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lfunc_lfunctions • Show schema
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{'Lhash': '1615414548646247498971739883217', 'a10': [7.484468129469143, 0.0], 'a2': [0.0, -3.587274833019038], 'a3': [-2.7432873581808304, 1.214238226397621], 'a4': [-8.868540727611766, 0.0], 'a5': [0.0, 2.0863938443127985], 'a6': [4.355806230845859, 9.840925699741376], 'a7': [8.863025611526899, 0.0], 'a8': [0.0, 17.464793625689882], 'a9': [6.051251059109519, -6.662008752593014], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.89103359627878, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [2.7432873581808304, -1.214238226397621]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '363.122', 'coefficient_field': 'CDF', 'conductor': 363, 'conductor_radical': 33, 'conjugate': '845716841347235292978160576845', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 3.587274833019038], [-4.0, 0]], [[1.0, 0], [2.7432873581808304, -1.214238226397621]], [[1.0, 0], [0, -2.0863938443127985], [-25.0, 0]], [[1.0, 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'5.14893809324030290490712389730', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.89103359627878, 'bad_primes': [3, 11], 'central_character': '3.2', 'conductor': 363, 'conductor_radical': 33, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/363/3/b/m/122/1'], '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': '2-363-3.2-c2-0-31', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-363-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.145001366657697, 'root_angle': 0.43367995582298263, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27433738315227101277751307437', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1615414548646247498971739883217', 'Lhash_array': ['1615414548646247498971739883217'], 'label': '2-363-3.2-c2-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/363/3/b/m/122/1'}