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lfunc_lfunctions • Show schema
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{'Lhash': '248579188160354577738471030700', 'a10': [-1.8022975435074746, 0.0], 'a2': [0.7756098925892831, 0.0], 'a3': [-1.0, 0.0], 'a4': [-1.3984292945176406, 0.0], 'a5': [-2.3237165496828753, 0.0], 'a6': [-0.7756098925892831, 0.0], 'a7': [0.0, 0.0], 'a8': [-2.635855380093101, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.12583729822571, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [41, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 41], 'central_character': '6027.1', 'coefficient_field': 'CDF', 'conductor': 6027, 'conductor_radical': 861, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7756098925892831, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.3237165496828753, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.7601897368529943, 0], [11.0, 0]], [[1.0, 0], [5.4909923441545985, 0], [13.0, 0]], [[1.0, 0], [0.3432751935449323, 0], [17.0, 0]], 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'3.06536683232911723053215572641524', '3.99024077629256095920606970311131', '4.30918256353712158147321895322886', '5.20182934075156603843261802491503', '5.64370754479301514293197216483493', '6.72300861728896390910933763681448', '7.24906490824916635415648935117332', '8.056902656797055181652016842369740'], 'prelabel': '2-6027-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.937278810760435, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.19609440339128153247876485776', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86842303893420165931777436065', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06536683232911723053215572642', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.12583729822571, 'bad_primes': [3, 7, 41], 'central_character': '1.1', 'conductor': 6027, 'conductor_radical': 861, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6027/2/a/bd/1/5'], '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': '2-6027-1.1-c1-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-6027-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.937278810760435, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.19609440339128153247876485776', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '248579188160354577738471030700', 'Lhash_array': ['248579188160354577738471030700'], 'label': '2-6027-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6027/2/a/bd/1/5'}