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lfunc_lfunctions • Show schema
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{'Lhash': '419073419971397755943931603613', 'a10': [0.7338753392551095, -3.0759432677527063], 'a2': [0.9042622695965579, 1.0873406769656335], 'a3': [-1.7878197026591849, 1.7878197026591849], 'a4': [-0.3646194955681641, 1.966482296755203], 'a5': [-1.3404912275951706, -1.7897159743211748], 'a6': [-3.5606269877379733, -0.3273111838258978], 'a7': [-2.3445942976252856, -2.3445942976252856], 'a8': [-2.467947844396356, 1.3817501356393562], 'a9': [0.0, -3.3925985784327524], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.076110452553291, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9042622695965579, -1.0873406769656335]]], [5, [[1.0, 0], [1.3404912275951706, 1.7897159743211748]]], [13, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.183', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '4609470218300209151279271889305', 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[59.0, 0]], [[1.0, 0], [-8.82521139681841, 0], [61.0, 0]], [[1.0, 0], [2.581481704337499, 2.581481704337499], [0, 67.0]], [[1.0, 0], [0, 8.531610897963702], [-71.0, 0]], [[1.0, 0], [-2.7674910038634493, -2.7674910038634493], [0, 73.0]], [[1.0, 0], [7.025978321236462, 0], [79.0, 0]], [[1.0, 0], [-6.935581683922818, 6.935581683922818], [0, -83.0]], [[1.0, 0], [0, 9.424479779257506], [-89.0, 0]], [[1.0, 0], [11.814751382800301, -11.814751382800301], [0, -97.0]], [[1.0, 0], [4.699374609619536, 0], [101.0, 0]], [[1.0, 0], [-0.8549998297410262, 0.8549998297410262], [0, -103.0]], [[1.0, 0], [-12.99128116283683, -12.99128116283683], [0, 107.0]], [[1.0, 0], [0, 2.622877683170163], [-109.0, 0]], [[1.0, 0], [-10.898044833452145, -10.898044833452145], [0, 113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-260-20.3-c1-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 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'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.7799372920044412, 'root_number': '-0.7703876534003884 + 0.6375757707819856*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.389968646002', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33059063743270208101684517845', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.50214223503006783684390585541', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.66175644745402116693559563515', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.076110452553291, 'bad_primes': [2, 5, 13], 'central_character': '20.3', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/o/a/183/26'], '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': '2-260-20.3-c1-0-2', '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': '2-260-20.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.3899686460022206, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.33059063743270208101684517845', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '419073419971397755943931603613', 'Lhash_array': ['419073419971397755943931603613'], 'label': '2-260-20.3-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/o/a/183/26'}