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lfunc_lfunctions • Show schema
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{'Lhash': '4453587050007468566114995911461', 'a10': [0.1501683474320005, -0.26009920744088016], 'a2': [2.0536451458980234, 0.0], 'a3': [-1.7086745968250738, -0.2836038119713336], 'a4': [2.2174583852705134, 0.0], 'a5': [0.07312283124080547, -0.12665245890235985], 'a6': [-3.5090112916890748, -0.582421591813105], 'a7': [-2.3303539672252174, 1.2527770701276786], 'a8': [0.4465823573456119, 0.0], 'a9': [2.8391377556706567, 0.969173258156345], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5030575327340666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.7086745968250738, 0.2836038119713336]]], [7, [[1.0, 0], [2.3303539672252174, -1.2527770701276786]]]], 'bad_primes': [3, 7], 'central_character': '63.25', 'coefficient_field': 'CDF', 'conductor': 63, 'conductor_radical': 21, 'conjugate': '4171067518419172080505442778538', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0536451458980234, 0], [2.0, 0]], [[1.0, 0], 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'10.80325049402749215865202121243767', '11.97244737586254092887587628727606', '12.86944437053201546120144885180734', '13.58431647917980547469410239087838', '15.06824978159329019458757615967799'], 'prelabel': '2-63-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7092654881876508, 'root_angle': 0.011713909990198125, 'root_number': '0.9972926933658288 + 0.07353423528623251*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0117139099902', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.51326071174946722430497290653', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.89905415517488434285814136983', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.07013110388134911569095207318', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5030575327340666, 'bad_primes': [3, 7], 'central_character': '63.25', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/2/h/b/25/5'], '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': '2-63-63.25-c1-0-5', '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': '2-63-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7092654881876508, 'root_angle': 0.011713909990198125, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.51326071174946722430497290653', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4453587050007468566114995911461', 'Lhash_array': ['4453587050007468566114995911461'], 'factors': ['2-63-63.25-c1-0-5'], 'label': '2-63-63.25-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/2/h/b/25/5'}