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lfunc_lfunctions • Show schema
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{'Lhash': '673286192092831347203189063856', 'a10': [-0.2675189107869173, -4.272741883682712e-62], 'a2': [0.2316781727342133, -0.13375945539345865], 'a3': [1.7034779833073845, 0.31330936849543145], 'a4': [-0.9642168161856907, 1.6700725151459173], 'a5': [-0.8660254037844386, -0.5], 'a6': [0.43656675696523495, -0.1552693453284112], 'a7': [-3.308045108835775, 1.9099007340777596], 'a8': [0.0, 1.050930286430685], 'a9': [2.803674479225988, 1.0674312223918154], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.7034779833073845, -0.31330936849543145]]], [5, [[1.0, 0], [0.8660254037844386, 0.5]]], [13, [[1.0, 0], [-3.3717536630737626, 1.2772146395765527]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.571', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '3124723835639720114931467297713', 'degree': 2, 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[[1.0, 0], [7.170720163877618, -12.420051650694662], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-585-117.103-c1-0-11', '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/571/30', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1502648489579836, 0.8966568846379211, 0.6376774079940087, 0.3658795924665493, 0.07555362932380197, -0.23572359773128745, -0.5660762195618882, -0.9088679978975548, -1.252743623423034, -1.5821321375215769, -1.8781949633025412, -2.1202049434501573, -2.287318484787217, -2.360655913573051, -2.325546304397049, -2.1737343541305933, -1.9053001098553015, -1.5300184504670713, -1.0678933845259995, -0.5486487621496698, -0.01004391025622598, 0.5049935297844838, 0.9522744307907393, 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'6.07894478226650579674073770508400', '6.64598457476382376493346340503923', '7.80645233175630873438948286496761', '8.689547720272661891286552676787277', '9.456067627345003990030679637342654', '10.45113690310715457706969302277083'], 'prelabel': '2-585-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.7216860174492753, 'root_number': '-0.6414962680998446 - 0.7671261552143639*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.360843008725', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53112915496715897744030148530', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.50235108981030253941087013658', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.70361900841438319629031846383', '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': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/30'], '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-c1-0-11', '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': -0.36084300872463765, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.53112915496715897744030148530', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '673286192092831347203189063856', 'Lhash_array': ['673286192092831347203189063856'], 'label': '2-585-117.103-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/30'}