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lfunc_lfunctions • Show schema
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{'Lhash': '4418707591265572744384639392037', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.5, 0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.04940743625066724, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5, 0.8660254037844386]]], [11, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [3, 11], 'central_character': '99.43', 'coefficient_field': 'CDF', 'conductor': 99, 'conductor_radical': 33, 'conjugate': '2785661149704576824755601970302', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], 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'4.83958004195883381465049249391284', '5.87745731392387153437427664512540', '7.900036263668485527728149050920388', '8.995618197728112279657030086600284', '9.771058824857733952186506670258999', '11.18660620224420896302432564704690', '12.17300394541636825118828706017721', '13.21712899441185516945422273869572', '14.04537565277773264555820701746158'], 'prelabel': '2-99-99.43-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.22227783571617582, 'root_angle': 0.22222222222222227, 'root_number': '0.76604444311897803520239265055524 + 0.64278760968653932632264340990740*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1111111111111111', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.48574567035271635281071490245', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.83958004195883381465049249391', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.87745731392387153437427664513', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.04940743625066724, 'bad_primes': [3, 11], 'central_character': '99.43', 'conductor': 99, 'conductor_radical': 33, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/99/1/h/a/43/1', 'ArtinRepresentation/2.99.6t5.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': '2-99-99.43-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': '2-99-99.43-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.22227783571617582, 'root_angle': 0.11111111111111113, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.48574567035271635281071490245', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24596377
{'Lhash': '4418707591265572744384639392037', 'Lhash_array': ['4418707591265572744384639392037'], 'label': '2-99-99.43-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.99.6t5.a.a'}
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id: 19802147
{'Lhash': '4418707591265572744384639392037', 'Lhash_array': ['4418707591265572744384639392037'], 'label': '2-99-99.43-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/99/1/h/a/43/1'}