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lfunc_lfunctions • Show schema
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{'Lhash': '950962680728975951718087562252,1352716535396486115749363111537', 'a10': -2, 'a2': -2, 'a3': 2, 'a4': 3, 'a5': 1, 'a6': -4, 'a7': 0, 'a8': -4, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 931.3985971344308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 1]], [3, [1, -2, 1]], [7, [1]], [13, [1, -2, 1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '3822.1', 'coefficient_field': '1.1.1.1', 'conductor': 14607684, 'conductor_radical': 546, 'degree': 4, 'euler_factors': [[1, 2, 1], [1, -2, 1], [1, -1, -4, -5, 25], [1], [1, -3, 10, -33, 121], [1, -2, 1], [1, -7, 32, -119, 289], [1, 3, 26, 57, 361], [1, 3, 34, 69, 529], [1, -9, 64, -261, 841], [1, 16, 126, 496, 961], [1, 1, 60, 37, 1369], [1, -2, 26, -82, 1681], [1, -3, 74, -129, 1849], [1, 0, 94, 0, 2209], [1, -20, 206, -1060, 2809], [1, 16, 182, 944, 3481], [1, -17, 180, -1037, 3721], [1, -10, 102, -670, 4489], [1, 0, 142, 0, 5041], [1, -3, 20, 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'rational': True, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 890810253261089907, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.75017728115126000794265505029', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.06710519062030289478825316279', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.79978323713822224518898510137', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 931.3985971344308, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 14607684, 'conductor_radical': 546, 'degree': 4, 'dirichlet_coefficients': [1, -2, 2, 3, 1, -4, 0, -4, 3, -2, 3, 6, 2, 0, 2, 5, 7, -6, -3, 3, 0, -6, -3, -8, 5, -4, 4, 0, 9, -4, -16, -6, 6, -14, 0, 9, -1, 6, 4, -4, 2, 0, 3, 9, 3, 6, 0, 10, 0, -10, 14, 6, 20, -8, 3, 0, -6, -18, -16, 6, 17, 32, 0, 7, 2, -12, 10, 21, -6, 0, 0, -12, 3, 2, 10, -9, 0, -8, 10, 5, 5, -4, -6, 0, 7, -6, 18, -12, 28, -6, 0, -9, -32, 0, -3, -12, 0, 0, 9, 15], 'euler11': [1, -3, 10, -33, 121], 'euler13': [1, -2, 1, 0, 0], 'euler17': [1, -7, 32, -119, 289], 'euler19': [1, 3, 26, 57, 361], 'euler2': [1, 2, 1, 0, 0], 'euler23': [1, 3, 34, 69, 529], 'euler29': [1, -9, 64, -261, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, 16, 126, 496, 961], 'euler37': [1, 1, 60, 37, 1369], 'euler41': [1, -2, 26, -82, 1681], 'euler43': [1, -3, 74, -129, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, -1, -4, -5, 25], 'euler53': [1, -20, 206, -1060, 2809], 'euler59': [1, 16, 182, 944, 3481], 'euler61': [1, -17, 180, -1037, 3721], 'euler67': [1, -10, 102, -670, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -3, 20, -219, 5329], 'euler79': [1, -10, 126, -790, 6241], 'euler83': [1, 6, 118, 498, 6889], 'euler89': [1, -28, 374, -2492, 7921], 'euler97': [1, 0, -34, 0, 9409], 'euler_factors': [[1, 2, 1, 0, 0], [1, -2, 1, 0, 0], [1, -1, -4, -5, 25], [1, 0, 0, 0, 0], [1, -3, 10, -33, 121], [1, -2, 1, 0, 0], [1, -7, 32, -119, 289], [1, 3, 26, 57, 361], [1, 3, 34, 69, 529], [1, -9, 64, -261, 841], [1, 16, 126, 496, 961], [1, 1, 60, 37, 1369], [1, -2, 26, -82, 1681], [1, -3, 74, -129, 1849], [1, 0, 94, 0, 2209], [1, -20, 206, -1060, 2809], [1, 16, 182, 944, 3481], [1, -17, 180, -1037, 3721], [1, -10, 102, -670, 4489], [1, 0, 142, 0, 5041], [1, -3, 20, -219, 5329], [1, -10, 126, -790, 6241], [1, 6, 118, 498, 6889], [1, -28, 374, -2492, 7921], [1, 0, -34, 0, 9409]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3822/2/a/bm'], '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': '4-3822e2-1.1-c1e2-0-6', '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': '4-3822e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 890810253261089907, 'z1': {'__RealLiteral__': 0, 'data': '0.75017728115126000794265505029', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '950962680728975951718087562252,1352716535396486115749363111537', 'Lhash_array': ['950962680728975951718087562252', '1352716535396486115749363111537'], 'label': '4-3822e2-1.1-c1e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3822/2/a/bm'}