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lfunc_lfunctions • Show schema
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{'Lhash': '709724111256934644243681546217,856907748698662604366627297464,1834070711265657002905612240479', 'a10': 0, 'a2': 1, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -5, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4227.721822676464, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '2025.1', 'coefficient_field': '1.1.1.1', 'conductor': 8303765625, 'conductor_radical': 15, 'degree': 6, 'euler_factors': [[1, -1, 1, -1, 2, -4, 8], [1], [1], [1, 5, 24, 67, 168, 245, 343], [1, -2, 25, -32, 275, -242, 1331], [1, 4, 35, 100, 455, 676, 2197], [1, 2, 43, 56, 731, 578, 4913], [1, -4, 53, -148, 1007, -1444, 6859], [1, -3, 36, -21, 828, -1587, 12167], [1, -7, 58, -355, 1682, -5887, 24389], [1, -8, 33, -28, 1023, -7688, 29791], [1, 6, 99, 440, 3663, 8214, 50653], [1, -13, 142, -1069, 5822, -21853, 68921], [1, 10, 125, 856, 5375, 18490, 79507], [1, -13, 130, 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'data': '0.67598102232932628298150578290', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.44682668152837115788130489290', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4227.721822676464, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 8303765625, 'conductor_radical': 15, 'degree': 6, 'dirichlet_coefficients': [1, 1, 0, 0, 0, 0, -5, 0, 0, 0, 2, 0, -4, -5, 0, -1, -2, 0, 4, 0, 0, 2, 3, 0, 0, -4, 0, 0, 7, 0, 8, 1, 0, -2, 0, 0, -6, 4, 0, 0, 13, 0, -10, 0, 0, 3, 13, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 7, 2, 0, 1, 8, 0, -2, 0, 0, -11, 0, 0, 0, 10, 0, 8, -6, 0, 0, -10, 0, 2, 0, 0, 13, -15, 0, 0, -10, 0, 0, 9, 0, 20, 0, 0, 13, 0, 0, 18, 1, 0, 0], 'euler11': [1, -2, 25, -32, 275, -242, 1331], 'euler13': [1, 4, 35, 100, 455, 676, 2197], 'euler17': [1, 2, 43, 56, 731, 578, 4913], 'euler19': [1, -4, 53, -148, 1007, -1444, 6859], 'euler2': [1, -1, 1, -1, 2, -4, 8], 'euler23': [1, -3, 36, -21, 828, -1587, 12167], 'euler29': [1, -7, 58, -355, 1682, -5887, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -8, 33, -28, 1023, -7688, 29791], 'euler37': [1, 6, 99, 440, 3663, 8214, 50653], 'euler41': [1, -13, 142, -1069, 5822, -21853, 68921], 'euler43': [1, 10, 125, 856, 5375, 18490, 79507], 'euler47': [1, -13, 130, -853, 6110, -28717, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, 2, 139, 188, 7367, 5618, 148877], 'euler59': [1, -2, 157, -212, 9263, -6962, 205379], 'euler61': [1, -1, 146, -193, 8906, -3721, 226981], 'euler67': [1, 11, 162, 967, 10854, 49379, 300763], 'euler7': [1, 5, 24, 67, 168, 245, 343], 'euler71': [1, -10, 121, -712, 8591, -50410, 357911], 'euler73': [1, -8, 155, -1040, 11315, -42632, 389017], 'euler79': [1, -2, 153, -340, 12087, -12482, 493039], 'euler83': [1, 15, 276, 2409, 22908, 103335, 571787], 'euler89': [1, -9, 294, -1629, 26166, -71289, 704969], 'euler97': [1, -18, 255, -2188, 24735, -169362, 912673], 'euler_factors': [[1, -1, 1, -1, 2, -4, 8], [1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 5, 24, 67, 168, 245, 343], [1, -2, 25, -32, 275, -242, 1331], [1, 4, 35, 100, 455, 676, 2197], [1, 2, 43, 56, 731, 578, 4913], [1, -4, 53, -148, 1007, -1444, 6859], [1, -3, 36, -21, 828, -1587, 12167], [1, -7, 58, -355, 1682, -5887, 24389], [1, -8, 33, -28, 1023, -7688, 29791], [1, 6, 99, 440, 3663, 8214, 50653], [1, -13, 142, -1069, 5822, -21853, 68921], [1, 10, 125, 856, 5375, 18490, 79507], [1, -13, 130, -853, 6110, -28717, 103823], [1, 2, 139, 188, 7367, 5618, 148877], [1, -2, 157, -212, 9263, -6962, 205379], [1, -1, 146, -193, 8906, -3721, 226981], [1, 11, 162, 967, 10854, 49379, 300763], [1, -10, 121, -712, 8591, -50410, 357911], [1, -8, 155, -1040, 11315, -42632, 389017], [1, -2, 153, -340, 12087, -12482, 493039], [1, 15, 276, 2409, 22908, 103335, 571787], [1, -9, 294, -1629, 26166, -71289, 704969], [1, -18, 255, -2188, 24735, -169362, 912673]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2025/2/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': '6-45e6-1.1-c1e3-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-45e6-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.021157346997166, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 184590075334664835, 'z1': {'__RealLiteral__': 0, 'data': '0.55987360486332355815705329965', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '709724111256934644243681546217,856907748698662604366627297464,1834070711265657002905612240479', 'Lhash_array': ['709724111256934644243681546217', '856907748698662604366627297464', '1834070711265657002905612240479'], 'label': '6-45e6-1.1-c1e3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2025/2/a/o'}