Table lfunc_lfunctions
L-functions
{'Lhash': '1092323981543683872361466313776', 'a10': [-1.3760819832967677, 1.2281251079644595], 'a2': [-1.4119366074672095, -0.08021855454935205], 'a3': [0.0, -1.0], 'a4': [1.9871299670120253, 0.22652702753267082], 'a5': [0.9222110530630557, -0.9222110530630557], 'a6': [-0.08021855454935205, 1.4119366074672095], 'a7': [0.0, 1.2383667232957094], 'a8': [-2.7875298735043548, -0.47924649640951666], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.090715699489701, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [1.4119366074672095, 0.08021855454935205]]], [3, [[1.0, 0], [0, 1.0]]], [37, [[1.0, 0], [5.159956047109977, 3.2210019546552884]]]], 'bad_primes': [2, 3, 37], 'central_character': '888.43', 'coefficient_field': 'CDF', 'conductor': 888, 'conductor_radical': 222, 'conjugate': '1491110914565531089533138981953', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4119366074672095, 0.08021855454935205]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-0.9222110530630557, 0.9222110530630557], [0, -5.0]], [[1.0, 0], [0, -1.2383667232957094], [-7.0, 0]], [[1.0, 0], [0, -1.1236638217744197], [-11.0, 0]], [[1.0, 0], [1.4531901462647425, -1.4531901462647425], [0, -13.0]], [[1.0, 0], [-2.7376456169221797, -2.7376456169221797], [0, 17.0]], [[1.0, 0], [-4.435253477434193, -4.435253477434193], [0, 19.0]], [[1.0, 0], [-5.251546943228648, 5.251546943228648], [0, -23.0]], [[1.0, 0], [2.1993565365242453, 2.1993565365242453], [0, 29.0]], [[1.0, 0], [-4.609619823170603, -4.609619823170603], [0, 31.0]], [[1.0, 0], [5.159956047109977, 3.2210019546552884]], [[1.0, 0], [0, -2.8483734281072377], [-41.0, 0]], [[1.0, 0], [-1.2567338795646774, -1.2567338795646774], [0, 43.0]], [[1.0, 0], [0, -2.710868121980414], [-47.0, 0]], [[1.0, 0], [0, 8.172772755242878], [-53.0, 0]], [[1.0, 0], [-0.5803602867016363, -0.5803602867016363], [0, 59.0]], [[1.0, 0], [-2.219094275018857, -2.219094275018857], [0, 61.0]], [[1.0, 0], [0, 9.618196157398469], [-67.0, 0]], [[1.0, 0], [0, 8.74563483401162], [-71.0, 0]], [[1.0, 0], [0, -12.192609096843215], [-73.0, 0]], [[1.0, 0], [-4.3537262339948875, 4.3537262339948875], [0, -79.0]], [[1.0, 0], [-11.87310361507007, 0], [83.0, 0]], [[1.0, 0], [5.93044690253863, -5.93044690253863], [0, -89.0]], [[1.0, 0], [5.868538916811612, 5.868538916811612], [0, 97.0]], [[1.0, 0], [-1.1569255478596425, 0], [101.0, 0]], [[1.0, 0], [-3.8439623735051365, -3.8439623735051365], [0, 103.0]], [[1.0, 0], [-20.261476490397854, 0], [107.0, 0]], [[1.0, 0], [8.121777008502782, -8.121777008502782], [0, -109.0]], [[1.0, 0], [-1.8853495877323552, 1.8853495877323552], [0, -113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 16463950, 'index': 30, 'label': '2-888-296.43-c1-0-30', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/888/2/r/e/43/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.079320615008165, 1.0351161066379344, 0.9624330850334456, 0.8555108622728073, 0.7073640498502949, 0.5116046190286483, 0.26434607340023347, -0.034080538203089615, -0.3777822327448965, -0.754475266122859, -1.1453079022239132, -1.525460938361466, -1.8656158241148793, -2.1343078563348556, -2.3010759920357637, -2.3401923208007553, -2.2346204930628457, -1.979735116077232, -1.5862570550919108, -1.0818453428123438, -0.5108526567033338, 0.0680933366598091, 0.5867801095475401, 0.9741628449936044, 1.1646322562488485, 1.1069274932133082, 0.7725707975666035, 0.16257158139625696, -0.6888124115458153, -1.7142348598607815, -2.817893187825213, -3.8846019468315434, -4.792603923051679, -5.428750524393188, -5.704135286448722, -5.567943162302731, -5.017271495501962, -4.101033508631508, -2.916763302245701, -1.6001311237271925, -0.3081174149950768, 0.8020927947135872, 1.5955431703465477, 1.9798290959607676, 1.9199229952868535, 1.444752134923308, 0.643953124372323, -0.3452178745338402, -1.3591485477572063, -2.234104332194041, -2.8331538614802545, -3.06912862835592, -2.9194097595698754, -2.4295971946120742, -1.7050149613861456, -0.8912236396069422, -0.1468395193410141, 0.38642550121742697, 0.6108450282137416, 0.49155633498061935, 0.06332768185186319, -0.5764155262097469, -1.2872134177547367, -1.91412347546174, -2.3195081163984312, -2.4115016365126105, -2.163095612412387, -1.617603691615635, -0.8790884768666818, -0.08958507502623088, 0.6020650395545347, 1.0729357673437299, 1.2529082212265592, 1.1394688351605022, 0.796772886226876, 0.338922224507115, -0.09883471338073962, -0.3942321113386447, -0.46914835005366945, -0.309909314603487, 0.028780078467572814, 0.43790852691138604, 0.7833536904150347, 0.9432622884489238, 0.8441318732603029, 0.4858284179169961, -0.052011258213695316, -0.6254111404637438, -1.0610403133188835, -1.2031214783432478, -0.9608291903190024, -0.34358239343074204, 0.5263645576310727, 1.4297216098993113, 2.093248742831456, 2.2519274904222826, 1.716410714392692, 0.4293740159981816, -1.5042454015503723, -3.8228861556950915, -6.151541059385898, -8.075034737118994, -9.226072265602387, -9.368131113024948, -8.453320607486209, -6.640301470230412, -4.266270832597617, -1.7778435383989226, 0.3642301131890364, 1.784754418927674, 2.27476456480391, 1.8338681088096178, 0.6639555016170873, -0.8842120680190171, -2.398385187895482, -3.504535878973362, -3.9541703197911584, -3.677746850756679, -2.791489366100523, -1.556997915493604, -0.305324503792081, 0.6536646053224472, 1.112256309539987, 1.0148242597905162, 0.4641682215191726, -0.31612117902402737, -1.051467645312555, -1.4976975558883683, -1.510526287246319, -1.083473445085151, -0.34398281087405774, 0.490125175646295, 1.180076157317042, 1.5401022367203387, 1.4934310458193545, 1.0933856412727654, 0.5034012737795518, -0.05757725718061007, -0.38709864067949923, -0.3658595363339402, 0.002258680731776968, 0.5898895952718287, 1.1863272686373199, 1.5659528794427415, 1.5634739086935374, 1.1317977386998777, 0.36328093953156393, -0.5336992644444022, -1.2967892863042425, -1.6916402008483158, -1.5881079795304607, -1.005936573280133, -0.11415200802611027, 0.8172519153090045, 1.4994369812220847, 1.7153683904292987, 1.3900717267784735, 0.6171747483428177, -0.3682341588863321, -1.2633084094240297, -1.7951657315932548, -1.8114303176915862, -1.3335919587405651, -0.5542505467606172, 0.22294913460551177, 0.6830124476313378, 0.6073703145234498, -0.04590027587883735, -1.1175620109316382, -2.2894354831797012, -3.1827919450095563, -3.4832058589105594, -3.0518344922469867, -1.985424274977897, -0.6021695786435448, 0.6463865558033646, 1.3130639572951297, 1.1006004861170953, -0.031430512321371396, -1.834728205527939, -3.829515833125371, -5.437297551796899, -6.15096580124075, -5.690827016082227, -4.097719458645266, -1.7325539586606897, 0.820040455577189, 2.916526636240646, 4.038579018685809, 3.940780909705833, 2.717034513514799, 0.7658825173540041, -1.3336801604903583, -2.9966306874078015, -3.8021724710121854, -3.607679624891196, -2.5730352271703376, -1.091247674369052, 0.3488576272176298, 1.3212151107439463, 1.5906073954745792, 1.1705510209498873, 0.29607880685069604, -0.6745153649318275, -1.3916802811282394, -1.6333661881984731, -1.3703525171543707, -0.758492178993427, -0.06494197328281973, 0.4412396506401114, 0.5920867381717089, 0.3792193464608336, -0.05242665445192082, -0.4709456375242807, -0.6564438940999732, -0.4931281508495565, -0.018036142588056758, 0.5930090447221051, 1.0970443835144403, 1.2852354697730208, 1.0735625475682578, 0.545948271482779, -0.06938436285899634, -0.4837502217089088, -0.46141538594883236, 0.08097284418557547, 1.0289313045106336, 2.0993555494694998, 2.936921390070788, 3.243668660540318, 2.8932122082756737, 1.9845954261604972, 0.8119477817889144, -0.2424840258105727, -0.8542758389395155, -0.8869430424291856, -0.45448699034676643, 0.11225744849433156, 0.38867043337401525, 0.027079751275819488, -1.0876317347923088, -2.758887825471559, -4.512368504290557, -5.739677567184992, -5.90721058761576, -4.758619019910756, -2.4369658319686955, 0.5227907917618023, 3.336695453117451, 5.208063214249669, 5.580410604722658, 4.321623811743876, 1.7751237968211033, -1.34189658720582, -4.160928574939132, -5.931473913887777, -6.247308986117379], 'positive_zeros': ['0.861691684875170251840468048137308', '2.60991172666440068703443026861150', '3.40157127779760400523593485253018', '5.03206919823621882256025272295409', '5.83279017747654544118284644301459', '7.02897036896174178950331051023978', '7.51397555957147333921401327353739', '8.639772827000564646284204481152088', '9.469197496399455455299500623624372', '9.990835836280412214603866150797377'], 'prelabel': '2-888-296.43-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6628397810401023, 'root_angle': 0.004055680179631125, 'root_number': '0.999675336369775 + 0.02547983229884546*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00405568017963', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.861691684875170251840468048137', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.60991172666440068703443026861', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.40157127779760400523593485253', 'prec': 100}}