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lfunc_lfunctions • Show schema
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{'Lhash': '2873381353870375698792419529482', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.8090169943749475, 0.5877852522924731], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5, -1.5388417685876268], 'a8': [0.0, 0.0], 'a9': [0.30901699437494745, -0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.04641304617486922, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8090169943749475, -0.5877852522924731]]], [31, [[1.0, 0], [0.8090169943749475, -0.5877852522924731]]]], 'bad_primes': [3, 31], 'central_character': '93.2', 'coefficient_field': 'CDF', 'conductor': 93, 'conductor_radical': 93, 'conjugate': '4466936583316900092069089166657', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.5, 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'12.82898227684058972867745113270532', '14.29554481691611927434390427375054'], 'prelabel': '2-93-93.2-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.21543687283023122, 'root_angle': -0.19528300162216441, 'root_number': '0.81763817087247298139584954575671 - 0.57573242181791071637766949760905*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0976415008110822', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.26669821585936102709468412872', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.22099923391254890010555720139', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.95144901391539568473880923115', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.04641304617486922, 'bad_primes': [3, 31], 'central_character': '93.2', 'conductor': 93, 'conductor_radical': 93, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/93/1/l/a/2/1'], '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': '2-93-93.2-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': '2-93-93.2-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.21543687283023122, 'root_angle': -0.09764150081108221, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.26669821585936102709468412872', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2873381353870375698792419529482', 'Lhash_array': ['2873381353870375698792419529482'], 'label': '2-93-93.2-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/93/1/l/a/2/1'}