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: | \( x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 \) |
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 | 197.5 | ||
Root | \(0.402430i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 260.197 |
Dual form | 260.2.bk.c.33.5 |
$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{1}{12}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | 0.892333 | − | 0.451378i | \(-0.149067\pi\) |
0.547094 | + | 0.837071i | \(0.315734\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.380790 | + | 2.20341i | −0.170295 | + | 0.985393i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.749297 | − | 0.432607i | −0.283208 | − | 0.163510i | 0.351667 | − | 0.936125i | \(-0.385615\pi\) |
−0.634875 | + | 0.772615i | \(0.718948\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.17149 | + | 1.83106i | 1.05716 | + | 0.610354i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.417628 | − | 1.55861i | 0.125920 | − | 0.469938i | −0.873951 | − | 0.486014i | \(-0.838451\pi\) |
0.999871 | + | 0.0160756i | \(0.00511723\pi\) | |||||||
\(12\) | 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 | −0.914623 | − | 0.404308i | \(-0.867513\pi\) |
0.589933 | − | 0.807452i | \(-0.299154\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.16619 | + | 0.312480i | −0.267543 | + | 0.0716878i | −0.390096 | − | 0.920774i | \(-0.627558\pi\) |
0.122554 | + | 0.992462i | \(0.460892\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.57912 | − | 1.57912i | −0.344592 | − | 0.344592i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.704305 | − | 2.62850i | 0.146858 | − | 0.548080i | −0.852808 | − | 0.522225i | \(-0.825102\pi\) |
0.999666 | − | 0.0258557i | \(-0.00823103\pi\) | |||||||
\(24\) | 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 | 0.166204 | − | 0.986091i | \(-0.446849\pi\) |
0.937082 | + | 0.349109i | \(0.113516\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.191663 | − | 0.191663i | 0.0344237 | − | 0.0344237i | −0.689685 | − | 0.724109i | \(-0.742251\pi\) |
0.724109 | + | 0.689685i | \(0.242251\pi\) | |||||||
\(32\) | 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 | −0.988496 | − | 0.151249i | \(-0.951670\pi\) |
−0.363262 | + | 0.931687i | \(0.618337\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.06370 | + | 9.24533i | 0.170328 | + | 1.48044i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.417297 | + | 0.111814i | 0.0651709 | + | 0.0174625i | 0.291257 | − | 0.956645i | \(-0.405926\pi\) |
−0.226086 | + | 0.974107i | \(0.572593\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.5499 | − | 3.09480i | 1.76135 | − | 0.471952i | 0.774362 | − | 0.632743i | \(-0.218071\pi\) |
0.986989 | + | 0.160791i | \(0.0514044\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.24225 | + | 6.29083i | −0.781468 | + | 0.937782i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.52128i | 0.221902i | 0.993826 | + | 0.110951i | \(0.0353897\pi\) | ||||
−0.993826 | + | 0.110951i | \(0.964610\pi\) | |||||||
\(48\) | 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 | −0.957916 | − | 0.287049i | \(-0.907326\pi\) |
0.287049 | + | 0.957916i | \(0.407326\pi\) | |||||||
\(54\) | 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 | −0.817828 | − | 0.575463i | \(-0.804822\pi\) |
0.420528 | − | 0.907279i | \(-0.361845\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.94152 | + | 5.09486i | −0.376623 | + | 0.652330i | −0.990569 | − | 0.137018i | \(-0.956248\pi\) |
0.613946 | + | 0.789348i | \(0.289581\pi\) | |||||||
\(62\) | 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 | 0.901099 | + | 0.433614i | \(0.142762\pi\) |
−0.0750284 | + | 0.997181i | \(0.523905\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.51189 | − | 6.08277i | 0.422782 | − | 0.732279i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.85102 | − | 14.3722i | −0.457031 | − | 1.70566i | −0.682046 | − | 0.731309i | \(-0.738910\pi\) |
0.225015 | − | 0.974355i | \(-0.427757\pi\) | |||||||
\(72\) | 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 | \(0.0719074\pi\) | ||||
−0.974592 | + | 0.223987i | \(0.928093\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.28761 | − | 5.69431i | −0.365290 | − | 0.632701i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.25583i | 0.686667i | 0.939214 | + | 0.343333i | \(0.111556\pi\) | ||||
−0.939214 | + | 0.343333i | \(0.888444\pi\) | |||||||
\(84\) | 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 | −0.301683 | − | 0.953408i | \(-0.597548\pi\) |
−0.737969 | + | 0.674835i | \(0.764215\pi\) | |||||||
\(90\) | 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 | −0.900641 | − | 0.434564i | \(-0.856903\pi\) |
0.826664 | + | 0.562696i | \(0.190236\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.17841 | − | 4.17841i | 0.419946 | − | 0.419946i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.0529 | + | 5.80403i | −1.00030 | + | 0.577523i | −0.908337 | − | 0.418240i | \(-0.862647\pi\) |
−0.0919621 | + | 0.995763i | \(0.529314\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.8660 | + | 10.8660i | 1.07066 | + | 1.07066i | 0.997306 | + | 0.0733504i | \(0.0233691\pi\) |
0.0733504 | + | 0.997306i | \(0.476631\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.08076 | − | 2.87813i | 0.398241 | − | 0.280877i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.84601 | + | 6.88942i | −0.178461 | + | 0.666025i | 0.817475 | + | 0.575964i | \(0.195373\pi\) |
−0.995936 | + | 0.0900615i | \(0.971294\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.56805 | + | 4.56805i | 0.437540 | + | 0.437540i | 0.891183 | − | 0.453643i | \(-0.149876\pi\) |
−0.453643 | + | 0.891183i | \(0.649876\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −23.6711 | + | 6.34266i | −2.24677 | + | 0.602019i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.23652 | + | 8.34679i | 0.210394 | + | 0.785200i | 0.987737 | + | 0.156124i | \(0.0498999\pi\) |
−0.777344 | + | 0.629076i | \(0.783433\pi\) | |||||||
\(114\) | 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 | 0.0514670 | − | 0.998675i | \(-0.483610\pi\) |
−0.454766 | + | 0.890611i | \(0.650277\pi\) | |||||||
\(128\) | 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 | 0.971835 | − | 0.235661i | \(-0.0757253\pi\) |
0.281830 | + | 0.959464i | \(0.409059\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.69425 | − | 1.55553i | −0.228524 | − | 0.131938i | 0.381367 | − | 0.924424i | \(-0.375453\pi\) |
−0.609891 | + | 0.792485i | \(0.708787\pi\) | |||||||
\(140\) | 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 | 0.463029 | − | 0.886343i | \(-0.346763\pi\) |
0.844166 | + | 0.536082i | \(0.180096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.3067 | + | 12.3067i | 1.00151 | + | 1.00151i | 0.999999 | + | 0.00150662i | \(0.000479574\pi\) |
0.00150662 | + | 0.999999i | \(0.499520\pi\) | |||||||
\(152\) | 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 | 0.434849 | − | 0.900503i | \(-0.356802\pi\) |
−0.900503 | + | 0.434849i | \(0.856802\pi\) | |||||||
\(158\) | 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 | −0.950733 | − | 0.310010i | \(-0.899668\pi\) |
0.743843 | + | 0.668354i | \(0.233001\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.15442 | + | 5.96189i | 0.556971 | + | 0.464132i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.81358 | + | 3.93382i | −0.527251 | + | 0.304408i | −0.739896 | − | 0.672721i | \(-0.765125\pi\) |
0.212645 | + | 0.977129i | \(0.431792\pi\) | |||||||
\(168\) | 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 | −0.901034 | − | 0.433749i | \(-0.857191\pi\) |
−0.563444 | + | 0.826154i | \(0.690524\pi\) | |||||||
\(174\) | 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 | 0.803103 | − | 0.595840i | \(-0.203181\pi\) |
−0.917564 | + | 0.397588i | \(0.869847\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 23.3657i | − | 1.73676i | −0.495901 | − | 0.868379i | \(-0.665162\pi\) | ||
0.495901 | − | 0.868379i | \(-0.334838\pi\) | |||||||
\(182\) | 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 | −0.698541 | − | 0.715570i | \(-0.746167\pi\) |
0.968972 | + | 0.247170i | \(0.0795006\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00100 | − | 1.73378i | −0.0720536 | − | 0.124800i | 0.827748 | − | 0.561101i | \(-0.189622\pi\) |
−0.899801 | + | 0.436300i | \(0.856289\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −20.7763 | − | 1.17678i | −1.48782 | − | 0.0842707i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.59042 | + | 2.75469i | 0.113313 | + | 0.196264i | 0.917104 | − | 0.398648i | \(-0.130520\pi\) |
−0.803791 | + | 0.594912i | \(0.797187\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.20225 | + | 14.2067i | −0.581442 | + | 1.00709i | 0.413867 | + | 0.910337i | \(0.364178\pi\) |
−0.995309 | + | 0.0967496i | \(0.969155\pi\) | |||||||
\(200\) | 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 | 0.992422 | − | 0.122876i | \(-0.0392117\pi\) |
−0.602625 | + | 0.798025i | \(0.705878\pi\) | |||||||
\(212\) | 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 | −0.177808 | − | 0.984065i | \(-0.556901\pi\) |
0.763321 | + | 0.646019i | \(0.223567\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.8651 | − | 13.9463i | −0.791004 | − | 0.929752i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.86958 | − | 11.8985i | 0.455950 | − | 0.789728i | −0.542792 | − | 0.839867i | \(-0.682633\pi\) |
0.998742 | + | 0.0501387i | \(0.0159663\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.36743 | + | 3.36743i | −0.222526 | + | 0.222526i | −0.809561 | − | 0.587035i | \(-0.800295\pi\) |
0.587035 | + | 0.809561i | \(0.300295\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.12071 | + | 1.80174i | −0.205328 | + | 0.118546i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.1541 | + | 19.1541i | 1.25482 | + | 1.25482i | 0.953532 | + | 0.301293i | \(0.0974181\pi\) |
0.301293 | + | 0.953532i | \(0.402582\pi\) | |||||||
\(234\) | 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 | −0.975786 | − | 0.218727i | \(-0.929810\pi\) |
−0.218727 | − | 0.975786i | \(-0.570190\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.850786 | − | 0.227967i | 0.0548040 | − | 0.0146847i | −0.231313 | − | 0.972879i | \(-0.574302\pi\) |
0.286117 | + | 0.958195i | \(0.407635\pi\) | |||||||
\(242\) | 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 | 0.666844 | − | 0.745198i | \(-0.267645\pi\) |
−0.311938 | + | 0.950102i | \(0.600978\pi\) | |||||||
\(252\) | 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 | −0.0788324 | − | 0.996888i | \(-0.525119\pi\) |
−0.566715 | + | 0.823914i | \(0.691786\pi\) | |||||||
\(258\) | 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 | −0.0566092 | − | 0.998396i | \(-0.518029\pi\) |
−0.548223 | + | 0.836332i | \(0.684696\pi\) | |||||||
\(264\) | 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 | −0.0828917 | − | 0.996559i | \(-0.526416\pi\) |
−0.904491 | + | 0.426493i | \(0.859749\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.74484 | + | 17.7080i | −0.288228 | + | 1.07568i | 0.658220 | + | 0.752826i | \(0.271310\pi\) |
−0.946448 | + | 0.322856i | \(0.895357\pi\) | |||||||
\(272\) | 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 | 0.987580 | + | 0.157120i | \(0.0502208\pi\) |
−0.776709 | + | 0.629859i | \(0.783113\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.958804 | − | 0.256911i | 0.0574021 | − | 0.0153809i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.1478 | + | 17.1478i | 1.02295 | + | 1.02295i | 0.999730 | + | 0.0232200i | \(0.00739181\pi\) |
0.0232200 | + | 0.999730i | \(0.492608\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.37015 | − | 8.84554i | 0.140891 | − | 0.525813i | −0.859013 | − | 0.511954i | \(-0.828922\pi\) |
0.999904 | − | 0.0138586i | \(-0.00441148\pi\) | |||||||
\(284\) | 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 | −0.468250 | − | 0.883596i | \(-0.655115\pi\) |
0.999342 | − | 0.0362820i | \(-0.0115515\pi\) | |||||||
\(294\) | 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 | \(-0.704812\pi\) | ||
0.599948 | − | 0.800039i | \(-0.295188\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.8317 | + | 34.3495i | 1.12819 | + | 1.95408i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.5168i | 0.653060i | 0.945187 | + | 0.326530i | \(0.105879\pi\) | ||||
−0.945187 | + | 0.326530i | \(0.894121\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.3376 | + | 10.3376i | −0.584316 | + | 0.584316i | −0.936086 | − | 0.351771i | \(-0.885580\pi\) |
0.351771 | + | 0.936086i | \(0.385580\pi\) | |||||||
\(314\) | 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 | −0.498370 | − | 0.866965i | \(-0.666068\pi\) |
−0.00188163 | − | 0.999998i | \(-0.500599\pi\) | |||||||
\(332\) | 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 | −0.808624 | − | 0.588326i | \(-0.799787\pi\) |
0.588326 | + | 0.808624i | \(0.299787\pi\) | |||||||
\(338\) | 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 | −0.264616 | − | 0.964354i | \(-0.585245\pi\) |
0.253013 | + | 0.967463i | \(0.418578\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.9175 | − | 3.19329i | −0.637930 | − | 0.170933i | −0.0746643 | − | 0.997209i | \(-0.523789\pi\) |
−0.563266 | + | 0.826276i | \(0.690455\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.45083 | + | 5.65356i | −0.130816 | + | 0.301765i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.0318 | + | 6.36920i | −0.587162 | + | 0.338998i | −0.763975 | − | 0.645246i | \(-0.776755\pi\) |
0.176812 | + | 0.984245i | \(0.443421\pi\) | |||||||
\(354\) | 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 | −0.00625094 | − | 0.999980i | \(-0.501990\pi\) |
0.999980 | + | 0.00625094i | \(0.00198975\pi\) | |||||||
\(360\) | 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 | −0.672787 | − | 0.739837i | \(-0.734903\pi\) |
0.952569 | − | 0.304324i | \(-0.0984305\pi\) | |||||||
\(368\) | 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 | 0.988563 | − | 0.150805i | \(-0.0481867\pi\) |
−0.931524 | + | 0.363680i | \(0.881520\pi\) | |||||||
\(374\) | 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 | −0.855278 | − | 0.518169i | \(-0.826614\pi\) |
0.999777 | − | 0.0211086i | \(-0.00671957\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.5177 | − | 6.07241i | −0.538839 | − | 0.311099i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.6937 | − | 6.75134i | −0.597518 | − | 0.344977i | 0.170546 | − | 0.985350i | \(-0.445447\pi\) |
−0.768065 | + | 0.640372i | \(0.778780\pi\) | |||||||
\(384\) | 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 | 0.739110 | − | 0.673584i | \(-0.235246\pi\) |
−0.213786 | + | 0.976881i | \(0.568579\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.33500 | + | 1.34811i | 0.116896 | + | 0.0674900i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.23948 | + | 12.0899i | −0.161772 | + | 0.603740i | 0.836658 | + | 0.547725i | \(0.184506\pi\) |
−0.998430 | + | 0.0560149i | \(0.982161\pi\) | |||||||
\(402\) | 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 | 0.0509825 | − | 0.998700i | \(-0.483765\pi\) |
0.543502 | + | 0.839408i | \(0.317098\pi\) | |||||||
\(410\) | 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 | −0.642141 | − | 0.766586i | \(-0.721954\pi\) |
0.342813 | + | 0.939404i | \(0.388620\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.6378 | + | 12.6378i | −0.615930 | + | 0.615930i | −0.944485 | − | 0.328555i | \(-0.893438\pi\) |
0.328555 | + | 0.944485i | \(0.393438\pi\) | |||||||
\(422\) | 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 | 0.298660 | − | 0.954359i | \(-0.403460\pi\) |
−0.218532 | + | 0.975830i | \(0.570127\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.5451 | − | 4.16531i | 0.747052 | − | 0.200172i | 0.134842 | − | 0.990867i | \(-0.456947\pi\) |
0.612210 | + | 0.790695i | \(0.290281\pi\) | |||||||
\(434\) | 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 | 0.627718 | − | 0.778441i | \(-0.283989\pi\) |
−0.988008 | + | 0.154400i | \(0.950656\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 22.8934i | − | 1.09016i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.3798 | + | 13.3798i | −0.635694 | + | 0.635694i | −0.949490 | − | 0.313797i | \(-0.898399\pi\) |
0.313797 | + | 0.949490i | \(0.398399\pi\) | |||||||
\(444\) | 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 | −0.982196 | − | 0.187858i | \(-0.939846\pi\) |
0.756678 | − | 0.653788i | \(-0.226821\pi\) | |||||||
\(450\) | 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 | 0.634638 | − | 0.772809i | \(-0.281149\pi\) |
−0.986592 | + | 0.163208i | \(0.947816\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.41990 | − | 7.65549i | 0.206303 | − | 0.357328i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.12241 | + | 11.6530i | 0.145425 | + | 0.542734i | 0.999736 | + | 0.0229718i | \(0.00731278\pi\) |
−0.854311 | + | 0.519762i | \(0.826021\pi\) | |||||||
\(462\) | 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 | −0.995272 | − | 0.0971268i | \(-0.969035\pi\) |
0.0971268 | + | 0.995272i | \(0.469035\pi\) | |||||||
\(468\) | 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 | 0.374831 | − | 0.927093i | \(-0.377701\pi\) |
−0.138933 | + | 0.990302i | \(0.544367\pi\) | |||||||
\(480\) | 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 | −0.699735 | − | 0.714403i | \(-0.746699\pi\) |
0.968558 | + | 0.248787i | \(0.0800319\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.64173 | + | 9.64173i | −0.436014 | + | 0.436014i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.9915 | − | 9.81007i | 0.766817 | − | 0.442722i | −0.0649209 | − | 0.997890i | \(-0.520680\pi\) |
0.831738 | + | 0.555168i | \(0.187346\pi\) | |||||||
\(492\) | 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 | 0.989837 | + | 0.142203i | \(0.0454187\pi\) |
0.142203 | + | 0.989837i | \(0.454581\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.6153 | + | 5.25591i | −0.876347 | + | 0.234817i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.69726 | − | 13.7984i | −0.164853 | − | 0.615239i | −0.998059 | − | 0.0622762i | \(-0.980164\pi\) |
0.833206 | − | 0.552962i | \(-0.186503\pi\) | |||||||
\(504\) | 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 | −0.413653 | − | 0.910435i | \(-0.635747\pi\) |
0.813451 | − | 0.581633i | \(-0.197586\pi\) | |||||||
\(510\) | 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 | 0.634630 | − | 0.772816i | \(-0.281153\pi\) |
0.163197 | + | 0.986593i | \(0.447819\pi\) | |||||||
\(524\) | 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 | 0.111700 | − | 0.993742i | \(-0.464371\pi\) |
−0.993742 | + | 0.111700i | \(0.964371\pi\) | |||||||
\(542\) | 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 | −0.963135 | − | 0.269018i | \(-0.913301\pi\) |
−0.269018 | − | 0.963135i | \(-0.586699\pi\) | |||||||
\(548\) | 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 | −0.355727 | − | 0.934590i | \(-0.615767\pi\) |
0.631515 | + | 0.775364i | \(0.282434\pi\) | |||||||
\(558\) | 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 | 0.262415 | − | 0.964955i | \(-0.415481\pi\) |
0.709736 | + | 0.704468i | \(0.248814\pi\) | |||||||
\(564\) | 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 | 0.893738 | − | 0.448589i | \(-0.148073\pi\) |
−0.835358 | + | 0.549706i | \(0.814740\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 28.8794i | − | 1.20857i | −0.796769 | − | 0.604284i | \(-0.793459\pi\) | ||
0.796769 | − | 0.604284i | \(-0.206541\pi\) | |||||||
\(572\) | 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 | 0.916530 | − | 0.399967i | \(-0.130978\pi\) |
−0.804646 | + | 0.593754i | \(0.797645\pi\) | |||||||
\(588\) | 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 | \(-0.747450\pi\) | ||
0.701418 | − | 0.712750i | \(-0.252550\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.6867 | + | 20.2419i | 0.476710 | + | 0.825686i | 0.999644 | − | 0.0266875i | \(-0.00849591\pi\) |
−0.522934 | + | 0.852373i | \(0.675163\pi\) | |||||||
\(602\) | 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 | −0.829940 | − | 0.557853i | \(-0.811625\pi\) |
−0.439823 | + | 0.898085i | \(0.644959\pi\) | |||||||
\(608\) | 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 | 0.377146 | − | 0.926154i | \(-0.376905\pi\) |
0.990646 | + | 0.136458i | \(0.0435720\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.59622 | + | 1.91550i | −0.0643658 | + | 0.0772406i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.14533 | − | 12.3761i | 0.287660 | − | 0.498242i | −0.685591 | − | 0.727987i | \(-0.740456\pi\) |
0.973251 | + | 0.229745i | \(0.0737893\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.85038 | + | 6.85038i | −0.275340 | + | 0.275340i | −0.831245 | − | 0.555906i | \(-0.812372\pi\) |
0.555906 | + | 0.831245i | \(0.312372\pi\) | |||||||
\(620\) | 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 | 0.574921 | − | 0.818209i | \(-0.305033\pi\) |
0.907000 | + | 0.421130i | \(0.138366\pi\) | |||||||
\(632\) | 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 | 0.622503 | − | 0.782617i | \(-0.286116\pi\) |
−0.366515 | + | 0.930412i | \(0.619449\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.7800 | − | 11.9973i | −0.819482 | − | 0.473128i | 0.0307558 | − | 0.999527i | \(-0.490209\pi\) |
−0.850238 | + | 0.526399i | \(0.823542\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.7525 | + | 68.0044i | −0.462752 | + | 2.67767i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.5414 | + | 6.03995i | 0.886195 | + | 0.237455i | 0.673078 | − | 0.739572i | \(-0.264972\pi\) |
0.213117 | + | 0.977027i | \(0.431639\pi\) | |||||||
\(648\) | 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 | 0.634574 | − | 0.772862i | \(-0.281176\pi\) |
0.163126 | + | 0.986605i | \(0.447842\pi\) | |||||||
\(654\) | 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 | 0.731423 | − | 0.681924i | \(-0.238856\pi\) |
−0.224852 | + | 0.974393i | \(0.572190\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.43378 | − | 5.35096i | 0.0557677 | − | 0.208128i | −0.932420 | − | 0.361377i | \(-0.882307\pi\) |
0.988188 | + | 0.153249i | \(0.0489735\pi\) | |||||||
\(662\) | 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 | −0.611151 | − | 0.791514i | \(-0.709293\pi\) |
0.925029 | − | 0.379896i | \(-0.124040\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.66394 | − | 7.71969i | −0.141025 | − | 0.297131i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.4080 | + | 19.4080i | 0.745910 | + | 0.745910i | 0.973708 | − | 0.227798i | \(-0.0731527\pi\) |
−0.227798 | + | 0.973708i | \(0.573153\pi\) | |||||||
\(678\) | 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 | −0.999233 | − | 0.0391672i | \(-0.987530\pi\) |
0.533536 | + | 0.845777i | \(0.320863\pi\) | |||||||
\(684\) | 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 | 0.0327325 | − | 0.999464i | \(-0.489579\pi\) |
−0.471385 | + | 0.881928i | \(0.656246\pi\) | |||||||
\(692\) | 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 | \(0.131516\pi\) | ||||
−0.915853 | + | 0.401515i | \(0.868484\pi\) | |||||||
\(702\) | 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 | −0.987970 | − | 0.154644i | \(-0.950577\pi\) |
0.778285 | − | 0.627911i | \(-0.216090\pi\) | |||||||
\(710\) | 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 | −0.932812 | − | 0.360363i | \(-0.882653\pi\) |
0.778489 | + | 0.627658i | \(0.215986\pi\) | |||||||
\(720\) | 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 | −0.750495 | − | 0.660876i | \(-0.770185\pi\) |
0.660876 | + | 0.750495i | \(0.270185\pi\) | |||||||
\(728\) | 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 | \(0.204315\pi\) | ||||
−0.800974 | + | 0.598699i | \(0.795685\pi\) | |||||||
\(734\) | 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 | 0.948154 | − | 0.317810i | \(-0.102947\pi\) |
0.662221 | + | 0.749309i | \(0.269614\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.12945 | − | 10.4494i | −0.151699 | − | 0.383870i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.1203 | − | 7.57500i | 0.481336 | − | 0.277900i | −0.239637 | − | 0.970863i | \(-0.577028\pi\) |
0.720973 | + | 0.692963i | \(0.243695\pi\) | |||||||
\(744\) | 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 | −0.597185 | − | 0.802103i | \(-0.703714\pi\) |
0.396049 | + | 0.918229i | \(0.370381\pi\) | |||||||
\(752\) | 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 | 0.695751 | + | 0.718283i | \(0.255072\pi\) |
−0.961680 | + | 0.274176i | \(0.911595\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.01399 | − | 8.01399i | −0.290889 | − | 0.290889i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.4842 | − | 8.43618i | 1.14130 | − | 0.305811i | 0.361828 | − | 0.932245i | \(-0.382153\pi\) |
0.779475 | + | 0.626434i | \(0.215486\pi\) | |||||||
\(762\) | 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 | 0.446848 | + | 0.894610i | \(0.352547\pi\) |
−0.834286 | + | 0.551331i | \(0.814120\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.9490 | − | 13.8270i | −0.862503 | − | 0.497966i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.93793 | − | 1.11886i | −0.0697025 | − | 0.0402427i | 0.464744 | − | 0.885445i | \(-0.346146\pi\) |
−0.534446 | + | 0.845202i | \(0.679480\pi\) | |||||||
\(774\) | 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 | 0.986013 | − | 0.166669i | \(-0.0533013\pi\) |
0.348666 | + | 0.937247i | \(0.386635\pi\) | |||||||
\(788\) | 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 | 0.988305 | + | 0.152488i | \(0.0487286\pi\) |
−0.779653 | + | 0.626211i | \(0.784605\pi\) | |||||||
\(798\) | 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 | 0.0164333 | − | 0.999865i | \(-0.494769\pi\) |
0.874125 | + | 0.485701i | \(0.161436\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.1564 | + | 16.1564i | −0.567327 | + | 0.567327i | −0.931379 | − | 0.364052i | \(-0.881393\pi\) |
0.364052 | + | 0.931379i | \(0.381393\pi\) | |||||||
\(812\) | 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 | 0.677159 | − | 0.735837i | \(-0.263211\pi\) |
0.218518 | + | 0.975833i | \(0.429878\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.5702 | − | 10.8708i | 1.41419 | − | 0.378931i | 0.530770 | − | 0.847516i | \(-0.321903\pi\) |
0.883418 | + | 0.468585i | \(0.155236\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15.8608 | + | 13.4939i | −0.552202 | + | 0.469796i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.4948i | 1.68633i | 0.537655 | + | 0.843165i | \(0.319310\pi\) | ||||
−0.537655 | + | 0.843165i | \(0.680690\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.4336 | + | 35.3921i | 0.709689 | + | 1.22922i | 0.964973 | + | 0.262351i | \(0.0844978\pi\) |
−0.255284 | + | 0.966866i | \(0.582169\pi\) | |||||||
\(830\) | 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 | 0.961687 | + | 0.274149i | \(0.0883960\pi\) |
−0.695771 | + | 0.718263i | \(0.744937\pi\) | |||||||
\(840\) | 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 | −0.746717 | − | 0.665142i | \(-0.768371\pi\) |
0.665142 | + | 0.746717i | \(0.268371\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.237935i | 0.00811823i | 0.999992 | + | 0.00405912i | \(0.00129206\pi\) | ||||
−0.999992 | + | 0.00405912i | \(0.998708\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.482394 | − | 0.835530i | −0.0164399 | − | 0.0284748i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 48.8736i | − | 1.66368i | −0.555017 | − | 0.831839i | \(-0.687288\pi\) | ||
0.555017 | − | 0.831839i | \(-0.312712\pi\) | |||||||
\(864\) | 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 | −0.405725 | − | 0.913995i | \(-0.632981\pi\) |
0.994406 | − | 0.105629i | \(-0.0336856\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 33.1837 | − | 33.1837i | 1.11926 | − | 1.11926i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.6799 | + | 14.2489i | −0.831486 | + | 0.480058i | −0.854361 | − | 0.519680i | \(-0.826051\pi\) |
0.0228755 | + | 0.999738i | \(0.492718\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.7320 | − | 10.7320i | −0.361160 | − | 0.361160i | 0.503080 | − | 0.864240i | \(-0.332200\pi\) |
−0.864240 | + | 0.503080i | \(0.832200\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 67.0577 | + | 11.5888i | 2.25412 | + | 0.389555i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.36490 | + | 12.5580i | −0.112982 | + | 0.421655i | −0.999128 | − | 0.0417512i | \(-0.986706\pi\) |
0.886146 | + | 0.463406i | \(0.153373\pi\) | |||||||
\(888\) | 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 | 0.956804 | − | 0.290732i | \(-0.0938990\pi\) |
0.683251 | + | 0.730184i | \(0.260566\pi\) | |||||||
\(908\) | 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 | −0.00196918 | − | 0.999998i | \(-0.500627\pi\) |
−0.867008 | + | 0.498294i | \(0.833960\pi\) | |||||||
\(920\) | 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 | 0.156214 | − | 0.987723i | \(-0.450071\pi\) |
0.629147 | + | 0.777286i | \(0.283404\pi\) | |||||||
\(930\) | 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 | 0.987242 | − | 0.159228i | \(-0.0509005\pi\) |
−0.159228 | + | 0.987242i | \(0.550901\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.6792 | + | 18.8674i | −1.06645 | + | 0.615713i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.5969 | − | 27.5969i | 0.899632 | − | 0.899632i | −0.0957715 | − | 0.995403i | \(-0.530532\pi\) |
0.995403 | + | 0.0957715i | \(0.0305318\pi\) | |||||||
\(942\) | 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 | −0.999910 | − | 0.0134210i | \(-0.995728\pi\) |
−0.488332 | + | 0.872658i | \(0.662394\pi\) | |||||||
\(948\) | 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 | −0.908509 | − | 0.417865i | \(-0.862779\pi\) |
−0.577860 | + | 0.816136i | \(0.696112\pi\) | |||||||
\(954\) | 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 | −0.875457 | − | 0.483296i | \(-0.839440\pi\) |
0.856275 | + | 0.516520i | \(0.172773\pi\) | |||||||
\(972\) | 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 | 0.703714 | − | 0.710483i | \(-0.251524\pi\) |
−0.967154 | + | 0.254193i | \(0.918190\pi\) | |||||||
\(978\) | 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 | 0.876342 | − | 0.481690i | \(-0.159977\pi\) |
−0.855327 | + | 0.518089i | \(0.826643\pi\) | |||||||
\(992\) | 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 | 0.548972 | − | 0.835841i | \(-0.315019\pi\) |
0.893344 | + | 0.449373i | \(0.148353\pi\) | |||||||
\(998\) | 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.197.5 | yes | 20 | |
5.2 | odd | 4 | 1300.2.bn.d.93.5 | 20 | |||
5.3 | odd | 4 | 260.2.bf.c.93.1 | ✓ | 20 | ||
5.4 | even | 2 | 1300.2.bs.d.457.1 | 20 | |||
13.7 | odd | 12 | 260.2.bf.c.137.1 | yes | 20 | ||
65.7 | even | 12 | 1300.2.bs.d.293.1 | 20 | |||
65.33 | even | 12 | inner | 260.2.bk.c.33.5 | yes | 20 | |
65.59 | odd | 12 | 1300.2.bn.d.657.5 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.bf.c.93.1 | ✓ | 20 | 5.3 | odd | 4 | ||
260.2.bf.c.137.1 | yes | 20 | 13.7 | odd | 12 | ||
260.2.bk.c.33.5 | yes | 20 | 65.33 | even | 12 | inner | |
260.2.bk.c.197.5 | yes | 20 | 1.1 | even | 1 | trivial | |
1300.2.bn.d.93.5 | 20 | 5.2 | odd | 4 | |||
1300.2.bn.d.657.5 | 20 | 65.59 | odd | 12 | |||
1300.2.bs.d.293.1 | 20 | 65.7 | even | 12 | |||
1300.2.bs.d.457.1 | 20 | 5.4 | even | 2 |