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lfunc_lfunctions • Show schema
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{'Lhash': '1071032316866644820686708855655', 'a10': [1.0196097122333259, -6.1825029094147364e-61], 'a2': [-0.8830079127394013, 0.5098048561166629], 'a3': [-0.5974464743793084, -1.6257483539132784], 'a4': [-0.48019801735973733, 0.8317273637609067], 'a5': [-0.8660254037844386, -0.5], 'a6': [1.3563643699638477, 1.1309675467201306], 'a7': [-3.3245302373988603, 1.9194184274912824], 'a8': [0.0, -3.0184485490570023], 'a9': [-2.286115420503469, 1.9425952445469046], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5974464743793084, 1.6257483539132784]]], [5, [[1.0, 0], [0.8660254037844386, 0.5]]], [13, [[1.0, 0], [-3.564103273327083, -0.545131045767137]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.571', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '828391551581105537371862483686', 'degree': 2, 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[[1.0, 0], [-0.09078793851921821, 0.15724932222972549], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-585-117.103-c1-0-21', '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/571/19', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5832939510702044, 0.600576815632013, 0.5906236390336994, 0.5493439300351896, 0.4704872334792772, 0.34676808277571375, 0.17121526313778265, -0.061428811898266926, -0.35337506927658807, -0.7026112597332288, -1.1019768979698414, -1.5386007894223237, -1.9938210298986534, -2.443697099740791, -2.8601894288911507, -3.2130235038121926, -3.4721770467725674, -3.6108374004417536, -3.608582629346824, -3.4544572295788782, -3.149556307852722, -2.7087148008699393, -2.1609322366037795, 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'5.91275638516258789933333710513657', '7.28334550919106136535762182760383', '8.388245987282979174431445739203856', '9.322411840165098675279856608970805', '9.967760907654123883787982422067946', '10.64888703903421286620927917284568'], 'prelabel': '2-585-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.10189031066913187, 'root_number': '0.9492046327376591 + 0.3146594431911517*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0509451553346', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.844895523004378983565483584652', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.21140374940184522585971071428', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.80274068627446568435582322801', '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': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/19'], '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-c1-0-21', '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': 0.050945155334565936, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.844895523004378983565483584652', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1071032316866644820686708855655', 'Lhash_array': ['1071032316866644820686708855655'], 'label': '2-585-117.103-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/19'}