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lfunc_lfunctions • Show schema
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{'Lhash': '1459051020539834497928299940341', 'a10': 0, 'a2': 1, 'a3': -2, 'a4': -7, 'a5': 0, 'a6': -2, 'a7': 0, 'a8': -15, 'a9': -23, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.27733975703228, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '1225.1', 'coefficient_field': '1.1.1.1', 'conductor': 1225, 'conductor_radical': 35, 'degree': 2, 'euler_factors': [[1, -1, 8], [1, 2, 27], [1], [1], [1, 8, 1331], [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, 1442897]], 'euler_factors_factorization': [[[[1, -1, 8], 1]], [[[1, 2, 27], 1]], [1], [1], [[[1, 8, 1331], 1]], [[[1, -28, 2197], 1]], [[[1, -54, 4913], 1]], [[[1, -110, 6859], 1]], [[[1, 48, 12167], 1]], [[[1, 110, 24389], 1]], [[[1, 12, 29791], 1]], [[[1, -246, 50653], 1]], [[[1, 182, 68921], 1]], [[[1, 128, 79507], 1]], [[[1, -324, 103823], 1]], [[[1, -162, 148877], 1]], [[[1, 810, 205379], 1]], [[[1, -488, 226981], 1]], [[[1, 244, 300763], 1]], [[[1, 768, 357911], 1]], [[[1, 702, 389017], 1]], [[[1, -440, 493039], 1]], [[[1, 1302, 571787], 1]], [[[1, 730, 704969], 1]], [[[1, -294, 912673], 1]], [[[1, -688, 1030301], 1]], [[[1, -1388, 1092727], 1]], [[[1, 244, 1225043], 1]], [[[1, -90, 1295029], 1]], [[[1, 1318, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 122, 'label': '2-35e2-1.1-c3-0-122', '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/1225/4/a/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-6.539027772440028e-61, 0.17884639663653662, 0.3550783088938621, 0.5260996393734769, 0.6893513453190114, 0.8423306494566575, 0.9826110208101646, 1.1078631003583066, 1.2158766801241156, 1.3045837660309851, 1.372082667414387, 1.4166629625276606, 1.4368310930122827, 1.4313362444967996, 1.3991960786192539, 1.3397217971178044, 1.2525419443159096, 1.1376242932187306, 0.9952951151216071, 0.8262551053556709, 0.6315912304256146, 0.4127837757788443, 0.17170790978109435, -0.08937086132429259, -0.3678078906254656, -0.6605976786687755, -0.9643995656153185, -1.2755709953437684, -1.5902083569222696, -1.9041952319240032, -2.2132576880684165, -2.5130260645785887, -2.7991024968878384, -3.0671332327600473, -3.31288460369967, -3.532321340144264, -3.7216857618929056, -3.877576242043185, -3.9970232387295046, -4.077561119185071, 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 950925927810616993, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15098830882669493082327319620', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.89266512499027057938802213026', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.67309813869389593628344148345', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 72.27733975703228, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 1225, 'conductor_radical': 35, 'degree': 2, 'dirichlet_coefficients': [1, 1, -2, -7, 0, -2, 0, -15, -23, 0, -8, 14, 28, 0, 0, 41, 54, -23, 110, 0, 0, -8, -48, 30, 0, 28, 100, 0, -110, 0, -12, 161, 16, 54, 0, 161, 246, 110, -56, 0, -182, 0, -128, 56, 0, -48, 324, -82, 0, 0, -108, -196, 162, 100, 0, 0, -220, -110, -810, 0, 488, -12, 0, -167, 0, 16, -244, -378, 96, 0, -768, 345, -702, 246, 0, -770, 0, -56, 440, 0, 421, -182, -1302, 0, 0, -128, 220, 120, -730, 0, 0, 336, 24, 324, 0, -322, 294, 0, 184, 0], 'euler11': [1, 8, 1331], '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, 0, 0], 'euler53': [1, -162, 148877], 'euler59': [1, 810, 205379], 'euler61': [1, -488, 226981], 'euler67': [1, 244, 300763], 'euler7': [1, 0, 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, 0, 0], [1, 0, 0], [1, 8, 1331], [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': 122, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1225/4/a/j/1/1', 'ModularForm/GL2/Q/holomorphic/1225/4/a/j'], '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': '2-35e2-1.1-c3-0-122', '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': '2-35e2-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.501608068890983, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 950925927810616993, 'z1': {'__RealLiteral__': 0, 'data': '1.15098830882669493082327319620', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20323261
{'Lhash': '1459051020539834497928299940341', 'Lhash_array': ['1459051020539834497928299940341'], 'factors': ['2-35e2-1.1-c3-0-122'], 'label': '2-35e2-1.1-c3-0-122', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1225/4/a/j'}
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id: 24586853
{'Lhash': '1459051020539834497928299940341', 'Lhash_array': ['1459051020539834497928299940341'], 'factors': ['2-35e2-1.1-c3-0-122'], 'label': '2-35e2-1.1-c3-0-122', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1225/4/a/j/1/1'}