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lfunc_lfunctions • Show schema
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{'Lhash': '2138816855389610594300336522570', 'a10': [-2.010758290225991, -0.9781876600568268], 'a2': [0.28173255684142967, 0.9594929736144974], 'a3': [1.6215368840479951, -1.4050697083280965], 'a4': [-0.8412535328311812, 0.5406408174555976], 'a5': [-1.5050602609964019, 1.6537211405703933], 'a6': [1.8049942449349063, 1.159999365233081], 'a7': [4.061645188701623, 1.8548912059936296], 'a8': [-0.7557495743542583, -0.6548607339452851], 'a9': [0.22821646624702388, -1.5872803877823356], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.28173255684142967, -0.9594929736144974]]], [5, [[1.0, 0], [1.5050602609964019, -1.6537211405703933]]], [23, [[1.0, 0], [2.84315665531223, 3.862183350561412]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.9', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': 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'root_angle': -0.23234612279296168, 'root_number': '0.7452164987019824 - 0.666822592645419*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.116173061396', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68722900064460611567204512196', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.65407894396793212787755871520', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.28234771476724477954304684100', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'bad_primes': [2, 5, 23], 'central_character': '115.9', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/j/a/9/11'], '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': '2-230-115.9-c1-0-6', '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': '2-230-115.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': -0.11617306139648084, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68722900064460611567204512196', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2138816855389610594300336522570', 'Lhash_array': ['2138816855389610594300336522570'], 'label': '2-230-115.9-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/j/a/9/11'}