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lfunc_lfunctions • Show schema
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{'Lhash': '996364729015006765949803893289', 'a10': [0, 0], 'a2': [1.3070950148596003, 0], 'a3': [-2.3826716820551894, -1.8228756555322954], 'a4': [-2.291502622129181, 0], 'a5': [0, 0], 'a6': [-3.1143782776614763, -2.3826716820551894], 'a7': [0, 2.6457513110645907], 'a8': [-8.223591713361156, 0], 'a9': [2.3542486889354093, 8.68662840868918], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.30521387891559, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [2.3826716820551894, 1.8228756555322954]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, -2.6457513110645907]]]], 'bad_primes': [3, 5, 7], 'central_character': '525.449', 'coefficient_field': 'CDF', 'conductor': 525, 'conductor_radical': 105, 'conjugate': '1098861228927237676145289172464', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3070950148596003, 0], [4.0, 0]], [[1.0, 0], [2.3826716820551894, 1.8228756555322954]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 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2.1299490683039957, 2.374694338575222, 2.5045716957526962, 2.5107283045782944, 2.3921002858870684], 'positive_zeros': ['0.78599318206106636357645982163798', '3.17327799657007449077573910941973', '4.14567559639081434435758691614762', '4.92614378384085033526829787550865', '5.81764481927230000392305104235798', '6.67472077336989478622845966624357', '8.017560198640517302268656059873521', '9.163272001706818688673851176144617', '9.841610928299728130553858968652637', '10.67617688352746242165149670337412'], 'prelabel': '2-525-15.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.782223404152059, 'root_angle': 0.06029409441960756, 'root_number': '0.98211370523853604689127178226505433605739982610629766441 + 0.1882887940973491214690726055585472722926433861473400051*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.03014704720980379', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78599318206106636357645982164', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.17327799657007449077573910942', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.14567559639081434435758691615', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.30521387891559, 'bad_primes': [3, 5, 7], 'central_character': '15.14', 'conductor': 525, 'conductor_radical': 105, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/525/3/f/a/449/5'], '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': '2-525-15.14-c2-0-26', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-525-15.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.782223404152059, 'root_angle': 0.03014704720980378, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78599318206106636357645982164', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '996364729015006765949803893289', 'Lhash_array': ['996364729015006765949803893289'], 'label': '2-525-15.14-c2-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/525/3/f/a/449/5'}