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lfunc_lfunctions • Show schema
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{'Lhash': '735541417606451851219811496385,990662271742580691305901360677', 'a10': 0, 'a2': -3, 'a3': -2, 'a4': 4, 'a5': 0, 'a6': 6, 'a7': 0, 'a8': -3, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 166.71483765276056, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 2, 1]], [7, [1]], [11, [1, 2, 1]]], 'bad_primes': [3, 7, 11], 'central_character': '1617.1', 'coefficient_field': '1.1.1.1', 'conductor': 2614689, 'conductor_radical': 231, 'degree': 4, 'euler_factors': [[1, 3, 5, 6, 4], [1, 2, 1], [1, 0, 5, 0, 25], [1], [1, 2, 1], [1, 2, 7, 26, 169], [1, -12, 70, -204, 289], [1, 4, 37, 76, 361], [1, -4, 30, -92, 529], [1, 16, 117, 464, 841], [1, -8, 58, -248, 961], [1, 10, 79, 370, 1369], [1, -12, 118, -492, 1681], [1, -8, 82, -344, 1849], [1, -14, 123, -658, 2209], [1, 8, 42, 424, 2809], [1, 6, 47, 354, 3481], [1, -4, 46, -244, 3721], [1, 12, 125, 804, 4489], [1, 0, 122, 0, 5041], [1, 2, 147, 146, 5329], [1, -4, 142, 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'1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1663232081558288070, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58023986852057187785248996683', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.78149473645515618841021118899', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.74450108306809813732576957408', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 166.71483765276056, 'bad_primes': [3, 7, 11], 'central_character': '1.1', 'conductor': 2614689, 'conductor_radical': 231, 'degree': 4, 'dirichlet_coefficients': [1, -3, -2, 4, 0, 6, 0, -3, 3, 0, -2, -8, -2, 0, 0, 3, 12, -9, -4, 0, 0, 6, 4, 6, -5, 6, -4, 0, -16, 0, 8, -6, 4, -36, 0, 12, -10, 12, 4, 0, 12, 0, 8, -8, 0, -12, 14, -6, 0, 15, -24, -8, -8, 12, 0, 0, 8, 48, -6, 0, 4, -24, 0, 5, 0, -12, -12, 48, -8, 0, 0, -9, -2, 30, 10, -16, 0, -12, 4, 0, 5, -36, 16, 0, 0, -24, 32, 6, 0, 0, 0, 16, -16, -42, 0, 12, 4, 0, -6, -20], 'euler11': [1, 2, 1, 0, 0], 'euler13': [1, 2, 7, 26, 169], 'euler17': [1, -12, 70, -204, 289], 'euler19': [1, 4, 37, 76, 361], 'euler2': [1, 3, 5, 6, 4], 'euler23': [1, -4, 30, -92, 529], 'euler29': [1, 16, 117, 464, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, -8, 58, -248, 961], 'euler37': [1, 10, 79, 370, 1369], 'euler41': [1, -12, 118, -492, 1681], 'euler43': [1, -8, 82, -344, 1849], 'euler47': [1, -14, 123, -658, 2209], 'euler5': [1, 0, 5, 0, 25], 'euler53': [1, 8, 42, 424, 2809], 'euler59': [1, 6, 47, 354, 3481], 'euler61': [1, -4, 46, -244, 3721], 'euler67': [1, 12, 125, 804, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, 122, 0, 5041], 'euler73': [1, 2, 147, 146, 5329], 'euler79': [1, -4, 142, -316, 6241], 'euler83': [1, -16, 210, -1328, 6889], 'euler89': [1, 0, -2, 0, 7921], 'euler97': [1, -4, 118, -388, 9409], 'euler_factors': [[1, 3, 5, 6, 4], [1, 2, 1, 0, 0], [1, 0, 5, 0, 25], [1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, 2, 7, 26, 169], [1, -12, 70, -204, 289], [1, 4, 37, 76, 361], [1, -4, 30, -92, 529], [1, 16, 117, 464, 841], [1, -8, 58, -248, 961], [1, 10, 79, 370, 1369], [1, -12, 118, -492, 1681], [1, -8, 82, -344, 1849], [1, -14, 123, -658, 2209], [1, 8, 42, 424, 2809], [1, 6, 47, 354, 3481], [1, -4, 46, -244, 3721], [1, 12, 125, 804, 4489], [1, 0, 122, 0, 5041], [1, 2, 147, 146, 5329], [1, -4, 142, -316, 6241], [1, -16, 210, -1328, 6889], [1, 0, -2, 0, 7921], [1, -4, 118, -388, 9409]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1617/2/a/k'], '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': '4-1617e2-1.1-c1e2-0-0', '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': '4-1617e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.5933007119974034, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1663232081558288070, 'z1': {'__RealLiteral__': 0, 'data': '0.58023986852057187785248996683', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '735541417606451851219811496385,990662271742580691305901360677', 'Lhash_array': ['735541417606451851219811496385', '990662271742580691305901360677'], 'label': '4-1617e2-1.1-c1e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1617/2/a/k'}