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lfunc_lfunctions • Show schema
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{'Lhash': '460289859686014022558706626654,1201867285886859758816852894530', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1713.5003589886464, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '5184.1', 'coefficient_field': '1.1.1.1', 'conductor': 26873856, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, -1, 2, -5, 25], [1, 3, 8, 21, 49], [1, -2, 23, -22, 121], [1, 5, 24, 65, 169], [1, 5, 32, 85, 289], [1, -7, 42, -133, 361], [1, 5, 44, 115, 529], [1, -3, 52, -87, 841], [1, 7, 66, 217, 961], [1, 6, 50, 222, 1369], [1, 12, 85, 492, 1681], [1, -8, 69, -344, 1849], [1, 3, 88, 141, 2209], [1, -10, 98, -530, 2809], [1, -14, 167, -826, 3481], [1, -1, 114, -61, 3721], [1, -4, 105, -268, 4489], [1, -8, 158, -568, 5041], [1, 7, 84, 511, 5329], [1, -7, 162, -553, 6241], [1, 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'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 852847239903369537, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.36310467537596153058026890106', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.948106115100228775667493297987', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.94523409503151156779672443085', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 1713.5003589886464, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 26873856, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, -3, 0, 0, 0, 2, 0, -5, 0, 0, 0, -5, 0, 7, 0, 0, 0, -5, 0, -1, 0, 0, 0, 3, 0, -7, 0, 0, 0, -3, 0, -6, 0, 0, 0, -12, 0, 8, 0, 0, 0, -3, 0, 1, 0, 0, 0, 10, 0, 2, 0, 0, 0, 14, 0, 1, 0, 0, 0, -5, 0, 4, 0, 0, 0, 8, 0, -7, 0, 0, 0, -6, 0, 7, 0, 0, 0, 25, 0, -5, 0, 0, 0, 12, 0, 15, 0, 0, 0, 7, 0, -8, 0, 0, 0], 'euler11': [1, -2, 23, -22, 121], 'euler13': [1, 5, 24, 65, 169], 'euler17': [1, 5, 32, 85, 289], 'euler19': [1, -7, 42, -133, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 5, 44, 115, 529], 'euler29': [1, -3, 52, -87, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 7, 66, 217, 961], 'euler37': [1, 6, 50, 222, 1369], 'euler41': [1, 12, 85, 492, 1681], 'euler43': [1, -8, 69, -344, 1849], 'euler47': [1, 3, 88, 141, 2209], 'euler5': [1, -1, 2, -5, 25], 'euler53': [1, -10, 98, -530, 2809], 'euler59': [1, -14, 167, -826, 3481], 'euler61': [1, -1, 114, -61, 3721], 'euler67': [1, -4, 105, -268, 4489], 'euler7': [1, 3, 8, 21, 49], 'euler71': [1, -8, 158, -568, 5041], 'euler73': [1, 7, 84, 511, 5329], 'euler79': [1, -7, 162, -553, 6241], 'euler83': [1, -25, 314, -2075, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, 8, 177, 776, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -1, 2, -5, 25], [1, 3, 8, 21, 49], [1, -2, 23, -22, 121], [1, 5, 24, 65, 169], [1, 5, 32, 85, 289], [1, -7, 42, -133, 361], [1, 5, 44, 115, 529], [1, -3, 52, -87, 841], [1, 7, 66, 217, 961], [1, 6, 50, 222, 1369], [1, 12, 85, 492, 1681], [1, -8, 69, -344, 1849], [1, 3, 88, 141, 2209], [1, -10, 98, -530, 2809], [1, -14, 167, -826, 3481], [1, -1, 114, -61, 3721], [1, -4, 105, -268, 4489], [1, -8, 158, -568, 5041], [1, 7, 84, 511, 5329], [1, -7, 162, -553, 6241], [1, -25, 314, -2075, 6889], [1, -12, 214, -1068, 7921], [1, 8, 177, 776, 9409]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5184/2/a/bs'], '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': '4-72e4-1.1-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': '4-72e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 852847239903369537, 'z1': {'__RealLiteral__': 0, 'data': '0.36310467537596153058026890106', 'prec': 103}}
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{'Lhash': '460289859686014022558706626654,1201867285886859758816852894530', 'Lhash_array': ['460289859686014022558706626654', '1201867285886859758816852894530'], 'label': '4-72e4-1.1-c1e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/a/bs'}