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lfunc_lfunctions • Show schema
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{'Lhash': '1644557090825474131003879694053,2165662754575386308693176452873', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 217.74999203625867, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 1]], [7, [1, -2, 1]], [11, [1, 2, 1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '1848.1', 'coefficient_field': '1.1.1.1', 'conductor': 3415104, 'conductor_radical': 462, 'degree': 4, 'euler_factors': [[1], [1, 2, 1], [1, 3, 4, 15, 25], [1, -2, 1], [1, 2, 1], [1, 5, 24, 65, 169], [1, -2, 2, -34, 289], [1, -9, 50, -171, 361], [1, 2, 14, 46, 529], [1, 3, 52, 87, 841], [1, 16, 126, 496, 961], [1, 5, 72, 185, 1369], [1, 10, 74, 410, 1681], [1, -10, 78, -430, 1849], [1, -1, 86, -47, 2209], [1, 20, 206, 1060, 2809], [1, 7, 122, 413, 3481], [1, 20, 222, 1220, 3721], [1, -5, 66, -335, 4489], [1, -4, 14, -284, 5041], [1, -1, 72, -73, 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'5.51985962984313655979795981121647', '6.36266198335412773342705106865129', '6.63833068251119298999507673293955', '7.40225518436017348266008794346691', '7.56178852228549957839936062625814', '7.76316581981646369724033447260416', '7.77735130341480161855656883339042', '8.686256437389933871526925666901672', '9.142866583232895902701417482665338'], 'prelabel': '4-1848e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.841400043412899, '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': 1797852734969140318, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29732679535621725178380720317', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.70840668097776916950195189942', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.59446973183155979355063936592', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 217.74999203625867, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 3415104, 'conductor_radical': 462, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, -3, 0, 2, 0, 3, 0, -2, 0, -5, 0, 6, 0, 2, 0, 9, 0, -4, 0, -2, 0, 5, 0, -4, 0, -3, 0, -16, 0, 4, 0, -6, 0, -5, 0, 10, 0, -10, 0, 10, 0, -9, 0, 1, 0, 3, 0, -4, 0, -20, 0, 6, 0, -18, 0, -7, 0, -20, 0, 6, 0, 15, 0, 5, 0, 4, 0, 4, 0, 1, 0, -10, 0, -4, 0, 32, 0, 5, 0, -12, 0, -6, 0, 6, 0, -8, 0, -10, 0, 32, 0, -27, 0, 8, 0, -6, 0], 'euler11': [1, 2, 1, 0, 0], 'euler13': [1, 5, 24, 65, 169], 'euler17': [1, -2, 2, -34, 289], 'euler19': [1, -9, 50, -171, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 2, 14, 46, 529], 'euler29': [1, 3, 52, 87, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 16, 126, 496, 961], 'euler37': [1, 5, 72, 185, 1369], 'euler41': [1, 10, 74, 410, 1681], 'euler43': [1, -10, 78, -430, 1849], 'euler47': [1, -1, 86, -47, 2209], 'euler5': [1, 3, 4, 15, 25], 'euler53': [1, 20, 206, 1060, 2809], 'euler59': [1, 7, 122, 413, 3481], 'euler61': [1, 20, 222, 1220, 3721], 'euler67': [1, -5, 66, -335, 4489], 'euler7': [1, -2, 1, 0, 0], 'euler71': [1, -4, 14, -284, 5041], 'euler73': [1, -1, 72, -73, 5329], 'euler79': [1, -32, 414, -2528, 6241], 'euler83': [1, 12, 70, 996, 6889], 'euler89': [1, 8, 62, 712, 7921], 'euler97': [1, -8, 78, -776, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, 3, 4, 15, 25], [1, -2, 1, 0, 0], [1, 2, 1, 0, 0], [1, 5, 24, 65, 169], [1, -2, 2, -34, 289], [1, -9, 50, -171, 361], [1, 2, 14, 46, 529], [1, 3, 52, 87, 841], [1, 16, 126, 496, 961], [1, 5, 72, 185, 1369], [1, 10, 74, 410, 1681], [1, -10, 78, -430, 1849], [1, -1, 86, -47, 2209], [1, 20, 206, 1060, 2809], [1, 7, 122, 413, 3481], [1, 20, 222, 1220, 3721], [1, -5, 66, -335, 4489], [1, -4, 14, -284, 5041], [1, -1, 72, -73, 5329], [1, -32, 414, -2528, 6241], [1, 12, 70, 996, 6889], [1, 8, 62, 712, 7921], [1, -8, 78, -776, 9409]], 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1848/2/a/o'], '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': '4-1848e2-1.1-c1e2-0-13', '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': 2, 'prelabel': '4-1848e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.841400043412899, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1797852734969140318, 'z1': {'__RealLiteral__': 0, 'data': '1.29732679535621725178380720317', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1644557090825474131003879694053,2165662754575386308693176452873', 'Lhash_array': ['1644557090825474131003879694053', '2165662754575386308693176452873'], 'label': '4-1848e2-1.1-c1e2-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1848/2/a/o'}