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lfunc_lfunctions • Show schema
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{'Lhash': '3655083256959480111112985617699', 'a10': [0.0, 0.0], 'a2': [1.3449970239279148, -1.3449970239279148], 'a3': [-0.9654514594151783, -0.3999030883026646], 'a4': [0.0, -2.618033988749895], 'a5': [0.0, 0.0], 'a6': [-1.8363978032869426, 0.7606608760336108], 'a7': [0.06004999210678571, 0.14497350536459938], 'a8': [-2.1762508994828216, -2.1762508994828216], 'a9': [0.06506725926634138, 0.06506725926634138], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.39875294509376896, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [-0.8090169943749475, -0.5877852522924731]]], [47, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [17, 47], 'central_character': '799.281', 'coefficient_field': 'CDF', 'conductor': 799, 'conductor_radical': 799, 'conjugate': '1420181396724318208502613219968', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3449970239279148, 1.3449970239279148], [0, -1.0]], [[1.0, 0], [0.9654514594151783, 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'11.32135055946026197356191293526671'], 'prelabel': '2-799-799.281-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6314688789590259, 'root_angle': 0.935188948910427, 'root_number': '-0.97934301273618332142138712346617 + 0.20220599250471256171609537139653*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.46759447445521346', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.88335228674321957833288608823', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.07980234028456895739692246494', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.81461616176181746872550031763', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.39875294509376896, 'bad_primes': [17, 47], 'central_character': '799.281', 'conductor': 799, 'conductor_radical': 799, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/799/1/h/b/281/4'], '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': '2-799-799.281-c0-0-4', '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': '2-799-799.281-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6314688789590259, 'root_angle': 0.4675944744552135, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.88335228674321957833288608823', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3655083256959480111112985617699', 'Lhash_array': ['3655083256959480111112985617699'], 'label': '2-799-799.281-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/799/1/h/b/281/4'}