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lfunc_lfunctions • Show schema
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{'Lhash': '954747121522508146644252832833', 'a10': 16, 'a2': 1, 'a3': -2, 'a4': -7, 'a5': 16, 'a6': -2, 'a7': 7, 'a8': -15, 'a9': -23, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 49.974617774862324, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[7, [1, -7]], [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, -1, 8], [1, 2, 27], [1, -16, 125], [1, -7], [1], [1, 28, 2197], [1, 54, 4913], [1, -110, 6859], [1, -48, 12167], [1, -110, 24389], [1, -12, 29791], [1, 246, 50653], [1, 182, 68921], [1, 128, 79507], [1, -324, 103823], [1, 162, 148877], [1, -810, 205379], [1, -488, 226981], [1, -244, 300763], [1, 768, 357911], [1, -702, 389017], [1, 440, 493039], [1, -1302, 571787], [1, -730, 704969], [1, -294, 912673], [1, -688, 1030301], [1, -1388, 1092727], [1, 244, 1225043], [1, 90, 1295029], [1, -1318, 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'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/847/4/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.9636966961188758, 1.9498854682831306, 1.9085907342372195, 1.8402299359348941, 1.7455006888093971, 1.6253832554765162, 1.4811433356641057, 1.3143345354062888, 1.12679974656386, 0.9206705702134954, 0.6983638589475027, 0.4625744367068705, 0.2162630819877621, -0.03736106878742506, -0.2948644275220457, -0.5526197467202416, -0.8068441844507516, -1.0536448072026077, -1.2890714481592858, -1.509176570850007, -1.710081507730286, -1.888048157704024, -2.0395549441985716, -2.161375564874899, -2.250658814455824, -2.3050075427007655, -2.3225546294081405, -2.302033726350544, -2.2428424405282206, -2.1450956214611216, -2.0096664736141463, -1.8382133481052911, -1.6331902783576555, -1.3978396129343487, 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'9.787081795200737663507816397654976'], 'prelabel': '2-847-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.069272789676624, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 1483371668026835749, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.75316267854140113947099853893', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21345251215478291384990864744', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.31918745569909271743506679309', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 49.974617774862324, 'bad_primes': [7, 11], 'central_character': '1.1', 'conductor': 847, 'conductor_radical': 77, 'degree': 2, 'dirichlet_coefficients': [1, 1, -2, -7, 16, -2, 7, -15, -23, 16, 0, 14, -28, 7, -32, 41, -54, -23, 110, -112, -14, 0, 48, 30, 131, -28, 100, -49, 110, -32, 12, 161, 0, -54, 112, 161, -246, 110, 56, -240, -182, -14, -128, 0, -368, 48, 324, -82, 49, 131, 108, 196, -162, 100, 0, -105, -220, 110, 810, 224, 488, 12, -161, -167, -448, 0, 244, 378, -96, 112, -768, 345, 702, -246, -262, -770, 0, 56, -440, 656, 421, -182, 1302, 98, -864, -128, -220, 0, 730, -368, -196, -336, -24, 324, 1760, -322, 294, 49, 0, -917], 'euler11': [1, 0, 0], 'euler13': [1, 28, 2197], 'euler17': [1, 54, 4913], 'euler19': [1, -110, 6859], 'euler2': [1, -1, 8], 'euler23': [1, -48, 12167], 'euler29': [1, -110, 24389], 'euler3': [1, 2, 27], 'euler31': [1, -12, 29791], 'euler37': [1, 246, 50653], 'euler41': [1, 182, 68921], 'euler43': [1, 128, 79507], 'euler47': [1, -324, 103823], 'euler5': [1, -16, 125], 'euler53': [1, 162, 148877], 'euler59': [1, -810, 205379], 'euler61': [1, -488, 226981], 'euler67': [1, -244, 300763], 'euler7': [1, -7, 0], 'euler71': [1, 768, 357911], 'euler73': [1, -702, 389017], 'euler79': [1, 440, 493039], 'euler83': [1, -1302, 571787], 'euler89': [1, -730, 704969], 'euler97': [1, -294, 912673], 'euler_factors': [[1, -1, 8], [1, 2, 27], [1, -16, 125], [1, -7, 0], [1, 0, 0], [1, 28, 2197], [1, 54, 4913], [1, -110, 6859], [1, -48, 12167], [1, -110, 24389], [1, -12, 29791], [1, 246, 50653], [1, 182, 68921], [1, 128, 79507], [1, -324, 103823], [1, 162, 148877], [1, -810, 205379], [1, -488, 226981], [1, -244, 300763], [1, 768, 357911], [1, -702, 389017], [1, 440, 493039], [1, -1302, 571787], [1, -730, 704969], [1, -294, 912673]], 'index': 48, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/847/4/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/847/4/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': '2-847-1.1-c3-0-48', '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': '2-847-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.069272789676624, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1483371668026835749, 'z1': {'__RealLiteral__': 0, 'data': '0.75316267854140113947099853893', 'prec': 103}}
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lfunc_instances • Show schema
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id: 19988647
{'Lhash': '954747121522508146644252832833', 'Lhash_array': ['954747121522508146644252832833'], 'label': '2-847-1.1-c3-0-48', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/4/a/b'}
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id: 24574182
{'Lhash': '954747121522508146644252832833', 'Lhash_array': ['954747121522508146644252832833'], 'label': '2-847-1.1-c3-0-48', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/4/a/b/1/1'}