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lfunc_lfunctions • Show schema
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{'A10': -3, 'A2': 1, 'A3': 1, 'A4': 1, 'A5': -3, 'A6': 1, 'A7': 0, 'A8': 1, 'A9': -2, 'Lhash': '952689608601427572350128794955', 'a10': [-0.9486832980505138, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.5773502691896257, 0], 'a4': [0.5, 0], 'a5': [-1.3416407864998738, 0], 'a6': [0.40824829046386296, 0], 'a7': [0.0, 0], 'a8': [0.3535533905932738, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.22777793843102, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1, 3]], [17, [1, 0, -1]]], 'bad_primes': [2, 3, 17], 'central_character': '332928.1', 'coefficient_field': '1.1.1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'euler_factors': [[1, -1], [1, -1, 3], [1, 3, 10, 15, 25], [1, 0, 10, 0, 49], [1, 0, -5, 0, 121], [1, 0, -20, 0, 169], [1, 0, -1], [1, 2, 39, 38, 361], [1, -6, 46, -138, 529], [1, -12, 94, -348, 841], [1, 0, -8, 0, 961], [1, 0, 28, 0, 1369], [1, 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'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 890514276664793306, 'z1': {'__RealLiteral__': 0, 'data': '0.75153958703597358941007013710592', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.04397086816987791248313455789214', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.78201610350151334029445584967911', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.22777793843102, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'dirichlet_coefficients': [1, 1, 1, 1, -3, 1, 0, 1, -2, -3, 0, 1, 0, 0, -3, 1, 0, -2, -2, -3, 0, 0, 6, 1, -1, 0, -5, 0, 12, -3, 0, 1, 0, 0, 0, -2, 0, -2, 0, -3, 0, 0, 7, 0, 6, 6, 3, 1, -10, -1, 0, 0, 3, -5, 0, 0, -2, 12, 0, -3, 0, 0, 0, 1, 0, 0, 4, 0, 6, 0, 9, -2, 4, 0, -1, -2, 0, 0, 0, -3, 1, 0, 0, 0, 0, 7, 12, 0, 0, 6, 0, 6, 0, 3, 6, 1, 13, -10, 0, -1], 'euler11': [1, 0, -5, 0, 121], 'euler13': [1, 0, -20, 0, 169], 'euler17': [1, 0, -1, 0, 0], 'euler19': [1, 2, 39, 38, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, -6, 46, -138, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, -1, 3, 0, 0], 'euler31': [1, 0, -8, 0, 961], 'euler37': [1, 0, 28, 0, 1369], 'euler41': [1, 0, -35, 0, 1681], 'euler43': [1, -7, 78, -301, 1849], 'euler47': [1, -3, 94, -141, 2209], 'euler5': [1, 3, 10, 15, 25], 'euler53': [1, -3, -2, -159, 2809], 'euler59': [1, 0, 1, 0, 3481], 'euler61': [1, 0, -80, 0, 3721], 'euler67': [1, -4, 138, -268, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, -9, 52, -639, 5041], 'euler73': [1, -4, 69, -292, 5329], 'euler79': [1, 0, -32, 0, 6241], 'euler83': [1, 0, -113, 0, 6889], 'euler89': [1, 0, 61, 0, 7921], 'euler97': [1, -13, 216, -1261, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, -1, 3, 0, 0], [1, 3, 10, 15, 25], [1, 0, 10, 0, 49], [1, 0, -5, 0, 121], [1, 0, -20, 0, 169], [1, 0, -1, 0, 0], [1, 2, 39, 38, 361], [1, -6, 46, -138, 529], [1, -12, 94, -348, 841], [1, 0, -8, 0, 961], [1, 0, 28, 0, 1369], [1, 0, -35, 0, 1681], [1, -7, 78, -301, 1849], [1, -3, 94, -141, 2209], [1, -3, -2, -159, 2809], [1, 0, 1, 0, 3481], [1, 0, -80, 0, 3721], [1, -4, 138, -268, 4489], [1, -9, 52, -639, 5041], [1, -4, 69, -292, 5329], [1, 0, -32, 0, 6241], [1, 0, -113, 0, 6889], [1, 0, 61, 0, 7921], [1, -13, 216, -1261, 9409]], 'index': 4, 'instance_types': ['HMF', 'ECNF', 'HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-578.1-f', 'EllipticCurve/2.2.24.1/578.1/b', 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-578.1-b', 'EllipticCurve/2.2.24.1/578.1/f'], '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': '4-332928-1.1-c1e2-0-4', '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': '4-332928-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.1464764795303726, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 890514276664793306, 'z1': {'__RealLiteral__': 0, 'data': '0.75153958703597358941007013710592', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9513086
{'Lhash': '952689608601427572350128794955', 'Lhash_array': ['952689608601427572350128794955'], 'label': '4-332928-1.1-c1e2-0-4', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/578.1/f'}
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id: 9512906
{'Lhash': '952689608601427572350128794955', 'Lhash_array': ['952689608601427572350128794955'], 'label': '4-332928-1.1-c1e2-0-4', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-578.1-b'}
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id: 9512892
{'Lhash': '952689608601427572350128794955', 'Lhash_array': ['952689608601427572350128794955'], 'label': '4-332928-1.1-c1e2-0-4', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/578.1/b'}
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id: 9512657
{'Lhash': '952689608601427572350128794955', 'Lhash_array': ['952689608601427572350128794955'], 'label': '4-332928-1.1-c1e2-0-4', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-578.1-f'}