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lfunc_lfunctions • Show schema
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{'Lhash': '43000606009756368184494763972', 'a10': [2.544008691863812, -6.0841554519945135e-61], 'a2': [-2.203176154602479, 1.272004345931906], 'a3': [0.3504505075012827, 1.6962265302111312], 'a4': [2.2359901121393113, -3.8728484794469185], 'a5': [-0.8660254037844386, -0.5], 'a6': [-2.929711719608719, -3.2913112755895924], 'a7': [-0.5862235934760986, 0.3384563494987353], 'a8': [0.0, 6.288739176680269], 'a9': [-2.7543688835841866, 1.1888868966992614], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.3504505075012827, -1.6962265302111312]]], [5, [[1.0, 0], [0.8660254037844386, 0.5]]], [13, [[1.0, 0], [-2.203346485167695, -2.8539909366182585]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.571', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '2742697393536437951745611063311', 'degree': 2, 'euler_factors': 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[4.485922426986772, -7.769845562353775], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-585-117.103-c1-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.03701142926881296, -0.09298831903496381, -0.20636418957457867, -0.3033343348870883, -0.3819579034305361, -0.438334619695983, -0.46725092365115445, -0.46312443474169956, -0.42111066752222515, -0.33825717069250266, -0.21459580992717167, -0.05405387823451901, 0.13494929040348483, 0.3393589049172731, 0.5419204745137592, 0.722284357735015, 0.8588071680437884, 0.9309938697402341, 0.9224242392254908, 0.8239021587595343, 0.6364703357916899, 0.37386308710764127, 0.06394259137704278, -0.25130604459380634, 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'6.88385427468876372879174992602784', '7.79966744457587514837827872539576', '8.228143454556015573121589154311339', '8.996947843622683834511671832650053', '10.16231311098424784416969444173985'], 'prelabel': '2-585-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.4388012882451259, 'root_number': '0.19107913738539573 + 0.981574634582645*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.219400644123', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.03392149698190848900354842684', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.41238877975415034102922596301', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.77489896749691386638138772757', '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': '117.103', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/5'], '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': '2-585-117.103-c1-0-1', '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': '2-585-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.21940064412256294, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.03392149698190848900354842684', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '43000606009756368184494763972', 'Lhash_array': ['43000606009756368184494763972'], 'label': '2-585-117.103-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/5'}