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lfunc_lfunctions • Show schema
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{'Lhash': '4162916578406951986772062330497', 'a10': [0.0, 0.0], 'a2': [0.6180339887498949, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.6180339887498949, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.618033988749895, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.05140369630119925, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[103, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [103], 'central_character': '103.102', 'coefficient_field': 'CDF', 'conductor': 103, 'conductor_radical': 103, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [1.0, 0]], [[1.0, 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False, 'root_analytic_conductor': 0.22672383267137852, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.28396214040166531134869327212', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.46895357445124374556423870030', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.03454633619783779298064033402', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.05140369630119925, 'bad_primes': [103], 'central_character': '103.102', 'conductor': 103, 'conductor_radical': 103, 'degree': 2, 'index': 1, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/103/1/b/a/102/2', 'ArtinRepresentation/2.103.5t2.a.a'], 'is_instance_Artin': True, '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': '2-103-103.102-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-103-103.102-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.22672383267137852, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.28396214040166531134869327212', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24596380
{'Lhash': '4162916578406951986772062330497', 'Lhash_array': ['4162916578406951986772062330497'], 'label': '2-103-103.102-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.103.5t2.a.a'}
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id: 19803028
{'Lhash': '4162916578406951986772062330497', 'Lhash_array': ['4162916578406951986772062330497'], 'label': '2-103-103.102-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/103/1/b/a/102/2'}