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lfunc_lfunctions • Show schema
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{'Lhash': '1051808355649655222782807143556', 'a10': [-1.3168822432642346, 0.0], 'a2': [-0.7198260196293791, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.4818505014645247, 0.0], 'a5': [1.8294451816874657, 0.0], 'a6': [-0.7198260196293791, 0.0], 'a7': [0.4147545353966429, 0.0], 'a8': [2.5063265874137666, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.17172697437388, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]], [79, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 17, 79], 'central_character': '4029.1', 'coefficient_field': 'CDF', 'conductor': 4029, 'conductor_radical': 4029, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7198260196293791, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.8294451816874657, 0], [5.0, 0]], [[1.0, 0], [-0.4147545353966429, 0], [7.0, 0]], [[1.0, 0], [2.7595638627901398, 0], [11.0, 0]], [[1.0, 0], [-0.24556435285694933, 0], [13.0, 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'3.78877765740468332612222239803662', '4.82471655141435838099510779288157', '5.29226110778074461496593027115982', '6.25461558526168835587736226467314', '7.23616666472074169492008437733782', '7.917004666507085227025489292047197', '8.476907287149823657082666403650899'], 'prelabel': '2-4029-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6720126035097875, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.829730491556810945611693655345', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.89363001016625889877573993108', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.83586911066810752901695186327', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.17172697437388, 'bad_primes': [3, 17, 79], 'central_character': '1.1', 'conductor': 4029, 'conductor_radical': 4029, 'degree': 2, 'index': 63, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4029/2/a/k/1/11'], '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': '2-4029-1.1-c1-0-63', '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': '2-4029-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6720126035097875, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.829730491556810945611693655345', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1051808355649655222782807143556', 'Lhash_array': ['1051808355649655222782807143556'], 'label': '2-4029-1.1-c1-0-63', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4029/2/a/k/1/11'}