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lfunc_lfunctions • Show schema
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{'Lhash': '1486928926923797769728200121269', 'a10': [0.0, 0.0], 'a2': [-1.4064663525068084, 0.14782557040713343], 'a3': [-0.3818348846386595, 1.6894384039890242], 'a4': [1.9562952014676114, -0.4158233816355187], 'a5': [0.0, 0.0], 'a6': [0.28729572172019874, -2.4325832294664185], 'a7': [0.0, 0.0], 'a8': [-2.6899940478558295, 0.8740320488976422], 'a9': [-2.708404241745963, -1.29017303618254], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.32415184008541, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.4064663525068084, -0.14782557040713343]]], [3, [[1.0, 0], [0.3818348846386595, -1.6894384039890242]]], [11, [[1.0, 0], [2.272048007052757, 2.4161535244366394]]]], 'bad_primes': [2, 3, 11], 'central_character': '792.547', 'coefficient_field': 'CDF', 'conductor': 792, 'conductor_radical': 66, 'conjugate': '792312343500132147675500478648', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4064663525068084, 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'6.08009175960483589935943344327134', '7.24245939759197235167421223565024', '7.67965072267564696266818890492985', '8.396756226966981977916476478610857', '9.558373409149989371304997386559963', '10.19032415172313926377821378007470'], 'prelabel': '2-792-792.547-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.514786639078037, 'root_angle': 0.06804355712271333, 'root_number': '0.9772391036335905 + 0.21214083607221104*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0340217785614', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17298009929241482132312230799', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26097673088986791964341177378', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.45834706120501234226277907176', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.32415184008541, 'bad_primes': [2, 3, 11], 'central_character': '792.547', 'conductor': 792, 'conductor_radical': 66, 'degree': 2, 'index': 58, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/792/2/ce/a/547/1'], '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': '2-792-792.547-c1-0-58', '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': '2-792-792.547-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.514786639078037, 'root_angle': 0.034021778561356665, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17298009929241482132312230799', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1486928926923797769728200121269', 'Lhash_array': ['1486928926923797769728200121269'], 'label': '2-792-792.547-c1-0-58', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/792/2/ce/a/547/1'}