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  • lfunc_lfunctions • Show schema
    {'Lhash': '1312933132644989733116178083381,1462332401569631678846535513022,2254217084526149970572794868530', 'a10': 0, 'a2': 2, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -8, 'a8': -2, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 172768.2590114603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [1]], [5, [1]], [31, [1, -3, 3, -1]]], 'bad_primes': [3, 5, 31], 'central_character': '6975.1', 'coefficient_field': '1.1.1.1', 'conductor': 339338109375, 'conductor_radical': 465, 'degree': 6, 'euler_factors': [[1, -2, 4, -6, 8, -8, 8], [1], [1], [1, 8, 37, 116, 259, 392, 343], [1, 3, 32, 65, 352, 363, 1331], [1, 4, 23, 114, 299, 676, 2197], [1, -7, 44, -179, 748, -2023, 4913], [1, -9, 84, -369, 1596, -3249, 6859], [1, -9, 92, -431, 2116, -4761, 12167], [1, 9, 80, 509, 2320, 7569, 24389], [1, -3, 3, -1], [1, 8, 119, 594, 4403, 10952, 50653], [1, 2, 65, 298, 2665, 3362, 68921], [1, 4, 49, 280, 2107, 7396, 79507], [1, 20, 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'6.77417623031062437807610965152030', '7.06757445413840345543504870411267', '7.21212712800466209942020080547968', '7.58217387195023104055332521475245', '7.896179137841743419878807482468177'], 'prelabel': '6-6975e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.4629521913143115, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1e3-0', 'trace_hash': 640869174205707286, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03572161951298536661248239314', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.15357686203623579087452051311', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.77826372986396874959286586911', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 172768.2590114603, 'bad_primes': [3, 5, 31], 'central_character': '1.1', 'conductor': 339338109375, 'conductor_radical': 465, 'degree': 6, 'dirichlet_coefficients': [1, 2, 0, 0, 0, 0, -8, -2, 0, 0, -3, 0, -4, -16, 0, 0, 7, 0, 9, 0, 0, -6, 9, 0, 0, -8, 0, 0, -9, 0, 3, 0, 0, 14, 0, 0, -8, 18, 0, 0, -2, 0, -4, 0, 0, 18, -20, 0, 27, 0, 0, 0, -25, 0, 0, 16, 0, -18, -2, 0, 2, 6, 0, -4, 0, 0, -15, 0, 0, 0, 12, 0, -2, -16, 0, 0, 24, 0, 12, 0, 0, -4, 13, 0, 0, -8, 0, 6, 15, 0, 32, 0, 0, -40, 0, 0, -7, 54, 0, 0], 'euler11': [1, 3, 32, 65, 352, 363, 1331], 'euler13': [1, 4, 23, 114, 299, 676, 2197], 'euler17': [1, -7, 44, -179, 748, -2023, 4913], 'euler19': [1, -9, 84, -369, 1596, -3249, 6859], 'euler2': [1, -2, 4, -6, 8, -8, 8], 'euler23': [1, -9, 92, -431, 2116, -4761, 12167], 'euler29': [1, 9, 80, 509, 2320, 7569, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -3, 3, -1, 0, 0, 0], 'euler37': [1, 8, 119, 594, 4403, 10952, 50653], 'euler41': [1, 2, 65, 298, 2665, 3362, 68921], 'euler43': [1, 4, 49, 280, 2107, 7396, 79507], 'euler47': [1, 20, 261, 2088, 12267, 44180, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, 25, 288, 2301, 15264, 70225, 148877], 'euler59': [1, 2, 103, 162, 6077, 6962, 205379], 'euler61': [1, -2, 131, -204, 7991, -7442, 226981], 'euler67': [1, 15, 236, 2011, 15812, 67335, 300763], 'euler7': [1, 8, 37, 116, 259, 392, 343], 'euler71': [1, -12, 101, -520, 7171, -60492, 357911], 'euler73': [1, 2, 71, 588, 5183, 10658, 389017], 'euler79': [1, -12, 165, -1982, 13035, -74892, 493039], 'euler83': [1, -13, 192, -1287, 15936, -89557, 571787], 'euler89': [1, -15, 338, -2773, 30082, -118815, 704969], 'euler97': [1, 7, 262, 1255, 25414, 65863, 912673], 'euler_factors': [[1, -2, 4, -6, 8, -8, 8], [1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 8, 37, 116, 259, 392, 343], [1, 3, 32, 65, 352, 363, 1331], [1, 4, 23, 114, 299, 676, 2197], [1, -7, 44, -179, 748, -2023, 4913], [1, -9, 84, -369, 1596, -3249, 6859], [1, -9, 92, -431, 2116, -4761, 12167], [1, 9, 80, 509, 2320, 7569, 24389], [1, -3, 3, -1, 0, 0, 0], [1, 8, 119, 594, 4403, 10952, 50653], [1, 2, 65, 298, 2665, 3362, 68921], [1, 4, 49, 280, 2107, 7396, 79507], [1, 20, 261, 2088, 12267, 44180, 103823], [1, 25, 288, 2301, 15264, 70225, 148877], [1, 2, 103, 162, 6077, 6962, 205379], [1, -2, 131, -204, 7991, -7442, 226981], [1, 15, 236, 2011, 15812, 67335, 300763], [1, -12, 101, -520, 7171, -60492, 357911], [1, 2, 71, 588, 5183, 10658, 389017], [1, -12, 165, -1982, 13035, -74892, 493039], [1, -13, 192, -1287, 15936, -89557, 571787], [1, -15, 338, -2773, 30082, -118815, 704969], [1, 7, 262, 1255, 25414, 65863, 912673]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6975/2/a/bg'], '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': '6-6975e3-1.1-c1e3-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'prelabel': '6-6975e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.4629521913143115, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 640869174205707286, 'z1': {'__RealLiteral__': 0, 'data': '1.03572161951298536661248239314', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1312933132644989733116178083381,1462332401569631678846535513022,2254217084526149970572794868530', 'Lhash_array': ['1312933132644989733116178083381', '1462332401569631678846535513022', '2254217084526149970572794868530'], 'factors': ['2-6975-1.1-c1-0-128', '2-6975-1.1-c1-0-155', '2-6975-1.1-c1-0-227'], 'label': '6-6975e3-1.1-c1e3-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6975/2/a/bg'}