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lfunc_lfunctions • Show schema
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{'Lhash': '1688201224994944230735761801958', 'a10': [3.9623886081840314, -4.481194304092016], 'a2': [0.0, 2.675130870566646], 'a3': [0.0, 0.0], 'a4': [-5.156325174658662, 0.0], 'a5': [-1.6751308705666461, -1.4811943040920157], 'a6': [0.0, 0.0], 'a7': [0.0, -0.8060634335253696], 'a8': [0.0, -8.443582912276048], '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], [1.6751308705666461, 1.4811943040920157]]], [13, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.469', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '827312646990423552436812414950', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.675130870566646], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.6751308705666461, 1.4811943040920157]], [[1.0, 0], [0, 0.8060634335253696], [-7.0, 0]], [[1.0, 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['1.33175594654473272691716627954208', '2.70272030596729739694972576360753', '3.67585058022720638016301710304238', '4.33846474712727425608845723227703', '5.72469226326141289095688224519761', '7.16172058992983089819421296486145', '8.321331678040065513823565223499236', '9.194995284923712443848544276455505', '9.867563046735222319506349214945413', '10.85208683009363453562040525886885'], 'prelabel': '2-585-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.26953360702095547, 'root_number': '0.6624102303670484 - 0.7491412995590845*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.13476680351', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33175594654473272691716627954', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.70272030596729739694972576361', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.67585058022720638016301710304', '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': '5.4', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/c/b/469/6'], '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': '2-585-5.4-c1-0-13', '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': '2-585-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.13476680351047773, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33175594654473272691716627954', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1688201224994944230735761801958', 'Lhash_array': ['1688201224994944230735761801958'], 'label': '2-585-5.4-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/c/b/469/6'}