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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 1, 'A9': 2, 'Lhash': '1352501560283934928705853688923', 'a10': [0.0, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.3535533905932738, 0], 'a9': [0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.893364416197777, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [7, [1, 0, 1]], [17, [1, -6, 17]]], 'bad_primes': [2, 7, 17], 'central_character': '453152.1', 'coefficient_field': '1.1.1.1', 'conductor': 453152, 'conductor_radical': 238, 'degree': 4, 'euler_factors': [[1, -1], [1, 0, -2, 0, 9], [1, 0, 10, 0, 25], [1, 0, 1], [1, 0, -22, 0, 121], [1, -8, 42, -104, 169], [1, -6, 17], [1, 0, 34, 0, 361], [1, 0, -46, 0, 529], [1, 0, 22, 0, 841], [1, 0, -46, 0, 961], [1, 0, 70, 0, 1369], [1, 0, 46, 0, 1681], [1, 0, 22, 0, 1849], [1, 0, -50, 0, 2209], [1, -12, 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0.09566069561015927, 0.3511877643844705, 0.40687361923501325, 0.2813992874965367, 0.028348624092401752], 'positive_zeros': ['1.06693560515841577648054251789565', '1.64893568141364615823925507109774', '2.46424226435271921075104708179453', '3.38179088440528658396943141493001', '3.73940051357221662734724785909802', '4.00437577532359061015721712376373', '4.72476803437976548009006900145204', '5.42717660586362568204157976090204', '5.75674549062065341809885026160015', '6.19002274250768406878646019465909', '6.53665060632888009337431021868552', '7.27776442666612344143570168035307', '7.63282182808416058464170813975879', '7.975072260169784816600891236211091', '8.655064726124824394184183303483787'], 'prelabel': '4-453152-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.318459579844619, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1267977963859238460, 'z1': {'__RealLiteral__': 0, 'data': '1.06693560515841577648054251789565', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.64893568141364615823925507109774', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.46424226435271921075104708179453', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.893364416197777, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 453152, 'conductor_radical': 238, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 8, 0, 0, 1, 6, 2, 0, 0, 0, 0, 0, 0, -10, 8, 0, 0, 0, 0, 0, 1, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -10, 0, 8, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -10], 'euler11': [1, 0, -22, 0, 121], 'euler13': [1, -8, 42, -104, 169], 'euler17': [1, -6, 17, 0, 0], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, 0, -46, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, -2, 0, 9], 'euler31': [1, 0, -46, 0, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 0, 82, 0, 3481], 'euler61': [1, 0, 58, 0, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, 1, 0, 0], 'euler71': [1, 0, -142, 0, 5041], 'euler73': [1, 0, 142, 0, 5329], 'euler79': [1, 0, -94, 0, 6241], 'euler83': [1, 0, 130, 0, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, 0, 94, 0, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, 0, -2, 0, 9], [1, 0, 10, 0, 25], [1, 0, 1, 0, 0], [1, 0, -22, 0, 121], [1, -8, 42, -104, 169], [1, -6, 17, 0, 0], [1, 0, 34, 0, 361], [1, 0, -46, 0, 529], [1, 0, 22, 0, 841], [1, 0, -46, 0, 961], [1, 0, 70, 0, 1369], [1, 0, 46, 0, 1681], [1, 0, 22, 0, 1849], [1, 0, -50, 0, 2209], [1, -12, 142, -636, 2809], [1, 0, 82, 0, 3481], [1, 0, 58, 0, 3721], [1, 0, 118, 0, 4489], [1, 0, -142, 0, 5041], [1, 0, 142, 0, 5329], [1, 0, -94, 0, 6241], [1, 0, 130, 0, 6889], [1, -12, 214, -1068, 7921], [1, 0, 94, 0, 9409]], 'index': 3, 'instance_types': ['BMF', 'ECNF', 'ECNF', 'BMF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/28322.1/a', 'EllipticCurve/2.0.4.1/28322.1/a', 'EllipticCurve/2.0.4.1/28322.3/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/28322.3/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': '4-453152-1.1-c1e2-0-3', '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': '4-453152-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.318459579844619, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1267977963859238460, 'z1': {'__RealLiteral__': 0, 'data': '1.06693560515841577648054251789565', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9663896
{'Lhash': '1352501560283934928705853688923', 'Lhash_array': ['1352501560283934928705853688923'], 'label': '4-453152-1.1-c1e2-0-3', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/28322.3/a'}
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id: 9663687
{'Lhash': '1352501560283934928705853688923', 'Lhash_array': ['1352501560283934928705853688923'], 'label': '4-453152-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/28322.3/a'}
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id: 9663655
{'Lhash': '1352501560283934928705853688923', 'Lhash_array': ['1352501560283934928705853688923'], 'label': '4-453152-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/28322.1/a'}
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id: 9663533
{'Lhash': '1352501560283934928705853688923', 'Lhash_array': ['1352501560283934928705853688923'], 'label': '4-453152-1.1-c1e2-0-3', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/28322.1/a'}