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lfunc_lfunctions • Show schema
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{'Lhash': '823582917908884411717168919378', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 16, 'a6': 0, 'a7': -28, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 110.45157553074648, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [13, [1, 13]]], 'bad_primes': [2, 3, 13], 'central_character': '1872.1', 'coefficient_field': '1.1.1.1', 'conductor': 1872, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[1], [1], [1, -16, 125], [1, 28, 343], [1, -34, 1331], [1, 13], [1, 138, 4913], [1, 108, 6859], [1, 52, 12167], [1, -190, 24389], [1, -176, 29791], [1, -342, 50653], [1, 240, 68921], [1, -140, 79507], [1, -454, 103823], [1, 198, 148877], [1, 154, 205379], [1, -34, 226981], [1, -656, 300763], [1, -550, 357911], [1, -614, 389017], [1, 8, 493039], [1, -762, 571787], [1, -444, 704969], [1, -1022, 912673], [1, -1190, 1030301], [1, -224, 1092727], [1, 640, 1225043], [1, 1934, 1295029], [1, -418, 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'9.153783204566902111820325221223607'], 'prelabel': '2-1872-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.509594451297657, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 494008916430755642, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64969236614616481216090046033', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.10152691088045426321000263779', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.64208343378806915709390516261', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 110.45157553074648, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 1872, 'conductor_radical': 78, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 16, 0, -28, 0, 0, 0, 34, 0, -13, 0, 0, 0, -138, 0, -108, 0, 0, 0, -52, 0, 131, 0, 0, 0, 190, 0, 176, 0, 0, 0, -448, 0, 342, 0, 0, 0, -240, 0, 140, 0, 0, 0, 454, 0, 441, 0, 0, 0, -198, 0, 544, 0, 0, 0, -154, 0, 34, 0, 0, 0, -208, 0, 656, 0, 0, 0, 550, 0, 614, 0, 0, 0, -952, 0, -8, 0, 0, 0, 762, 0, -2208, 0, 0, 0, 444, 0, 364, 0, 0, 0, -1728, 0, 1022, 0, 0, 0], 'euler11': [1, -34, 1331], 'euler13': [1, 13, 0], 'euler17': [1, 138, 4913], 'euler19': [1, 108, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 52, 12167], 'euler29': [1, -190, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -176, 29791], 'euler37': [1, -342, 50653], 'euler41': [1, 240, 68921], 'euler43': [1, -140, 79507], 'euler47': [1, -454, 103823], 'euler5': [1, -16, 125], 'euler53': [1, 198, 148877], 'euler59': [1, 154, 205379], 'euler61': [1, -34, 226981], 'euler67': [1, -656, 300763], 'euler7': [1, 28, 343], 'euler71': [1, -550, 357911], 'euler73': [1, -614, 389017], 'euler79': [1, 8, 493039], 'euler83': [1, -762, 571787], 'euler89': [1, -444, 704969], 'euler97': [1, -1022, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -16, 125], [1, 28, 343], [1, -34, 1331], [1, 13, 0], [1, 138, 4913], [1, 108, 6859], [1, 52, 12167], [1, -190, 24389], [1, -176, 29791], [1, -342, 50653], [1, 240, 68921], [1, -140, 79507], [1, -454, 103823], [1, 198, 148877], [1, 154, 205379], [1, -34, 226981], [1, -656, 300763], [1, -550, 357911], [1, -614, 389017], [1, 8, 493039], [1, -762, 571787], [1, -444, 704969], [1, -1022, 912673]], 'index': 23, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1872/4/a/o/1/1', 'ModularForm/GL2/Q/holomorphic/1872/4/a/o'], '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': '2-1872-1.1-c3-0-23', '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': '2-1872-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.509594451297657, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 494008916430755642, 'z1': {'__RealLiteral__': 0, 'data': '0.64969236614616481216090046033', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21087518
{'Lhash': '823582917908884411717168919378', 'Lhash_array': ['823582917908884411717168919378'], 'factors': ['2-1872-1.1-c3-0-23'], 'label': '2-1872-1.1-c3-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1872/4/a/o'}
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id: 24592427
{'Lhash': '823582917908884411717168919378', 'Lhash_array': ['823582917908884411717168919378'], 'factors': ['2-1872-1.1-c3-0-23'], 'label': '2-1872-1.1-c3-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1872/4/a/o/1/1'}