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lfunc_lfunctions • Show schema
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{'Lhash': '1684574241150143654270215056907', 'a10': 0, 'a2': 0, 'a3': -3, 'a4': -2, 'a5': -1, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.763329051202452, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1, -1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.1', 'coefficient_field': '1.1.1.1', 'conductor': 847, 'conductor_radical': 77, 'degree': 2, 'euler_factors': [[1, 0, 2], [1, 3, 3], [1, 1, 5], [1, -1], [1], [1, -4, 13], [1, 2, 17], [1, -6, 19], [1, 5, 23], [1, 10, 29], [1, -1, 31], [1, 5, 37], [1, -2, 41], [1, -8, 43], [1, -8, 47], [1, 6, 53], [1, -3, 59], [1, -2, 61], [1, 3, 67], [1, -1, 71], [1, 10, 73], [1, 6, 79], [1, 12, 83], [1, 15, 89], [1, 5, 97], [1, -12, 101], [1, 12, 103], [1, -10, 107], [1, 4, 109], [1, 19, 113]], 'euler_factors_factorization': [[[[1, 0, 2], 1]], [[[1, 3, 3], 1]], [[[1, 1, 5], 1]], [[[1, -1], 1]], [1], [[[1, -4, 13], 1]], [[[1, 2, 17], 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-2.0617461907210846, -1.7469624487720292, -0.5634489169947895, 1.1216146417391482, 2.738760007278179, 3.709996511751574, 3.6492737690116366, 2.4985671962995584, 0.5509765537440323], 'positive_zeros': ['1.32889476078570135837429482479693', '3.79024025385094143595808125255989', '4.39514744576497898862871693801358', '5.58596676881303008604275522262935', '5.80118601537640384820432803021459', '7.17057178520211720164419084101278', '7.956327480837723148155835866572624', '9.057617126467774810255940907586286', '9.901287739646014110658752080721249'], 'prelabel': '2-847-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.6006401233547196, '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': 583392718229927299, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32889476078570135837429482480', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.79024025385094143595808125256', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.39514744576497898862871693801', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.763329051202452, 'bad_primes': [7, 11], 'central_character': '1.1', 'conductor': 847, 'conductor_radical': 77, 'degree': 2, 'dirichlet_coefficients': [1, 0, -3, -2, -1, 0, 1, 0, 6, 0, 0, 6, 4, 0, 3, 4, -2, 0, 6, 2, -3, 0, -5, 0, -4, 0, -9, -2, -10, 0, 1, 0, 0, 0, -1, -12, -5, 0, -12, 0, 2, 0, 8, 0, -6, 0, 8, -12, 1, 0, 6, -8, -6, 0, 0, 0, -18, 0, 3, -6, 2, 0, 6, -8, -4, 0, -3, 4, 15, 0, 1, 0, -10, 0, 12, -12, 0, 0, -6, -4, 9, 0, -12, 6, 2, 0, 30, 0, -15, 0, 4, 10, -3, 0, -6, 0, -5, 0, 0, 8], 'euler11': [1, 0, 0], 'euler13': [1, -4, 13], 'euler17': [1, 2, 17], 'euler19': [1, -6, 19], 'euler2': [1, 0, 2], 'euler23': [1, 5, 23], 'euler29': [1, 10, 29], 'euler3': [1, 3, 3], 'euler31': [1, -1, 31], 'euler37': [1, 5, 37], 'euler41': [1, -2, 41], 'euler43': [1, -8, 43], 'euler47': [1, -8, 47], 'euler5': [1, 1, 5], 'euler53': [1, 6, 53], 'euler59': [1, -3, 59], 'euler61': [1, -2, 61], 'euler67': [1, 3, 67], 'euler7': [1, -1, 0], 'euler71': [1, -1, 71], 'euler73': [1, 10, 73], 'euler79': [1, 6, 79], 'euler83': [1, 12, 83], 'euler89': [1, 15, 89], 'euler97': [1, 5, 97], 'euler_factors': [[1, 0, 2], [1, 3, 3], [1, 1, 5], [1, -1, 0], [1, 0, 0], [1, -4, 13], [1, 2, 17], [1, -6, 19], [1, 5, 23], [1, 10, 29], [1, -1, 31], [1, 5, 37], [1, -2, 41], [1, -8, 43], [1, -8, 47], [1, 6, 53], [1, -3, 59], [1, -2, 61], [1, 3, 67], [1, -1, 71], [1, 10, 73], [1, 6, 79], [1, 12, 83], [1, 15, 89], [1, 5, 97]], 'index': 21, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/847/b', 'ModularForm/GL2/Q/holomorphic/847/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/847/2/a/b'], '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': '2-847-1.1-c1-0-21', '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': '2-847-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.6006401233547196, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 583392718229927299, 'z1': {'__RealLiteral__': 0, 'data': '1.32889476078570135837429482480', 'prec': 103}}
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lfunc_instances • Show schema
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id: 15917649
{'Lhash': '1684574241150143654270215056907', 'Lhash_array': ['1684574241150143654270215056907'], 'label': '2-847-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/2/a/b'}
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id: 24550755
{'Lhash': '1684574241150143654270215056907', 'Lhash_array': ['1684574241150143654270215056907'], 'label': '2-847-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/2/a/b/1/1'}
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id: 88432
{'Lhash': '583392718229927299', 'Lhash_array': ['583392718229927299'], 'label': '2-847-1.1-c1-0-21', 'type': 'ECQ', 'url': 'EllipticCurve/Q/847/b'}