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{'Lhash': '1854025434530800776222806263384,2145271516589596346573613267969,2306923543785287759282689041289', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41390.118034291074, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3, 3, -1]], [19, [1]]], 'bad_primes': [2, 3, 19], 'central_character': '4332.1', 'coefficient_field': '1.1.1.1', 'conductor': 81295282368, 'conductor_radical': 114, 'degree': 6, 'euler_factors': [[1], [1, -3, 3, -1], [1, -3, 15, -27, 75, -75, 125], [1, 3, 15, 25, 105, 147, 343], [1, 3, 15, 63, 165, 363, 1331], [1, 9, 54, 217, 702, 1521, 2197], [1, 3, 33, 99, 561, 867, 4913], [1], [1, 12, 96, 495, 2208, 6348, 12167], [1, -3, 42, -63, 1218, -2523, 24389], [1, -6, 78, -353, 2418, -5766, 29791], [1, 6, 102, 427, 3774, 8214, 50653], [1, 18, 204, 1503, 8364, 30258, 68921], [1, 21, 240, 1825, 10320, 38829, 79507], 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'5.81424451788120511546486821619529', '6.11626791364696536639153149591685', '6.52094437352877995551163102860633', '6.68378800929815819077939688638029', '6.70411091627965346639914496497680', '7.04704844059734516184952481446243', '7.30884313479398226268590885441937', '7.46653754515956496378078409800675', '8.077248767350792655722011349523980', '8.147527554249994222343430382393890', '8.167919246004900937174280761350501'], 'prelabel': '6-4332e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.881427901081392, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e3-0', 'trace_hash': 2052789154732278281, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46256818258674725927074227038', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.69232083052172181852257790814', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.81984179502612656483197352897', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41390.118034291074, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 81295282368, 'conductor_radical': 114, 'degree': 6, 'dirichlet_coefficients': [1, 0, 3, 0, 3, 0, -3, 0, 6, 0, -3, 0, -9, 0, 9, 0, -3, 0, 0, 0, -9, 0, -12, 0, -6, 0, 10, 0, 3, 0, 6, 0, -9, 0, -9, 0, -6, 0, -27, 0, -18, 0, -21, 0, 18, 0, -15, 0, -6, 0, -9, 0, 6, 0, -9, 0, 0, 0, 9, 0, 15, 0, -18, 0, -27, 0, -6, 0, -36, 0, 9, 0, -6, 0, -18, 0, 9, 0, -27, 0, 15, 0, -15, 0, -9, 0, 9, 0, 12, 0, 27, 0, 18, 0, 0, 0, 6, 0, -18, 0], 'euler11': [1, 3, 15, 63, 165, 363, 1331], 'euler13': [1, 9, 54, 217, 702, 1521, 2197], 'euler17': [1, 3, 33, 99, 561, 867, 4913], 'euler19': [1, 0, 0, 0, 0, 0, 0], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 12, 96, 495, 2208, 6348, 12167], 'euler29': [1, -3, 42, -63, 1218, -2523, 24389], 'euler3': [1, -3, 3, -1, 0, 0, 0], 'euler31': [1, -6, 78, -353, 2418, -5766, 29791], 'euler37': [1, 6, 102, 427, 3774, 8214, 50653], 'euler41': [1, 18, 204, 1503, 8364, 30258, 68921], 'euler43': [1, 21, 240, 1825, 10320, 38829, 79507], 'euler47': [1, 15, 213, 1521, 10011, 33135, 103823], 'euler5': [1, -3, 15, -27, 75, -75, 125], 'euler53': [1, -6, 114, -423, 6042, -16854, 148877], 'euler59': [1, -9, 141, -1071, 8319, -31329, 205379], 'euler61': [1, -15, 249, -1901, 15189, -55815, 226981], 'euler67': [1, 6, 201, 796, 13467, 26934, 300763], 'euler7': [1, 3, 15, 25, 105, 147, 343], 'euler71': [1, -9, 132, -765, 9372, -45369, 357911], 'euler73': [1, 6, 192, 895, 14016, 31974, 389017], 'euler79': [1, 27, 468, 4879, 36972, 168507, 493039], 'euler83': [1, 15, 213, 2493, 17679, 103335, 571787], 'euler89': [1, -12, 186, -1755, 16554, -95052, 704969], 'euler97': [1, -6, 186, -785, 18042, -56454, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, -3, 3, -1, 0, 0, 0], [1, -3, 15, -27, 75, -75, 125], [1, 3, 15, 25, 105, 147, 343], [1, 3, 15, 63, 165, 363, 1331], [1, 9, 54, 217, 702, 1521, 2197], [1, 3, 33, 99, 561, 867, 4913], [1, 0, 0, 0, 0, 0, 0], [1, 12, 96, 495, 2208, 6348, 12167], [1, -3, 42, -63, 1218, -2523, 24389], [1, -6, 78, -353, 2418, -5766, 29791], [1, 6, 102, 427, 3774, 8214, 50653], [1, 18, 204, 1503, 8364, 30258, 68921], [1, 21, 240, 1825, 10320, 38829, 79507], [1, 15, 213, 1521, 10011, 33135, 103823], [1, -6, 114, -423, 6042, -16854, 148877], [1, -9, 141, -1071, 8319, -31329, 205379], [1, -15, 249, -1901, 15189, -55815, 226981], [1, 6, 201, 796, 13467, 26934, 300763], [1, -9, 132, -765, 9372, -45369, 357911], [1, 6, 192, 895, 14016, 31974, 389017], [1, 27, 468, 4879, 36972, 168507, 493039], [1, 15, 213, 2493, 17679, 103335, 571787], [1, -12, 186, -1755, 16554, -95052, 704969], [1, -6, 186, -785, 18042, -56454, 912673]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4332/2/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': '6-4332e3-1.1-c1e3-0-1', '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': 3, 'prelabel': '6-4332e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.881427901081392, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 2052789154732278281, 'z1': {'__RealLiteral__': 0, 'data': '1.46256818258674725927074227038', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1854025434530800776222806263384,2145271516589596346573613267969,2306923543785287759282689041289', 'Lhash_array': ['1854025434530800776222806263384', '2145271516589596346573613267969', '2306923543785287759282689041289'], 'label': '6-4332e3-1.1-c1e3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4332/2/a/o'}