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lfunc_lfunctions • Show schema
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{'Lhash': '1430769650377481120857425933122', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5, 0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5030575327340664, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 7], 'central_character': '1008.415', 'coefficient_field': 'CDF', 'conductor': 1008, 'conductor_radical': 42, 'conjugate': '2039207521267992304023746167204', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-1.5, -0.8660254037844386], 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'4.77723423080864028136684722524769', '5.90656580584473475784357339622142', '6.74660570911995325271643102216543', '7.52917761798086390072529399693386', '8.399741372738161205283802021324482', '9.441866102141382422424133166892034', '9.943164268862807875968095886511986'], 'prelabel': '2-1008-28.23-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7092654881876507, 'root_angle': -0.0934198098603064, 'root_number': '0.83262043355876010118361245995543 - 0.55384403365967783611687467980447*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.09341980986030639', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12867824155953033217823816685', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87279342299094172998720509360', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.78503175262904335487523784256', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5030575327340664, 'bad_primes': [2, 3, 7], 'central_character': '28.23', 'conductor': 1008, 'conductor_radical': 42, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1008/1/cd/a/415/1'], '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': '2-1008-28.23-c0-0-0', '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': '2-1008-28.23-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7092654881876507, 'root_angle': -0.0934198098603064, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12867824155953033217823816685', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1430769650377481120857425933122', 'Lhash_array': ['1430769650377481120857425933122'], 'factors': ['2-1008-28.23-c0-0-0'], 'label': '2-1008-28.23-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/1/cd/a/415/1'}