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lfunc_lfunctions • Show schema
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{'Lhash': '2181677706644243988437304414131', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.698769936974083, -0.3379063497969073], 'a4': [1.4142135623730951, 1.4142135623730951], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.902746815473341, -4.344267611596298], 'a8': [0.0, 0.0], 'a9': [2.7716385975338604, -1.1480502970952693], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.923029855245012, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.698769936974083, 0.3379063497969073]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 17], 'central_character': '867.329', 'coefficient_field': 'CDF', 'conductor': 867, 'conductor_radical': 51, 'conjugate': '1466578167329543143909482873787', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-1.4142135623730951, -1.4142135623730951]], [[1.0, 0], [-1.698769936974083, 0.3379063497969073]], [[1.0, 0], [0, 0], [1.913417161825449, 4.619397662556434]], [[1.0, 0], [2.902746815473341, 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'primitive': True, 'rational': False, 'root_analytic_conductor': 2.631165113641676, 'root_angle': 0.17964825892854497, 'root_number': '0.8449195130482166 + 0.5348934627291351*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0898241294643', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72104025056387935453142538470', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.70109591810614696489657140602', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50176973747354530177423554962', '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': '51.23', 'conductor': 867, 'conductor_radical': 51, 'degree': 2, 'index': 59, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/867/2/i/j/329/4'], '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': '2-867-51.23-c1-0-59', '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': '2-867-51.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.631165113641676, 'root_angle': 0.08982412946427248, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72104025056387935453142538470', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2181677706644243988437304414131', 'Lhash_array': ['2181677706644243988437304414131'], 'label': '2-867-51.23-c1-0-59', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/867/2/i/j/329/4'}