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lfunc_lfunctions • Show schema
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{'Lhash': '1286628327567226696138995245622', 'a10': [-2.5427002819122793, 1.3480543719856573], 'a2': [0.7821312770885673, 0.31162958334661706], 'a3': [-1.7218974515240826, -0.18726763317474265], 'a4': [-2.389365630309116, -2.263327347410758], 'a5': [-2.21294881254362, 2.605284749628128], 'a6': [-1.288391718275528, -0.6830620584763665], 'a7': [9.586652726762344, 5.768097564175932], 'a8': [-2.577542975327359, -5.5712678391985015], 'a9': [2.92986166713026, 0.6449113206330722], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.8229006791772555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.7218974515240826, 0.18726763317474265]]], [59, [[1.0, 0], [46.9141931988413, 35.7779048646199]]]], 'bad_primes': [3, 59], 'central_character': '177.10', 'coefficient_field': 'CDF', 'conductor': 177, 'conductor_radical': 177, 'conjugate': '1972618823475563427791611688949', 'degree': 2, 'euler_factors': [[[1.0, 0], 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2.1961103522312477, 'root_angle': -0.2294106346607232, 'root_number': '0.7513342323776631 - 0.6599218675399897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.11470531733', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01497078716767894942587346157', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.70936028617703402120290787647', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.53817976121147452725856585580', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.8229006791772555, 'bad_primes': [3, 59], 'central_character': '59.10', 'conductor': 177, 'conductor_radical': 177, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/177/3/g/a/10/12'], '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': '2-177-59.10-c2-0-6', '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': '2-177-59.10-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1961103522312477, 'root_angle': -0.1147053173303616, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01497078716767894942587346157', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1286628327567226696138995245622', 'Lhash_array': ['1286628327567226696138995245622'], 'label': '2-177-59.10-c2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/177/3/g/a/10/12'}