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lfunc_lfunctions • Show schema
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{'Lhash': '232262393353172234149958175841', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 17.0], 'a4': [-16.0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 49.0], 'a8': [0, 0], 'a9': [-208.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.089743539672764, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, -49.0]]]], 'bad_primes': [5, 7], 'central_character': '175.76', 'coefficient_field': 'CDF', 'conductor': 175, 'conductor_radical': 35, 'conjugate': '3721619348164601561225762553747', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [16.0, 0]], [[1.0, 0], [0, -17.0], [-81.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -49.0]], [[1.0, 0], [73.0, 0], [14641.0, 0]], [[1.0, 0], [0, 23.0], [-28561.0, 0]], [[1.0, 0], [0, -263.0], [-83521.0, 0]], [[1.0, 0], [0, 0], [-130321.0, 0]], [[1.0, 0], [0, 0], [279841.0, 0]], [[1.0, 0], [-1153.0, 0], [707281.0, 0]], [[1.0, 0], [0, 0], [-923521.0, 0]], [[1.0, 0], 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'root_analytic_conductor': 4.25320391465925, 'root_angle': 0.5, 'root_number': '0.e-56 + 1.00000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.18322272186938216413664157224', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.20475748403600318982388483949', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.95453367665585126965804070782', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.089743539672764, 'bad_primes': [5, 7], 'central_character': '7.6', 'conductor': 175, 'conductor_radical': 35, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/175/5/d/c/76/2'], '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': '2-175-7.6-c4-0-1', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-175-7.6-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.25320391465925, 'root_angle': 0.25, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.18322272186938216413664157224', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '232262393353172234149958175841', 'Lhash_array': ['232262393353172234149958175841'], 'label': '2-175-7.6-c4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/175/5/d/c/76/2'}