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lfunc_lfunctions • Show schema
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{'Lhash': '869391595472065433375291150077', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.5, -0.8660254037844386], 'a4': [0, 0], 'a5': [-1.4142135623730951, 2.449489742783178], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.198766312851504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.5, 0.8660254037844386]]]], 'bad_primes': [2, 3], 'central_character': '1152.959', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '2047813043805093110478109225712', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5, 0.8660254037844386]], [[1.0, 0], [1.4142135623730951, -2.449489742783178], [-2.5, -4.330127018922194]], [[1.0, 0], [0, 0], [3.5, -6.06217782649107]], [[1.0, 0], [4.5, -2.598076211353316], [5.5, -9.526279441628825]], [[1.0, 0], [-4.242640687119285, -2.449489742783178], 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0.9396926207859083840541092773247314699362081342644646331*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.19444444444444445', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68582904099563324611671374407', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.41018230680628188104764811609', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49864711531740078752660333351', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.198766312851504, 'bad_primes': [2, 3], 'central_character': '72.59', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/2/p/b/959/1'], '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': '2-1152-72.59-c1-0-16', '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': '2-1152-72.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.19444444444444448, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68582904099563324611671374407', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '869391595472065433375291150077', 'Lhash_array': ['869391595472065433375291150077'], 'label': '2-1152-72.59-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/p/b/959/1'}