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lfunc_lfunctions • Show schema
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{'Lhash': '1407577050787462385678897138397', 'a10': [0.0, 0.0], 'a2': [1.4460703197968103, 1.4460703197968103], 'a3': [-2.952400829552802, -1.2229244651623472], 'a4': [0.0, 2.182238739594498], 'a5': [0.0, 0.0], 'a6': [-2.50094443933513, -6.037813984184447], 'a7': [-0.45058390354093353, -1.0878057709155322], 'a8': [-0.2635300324447836, 0.2635300324447836], 'a9': [5.099806067291818, 5.099806067291818], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.393642085904418, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-3.891413562985862, -1.3626813574015306]]]], 'bad_primes': [5, 17], 'central_character': '425.399', 'coefficient_field': 'CDF', 'conductor': 425, 'conductor_radical': 85, 'conjugate': '1698616591517135791410824581368', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4460703197968103, -1.4460703197968103], [0, 2.0]], [[1.0, 0], [2.952400829552802, 1.2229244651623472], 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['1.11038250645251968547076724887196', '3.31741739835759339850609216981720', '4.03339764463689725063026586580794', '5.39837444136033258716398439215840', '5.62229532557319033352180788092210', '6.73579563830629869273236875908329', '8.535625009128286265736648786509334', '9.838455319350271716709430100425407', '10.52505165400800734076738022586690', '11.35587195925883189046273403977223'], 'prelabel': '2-425-85.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8421840532108669, 'root_angle': -0.31454517688798245, 'root_number': '0.5502165163157734 - 0.835022026759375*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.157272588444', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11038250645251968547076724887', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.31741739835759339850609216982', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.03339764463689725063026586581', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.393642085904418, 'bad_primes': [5, 17], 'central_character': '85.59', 'conductor': 425, 'conductor_radical': 85, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/425/2/n/c/399/6'], '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': '2-425-85.59-c1-0-5', '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': '2-425-85.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8421840532108669, 'root_angle': -0.15727258844399122, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11038250645251968547076724887', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1407577050787462385678897138397', 'Lhash_array': ['1407577050787462385678897138397'], 'label': '2-425-85.59-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/425/2/n/c/399/6'}