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lfunc_lfunctions • Show schema
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{'Lhash': '1628610376654436549999122198020', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': -11, 'a8': 0, 'a9': -23, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 117.05978945138943, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [31, [1, -31]]], 'bad_primes': [2, 31], 'central_character': '1984.1', 'coefficient_field': '1.1.1.1', 'conductor': 1984, 'conductor_radical': 62, 'degree': 2, 'euler_factors': [[1], [1, -2, 27], [1, 1, 125], [1, 11, 343], [1, -18, 1331], [1, -82, 2197], [1, 6, 4913], [1, 25, 6859], [1, -58, 12167], [1, 180, 24389], [1, -31], [1, -146, 50653], [1, -47, 68921], [1, -12, 79507], [1, 136, 103823], [1, -232, 148877], [1, 715, 205379], [1, -518, 226981], [1, -436, 300763], [1, -387, 357911], [1, -678, 389017], [1, -660, 493039], [1, -382, 571787], [1, 800, 704969], [1, 1631, 912673], [1, 377, 1030301], [1, 1117, 1092727], [1, 549, 1225043], [1, 415, 1295029], [1, 1567, 1442897]], 'euler_factors_factorization': [[1], [[[1, -2, 27], 1]], [[[1, 1, 125], 1]], [[[1, 11, 343], 1]], [[[1, -18, 1331], 1]], [[[1, -82, 2197], 1]], [[[1, 6, 4913], 1]], [[[1, 25, 6859], 1]], [[[1, -58, 12167], 1]], [[[1, 180, 24389], 1]], [[[1, -31], 1]], [[[1, -146, 50653], 1]], [[[1, -47, 68921], 1]], [[[1, -12, 79507], 1]], [[[1, 136, 103823], 1]], [[[1, -232, 148877], 1]], [[[1, 715, 205379], 1]], [[[1, -518, 226981], 1]], [[[1, -436, 300763], 1]], [[[1, -387, 357911], 1]], [[[1, -678, 389017], 1]], [[[1, -660, 493039], 1]], [[[1, -382, 571787], 1]], [[[1, 800, 704969], 1]], [[[1, 1631, 912673], 1]], [[[1, 377, 1030301], 1]], [[[1, 1117, 1092727], 1]], [[[1, 549, 1225043], 1]], [[[1, 415, 1295029], 1]], [[[1, 1567, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 135, 'label': '2-1984-1.1-c3-0-135', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1984/4/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.43421055231956e-60, 0.25560104658225363, 0.5076751814825101, 0.7527309637774512, 0.9873480835686783, 1.2082133730030495, 1.412157274067155, 1.5961907895162373, 1.7575428428601878, 1.8936978567316622, 2.0024332315881956, 2.081856274481786, 2.130439996810194, 2.147057076870903, 2.1310111738577753, 2.0820646905124574, 2.0004620172772394, 1.886947256111081, 1.74277542091399, 1.5697161466006897, 1.370049012079015, 1.1465496944181612, 0.9024663218697581, 0.6414855804670382, 0.36768834980064974, 0.08549489418061901, -0.2004000894957425, -0.48510197258134324, -0.7635993455560648, -1.0308546136234396, -1.2819005314349976, -1.5119408869411868, -1.7164532856065833, -1.891291762937697, -2.0327867750330317, -2.137839992704925, -2.2040112627982587, -2.2295951076061344, -2.213684215210478, -2.156217533800483, -2.0580108231090994, 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{'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 422854838010978941, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28474705597995180875405758329', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46876720775046336767675192298', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52819769430534864452598647562', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 117.05978945138943, 'bad_primes': [2, 31], 'central_character': '1.1', 'conductor': 1984, 'conductor_radical': 62, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, -1, 0, -11, 0, -23, 0, 18, 0, 82, 0, -2, 0, -6, 0, -25, 0, -22, 0, 58, 0, -124, 0, -100, 0, -180, 0, 31, 0, 36, 0, 11, 0, 146, 0, 164, 0, 47, 0, 12, 0, 23, 0, -136, 0, -222, 0, -12, 0, 232, 0, -18, 0, -50, 0, -715, 0, 518, 0, 253, 0, -82, 0, 436, 0, 116, 0, 387, 0, 678, 0, -248, 0, -198, 0, 660, 0, 421, 0, 382, 0, 6, 0, -360, 0, -800, 0, -902, 0, 62, 0, 25, 0, -1631, 0, -414, 0], 'euler11': [1, -18, 1331], 'euler13': [1, -82, 2197], 'euler17': [1, 6, 4913], 'euler19': [1, 25, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -58, 12167], 'euler29': [1, 180, 24389], 'euler3': [1, -2, 27], 'euler31': [1, -31, 0], 'euler37': [1, -146, 50653], 'euler41': [1, -47, 68921], 'euler43': [1, -12, 79507], 'euler47': [1, 136, 103823], 'euler5': [1, 1, 125], 'euler53': [1, -232, 148877], 'euler59': [1, 715, 205379], 'euler61': [1, -518, 226981], 'euler67': [1, -436, 300763], 'euler7': [1, 11, 343], 'euler71': [1, -387, 357911], 'euler73': [1, -678, 389017], 'euler79': [1, -660, 493039], 'euler83': [1, -382, 571787], 'euler89': [1, 800, 704969], 'euler97': [1, 1631, 912673], 'euler_factors': [[1, 0, 0], [1, -2, 27], [1, 1, 125], [1, 11, 343], [1, -18, 1331], [1, -82, 2197], [1, 6, 4913], [1, 25, 6859], [1, -58, 12167], [1, 180, 24389], [1, -31, 0], [1, -146, 50653], [1, -47, 68921], [1, -12, 79507], [1, 136, 103823], [1, -232, 148877], [1, 715, 205379], [1, -518, 226981], [1, -436, 300763], [1, -387, 357911], [1, -678, 389017], [1, -660, 493039], [1, -382, 571787], [1, 800, 704969], [1, 1631, 912673]], 'index': 135, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1984/4/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/1984/4/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': '2-1984-1.1-c3-0-135', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1984-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.81941724176443, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 422854838010978941, 'z1': {'__RealLiteral__': 0, 'data': '1.28474705597995180875405758329', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21141973
{'Lhash': '1628610376654436549999122198020', 'Lhash_array': ['1628610376654436549999122198020'], 'factors': ['2-1984-1.1-c3-0-135'], 'label': '2-1984-1.1-c3-0-135', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1984/4/a/c'}
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id: 24592693
{'Lhash': '1628610376654436549999122198020', 'Lhash_array': ['1628610376654436549999122198020'], 'factors': ['2-1984-1.1-c3-0-135'], 'label': '2-1984-1.1-c3-0-135', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1984/4/a/c/1/1'}