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lfunc_lfunctions • Show schema
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{'Lhash': '962166427319139509904112365813', 'a10': 18, 'a2': -2, 'a3': 0, 'a4': 4, 'a5': -9, 'a6': 0, 'a7': 0, 'a8': -8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 52.039684625063245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '882.1', 'coefficient_field': '1.1.1.1', 'conductor': 882, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[1, 2], [1], [1, 9, 125], [1], [1, -57, 1331], [1, -70, 2197], [1, -51, 4913], [1, 5, 6859], [1, 69, 12167], [1, 114, 24389], [1, 23, 29791], [1, 253, 50653], [1, 42, 68921], [1, 124, 79507], [1, -201, 103823], [1, -393, 148877], [1, -219, 205379], [1, -709, 226981], [1, -419, 300763], [1, -96, 357911], [1, -313, 389017], [1, -461, 493039], [1, 588, 571787], [1, 1017, 704969], [1, -1834, 912673], [1, 285, 1030301], [1, -499, 1092727], [1, -1107, 1225043], [1, -923, 1295029], [1, 1542, 1442897]], 'euler_factors_factorization': [[[[1, 2], 1]], [1], [[[1, 9, 125], 1]], [1], [[[1, -57, 1331], 1]], [[[1, -70, 2197], 1]], [[[1, -51, 4913], 1]], [[[1, 5, 6859], 1]], [[[1, 69, 12167], 1]], [[[1, 114, 24389], 1]], [[[1, 23, 29791], 1]], [[[1, 253, 50653], 1]], [[[1, 42, 68921], 1]], [[[1, 124, 79507], 1]], [[[1, -201, 103823], 1]], [[[1, -393, 148877], 1]], [[[1, -219, 205379], 1]], [[[1, -709, 226981], 1]], [[[1, -419, 300763], 1]], [[[1, -96, 357911], 1]], [[[1, -313, 389017], 1]], [[[1, -461, 493039], 1]], [[[1, 588, 571787], 1]], [[[1, 1017, 704969], 1]], [[[1, -1834, 912673], 1]], [[[1, 285, 1030301], 1]], [[[1, -499, 1092727], 1]], [[[1, -1107, 1225043], 1]], [[[1, -923, 1295029], 1]], [[[1, 1542, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-882-1.1-c3-0-9', 'leading_term': '1.413343085868019882654935736800000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/882/4/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.4133430858680198, 1.4029992140552563, 1.3721065316552452, 1.3210819416233075, 1.250620538290982, 1.161695680655324, 1.0555584889766594, 0.9337361944296445, 0.7980286578948, 0.650502294268752, 0.493480597389533, 0.3295304607954009, 0.16144353250817714, -0.0077880721949332215, -0.17500224895132555, -0.33690395669674217, -0.49010902730185846, -0.6311946857556837, -0.7567564809726991, -0.8634710575303889, -0.9481639200203278, -1.0078810625976395, -1.0399630656793415, -1.0421200089293796, -1.0125053242796567, -0.9497865244097913, -0.853210600268173, -0.7226617947897092, -0.5587094370643503, -0.36264356879584253, -0.13649621842138188, 0.11695361864941466, 0.3941929511402472, 0.6910070077934931, 1.0025315512416162, 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'rational': True, 'root_analytic_conductor': 7.213853659803701, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 215245269405830803, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.75901547882824325681257028093', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.79010103899284419972114530943', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56898143194228684870629988144', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 52.039684625063245, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 882, 'conductor_radical': 42, 'degree': 2, 'dirichlet_coefficients': [1, -2, 0, 4, -9, 0, 0, -8, 0, 18, 57, 0, 70, 0, 0, 16, 51, 0, -5, -36, 0, -114, -69, 0, -44, -140, 0, 0, -114, 0, -23, -32, 0, -102, 0, 0, -253, 10, 0, 72, -42, 0, -124, 228, 0, 138, 201, 0, 0, 88, 0, 280, 393, 0, -513, 0, 0, 228, 219, 0, 709, 46, 0, 64, -630, 0, 419, 204, 0, 0, 96, 0, 313, 506, 0, -20, 0, 0, 461, -144, 0, 84, -588, 0, -459, 248, 0, -456, -1017, 0, 0, -276, 0, -402, 45, 0, 1834, 0, 0, -176], 'euler11': [1, -57, 1331], 'euler13': [1, -70, 2197], 'euler17': [1, -51, 4913], 'euler19': [1, 5, 6859], 'euler2': [1, 2, 0], 'euler23': [1, 69, 12167], 'euler29': [1, 114, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 23, 29791], 'euler37': [1, 253, 50653], 'euler41': [1, 42, 68921], 'euler43': [1, 124, 79507], 'euler47': [1, -201, 103823], 'euler5': [1, 9, 125], 'euler53': [1, -393, 148877], 'euler59': [1, -219, 205379], 'euler61': [1, -709, 226981], 'euler67': [1, -419, 300763], 'euler7': [1, 0, 0], 'euler71': [1, -96, 357911], 'euler73': [1, -313, 389017], 'euler79': [1, -461, 493039], 'euler83': [1, 588, 571787], 'euler89': [1, 1017, 704969], 'euler97': [1, -1834, 912673], 'euler_factors': [[1, 2, 0], [1, 0, 0], [1, 9, 125], [1, 0, 0], [1, -57, 1331], [1, -70, 2197], [1, -51, 4913], [1, 5, 6859], [1, 69, 12167], [1, 114, 24389], [1, 23, 29791], [1, 253, 50653], [1, 42, 68921], [1, 124, 79507], [1, -201, 103823], [1, -393, 148877], [1, -219, 205379], [1, -709, 226981], [1, -419, 300763], [1, -96, 357911], [1, -313, 389017], [1, -461, 493039], [1, 588, 571787], [1, 1017, 704969], [1, -1834, 912673]], 'index': 9, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/4/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/882/4/a/c'], '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': '2-882-1.1-c3-0-9', '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': '2-882-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.213853659803701, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 215245269405830803, 'z1': {'__RealLiteral__': 0, 'data': '0.75901547882824325681257028093', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20131965
{'Lhash': '962166427319139509904112365813', 'Lhash_array': ['962166427319139509904112365813'], 'label': '2-882-1.1-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/4/a/c'}
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id: 24575447
{'Lhash': '962166427319139509904112365813', 'Lhash_array': ['962166427319139509904112365813'], 'label': '2-882-1.1-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/4/a/c/1/1'}