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lfunc_lfunctions • Show schema
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{'Lhash': '3021212210232437815449685260023', 'a10': [-2.1771243444677046, -3.7708899790131505], 'a2': [3.0362191894849895, 1.752961966367866], 'a3': [2.0869930281210474, -2.1551009490448796], 'a4': [4.145751311064591, 7.180651906309156], 'a5': [-1.0755766671955889, -0.6209844783394538], 'a6': [10.114378277661476, -2.884939454396278], 'a7': [0.0, 0.0], 'a8': [0.0, 15.045681750320846], 'a9': [-0.288920201148283, -8.995361311107432], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.005459886096365, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-2.0869930281210474, 2.1551009490448796]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '147.128', 'coefficient_field': 'CDF', 'conductor': 147, 'conductor_radical': 21, 'conjugate': '3225373548000423240313211097357', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.0362191894849895, -1.752961966367866], [2.0, 3.4641016151377544]], [[1.0, 0], 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'8.762793710174122290772207365173947', '10.10707113953984829066410815419261', '10.81972370367779487675207250852842', '11.77804322904892101243769191545552', '12.94082841544004665066295999689523'], 'prelabel': '2-147-21.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0013645060548977, 'root_angle': -0.21476420276378985, 'root_number': '0.7808933597094068 - 0.624664358485223*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.107382101382', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.38331619902873472056729161606', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.39564266806650787519888516008', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.59491788229925712226805025158', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.005459886096365, 'bad_primes': [3, 7], 'central_character': '21.2', 'conductor': 147, 'conductor_radical': 21, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/147/3/h/e/128/4'], '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': '2-147-21.2-c2-0-17', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-147-21.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0013645060548977, 'root_angle': -0.10738210138189493, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.38331619902873472056729161606', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3021212210232437815449685260023', 'Lhash_array': ['3021212210232437815449685260023'], 'label': '2-147-21.2-c2-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/147/3/h/e/128/4'}