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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 1, 'A5': -6, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 0, 'Lhash': '578350644786880522,689246320802081722', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-2.6832815729997477, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.110407724657517, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [3, [1]], [7, [1, 1, 7]]], 'bad_primes': [2, 3, 7], 'central_character': '142884.1', 'coefficient_field': '1.1.1.1', 'conductor': 142884, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1, 0, -1], [1], [1, 6, 19, 30, 25], [1, 1, 7], [1, 0, 13, 0, 121], [1, 0, 10, 0, 169], [1, 0, 34, 0, 289], [1, 0, 34, 0, 361], [1, 0, 10, 0, 529], [1, 0, 22, 0, 841], [1, 0, 37, 0, 961], [1, -4, 78, -148, 1369], [1, -12, 118, -492, 1681], [1, 20, 186, 860, 1849], [1, 12, 130, 564, 2209], [1, 0, 25, 0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.110407724657517, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 142884, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 1, -6, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -6, 0, 0, 0, 0, 17, 0, 0, -1, 0, 0, 0, 0, 0, 0, 6, 0, 4, 0, 0, 0, 12, 0, -20, 0, 0, 0, -12, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 1, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -6, 0, 0, 6, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17], 'euler11': [1, 0, 13, 0, 121], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, 0, 34, 0, 289], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 0, 10, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 37, 0, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, -12, 118, -492, 1681], 'euler43': [1, 20, 186, 860, 1849], 'euler47': [1, 12, 130, 564, 2209], 'euler5': [1, 6, 19, 30, 25], 'euler53': [1, 0, 25, 0, 2809], 'euler59': [1, 24, 262, 1416, 3481], 'euler61': [1, 0, 58, 0, 3721], 'euler67': [1, -28, 330, -1876, 4489], 'euler7': [1, 1, 7, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, 97, 0, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, -6, 175, -498, 6889], 'euler89': [1, -36, 502, -3204, 7921], 'euler97': [1, 0, 193, 0, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 0, 0, 0, 0], [1, 6, 19, 30, 25], [1, 1, 7, 0, 0], [1, 0, 13, 0, 121], [1, 0, 10, 0, 169], [1, 0, 34, 0, 289], [1, 0, 34, 0, 361], [1, 0, 10, 0, 529], [1, 0, 22, 0, 841], [1, 0, 37, 0, 961], [1, -4, 78, -148, 1369], [1, -12, 118, -492, 1681], [1, 20, 186, 860, 1849], [1, 12, 130, 564, 2209], [1, 0, 25, 0, 2809], [1, 24, 262, 1416, 3481], [1, 0, 58, 0, 3721], [1, -28, 330, -1876, 4489], [1, 0, 142, 0, 5041], [1, 0, 97, 0, 5329], [1, -16, 222, -1264, 6241], [1, -6, 175, -498, 6889], [1, -36, 502, -3204, 7921], [1, 0, 193, 0, 9409]], 'index': 1, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.21.1/holomorphic/2.2.21.1-324.1-d', 'EllipticCurve/2.2.21.1/324.1/d'], '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': '4-378e2-1.1-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': '4-378e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1267596965588962244, 'z1': {'__RealLiteral__': 0, 'data': '0.55647773141554817914458641913294', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9547920
{'Lhash': '578350644786880522,689246320802081722', 'Lhash_array': ['578350644786880522', '689246320802081722'], 'label': '4-378e2-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.21.1/324.1/d'}
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id: 9547614
{'Lhash': '578350644786880522,689246320802081722', 'Lhash_array': ['578350644786880522', '689246320802081722'], 'label': '4-378e2-1.1-c1e2-0-1', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.21.1/holomorphic/2.2.21.1-324.1-d'}