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lfunc_lfunctions • Show schema
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{'Lhash': '143188257013499865582668993572', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [2.463075497382991, 0], 'a6': [0, 0], 'a7': [0, 5.483314773547883], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.389726454306206, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.127', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '2388746556612811882812668653975', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.463075497382991, 0], [25.0, 0]], [[1.0, 0], [0, -5.483314773547883], [-49.0, 0]], [[1.0, 0], [0, -10.583005244258363], [-121.0, 0]], [[1.0, 0], [8.966629547095765, 0], [169.0, 0]], [[1.0, 0], [16.239859493750743, 0], [289.0, 0]], [[1.0, 0], [0, 2.9666295470957658], [-361.0, 0]], [[1.0, 0], [0, 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'2.81393917996652912960625962012594', '3.90909901955442397979229453989854', '4.85903610039301446697602974395690', '5.88597483677872065078760960965107', '6.62910100496553485310176512791326', '7.57682414699611012794495313832601', '8.321600655618771920154026780985044', '9.384420348914755511148742616139143'], 'prelabel': '2-1152-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.602653519030621, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.11295561804468839637723482487', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.56219875144283458474411231081', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81393917996652912960625962013', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.389726454306206, 'bad_primes': [2, 3], 'central_character': '4.3', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/3/g/e/127/6'], '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': '2-1152-4.3-c2-0-2', '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': '2-1152-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.602653519030621, 'root_angle': 0.5, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.11295561804468839637723482487', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '143188257013499865582668993572', 'Lhash_array': ['143188257013499865582668993572'], 'label': '2-1152-4.3-c2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/3/g/e/127/6'}