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lfunc_lfunctions • Show schema
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{'Lhash': '2882488270609145677157633308175', 'a10': [0.06306026001601056, 0.0], 'a2': [0.7653668647301796, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.4142135623730951, 0.0], 'a5': [0.08239220029239397, 0.0], 'a6': [0.7653668647301796, 0.0], 'a7': [-2.7653668647301797, 0.0], 'a8': [-2.613125929752753, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.923029855245012, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 17], 'central_character': '867.1', 'coefficient_field': 'CDF', 'conductor': 867, 'conductor_radical': 51, 'conjugate': '2882488270609145677157633308175', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7653668647301796, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.08239220029239397, 0], [5.0, 0]], [[1.0, 0], [2.7653668647301797, 0], [7.0, 0]], [[1.0, 0], [0.6681786379192989, 0], [11.0, 0]], [[1.0, 0], [3.281304567672052, 0], 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'5.32430448440947130676770502512264', '6.03386340767076854659317610013467', '7.25212660308827933121795031778073', '8.021926555524374426655054812912948', '9.100701719497635542874776313839184', '9.703766931908428812076985882971205'], 'prelabel': '2-867-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.631165113641676, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.27388230644167949692486693486', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.46076222304891927892173669255', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.06709772566297443622278676198', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.923029855245012, 'bad_primes': [3, 17], 'central_character': '1.1', 'conductor': 867, 'conductor_radical': 51, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/867/2/a/n/1/3'], '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': '2-867-1.1-c1-0-40', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-867-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.631165113641676, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.27388230644167949692486693486', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2882488270609145677157633308175', 'Lhash_array': ['2882488270609145677157633308175'], 'label': '2-867-1.1-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/867/2/a/n/1/3'}