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lfunc_lfunctions • Show schema
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{'Lhash': '2240983066163690262649302793541', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.9312461099755205, 0.4472190584852876], 'a4': [0.0, 0.0], 'a5': [1.4627152168468063, -1.73577040935684], 'a6': [0.0, 0.0], 'a7': [-0.6908958030342577, -0.9585453154951874], 'a8': [0.0, 0.0], 'a9': [5.528686682659488, -1.7272245178438315], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.334006855021532, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [167, [[1.0, 0], [-7.349468893348339, -10.629454689009457]]]], 'bad_primes': [2, 167], 'central_character': '668.509', 'coefficient_field': 'CDF', 'conductor': 668, 'conductor_radical': 334, 'conjugate': '217809421435279435333514032203', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.9312461099755205, -0.4472190584852876], [2.8635121883146657, -0.8945937331399963]], [[1.0, 0], [-1.4627152168468063, 1.73577040935684], [-0.8475246712804833, 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[-40.5551585226055, 79.2229708935883]], [[1.0, 0], [9.534171890781089, -1.8262217454099658], [90.13415301480383, -35.84458760125342]], [[1.0, 0], [5.1138577007362676, 1.812727482183284], [78.45162932278464, 63.610862724855394]], [[1.0, 0], [-0.13176112294619693, -6.961352871825951], [-102.92622674608214, 3.8976721019200395]], [[1.0, 0], [0.09713326205850141, -5.131854508077325], [-106.92336176534747, -4.0490380087907205]], [[1.0, 0], [6.871082914994572, 13.422401036322587], [-63.73435772642114, 88.42472304282656]], [[1.0, 0], [-7.234770786771952, 6.334638029950444], [14.926129505512364, -112.00986857408893]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-668-167.8-c1-0-9', '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/668/2/e/a/509/2', 'plot_delta': {'__RealLiteral__': 0, 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'0.451558749871', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.76782393015884729208316505240', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.24139775578602491509707368890', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.99185100605990150221063520985', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.334006855021532, 'bad_primes': [2, 167], 'central_character': '167.8', 'conductor': 668, 'conductor_radical': 334, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/668/2/e/a/509/2'], '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': '2-668-167.8-c1-0-9', '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': '2-668-167.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3095468938780033, 'root_angle': 0.4515587498711073, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.76782393015884729208316505240', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2240983066163690262649302793541', 'Lhash_array': ['2240983066163690262649302793541'], 'label': '2-668-167.8-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/668/2/e/a/509/2'}