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lfunc_lfunctions • Show schema
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{'Lhash': '1008742546259618123185622255346', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.0, 0], 'a4': [0, 0], 'a5': [0, 1.0], 'a6': [0, 0], 'a7': [0, 4.701562118716424], 'a8': [0, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.456662715319746, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, -1.0]]], [13, [[1.0, 0], [-2.0, 3.0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.961', 'coefficient_field': 'CDF', 'conductor': 1560, 'conductor_radical': 390, 'conjugate': '1398824916137226656236617912604', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -4.701562118716424], [-7.0, 0]], [[1.0, 0], [0, 2.7015621187164243], [-11.0, 0]], [[1.0, 0], [-2.0, 3.0]], [[1.0, 0], [-6.701562118716424, 0], [17.0, 0]], [[1.0, 0], [0, 7.4031242374328485], [-19.0, 0]], [[1.0, 0], 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'6.02346402499296233392244566943864', '7.05675592422637277268834852975521', '7.53284828160321113745482430397915', '8.370259517727605205008542408426379', '9.650985598829725419863561454865186'], 'prelabel': '2-1560-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5293997670028463, 'root_angle': -0.1564164790945006, 'root_number': '0.5547001962252291220183417334569993763463533190531148020 - 0.8320502943378436830275126001854990645195299785796722030*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1564164790945006', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.795757558177310728955073776668', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.74885985166863053704684536533', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79222527395488031424655847036', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.456662715319746, 'bad_primes': [2, 3, 5, 13], 'central_character': '13.12', 'conductor': 1560, 'conductor_radical': 390, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1560/2/g/f/961/4'], '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': '2-1560-13.12-c1-0-11', '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': '2-1560-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5293997670028463, 'root_angle': -0.1564164790945006, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.795757558177310728955073776668', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1008742546259618123185622255346', 'Lhash_array': ['1008742546259618123185622255346'], 'factors': ['2-1560-13.12-c1-0-11'], 'label': '2-1560-13.12-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/2/g/f/961/4'}