Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [260,2,Mod(33,260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(260, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 11]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("260.33");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.bk (of order \(12\), degree \(4\), 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: | \(2.07611045255\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + 6399 x^{4} + 666 x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 33.5 | ||
Root | \(-0.402430i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 260.33 |
Dual form | 260.2.bk.c.197.5 |
$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{11}{12}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | 2.49316 | − | 0.668040i | 1.43943 | − | 0.385693i | 0.547094 | − | 0.837071i | \(-0.315734\pi\) |
0.892333 | + | 0.451378i | \(0.149067\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.380790 | − | 2.20341i | −0.170295 | − | 0.985393i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.749297 | + | 0.432607i | −0.283208 | + | 0.163510i | −0.634875 | − | 0.772615i | \(-0.718948\pi\) |
0.351667 | + | 0.936125i | \(0.385615\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.17149 | − | 1.83106i | 1.05716 | − | 0.610354i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.417628 | + | 1.55861i | 0.125920 | + | 0.469938i | 0.999871 | − | 0.0160756i | \(-0.00511723\pi\) |
−0.873951 | + | 0.486014i | \(0.838451\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.32514 | − | 3.35321i | 0.367527 | − | 0.930013i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.42134 | − | 5.23906i | −0.625186 | − | 1.35272i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.33873 | + | 4.99621i | −0.324690 | + | 1.21176i | 0.589933 | + | 0.807452i | \(0.299154\pi\) |
−0.914623 | + | 0.404308i | \(0.867513\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.16619 | − | 0.312480i | −0.267543 | − | 0.0716878i | 0.122554 | − | 0.992462i | \(-0.460892\pi\) |
−0.390096 | + | 0.920774i | \(0.627558\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.57912 | + | 1.57912i | −0.344592 | + | 0.344592i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.704305 | + | 2.62850i | 0.146858 | + | 0.548080i | 0.999666 | + | 0.0258557i | \(0.00823103\pi\) |
−0.852808 | + | 0.522225i | \(0.825102\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.71000 | + | 1.67807i | −0.941999 | + | 0.335614i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.20845 | − | 1.20845i | 0.232567 | − | 0.232567i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.94138 | + | 3.43026i | 1.10329 | + | 0.636983i | 0.937082 | − | 0.349109i | \(-0.113516\pi\) |
0.166204 | + | 0.986091i | \(0.446849\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.191663 | + | 0.191663i | 0.0344237 | + | 0.0344237i | 0.724109 | − | 0.689685i | \(-0.242251\pi\) |
−0.689685 | + | 0.724109i | \(0.742251\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.08243 | + | 3.60687i | 0.362504 | + | 0.627875i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.23853 | + | 1.48627i | 0.209351 | + | 0.251226i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.22242 | − | 4.74722i | −1.35176 | − | 0.780438i | −0.363262 | − | 0.931687i | \(-0.618337\pi\) |
−0.988496 | + | 0.151249i | \(0.951670\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.06370 | − | 9.24533i | 0.170328 | − | 1.48044i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.417297 | − | 0.111814i | 0.0651709 | − | 0.0174625i | −0.226086 | − | 0.974107i | \(-0.572593\pi\) |
0.291257 | + | 0.956645i | \(0.405926\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.5499 | + | 3.09480i | 1.76135 | + | 0.471952i | 0.986989 | − | 0.160791i | \(-0.0514044\pi\) |
0.774362 | + | 0.632743i | \(0.218071\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.24225 | − | 6.29083i | −0.781468 | − | 0.937782i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 1.52128i | − | 0.221902i | −0.993826 | − | 0.110951i | \(-0.964610\pi\) | ||
0.993826 | − | 0.110951i | \(-0.0353897\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.12570 | + | 5.41387i | −0.446529 | + | 0.773411i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.3507i | 1.86947i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.88398 | − | 4.88398i | −0.670867 | − | 0.670867i | 0.287049 | − | 0.957916i | \(-0.407326\pi\) |
−0.957916 | + | 0.287049i | \(0.907326\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.27522 | − | 1.51371i | 0.441630 | − | 0.204108i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.11625 | −0.412757 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.05172 | + | 11.3892i | −0.397300 | + | 1.48274i | 0.420528 | + | 0.907279i | \(0.361845\pi\) |
−0.817828 | + | 0.575463i | \(0.804822\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.94152 | − | 5.09486i | −0.376623 | − | 0.652330i | 0.613946 | − | 0.789348i | \(-0.289581\pi\) |
−0.990569 | + | 0.137018i | \(0.956248\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.58426 | + | 2.74402i | −0.199598 | + | 0.345714i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.89308 | − | 1.64294i | −0.979016 | − | 0.203782i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.76168 | − | 11.7116i | 0.826070 | − | 1.43080i | −0.0750284 | − | 0.997181i | \(-0.523905\pi\) |
0.901099 | − | 0.433614i | \(-0.142762\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.51189 | + | 6.08277i | 0.422782 | + | 0.732279i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.85102 | + | 14.3722i | −0.457031 | + | 1.70566i | 0.225015 | + | 0.974355i | \(0.427757\pi\) |
−0.682046 | + | 0.731309i | \(0.738910\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.9921 | −1.28653 | −0.643266 | − | 0.765643i | \(-0.722421\pi\) | ||||
−0.643266 | + | 0.765643i | \(0.722421\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.6218 | + | 7.33017i | −1.22649 | + | 0.846415i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.987192 | − | 0.987192i | −0.112501 | − | 0.112501i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.98168i | − | 0.447974i | −0.974592 | − | 0.223987i | \(-0.928093\pi\) | ||
0.974592 | − | 0.223987i | \(-0.0719074\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.28761 | + | 5.69431i | −0.365290 | + | 0.632701i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.25583i | − | 0.686667i | −0.939214 | − | 0.343333i | \(-0.888444\pi\) | ||
0.939214 | − | 0.343333i | \(-0.111556\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.5185 | + | 1.04726i | 1.24935 | + | 0.113591i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 17.1044 | + | 4.58310i | 1.83378 | + | 0.491360i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.80805 | + | 2.62806i | −1.03965 | + | 0.278574i | −0.737969 | − | 0.674835i | \(-0.764215\pi\) |
−0.301683 | + | 0.953408i | \(0.597548\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.457701 | + | 3.08581i | 0.0479801 | + | 0.323481i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.605885 | + | 0.349808i | 0.0628274 | + | 0.0362734i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.244446 | + | 2.68858i | −0.0250796 | + | 0.275843i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.728593 | − | 1.26196i | −0.0739774 | − | 0.128133i | 0.826664 | − | 0.562696i | \(-0.190236\pi\) |
−0.900641 | + | 0.434564i | \(0.856903\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.17841 | + | 4.17841i | 0.419946 | + | 0.419946i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.0529 | − | 5.80403i | −1.00030 | − | 0.577523i | −0.0919621 | − | 0.995763i | \(-0.529314\pi\) |
−0.908337 | + | 0.418240i | \(0.862647\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.8660 | − | 10.8660i | 1.07066 | − | 1.07066i | 0.0733504 | − | 0.997306i | \(-0.476631\pi\) |
0.997306 | − | 0.0733504i | \(-0.0233691\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.08076 | + | 2.87813i | 0.398241 | + | 0.280877i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.84601 | − | 6.88942i | −0.178461 | − | 0.666025i | −0.995936 | − | 0.0900615i | \(-0.971294\pi\) |
0.817475 | − | 0.575964i | \(-0.195373\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.56805 | − | 4.56805i | 0.437540 | − | 0.437540i | −0.453643 | − | 0.891183i | \(-0.649876\pi\) |
0.891183 | + | 0.453643i | \(0.149876\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −23.6711 | − | 6.34266i | −2.24677 | − | 0.602019i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.23652 | − | 8.34679i | 0.210394 | − | 0.785200i | −0.777344 | − | 0.629076i | \(-0.783433\pi\) |
0.987737 | − | 0.156124i | \(-0.0498999\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.52346 | − | 2.55278i | 0.515065 | − | 0.238048i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.93727 | − | 13.0611i | −0.179101 | − | 1.20750i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.15829 | − | 4.32280i | −0.106180 | − | 0.396270i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.27143 | − | 4.19816i | 0.661039 | − | 0.381651i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.965692 | − | 0.557543i | 0.0870735 | − | 0.0502719i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.49100 | + | 9.73904i | 0.491130 | + | 0.871086i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.54494 | + | 1.21781i | −0.403299 | + | 0.108064i | −0.454766 | − | 0.890611i | \(-0.650277\pi\) |
0.0514670 | + | 0.998675i | \(0.483610\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 30.8633 | 2.71736 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.3255 | 1.33900 | 0.669498 | − | 0.742814i | \(-0.266509\pi\) | ||||
0.669498 | + | 0.742814i | \(0.266509\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00900 | − | 0.270362i | 0.0874918 | − | 0.0234434i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.12288 | − | 2.20255i | −0.268775 | − | 0.189565i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.6738 | − | 8.47191i | 1.25367 | − | 0.723804i | 0.281830 | − | 0.959464i | \(-0.409059\pi\) |
0.971835 | + | 0.235661i | \(0.0757253\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.69425 | + | 1.55553i | −0.228524 | + | 0.131938i | −0.609891 | − | 0.792485i | \(-0.708787\pi\) |
0.381367 | + | 0.924424i | \(0.375453\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.01628 | − | 3.79280i | −0.0855861 | − | 0.319412i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.77975 | + | 0.664975i | 0.483327 | + | 0.0556080i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.29583 | − | 14.3975i | 0.439795 | − | 1.19565i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.17619 | + | 15.5857i | −0.344446 | + | 1.28549i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.9563 | + | 4.27549i | 1.30719 | + | 0.350262i | 0.844166 | − | 0.536082i | \(-0.180096\pi\) |
0.463029 | + | 0.886343i | \(0.346763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.3067 | − | 12.3067i | 1.00151 | − | 1.00151i | 0.00150662 | − | 0.999999i | \(-0.499520\pi\) |
0.999999 | − | 0.00150662i | \(-0.000479574\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.90260 | + | 18.2968i | 0.396352 | + | 1.47920i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.349328 | − | 0.495295i | 0.0280587 | − | 0.0397830i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.83463 | + | 5.83463i | −0.465654 | + | 0.465654i | −0.900503 | − | 0.434849i | \(-0.856802\pi\) |
0.434849 | + | 0.900503i | \(0.356802\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.4392 | − | 8.91385i | −1.22441 | − | 0.706914i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.66484 | − | 1.66484i | −0.131208 | − | 0.131208i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.64140 | − | 4.57504i | −0.206890 | − | 0.358344i | 0.743843 | − | 0.668354i | \(-0.233001\pi\) |
−0.950733 | + | 0.310010i | \(0.899668\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.15442 | − | 5.96189i | 0.556971 | − | 0.464132i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.81358 | − | 3.93382i | −0.527251 | − | 0.304408i | 0.212645 | − | 0.977129i | \(-0.431792\pi\) |
−0.739896 | + | 0.672721i | \(0.765125\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.48803 | − | 8.88692i | −0.729848 | − | 0.683609i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.27073 | + | 1.14434i | −0.326591 | + | 0.0875098i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.2622 | − | 5.16129i | −1.46448 | − | 0.392406i | −0.563444 | − | 0.826154i | \(-0.690524\pi\) |
−0.901034 | + | 0.433749i | \(0.857191\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.80324 | − | 3.29495i | 0.211905 | − | 0.249075i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 30.4337i | 2.28753i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.53139 | + | 2.65244i | −0.114461 | + | 0.198253i | −0.917564 | − | 0.397588i | \(-0.869847\pi\) |
0.803103 | + | 0.595840i | \(0.203181\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.3657i | 1.73676i | 0.495901 | + | 0.868379i | \(0.334838\pi\) | ||||
−0.495901 | + | 0.868379i | \(0.665162\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.7372 | − | 10.7372i | −0.793720 | − | 0.793720i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.32903 | + | 19.9250i | −0.538841 | + | 1.46492i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.34623 | −0.610337 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.382706 | + | 1.42828i | −0.0278377 | + | 0.103892i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.73743 | + | 6.47341i | 0.270431 | + | 0.468400i | 0.968972 | − | 0.247170i | \(-0.0795006\pi\) |
−0.698541 | + | 0.715570i | \(0.746167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00100 | + | 1.73378i | −0.0720536 | + | 0.124800i | −0.899801 | − | 0.436300i | \(-0.856289\pi\) |
0.827748 | + | 0.561101i | \(0.189622\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −20.7763 | + | 1.17678i | −1.48782 | + | 0.0842707i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.59042 | − | 2.75469i | 0.113313 | − | 0.196264i | −0.803791 | − | 0.594912i | \(-0.797187\pi\) |
0.917104 | + | 0.398648i | \(0.130520\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.20225 | − | 14.2067i | −0.581442 | − | 1.00709i | −0.995309 | − | 0.0967496i | \(-0.969155\pi\) |
0.413867 | − | 0.910337i | \(-0.364178\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.03414 | − | 33.7159i | 0.637219 | − | 2.37813i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.93581 | −0.416612 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.405275 | − | 0.876897i | −0.0283057 | − | 0.0612452i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.04664 | + | 7.04664i | 0.489775 | + | 0.489775i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.94813i | − | 0.134755i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.66213 | − | 9.80710i | 0.389797 | − | 0.675149i | −0.602625 | − | 0.798025i | \(-0.705878\pi\) |
0.992422 | + | 0.122876i | \(0.0392117\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 38.4048i | 2.63145i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.42099 | − | 26.6277i | 0.165110 | − | 1.81599i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.226527 | − | 0.0606978i | −0.0153777 | − | 0.00412044i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −27.4051 | + | 7.34318i | −1.85187 | + | 0.496206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.9794 | + | 11.1097i | 1.00762 | + | 0.747320i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.74357 | + | 5.04810i | 0.585513 | + | 0.338046i | 0.763321 | − | 0.646019i | \(-0.223567\pi\) |
−0.177808 | + | 0.984065i | \(0.556901\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.8651 | + | 13.9463i | −0.791004 | + | 0.929752i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.86958 | + | 11.8985i | 0.455950 | + | 0.789728i | 0.998742 | − | 0.0501387i | \(-0.0159663\pi\) |
−0.542792 | + | 0.839867i | \(0.682633\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.36743 | − | 3.36743i | −0.222526 | − | 0.222526i | 0.587035 | − | 0.809561i | \(-0.300295\pi\) |
−0.809561 | + | 0.587035i | \(0.800295\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.12071 | − | 1.80174i | −0.205328 | − | 0.118546i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.1541 | − | 19.1541i | 1.25482 | − | 1.25482i | 0.301293 | − | 0.953532i | \(-0.402582\pi\) |
0.953532 | − | 0.301293i | \(-0.0974181\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.35201 | + | 0.579291i | −0.218661 | + | 0.0377888i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.65992 | − | 9.92697i | −0.172781 | − | 0.644826i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.4667 | + | 18.4667i | −1.19451 | + | 1.19451i | −0.218727 | + | 0.975786i | \(0.570190\pi\) |
−0.975786 | + | 0.218727i | \(0.929810\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.850786 | + | 0.227967i | 0.0548040 | + | 0.0146847i | 0.286117 | − | 0.958195i | \(-0.407635\pi\) |
−0.231313 | + | 0.972879i | \(0.574302\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.71949 | + | 21.3454i | −0.366905 | + | 1.36931i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.1192 | + | 4.82564i | 0.838155 | + | 0.308299i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.59317 | + | 3.49640i | −0.165000 | + | 0.222471i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.17915 | − | 15.5968i | −0.264843 | − | 0.988406i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.62276 | − | 3.24630i | 0.354905 | − | 0.204905i | −0.311938 | − | 0.950102i | \(-0.600978\pi\) |
0.666844 | + | 0.745198i | \(0.267645\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.80266 | + | 2.19547i | −0.239071 | + | 0.138028i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 29.4170 | − | 5.08381i | 1.84216 | − | 0.318361i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.3489 | + | 2.77298i | −0.645547 | + | 0.172974i | −0.566715 | − | 0.823914i | \(-0.691786\pi\) |
−0.0788324 | + | 0.996888i | \(0.525119\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.21472 | 0.510438 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 25.1240 | 1.55514 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.80873 | + | 2.62824i | −0.604832 | + | 0.162064i | −0.548223 | − | 0.836332i | \(-0.684696\pi\) |
−0.0566092 | + | 0.998396i | \(0.518029\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.90162 | + | 12.6212i | −0.546822 | + | 0.775312i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −22.6974 | + | 13.1043i | −1.38906 | + | 0.801973i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.1943 | + | 9.34977i | −0.987383 | + | 0.570066i | −0.904491 | − | 0.426493i | \(-0.859749\pi\) |
−0.0828917 | + | 0.996559i | \(0.526416\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.74484 | − | 17.7080i | −0.288228 | − | 1.07568i | −0.946448 | − | 0.322856i | \(-0.895357\pi\) |
0.658220 | − | 0.752826i | \(-0.271310\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.20257 | + | 7.38767i | 0.193828 | + | 0.447122i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.58248 | − | 6.64023i | −0.276334 | − | 0.400421i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.50958 | − | 13.0979i | 0.210870 | − | 0.786979i | −0.776709 | − | 0.629859i | \(-0.783113\pi\) |
0.987580 | − | 0.157120i | \(-0.0502208\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.958804 | + | 0.256911i | 0.0574021 | + | 0.0153809i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.1478 | − | 17.1478i | 1.02295 | − | 1.02295i | 0.0232200 | − | 0.999730i | \(-0.492608\pi\) |
0.999730 | − | 0.0232200i | \(-0.00739181\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.37015 | + | 8.84554i | 0.140891 | + | 0.525813i | 0.999904 | + | 0.0138586i | \(0.00441148\pi\) |
−0.859013 | + | 0.511954i | \(0.828922\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.18664 | + | 6.86636i | 0.0702904 | + | 0.406728i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.264308 | + | 0.264308i | −0.0156016 | + | 0.0156016i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.44752 | − | 4.87718i | −0.496913 | − | 0.286893i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.65954 | − | 2.65954i | −0.155905 | − | 0.155905i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.09083 | + | 15.7458i | 0.531092 | + | 0.919878i | 0.999342 | + | 0.0362820i | \(0.0115515\pi\) |
−0.468250 | + | 0.883596i | \(0.655115\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.2570 | + | 2.38729i | 1.52874 | + | 0.138993i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.38819 | + | 1.37882i | 0.138577 | + | 0.0800073i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.74721 | + | 1.12144i | 0.563696 | + | 0.0648546i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.99318 | + | 2.67766i | −0.575997 | + | 0.154338i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −28.9408 | − | 7.75465i | −1.66260 | − | 0.445493i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.1059 | + | 8.42144i | −0.578665 | + | 0.482210i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0356i | 1.60008i | 0.599948 | + | 0.800039i | \(0.295188\pi\) | ||||
−0.599948 | + | 0.800039i | \(0.704812\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.8317 | − | 34.3495i | 1.12819 | − | 1.95408i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 11.5168i | − | 0.653060i | −0.945187 | − | 0.326530i | \(-0.894121\pi\) | ||
0.945187 | − | 0.326530i | \(-0.105879\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.3376 | − | 10.3376i | −0.584316 | − | 0.584316i | 0.351771 | − | 0.936086i | \(-0.385580\pi\) |
−0.936086 | + | 0.351771i | \(0.885580\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.64946 | + | 2.44587i | 0.374655 | + | 0.137809i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.31106 | 0.129802 | 0.0649010 | − | 0.997892i | \(-0.479327\pi\) | ||||
0.0649010 | + | 0.997892i | \(0.479327\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.86514 | + | 10.6928i | −0.160417 | + | 0.598685i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.20481 | − | 15.9432i | −0.513763 | − | 0.889863i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.12243 | − | 5.40821i | 0.173737 | − | 0.300921i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.614460 | + | 18.0173i | −0.0340841 | + | 0.999419i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.33724 | − | 14.4405i | 0.461050 | − | 0.798563i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.658118 | + | 1.13989i | 0.0362832 | + | 0.0628444i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.10127 | + | 33.9664i | −0.500251 | + | 1.86696i | −0.00188163 | + | 0.999998i | \(0.500599\pi\) |
−0.498370 | + | 0.866965i | \(0.666068\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −34.7698 | −1.90537 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −28.3801 | − | 10.4391i | −1.55057 | − | 0.570347i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.04414 | − | 4.04414i | −0.220298 | − | 0.220298i | 0.588326 | − | 0.808624i | \(-0.299787\pi\) |
−0.808624 | + | 0.588326i | \(0.799787\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 22.3040i | − | 1.21139i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.218684 | + | 0.378771i | −0.0118424 | + | 0.0205116i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 11.4653i | − | 0.619068i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.0655 | − | 10.0544i | 0.649585 | − | 0.541309i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.216132 | − | 0.0579124i | −0.0116026 | − | 0.00310890i | 0.253013 | − | 0.967463i | \(-0.418578\pi\) |
−0.264616 | + | 0.964354i | \(0.585245\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.9175 | + | 3.19329i | −0.637930 | + | 0.170933i | −0.563266 | − | 0.826276i | \(-0.690455\pi\) |
−0.0746643 | + | 0.997209i | \(0.523789\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.45083 | − | 5.65356i | −0.130816 | − | 0.301765i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.0318 | − | 6.36920i | −0.587162 | − | 0.338998i | 0.176812 | − | 0.984245i | \(-0.443421\pi\) |
−0.763975 | + | 0.645246i | \(0.776755\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.1342 | + | 3.01256i | 1.75858 | + | 0.159890i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.77560 | − | 10.0036i | −0.305677 | − | 0.529449i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.8285 | + | 18.8285i | 0.993730 | + | 0.993730i | 0.999980 | − | 0.00625094i | \(-0.00198975\pi\) |
−0.00625094 | + | 0.999980i | \(0.501990\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.1921 | − | 8.77118i | −0.799586 | − | 0.461641i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.3243 | − | 15.3243i | 0.804317 | − | 0.804317i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.18570 | + | 24.2201i | 0.219089 | + | 1.26774i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.35985 | + | 20.0032i | 0.279782 | + | 1.04416i | 0.952569 | + | 0.304324i | \(0.0984305\pi\) |
−0.672787 | + | 0.739837i | \(0.734903\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.11872 | − | 1.11872i | 0.0582380 | − | 0.0582380i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.77240 | + | 1.54671i | 0.299688 | + | 0.0803012i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.10162 | − | 4.11130i | 0.0570397 | − | 0.212875i | −0.931524 | − | 0.363680i | \(-0.881520\pi\) |
0.988563 | + | 0.150805i | \(0.0481867\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.1960 | + | 20.6128i | 1.04292 | + | 1.06444i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.3755 | − | 15.3771i | 0.997889 | − | 0.791962i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.81310 | + | 10.4986i | 0.144499 | + | 0.539278i | 0.999777 | + | 0.0211086i | \(0.00671957\pi\) |
−0.855278 | + | 0.518169i | \(0.826614\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.5177 | + | 6.07241i | −0.538839 | + | 0.311099i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.6937 | + | 6.75134i | −0.597518 | + | 0.344977i | −0.768065 | − | 0.640372i | \(-0.778780\pi\) |
0.170546 | + | 0.985350i | \(0.445447\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.79927 | + | 2.55110i | −0.0916994 | + | 0.130016i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 42.2973 | − | 11.3335i | 2.15009 | − | 0.576116i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.82344 | −0.396664 | −0.198332 | − | 0.980135i | \(-0.563552\pi\) | ||||
−0.198332 | + | 0.980135i | \(0.563552\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.0754 | −0.711825 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 38.2090 | − | 10.2381i | 1.92739 | − | 0.516442i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.77327 | + | 1.51619i | −0.441431 | + | 0.0762877i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.4670 | − | 6.04313i | 0.525324 | − | 0.303296i | −0.213786 | − | 0.976881i | \(-0.568579\pi\) |
0.739110 | + | 0.673584i | \(0.235246\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.33500 | − | 1.34811i | 0.116896 | − | 0.0674900i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.23948 | − | 12.0899i | −0.161772 | − | 0.603740i | −0.998430 | − | 0.0560149i | \(-0.982161\pi\) |
0.836658 | − | 0.547725i | \(-0.184506\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.896666 | − | 0.388707i | 0.0446661 | − | 0.0193629i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.7988 | + | 5.07561i | 0.685666 | + | 0.252209i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.96514 | − | 14.7981i | 0.196545 | − | 0.733515i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.0227 | + | 3.22147i | 0.594484 | + | 0.159292i | 0.543502 | − | 0.839408i | \(-0.317098\pi\) |
0.0509825 | + | 0.998700i | \(0.483765\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 30.9245 | − | 30.9245i | 1.52539 | − | 1.52539i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.64039 | − | 9.85406i | −0.129925 | − | 0.484887i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.7841 | + | 2.38216i | −0.676637 | + | 0.116936i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.67805 | + | 5.67805i | −0.278055 | + | 0.278055i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.12710 | − | 3.53748i | −0.299328 | − | 0.172817i | 0.342813 | − | 0.939404i | \(-0.388620\pi\) |
−0.642141 | + | 0.766586i | \(0.721954\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.6378 | − | 12.6378i | −0.615930 | − | 0.615930i | 0.328555 | − | 0.944485i | \(-0.393438\pi\) |
−0.944485 | + | 0.328555i | \(0.893438\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.78557 | − | 4.82474i | −0.135439 | − | 0.234587i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.07859 | − | 25.7786i | −0.100826 | − | 1.25045i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.40815 | + | 2.54504i | 0.213325 | + | 0.123163i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.8541 | − | 2.20322i | 0.717162 | − | 0.106372i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.66350 | − | 0.445735i | 0.0801282 | − | 0.0214703i | −0.218532 | − | 0.975830i | \(-0.570127\pi\) |
0.298660 | + | 0.954359i | \(0.403460\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.5451 | + | 4.16531i | 0.747052 | + | 0.200172i | 0.612210 | − | 0.790695i | \(-0.290281\pi\) |
0.134842 | + | 0.990867i | \(0.456947\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.58525 | − | 39.4330i | 0.171900 | − | 1.89067i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 3.28541i | − | 0.157163i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.54892 | + | 13.0751i | −0.360290 | + | 0.624041i | −0.988008 | − | 0.154400i | \(-0.950656\pi\) |
0.627718 | + | 0.778441i | \(0.283989\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 22.8934i | 1.09016i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.3798 | − | 13.3798i | −0.635694 | − | 0.635694i | 0.313797 | − | 0.949490i | \(-0.398399\pi\) |
−0.949490 | + | 0.313797i | \(0.898399\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.52550 | + | 20.6104i | 0.451552 | + | 0.977026i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 42.6379 | 2.01670 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.77864 | + | 17.8341i | −0.225518 | + | 0.841645i | 0.756678 | + | 0.653788i | \(0.226821\pi\) |
−0.982196 | + | 0.187858i | \(0.939846\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.348550 | + | 0.603706i | 0.0164126 | + | 0.0284274i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.4612 | − | 38.9040i | 1.05532 | − | 1.82787i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.62502 | − | 2.18355i | 0.310585 | − | 0.102366i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.52390 | + | 13.0318i | −0.351953 | + | 0.609601i | −0.986592 | − | 0.163208i | \(-0.947816\pi\) |
0.634638 | + | 0.772809i | \(0.281149\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.41990 | + | 7.65549i | 0.206303 | + | 0.357328i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.12241 | − | 11.6530i | 0.145425 | − | 0.542734i | −0.854311 | − | 0.519762i | \(-0.826021\pi\) |
0.999736 | − | 0.0229718i | \(-0.00731278\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.5516 | −1.51280 | −0.756400 | − | 0.654109i | \(-0.773044\pi\) | ||||
−0.756400 | + | 0.654109i | \(0.773044\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.540054 | − | 1.46821i | 0.0250444 | − | 0.0680868i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.4091 | − | 19.4091i | −0.898145 | − | 0.898145i | 0.0971268 | − | 0.995272i | \(-0.469035\pi\) |
−0.995272 | + | 0.0971268i | \(0.969035\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.7006i | 0.540283i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.6489 | + | 18.4444i | −0.490675 | + | 0.849874i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.2943i | 0.887153i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.01712 | − | 0.485173i | 0.276084 | − | 0.0222613i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.4324 | − | 6.54664i | −1.11868 | − | 0.299750i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.16289 | − | 1.38339i | 0.235899 | − | 0.0632088i | −0.138933 | − | 0.990302i | \(-0.544367\pi\) |
0.374831 | + | 0.927093i | \(0.377701\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.8142 | + | 21.2808i | −1.22262 | + | 0.970321i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.26290 | − | 3.03853i | −0.239470 | − | 0.138258i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.50317 | + | 2.08593i | −0.113663 | + | 0.0947171i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.93242 | + | 10.2752i | 0.268823 | + | 0.465616i | 0.968558 | − | 0.248787i | \(-0.0800319\pi\) |
−0.699735 | + | 0.714403i | \(0.746699\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.64173 | − | 9.64173i | −0.436014 | − | 0.436014i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.9915 | + | 9.81007i | 0.766817 | + | 0.442722i | 0.831738 | − | 0.555168i | \(-0.187346\pi\) |
−0.0649209 | + | 0.997890i | \(0.520680\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.0922 | + | 25.0922i | −1.13010 | + | 1.13010i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.61564 | − | 10.7978i | 0.342297 | − | 0.485326i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.33195 | − | 12.4350i | −0.149459 | − | 0.557787i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.2879 | − | 25.2879i | 1.13204 | − | 1.13204i | 0.142203 | − | 0.989837i | \(-0.454581\pi\) |
0.989837 | − | 0.142203i | \(-0.0454187\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.6153 | − | 5.25591i | −0.876347 | − | 0.234817i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.69726 | + | 13.7984i | −0.164853 | + | 0.615239i | 0.833206 | + | 0.552962i | \(0.186503\pi\) |
−0.998059 | + | 0.0622762i | \(0.980164\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.96060 | + | 24.3607i | −0.398741 | + | 1.08404i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −29.5920 | − | 15.8181i | −1.31423 | − | 0.702508i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.01986 | + | 33.6626i | 0.399798 | + | 1.49207i | 0.813451 | + | 0.581633i | \(0.197586\pi\) |
−0.413653 | + | 0.910435i | \(0.635747\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.23637 | − | 4.75527i | 0.364356 | − | 0.210361i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.78690 | + | 1.03167i | −0.0788938 | + | 0.0455493i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −28.0798 | − | 19.8045i | −1.23734 | − | 0.872691i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.37109 | − | 0.635331i | 0.104280 | − | 0.0279418i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −51.4717 | −2.25936 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.2982 | 0.889281 | 0.444641 | − | 0.895709i | \(-0.353331\pi\) | ||||
0.444641 | + | 0.895709i | \(0.353331\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.2457 | − | 4.88891i | 0.797827 | − | 0.213777i | 0.163197 | − | 0.986593i | \(-0.447819\pi\) |
0.634630 | + | 0.772816i | \(0.281153\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.78777 | − | 10.0875i | 0.208955 | − | 0.440256i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.21417 | + | 0.701004i | −0.0528903 | + | 0.0305362i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.5056 | − | 7.79747i | 0.587201 | − | 0.339020i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.1758 | + | 41.7085i | 0.484987 | + | 1.80999i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.178038 | − | 1.54745i | 0.00771170 | − | 0.0670277i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.4772 | + | 6.69094i | −0.625906 | + | 0.289275i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.04605 | + | 7.63598i | −0.0882938 | + | 0.329517i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.74349 | − | 2.61076i | −0.419682 | − | 0.112453i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.5158 | + | 20.5158i | −0.882042 | + | 0.882042i | −0.993742 | − | 0.111700i | \(-0.964371\pi\) |
0.111700 | + | 0.993742i | \(0.464371\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.6092 | + | 58.2544i | 0.669856 | + | 2.49993i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.8047 | − | 8.32580i | −0.505660 | − | 0.356638i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.8176 | + | 28.8176i | −1.23215 | + | 1.23215i | −0.269018 | + | 0.963135i | \(0.586699\pi\) |
−0.963135 | + | 0.269018i | \(0.913301\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.6580 | − | 10.7722i | −0.796304 | − | 0.459747i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.85689 | − | 5.85689i | −0.249512 | − | 0.249512i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.72250 | + | 2.98347i | 0.0732484 | + | 0.126870i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.96172 | + | 54.5724i | −0.210613 | + | 2.31647i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.50881 | + | 3.75786i | 0.275787 | + | 0.159226i | 0.631515 | − | 0.775364i | \(-0.282434\pi\) |
−0.355727 | + | 0.934590i | \(0.615767\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.6828 | − | 34.6284i | 1.08627 | − | 1.46462i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.8085 | + | 5.57562i | −0.878535 | + | 0.235403i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.0668 | + | 6.18074i | 0.972151 | + | 0.260487i | 0.709736 | − | 0.704468i | \(-0.248814\pi\) |
0.262415 | + | 0.964955i | \(0.415481\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.2430 | − | 1.74957i | −0.809560 | − | 0.0736051i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 5.68898i | − | 0.238915i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.39258 | − | 2.41202i | 0.0583801 | − | 0.101117i | −0.835358 | − | 0.549706i | \(-0.814740\pi\) |
0.893738 | + | 0.448589i | \(0.148073\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.8794i | 1.20857i | 0.796769 | + | 0.604284i | \(0.206541\pi\) | ||||
−0.796769 | + | 0.604284i | \(0.793459\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.6425 | + | 13.6425i | 0.569924 | + | 0.569924i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.72809 | − | 11.1984i | −0.322283 | − | 0.467004i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.20458 | 0.175039 | 0.0875196 | − | 0.996163i | \(-0.472106\pi\) | ||||
0.0875196 | + | 0.996163i | \(0.472106\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.33742 | + | 4.99131i | −0.0555811 | + | 0.207432i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.70632 | + | 4.68748i | 0.112277 | + | 0.194469i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.57253 | − | 9.65190i | 0.230790 | − | 0.399741i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −28.0412 | + | 9.24214i | −1.15936 | + | 0.382115i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.71072 | − | 4.69510i | 0.111883 | − | 0.193787i | −0.804646 | − | 0.593754i | \(-0.797645\pi\) |
0.916530 | + | 0.399967i | \(0.130978\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.163625 | − | 0.283406i | −0.00674204 | − | 0.0116776i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.12493 | − | 7.93036i | 0.0874081 | − | 0.326211i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.8446 | −0.650660 | −0.325330 | − | 0.945601i | \(-0.605475\pi\) | ||||
−0.325330 | + | 0.945601i | \(0.605475\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.08381 | + | 4.19826i | −0.372400 | + | 0.172112i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29.9402 | − | 29.9402i | −1.22537 | − | 1.22537i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.8884i | 1.42550i | 0.701418 | + | 0.712750i | \(0.252550\pi\) | ||||
−0.701418 | + | 0.712750i | \(0.747450\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.6867 | − | 20.2419i | 0.476710 | − | 0.825686i | −0.522934 | − | 0.852373i | \(-0.675163\pi\) |
0.999644 | + | 0.0266875i | \(0.00849591\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 49.5242i | − | 2.01678i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.0192 | − | 14.4233i | −0.488648 | − | 0.586391i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.2836 | − | 8.38242i | −1.26976 | − | 0.340232i | −0.439823 | − | 0.898085i | \(-0.644959\pi\) |
−0.829940 | + | 0.557853i | \(0.811625\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.7989 | + | 3.96536i | −0.599683 | + | 0.160685i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.10118 | − | 2.01591i | −0.206372 | − | 0.0815549i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.8649 | + | 19.5519i | 1.36779 | + | 0.789695i | 0.990646 | − | 0.136458i | \(-0.0435720\pi\) |
0.377146 | + | 0.926154i | \(0.376905\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.59622 | − | 1.91550i | −0.0643658 | − | 0.0772406i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.14533 | + | 12.3761i | 0.287660 | + | 0.498242i | 0.973251 | − | 0.229745i | \(-0.0737893\pi\) |
−0.685591 | + | 0.727987i | \(0.740456\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.85038 | − | 6.85038i | −0.275340 | − | 0.275340i | 0.555906 | − | 0.831245i | \(-0.312372\pi\) |
−0.831245 | + | 0.555906i | \(0.812372\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.02754 | + | 2.32530i | 0.161620 | + | 0.0933111i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.21223 | − | 6.21223i | 0.248888 | − | 0.248888i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.3681 | − | 15.8074i | 0.774726 | − | 0.632297i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.30143 | − | 4.85701i | −0.0519742 | − | 0.193970i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.7257 | − | 34.7257i | 1.38461 | − | 1.38461i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.2254 | + | 9.97452i | 1.48192 | + | 0.397080i | 0.907000 | − | 0.421130i | \(-0.138366\pi\) |
0.574921 | + | 0.818209i | \(0.305033\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.56506 | − | 28.2332i | 0.300684 | − | 1.12217i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.41401 | + | 9.55063i | 0.175165 | + | 0.379005i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.0119 | + | 17.6553i | 0.555171 | + | 0.699527i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.1029 | + | 52.6327i | 0.557902 | + | 2.08212i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.48111 | − | 3.74187i | 0.255988 | − | 0.147795i | −0.366515 | − | 0.930412i | \(-0.619449\pi\) |
0.622503 | + | 0.782617i | \(0.286116\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.7800 | + | 11.9973i | −0.819482 | + | 0.473128i | −0.850238 | − | 0.526399i | \(-0.823542\pi\) |
0.0307558 | + | 0.999527i | \(0.490209\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.7525 | − | 68.0044i | −0.462752 | − | 2.67767i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.5414 | − | 6.03995i | 0.886195 | − | 0.237455i | 0.213117 | − | 0.977027i | \(-0.431639\pi\) |
0.673078 | + | 0.739572i | \(0.264972\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.0257 | −0.746825 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.605318 | −0.0237243 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.3843 | − | 5.46196i | 0.797700 | − | 0.213743i | 0.163126 | − | 0.986605i | \(-0.447842\pi\) |
0.634574 | + | 0.772862i | \(0.281176\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.83581 | − | 33.7683i | −0.228024 | − | 1.31944i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −34.8614 | + | 20.1273i | −1.36007 | + | 0.785239i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.0042 | − | 7.50797i | 0.506571 | − | 0.292469i | −0.224852 | − | 0.974393i | \(-0.572190\pi\) |
0.731423 | + | 0.681924i | \(0.238856\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.43378 | + | 5.35096i | 0.0557677 | + | 0.208128i | 0.988188 | − | 0.153249i | \(-0.0489735\pi\) |
−0.932420 | + | 0.361377i | \(0.882307\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 44.7676 | + | 17.6915i | 1.73863 | + | 0.687080i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.979937 | − | 2.12030i | −0.0380003 | − | 0.0822216i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.83189 | + | 18.0329i | −0.187092 | + | 0.698235i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.1715 | + | 6.74467i | 0.973185 | + | 0.260764i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.71243 | − | 6.71243i | 0.259130 | − | 0.259130i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.14271 | + | 30.3890i | 0.313878 | + | 1.17141i | 0.925029 | + | 0.379896i | \(0.124040\pi\) |
−0.611151 | + | 0.791514i | \(0.709293\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.66394 | + | 7.71969i | −0.141025 | + | 0.297131i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.4080 | − | 19.4080i | 0.745910 | − | 0.745910i | −0.227798 | − | 0.973708i | \(-0.573153\pi\) |
0.973708 | + | 0.227798i | \(0.0731527\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.09187 | + | 0.630389i | 0.0419019 | + | 0.0241921i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.0756 | + | 25.0756i | 0.960899 | + | 0.960899i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.1706 | − | 21.0802i | −0.465697 | − | 0.806610i | 0.533536 | − | 0.845777i | \(-0.320863\pi\) |
−0.999233 | + | 0.0391672i | \(0.987530\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.2547 | − | 29.1063i | −0.926724 | − | 1.11209i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.6451 | − | 6.14597i | −0.406137 | − | 0.234483i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.8490 | + | 9.90507i | −0.870476 | + | 0.377353i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.5308 | + | 3.08967i | −0.438652 | + | 0.117537i | −0.471385 | − | 0.881928i | \(-0.656246\pi\) |
0.0327325 | + | 0.999464i | \(0.489579\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.93848 | − | 1.32326i | −0.187597 | − | 0.0502666i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.45341 | + | 5.34420i | 0.168927 | + | 0.202717i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.23460i | 0.0846413i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 34.9585 | − | 60.5498i | 1.32225 | − | 2.29020i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.2613i | − | 0.803029i | −0.915853 | − | 0.401515i | \(-0.868484\pi\) | ||
0.915853 | − | 0.401515i | \(-0.131516\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.10550 | + | 8.10550i | 0.305705 | + | 0.305705i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.97010 | + | 3.68354i | −0.300171 | + | 0.138730i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.0435 | 0.377723 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.58329 | + | 20.8371i | −0.209685 | + | 0.782555i | 0.778285 | + | 0.627911i | \(0.216090\pi\) |
−0.987970 | + | 0.154644i | \(0.950577\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.29071 | − | 12.6279i | −0.273423 | − | 0.473582i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.368797 | + | 0.638775i | −0.0138116 | + | 0.0239223i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.735666 | − | 12.9884i | −0.0275123 | − | 0.485737i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −33.7040 | + | 58.3770i | −1.25870 | + | 2.18013i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.13804 | − | 7.16730i | −0.154323 | − | 0.267295i | 0.778489 | − | 0.627658i | \(-0.215986\pi\) |
−0.932812 | + | 0.360363i | \(0.882653\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.44115 | + | 12.8425i | −0.128155 | + | 0.478282i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.27344 | 0.0845500 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −33.7401 | − | 6.18644i | −1.25308 | − | 0.229758i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.41639 | − | 2.41639i | −0.0896190 | − | 0.0896190i | 0.660876 | − | 0.750495i | \(-0.270185\pi\) |
−0.750495 | + | 0.660876i | \(0.770185\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 37.3127i | 1.38195i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.9246 | + | 53.5629i | −1.14379 | + | 1.98110i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 32.4183i | − | 1.19740i | −0.800974 | − | 0.598699i | \(-0.795685\pi\) | ||
0.800974 | − | 0.598699i | \(-0.204315\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 35.9320 | + | 3.26694i | 1.32537 | + | 0.120503i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.0776 | + | 5.64773i | 0.776404 | + | 0.208037i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.7773 | − | 11.7301i | 1.61038 | − | 0.431499i | 0.662221 | − | 0.749309i | \(-0.269614\pi\) |
0.948154 | + | 0.317810i | \(0.102947\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.12945 | + | 10.4494i | −0.151699 | + | 0.383870i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.1203 | + | 7.57500i | 0.481336 | + | 0.277900i | 0.720973 | − | 0.692963i | \(-0.243695\pi\) |
−0.239637 | + | 0.970863i | \(0.577028\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.34462 | − | 36.7864i | 0.122537 | − | 1.34775i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.4548 | − | 19.8403i | −0.419110 | − | 0.725919i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.36362 | + | 4.36362i | 0.159443 | + | 0.159443i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.51200 | − | 3.18236i | −0.201136 | − | 0.116126i | 0.396049 | − | 0.918229i | \(-0.370381\pi\) |
−0.597185 | + | 0.802103i | \(0.703714\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.8498 | − | 11.8498i | 0.431830 | − | 0.431830i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31.8029 | − | 22.4304i | −1.15743 | − | 0.816326i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.31666 | − | 27.3061i | −0.265928 | − | 0.992459i | −0.961680 | − | 0.274176i | \(-0.911595\pi\) |
0.695751 | − | 0.718283i | \(-0.255072\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.01399 | + | 8.01399i | −0.290889 | + | 0.290889i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.4842 | + | 8.43618i | 1.14130 | + | 0.305811i | 0.779475 | − | 0.626434i | \(-0.215486\pi\) |
0.361828 | + | 0.932245i | \(0.382153\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.44666 | + | 5.39900i | −0.0523725 | + | 0.195457i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 38.4483 | − | 17.7696i | 1.39010 | − | 0.642463i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.1463 | + | 25.3252i | 1.23295 | + | 0.914441i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.7440 | − | 40.0972i | −0.387439 | − | 1.44594i | −0.834286 | − | 0.551331i | \(-0.814120\pi\) |
0.446848 | − | 0.894610i | \(-0.352547\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.9490 | + | 13.8270i | −0.862503 | + | 0.497966i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.93793 | + | 1.11886i | −0.0697025 | + | 0.0402427i | −0.534446 | − | 0.845202i | \(-0.679480\pi\) |
0.464744 | + | 0.885445i | \(0.346146\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.22436 | − | 0.581108i | −0.0439802 | − | 0.0208740i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20.4806 | − | 5.48776i | 0.734738 | − | 0.196872i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.521588 | −0.0186878 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.0089 | −0.859106 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.3252 | − | 3.03457i | 0.404729 | − | 0.108447i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.0778 | + | 10.6343i | 0.538150 | + | 0.379554i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.4425 | − | 21.6174i | 1.33468 | − | 0.770577i | 0.348666 | − | 0.937247i | \(-0.386635\pi\) |
0.986013 | + | 0.166669i | \(0.0533013\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.6990 | + | 13.1053i | −0.808105 | + | 0.466559i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.93507 | + | 7.22176i | 0.0688030 | + | 0.256776i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.9820 | + | 3.11215i | −0.745094 | + | 0.110516i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.7617 | + | 37.4132i | −0.488078 | + | 1.32691i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.89049 | − | 21.9836i | 0.208652 | − | 0.778699i | −0.779653 | − | 0.626211i | \(-0.784605\pi\) |
0.988305 | − | 0.152488i | \(-0.0487286\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.60066 | + | 2.03659i | 0.268892 | + | 0.0720494i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −26.2940 | + | 26.2940i | −0.929053 | + | 0.929053i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.59062 | − | 17.1324i | −0.161999 | − | 0.604590i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.03437 | + | 4.30228i | −0.106947 | + | 0.151635i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −34.1289 | + | 34.1289i | −1.20139 | + | 1.20139i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.3301 | + | 14.6243i | 0.890558 | + | 0.514164i | 0.874125 | − | 0.485701i | \(-0.161436\pi\) |
0.0164333 | + | 0.999865i | \(0.494769\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.1564 | − | 16.1564i | −0.567327 | − | 0.567327i | 0.364052 | − | 0.931379i | \(-0.381393\pi\) |
−0.931379 | + | 0.364052i | \(0.881393\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.6593 | − | 40.9790i | −0.829767 | − | 1.43720i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.07484 | + | 7.56220i | −0.317878 | + | 0.264892i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.5024 | − | 7.21825i | −0.437403 | − | 0.252535i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.10191 | + | 8.94856i | 0.248161 | + | 0.312688i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.6639 | − | 6.87663i | 0.895677 | − | 0.239996i | 0.218518 | − | 0.975833i | \(-0.429878\pi\) |
0.677159 | + | 0.735837i | \(0.263211\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.5702 | + | 10.8708i | 1.41419 | + | 0.378931i | 0.883418 | − | 0.468585i | \(-0.155236\pi\) |
0.530770 | + | 0.847516i | \(0.321903\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15.8608 | − | 13.4939i | −0.552202 | − | 0.469796i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 48.4948i | − | 1.68633i | −0.537655 | − | 0.843165i | \(-0.680690\pi\) | ||
0.537655 | − | 0.843165i | \(-0.319310\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.4336 | − | 35.3921i | 0.709689 | − | 1.22922i | −0.255284 | − | 0.966866i | \(-0.582169\pi\) |
0.964973 | − | 0.262351i | \(-0.0844978\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 34.9998i | − | 1.21413i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.8644 | − | 22.8644i | −0.792205 | − | 0.792205i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.07327 | + | 16.5111i | −0.210174 | + | 0.571389i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.463232 | 0.0160116 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.70239 | − | 28.7457i | 0.265916 | − | 0.992412i | −0.695771 | − | 0.718263i | \(-0.744937\pi\) |
0.961687 | − | 0.274149i | \(-0.0883960\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.03332 | + | 15.6462i | 0.311494 | + | 0.539523i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.2967 | − | 54.2075i | 1.07792 | − | 1.86701i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.9685 | + | 24.2900i | −0.549334 | + | 0.835603i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.63231 | + | 6.29135i | −0.124808 | + | 0.216173i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.8183 | + | 20.4700i | 0.405605 | + | 0.702528i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.68697 | − | 24.9561i | 0.229227 | − | 0.855485i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.67930 | −0.297174 | −0.148587 | − | 0.988899i | \(-0.547472\pi\) | ||||
−0.148587 | + | 0.988899i | \(0.547472\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.14770 | + | 8.97441i | 0.141848 | + | 0.306918i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.38807 | − | 2.38807i | −0.0815751 | − | 0.0815751i | 0.665142 | − | 0.746717i | \(-0.268371\pi\) |
−0.746717 | + | 0.665142i | \(0.768371\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 0.237935i | − | 0.00811823i | −0.999992 | − | 0.00405912i | \(-0.998708\pi\) | ||
0.999992 | − | 0.00405912i | \(-0.00129206\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.482394 | + | 0.835530i | −0.0164399 | + | 0.0284748i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48.8736i | 1.66368i | 0.555017 | + | 0.831839i | \(0.312712\pi\) | ||||
−0.555017 | + | 0.831839i | \(0.687288\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.03756 | + | 44.4078i | −0.137281 | + | 1.50991i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −24.3192 | − | 6.51630i | −0.825922 | − | 0.221305i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.20588 | − | 1.66286i | 0.210520 | − | 0.0564087i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.3112 | − | 38.1927i | −1.02706 | − | 1.29411i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.62145 | − | 2.66820i | −0.156412 | − | 0.0903048i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.32757 | − | 4.92200i | −0.281523 | − | 0.166394i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.4333 | + | 30.1953i | 0.588680 | + | 1.01962i | 0.994406 | + | 0.105629i | \(0.0336856\pi\) |
−0.405725 | + | 0.913995i | \(0.632981\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 33.1837 | + | 33.1837i | 1.11926 | + | 1.11926i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.6799 | − | 14.2489i | −0.831486 | − | 0.480058i | 0.0228755 | − | 0.999738i | \(-0.492718\pi\) |
−0.854361 | + | 0.519680i | \(0.826051\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.7320 | + | 10.7320i | −0.361160 | + | 0.361160i | −0.864240 | − | 0.503080i | \(-0.832200\pi\) |
0.503080 | + | 0.864240i | \(0.332200\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 67.0577 | − | 11.5888i | 2.25412 | − | 0.389555i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.36490 | − | 12.5580i | −0.112982 | − | 0.421655i | 0.886146 | − | 0.463406i | \(-0.153373\pi\) |
−0.999128 | + | 0.0417512i | \(0.986706\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.87868 | − | 2.87868i | 0.0965478 | − | 0.0965478i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.2482 | − | 2.74600i | −0.343328 | − | 0.0919943i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.475371 | + | 1.77411i | −0.0159077 | + | 0.0593683i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.42754 | + | 2.36424i | 0.214849 | + | 0.0790279i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.0505 | − | 3.71560i | 0.836413 | − | 0.124060i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.481289 | + | 1.79620i | 0.0160519 | + | 0.0599065i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.9398 | − | 17.8631i | 1.03075 | − | 0.595105i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −23.1258 | + | 13.3517i | −0.769578 | + | 0.444316i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 51.4841 | − | 8.89743i | 1.71139 | − | 0.295761i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.3926 | − | 13.2347i | 1.64006 | − | 0.439451i | 0.683251 | − | 0.730184i | \(-0.260566\pi\) |
0.956804 | + | 0.290732i | \(0.0938990\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −42.5102 | −1.40997 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.3842 | −1.50365 | −0.751823 | − | 0.659365i | \(-0.770825\pi\) | ||||
−0.751823 | + | 0.659365i | \(0.770825\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.75039 | − | 2.61261i | 0.322691 | − | 0.0864647i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −19.5699 | + | 27.7472i | −0.646960 | + | 0.917293i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.4834 | + | 6.62993i | −0.379214 | + | 0.218940i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.3431 | + | 15.2092i | −0.868977 | + | 0.501704i | −0.867008 | − | 0.498294i | \(-0.833960\pi\) |
−0.00196918 | + | 0.999998i | \(0.500627\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.7289 | + | 69.8973i | 0.617139 | + | 2.30319i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 43.0898 | + | 31.9584i | 1.41832 | + | 1.05192i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 46.6938 | + | 8.56156i | 1.53528 | + | 0.281503i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.5651 | − | 54.3576i | 0.478380 | − | 1.78534i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.9374 | + | 6.41401i | 0.785361 | + | 0.210437i | 0.629147 | − | 0.777286i | \(-0.283404\pi\) |
0.156214 | + | 0.987723i | \(0.450071\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.33689 | − | 5.33689i | 0.174910 | − | 0.174910i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.69371 | − | 28.7133i | −0.251881 | − | 0.940031i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.17817 | + | 18.3901i | 0.103937 | + | 0.601422i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.3459 | − | 25.3459i | 0.828014 | − | 0.828014i | −0.159228 | − | 0.987242i | \(-0.550901\pi\) |
0.987242 | + | 0.159228i | \(0.0509005\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.6792 | − | 18.8674i | −1.06645 | − | 0.615713i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.5969 | + | 27.5969i | 0.899632 | + | 0.899632i | 0.995403 | − | 0.0957715i | \(-0.0305318\pi\) |
−0.0957715 | + | 0.995403i | \(0.530532\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.587809 | + | 1.01811i | 0.0191417 | + | 0.0331544i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.29280 | + | 0.299382i | 0.107115 | + | 0.00973889i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.7982 | − | 26.4416i | −1.48824 | − | 0.859237i | −0.488332 | − | 0.872658i | \(-0.662394\pi\) |
−0.999910 | + | 0.0134210i | \(0.995728\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.5661 | + | 36.8589i | −0.472835 | + | 1.19649i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.76184 | − | 1.54388i | 0.186840 | − | 0.0500637i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.8852 | − | 12.2949i | −1.48637 | − | 0.398271i | −0.577860 | − | 0.816136i | \(-0.696112\pi\) |
−0.908509 | + | 0.417865i | \(0.862779\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.8404 | − | 10.7001i | 0.415505 | − | 0.346247i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 28.5730i | 0.923634i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.33001 | + | 12.6960i | −0.236699 | + | 0.409974i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 30.9265i | − | 0.997630i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.4696 | − | 18.4696i | −0.595173 | − | 0.595173i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.20140 | + | 1.54540i | 0.135248 | + | 0.0497482i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.7754 | −1.27909 | −0.639546 | − | 0.768753i | \(-0.720878\pi\) | ||||
−0.639546 | + | 0.768753i | \(0.720878\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.17182 | − | 15.5694i | 0.134018 | − | 0.500163i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.597739 | − | 1.03531i | −0.0191824 | − | 0.0332248i | 0.856275 | − | 0.516520i | \(-0.172773\pi\) |
−0.875457 | + | 0.483296i | \(0.839440\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.34586 | − | 2.33111i | 0.0431464 | − | 0.0747318i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.5043 | + | 45.3304i | 0.336407 | + | 1.45174i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.23433 | + | 14.2623i | −0.263439 | + | 0.456291i | −0.967154 | − | 0.254193i | \(-0.918190\pi\) |
0.703714 | + | 0.710483i | \(0.251524\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.19223 | − | 14.1894i | −0.261825 | − | 0.453494i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.12315 | − | 22.8519i | 0.195497 | − | 0.729605i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.80446 | −0.0575534 | −0.0287767 | − | 0.999586i | \(-0.509161\pi\) | ||||
−0.0287767 | + | 0.999586i | \(0.509161\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.67533 | − | 2.45539i | −0.212694 | − | 0.0782351i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.40229 | + | 2.40229i | 0.0764657 | + | 0.0764657i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.5387i | 1.03467i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.661562 | − | 1.14586i | 0.0210152 | − | 0.0363994i | −0.855327 | − | 0.518089i | \(-0.826643\pi\) |
0.876342 | + | 0.481690i | \(0.159977\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 90.7637i | 2.88030i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.1798 | + | 23.4827i | −0.893360 | + | 0.744451i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.5416 | + | 12.2028i | 1.44232 | + | 0.386467i | 0.893344 | − | 0.449373i | \(-0.148353\pi\) |
0.548972 | + | 0.835841i | \(0.315019\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −15.6732 | + | 4.19962i | −0.495878 | + | 0.132870i |
(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 | 260.2.bk.c.33.5 | yes | 20 | |
5.2 | odd | 4 | 260.2.bf.c.137.1 | yes | 20 | ||
5.3 | odd | 4 | 1300.2.bn.d.657.5 | 20 | |||
5.4 | even | 2 | 1300.2.bs.d.293.1 | 20 | |||
13.2 | odd | 12 | 260.2.bf.c.93.1 | ✓ | 20 | ||
65.2 | even | 12 | inner | 260.2.bk.c.197.5 | yes | 20 | |
65.28 | even | 12 | 1300.2.bs.d.457.1 | 20 | |||
65.54 | odd | 12 | 1300.2.bn.d.93.5 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.bf.c.93.1 | ✓ | 20 | 13.2 | odd | 12 | ||
260.2.bf.c.137.1 | yes | 20 | 5.2 | odd | 4 | ||
260.2.bk.c.33.5 | yes | 20 | 1.1 | even | 1 | trivial | |
260.2.bk.c.197.5 | yes | 20 | 65.2 | even | 12 | inner | |
1300.2.bn.d.93.5 | 20 | 65.54 | odd | 12 | |||
1300.2.bn.d.657.5 | 20 | 5.3 | odd | 4 | |||
1300.2.bs.d.293.1 | 20 | 5.4 | even | 2 | |||
1300.2.bs.d.457.1 | 20 | 65.28 | even | 12 |