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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -6, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': -2, 'Lhash': '685433102328794143,1845375492880582855', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896257, 0], 'a4': [0.0, 0], 'a5': [-2.6832815729997477, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 54.43749800906467, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1, 3]], [7, [1, -2, 7]], [11, [1, 0, -1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '853776.1', 'coefficient_field': '1.1.1.1', 'conductor': 853776, 'conductor_radical': 462, 'degree': 4, 'euler_factors': [[1], [1, -1, 3], [1, 6, 19, 30, 25], [1, -2, 7], [1, 0, -1], [1, 0, 10, 0, 169], [1, -12, 70, -204, 289], [1, 0, -26, 0, 361], [1, 0, 37, 0, 529], [1, 0, 58, 0, 841], [1, 0, 37, 0, 961], [1, 2, 75, 74, 1369], [1, 0, 82, 0, 1681], [1, 20, 186, 860, 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{'__RealLiteral__': 0, 'data': '1.00356671220607536314623203551504', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.87692294389813555618766341906242', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.00610279743917756108045023038459', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 54.43749800906467, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 853776, 'conductor_radical': 462, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 0, -6, 0, 2, 0, -2, 0, 0, 0, 0, 0, -6, 0, 12, 0, 0, 0, 2, 0, 0, 0, 17, 0, -5, 0, 0, 0, 0, 0, 0, 0, -12, 0, -2, 0, 0, 0, 0, 0, -20, 0, 12, 0, 0, 0, -3, 0, 12, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 4, 0, 1, 0, 12, 0, -72, 0, 0, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -1, 0, 0], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, -12, 70, -204, 289], 'euler19': [1, 0, -26, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 37, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, -1, 3, 0, 0], 'euler31': [1, 0, 37, 0, 961], 'euler37': [1, 2, 75, 74, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, 20, 186, 860, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 6, 19, 30, 25], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, -6, 127, -354, 3481], 'euler61': [1, 0, 106, 0, 3721], 'euler67': [1, 2, 135, 134, 4489], 'euler7': [1, -2, 7, 0, 0], 'euler71': [1, 0, -83, 0, 5041], 'euler73': [1, 0, 130, 0, 5329], 'euler79': [1, -4, 162, -316, 6241], 'euler83': [1, -12, 202, -996, 6889], 'euler89': [1, 18, 259, 1602, 7921], 'euler97': [1, 0, 145, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -1, 3, 0, 0], [1, 6, 19, 30, 25], [1, -2, 7, 0, 0], [1, 0, -1, 0, 0], [1, 0, 10, 0, 169], [1, -12, 70, -204, 289], [1, 0, -26, 0, 361], [1, 0, 37, 0, 529], [1, 0, 58, 0, 841], [1, 0, 37, 0, 961], [1, 2, 75, 74, 1369], [1, 0, 82, 0, 1681], [1, 20, 186, 860, 1849], [1, 0, 94, 0, 2209], [1, 0, 70, 0, 2809], [1, -6, 127, -354, 3481], [1, 0, 106, 0, 3721], [1, 2, 135, 134, 4489], [1, 0, -83, 0, 5041], [1, 0, 130, 0, 5329], [1, -4, 162, -316, 6241], [1, -12, 202, -996, 6889], [1, 18, 259, 1602, 7921], [1, 0, 145, 0, 9409]], 'index': 30, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.21.1/holomorphic/2.2.21.1-1936.1-a', 'EllipticCurve/2.2.21.1/1936.1/a'], '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': '4-924e2-1.1-c1e2-0-30', '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': 1, 'prelabel': '4-924e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.716280019947559, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 224965585995683047, 'z1': {'__RealLiteral__': 0, 'data': '1.00356671220607536314623203551504', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9546107
{'Lhash': '685433102328794143,1845375492880582855', 'Lhash_array': ['685433102328794143', '1845375492880582855'], 'label': '4-924e2-1.1-c1e2-0-30', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.21.1/1936.1/a'}
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id: 9545709
{'Lhash': '685433102328794143,1845375492880582855', 'Lhash_array': ['685433102328794143', '1845375492880582855'], 'label': '4-924e2-1.1-c1e2-0-30', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.21.1/holomorphic/2.2.21.1-1936.1-a'}