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lfunc_lfunctions • Show schema
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{'Lhash': '983658330557901857851969408118,2924266424115151383005189613494', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -5, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.998851975120723, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -1, 1]], [7, [1, 5, 7]]], 'bad_primes': [2, 5, 7], 'central_character': '280.1', 'coefficient_field': '1.1.1.1', 'conductor': 78400, 'conductor_radical': 70, 'degree': 4, 'euler_factors': [[1], [1, 1, -2, 3, 9], [1, -1, 1], [1, 5, 7], [1, 2, -7, 22, 121], [1, 0, 26, 0, 169], [1, 4, -1, 68, 289], [1, -2, -15, -38, 361], [1, 1, -22, 23, 529], [1, -18, 139, -522, 841], [1, 4, -15, 124, 961], [1, 4, -21, 148, 1369], [1, -2, 83, -82, 1681], [1, -18, 167, -774, 1849], [1, 0, -47, 0, 2209], [1, -10, 47, -530, 2809], [1, -10, 41, -590, 3481], [1, 9, 20, 549, 3721], [1, 5, -42, 335, 4489], [1, -28, 338, -1988, 5041], [1, 12, 71, 876, 5329], [1, 14, 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'root_analytic_conductor': 1.4952629389494851, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1017878339870794935, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77596960107209571803117472311', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.30683945843488954610806465251', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.84302711075337274392253178577', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.998851975120723, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 78400, 'conductor_radical': 70, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, -5, 0, 3, 0, -2, 0, 0, 0, -1, 0, -4, 0, 2, 0, 5, 0, -1, 0, 0, 0, -8, 0, 18, 0, -4, 0, 2, 0, -5, 0, -4, 0, 0, 0, 2, 0, 18, 0, 3, 0, 0, 0, 18, 0, 4, 0, 10, 0, -2, 0, -2, 0, 10, 0, -9, 0, -15, 0, 0, 0, -5, 0, 1, 0, 28, 0, -12, 0, 0, 0, 10, 0, -14, 0, 8, 0, 22, 0, -4, 0, -18, 0, 15, 0, 0, 0, 4, 0, 2, 0, -36, 0, -6, 0], 'euler11': [1, 2, -7, 22, 121], 'euler13': [1, 0, 26, 0, 169], 'euler17': [1, 4, -1, 68, 289], 'euler19': [1, -2, -15, -38, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 1, -22, 23, 529], 'euler29': [1, -18, 139, -522, 841], 'euler3': [1, 1, -2, 3, 9], 'euler31': [1, 4, -15, 124, 961], 'euler37': [1, 4, -21, 148, 1369], 'euler41': [1, -2, 83, -82, 1681], 'euler43': [1, -18, 167, -774, 1849], 'euler47': [1, 0, -47, 0, 2209], 'euler5': [1, -1, 1, 0, 0], 'euler53': [1, -10, 47, -530, 2809], 'euler59': [1, -10, 41, -590, 3481], 'euler61': [1, 9, 20, 549, 3721], 'euler67': [1, 5, -42, 335, 4489], 'euler7': [1, 5, 7, 0, 0], 'euler71': [1, -28, 338, -1988, 5041], 'euler73': [1, 12, 71, 876, 5329], 'euler79': [1, 14, 117, 1106, 6241], 'euler83': [1, -22, 287, -1826, 6889], 'euler89': [1, -15, 136, -1335, 7921], 'euler97': [1, 36, 518, 3492, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 1, -2, 3, 9], [1, -1, 1, 0, 0], [1, 5, 7, 0, 0], [1, 2, -7, 22, 121], [1, 0, 26, 0, 169], [1, 4, -1, 68, 289], [1, -2, -15, -38, 361], [1, 1, -22, 23, 529], [1, -18, 139, -522, 841], [1, 4, -15, 124, 961], [1, 4, -21, 148, 1369], [1, -2, 83, -82, 1681], [1, -18, 167, -774, 1849], [1, 0, -47, 0, 2209], [1, -10, 47, -530, 2809], [1, -10, 41, -590, 3481], [1, 9, 20, 549, 3721], [1, 5, -42, 335, 4489], [1, -28, 338, -1988, 5041], [1, 12, 71, 876, 5329], [1, 14, 117, 1106, 6241], [1, -22, 287, -1826, 6889], [1, -15, 136, -1335, 7921], [1, 36, 518, 3492, 9409]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/280/2/q/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '4-280e2-1.1-c1e2-0-2', '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': '4-280e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.4952629389494851, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1017878339870794935, 'z1': {'__RealLiteral__': 0, 'data': '0.77596960107209571803117472311', 'prec': 103}}
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{'Lhash': '983658330557901857851969408118,2924266424115151383005189613494', 'Lhash_array': ['983658330557901857851969408118', '2924266424115151383005189613494'], 'label': '4-280e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/280/2/q/a'}