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lfunc_lfunctions • Show schema
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{'Lhash': '2300427019184228361233306441853', 'a10': [-0.8121077547328197, 3.7369083317039786], 'a2': [1.2092974359046575, 1.2092974359046575], 'a3': [0.0, 0.0], 'a4': [0.0, 0.9248005769711589], 'a5': [1.2092974359046575, 1.8808507945912192], 'a6': [0.0, 0.0], 'a7': [2.185064768655245, -2.185064768655245], 'a8': [1.3002359053549448, -1.3002359053549448], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.8272093728194765, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.2092974359046575, -1.8808507945912192]]], [19, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [3, 5, 19], 'central_character': '855.818', 'coefficient_field': 'CDF', 'conductor': 855, 'conductor_radical': 285, 'conjugate': '1722571185893160896069421683339', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.2092974359046575, -1.2092974359046575], [0, 2.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.2092974359046575, 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50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.81471694074854427549700048966', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.16159398193072171034659577413', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83440468046013658596891285774', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.8272093728194765, 'bad_primes': [3, 5, 19], 'central_character': '15.8', 'conductor': 855, 'conductor_radical': 285, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/855/2/n/d/818/8'], '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': '2-855-15.8-c1-0-26', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-855-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.612892912619933, 'root_angle': -0.10079444765396978, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.81471694074854427549700048966', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2300427019184228361233306441853', 'Lhash_array': ['2300427019184228361233306441853'], 'label': '2-855-15.8-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/855/2/n/d/818/8'}