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lfunc_lfunctions • Show schema
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{'Lhash': '701935132825253054520092512222,2338098799070002730304436281178', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -4, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 94.28038859852178, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [19, [1, -1, 19]]], 'bad_primes': [2, 19], 'central_character': '1216.1', 'coefficient_field': '1.1.1.1', 'conductor': 1478656, 'conductor_radical': 38, 'degree': 4, 'euler_factors': [[1], [1, 1, -2, 3, 9], [1, 4, 11, 20, 25], [1, 0, 14, 0, 49], [1, -6, 31, -66, 121], [1, -2, -9, -26, 169], [1, 2, -13, 34, 289], [1, -1, 19], [1, -6, 13, -138, 529], [1, 4, -13, 116, 841], [1, -20, 162, -620, 961], [1, 4, 78, 148, 1369], [1, 9, 40, 369, 1681], [1, -4, -27, -172, 1849], [1, 12, 97, 564, 2209], [1, 2, -49, 106, 2809], [1, -1, -58, -59, 3481], [1, 8, 3, 488, 3721], [1, 9, 14, 603, 4489], [1, 6, -35, 426, 5041], [1, -9, 8, -657, 5329], [1, 4, -63, 316, 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'8.948549508496821513849176904799389', '9.588603199068747606250465893550050', '10.19047343942992710068432091140912'], 'prelabel': '4-1216e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.1160566242909806, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 726220335524297580, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55372918428696028243036519220', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.33760290872410049724095802904', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.84443473513052294899388421909', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 94.28038859852178, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 1478656, 'conductor_radical': 38, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 0, -4, 0, 0, 0, 3, 0, 6, 0, 2, 0, 4, 0, -2, 0, 1, 0, 0, 0, 6, 0, 5, 0, -8, 0, -4, 0, 20, 0, -6, 0, 0, 0, -4, 0, -2, 0, -9, 0, 4, 0, -12, 0, -12, 0, -14, 0, 2, 0, -2, 0, -24, 0, -1, 0, 1, 0, -8, 0, 0, 0, -8, 0, -9, 0, -6, 0, -6, 0, 9, 0, -5, 0, 0, 0, -4, 0, 8, 0, -10, 0, 8, 0, 4, 0, 18, 0, 0, 0, -20, 0, -4, 0, -1, 0, 18, 0], 'euler11': [1, -6, 31, -66, 121], 'euler13': [1, -2, -9, -26, 169], 'euler17': [1, 2, -13, 34, 289], 'euler19': [1, -1, 19, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -6, 13, -138, 529], 'euler29': [1, 4, -13, 116, 841], 'euler3': [1, 1, -2, 3, 9], 'euler31': [1, -20, 162, -620, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, 9, 40, 369, 1681], 'euler43': [1, -4, -27, -172, 1849], 'euler47': [1, 12, 97, 564, 2209], 'euler5': [1, 4, 11, 20, 25], 'euler53': [1, 2, -49, 106, 2809], 'euler59': [1, -1, -58, -59, 3481], 'euler61': [1, 8, 3, 488, 3721], 'euler67': [1, 9, 14, 603, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, 6, -35, 426, 5041], 'euler73': [1, -9, 8, -657, 5329], 'euler79': [1, 4, -63, 316, 6241], 'euler83': [1, 10, 191, 830, 6889], 'euler89': [1, -18, 235, -1602, 7921], 'euler97': [1, 1, -96, 97, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 1, -2, 3, 9], [1, 4, 11, 20, 25], [1, 0, 14, 0, 49], [1, -6, 31, -66, 121], [1, -2, -9, -26, 169], [1, 2, -13, 34, 289], [1, -1, 19, 0, 0], [1, -6, 13, -138, 529], [1, 4, -13, 116, 841], [1, -20, 162, -620, 961], [1, 4, 78, 148, 1369], [1, 9, 40, 369, 1681], [1, -4, -27, -172, 1849], [1, 12, 97, 564, 2209], [1, 2, -49, 106, 2809], [1, -1, -58, -59, 3481], [1, 8, 3, 488, 3721], [1, 9, 14, 603, 4489], [1, 6, -35, 426, 5041], [1, -9, 8, -657, 5329], [1, 4, -63, 316, 6241], [1, 10, 191, 830, 6889], [1, -18, 235, -1602, 7921], [1, 1, -96, 97, 9409]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1216/2/i/b'], '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': '4-1216e2-1.1-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': '4-1216e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.1160566242909806, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 726220335524297580, 'z1': {'__RealLiteral__': 0, 'data': '0.55372918428696028243036519220', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '701935132825253054520092512222,2338098799070002730304436281178', 'Lhash_array': ['701935132825253054520092512222', '2338098799070002730304436281178'], 'label': '4-1216e2-1.1-c1e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1216/2/i/b'}