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lfunc_lfunctions • Show schema
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{'Lhash': '1841400039686323952238428276157', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.25881904510252074, -0.9659258262890683], 'a4': [0.0, 0.0], 'a5': [0.36602540378443865, 1.3660254037844386], 'a6': [0.0, 0.0], 'a7': [0.7071067811865476, -0.7071067811865476], 'a8': [0.0, 0.0], 'a9': [1.240336064878181e-78, -4.85040625337984e-78], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9502197840532366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [17, [[1.0, 0], [-0.8660254037844386, 0.5]]]], 'bad_primes': [2, 7, 17], 'central_character': '1904.191', 'coefficient_field': 'CDF', 'conductor': 1904, 'conductor_radical': 238, 'conjugate': '1571940318369735459867851180928', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.25881904510252074, 0.9659258262890683], [-0.8660254037844386, -0.5]], [[1.0, 0], [-0.36602540378443865, 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0.55029116190045774068925302174246*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09274163940070261', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45260850218096057634228639266', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.58161704036015341718477187376', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86835255858916967228926960950', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9502197840532366, 'bad_primes': [2, 7, 17], 'central_character': '476.191', 'conductor': 1904, 'conductor_radical': 238, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1904/1/dm/a/191/2'], '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': '2-1904-476.191-c0-0-1', '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': '2-1904-476.191-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9747921748009862, 'root_angle': 0.09274163940070261, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45260850218096057634228639266', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1841400039686323952238428276157', 'Lhash_array': ['1841400039686323952238428276157'], 'label': '2-1904-476.191-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1904/1/dm/a/191/2'}