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lfunc_lfunctions • Show schema
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{'Lhash': '1281664578677242362029577914787,2303671838984479053570907549760', 'a10': 3, 'a2': 1, 'a3': 0, 'a4': 2, 'a5': 3, 'a6': 0, 'a7': -5, 'a8': 5, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.76830292964223, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1, 5, 7]], [13, [1, 2, 13]]], 'bad_primes': [3, 7, 13], 'central_character': '819.1', 'coefficient_field': '1.1.1.1', 'conductor': 670761, 'conductor_radical': 273, 'degree': 4, 'euler_factors': [[1, -1, -1, -2, 4], [1], [1, -3, 4, -15, 25], [1, 5, 7], [1, -6, 31, -66, 121], [1, 2, 13], [1, 2, -13, 34, 289], [1, 2, 39, 38, 361], [1, 0, -23, 0, 529], [1, -7, 20, -203, 841], [1, 3, -22, 93, 961], [1, 2, -33, 74, 1369], [1, -3, -32, -123, 1681], [1, -7, 6, -301, 1849], [1, -1, -46, -47, 2209], [1, -3, -44, -159, 2809], [1, 4, -43, 236, 3481], [1, 26, 291, 1586, 3721], [1, 6, 143, 402, 4489], [1, -13, 98, -923, 5041], [1, -13, 96, -949, 5329], [1, 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'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 501866077153765371, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01105507972503611508071023563', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.81727665223344909936360619514', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.37982520516258210570106036149', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.76830292964223, 'bad_primes': [3, 7, 13], 'central_character': '1.1', 'conductor': 670761, 'conductor_radical': 273, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 2, 3, 0, -5, 5, 0, 3, 6, 0, -2, -5, 0, 5, -2, 0, -2, 6, 0, 6, 0, 0, 5, -2, 0, -10, 7, 0, -3, 10, 0, -2, -15, 0, -2, -2, 0, 15, 3, 0, 7, 12, 0, 0, 1, 0, 18, 5, 0, -4, 3, 0, 18, -25, 0, 7, -4, 0, -26, -3, 0, 17, -6, 0, -6, -4, 0, -15, 13, 0, 13, -2, 0, -4, -30, 0, 3, 15, 0, 3, 0, 0, -6, 7, 0, 30, 6, 0, 10, 0, 0, 1, -6, 0, 5, 18, 0, 10], 'euler11': [1, -6, 31, -66, 121], 'euler13': [1, 2, 13, 0, 0], 'euler17': [1, 2, -13, 34, 289], 'euler19': [1, 2, 39, 38, 361], 'euler2': [1, -1, -1, -2, 4], 'euler23': [1, 0, -23, 0, 529], 'euler29': [1, -7, 20, -203, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 3, -22, 93, 961], 'euler37': [1, 2, -33, 74, 1369], 'euler41': [1, -3, -32, -123, 1681], 'euler43': [1, -7, 6, -301, 1849], 'euler47': [1, -1, -46, -47, 2209], 'euler5': [1, -3, 4, -15, 25], 'euler53': [1, -3, -44, -159, 2809], 'euler59': [1, 4, -43, 236, 3481], 'euler61': [1, 26, 291, 1586, 3721], 'euler67': [1, 6, 143, 402, 4489], 'euler7': [1, 5, 7, 0, 0], 'euler71': [1, -13, 98, -923, 5041], 'euler73': [1, -13, 96, -949, 5329], 'euler79': [1, -3, -70, -237, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, -6, -53, -534, 7921], 'euler97': [1, -5, -72, -485, 9409], 'euler_factors': [[1, -1, -1, -2, 4], [1, 0, 0, 0, 0], [1, -3, 4, -15, 25], [1, 5, 7, 0, 0], [1, -6, 31, -66, 121], [1, 2, 13, 0, 0], [1, 2, -13, 34, 289], [1, 2, 39, 38, 361], [1, 0, -23, 0, 529], [1, -7, 20, -203, 841], [1, 3, -22, 93, 961], [1, 2, -33, 74, 1369], [1, -3, -32, -123, 1681], [1, -7, 6, -301, 1849], [1, -1, -46, -47, 2209], [1, -3, -44, -159, 2809], [1, 4, -43, 236, 3481], [1, 26, 291, 1586, 3721], [1, 6, 143, 402, 4489], [1, -13, 98, -923, 5041], [1, -13, 96, -949, 5329], [1, -3, -70, -237, 6241], [1, 0, 166, 0, 6889], [1, -6, -53, -534, 7921], [1, -5, -72, -485, 9409]], 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/2/n/c'], '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': '4-819e2-1.1-c1e2-0-26', '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': '4-819e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 501866077153765371, 'z1': {'__RealLiteral__': 0, 'data': '1.01105507972503611508071023563', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1281664578677242362029577914787,2303671838984479053570907549760', 'Lhash_array': ['1281664578677242362029577914787', '2303671838984479053570907549760'], 'label': '4-819e2-1.1-c1e2-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/n/c'}