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lfunc_lfunctions • Show schema
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{'Lhash': '954033100297681912622525412915', 'a10': -18, 'a2': 2, 'a3': -3, 'a4': 4, 'a5': -9, 'a6': -6, 'a7': 7, 'a8': 8, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.99584506554546, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2]], [3, [1, 3]], [7, [1, -7]], [23, [1, 23]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '966.1', 'coefficient_field': '1.1.1.1', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[1, -2], [1, 3], [1, 9, 125], [1, -7], [1, 12, 1331], [1, -11, 2197], [1, -96, 4913], [1, 40, 6859], [1, 23], [1, 231, 24389], [1, 94, 29791], [1, -47, 50653], [1, 27, 68921], [1, -479, 79507], [1, -423, 103823], [1, -516, 148877], [1, -882, 205379], [1, -842, 226981], [1, 844, 300763], [1, -654, 357911], [1, 496, 389017], [1, -260, 493039], [1, 156, 571787], [1, 414, 704969], [1, -1343, 912673], [1, -270, 1030301], [1, -449, 1092727], [1, -276, 1225043], [1, 589, 1295029], [1, -1779, 1442897]], 'euler_factors_factorization': [[[[1, -2], 1]], [[[1, 3], 1]], [[[1, 9, 125], 1]], [[[1, -7], 1]], [[[1, 12, 1331], 1]], [[[1, -11, 2197], 1]], [[[1, -96, 4913], 1]], [[[1, 40, 6859], 1]], [[[1, 23], 1]], [[[1, 231, 24389], 1]], [[[1, 94, 29791], 1]], [[[1, -47, 50653], 1]], [[[1, 27, 68921], 1]], [[[1, -479, 79507], 1]], [[[1, -423, 103823], 1]], [[[1, -516, 148877], 1]], [[[1, -882, 205379], 1]], [[[1, -842, 226981], 1]], [[[1, 844, 300763], 1]], [[[1, -654, 357911], 1]], [[[1, 496, 389017], 1]], [[[1, -260, 493039], 1]], [[[1, 156, 571787], 1]], [[[1, 414, 704969], 1]], [[[1, -1343, 912673], 1]], [[[1, -270, 1030301], 1]], [[[1, -449, 1092727], 1]], [[[1, -276, 1225043], 1]], [[[1, 589, 1295029], 1]], [[[1, -1779, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-966-1.1-c3-0-15', 'leading_term': '2.27963672141354656354403419971000000000000000000000000000000000000000000000000000000000000', 'load_key': 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'2-966-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.549559262999758, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 136112200888972879, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.75259941511163770091287571706', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18702741690359664785202207519', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62878726202766341279771401105', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 56.99584506554546, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'dirichlet_coefficients': [1, 2, -3, 4, -9, -6, 7, 8, 9, -18, -12, -12, 11, 14, 27, 16, 96, 18, -40, -36, -21, -24, -23, -24, -44, 22, -27, 28, -231, 54, -94, 32, 36, 192, -63, 36, 47, -80, -33, -72, -27, -42, 479, -48, -81, -46, 423, -48, 49, -88, -288, 44, 516, -54, 108, 56, 120, -462, 882, 108, 842, -188, 63, 64, -99, 72, -844, 384, 69, -126, 654, 72, -496, 94, 132, -160, -84, -66, 260, -144, 81, -54, -156, -84, -864, 958, 693, -96, -414, -162, 77, -92, 282, 846, 360, -96, 1343, 98, -108, -176], 'euler11': [1, 12, 1331], 'euler13': [1, -11, 2197], 'euler17': [1, -96, 4913], 'euler19': [1, 40, 6859], 'euler2': [1, -2, 0], 'euler23': [1, 23, 0], 'euler29': [1, 231, 24389], 'euler3': [1, 3, 0], 'euler31': [1, 94, 29791], 'euler37': [1, -47, 50653], 'euler41': [1, 27, 68921], 'euler43': [1, -479, 79507], 'euler47': [1, -423, 103823], 'euler5': [1, 9, 125], 'euler53': [1, -516, 148877], 'euler59': [1, -882, 205379], 'euler61': [1, -842, 226981], 'euler67': [1, 844, 300763], 'euler7': [1, -7, 0], 'euler71': [1, -654, 357911], 'euler73': [1, 496, 389017], 'euler79': [1, -260, 493039], 'euler83': [1, 156, 571787], 'euler89': [1, 414, 704969], 'euler97': [1, -1343, 912673], 'euler_factors': [[1, -2, 0], [1, 3, 0], [1, 9, 125], [1, -7, 0], [1, 12, 1331], [1, -11, 2197], [1, -96, 4913], [1, 40, 6859], [1, 23, 0], [1, 231, 24389], [1, 94, 29791], [1, -47, 50653], [1, 27, 68921], [1, -479, 79507], [1, -423, 103823], [1, -516, 148877], [1, -882, 205379], [1, -842, 226981], [1, 844, 300763], [1, -654, 357911], [1, 496, 389017], [1, -260, 493039], [1, 156, 571787], [1, 414, 704969], [1, -1343, 912673]], 'index': 15, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/966/4/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/966/4/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': 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': '2-966-1.1-c3-0-15', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-966-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.549559262999758, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 136112200888972879, 'z1': {'__RealLiteral__': 0, 'data': '0.75259941511163770091287571706', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20422223
{'Lhash': '954033100297681912622525412915', 'Lhash_array': ['954033100297681912622525412915'], 'label': '2-966-1.1-c3-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/966/4/a/b'}
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id: 24578304
{'Lhash': '954033100297681912622525412915', 'Lhash_array': ['954033100297681912622525412915'], 'label': '2-966-1.1-c3-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/966/4/a/b/1/1'}