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lfunc_lfunctions • Show schema
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{'Lhash': '1142177159145838509268182972188', 'a10': [-2.6756379191452906, -2.5143033246678455], 'a2': [-1.3767386367626386, -0.32340489489949226], 'a3': [-0.609093487506609, 1.6214207114370522], 'a4': [1.7908185479100966, 0.8904880282525828], 'a5': [2.2483960518670796, 1.29811206579035], 'a6': [1.3629379324210098, -2.0352887245715148], 'a7': [-2.5367843988886802, 0.751481811859074], 'a8': [-2.1775008991527116, -1.805128758340837], 'a9': [-2.258010246954073, -1.9751935916892824], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3767386367626386, 0.32340489489949226]]], [3, [[1.0, 0], [0.609093487506609, -1.6214207114370522]]], [7, [[1.0, 0], [2.5367843988886802, -0.751481811859074]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.5', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'6.33044094209337259361617931184659', '7.18039184713783458086471500986242', '8.519884775868176765358707960997421', '9.388840534899183721347308801516293', '10.31601049526535425806677455007386', '11.53064342762322074533502688193912', '12.42394819853691461209662471695700'], 'prelabel': '2-168-168.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.5499527239006924, 'root_number': '-0.15628776962442237 - 0.9877115636995567*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.27497636195', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.901018907686549829448010697352', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.63158985340794623632906315417', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.46715240226268151958948483198', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.5', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/2'], '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': '2-168-168.5-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': '2-168-168.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.2749763619503462, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.901018907686549829448010697352', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1142177159145838509268182972188', 'Lhash_array': ['1142177159145838509268182972188'], 'label': '2-168-168.5-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/2'}