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lfunc_lfunctions • Show schema
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{'Lhash': '1385870426228947460621677524306,1395423005341270375197008174661,2010837210846798852176788837408', 'a10': 0, 'a2': 7, 'a3': -27, 'a4': -11, 'a5': 0, 'a6': -189, 'a7': 172, 'a8': -189, 'a9': 486, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2316559.737050521, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 27, 243, 729]], [5, [1]], [11, [1, 363, 43923, 1771561]]], '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, -7, 60, -308, 1920, -7168, 32768], [1, 27, 243, 729], [1], [1, -172, 53317, -5399144, 896098819, -48585742828, 4747561509943], [1, 363, 43923, 1771561], [1, -654, 555091, -167732852, 206101402663, -90159453669246, 51185893014090757], [1, -2366, 4754783, -6580937060, 6751111926031, -4769841568462334, 2862423051509815793], [1, 2872, 9249705, 14234256272, 22903185300795, 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'8.323033958376440858631661080610615', '8.923843061495281321639171255842675', '9.037370170049969316019210695283298', '9.294962060099826244160204489984342'], 'prelabel': '6-825e3-1.1-c5e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 11.502897519569103, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5e3-0', 'trace_hash': 1887677401693803912, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09325899895399695595104985822', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.10079465515973933975113574052', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.58627086240070032123947857490', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2316559.737050521, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 561515625, 'conductor_radical': 165, 'degree': 6, 'dirichlet_coefficients': [1, 7, -27, -11, 0, -189, 172, -189, 486, 0, -363, 297, 654, 1204, 0, -427, 2366, 3402, -2872, 0, -4644, -2541, -2272, 5103, 0, 4578, -7290, -1892, -7738, 0, 568, -1309, 9801, 16562, 0, -5346, 9126, -20104, -17658, 0, -8758, -32508, 14672, 3993, 0, -15904, 19392, 11529, -23733, 0, -63882, -7194, 4598, -51030, 0, -32508, 77544, -54166, -9348, 0, -60078, 3976, 83592, -3227, 0, 68607, 38468, -26026, 61344, 0, -74032, -91854, 44442, 63882, 0, 31592, -62436, -123606, -108116, 0, 98415, -61306, 81892, 51084, 0, 102704, 208926, 68607, 167342, 0, 112488, 24992, -15336, 135744, 0, 35343, -159702, -166131, -176418, 0], 'euler11': [1, 363, 43923, 1771561, 0, 0, 0], 'euler13': [1, -654, 555091, -167732852, 206101402663, -90159453669246, 51185893014090757], 'euler17': [1, -2366, 4754783, 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['ModularForm/GL2/Q/holomorphic/825/6/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-c5e3-0-3', 'motivic_weight': 5, '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': [5, 5, 5], 'order_of_vanishing': 3, 'prelabel': '6-825e3-1.1-c5e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 11.502897519569103, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5e3-0', 'trace_hash': 1887677401693803912, 'z1': {'__RealLiteral__': 0, 'data': '1.09325899895399695595104985822', 'prec': 103}}
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lfunc_instances • Show schema
Hide schema
{'Lhash': '1385870426228947460621677524306,1395423005341270375197008174661,2010837210846798852176788837408', 'Lhash_array': ['1385870426228947460621677524306', '1395423005341270375197008174661', '2010837210846798852176788837408'], 'label': '6-825e3-1.1-c5e3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/6/a/j'}