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lfunc_lfunctions • Show schema
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{'Lhash': '3046580657622291036036584335938', 'a10': [191.53505848947069, 2.391544945194379e-59], 'a2': [-1.4767338470373137, 2.557778052325274], 'a3': [11.32399525360481, 10.712942242742455], 'a4': [11.638514290028752, 20.158498074946216], 'a5': [-32.42545345488906, -56.162532842327636], 'a6': [-44.123855619003066, 13.144102113092346], 'a7': [80.095199702307, -138.72895532677134], 'a8': [-163.2589181356397, 0.0], 'a9': [13.465737007328512, 242.62661421791606], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.4434543783168259, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-11.32399525360481, -10.712942242742455]]]], 'bad_primes': [3], 'central_character': '9.7', 'coefficient_field': 'CDF', 'conductor': 9, 'conductor_radical': 3, 'conjugate': '5244710329820335644443828826428', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4767338470373137, -2.557778052325274], [-16.0, -27.712812921102035]], [[1.0, 0], 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['2.40332837540074594633476136564775', '6.70848782916142223454640995462001', '8.777365834679306994223103789856092', '10.89733283190714772643598390959828', '12.29970902841917084296562366337567', '14.70869059799347901399816426522177', '15.11330140471780305633477749716902', '18.14181633768460173281083568617756', '18.85480037486389477546965199426327', '19.87106248101471328136461937696762'], 'prelabel': '2-3e2-9.7-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2014384621431202, 'root_angle': -0.14771290935897344, 'root_number': '0.5993499110802748 - 0.800487154230514*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.147712909359', 'prec': 50}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.40332837540074594633476136565', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.70848782916142223454640995462', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.777365834679306994223103789856', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.4434543783168259, 'bad_primes': [3], 'central_character': '9.7', 'conductor': 9, 'conductor_radical': 3, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9/6/c/a/7/2'], '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': '2-3e2-9.7-c5-0-1', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-3e2-9.7-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2014384621431202, 'root_angle': -0.14771290935897344, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.40332837540074594633476136565', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3046580657622291036036584335938', 'Lhash_array': ['3046580657622291036036584335938'], 'factors': ['2-3e2-9.7-c5-0-1'], 'label': '2-3e2-9.7-c5-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9/6/c/a/7/2'}