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lfunc_lfunctions • Show schema
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{'Lhash': '1722382283569330657666129204895', 'a10': 2, 'a2': -2, 'a3': 1, 'a4': 2, 'a5': -1, 'a6': -2, 'a7': 2, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.384442802565047, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [1, 1]], [17, [1]]], 'bad_primes': [11, 17], 'central_character': '3179.1', 'coefficient_field': '1.1.1.1', 'conductor': 3179, 'conductor_radical': 187, 'degree': 2, 'euler_factors': [[1, 2, 2], [1, -1, 3], [1, 1, 5], [1, -2, 7], [1, 1], [1, -4, 13], [1], [1, 0, 19], [1, -1, 23], [1, 0, 29], [1, 7, 31], [1, 3, 37], [1, -8, 41], [1, 6, 43], [1, -8, 47], [1, 6, 53], [1, -5, 59], [1, 12, 61], [1, 7, 67], [1, -3, 71], [1, 4, 73], [1, -10, 79], [1, 6, 83], [1, -15, 89], [1, -7, 97], [1, -2, 101], [1, 16, 103], [1, 18, 107], [1, 10, 109], [1, 9, 113]], 'euler_factors_factorization': [[[[1, 2, 2], 1]], [[[1, -1, 3], 1]], [[[1, 1, 5], 1]], [[[1, -2, 7], 1]], [[[1, 1], 1]], [[[1, -4, 13], 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-8.901995981539367, -9.383237455115129, -9.621705168172303, -9.608660680487187, -9.346280602427697, -8.84768132752704, -8.136398199703802, -7.245337514839285], 'positive_zeros': ['1.35872004735313563095158147019552', '2.23424739606738503289626266309744', '3.36204123451452550822417446570934', '4.24329958875835728994074784591582', '5.32604921703423297753132504908635', '6.22323910317192896404427293385880', '7.29774796427450513185159809590337', '7.907366117668739819170581630667165', '8.263155997010663128403798948932380'], 'prelabel': '2-3179-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.038297609566653, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 526785585460647337, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35872004735313563095158147020', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23424739606738503289626266310', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36204123451452550822417446571', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.384442802565047, 'bad_primes': [11, 17], 'central_character': '1.1', 'conductor': 3179, 'conductor_radical': 187, 'degree': 2, 'dirichlet_coefficients': [1, -2, 1, 2, -1, -2, 2, 0, -2, 2, -1, 2, 4, -4, -1, -4, 0, 4, 0, -2, 2, 2, 1, 0, -4, -8, -5, 4, 0, 2, -7, 8, -1, 0, -2, -4, -3, 0, 4, 0, 8, -4, -6, -2, 2, -2, 8, -4, -3, 8, 0, 8, -6, 10, 1, 0, 0, 0, 5, -2, -12, 14, -4, -8, -4, 2, -7, 0, 1, 4, 3, 0, -4, 6, -4, 0, -2, -8, 10, 4, 1, -16, -6, 4, 0, 12, 0, 0, 15, -4, 8, 2, -7, -16, 0, 8, 7, 6, 2, -8], 'euler11': [1, 1, 0], 'euler13': [1, -4, 13], 'euler17': [1, 0, 0], 'euler19': [1, 0, 19], 'euler2': [1, 2, 2], 'euler23': [1, -1, 23], 'euler29': [1, 0, 29], 'euler3': [1, -1, 3], 'euler31': [1, 7, 31], 'euler37': [1, 3, 37], 'euler41': [1, -8, 41], 'euler43': [1, 6, 43], 'euler47': [1, -8, 47], 'euler5': [1, 1, 5], 'euler53': [1, 6, 53], 'euler59': [1, -5, 59], 'euler61': [1, 12, 61], 'euler67': [1, 7, 67], 'euler7': [1, -2, 7], 'euler71': [1, -3, 71], 'euler73': [1, 4, 73], 'euler79': [1, -10, 79], 'euler83': [1, 6, 83], 'euler89': [1, -15, 89], 'euler97': [1, -7, 97], 'euler_factors': [[1, 2, 2], [1, -1, 3], [1, 1, 5], [1, -2, 7], [1, 1, 0], [1, -4, 13], [1, 0, 0], [1, 0, 19], [1, -1, 23], [1, 0, 29], [1, 7, 31], [1, 3, 37], [1, -8, 41], [1, 6, 43], [1, -8, 47], [1, 6, 53], [1, -5, 59], [1, 12, 61], [1, 7, 67], [1, -3, 71], [1, 4, 73], [1, -10, 79], [1, 6, 83], [1, -15, 89], [1, -7, 97]], 'index': 149, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3179/a', 'ModularForm/GL2/Q/holomorphic/3179/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/3179/2/a/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-3179-1.1-c1-0-149', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-3179-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.038297609566653, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 526785585460647337, 'z1': {'__RealLiteral__': 0, 'data': '1.35872004735313563095158147020', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20536923
{'Lhash': '1722382283569330657666129204895', 'Lhash_array': ['1722382283569330657666129204895'], 'label': '2-3179-1.1-c1-0-149', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3179/2/a/a'}
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id: 24560409
{'Lhash': '1722382283569330657666129204895', 'Lhash_array': ['1722382283569330657666129204895'], 'label': '2-3179-1.1-c1-0-149', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3179/2/a/a/1/1'}
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id: 38036
{'Lhash': '526785585460647337', 'Lhash_array': ['526785585460647337'], 'label': '2-3179-1.1-c1-0-149', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3179/a'}