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lfunc_lfunctions • Show schema
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{'Lhash': '437214543777192182652037248376', 'a10': [0.0, -4.177135964542319], 'a2': [-1.3666569487778502, 0.0], 'a3': [-0.8595220793869838, 1.503735945918124], 'a4': [-0.13224878435721651, 0.0], 'a5': [0.0, 3.0564626831025694], 'a6': [1.1746718224222084, -2.055091179616038], 'a7': [0.0, 1.0], 'a8': [2.9140526176649137, 0.0], 'a9': [-1.5224435900925513, -2.584988494168998], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8445442866915778, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8595220793869838, -1.503735945918124]]], [7, [[1.0, 0], [0, -1.0]]], [11, [[1.0, 0], [2.2980330374531244, -2.391452311624459]]]], 'bad_primes': [3, 7, 11], 'central_character': '231.197', 'coefficient_field': 'CDF', 'conductor': 231, 'conductor_radical': 231, 'conjugate': '3407075696940231549864946448229', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3666569487778502, 0], [2.0, 0]], [[1.0, 0], [0.8595220793869838, 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'1.75061402159665175498096464850', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.42861425950657997918600048723', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8445442866915778, 'bad_primes': [3, 7, 11], 'central_character': '33.32', 'conductor': 231, 'conductor_radical': 231, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/231/2/g/a/197/8'], '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': '2-231-33.32-c1-0-0', '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': '2-231-33.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3581400099737795, 'root_angle': 0.45447406093263454, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.34490146077986751923827388280', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '437214543777192182652037248376', 'Lhash_array': ['437214543777192182652037248376'], 'label': '2-231-33.32-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/231/2/g/a/197/8'}