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lfunc_lfunctions • Show schema
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{'Lhash': '1823498253836740053241576406363', 'a10': [-0.5691939740564996, 0.9858728824278987], 'a2': [-0.07044842805036554, 0.6702720196982551], 'a3': [1.439390634342243, 1.5986052522284255], 'a4': [1.5119936020920006, 0.3213841613277472], 'a5': [1.543063187602444, 0.6870159943642353], 'a6': [-1.172903178651215, 0.852164040522777], 'a7': [1.5554267001569808, 2.140244794512713], 'a8': [-0.7384650829942342, 2.2727618287101117], 'a9': [-0.1701079644171833, 1.618469170031009], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.763329051202452, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-1.5554267001569808, -2.140244794512713]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 11], 'central_character': '847.81', 'coefficient_field': 'CDF', 'conductor': 847, 'conductor_radical': 77, 'conjugate': '2959667608488009593215283847211', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.07044842805036554, -0.6702720196982551], 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{'__RealLiteral__': 0, 'data': '-0.304501057906', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43848648319058512189549056188', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.91520515505015408841363777525', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.04320201138148886545589100846', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.763329051202452, 'bad_primes': [7, 11], 'central_character': '77.4', 'conductor': 847, 'conductor_radical': 77, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/847/2/n/h/81/2'], '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': '2-847-77.4-c1-0-32', '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': '2-847-77.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6006401233547196, 'root_angle': -0.30450105790571724, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43848648319058512189549056188', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1823498253836740053241576406363', 'Lhash_array': ['1823498253836740053241576406363'], 'label': '2-847-77.4-c1-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/2/n/h/81/2'}