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lfunc_lfunctions • Show schema
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{'Lhash': '3337924070548449081399102655621', 'a10': [0.2297934384885058, 1.3032233499673034], 'a2': [0.8936326403234123, -0.44879918020046217], 'a3': [1.511787549773279, -0.8452800745022362], 'a4': [0.5971585917027862, -0.8021231927550437], 'a5': [-0.3795346539179467, 1.2677340299714903], 'a6': [0.971621695235568, -1.4338588777657169], 'a7': [-0.7681690694400692, 1.780816070006899], 'a8': [0.17364817766693036, -0.984807753012208], 'a9': [1.571003191298988, -2.5557677854078205], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8936326403234123, 0.44879918020046217]]], [3, [[1.0, 0], [-1.511787549773279, 0.8452800745022362]]]], 'bad_primes': [2, 3], 'central_character': '162.25', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '2958765475286875491358188165999', 'degree': 2, 'euler_factors': [[[1.0, 0], 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0.1903794922779116, 'root_number': '0.8264098651321096 + 0.5630690320132413*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.095189746139', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.63315780385185401385809354712', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.13645821561245840735979459930', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.91625471803565595118624520757', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '81.25', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/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': '2-162-81.25-c1-0-7', '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': '2-162-81.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.0951897461389558, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.63315780385185401385809354712', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3337924070548449081399102655621', 'Lhash_array': ['3337924070548449081399102655621'], 'label': '2-162-81.25-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/b/25/5'}