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lfunc_lfunctions • Show schema
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{'Lhash': '2516985026098911457221136438238', 'a10': [0.6861406616345072, 0.39614349569663065], 'a2': [-0.5, 0.8660254037844386], 'a3': [1.1861406616345072, -1.2621688994810694], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.0, -0.7922869913932613], 'a6': [0.5, 1.6583123951777], 'a7': [0.5, -2.598076211353316], 'a8': [1.0, 0.0], 'a9': [-0.18614066163450715, -2.9942197070499468], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [-1.1861406616345072, 1.2621688994810694]]], [7, [[1.0, 0], [-0.5, 2.598076211353316]]], [13, [[1.0, 0], [-3.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.251', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '1079206903883743822665590603227', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], 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'9.033566501119402696354490860026387', '10.29179730426089407640361849457768', '10.76159431409444881683089407612609'], 'prelabel': '2-546-273.251-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.38601172788240307, 'root_number': '0.3504998134946579 + 0.936562801279343*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.193005863941', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.98555108611611931647074163913', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07639802422447340172642941994', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.92737892537179869299343608314', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.251', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/q/e/251/2'], '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': '2-546-273.251-c1-0-26', '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': '2-546-273.251-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.19300586394120153, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.98555108611611931647074163913', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2516985026098911457221136438238', 'Lhash_array': ['2516985026098911457221136438238'], 'label': '2-546-273.251-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/q/e/251/2'}