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lfunc_lfunctions • Show schema
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{'Lhash': '3499612052012978462306576261192', 'a10': [-1.316043934859248, 2.2794549601690837], 'a2': [1.316043934859248, -2.2794549601690837], 'a3': [0.0, 0.0], 'a4': [-2.4639432769596255, -4.267674942661825], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5448751141292003, -0.9437513814516657], 'a8': [-7.7064546824827485, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [3.426467470663875, 1.1221945787083027]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.451', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '871106812574480087998106309421', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.316043934859248, 2.2794549601690837], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.5448751141292003, 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'11.84255003046716754632586519751477'], 'prelabel': '2-585-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.813881152185215, 'root_number': '-0.8338724066770373 - 0.5519572532204333*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.406940576093', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.76070713127332083937670663946', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.22006604614652426237746807935', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.68524928320936213867480436477', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '13.9', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/j/i/451/5'], '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': '2-585-13.9-c1-0-22', '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': '2-585-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.4069405760926075, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.76070713127332083937670663946', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3499612052012978462306576261192', 'Lhash_array': ['3499612052012978462306576261192'], 'label': '2-585-13.9-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/j/i/451/5'}