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lfunc_lfunctions • Show schema
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{'Lhash': '3343819518139605469662487099663', 'a10': [0.0, -2.584225443216521], 'a2': [0.7071067811865476, 0.7071067811865476], 'a3': [1.2921127216082604, 1.1534490516091702], 'a4': [0.0, 1.0], 'a5': [-1.8273233350132132, -1.8273233350132132], 'a6': [0.09805002136057041, 1.7292733136526428], 'a7': [-2.6312232922920726, -2.6312232922920726], 'a8': [-0.7071067811865476, 0.7071067811865476], 'a9': [0.339110570683812, 2.9807723866223834], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [3, [[1.0, 0], [-1.2921127216082604, -1.1534490516091702]]], [13, [[1.0, 0], [-1.6312232922920724, -3.2154487355085934]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.5', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': '4694654220465070994139153305982', 'degree': 2, 'euler_factors': 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-0.2610516018040871, 'root_number': '0.682135077644392 - 0.7312261865162375*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.130525800902', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.63780849197529667581591007760', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.74591266769627696479587624501', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.12321585070243764219511816914', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'bad_primes': [2, 3, 13], 'central_character': '39.5', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/2/g/a/5/6'], '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': '2-78-39.5-c1-0-2', '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': '2-78-39.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': -0.13052580090204355, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.63780849197529667581591007760', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3343819518139605469662487099663', 'Lhash_array': ['3343819518139605469662487099663'], 'label': '2-78-39.5-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/2/g/a/5/6'}