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lfunc_lfunctions • Show schema
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{'Lhash': '1705506335459006115072130965326', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.5, -1.8660254037844386], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [3.866025403784439, 2.232050807568877], 'a8': [0, 0], 'a9': [-0.6339745962155614, -0.36602540378443865], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.380552262766455, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-2.0, 3.0]]]], 'bad_primes': [2, 5, 13], 'central_character': '1300.193', 'coefficient_field': 'CDF', 'conductor': 1300, 'conductor_radical': 130, 'conjugate': '1333108100716499502348517327570', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, 1.8660254037844386], [-2.598076211353316, -1.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.866025403784439, -2.232050807568877], [3.5, 6.06217782649107]], [[1.0, 0], [2.866025403784439, 0.7679491924311227], [9.526279441628825, 5.5]], [[1.0, 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'primitive': True, 'rational': False, 'root_analytic_conductor': 3.221886444734894, 'root_angle': 0.332001045004816, 'root_number': '0.50362036539021924848159589653602974340191421668178551646 + 0.8639250705728026585795062122961387651087318168737747818*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.16600052250240802', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34540727165036218867727149516', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.69833800552389329398593461356', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.13188842430656132952744746955', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.380552262766455, 'bad_primes': [2, 5, 13], 'central_character': '65.63', 'conductor': 1300, 'conductor_radical': 130, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1300/2/bs/b/193/1'], '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': '2-1300-65.63-c1-0-13', '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': '2-1300-65.63-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.221886444734894, 'root_angle': 0.166000522502408, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34540727165036218867727149516', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1705506335459006115072130965326', 'Lhash_array': ['1705506335459006115072130965326'], 'label': '2-1300-65.63-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1300/2/bs/b/193/1'}