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lfunc_lfunctions • Show schema
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{'Lhash': '1502654026090278244105374641641', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.618033988749895, 0.6180339887498949], 'a4': [0.0, 0.0], 'a5': [0.0, 1.2360679774997898], 'a6': [0.0, 0.0], 'a7': [0.0, 3.23606797749979], 'a8': [0.0, 0.0], 'a9': [2.23606797749979, 2.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0662554376171682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.618033988749895, -0.6180339887498949]]]], 'bad_primes': [2, 3], 'central_character': '384.383', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '3027353858821871442356110655013', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.618033988749895, -0.6180339887498949]], [[1.0, 0], [0, -1.2360679774997898], [-5.0, 0]], [[1.0, 0], [0, -3.23606797749979], [-7.0, 0]], [[1.0, 0], [0.7639320225002103, 0], [11.0, 0]], [[1.0, 0], [4.47213595499958, 0], [13.0, 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'7.31167834096556364237367427664753', '8.459874022653092865895918838826136', '9.155500414776418872618736695583456', '10.22985321993568977451284944311631', '10.96232619644934587218618543538609'], 'prelabel': '2-384-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': -0.38386023640061506, 'root_number': '0.3568220897730899 - 0.9341723589627157*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1919301182', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18538501525557478656219182913', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81637949391504147846896050728', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.08716589593396748958705805894', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.0662554376171682, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/2/c/c/383/4'], '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': '2-384-12.11-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': '2-384-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': -0.19193011820030753, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18538501525557478656219182913', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1502654026090278244105374641641', 'Lhash_array': ['1502654026090278244105374641641'], 'label': '2-384-12.11-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/2/c/c/383/4'}