 24, 95, 361], [1, -3, 28, -69, 529], [1, 3, 40, 87, 841], [1, 0, -17, 0, 961], [1, 0, -74, 0, 1369], [1, 0, 1, 0, 1681], [1, -7, 78, -301, 1849], [1, -15, 130, -705, 2209], [1, 18, 187, 954, 2809], [1, 0, -80, 0, 3481], [1, 0, 58, 0, 3721], [1, -10, 78, -670, 4489], [1, -9, 142, -639, 5041], [1, 5, -30, 365, 5329], [1, 0, 103, 0, 6241], [1, 0, -113, 0, 6889], [1, 0, 43, 0, 7921], [1, -7, 186, -679, 9409]], 'index': 1, 'instance_types': ['ECNF', 'HMF', 'ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.24.1/10.2/b', 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-10.2-b', 'EllipticCurve/2.2.24.1/10.1/b', 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-10.1-b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-5760-1.1-c1e2-0-1', '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': 0, 'prelabel': '4-5760-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.7784741112725984, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 255634874438691172, 'z1': {'__RealLiteral__': 0, 'data': '2.36023487352734216619085451403010', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9511376
{'Lhash': '2991953154106534405953928726056', 'Lhash_array': ['2991953154106534405953928726056'], 'label': '4-5760-1.1-c1e2-0-1', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-10.1-b'}
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id: 9511358
{'Lhash': '2991953154106534405953928726056', 'Lhash_array': ['2991953154106534405953928726056'], 'label': '4-5760-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/10.1/b'}
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id: 9510972
{'Lhash': '2991953154106534405953928726056', 'Lhash_array': ['2991953154106534405953928726056'], 'label': '4-5760-1.1-c1e2-0-1', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-10.2-b'}
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id: 9510677
{'Lhash': '2991953154106534405953928726056', 'Lhash_array': ['2991953154106534405953928726056'], 'label': '4-5760-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/10.2/b'}