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lfunc_lfunctions • Show schema
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{'Lhash': '2044897377230036552647172235717', 'a10': [0.0, 0.0], 'a2': [0.0, 2.7092753594369228], 'a3': [0.0, 1.0], 'a4': [-5.340172973252067, 0.0], 'a5': [0.0, 0.0], 'a6': [-2.7092753594369228, 0.0], 'a7': [0.0, -1.0783777456217782], 'a8': [0.0, -9.049448332688991], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.587658166755635, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.199', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'conjugate': '413163989270677783556675429546', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.7092753594369228], [-2.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0783777456217782], [-7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 4.340172973252067], [-13.0, 0]], [[1.0, 0], [0, 7.758723692125913], 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'4.26505844248580017466678776321128', '5.52707032904482241445914892365331', '6.58481070371980395265923008600188', '8.065116575860255601453218217379094', '8.825772603540461271510421507280670', '9.353033321869806272516238829173675', '10.51809633589231397078135498072211'], 'prelabel': '2-825-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.566643365712431, 'root_angle': -0.14758361765043326, 'root_number': '0.894427190999916 - 0.44721359549995787*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0737918088252', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.61313959608575948932764737755', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.15449222198825069803858356654', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58844764605204203956616777997', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.587658166755635, 'bad_primes': [3, 5, 11], 'central_character': '5.4', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/2/c/g/199/6'], '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': '2-825-5.4-c1-0-17', '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': '2-825-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.566643365712431, 'root_angle': -0.07379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.61313959608575948932764737755', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2044897377230036552647172235717', 'Lhash_array': ['2044897377230036552647172235717'], 'label': '2-825-5.4-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/2/c/g/199/6'}