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lfunc_lfunctions • Show schema
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{'Lhash': '109739165629322308571028358206', 'a10': [2.0479965961689675, 0.8976134703090879], 'a2': [0.28173255684142967, -0.9594929736144974], 'a3': [-1.780702718213009, -1.5429876887244123], 'a4': [-0.8412535328311812, -0.5406408174555976], 'a5': [-0.2842665003420669, 2.2179252820560196], 'a6': [-1.9821677754813818, 1.273861879502442], 'a7': [-3.9161138818336685, 1.788429285081128], 'a8': [-0.7557495743542583, 0.6548607339452851], 'a9': [0.36314664827624044, 2.5257404173187403], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.28173255684142967, 0.9594929736144974]]], [5, [[1.0, 0], [0.2842665003420669, -2.2179252820560196]]], [23, [[1.0, 0], [1.7086099158312509, -4.481144067704488]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.179', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': 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1.355197124587213, 'root_angle': -0.57808893308467, 'root_number': '-0.2428702664729619 - 0.9700587784579615*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.289044466542', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.086568937536545741996143920999', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.80623598136747716653243334357', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.49479097937511160678841403142', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'bad_primes': [2, 5, 23], 'central_character': '115.64', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/j/a/179/8'], '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': '2-230-115.64-c1-0-0', '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': '2-230-115.64-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': -0.289044466542335, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.086568937536545741996143920999', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '109739165629322308571028358206', 'Lhash_array': ['109739165629322308571028358206'], 'label': '2-230-115.64-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/j/a/179/8'}