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{'Lhash': '1736066525952513092754349094603,2075029462081080382229104378687,2820610214902799753041410858079', 'a10': 0, 'a2': -1, 'a3': -3, 'a4': -2, 'a5': 0, 'a6': 3, 'a7': -4, 'a8': 2, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 285.8861833044949, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 3, 3, 1]], [5, [1]], [11, [1, -3, 3, -1]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': '1.1.1.1', 'conductor': 561515625, 'conductor_radical': 165, 'degree': 6, 'euler_factors': [[1, 1, 3, 3, 6, 4, 8], [1, 3, 3, 1], [1], [1, 4, 21, 52, 147, 196, 343], [1, -3, 3, -1], [1, 2, 35, 48, 455, 338, 2197], [1, 0, 23, -52, 391, 0, 4913], [1, 6, 53, 188, 1007, 2166, 6859], [1, 12, 117, 616, 2691, 6348, 12167], [1, -8, 71, -304, 2059, -6728, 24389], [1, 8, 101, 480, 3131, 7688, 29791], [1, 4, 95, 264, 3515, 5476, 50653], [1, -8, 11, 272, 451, -13448, 68921], [1, 12, 129, 884, 5547, 22188, 79507], [1, 16, 189, 1536, 8883, 35344, 103823], [1, 16, 191, 1712, 10123, 44944, 148877], [1, -8, 113, -1024, 6667, -27848, 205379], [1, 22, 291, 2692, 17751, 81862, 226981], [1, 12, 185, 1544, 12395, 53868, 300763], [1, 12, 117, 760, 8307, 60492, 357911], [1, -10, 175, -1072, 12775, -53290, 389017], [1, 10, 25, -140, 1975, 62410, 493039], [1, -10, 189, -1056, 15687, -68890, 571787], [1, -18, 255, -2684, 22695, -142578, 704969], [1, 16, 131, 672, 12707, 150544, 912673], [1, -8, -33, 1680, -3333, -81608, 1030301], [1, -12, 21, 952, 2163, -127308, 1092727], [1, 6, 149, 16, 15943, 68694, 1225043], [1, 30, 627, 7540, 68343, 356430, 1295029], [1, 16, 363, 3600, 41019, 204304, 1442897]], 'euler_factors_factorization': [[[[1, 1, 3, 3, 6, 4, 8], 1]], [[[1, 1], 3]], [1], [[[1, 4, 21, 52, 147, 196, 343], 1]], [[[1, -1], 3]], [[[1, 2, 35, 48, 455, 338, 2197], 1]], [[[1, 0, 23, -52, 391, 0, 4913], 1]], [[[1, 6, 53, 188, 1007, 2166, 6859], 1]], [[[1, 4, 23], 3]], [[[1, -8, 71, -304, 2059, -6728, 24389], 1]], [[[1, 8, 101, 480, 3131, 7688, 29791], 1]], [[[1, 4, 95, 264, 3515, 5476, 50653], 1]], [[[1, -8, 11, 272, 451, -13448, 68921], 1]], [[[1, 12, 129, 884, 5547, 22188, 79507], 1]], [[[1, 16, 189, 1536, 8883, 35344, 103823], 1]], [[[1, 16, 191, 1712, 10123, 44944, 148877], 1]], [[[1, -8, 113, -1024, 6667, -27848, 205379], 1]], [[[1, 22, 291, 2692, 17751, 81862, 226981], 1]], [[[1, 12, 185, 1544, 12395, 53868, 300763], 1]], [[[1, 12, 117, 760, 8307, 60492, 357911], 1]], [[[1, -10, 175, -1072, 12775, -53290, 389017], 1]], [[[1, 10, 25, -140, 1975, 62410, 493039], 1]], [[[1, -10, 189, -1056, 15687, -68890, 571787], 1]], [[[1, -18, 255, -2684, 22695, -142578, 704969], 1]], [[[1, 16, 131, 672, 12707, 150544, 912673], 1]], [[[1, -8, -33, 1680, -3333, -81608, 1030301], 1]], [[[1, -12, 21, 952, 2163, -127308, 1092727], 1]], [[[1, 6, 149, 16, 15943, 68694, 1225043], 1]], [[[1, 10, 109], 3]], [[[1, 16, 363, 3600, 41019, 204304, 1442897], 1]]], 'gamma_factors': [[], [0, 0, 0]], 'group': 'GL2', 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'7.39033607072128127597643024710457', '8.068013884955445269719119145716712', '8.152398093026085170495732770404976', '8.214905430638894958424429450592950', '8.958755080134150296825081630491464', '9.083657907431766356766631054874894', '9.255685963136796812018701128103884', '9.667750402935049765515411567581219', '9.824727548796061474124841653804617', '9.955880833385090652789352521878135'], 'prelabel': '6-825e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.5666433657124306, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e3-0', 'trace_hash': 693206966125604422, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36951501118679666259017721234', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.63690961981755026140006473248', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.22506912740385525617645534196', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 285.8861833044949, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 561515625, 'conductor_radical': 165, 'degree': 6, 'dirichlet_coefficients': [1, -1, -3, -2, 0, 3, -4, 2, 6, 0, 3, 6, -2, 4, 0, 1, 0, -6, -6, 0, 12, -3, -12, -6, 0, 2, -10, 8, 8, 0, -8, 1, -9, 0, 0, -12, -4, 6, 6, 0, 8, -12, -12, -6, 0, 12, -16, -3, -5, 0, 0, 4, -16, 10, 0, -8, 18, -8, 8, 0, -22, 8, -24, -2, 0, 9, -12, 0, 36, 0, -12, 12, 10, 4, 0, 12, -12, -6, -10, 0, 15, -8, 10, -24, 0, 12, -24, 6, 18, 0, 8, 24, 24, 16, 0, -3, -16, 5, 18, 0], 'euler11': [1, -3, 3, -1, 0, 0, 0], 'euler13': [1, 2, 35, 48, 455, 338, 2197], 'euler17': [1, 0, 23, -52, 391, 0, 4913], 'euler19': [1, 6, 53, 188, 1007, 2166, 6859], 'euler2': [1, 1, 3, 3, 6, 4, 8], 'euler23': [1, 12, 117, 616, 2691, 6348, 12167], 'euler29': [1, -8, 71, -304, 2059, -6728, 24389], 'euler3': [1, 3, 3, 1, 0, 0, 0], 'euler31': [1, 8, 101, 480, 3131, 7688, 29791], 'euler37': [1, 4, 95, 264, 3515, 5476, 50653], 'euler41': [1, -8, 11, 272, 451, -13448, 68921], 'euler43': [1, 12, 129, 884, 5547, 22188, 79507], 'euler47': [1, 16, 189, 1536, 8883, 35344, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, 16, 191, 1712, 10123, 44944, 148877], 'euler59': [1, -8, 113, -1024, 6667, -27848, 205379], 'euler61': [1, 22, 291, 2692, 17751, 81862, 226981], 'euler67': [1, 12, 185, 1544, 12395, 53868, 300763], 'euler7': [1, 4, 21, 52, 147, 196, 343], 'euler71': [1, 12, 117, 760, 8307, 60492, 357911], 'euler73': [1, -10, 175, -1072, 12775, -53290, 389017], 'euler79': [1, 10, 25, -140, 1975, 62410, 493039], 'euler83': [1, -10, 189, -1056, 15687, -68890, 571787], 'euler89': [1, -18, 255, -2684, 22695, -142578, 704969], 'euler97': [1, 16, 131, 672, 12707, 150544, 912673], 'euler_factors': [[1, 1, 3, 3, 6, 4, 8], [1, 3, 3, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 4, 21, 52, 147, 196, 343], [1, -3, 3, -1, 0, 0, 0], [1, 2, 35, 48, 455, 338, 2197], [1, 0, 23, -52, 391, 0, 4913], [1, 6, 53, 188, 1007, 2166, 6859], [1, 12, 117, 616, 2691, 6348, 12167], [1, -8, 71, -304, 2059, -6728, 24389], [1, 8, 101, 480, 3131, 7688, 29791], [1, 4, 95, 264, 3515, 5476, 50653], [1, -8, 11, 272, 451, -13448, 68921], [1, 12, 129, 884, 5547, 22188, 79507], [1, 16, 189, 1536, 8883, 35344, 103823], [1, 16, 191, 1712, 10123, 44944, 148877], [1, -8, 113, -1024, 6667, -27848, 205379], [1, 22, 291, 2692, 17751, 81862, 226981], [1, 12, 185, 1544, 12395, 53868, 300763], [1, 12, 117, 760, 8307, 60492, 357911], [1, -10, 175, -1072, 12775, -53290, 389017], [1, 10, 25, -140, 1975, 62410, 493039], [1, -10, 189, -1056, 15687, -68890, 571787], [1, -18, 255, -2684, 22695, -142578, 704969], [1, 16, 131, 672, 12707, 150544, 912673]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/2/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': '6-825e3-1.1-c1e3-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'prelabel': '6-825e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.5666433657124306, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 693206966125604422, 'z1': {'__RealLiteral__': 0, 'data': '1.36951501118679666259017721234', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1736066525952513092754349094603,2075029462081080382229104378687,2820610214902799753041410858079', 'Lhash_array': ['1736066525952513092754349094603', '2075029462081080382229104378687', '2820610214902799753041410858079'], 'label': '6-825e3-1.1-c1e3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/2/a/j'}