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lfunc_lfunctions • Show schema
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{'Lhash': '2966235260779922599786844138011', 'a10': [1.3406653218024887, 2.8640210360463887], 'a2': [-1.3406653218024887, 0.4501294201851612], 'a3': [1.0, 0.0], 'a4': [1.594767010167541, -1.2069458079306137], 'a5': [-0.2541016883650524, -2.2215832939527678], 'a6': [-1.3406653218024887, 0.4501294201851612], 'a7': [0.0, -2.6426489071648906], 'a8': [-1.594767010167541, 2.335961939604599], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3406653218024887, -0.4501294201851612]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0.2541016883650524, 2.2215832939527678]]]], 'bad_primes': [2, 3, 5], 'central_character': '120.109', 'coefficient_field': 'CDF', 'conductor': 120, 'conductor_radical': 30, 'conjugate': '1827291455744123224245421370850', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3406653218024887, -0.4501294201851612]], [[1.0, 0], 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-6.771297679755069, -7.673991407275125, -7.780324451066512], 'positive_zeros': ['2.33994703291733375815870286355661', '3.52678672159251582304286585507741', '6.10440114465324932228124064920878', '7.19402210933065850364610019597351', '8.534368189674196953509191386461244', '9.072787065551751236076089592864845', '10.55241982272747408788185000101426', '11.14887282898754784888577455960140', '12.34882220356501551728628618784623', '13.49635622927998105435769137902422'], 'prelabel': '2-120-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': 0.15442440410432803, 'root_number': '0.8846103365049925 + 0.46633094744883047*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0772122020522', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.33994703291733375815870286356', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.52678672159251582304286585508', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.10440114465324932228124064921', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'bad_primes': [2, 3, 5], 'central_character': '40.29', 'conductor': 120, 'conductor_radical': 30, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/120/2/d/a/109/2'], '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': '2-120-40.29-c1-0-6', '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': '2-120-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': 0.07721220205216402, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.33994703291733375815870286356', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2966235260779922599786844138011', 'Lhash_array': ['2966235260779922599786844138011'], 'label': '2-120-40.29-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/120/2/d/a/109/2'}