Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(353,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.353");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 353.8 | ||
Character | \(\chi\) | \(=\) | 1216.353 |
Dual form | 1216.2.t.d.1185.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.495361 | + | 0.285997i | 0.285997 | + | 0.165120i | 0.636135 | − | 0.771578i | \(-0.280532\pi\) |
−0.350138 | + | 0.936698i | \(0.613865\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.355705 | − | 0.205367i | −0.159076 | − | 0.0918428i | 0.418349 | − | 0.908287i | \(-0.362609\pi\) |
−0.577425 | + | 0.816444i | \(0.695942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.565533 | −0.213751 | −0.106876 | − | 0.994272i | \(-0.534085\pi\) | ||||
−0.106876 | + | 0.994272i | \(0.534085\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.33641 | − | 2.31473i | −0.445471 | − | 0.771578i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.623114i | 0.187876i | 0.995578 | + | 0.0939380i | \(0.0299456\pi\) | ||||
−0.995578 | + | 0.0939380i | \(0.970054\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.87518 | + | 2.23733i | −1.07478 | + | 0.620525i | −0.929484 | − | 0.368863i | \(-0.879747\pi\) |
−0.145297 | + | 0.989388i | \(0.546414\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.117468 | − | 0.203461i | −0.0303302 | − | 0.0525334i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.03509 | + | 1.79283i | −0.251046 | + | 0.434824i | −0.963814 | − | 0.266575i | \(-0.914108\pi\) |
0.712768 | + | 0.701400i | \(0.247441\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.77510 | − | 3.98108i | 0.407236 | − | 0.913323i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.280143 | − | 0.161740i | −0.0611322 | − | 0.0352947i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.39843 | − | 4.15420i | −0.500107 | − | 0.866210i | −1.00000 | 0.000123335i | \(-0.999961\pi\) | |
0.499893 | − | 0.866087i | \(-0.333373\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.41565 | − | 4.18403i | −0.483130 | − | 0.836805i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 3.24482i | − | 0.624465i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.28597 | + | 1.31981i | −0.424495 | + | 0.245082i | −0.696999 | − | 0.717072i | \(-0.745482\pi\) |
0.272504 | + | 0.962155i | \(0.412148\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.12745 | −0.920918 | −0.460459 | − | 0.887681i | \(-0.652315\pi\) | ||||
−0.460459 | + | 0.887681i | \(0.652315\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.178209 | + | 0.308666i | −0.0310221 | + | 0.0537319i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.201163 | + | 0.116142i | 0.0340028 | + | 0.0196315i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.19500i | 0.854053i | 0.904239 | + | 0.427026i | \(0.140439\pi\) | ||||
−0.904239 | + | 0.427026i | \(0.859561\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.55948 | −0.409845 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.11982 | − | 1.93958i | 0.174886 | − | 0.302911i | −0.765236 | − | 0.643750i | \(-0.777378\pi\) |
0.940122 | + | 0.340839i | \(0.110711\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.626955 | + | 0.361972i | 0.0956097 | + | 0.0552003i | 0.547042 | − | 0.837105i | \(-0.315754\pi\) |
−0.451433 | + | 0.892305i | \(0.649087\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.09782i | 0.163653i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.18140 | − | 7.24240i | −0.609920 | − | 1.05641i | −0.991253 | − | 0.131975i | \(-0.957868\pi\) |
0.381333 | − | 0.924438i | \(-0.375465\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.68017 | −0.954310 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.02548 | + | 0.592064i | −0.143597 | + | 0.0829055i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.5214 | + | 6.07455i | −1.44523 | + | 0.834403i | −0.998192 | − | 0.0601121i | \(-0.980854\pi\) |
−0.447037 | + | 0.894515i | \(0.647521\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.127967 | − | 0.221645i | 0.0172551 | − | 0.0298866i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.01789 | − | 1.46440i | 0.267276 | − | 0.193964i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.71649 | + | 4.45512i | 1.00460 | + | 0.580007i | 0.909607 | − | 0.415471i | \(-0.136383\pi\) |
0.0949951 | + | 0.995478i | \(0.469716\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0512168 | + | 0.0295700i | −0.00655764 | + | 0.00378605i | −0.503275 | − | 0.864126i | \(-0.667872\pi\) |
0.496718 | + | 0.867912i | \(0.334538\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.755785 | + | 1.30906i | 0.0952199 | + | 0.164926i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.83789 | 0.227963 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.447132 | − | 0.258152i | 0.0546258 | − | 0.0315382i | −0.472438 | − | 0.881364i | \(-0.656626\pi\) |
0.527064 | + | 0.849825i | \(0.323293\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 2.74377i | − | 0.330311i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.32599 | − | 7.49284i | 0.513401 | − | 0.889236i | −0.486478 | − | 0.873693i | \(-0.661719\pi\) |
0.999879 | − | 0.0155438i | \(-0.00494794\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.86096 | − | 4.95533i | 0.334850 | − | 0.579977i | −0.648606 | − | 0.761124i | \(-0.724648\pi\) |
0.983456 | + | 0.181147i | \(0.0579811\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 2.76347i | − | 0.319098i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.352392i | − | 0.0401587i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.50179 | − | 7.79733i | 0.506491 | − | 0.877268i | −0.493481 | − | 0.869757i | \(-0.664276\pi\) |
0.999972 | − | 0.00751132i | \(-0.00239095\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.08123 | + | 5.33684i | −0.342359 | + | 0.592983i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 10.2514i | − | 1.12523i | −0.826718 | − | 0.562617i | \(-0.809795\pi\) | ||
0.826718 | − | 0.562617i | \(-0.190205\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.736374 | − | 0.425145i | 0.0798709 | − | 0.0461135i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.50984 | −0.161872 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.25944 | − | 7.37756i | −0.451499 | − | 0.782020i | 0.546980 | − | 0.837146i | \(-0.315777\pi\) |
−0.998479 | + | 0.0551257i | \(0.982444\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.19154 | − | 1.26529i | 0.229736 | − | 0.132638i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.53994 | − | 1.46643i | −0.263379 | − | 0.152062i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.44899 | + | 1.05155i | −0.148664 | + | 0.107886i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.33679 | + | 9.24359i | −0.541869 | + | 0.938544i | 0.456928 | + | 0.889504i | \(0.348950\pi\) |
−0.998797 | + | 0.0490405i | \(0.984384\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.44234 | − | 0.832737i | 0.144961 | − | 0.0836933i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.57456 | + | 2.64113i | −0.455186 | + | 0.262802i | −0.710018 | − | 0.704184i | \(-0.751313\pi\) |
0.254832 | + | 0.966985i | \(0.417980\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.5734 | −1.33743 | −0.668714 | − | 0.743520i | \(-0.733155\pi\) | ||||
−0.668714 | + | 0.743520i | \(0.733155\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0664322 | + | 0.115064i | 0.00648312 | + | 0.0112291i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.42282i | 0.137549i | 0.997632 | + | 0.0687747i | \(0.0219090\pi\) | ||||
−0.997632 | + | 0.0687747i | \(0.978091\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.44778 | + | 2.56793i | 0.426020 | + | 0.245963i | 0.697650 | − | 0.716439i | \(-0.254229\pi\) |
−0.271629 | + | 0.962402i | \(0.587562\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.48575 | + | 2.57340i | −0.141021 | + | 0.244256i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.40470 | −0.320288 | −0.160144 | − | 0.987094i | \(-0.551196\pi\) | ||||
−0.160144 | + | 0.987094i | \(0.551196\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.97023i | 0.183725i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.3577 | + | 5.98000i | 0.957566 | + | 0.552851i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.585377 | − | 1.01390i | 0.0536614 | − | 0.0929443i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6117 | 0.964703 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.10943 | − | 0.640527i | 0.100034 | − | 0.0577544i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.03804i | 0.361173i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.83599 | + | 4.91209i | 0.251654 | + | 0.435877i | 0.963981 | − | 0.265970i | \(-0.0856923\pi\) |
−0.712328 | + | 0.701847i | \(0.752359\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.207046 | + | 0.358614i | 0.0182294 | + | 0.0315742i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.82143 | + | 3.93835i | 0.595991 | + | 0.344095i | 0.767463 | − | 0.641094i | \(-0.221519\pi\) |
−0.171472 | + | 0.985189i | \(0.554852\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00388 | + | 2.25143i | −0.0870472 | + | 0.195224i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.666377 | + | 1.15420i | −0.0573526 | + | 0.0993376i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.05338 | − | 7.02067i | −0.346304 | − | 0.599816i | 0.639286 | − | 0.768969i | \(-0.279230\pi\) |
−0.985590 | + | 0.169153i | \(0.945897\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.50640 | + | 4.33382i | −0.636684 | + | 0.367590i | −0.783336 | − | 0.621598i | \(-0.786484\pi\) |
0.146652 | + | 0.989188i | \(0.453150\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 4.78347i | − | 0.402841i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.39411 | − | 2.41468i | −0.116582 | − | 0.201925i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.08418 | 0.0900361 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.30910 | − | 1.91051i | −0.272930 | − | 0.157576i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.69747 | − | 3.86678i | −0.548678 | − | 0.316779i | 0.199911 | − | 0.979814i | \(-0.435935\pi\) |
−0.748589 | + | 0.663035i | \(0.769268\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.2050 | 0.830469 | 0.415234 | − | 0.909714i | \(-0.363700\pi\) | ||||
0.415234 | + | 0.909714i | \(0.363700\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.53322 | 0.447334 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.82386 | + | 1.05301i | 0.146496 | + | 0.0845796i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.94882 | + | 2.27985i | 0.315150 | + | 0.181952i | 0.649229 | − | 0.760593i | \(-0.275092\pi\) |
−0.334079 | + | 0.942545i | \(0.608425\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.94920 | −0.551107 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.35639 | + | 2.34934i | 0.106898 | + | 0.185154i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.1835i | 0.954283i | 0.878827 | + | 0.477141i | \(0.158327\pi\) | ||||
−0.878827 | + | 0.477141i | \(0.841673\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.126780 | − | 0.0731962i | 0.00986977 | − | 0.00569832i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.79203 | + | 10.0321i | 0.448201 | + | 0.776306i | 0.998269 | − | 0.0588134i | \(-0.0187317\pi\) |
−0.550068 | + | 0.835120i | \(0.685398\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.51132 | − | 6.08179i | 0.270102 | − | 0.467830i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.5874 | + | 1.21148i | −0.886111 | + | 0.0926444i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.80088 | − | 2.77179i | −0.365004 | − | 0.210735i | 0.306270 | − | 0.951945i | \(-0.400919\pi\) |
−0.671274 | + | 0.741210i | \(0.734252\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.36613 | + | 2.36620i | 0.103270 | + | 0.178868i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.54830 | + | 4.41378i | 0.191542 | + | 0.331760i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 9.92221i | − | 0.741621i | −0.928709 | − | 0.370810i | \(-0.879080\pi\) | ||
0.928709 | − | 0.370810i | \(-0.120920\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.6482 | − | 9.61185i | 1.23745 | − | 0.714443i | 0.268879 | − | 0.963174i | \(-0.413347\pi\) |
0.968573 | + | 0.248731i | \(0.0800136\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.0338277 | −0.00250062 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.06688 | − | 1.84789i | 0.0784385 | − | 0.135860i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.11714 | − | 0.644979i | −0.0816931 | − | 0.0471655i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.83505i | 0.133480i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.7297 | 1.06580 | 0.532900 | − | 0.846178i | \(-0.321102\pi\) | ||||
0.532900 | + | 0.846178i | \(0.321102\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.85598 | + | 15.3390i | −0.637467 | + | 1.10413i | 0.348519 | + | 0.937302i | \(0.386685\pi\) |
−0.985987 | + | 0.166824i | \(0.946649\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.910421 | + | 0.525632i | 0.0651966 | + | 0.0376413i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 26.6926i | − | 1.90177i | −0.309547 | − | 0.950884i | \(-0.600178\pi\) | ||
0.309547 | − | 0.950884i | \(-0.399822\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.43770 | + | 11.1504i | 0.456356 | + | 0.790432i | 0.998765 | − | 0.0496824i | \(-0.0158209\pi\) |
−0.542409 | + | 0.840115i | \(0.682488\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.295322 | 0.0208304 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.29279 | − | 0.746395i | 0.0907363 | − | 0.0523866i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.796649 | + | 0.459946i | −0.0556404 | + | 0.0321240i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.41058 | + | 11.1034i | −0.445566 | + | 0.771743i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.48067 | + | 1.10609i | 0.171592 | + | 0.0765099i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.7910 | − | 7.96226i | −0.949414 | − | 0.548144i | −0.0565152 | − | 0.998402i | \(-0.517999\pi\) |
−0.892899 | + | 0.450257i | \(0.851332\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.28585 | − | 2.47444i | 0.293662 | − | 0.169546i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.148674 | − | 0.257511i | −0.0101395 | − | 0.0175621i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.89974 | 0.196847 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.83441 | − | 1.63645i | 0.191532 | − | 0.110581i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 9.26336i | − | 0.623121i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.43662 | − | 4.22035i | 0.163168 | − | 0.282616i | −0.772835 | − | 0.634607i | \(-0.781162\pi\) |
0.936003 | + | 0.351991i | \(0.114495\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.45660 | + | 11.1832i | −0.430440 | + | 0.745544i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.2093i | 1.40771i | 0.710344 | + | 0.703855i | \(0.248540\pi\) | ||||
−0.710344 | + | 0.703855i | \(0.751460\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.41777i | − | 0.225853i | −0.993603 | − | 0.112926i | \(-0.963978\pi\) | ||
0.993603 | − | 0.112926i | \(-0.0360224\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.100783 | − | 0.174561i | 0.00663102 | − | 0.0114853i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.03289 | − | 15.6454i | 0.591764 | − | 1.02497i | −0.402231 | − | 0.915538i | \(-0.631765\pi\) |
0.993995 | − | 0.109427i | \(-0.0349017\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.43488i | 0.224067i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.46002 | − | 2.57499i | 0.289709 | − | 0.167264i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.1989 | 1.56530 | 0.782649 | − | 0.622463i | \(-0.213868\pi\) | ||||
0.782649 | + | 0.622463i | \(0.213868\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.33257 | + | 10.9683i | 0.407917 | + | 0.706532i | 0.994656 | − | 0.103243i | \(-0.0329221\pi\) |
−0.586740 | + | 0.809776i | \(0.699589\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.4829 | + | 6.62967i | −0.736630 | + | 0.425293i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.37617 | + | 1.37188i | 0.151808 | + | 0.0876465i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.02818 | + | 19.3989i | 0.129050 | + | 1.23432i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.93186 | − | 5.07813i | 0.185799 | − | 0.321813i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.71329 | + | 2.14387i | −0.234381 | + | 0.135320i | −0.612591 | − | 0.790400i | \(-0.709873\pi\) |
0.378211 | + | 0.925720i | \(0.376540\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.58854 | − | 1.49449i | 0.162740 | − | 0.0939581i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.486361 | 0.0304571 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.67320 | + | 16.7545i | 0.603398 | + | 1.04512i | 0.992303 | + | 0.123837i | \(0.0395201\pi\) |
−0.388905 | + | 0.921278i | \(0.627147\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.93794i | − | 0.182555i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.11001 | + | 3.52761i | 0.378200 | + | 0.218354i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.72838 | − | 11.6539i | 0.414890 | − | 0.718610i | −0.580527 | − | 0.814241i | \(-0.697154\pi\) |
0.995417 | + | 0.0956310i | \(0.0304869\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.99004 | 0.306536 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 4.87274i | − | 0.298207i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.03510 | + | 4.63907i | 0.489909 | + | 0.282849i | 0.724537 | − | 0.689236i | \(-0.242054\pi\) |
−0.234628 | + | 0.972085i | \(0.575387\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.3590 | + | 19.6744i | −0.690010 | + | 1.19513i | 0.281824 | + | 0.959466i | \(0.409061\pi\) |
−0.971834 | + | 0.235666i | \(0.924273\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.44747 | 0.0876048 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.60713 | − | 1.50523i | 0.157216 | − | 0.0907685i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.3729i | 0.623249i | 0.950205 | + | 0.311625i | \(0.100873\pi\) | ||||
−0.950205 | + | 0.311625i | \(0.899127\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.85239 | + | 11.8687i | 0.410242 | + | 0.710560i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.30802 | − | 14.3899i | −0.495615 | − | 0.858430i | 0.504372 | − | 0.863486i | \(-0.331724\pi\) |
−0.999987 | + | 0.00505593i | \(0.998391\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.9865 | − | 6.34305i | −0.653079 | − | 0.377055i | 0.136556 | − | 0.990632i | \(-0.456397\pi\) |
−0.789635 | + | 0.613577i | \(0.789730\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.01851 | + | 0.106487i | −0.0603315 | + | 0.00630776i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.633293 | + | 1.09690i | −0.0373821 | + | 0.0647477i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.35718 | + | 11.0110i | 0.373952 | + | 0.647704i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.28727 | + | 3.05261i | −0.309945 | + | 0.178947i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 5.67796i | − | 0.331710i | −0.986150 | − | 0.165855i | \(-0.946962\pi\) | ||
0.986150 | − | 0.165855i | \(-0.0530383\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.82987 | − | 3.16942i | −0.106539 | − | 0.184531i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.02189 | 0.117322 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.5887 | + | 10.7322i | 1.07501 | + | 0.620657i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.354563 | − | 0.204707i | −0.0204367 | − | 0.0117991i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.02141 | −0.173576 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.0242908 | 0.00139089 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.09500 | + | 1.20955i | 0.119568 | + | 0.0690326i | 0.558591 | − | 0.829443i | \(-0.311342\pi\) |
−0.439023 | + | 0.898476i | \(0.644675\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.72373 | − | 3.88195i | −0.382500 | − | 0.220836i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.0441 | −1.02319 | −0.511594 | − | 0.859227i | \(-0.670945\pi\) | ||||
−0.511594 | + | 0.859227i | \(0.670945\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.902817 | + | 1.56372i | 0.0510302 | + | 0.0883869i | 0.890412 | − | 0.455155i | \(-0.150416\pi\) |
−0.839382 | + | 0.543542i | \(0.817083\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 0.620852i | − | 0.0349810i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.9141 | − | 8.03332i | 0.781495 | − | 0.451196i | −0.0554651 | − | 0.998461i | \(-0.517664\pi\) |
0.836960 | + | 0.547265i | \(0.184331\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.822391 | − | 1.42442i | −0.0460451 | − | 0.0797524i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.406922 | + | 0.704810i | −0.0227122 | + | 0.0393387i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.30000 | + | 7.30322i | 0.294900 | + | 0.406362i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.7221 | + | 10.8092i | 1.03852 | + | 0.599588i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.46884 | + | 2.54410i | 0.0812270 | + | 0.140689i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.36472 | + | 4.09582i | 0.130371 | + | 0.225810i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.3991i | 0.626550i | 0.949662 | + | 0.313275i | \(0.101426\pi\) | ||||
−0.949662 | + | 0.313275i | \(0.898574\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.0250 | − | 6.94266i | 0.658968 | − | 0.380455i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.212063 | −0.0115862 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.6969 | + | 20.2597i | −0.637172 | + | 1.10361i | 0.348878 | + | 0.937168i | \(0.386563\pi\) |
−0.986051 | + | 0.166446i | \(0.946771\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.68656 | − | 0.973734i | −0.0916012 | − | 0.0528860i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 3.19499i | − | 0.173018i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.73659 | 0.417736 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.563479 | + | 0.975974i | −0.0303367 | + | 0.0525447i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.3846 | − | 16.9652i | −1.57745 | − | 0.910741i | −0.995214 | − | 0.0977205i | \(-0.968845\pi\) |
−0.582235 | − | 0.813020i | \(-0.697822\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 21.1792i | − | 1.13370i | −0.823821 | − | 0.566849i | \(-0.808162\pi\) | ||
0.823821 | − | 0.566849i | \(-0.191838\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.25974 | + | 12.5742i | 0.387496 | + | 0.671163i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.34223 | 0.390787 | 0.195394 | − | 0.980725i | \(-0.437402\pi\) | ||||
0.195394 | + | 0.980725i | \(0.437402\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.07756 | + | 1.77683i | −0.163340 | + | 0.0943043i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.579945 | − | 0.334832i | 0.0306940 | − | 0.0177212i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.1915 | − | 26.3125i | 0.801778 | − | 1.38872i | −0.116667 | − | 0.993171i | \(-0.537221\pi\) |
0.918445 | − | 0.395549i | \(-0.129446\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.6980 | − | 14.1336i | −0.668318 | − | 0.743876i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.25663 | + | 3.03492i | 0.275902 | + | 0.159292i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.03532 | + | 1.17509i | −0.106533 | + | 0.0615071i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.3292 | + | 24.8189i | 0.747979 | + | 1.29554i | 0.948790 | + | 0.315907i | \(0.102309\pi\) |
−0.200811 | + | 0.979630i | \(0.564358\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.98614 | −0.311626 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.95021 | − | 3.43536i | 0.308920 | − | 0.178355i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 19.0463i | − | 0.986178i | −0.869979 | − | 0.493089i | \(-0.835868\pi\) | ||
0.869979 | − | 0.493089i | \(-0.164132\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.15487 | + | 2.00029i | −0.0596370 | + | 0.103294i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.90570 | − | 10.2290i | 0.304159 | − | 0.526819i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.35677i | − | 0.121059i | −0.998166 | − | 0.0605296i | \(-0.980721\pi\) | ||
0.998166 | − | 0.0605296i | \(-0.0192789\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.24434i | 0.166213i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.4562 | − | 23.3069i | 0.687582 | − | 1.19093i | −0.285036 | − | 0.958517i | \(-0.592005\pi\) |
0.972618 | − | 0.232410i | \(-0.0746612\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0723695 | + | 0.125348i | −0.00368829 | + | 0.00638831i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 1.93498i | − | 0.0983604i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.1945 | + | 15.1234i | −1.32811 | + | 0.766786i | −0.985008 | − | 0.172511i | \(-0.944812\pi\) |
−0.343105 | + | 0.939297i | \(0.611479\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.93034 | 0.502199 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.25271 | + | 3.90181i | 0.113634 | + | 0.196820i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.20262 | + | 1.84903i | −0.161141 | + | 0.0930350i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.5519 | + | 10.7110i | 0.931094 | + | 0.537567i | 0.887157 | − | 0.461467i | \(-0.152677\pi\) |
0.0439366 | + | 0.999034i | \(0.486010\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.14118 | + | 0.828166i | −0.0571306 | + | 0.0414601i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.34850 | − | 2.33566i | 0.0673407 | − | 0.116637i | −0.830389 | − | 0.557184i | \(-0.811882\pi\) |
0.897730 | + | 0.440546i | \(0.145215\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.8698 | − | 11.4718i | 0.989784 | − | 0.571452i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.19202 | − | 1.26556i | 0.108922 | − | 0.0628863i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.23708 | −0.160456 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.90473 | + | 5.03114i | 0.143630 | + | 0.248774i | 0.928861 | − | 0.370429i | \(-0.120789\pi\) |
−0.785231 | + | 0.619203i | \(0.787456\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 4.63702i | − | 0.228727i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.36393 | − | 2.51952i | −0.214735 | − | 0.123977i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.10529 | + | 3.64647i | −0.103345 | + | 0.178998i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.95783 | −0.242786 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.9036i | 1.90057i | 0.311389 | + | 0.950283i | \(0.399206\pi\) | ||||
−0.311389 | + | 0.950283i | \(0.600794\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.3148 | + | 9.99669i | 0.843870 | + | 0.487209i | 0.858578 | − | 0.512683i | \(-0.171348\pi\) |
−0.0147077 | + | 0.999892i | \(0.504682\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.1762 | + | 19.3577i | −0.543403 | + | 0.941202i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.0016 | 0.485151 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0289648 | − | 0.0167228i | 0.00140170 | − | 0.000809274i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 1.59485i | − | 0.0770000i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.2479 | − | 21.2139i | −0.589959 | − | 1.02184i | −0.994237 | − | 0.107203i | \(-0.965811\pi\) |
0.404279 | − | 0.914636i | \(-0.367523\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.95963 | − | 17.2506i | −0.478629 | − | 0.829010i | 0.521070 | − | 0.853514i | \(-0.325533\pi\) |
−0.999700 | + | 0.0245034i | \(0.992200\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.537059 | + | 0.310071i | 0.0257500 | + | 0.0148668i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.7957 | + | 2.17422i | −0.994791 | + | 0.104007i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.26447 | − | 16.0465i | 0.442169 | − | 0.765859i | −0.555681 | − | 0.831396i | \(-0.687542\pi\) |
0.997850 | + | 0.0655361i | \(0.0208758\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.92746 | + | 15.4628i | 0.425117 | + | 0.736325i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.5509 | − | 6.09155i | 0.501287 | − | 0.289418i | −0.227958 | − | 0.973671i | \(-0.573205\pi\) |
0.729245 | + | 0.684253i | \(0.239872\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.49899i | 0.165868i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.21177 | − | 3.83091i | −0.104613 | − | 0.181196i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0800 | 0.853249 | 0.426624 | − | 0.904429i | \(-0.359703\pi\) | ||||
0.426624 | + | 0.904429i | \(0.359703\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.20858 | + | 0.697773i | 0.0569098 | + | 0.0328569i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.05514 | + | 2.91859i | 0.237511 | + | 0.137127i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.03939 | −0.0487273 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.47704 | −0.162649 | −0.0813246 | − | 0.996688i | \(-0.525915\pi\) | ||||
−0.0813246 | + | 0.996688i | \(0.525915\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.81739 | + | 3.35867i | 0.271533 | + | 0.156769i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.3222 | − | 17.5065i | −1.41225 | − | 0.815361i | −0.416647 | − | 0.909068i | \(-0.636795\pi\) |
−0.995600 | + | 0.0937072i | \(0.970128\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.6790 | −1.00751 | −0.503755 | − | 0.863847i | \(-0.668048\pi\) | ||||
−0.503755 | + | 0.863847i | \(0.668048\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.602313 | + | 1.04324i | 0.0279316 | + | 0.0483790i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 17.1508i | − | 0.793643i | −0.917896 | − | 0.396822i | \(-0.870113\pi\) | ||
0.917896 | − | 0.396822i | \(-0.129887\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.252868 | + | 0.145993i | −0.0116763 | + | 0.00674134i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.30406 | + | 2.25870i | 0.0600878 | + | 0.104075i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.225550 | + | 0.390664i | −0.0103708 | + | 0.0179628i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.9450 | + | 2.18983i | −0.961021 | + | 0.100476i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28.1219 | + | 16.2362i | 1.28761 | + | 0.743404i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.4776 | − | 25.0759i | −0.661498 | − | 1.14575i | −0.980222 | − | 0.197901i | \(-0.936588\pi\) |
0.318724 | − | 0.947848i | \(-0.396746\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.6229 | − | 20.1315i | −0.529961 | − | 0.917919i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.55169i | 0.0706044i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.79665 | − | 2.19200i | 0.172397 | − | 0.0995334i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.3183 | −1.41917 | −0.709584 | − | 0.704621i | \(-0.751117\pi\) | ||||
−0.709584 | + | 0.704621i | \(0.751117\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.48443 | + | 6.03521i | −0.157571 | + | 0.272922i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.5766 | + | 13.0346i | 1.01887 | + | 0.588245i | 0.913776 | − | 0.406218i | \(-0.133153\pi\) |
0.105093 | + | 0.994462i | \(0.466486\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.46448i | − | 0.246108i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.684066 | −0.0307465 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.44649 | + | 4.23745i | −0.109740 | + | 0.190075i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.5755 | − | 8.41515i | −0.652487 | − | 0.376714i | 0.136921 | − | 0.990582i | \(-0.456279\pi\) |
−0.789409 | + | 0.613868i | \(0.789613\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.62600i | 0.296028i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.41768 | + | 7.65165i | 0.196975 | + | 0.341170i | 0.947546 | − | 0.319619i | \(-0.103555\pi\) |
−0.750571 | + | 0.660789i | \(0.770222\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.16960 | 0.0965458 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.47874 | − | 2.00845i | 0.154496 | − | 0.0891985i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.6411 | + | 22.3094i | −1.71274 | + | 0.988849i | −0.781907 | + | 0.623395i | \(0.785753\pi\) |
−0.930829 | + | 0.365454i | \(0.880914\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.61797 | + | 2.80240i | −0.0715746 | + | 0.123971i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.9179 | − | 5.75988i | −0.570339 | − | 0.254305i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.82814 | + | 2.78753i | 0.212753 | + | 0.122833i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.51284 | − | 2.60549i | 0.198475 | − | 0.114589i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.58544 | − | 2.74607i | −0.0695932 | − | 0.120539i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.0465 | −0.483955 | −0.241978 | − | 0.970282i | \(-0.577796\pi\) | ||||
−0.241978 | + | 0.970282i | \(0.577796\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.7906 | − | 12.5808i | 0.952838 | − | 0.550121i | 0.0588767 | − | 0.998265i | \(-0.481248\pi\) |
0.893961 | + | 0.448144i | \(0.147915\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.56283i | 0.0682076i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.30737 | − | 9.19263i | 0.231193 | − | 0.400437i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.00491365 | + | 0.00851069i | −0.000213637 | + | 0.000370030i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 23.8155i | − | 1.03350i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.0216i | 0.434084i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.292200 | − | 0.506106i | 0.0126329 | − | 0.0218808i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.83772 | − | 4.91507i | 0.122457 | − | 0.212101i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 4.16251i | − | 0.179292i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.9385 | + | 15.5529i | −1.15818 | + | 0.668673i | −0.950866 | − | 0.309602i | \(-0.899804\pi\) |
−0.207310 | + | 0.978275i | \(0.566471\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.9958 | 0.471876 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.05473 | − | 1.82685i | −0.0451798 | − | 0.0782538i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.3115 | + | 11.1495i | −0.825700 | + | 0.476718i | −0.852378 | − | 0.522926i | \(-0.824840\pi\) |
0.0266781 | + | 0.999644i | \(0.491507\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.136893 | + | 0.0790355i | 0.00584247 | + | 0.00337315i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.19643 | + | 11.4434i | 0.0509697 | + | 0.487507i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.54591 | + | 4.40964i | −0.108263 | + | 0.187517i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.05698 | − | 0.610248i | 0.0448663 | − | 0.0259036i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.0380 | + | 13.8784i | −1.01852 | + | 0.588045i | −0.913676 | − | 0.406443i | \(-0.866769\pi\) |
−0.104848 | + | 0.994488i | \(0.533436\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.23941 | −0.137013 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.368923 | − | 0.638994i | −0.0155760 | − | 0.0269784i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 30.7019i | − | 1.29393i | −0.762519 | − | 0.646966i | \(-0.776038\pi\) | ||
0.762519 | − | 0.646966i | \(-0.223962\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.21107 | + | 0.699212i | 0.0509502 | + | 0.0294161i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.74254 | − | 3.01816i | 0.0731796 | − | 0.126751i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.1756 | −0.887726 | −0.443863 | − | 0.896095i | \(-0.646392\pi\) | ||||
−0.443863 | + | 0.896095i | \(0.646392\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 36.3708i | − | 1.52207i | −0.648710 | − | 0.761036i | \(-0.724691\pi\) | ||
0.648710 | − | 0.761036i | \(-0.275309\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.29649 | + | 4.21263i | 0.304815 | + | 0.175985i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.5875 | + | 20.0702i | −0.483233 | + | 0.836984i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.46302 | −0.269059 | −0.134530 | − | 0.990910i | \(-0.542952\pi\) | ||||
−0.134530 | + | 0.990910i | \(0.542952\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.77381 | + | 5.06556i | −0.364627 | + | 0.210517i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.79749i | 0.240520i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.78514 | − | 6.55605i | −0.156764 | − | 0.271524i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.45618 | − | 4.25424i | −0.101551 | − | 0.175891i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.78374 | − | 4.49395i | −0.321269 | − | 0.185485i | 0.330689 | − | 0.943740i | \(-0.392719\pi\) |
−0.651958 | + | 0.758255i | \(0.726052\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.10174 | + | 20.4128i | −0.375031 | + | 0.841095i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.63399 | − | 13.2225i | 0.314020 | − | 0.543899i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.5388 | − | 21.7178i | −0.514907 | − | 0.891845i | −0.999850 | − | 0.0172992i | \(-0.994493\pi\) |
0.484944 | − | 0.874545i | \(-0.338840\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.416443 | + | 0.240434i | −0.0170725 | + | 0.00985682i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.36464i | 0.301415i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.0910 | − | 39.9948i | −0.943474 | − | 1.63415i | −0.758778 | − | 0.651349i | \(-0.774203\pi\) |
−0.184696 | − | 0.982796i | \(-0.559130\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.4513 | 0.630270 | 0.315135 | − | 0.949047i | \(-0.397950\pi\) | ||||
0.315135 | + | 0.949047i | \(0.397950\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.19510 | − | 0.689994i | −0.0486684 | − | 0.0280987i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.77465 | − | 2.17930i | −0.153461 | − | 0.0886009i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.7724 | −0.437238 | −0.218619 | − | 0.975810i | \(-0.570155\pi\) | ||||
−0.218619 | + | 0.975810i | \(0.570155\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.853866 | 0.0346004 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.4073 | + | 18.7104i | 1.31106 | + | 0.756941i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.0301 | − | 16.7605i | −1.17252 | − | 0.676952i | −0.218244 | − | 0.975894i | \(-0.570033\pi\) |
−0.954271 | + | 0.298942i | \(0.903366\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.526172 | −0.0212173 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.26156 | − | 14.3094i | −0.332598 | − | 0.576076i | 0.650423 | − | 0.759572i | \(-0.274592\pi\) |
−0.983020 | + | 0.183496i | \(0.941258\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.4924i | 0.984431i | 0.870473 | + | 0.492216i | \(0.163813\pi\) | ||||
−0.870473 | + | 0.492216i | \(0.836187\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.4796 | + | 7.78246i | −0.540918 | + | 0.312299i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.40885 | + | 4.17225i | 0.0965086 | + | 0.167158i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.2490 | + | 19.4838i | −0.449959 | + | 0.779351i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.912488 | + | 1.25738i | 0.0364413 | + | 0.0502148i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.31373 | − | 5.37729i | −0.371363 | − | 0.214406i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.4118 | − | 24.9620i | −0.573724 | − | 0.993720i | −0.996179 | − | 0.0873357i | \(-0.972165\pi\) |
0.422455 | − | 0.906384i | \(-0.361169\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.55436 | − | 7.88838i | −0.181019 | − | 0.313535i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 2.32967i | − | 0.0924503i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.8868 | − | 14.9458i | 1.02567 | − | 0.592173i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.1252 | −0.914820 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.9810 | − | 29.4120i | 0.670710 | − | 1.16170i | −0.306994 | − | 0.951712i | \(-0.599323\pi\) |
0.977703 | − | 0.209992i | \(-0.0673437\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.60391 | + | 4.96747i | 0.339305 | + | 0.195898i | 0.659965 | − | 0.751297i | \(-0.270571\pi\) |
−0.320660 | + | 0.947194i | \(0.603905\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 0.170081i | − | 0.00669694i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.41778 | 0.212995 | 0.106497 | − | 0.994313i | \(-0.466036\pi\) | ||||
0.106497 | + | 0.994313i | \(0.466036\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.77605 | + | 4.80826i | −0.108969 | + | 0.188741i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.43642 | + | 0.829317i | 0.0562977 | + | 0.0325035i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 36.9266i | − | 1.44505i | −0.691346 | − | 0.722524i | \(-0.742982\pi\) | ||
0.691346 | − | 0.722524i | \(-0.257018\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.61761 | − | 2.80179i | −0.0632053 | − | 0.109475i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.2937 | −0.596663 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.4165 | − | 7.74604i | 0.522634 | − | 0.301743i | −0.215378 | − | 0.976531i | \(-0.569098\pi\) |
0.738012 | + | 0.674788i | \(0.235765\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.0451 | + | 9.84101i | −0.662979 | + | 0.382771i | −0.793411 | − | 0.608686i | \(-0.791697\pi\) |
0.130432 | + | 0.991457i | \(0.458363\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.64929 | − | 4.58870i | 0.102890 | − | 0.178210i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.819454 | − | 0.594684i | 0.0317771 | − | 0.0230609i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.9655 | + | 6.33093i | 0.424586 | + | 0.245135i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.41401 | − | 1.39373i | 0.0933312 | − | 0.0538848i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0184255 | − | 0.0319139i | −0.000711309 | − | 0.00123202i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.4981 | 0.674502 | 0.337251 | − | 0.941415i | \(-0.390503\pi\) | ||||
0.337251 | + | 0.941415i | \(0.390503\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −13.5764 | + | 7.83834i | −0.522556 | + | 0.301698i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.58479i | 0.176208i | 0.996111 | + | 0.0881040i | \(0.0280808\pi\) | ||||
−0.996111 | + | 0.0881040i | \(0.971919\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.01813 | − | 5.22755i | 0.115825 | − | 0.200615i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.06579 | + | 10.5062i | −0.232441 | + | 0.402600i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.62342i | 0.329966i | 0.986296 | + | 0.164983i | \(0.0527570\pi\) | ||||
−0.986296 | + | 0.164983i | \(0.947243\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.32972i | 0.127222i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.977471 | − | 1.69303i | 0.0372928 | − | 0.0645931i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.1816 | − | 47.0799i | 1.03554 | − | 1.79360i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 35.4700i | − | 1.34934i | −0.738118 | − | 0.674672i | \(-0.764285\pi\) | ||
0.738118 | − | 0.674672i | \(-0.235715\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.815693 | + | 0.470940i | −0.0309856 | + | 0.0178895i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.56009 | 0.135042 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.31822 | + | 4.01527i | 0.0878088 | + | 0.152089i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.94908 | − | 5.16675i | 0.338485 | − | 0.195424i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.5390 | − | 7.81676i | −0.511362 | − | 0.295235i | 0.222031 | − | 0.975040i | \(-0.428731\pi\) |
−0.733393 | + | 0.679805i | \(0.762065\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.6817 | + | 9.22165i | 0.780026 | + | 0.347801i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.982365 | + | 1.70151i | −0.0369980 | + | 0.0640824i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.58707 | − | 1.49364i | 0.0972966 | − | 0.0561742i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.8542 | + | 16.0816i | −1.04609 | + | 0.603958i | −0.921551 | − | 0.388258i | \(-0.873077\pi\) |
−0.124534 | + | 0.992215i | \(0.539744\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24.0650 | −0.902507 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.2978 | + | 21.3005i | 0.460557 | + | 0.797708i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.14522i | 0.0428287i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.9872 | + | 6.92081i | 0.447670 | + | 0.258462i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.7342 | − | 28.9846i | 0.624082 | − | 1.08094i | −0.364636 | − | 0.931150i | \(-0.618806\pi\) |
0.988718 | − | 0.149791i | \(-0.0478602\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.67621 | 0.285877 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.24437i | 0.269421i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.0442 | + | 6.37639i | 0.410172 | + | 0.236813i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.4625 | + | 33.7100i | −0.721824 | + | 1.25024i | 0.238444 | + | 0.971156i | \(0.423363\pi\) |
−0.960268 | + | 0.279080i | \(0.909971\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.9031 | 0.403819 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.29791 | + | 0.749347i | −0.0480048 | + | 0.0277156i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.8177i | 1.69232i | 0.532932 | + | 0.846158i | \(0.321090\pi\) | ||||
−0.532932 | + | 0.846158i | \(0.678910\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.784709 | + | 1.35916i | 0.0289444 | + | 0.0501332i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.160858 | + | 0.278614i | 0.00592528 | + | 0.0102629i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.3064 | + | 16.9200i | 1.07805 | + | 0.622414i | 0.930370 | − | 0.366621i | \(-0.119486\pi\) |
0.147682 | + | 0.989035i | \(0.452819\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.54333 | + | 10.1895i | −0.166904 | + | 0.374321i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.57015 | − | 2.71958i | 0.0576032 | − | 0.0997717i | −0.835786 | − | 0.549056i | \(-0.814988\pi\) |
0.893389 | + | 0.449284i | \(0.148321\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.58822 | + | 2.75087i | 0.0581878 | + | 0.100784i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −23.7292 | + | 13.7001i | −0.868206 | + | 0.501259i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 0.804652i | − | 0.0294014i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.0858 | − | 39.9857i | −0.842412 | − | 1.45910i | −0.887850 | − | 0.460133i | \(-0.847802\pi\) |
0.0454379 | − | 0.998967i | \(-0.485532\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.45256 | −0.0893762 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.62996 | − | 2.09576i | −0.132108 | − | 0.0762725i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.6388 | + | 8.45169i | 0.532055 | + | 0.307182i | 0.741853 | − | 0.670563i | \(-0.233947\pi\) |
−0.209798 | + | 0.977745i | \(0.567281\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.70968 | 0.0620575 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.6686 | −1.43799 | −0.718993 | − | 0.695018i | \(-0.755396\pi\) | ||||
−0.718993 | + | 0.695018i | \(0.755396\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.51537 | − | 1.45225i | −0.0910624 | − | 0.0525749i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.96820 | − | 1.13634i | −0.0711603 | − | 0.0410844i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −39.8703 | −1.43963 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.1994 | − | 28.0582i | −0.584166 | − | 1.01180i | −0.994979 | − | 0.100085i | \(-0.968089\pi\) |
0.410813 | − | 0.911719i | \(-0.365245\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.0660i | 0.398533i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.91042 | + | 1.68033i | −0.104680 | + | 0.0604373i | −0.551426 | − | 0.834224i | \(-0.685916\pi\) |
0.446746 | + | 0.894661i | \(0.352583\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.3861 | + | 21.4534i | 0.444923 | + | 0.770629i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.840242 | − | 1.45534i | 0.0301435 | − | 0.0522101i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.73384 | − | 7.90103i | −0.205436 | − | 0.283084i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.66890 | + | 2.69559i | 0.167066 | + | 0.0964557i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.28254 | + | 7.41757i | 0.153045 | + | 0.265082i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.936410 | − | 1.62191i | −0.0334219 | − | 0.0578884i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 47.0238i | − | 1.67622i | −0.545502 | − | 0.838109i | \(-0.683661\pi\) | ||
0.545502 | − | 0.838109i | \(-0.316339\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.66595 | − | 3.84859i | 0.237314 | − | 0.137013i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.92547 | 0.0684619 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.132316 | − | 0.229178i | 0.00469868 | − | 0.00813835i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.47187 | + | 1.42713i | 0.0876681 | + | 0.0506152i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.27254i | 0.115919i | 0.998319 | + | 0.0579596i | \(0.0184595\pi\) | ||||
−0.998319 | + | 0.0579596i | \(0.981541\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.3125 | 0.612472 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.3847 | + | 19.7189i | −0.402259 | + | 0.696734i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.08773 | + | 1.78270i | 0.108964 | + | 0.0629103i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1.11423i | − | 0.0392714i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.65352 | + | 4.59603i | 0.0934082 | + | 0.161788i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.4070 | −1.38548 | −0.692738 | − | 0.721190i | \(-0.743596\pi\) | ||||
−0.692738 | + | 0.721190i | \(0.743596\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.7726 | + | 11.4157i | −0.694309 | + | 0.400860i | −0.805224 | − | 0.592970i | \(-0.797955\pi\) |
0.110915 | + | 0.993830i | \(0.464622\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.2536 | + | 6.49727i | −0.394681 | + | 0.227869i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.50208 | − | 4.33373i | 0.0876440 | − | 0.151804i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.55395 | − | 1.85342i | 0.0893514 | − | 0.0648430i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.85760 | − | 3.38188i | −0.204681 | − | 0.118173i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.3194 | − | 7.11259i | 0.429949 | − | 0.248231i | −0.269376 | − | 0.963035i | \(-0.586817\pi\) |
0.699325 | + | 0.714804i | \(0.253484\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.38028 | + | 11.0510i | 0.222403 | + | 0.385213i | 0.955537 | − | 0.294871i | \(-0.0952767\pi\) |
−0.733134 | + | 0.680084i | \(0.761943\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.72196 | 0.0599509 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.6616 | − | 17.1251i | 1.03143 | − | 0.595499i | 0.114040 | − | 0.993476i | \(-0.463621\pi\) |
0.917395 | + | 0.397977i | \(0.130288\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 50.6534i | − | 1.75927i | −0.475652 | − | 0.879633i | \(-0.657788\pi\) | ||
0.475652 | − | 0.879633i | \(-0.342212\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.96663 | + | 5.13835i | −0.102911 | + | 0.178247i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.91457 | − | 11.9764i | 0.239576 | − | 0.414957i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 4.75796i | − | 0.164656i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.6376i | 0.575081i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.1996 | − | 40.1828i | 0.800938 | − | 1.38726i | −0.118062 | − | 0.993006i | \(-0.537668\pi\) |
0.919000 | − | 0.394259i | \(-0.128999\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.0162 | + | 19.0806i | −0.379869 | + | 0.657953i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 9.50427i | − | 0.327344i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.49799 | + | 1.44222i | −0.0859336 | + | 0.0496138i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.00128 | −0.206206 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.62818 | − | 6.28420i | −0.124519 | − | 0.215673i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.5811 | − | 12.4598i | 0.739789 | − | 0.427118i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.5431 | − | 7.81910i | −0.463706 | − | 0.267721i | 0.249895 | − | 0.968273i | \(-0.419604\pi\) |
−0.713601 | + | 0.700552i | \(0.752937\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.37050 | + | 1.94874i | 0.149468 | + | 0.0666454i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.6351 | + | 44.4013i | −0.875679 | + | 1.51672i | −0.0196420 | + | 0.999807i | \(0.506253\pi\) |
−0.856037 | + | 0.516914i | \(0.827081\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0574 | − | 6.38399i | 0.377274 | − | 0.217819i | −0.299358 | − | 0.954141i | \(-0.596772\pi\) |
0.676631 | + | 0.736322i | \(0.263439\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.627417 | + | 0.362239i | −0.0213823 | + | 0.0123451i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.4704 | −0.492577 | −0.246289 | − | 0.969197i | \(-0.579211\pi\) | ||||
−0.246289 | + | 0.969197i | \(0.579211\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.13847 | + | 1.97188i | 0.0387090 | + | 0.0670459i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.27253i | 0.246988i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.85863 | + | 2.80513i | 0.164818 | + | 0.0951575i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.15514 | + | 2.00077i | −0.0391405 | + | 0.0677934i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 28.5286 | 0.965546 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 2.28364i | − | 0.0772013i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.2494 | + | 23.8154i | 1.39289 | + | 0.804188i | 0.993635 | − | 0.112650i | \(-0.0359339\pi\) |
0.399260 | + | 0.916838i | \(0.369267\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.62388 | − | 2.81264i | 0.0547720 | − | 0.0948679i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.7908 | 1.74488 | 0.872438 | − | 0.488725i | \(-0.162538\pi\) | ||||
0.872438 | + | 0.488725i | \(0.162538\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.9253 | + | 21.3188i | −1.24264 | + | 0.717436i | −0.969630 | − | 0.244577i | \(-0.921351\pi\) |
−0.273005 | + | 0.962013i | \(0.588018\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 2.09334i | − | 0.0703669i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.54128 | − | 7.86572i | −0.152481 | − | 0.264105i | 0.779658 | − | 0.626206i | \(-0.215393\pi\) |
−0.932139 | + | 0.362101i | \(0.882060\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.60385 | − | 2.77795i | −0.0537913 | − | 0.0931693i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.32546 | − | 1.91996i | −0.111407 | − | 0.0643210i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −36.2550 | + | 3.79052i | −1.21323 | + | 0.126845i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.03769 | + | 3.52938i | −0.0681125 | + | 0.117974i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.13873 | + | 10.6326i | 0.204966 | + | 0.355012i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.7212 | − | 6.76725i | 0.390925 | − | 0.225701i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 25.1508i | − | 0.837894i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.117091 | − | 0.202808i | −0.00389655 | − | 0.00674902i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.89581 | −0.262466 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.13860 | + | 5.27618i | 0.303442 | + | 0.175193i | 0.643988 | − | 0.765035i | \(-0.277279\pi\) |
−0.340546 | + | 0.940228i | \(0.610612\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.2270 | + | 7.05926i | 0.405544 | + | 0.234141i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.0098 | 0.961137 | 0.480569 | − | 0.876957i | \(-0.340430\pi\) | ||||
0.480569 | + | 0.876957i | \(0.340430\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.38778 | 0.211405 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.0120327 | + | 0.00694709i | 0.000397789 | + | 0.000229664i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.85774 | − | 2.22727i | −0.127394 | − | 0.0735508i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.0200 | −0.462476 | −0.231238 | − | 0.972897i | \(-0.574278\pi\) | ||||
−0.231238 | + | 0.972897i | \(0.574278\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.691854 | + | 1.19833i | 0.0227974 | + | 0.0394862i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 38.7148i | 1.27431i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.7360 | − | 12.5493i | 0.714676 | − | 0.412618i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.1397 | + | 31.4188i | 0.595785 | + | 1.03193i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.0890 | − | 26.1349i | 0.495054 | − | 0.857459i | −0.504929 | − | 0.863161i | \(-0.668481\pi\) |
0.999984 | + | 0.00570137i | \(0.00181481\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.8580 | + | 26.5943i | −0.388630 | + | 0.871594i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.93834 | − | 5.16056i | −0.292628 | − | 0.168949i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.264914 | + | 0.458845i | 0.00866362 | + | 0.0150058i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.42494 | + | 9.39628i | 0.177225 | + | 0.306963i | 0.940929 | − | 0.338604i | \(-0.109955\pi\) |
−0.763704 | + | 0.645567i | \(0.776621\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.03281i | 0.0337045i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.4879 | − | 18.1795i | 1.02648 | − | 0.592636i | 0.110503 | − | 0.993876i | \(-0.464754\pi\) |
0.915973 | + | 0.401240i | \(0.131421\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.7432 | −0.349846 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.376858 | − | 0.652737i | 0.0122592 | − | 0.0212336i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −49.9527 | − | 28.8402i | −1.62324 | − | 0.937180i | −0.986045 | − | 0.166480i | \(-0.946760\pi\) |
−0.637198 | − | 0.770700i | \(-0.719907\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.6037i | 0.831130i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.19001 | 0.298006 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.57213 | + | 14.8474i | −0.277679 | + | 0.480954i | −0.970807 | − | 0.239860i | \(-0.922898\pi\) |
0.693129 | + | 0.720814i | \(0.256232\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.23942 | − | 3.02498i | −0.169544 | − | 0.0978861i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 0.940805i | − | 0.0304119i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.29232 | + | 3.97042i | 0.0740229 | + | 0.128211i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.70924 | −0.151911 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.29345 | − | 1.90148i | 0.106130 | − | 0.0612742i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.30024 | − | 3.63744i | 0.202812 | − | 0.117093i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.2235 | + | 28.0999i | −0.521712 | + | 0.903631i | 0.477969 | + | 0.878377i | \(0.341373\pi\) |
−0.999681 | + | 0.0252548i | \(0.991960\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.536717 | + | 5.13351i | 0.0172418 | + | 0.164912i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.5884 | + | 21.7017i | 1.20627 | + | 0.696441i | 0.961943 | − | 0.273252i | \(-0.0880993\pi\) |
0.244328 | + | 0.969693i | \(0.421433\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.24511 | − | 2.45092i | 0.136092 | − | 0.0785728i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.18280 | + | 10.7089i | 0.198008 | + | 0.342960i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.4161 | 1.00509 | 0.502544 | − | 0.864551i | \(-0.332397\pi\) | ||||
0.502544 | + | 0.864551i | \(0.332397\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.59706 | − | 2.65412i | 0.146923 | − | 0.0848259i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 13.7272i | − | 0.438277i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.5214 | − | 35.5441i | 0.654531 | − | 1.13368i | −0.327480 | − | 0.944858i | \(-0.606199\pi\) |
0.982011 | − | 0.188823i | \(-0.0604672\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.48177 | + | 9.49470i | −0.174664 | + | 0.302526i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.70521i | 0.0861077i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 3.47266i | − | 0.110424i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.2514 | − | 29.8803i | 0.548009 | − | 0.949179i | −0.450402 | − | 0.892826i | \(-0.648719\pi\) |
0.998411 | − | 0.0563529i | \(-0.0179472\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.26010 | + | 5.64665i | −0.103456 | + | 0.179191i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 5.28835i | − | 0.167652i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.1621 | − | 17.9915i | 0.986915 | − | 0.569796i | 0.0825644 | − | 0.996586i | \(-0.473689\pi\) |
0.904351 | + | 0.426790i | \(0.140356\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.8568 | 0.533326 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1216.2.t.d.353.8 | yes | 24 | |
4.3 | odd | 2 | inner | 1216.2.t.d.353.6 | ✓ | 24 | |
8.3 | odd | 2 | 1216.2.t.e.353.8 | yes | 24 | ||
8.5 | even | 2 | 1216.2.t.e.353.6 | yes | 24 | ||
19.7 | even | 3 | 1216.2.t.e.1185.6 | yes | 24 | ||
76.7 | odd | 6 | 1216.2.t.e.1185.8 | yes | 24 | ||
152.45 | even | 6 | inner | 1216.2.t.d.1185.8 | yes | 24 | |
152.83 | odd | 6 | inner | 1216.2.t.d.1185.6 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.t.d.353.6 | ✓ | 24 | 4.3 | odd | 2 | inner | |
1216.2.t.d.353.8 | yes | 24 | 1.1 | even | 1 | trivial | |
1216.2.t.d.1185.6 | yes | 24 | 152.83 | odd | 6 | inner | |
1216.2.t.d.1185.8 | yes | 24 | 152.45 | even | 6 | inner | |
1216.2.t.e.353.6 | yes | 24 | 8.5 | even | 2 | ||
1216.2.t.e.353.8 | yes | 24 | 8.3 | odd | 2 | ||
1216.2.t.e.1185.6 | yes | 24 | 19.7 | even | 3 | ||
1216.2.t.e.1185.8 | yes | 24 | 76.7 | odd | 6 |