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lfunc_lfunctions • Show schema
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{'Lhash': '942908396642211474574173081529,1745572680532507364302202255741,2174973026229722031735831190517,2576155669623164572119651065357,3284105253627578641057850567994,5056772239347241184998774401936', 'a10': 0, 'a2': 1, 'a3': -3, 'a4': 2, 'a5': 0, 'a6': -3, 'a7': -2, 'a8': 3, 'a9': 7, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.445449704048513, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [7, [1, 2, -4, -13, -28, 98, 343]]], 'bad_primes': [5, 7], 'central_character': '175.1', 'coefficient_field': '1.1.1.1', 'conductor': 28722900390625, 'conductor_radical': 35, 'degree': 12, 'euler_factors': [[1, -1, -1, 0, -1, 2, 5, 4, -4, 0, -16, -32, 64], [1, 3, 2, -1, -5, -22, -53, -66, -45, -27, 162, 729, 729], [1], [1, 2, -4, -13, -28, 98, 343], [1, -2, -10, -30, 44, 388, 23, 4268, 5324, -39930, -146410, -322102, 1771561], [1, -8, 64, -414, 2088, -9176, 37099, -119288, 352872, -909558, 1827904, -2970344, 4826809], [1, 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-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.445449704048513, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 28722900390625, 'conductor_radical': 35, 'degree': 12, 'dirichlet_coefficients': [1, 1, -3, 2, 0, -3, -2, 3, 7, 0, 2, -6, 8, -2, 0, 6, -10, 7, 4, 0, 6, 2, -1, -9, 0, 8, -14, -4, -16, 0, -5, 8, -6, -10, 0, 14, 10, 4, -24, 0, -2, 6, 18, 4, 0, -1, -28, -18, 8, 0, 30, 16, -10, -14, 0, -6, -12, -16, 5, 0, -5, -5, -14, 9, 0, -6, 12, -20, 3, 0, 14, 21, 12, 10, 0, 8, -4, -24, 7, 0, 30, -2, 52, 12, 0, 18, 48, 6, 6, 0, -16, -2, 15, -28, 0, -24, -14, 8, 14, 0], 'euler11': [1, -2, -10, -30, 44, 388, 23, 4268, 5324, -39930, -146410, -322102, 1771561], 'euler13': [1, -8, 64, -414, 2088, -9176, 37099, -119288, 352872, -909558, 1827904, -2970344, 4826809], 'euler17': [1, 10, 20, 78, 1430, 4570, 2447, 77690, 413270, 383214, 1670420, 14198570, 24137569], 'euler19': [1, -4, -24, 158, 204, -1724, 2823, -32756, 73644, 1083722, -3127704, -9904396, 47045881], 'euler2': [1, -1, -1, 0, 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10870, -143977, 576110, 7893290, -70567698, -315619240, 4181954930, 22164361129], 'euler59': [1, -5, -90, 815, 2965, -29480, 26483, -1739320, 10321165, 167383885, -1090562490, -3574621495, 42180533641], 'euler61': [1, 5, -140, -269, 14425, 8210, -1000579, 500810, 53675425, -61057889, -1938417740, 4222981505, 51520374361], 'euler67': [1, -12, -85, 388, 18282, -44708, -1099813, -2995436, 82067898, 116696044, -1712845285, -16201501284, 90458382169], 'euler7': [1, 2, -4, -13, -28, 98, 343, 0, 0, 0, 0, 0, 0], 'euler71': [1, -14, 297, -2878, 40978, -335438, 3719273, -23816098, 206570098, -1030067858, 7547269257, -25259210914, 128100283921], 'euler73': [1, -12, -43, 364, 5670, 19828, -841663, 1447444, 30215430, 141602188, -1221124363, -24876859116, 151334226289], 'euler79': [1, -7, -96, 1499, 771, -65582, 599343, -5180978, 4811811, 739065461, -3739207776, -21539394793, 243087455521], 'euler83': [1, -52, 1572, -32726, 520252, -6516436, 66005591, -540864188, 3584016028, -18712301362, 74604480612, -204830113436, 326940373369], 'euler89': [1, -6, -94, -198, 3584, 53484, -294637, 4760076, 28388864, -139583862, -5897770654, -33504356694, 496981290961], 'euler97': [1, 14, 411, 5768, 90513, 962878, 11717751, 93399166, 851636817, 5264297864, 36385534491, 120222763598, 832972004929], 'euler_factors': [[1, -1, -1, 0, -1, 2, 5, 4, -4, 0, -16, -32, 64], [1, 3, 2, -1, -5, -22, -53, -66, -45, -27, 162, 729, 729], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, -4, -13, -28, 98, 343, 0, 0, 0, 0, 0, 0], [1, -2, -10, -30, 44, 388, 23, 4268, 5324, -39930, -146410, -322102, 1771561], [1, -8, 64, -414, 2088, -9176, 37099, -119288, 352872, -909558, 1827904, -2970344, 4826809], [1, 10, 20, 78, 1430, 4570, 2447, 77690, 413270, 383214, 1670420, 14198570, 24137569], [1, -4, -24, 158, 204, -1724, 2823, -32756, 73644, 1083722, -3127704, -9904396, 47045881], [1, 1, -58, -51, 2069, 1060, -53233, 24380, 1094501, -620517, -16230778, 6436343, 148035889], [1, 16, 228, 2090, 17704, 115300, 697739, 3343700, 14889064, 50973010, 161260068, 328178384, 594823321], [1, 5, -50, -119, 2065, 80, -77809, 2480, 1984465, -3545129, -46176050, 143145755, 887503681], [1, -10, -20, 118, 3370, -3970, -134113, -146890, 4613530, 5977054, -37483220, -693439570, 2565726409], [1, 2, 155, 528, 12617, 38474, 662351, 1577434, 21209177, 36390288, 437992955, 231712402, 4750104241], [1, -18, 299, -3404, 34233, -274826, 2000159, -11817518, 63296817, -270641828, 1022221499, -2646151974, 6321363049], [1, 28, 390, 4298, 42442, 351442, 2516387, 16517774, 93754378, 446231254, 1903075590, 6421660196, 10779215329], [1, 10, -40, -474, 2810, 10870, -143977, 576110, 7893290, -70567698, -315619240, 4181954930, 22164361129], [1, -5, -90, 815, 2965, -29480, 26483, -1739320, 10321165, 167383885, -1090562490, -3574621495, 42180533641], [1, 5, -140, -269, 14425, 8210, -1000579, 500810, 53675425, -61057889, -1938417740, 4222981505, 51520374361], [1, -12, -85, 388, 18282, -44708, -1099813, -2995436, 82067898, 116696044, -1712845285, -16201501284, 90458382169], [1, -14, 297, -2878, 40978, -335438, 3719273, -23816098, 206570098, -1030067858, 7547269257, -25259210914, 128100283921], [1, -12, -43, 364, 5670, 19828, -841663, 1447444, 30215430, 141602188, -1221124363, -24876859116, 151334226289], [1, -7, -96, 1499, 771, -65582, 599343, -5180978, 4811811, 739065461, -3739207776, -21539394793, 243087455521], [1, -52, 1572, -32726, 520252, -6516436, 66005591, -540864188, 3584016028, -18712301362, 74604480612, -204830113436, 326940373369], [1, -6, -94, -198, 3584, 53484, -294637, 4760076, 28388864, -139583862, -5897770654, -33504356694, 496981290961], [1, 14, 411, 5768, 90513, 962878, 11717751, 93399166, 851636817, 5264297864, 36385534491, 120222763598, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/175/2/e/e'], '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': '12-175e6-1.1-c1e6-0-0', '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}, {'__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, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-175e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.182109146979418, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 709716434115854332, 'z1': {'__RealLiteral__': 0, 'data': '0.74382357131566779211374008525', 'prec': 103}}
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{'Lhash': '942908396642211474574173081529,1745572680532507364302202255741,2174973026229722031735831190517,2576155669623164572119651065357,3284105253627578641057850567994,5056772239347241184998774401936', 'Lhash_array': ['942908396642211474574173081529', '1745572680532507364302202255741', '2174973026229722031735831190517', '2576155669623164572119651065357', '3284105253627578641057850567994', '5056772239347241184998774401936'], 'label': '12-175e6-1.1-c1e6-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/175/2/e/e'}