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lfunc_lfunctions • Show schema
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{'Lhash': '2075719319128720374865670430675', 'a10': [-0.3401894366355891, -0.5892253884510734], 'a2': [0.6167958067270042, 1.0683216751466047], 'a3': [0.5069436840529279, 1.656202916673813], 'a4': [0.23912586560796817, -0.41417814863688807], 'a5': [-0.5515430437842747, 0.0], 'a6': [-1.4566767357530754, 1.5631179398458568], 'a7': [-1.6215599846194932, 2.8086242808815696], 'a8': [3.0571505516558566, 0.0], 'a9': [-2.4860162023976904, 1.679203216235654], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.5069436840529279, -1.656202916673813]]], [19, [[1.0, 0], [-0.16410716773114237, 4.355808631872992]]]], 'bad_primes': [3, 19], 'central_character': '171.106', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '3644810808287702869108744570663', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6167958067270042, 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'7.42287944830095902003089338611687', '7.999449886720337560695518616509146', '9.808835218313912829675082849892962', '10.58340457937072656538549331039941', '12.03986769262935055597307363140467', '12.41463637907200579797361301283129'], 'prelabel': '2-171-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': -0.522641103425607, 'root_number': '-0.07106916147857889 - 0.9974713902096298*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.261320551713', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.63745382107262464065711448396', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.25588635941600057399310177910', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.27058666586534429632172274832', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '171.106', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/g/c/106/11'], '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': '2-171-171.106-c1-0-4', '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': '2-171-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': -0.2613205517128035, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.63745382107262464065711448396', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2075719319128720374865670430675', 'Lhash_array': ['2075719319128720374865670430675'], 'label': '2-171-171.106-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/g/c/106/11'}