Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(163,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.163");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.w (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 163.2 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.163 |
Dual form | 360.2.w.a.307.1 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 1.00000i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | 2.12132 | − | 0.707107i | 0.948683 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | + | 1.00000i | 0.377964 | + | 0.377964i | 0.870367 | − | 0.492403i | \(-0.163881\pi\) |
−0.492403 | + | 0.870367i | \(0.663881\pi\) | |||||||
\(8\) | − | 2.82843i | − | 1.00000i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | + | 3.00000i | 0.316228 | + | 0.948683i | ||||
\(11\) | 4.24264 | 1.27920 | 0.639602 | − | 0.768706i | \(-0.279099\pi\) | ||||
0.639602 | + | 0.768706i | \(0.279099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | + | 2.00000i | −0.554700 | + | 0.554700i | −0.927794 | − | 0.373094i | \(-0.878297\pi\) |
0.373094 | + | 0.927794i | \(0.378297\pi\) | |||||||
\(14\) | −1.41421 | + | 1.41421i | −0.377964 | + | 0.377964i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | 2.82843 | − | 2.82843i | 0.685994 | − | 0.685994i | −0.275350 | − | 0.961344i | \(-0.588794\pi\) |
0.961344 | + | 0.275350i | \(0.0887937\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00000i | 1.37649i | 0.725476 | + | 0.688247i | \(0.241620\pi\) | ||||
−0.725476 | + | 0.688247i | \(0.758380\pi\) | |||||||
\(20\) | −4.24264 | + | 1.41421i | −0.948683 | + | 0.316228i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.00000i | 1.27920i | ||||||||
\(23\) | −1.41421 | + | 1.41421i | −0.294884 | + | 0.294884i | −0.839006 | − | 0.544122i | \(-0.816863\pi\) |
0.544122 | + | 0.839006i | \(0.316863\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | − | 3.00000i | 0.800000 | − | 0.600000i | ||||
\(26\) | −2.82843 | − | 2.82843i | −0.554700 | − | 0.554700i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | − | 2.00000i | −0.377964 | − | 0.377964i | ||||
\(29\) | −4.24264 | −0.787839 | −0.393919 | − | 0.919145i | \(-0.628881\pi\) | ||||
−0.393919 | + | 0.919145i | \(0.628881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000i | 1.07763i | 0.842424 | + | 0.538816i | \(0.181128\pi\) | ||||
−0.842424 | + | 0.538816i | \(0.818872\pi\) | |||||||
\(32\) | 5.65685i | 1.00000i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.00000 | + | 4.00000i | 0.685994 | + | 0.685994i | ||||
\(35\) | 2.82843 | + | 1.41421i | 0.478091 | + | 0.239046i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.00000 | − | 8.00000i | −1.31519 | − | 1.31519i | −0.917534 | − | 0.397658i | \(-0.869823\pi\) |
−0.397658 | − | 0.917534i | \(-0.630177\pi\) | |||||||
\(38\) | −8.48528 | −1.37649 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.00000 | − | 6.00000i | −0.316228 | − | 0.948683i | ||||
\(41\) | 8.48528 | 1.32518 | 0.662589 | − | 0.748983i | \(-0.269458\pi\) | ||||
0.662589 | + | 0.748983i | \(0.269458\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | − | 2.00000i | −0.304997 | − | 0.304997i | 0.537968 | − | 0.842965i | \(-0.319192\pi\) |
−0.842965 | + | 0.537968i | \(0.819192\pi\) | |||||||
\(44\) | −8.48528 | −1.27920 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.00000 | − | 2.00000i | −0.294884 | − | 0.294884i | ||||
\(47\) | 1.41421 | + | 1.41421i | 0.206284 | + | 0.206284i | 0.802686 | − | 0.596402i | \(-0.203403\pi\) |
−0.596402 | + | 0.802686i | \(0.703403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.00000i | − | 0.714286i | ||||||
\(50\) | 4.24264 | + | 5.65685i | 0.600000 | + | 0.800000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.00000 | − | 4.00000i | 0.554700 | − | 0.554700i | ||||
\(53\) | −1.41421 | + | 1.41421i | −0.194257 | + | 0.194257i | −0.797533 | − | 0.603276i | \(-0.793862\pi\) |
0.603276 | + | 0.797533i | \(0.293862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.00000 | − | 3.00000i | 1.21356 | − | 0.404520i | ||||
\(56\) | 2.82843 | − | 2.82843i | 0.377964 | − | 0.377964i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 6.00000i | − | 0.787839i | ||||||
\(59\) | − | 9.89949i | − | 1.28880i | −0.764687 | − | 0.644402i | \(-0.777106\pi\) | ||
0.764687 | − | 0.644402i | \(-0.222894\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | −8.48528 | −1.07763 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −2.82843 | + | 5.65685i | −0.350823 | + | 0.701646i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.00000 | + | 8.00000i | −0.977356 | + | 0.977356i | −0.999749 | − | 0.0223937i | \(-0.992871\pi\) |
0.0223937 | + | 0.999749i | \(0.492871\pi\) | |||||||
\(68\) | −5.65685 | + | 5.65685i | −0.685994 | + | 0.685994i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.00000 | + | 4.00000i | −0.239046 | + | 0.478091i | ||||
\(71\) | − | 14.1421i | − | 1.67836i | −0.543852 | − | 0.839181i | \(-0.683035\pi\) | ||
0.543852 | − | 0.839181i | \(-0.316965\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.00000 | − | 5.00000i | −0.585206 | − | 0.585206i | 0.351123 | − | 0.936329i | \(-0.385800\pi\) |
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 11.3137 | − | 11.3137i | 1.31519 | − | 1.31519i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 12.0000i | − | 1.37649i | ||||||
\(77\) | 4.24264 | + | 4.24264i | 0.483494 | + | 0.483494i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.0000 | 1.57512 | 0.787562 | − | 0.616236i | \(-0.211343\pi\) | ||||
0.787562 | + | 0.616236i | \(0.211343\pi\) | |||||||
\(80\) | 8.48528 | − | 2.82843i | 0.948683 | − | 0.316228i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.0000i | 1.32518i | ||||||||
\(83\) | 1.41421 | + | 1.41421i | 0.155230 | + | 0.155230i | 0.780449 | − | 0.625219i | \(-0.214990\pi\) |
−0.625219 | + | 0.780449i | \(0.714990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | − | 8.00000i | 0.433861 | − | 0.867722i | ||||
\(86\) | 2.82843 | − | 2.82843i | 0.304997 | − | 0.304997i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 12.0000i | − | 1.27920i | ||||||
\(89\) | 2.82843i | 0.299813i | 0.988700 | + | 0.149906i | \(0.0478972\pi\) | ||||
−0.988700 | + | 0.149906i | \(0.952103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | 2.82843 | − | 2.82843i | 0.294884 | − | 0.294884i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.00000 | + | 2.00000i | −0.206284 | + | 0.206284i | ||||
\(95\) | 4.24264 | + | 12.7279i | 0.435286 | + | 1.30586i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00000 | − | 7.00000i | 0.710742 | − | 0.710742i | −0.255948 | − | 0.966691i | \(-0.582388\pi\) |
0.966691 | + | 0.255948i | \(0.0823876\pi\) | |||||||
\(98\) | 7.07107 | 0.714286 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.00000 | + | 6.00000i | −0.800000 | + | 0.600000i | ||||
\(101\) | − | 1.41421i | − | 0.140720i | −0.997522 | − | 0.0703598i | \(-0.977585\pi\) | ||
0.997522 | − | 0.0703598i | \(-0.0224147\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.00000 | + | 5.00000i | −0.492665 | + | 0.492665i | −0.909145 | − | 0.416480i | \(-0.863264\pi\) |
0.416480 | + | 0.909145i | \(0.363264\pi\) | |||||||
\(104\) | 5.65685 | + | 5.65685i | 0.554700 | + | 0.554700i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | − | 2.00000i | −0.194257 | − | 0.194257i | ||||
\(107\) | −9.89949 | + | 9.89949i | −0.957020 | + | 0.957020i | −0.999114 | − | 0.0420934i | \(-0.986597\pi\) |
0.0420934 | + | 0.999114i | \(0.486597\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.00000 | −0.383131 | −0.191565 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(110\) | 4.24264 | + | 12.7279i | 0.404520 | + | 1.21356i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.00000 | + | 4.00000i | 0.377964 | + | 0.377964i | ||||
\(113\) | −11.3137 | − | 11.3137i | −1.06430 | − | 1.06430i | −0.997785 | − | 0.0665190i | \(-0.978811\pi\) |
−0.0665190 | − | 0.997785i | \(-0.521189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.00000 | + | 4.00000i | −0.186501 | + | 0.373002i | ||||
\(116\) | 8.48528 | 0.787839 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.0000 | 1.28880 | ||||||||
\(119\) | 5.65685 | 0.518563 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 12.0000i | − | 1.07763i | ||||||
\(125\) | 6.36396 | − | 9.19239i | 0.569210 | − | 0.822192i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.0000 | − | 11.0000i | −0.976092 | − | 0.976092i | 0.0236286 | − | 0.999721i | \(-0.492478\pi\) |
−0.999721 | + | 0.0236286i | \(0.992478\pi\) | |||||||
\(128\) | − | 11.3137i | − | 1.00000i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.00000 | − | 4.00000i | −0.701646 | − | 0.350823i | ||||
\(131\) | −12.7279 | −1.11204 | −0.556022 | − | 0.831168i | \(-0.687673\pi\) | ||||
−0.556022 | + | 0.831168i | \(0.687673\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | + | 6.00000i | −0.520266 | + | 0.520266i | ||||
\(134\) | −11.3137 | − | 11.3137i | −0.977356 | − | 0.977356i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.00000 | − | 8.00000i | −0.685994 | − | 0.685994i | ||||
\(137\) | −5.65685 | + | 5.65685i | −0.483298 | + | 0.483298i | −0.906183 | − | 0.422885i | \(-0.861017\pi\) |
0.422885 | + | 0.906183i | \(0.361017\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.00000i | − | 0.508913i | −0.967084 | − | 0.254457i | \(-0.918103\pi\) | ||
0.967084 | − | 0.254457i | \(-0.0818966\pi\) | |||||||
\(140\) | −5.65685 | − | 2.82843i | −0.478091 | − | 0.239046i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 20.0000 | 1.67836 | ||||||||
\(143\) | −8.48528 | + | 8.48528i | −0.709575 | + | 0.709575i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.00000 | + | 3.00000i | −0.747409 | + | 0.249136i | ||||
\(146\) | 7.07107 | − | 7.07107i | 0.585206 | − | 0.585206i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 16.0000 | + | 16.0000i | 1.31519 | + | 1.31519i | ||||
\(149\) | −12.7279 | −1.04271 | −0.521356 | − | 0.853339i | \(-0.674574\pi\) | ||||
−0.521356 | + | 0.853339i | \(0.674574\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000i | 0.976546i | 0.872691 | + | 0.488273i | \(0.162373\pi\) | ||||
−0.872691 | + | 0.488273i | \(0.837627\pi\) | |||||||
\(152\) | 16.9706 | 1.37649 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.00000 | + | 6.00000i | −0.483494 | + | 0.483494i | ||||
\(155\) | 4.24264 | + | 12.7279i | 0.340777 | + | 1.02233i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.00000 | − | 8.00000i | −0.638470 | − | 0.638470i | 0.311708 | − | 0.950178i | \(-0.399099\pi\) |
−0.950178 | + | 0.311708i | \(0.899099\pi\) | |||||||
\(158\) | 19.7990i | 1.57512i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.00000 | + | 12.0000i | 0.316228 | + | 0.948683i | ||||
\(161\) | −2.82843 | −0.222911 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0000 | + | 10.0000i | 0.783260 | + | 0.783260i | 0.980380 | − | 0.197119i | \(-0.0631586\pi\) |
−0.197119 | + | 0.980380i | \(0.563159\pi\) | |||||||
\(164\) | −16.9706 | −1.32518 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.00000 | + | 2.00000i | −0.155230 | + | 0.155230i | ||||
\(167\) | −15.5563 | − | 15.5563i | −1.20379 | − | 1.20379i | −0.973006 | − | 0.230781i | \(-0.925872\pi\) |
−0.230781 | − | 0.973006i | \(-0.574128\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000i | 0.384615i | ||||||||
\(170\) | 11.3137 | + | 5.65685i | 0.867722 | + | 0.433861i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.00000 | + | 4.00000i | 0.304997 | + | 0.304997i | ||||
\(173\) | 2.82843 | − | 2.82843i | 0.215041 | − | 0.215041i | −0.591364 | − | 0.806405i | \(-0.701410\pi\) |
0.806405 | + | 0.591364i | \(0.201410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.00000 | + | 1.00000i | 0.529150 | + | 0.0755929i | ||||
\(176\) | 16.9706 | 1.27920 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.00000 | −0.299813 | ||||||||
\(179\) | − | 9.89949i | − | 0.739923i | −0.929047 | − | 0.369961i | \(-0.879371\pi\) | ||
0.929047 | − | 0.369961i | \(-0.120629\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.0000i | 1.78391i | 0.452128 | + | 0.891953i | \(0.350665\pi\) | ||||
−0.452128 | + | 0.891953i | \(0.649335\pi\) | |||||||
\(182\) | − | 5.65685i | − | 0.419314i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.00000 | + | 4.00000i | 0.294884 | + | 0.294884i | ||||
\(185\) | −22.6274 | − | 11.3137i | −1.66360 | − | 0.831800i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.0000 | − | 12.0000i | 0.877527 | − | 0.877527i | ||||
\(188\) | −2.82843 | − | 2.82843i | −0.206284 | − | 0.206284i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.0000 | + | 6.00000i | −1.30586 | + | 0.435286i | ||||
\(191\) | 11.3137i | 0.818631i | 0.912393 | + | 0.409316i | \(0.134232\pi\) | ||||
−0.912393 | + | 0.409316i | \(0.865768\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.0000 | + | 13.0000i | 0.935760 | + | 0.935760i | 0.998058 | − | 0.0622972i | \(-0.0198427\pi\) |
−0.0622972 | + | 0.998058i | \(0.519843\pi\) | |||||||
\(194\) | 9.89949 | + | 9.89949i | 0.710742 | + | 0.710742i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.0000i | 0.714286i | ||||||||
\(197\) | 9.89949 | + | 9.89949i | 0.705310 | + | 0.705310i | 0.965545 | − | 0.260235i | \(-0.0838002\pi\) |
−0.260235 | + | 0.965545i | \(0.583800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | −8.48528 | − | 11.3137i | −0.600000 | − | 0.800000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.00000 | 0.140720 | ||||||||
\(203\) | −4.24264 | − | 4.24264i | −0.297775 | − | 0.297775i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.0000 | − | 6.00000i | 1.25717 | − | 0.419058i | ||||
\(206\) | −7.07107 | − | 7.07107i | −0.492665 | − | 0.492665i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.00000 | + | 8.00000i | −0.554700 | + | 0.554700i | ||||
\(209\) | 25.4558i | 1.76082i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | 0.137686 | 0.0688428 | − | 0.997628i | \(-0.478069\pi\) | ||||
0.0688428 | + | 0.997628i | \(0.478069\pi\) | |||||||
\(212\) | 2.82843 | − | 2.82843i | 0.194257 | − | 0.194257i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.0000 | − | 14.0000i | −0.957020 | − | 0.957020i | ||||
\(215\) | −5.65685 | − | 2.82843i | −0.385794 | − | 0.192897i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | + | 6.00000i | −0.407307 | + | 0.407307i | ||||
\(218\) | − | 5.65685i | − | 0.383131i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −18.0000 | + | 6.00000i | −1.21356 | + | 0.404520i | ||||
\(221\) | 11.3137i | 0.761042i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.0000 | + | 11.0000i | −0.736614 | + | 0.736614i | −0.971921 | − | 0.235307i | \(-0.924391\pi\) |
0.235307 | + | 0.971921i | \(0.424391\pi\) | |||||||
\(224\) | −5.65685 | + | 5.65685i | −0.377964 | + | 0.377964i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.0000 | − | 16.0000i | 1.06430 | − | 1.06430i | ||||
\(227\) | −5.65685 | + | 5.65685i | −0.375459 | + | 0.375459i | −0.869461 | − | 0.494002i | \(-0.835534\pi\) |
0.494002 | + | 0.869461i | \(0.335534\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.0000 | 1.32164 | 0.660819 | − | 0.750546i | \(-0.270209\pi\) | ||||
0.660819 | + | 0.750546i | \(0.270209\pi\) | |||||||
\(230\) | −5.65685 | − | 2.82843i | −0.373002 | − | 0.186501i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.0000i | 0.787839i | ||||||||
\(233\) | 5.65685 | + | 5.65685i | 0.370593 | + | 0.370593i | 0.867693 | − | 0.497100i | \(-0.165602\pi\) |
−0.497100 | + | 0.867693i | \(0.665602\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | + | 2.00000i | 0.260931 | + | 0.130466i | ||||
\(236\) | 19.7990i | 1.28880i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.00000i | 0.518563i | ||||||||
\(239\) | 25.4558 | 1.64660 | 0.823301 | − | 0.567605i | \(-0.192130\pi\) | ||||
0.823301 | + | 0.567605i | \(0.192130\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.0000 | −1.03065 | −0.515325 | − | 0.856995i | \(-0.672329\pi\) | ||||
−0.515325 | + | 0.856995i | \(0.672329\pi\) | |||||||
\(242\) | 9.89949i | 0.636364i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.53553 | − | 10.6066i | −0.225877 | − | 0.677631i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.0000 | − | 12.0000i | −0.763542 | − | 0.763542i | ||||
\(248\) | 16.9706 | 1.07763 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.0000 | + | 9.00000i | 0.822192 | + | 0.569210i | ||||
\(251\) | −12.7279 | −0.803379 | −0.401690 | − | 0.915776i | \(-0.631577\pi\) | ||||
−0.401690 | + | 0.915776i | \(0.631577\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | + | 6.00000i | −0.377217 | + | 0.377217i | ||||
\(254\) | 15.5563 | − | 15.5563i | 0.976092 | − | 0.976092i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 19.7990 | − | 19.7990i | 1.23503 | − | 1.23503i | 0.273018 | − | 0.962009i | \(-0.411978\pi\) |
0.962009 | − | 0.273018i | \(-0.0880219\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 16.0000i | − | 0.994192i | ||||||
\(260\) | 5.65685 | − | 11.3137i | 0.350823 | − | 0.701646i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 18.0000i | − | 1.11204i | ||||||
\(263\) | 7.07107 | − | 7.07107i | 0.436021 | − | 0.436021i | −0.454650 | − | 0.890670i | \(-0.650236\pi\) |
0.890670 | + | 0.454650i | \(0.150236\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.00000 | + | 4.00000i | −0.122859 | + | 0.245718i | ||||
\(266\) | −8.48528 | − | 8.48528i | −0.520266 | − | 0.520266i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 16.0000 | − | 16.0000i | 0.977356 | − | 0.977356i | ||||
\(269\) | −21.2132 | −1.29339 | −0.646696 | − | 0.762748i | \(-0.723850\pi\) | ||||
−0.646696 | + | 0.762748i | \(0.723850\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 12.0000i | − | 0.728948i | −0.931214 | − | 0.364474i | \(-0.881249\pi\) | ||
0.931214 | − | 0.364474i | \(-0.118751\pi\) | |||||||
\(272\) | 11.3137 | − | 11.3137i | 0.685994 | − | 0.685994i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.00000 | − | 8.00000i | −0.483298 | − | 0.483298i | ||||
\(275\) | 16.9706 | − | 12.7279i | 1.02336 | − | 0.767523i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.00000 | + | 4.00000i | 0.240337 | + | 0.240337i | 0.816989 | − | 0.576653i | \(-0.195641\pi\) |
−0.576653 | + | 0.816989i | \(0.695641\pi\) | |||||||
\(278\) | 8.48528 | 0.508913 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.00000 | − | 8.00000i | 0.239046 | − | 0.478091i | ||||
\(281\) | 16.9706 | 1.01238 | 0.506189 | − | 0.862422i | \(-0.331054\pi\) | ||||
0.506189 | + | 0.862422i | \(0.331054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.00000 | − | 8.00000i | −0.475551 | − | 0.475551i | 0.428155 | − | 0.903705i | \(-0.359164\pi\) |
−0.903705 | + | 0.428155i | \(0.859164\pi\) | |||||||
\(284\) | 28.2843i | 1.67836i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.0000 | − | 12.0000i | −0.709575 | − | 0.709575i | ||||
\(287\) | 8.48528 | + | 8.48528i | 0.500870 | + | 0.500870i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000i | 0.0588235i | ||||||||
\(290\) | −4.24264 | − | 12.7279i | −0.249136 | − | 0.747409i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.0000 | + | 10.0000i | 0.585206 | + | 0.585206i | ||||
\(293\) | 15.5563 | − | 15.5563i | 0.908812 | − | 0.908812i | −0.0873648 | − | 0.996176i | \(-0.527845\pi\) |
0.996176 | + | 0.0873648i | \(0.0278446\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.00000 | − | 21.0000i | −0.407556 | − | 1.22267i | ||||
\(296\) | −22.6274 | + | 22.6274i | −1.31519 | + | 1.31519i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 18.0000i | − | 1.04271i | ||||||
\(299\) | − | 5.65685i | − | 0.327144i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 4.00000i | − | 0.230556i | ||||||
\(302\) | −16.9706 | −0.976546 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 24.0000i | 1.37649i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0000 | − | 10.0000i | 0.570730 | − | 0.570730i | −0.361602 | − | 0.932332i | \(-0.617770\pi\) |
0.932332 | + | 0.361602i | \(0.117770\pi\) | |||||||
\(308\) | −8.48528 | − | 8.48528i | −0.483494 | − | 0.483494i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −18.0000 | + | 6.00000i | −1.02233 | + | 0.340777i | ||||
\(311\) | − | 31.1127i | − | 1.76424i | −0.471025 | − | 0.882120i | \(-0.656116\pi\) | ||
0.471025 | − | 0.882120i | \(-0.343884\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.00000 | + | 1.00000i | 0.0565233 | + | 0.0565233i | 0.734803 | − | 0.678280i | \(-0.237274\pi\) |
−0.678280 | + | 0.734803i | \(0.737274\pi\) | |||||||
\(314\) | 11.3137 | − | 11.3137i | 0.638470 | − | 0.638470i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −28.0000 | −1.57512 | ||||||||
\(317\) | 5.65685 | + | 5.65685i | 0.317721 | + | 0.317721i | 0.847891 | − | 0.530170i | \(-0.177872\pi\) |
−0.530170 | + | 0.847891i | \(0.677872\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0000 | −1.00781 | ||||||||
\(320\) | −16.9706 | + | 5.65685i | −0.948683 | + | 0.316228i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 4.00000i | − | 0.222911i | ||||||
\(323\) | 16.9706 | + | 16.9706i | 0.944267 | + | 0.944267i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.00000 | + | 14.0000i | −0.110940 | + | 0.776580i | ||||
\(326\) | −14.1421 | + | 14.1421i | −0.783260 | + | 0.783260i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 24.0000i | − | 1.32518i | ||||||
\(329\) | 2.82843i | 0.155936i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | 0.109930 | 0.0549650 | − | 0.998488i | \(-0.482495\pi\) | ||||
0.0549650 | + | 0.998488i | \(0.482495\pi\) | |||||||
\(332\) | −2.82843 | − | 2.82843i | −0.155230 | − | 0.155230i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 22.0000 | − | 22.0000i | 1.20379 | − | 1.20379i | ||||
\(335\) | −11.3137 | + | 22.6274i | −0.618134 | + | 1.23627i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.0000 | + | 17.0000i | −0.926049 | + | 0.926049i | −0.997448 | − | 0.0713988i | \(-0.977254\pi\) |
0.0713988 | + | 0.997448i | \(0.477254\pi\) | |||||||
\(338\) | −7.07107 | −0.384615 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.00000 | + | 16.0000i | −0.433861 | + | 0.867722i | ||||
\(341\) | 25.4558i | 1.37851i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | − | 12.0000i | 0.647939 | − | 0.647939i | ||||
\(344\) | −5.65685 | + | 5.65685i | −0.304997 | + | 0.304997i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.00000 | + | 4.00000i | 0.215041 | + | 0.215041i | ||||
\(347\) | 11.3137 | − | 11.3137i | 0.607352 | − | 0.607352i | −0.334901 | − | 0.942253i | \(-0.608703\pi\) |
0.942253 | + | 0.334901i | \(0.108703\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.0000 | 1.07058 | 0.535288 | − | 0.844670i | \(-0.320203\pi\) | ||||
0.535288 | + | 0.844670i | \(0.320203\pi\) | |||||||
\(350\) | −1.41421 | + | 9.89949i | −0.0755929 | + | 0.529150i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 24.0000i | 1.27920i | ||||||||
\(353\) | 5.65685 | + | 5.65685i | 0.301084 | + | 0.301084i | 0.841438 | − | 0.540354i | \(-0.181710\pi\) |
−0.540354 | + | 0.841438i | \(0.681710\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.0000 | − | 30.0000i | −0.530745 | − | 1.59223i | ||||
\(356\) | − | 5.65685i | − | 0.299813i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.0000 | 0.739923 | ||||||||
\(359\) | 8.48528 | 0.447836 | 0.223918 | − | 0.974608i | \(-0.428115\pi\) | ||||
0.223918 | + | 0.974608i | \(0.428115\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | −33.9411 | −1.78391 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.00000 | 0.419314 | ||||||||
\(365\) | −14.1421 | − | 7.07107i | −0.740233 | − | 0.370117i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.00000 | − | 5.00000i | −0.260998 | − | 0.260998i | 0.564462 | − | 0.825459i | \(-0.309084\pi\) |
−0.825459 | + | 0.564462i | \(0.809084\pi\) | |||||||
\(368\) | −5.65685 | + | 5.65685i | −0.294884 | + | 0.294884i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 16.0000 | − | 32.0000i | 0.831800 | − | 1.66360i | ||||
\(371\) | −2.82843 | −0.146845 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.0000 | − | 16.0000i | 0.828449 | − | 0.828449i | −0.158854 | − | 0.987302i | \(-0.550780\pi\) |
0.987302 | + | 0.158854i | \(0.0507798\pi\) | |||||||
\(374\) | 16.9706 | + | 16.9706i | 0.877527 | + | 0.877527i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.00000 | − | 4.00000i | 0.206284 | − | 0.206284i | ||||
\(377\) | 8.48528 | − | 8.48528i | 0.437014 | − | 0.437014i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.0000i | 0.924598i | 0.886724 | + | 0.462299i | \(0.152975\pi\) | ||||
−0.886724 | + | 0.462299i | \(0.847025\pi\) | |||||||
\(380\) | −8.48528 | − | 25.4558i | −0.435286 | − | 1.30586i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16.0000 | −0.818631 | ||||||||
\(383\) | −18.3848 | + | 18.3848i | −0.939418 | + | 0.939418i | −0.998267 | − | 0.0588487i | \(-0.981257\pi\) |
0.0588487 | + | 0.998267i | \(0.481257\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.0000 | + | 6.00000i | 0.611577 | + | 0.305788i | ||||
\(386\) | −18.3848 | + | 18.3848i | −0.935760 | + | 0.935760i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.0000 | + | 14.0000i | −0.710742 | + | 0.710742i | ||||
\(389\) | 4.24264 | 0.215110 | 0.107555 | − | 0.994199i | \(-0.465698\pi\) | ||||
0.107555 | + | 0.994199i | \(0.465698\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000i | 0.404577i | ||||||||
\(392\) | −14.1421 | −0.714286 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.0000 | + | 14.0000i | −0.705310 | + | 0.705310i | ||||
\(395\) | 29.6985 | − | 9.89949i | 1.49429 | − | 0.498098i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0000 | + | 10.0000i | 0.501886 | + | 0.501886i | 0.912024 | − | 0.410138i | \(-0.134519\pi\) |
−0.410138 | + | 0.912024i | \(0.634519\pi\) | |||||||
\(398\) | − | 5.65685i | − | 0.283552i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.0000 | − | 12.0000i | 0.800000 | − | 0.600000i | ||||
\(401\) | 8.48528 | 0.423735 | 0.211867 | − | 0.977298i | \(-0.432046\pi\) | ||||
0.211867 | + | 0.977298i | \(0.432046\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0000 | − | 12.0000i | −0.597763 | − | 0.597763i | ||||
\(404\) | 2.82843i | 0.140720i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.00000 | − | 6.00000i | 0.297775 | − | 0.297775i | ||||
\(407\) | −33.9411 | − | 33.9411i | −1.68240 | − | 1.68240i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.0000i | 0.593362i | 0.954977 | + | 0.296681i | \(0.0958798\pi\) | ||||
−0.954977 | + | 0.296681i | \(0.904120\pi\) | |||||||
\(410\) | 8.48528 | + | 25.4558i | 0.419058 | + | 1.25717i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.0000 | − | 10.0000i | 0.492665 | − | 0.492665i | ||||
\(413\) | 9.89949 | − | 9.89949i | 0.487122 | − | 0.487122i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.00000 | + | 2.00000i | 0.196352 | + | 0.0981761i | ||||
\(416\) | −11.3137 | − | 11.3137i | −0.554700 | − | 0.554700i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −36.0000 | −1.76082 | ||||||||
\(419\) | − | 9.89949i | − | 0.483622i | −0.970323 | − | 0.241811i | \(-0.922259\pi\) | ||
0.970323 | − | 0.241811i | \(-0.0777414\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 12.0000i | − | 0.584844i | −0.956289 | − | 0.292422i | \(-0.905539\pi\) | ||
0.956289 | − | 0.292422i | \(-0.0944612\pi\) | |||||||
\(422\) | 2.82843i | 0.137686i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.00000 | + | 4.00000i | 0.194257 | + | 0.194257i | ||||
\(425\) | 2.82843 | − | 19.7990i | 0.137199 | − | 0.960392i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 19.7990 | − | 19.7990i | 0.957020 | − | 0.957020i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.00000 | − | 8.00000i | 0.192897 | − | 0.385794i | ||||
\(431\) | 36.7696i | 1.77113i | 0.464518 | + | 0.885564i | \(0.346227\pi\) | ||||
−0.464518 | + | 0.885564i | \(0.653773\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.0000 | − | 23.0000i | −1.10531 | − | 1.10531i | −0.993759 | − | 0.111551i | \(-0.964418\pi\) |
−0.111551 | − | 0.993759i | \(-0.535582\pi\) | |||||||
\(434\) | −8.48528 | − | 8.48528i | −0.407307 | − | 0.407307i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.00000 | 0.383131 | ||||||||
\(437\) | −8.48528 | − | 8.48528i | −0.405906 | − | 0.405906i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.00000 | −0.190910 | −0.0954548 | − | 0.995434i | \(-0.530431\pi\) | ||||
−0.0954548 | + | 0.995434i | \(0.530431\pi\) | |||||||
\(440\) | −8.48528 | − | 25.4558i | −0.404520 | − | 1.21356i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16.0000 | −0.761042 | ||||||||
\(443\) | 22.6274 | + | 22.6274i | 1.07506 | + | 1.07506i | 0.996944 | + | 0.0781168i | \(0.0248907\pi\) |
0.0781168 | + | 0.996944i | \(0.475109\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.00000 | + | 6.00000i | 0.0948091 | + | 0.284427i | ||||
\(446\) | −15.5563 | − | 15.5563i | −0.736614 | − | 0.736614i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.00000 | − | 8.00000i | −0.377964 | − | 0.377964i | ||||
\(449\) | 11.3137i | 0.533927i | 0.963707 | + | 0.266963i | \(0.0860203\pi\) | ||||
−0.963707 | + | 0.266963i | \(0.913980\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.0000 | 1.69517 | ||||||||
\(452\) | 22.6274 | + | 22.6274i | 1.06430 | + | 1.06430i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.00000 | − | 8.00000i | −0.375459 | − | 0.375459i | ||||
\(455\) | −8.48528 | + | 2.82843i | −0.397796 | + | 0.132599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.00000 | − | 1.00000i | 0.0467780 | − | 0.0467780i | −0.683331 | − | 0.730109i | \(-0.739469\pi\) |
0.730109 | + | 0.683331i | \(0.239469\pi\) | |||||||
\(458\) | 28.2843i | 1.32164i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.00000 | − | 8.00000i | 0.186501 | − | 0.373002i | ||||
\(461\) | 7.07107i | 0.329332i | 0.986349 | + | 0.164666i | \(0.0526547\pi\) | ||||
−0.986349 | + | 0.164666i | \(0.947345\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.00000 | + | 5.00000i | −0.232370 | + | 0.232370i | −0.813681 | − | 0.581311i | \(-0.802540\pi\) |
0.581311 | + | 0.813681i | \(0.302540\pi\) | |||||||
\(464\) | −16.9706 | −0.787839 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.00000 | + | 8.00000i | −0.370593 | + | 0.370593i | ||||
\(467\) | −9.89949 | + | 9.89949i | −0.458094 | + | 0.458094i | −0.898029 | − | 0.439935i | \(-0.855001\pi\) |
0.439935 | + | 0.898029i | \(0.355001\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | −2.82843 | + | 5.65685i | −0.130466 | + | 0.260931i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −28.0000 | −1.28880 | ||||||||
\(473\) | −8.48528 | − | 8.48528i | −0.390154 | − | 0.390154i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.0000 | + | 24.0000i | 0.825897 | + | 1.10120i | ||||
\(476\) | −11.3137 | −0.518563 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 36.0000i | 1.64660i | ||||||||
\(479\) | 25.4558 | 1.16311 | 0.581554 | − | 0.813508i | \(-0.302445\pi\) | ||||
0.581554 | + | 0.813508i | \(0.302445\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.0000 | 1.45907 | ||||||||
\(482\) | − | 22.6274i | − | 1.03065i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −14.0000 | −0.636364 | ||||||||
\(485\) | 9.89949 | − | 19.7990i | 0.449513 | − | 0.899026i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.00000 | + | 7.00000i | 0.317200 | + | 0.317200i | 0.847691 | − | 0.530491i | \(-0.177992\pi\) |
−0.530491 | + | 0.847691i | \(0.677992\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 15.0000 | − | 5.00000i | 0.677631 | − | 0.225877i | ||||
\(491\) | −12.7279 | −0.574403 | −0.287202 | − | 0.957870i | \(-0.592725\pi\) | ||||
−0.287202 | + | 0.957870i | \(0.592725\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.0000 | + | 12.0000i | −0.540453 | + | 0.540453i | ||||
\(494\) | 16.9706 | − | 16.9706i | 0.763542 | − | 0.763542i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.0000i | 1.07763i | ||||||||
\(497\) | 14.1421 | − | 14.1421i | 0.634361 | − | 0.634361i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 18.0000i | − | 0.805791i | −0.915246 | − | 0.402895i | \(-0.868004\pi\) | ||
0.915246 | − | 0.402895i | \(-0.131996\pi\) | |||||||
\(500\) | −12.7279 | + | 18.3848i | −0.569210 | + | 0.822192i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 18.0000i | − | 0.803379i | ||||||
\(503\) | 24.0416 | − | 24.0416i | 1.07196 | − | 1.07196i | 0.0747619 | − | 0.997201i | \(-0.476180\pi\) |
0.997201 | − | 0.0747619i | \(-0.0238197\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.00000 | − | 3.00000i | −0.0444994 | − | 0.133498i | ||||
\(506\) | −8.48528 | − | 8.48528i | −0.377217 | − | 0.377217i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 22.0000 | + | 22.0000i | 0.976092 | + | 0.976092i | ||||
\(509\) | 21.2132 | 0.940259 | 0.470129 | − | 0.882598i | \(-0.344207\pi\) | ||||
0.470129 | + | 0.882598i | \(0.344207\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 10.0000i | − | 0.442374i | ||||||
\(512\) | 22.6274i | 1.00000i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 28.0000 | + | 28.0000i | 1.23503 | + | 1.23503i | ||||
\(515\) | −7.07107 | + | 14.1421i | −0.311588 | + | 0.623177i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.00000 | + | 6.00000i | 0.263880 | + | 0.263880i | ||||
\(518\) | 22.6274 | 0.994192 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 16.0000 | + | 8.00000i | 0.701646 | + | 0.350823i | ||||
\(521\) | −16.9706 | −0.743494 | −0.371747 | − | 0.928334i | \(-0.621241\pi\) | ||||
−0.371747 | + | 0.928334i | \(0.621241\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.00000 | + | 4.00000i | 0.174908 | + | 0.174908i | 0.789132 | − | 0.614224i | \(-0.210531\pi\) |
−0.614224 | + | 0.789132i | \(0.710531\pi\) | |||||||
\(524\) | 25.4558 | 1.11204 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.0000 | + | 10.0000i | 0.436021 | + | 0.436021i | ||||
\(527\) | 16.9706 | + | 16.9706i | 0.739249 | + | 0.739249i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0000i | 0.826087i | ||||||||
\(530\) | −5.65685 | − | 2.82843i | −0.245718 | − | 0.122859i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.0000 | − | 12.0000i | 0.520266 | − | 0.520266i | ||||
\(533\) | −16.9706 | + | 16.9706i | −0.735077 | + | 0.735077i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.0000 | + | 28.0000i | −0.605273 | + | 1.21055i | ||||
\(536\) | 22.6274 | + | 22.6274i | 0.977356 | + | 0.977356i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 30.0000i | − | 1.29339i | ||||||
\(539\) | − | 21.2132i | − | 0.913717i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.0000i | 0.515920i | 0.966156 | + | 0.257960i | \(0.0830503\pi\) | ||||
−0.966156 | + | 0.257960i | \(0.916950\pi\) | |||||||
\(542\) | 16.9706 | 0.728948 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16.0000 | + | 16.0000i | 0.685994 | + | 0.685994i | ||||
\(545\) | −8.48528 | + | 2.82843i | −0.363470 | + | 0.121157i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.0000 | + | 26.0000i | −1.11168 | + | 1.11168i | −0.118756 | + | 0.992923i | \(0.537891\pi\) |
−0.992923 | + | 0.118756i | \(0.962109\pi\) | |||||||
\(548\) | 11.3137 | − | 11.3137i | 0.483298 | − | 0.483298i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 18.0000 | + | 24.0000i | 0.767523 | + | 1.02336i | ||||
\(551\) | − | 25.4558i | − | 1.08446i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.0000 | + | 14.0000i | 0.595341 | + | 0.595341i | ||||
\(554\) | −5.65685 | + | 5.65685i | −0.240337 | + | 0.240337i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.0000i | 0.508913i | ||||||||
\(557\) | 1.41421 | + | 1.41421i | 0.0599222 | + | 0.0599222i | 0.736433 | − | 0.676511i | \(-0.236509\pi\) |
−0.676511 | + | 0.736433i | \(0.736509\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 11.3137 | + | 5.65685i | 0.478091 | + | 0.239046i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 24.0000i | 1.01238i | ||||||||
\(563\) | −11.3137 | − | 11.3137i | −0.476816 | − | 0.476816i | 0.427296 | − | 0.904112i | \(-0.359466\pi\) |
−0.904112 | + | 0.427296i | \(0.859466\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.0000 | − | 16.0000i | −1.34625 | − | 0.673125i | ||||
\(566\) | 11.3137 | − | 11.3137i | 0.475551 | − | 0.475551i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −40.0000 | −1.67836 | ||||||||
\(569\) | 36.7696i | 1.54146i | 0.637162 | + | 0.770730i | \(0.280108\pi\) | ||||
−0.637162 | + | 0.770730i | \(0.719892\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.0000 | −1.42286 | −0.711428 | − | 0.702759i | \(-0.751951\pi\) | ||||
−0.711428 | + | 0.702759i | \(0.751951\pi\) | |||||||
\(572\) | 16.9706 | − | 16.9706i | 0.709575 | − | 0.709575i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.0000 | + | 12.0000i | −0.500870 | + | 0.500870i | ||||
\(575\) | −1.41421 | + | 9.89949i | −0.0589768 | + | 0.412837i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.00000 | − | 7.00000i | 0.291414 | − | 0.291414i | −0.546225 | − | 0.837639i | \(-0.683936\pi\) |
0.837639 | + | 0.546225i | \(0.183936\pi\) | |||||||
\(578\) | −1.41421 | −0.0588235 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 18.0000 | − | 6.00000i | 0.747409 | − | 0.249136i | ||||
\(581\) | 2.82843i | 0.117343i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.00000 | + | 6.00000i | −0.248495 | + | 0.248495i | ||||
\(584\) | −14.1421 | + | 14.1421i | −0.585206 | + | 0.585206i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.0000 | + | 22.0000i | 0.908812 | + | 0.908812i | ||||
\(587\) | −18.3848 | + | 18.3848i | −0.758821 | + | 0.758821i | −0.976108 | − | 0.217287i | \(-0.930279\pi\) |
0.217287 | + | 0.976108i | \(0.430279\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.0000 | −1.48335 | ||||||||
\(590\) | 29.6985 | − | 9.89949i | 1.22267 | − | 0.407556i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −32.0000 | − | 32.0000i | −1.31519 | − | 1.31519i | ||||
\(593\) | −2.82843 | − | 2.82843i | −0.116150 | − | 0.116150i | 0.646643 | − | 0.762793i | \(-0.276172\pi\) |
−0.762793 | + | 0.646643i | \(0.776172\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.0000 | − | 4.00000i | 0.491952 | − | 0.163984i | ||||
\(596\) | 25.4558 | 1.04271 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.00000 | 0.327144 | ||||||||
\(599\) | −8.48528 | −0.346699 | −0.173350 | − | 0.984860i | \(-0.555459\pi\) | ||||
−0.173350 | + | 0.984860i | \(0.555459\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0000 | 0.571072 | 0.285536 | − | 0.958368i | \(-0.407828\pi\) | ||||
0.285536 | + | 0.958368i | \(0.407828\pi\) | |||||||
\(602\) | 5.65685 | 0.230556 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 24.0000i | − | 0.976546i | ||||||
\(605\) | 14.8492 | − | 4.94975i | 0.603708 | − | 0.201236i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.0000 | + | 31.0000i | 1.25825 | + | 1.25825i | 0.951927 | + | 0.306324i | \(0.0990990\pi\) |
0.306324 | + | 0.951927i | \(0.400901\pi\) | |||||||
\(608\) | −33.9411 | −1.37649 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.65685 | −0.228852 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.0000 | − | 10.0000i | 0.403896 | − | 0.403896i | −0.475707 | − | 0.879604i | \(-0.657808\pi\) |
0.879604 | + | 0.475707i | \(0.157808\pi\) | |||||||
\(614\) | 14.1421 | + | 14.1421i | 0.570730 | + | 0.570730i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.0000 | − | 12.0000i | 0.483494 | − | 0.483494i | ||||
\(617\) | −5.65685 | + | 5.65685i | −0.227736 | + | 0.227736i | −0.811746 | − | 0.584010i | \(-0.801483\pi\) |
0.584010 | + | 0.811746i | \(0.301483\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.0000i | 1.20580i | 0.797816 | + | 0.602901i | \(0.205989\pi\) | ||||
−0.797816 | + | 0.602901i | \(0.794011\pi\) | |||||||
\(620\) | −8.48528 | − | 25.4558i | −0.340777 | − | 1.02233i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 44.0000 | 1.76424 | ||||||||
\(623\) | −2.82843 | + | 2.82843i | −0.113319 | + | 0.113319i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.00000 | − | 24.0000i | 0.280000 | − | 0.960000i | ||||
\(626\) | −1.41421 | + | 1.41421i | −0.0565233 | + | 0.0565233i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.0000 | + | 16.0000i | 0.638470 | + | 0.638470i | ||||
\(629\) | −45.2548 | −1.80443 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.0000i | − | 1.19428i | −0.802137 | − | 0.597141i | \(-0.796303\pi\) | ||
0.802137 | − | 0.597141i | \(-0.203697\pi\) | |||||||
\(632\) | − | 39.5980i | − | 1.57512i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.00000 | + | 8.00000i | −0.317721 | + | 0.317721i | ||||
\(635\) | −31.1127 | − | 15.5563i | −1.23467 | − | 0.617335i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.0000 | + | 10.0000i | 0.396214 | + | 0.396214i | ||||
\(638\) | − | 25.4558i | − | 1.00781i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.00000 | − | 24.0000i | −0.316228 | − | 0.948683i | ||||
\(641\) | −16.9706 | −0.670297 | −0.335148 | − | 0.942165i | \(-0.608786\pi\) | ||||
−0.335148 | + | 0.942165i | \(0.608786\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.0000 | + | 10.0000i | 0.394362 | + | 0.394362i | 0.876239 | − | 0.481877i | \(-0.160045\pi\) |
−0.481877 | + | 0.876239i | \(0.660045\pi\) | |||||||
\(644\) | 5.65685 | 0.222911 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −24.0000 | + | 24.0000i | −0.944267 | + | 0.944267i | ||||
\(647\) | −7.07107 | − | 7.07107i | −0.277992 | − | 0.277992i | 0.554315 | − | 0.832307i | \(-0.312980\pi\) |
−0.832307 | + | 0.554315i | \(0.812980\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 42.0000i | − | 1.64864i | ||||||
\(650\) | −19.7990 | − | 2.82843i | −0.776580 | − | 0.110940i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.0000 | − | 20.0000i | −0.783260 | − | 0.783260i | ||||
\(653\) | −5.65685 | + | 5.65685i | −0.221370 | + | 0.221370i | −0.809075 | − | 0.587705i | \(-0.800031\pi\) |
0.587705 | + | 0.809075i | \(0.300031\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.0000 | + | 9.00000i | −1.05498 | + | 0.351659i | ||||
\(656\) | 33.9411 | 1.32518 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.00000 | −0.155936 | ||||||||
\(659\) | − | 1.41421i | − | 0.0550899i | −0.999621 | − | 0.0275450i | \(-0.991231\pi\) | ||
0.999621 | − | 0.0275450i | \(-0.00876895\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 24.0000i | − | 0.933492i | −0.884391 | − | 0.466746i | \(-0.845426\pi\) | ||
0.884391 | − | 0.466746i | \(-0.154574\pi\) | |||||||
\(662\) | 2.82843i | 0.109930i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.00000 | − | 4.00000i | 0.155230 | − | 0.155230i | ||||
\(665\) | −8.48528 | + | 16.9706i | −0.329045 | + | 0.658090i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.00000 | − | 6.00000i | 0.232321 | − | 0.232321i | ||||
\(668\) | 31.1127 | + | 31.1127i | 1.20379 | + | 1.20379i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −32.0000 | − | 16.0000i | −1.23627 | − | 0.618134i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.00000 | − | 5.00000i | −0.192736 | − | 0.192736i | 0.604141 | − | 0.796877i | \(-0.293516\pi\) |
−0.796877 | + | 0.604141i | \(0.793516\pi\) | |||||||
\(674\) | −24.0416 | − | 24.0416i | −0.926049 | − | 0.926049i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | − | 10.0000i | − | 0.384615i | ||||||
\(677\) | 22.6274 | + | 22.6274i | 0.869642 | + | 0.869642i | 0.992433 | − | 0.122790i | \(-0.0391843\pi\) |
−0.122790 | + | 0.992433i | \(0.539184\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.0000 | 0.537271 | ||||||||
\(680\) | −22.6274 | − | 11.3137i | −0.867722 | − | 0.433861i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −36.0000 | −1.37851 | ||||||||
\(683\) | −15.5563 | − | 15.5563i | −0.595247 | − | 0.595247i | 0.343797 | − | 0.939044i | \(-0.388287\pi\) |
−0.939044 | + | 0.343797i | \(0.888287\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.00000 | + | 16.0000i | −0.305664 | + | 0.611329i | ||||
\(686\) | 16.9706 | + | 16.9706i | 0.647939 | + | 0.647939i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.00000 | − | 8.00000i | −0.304997 | − | 0.304997i | ||||
\(689\) | − | 5.65685i | − | 0.215509i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.0000 | −0.836919 | −0.418460 | − | 0.908235i | \(-0.637430\pi\) | ||||
−0.418460 | + | 0.908235i | \(0.637430\pi\) | |||||||
\(692\) | −5.65685 | + | 5.65685i | −0.215041 | + | 0.215041i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.0000 | + | 16.0000i | 0.607352 | + | 0.607352i | ||||
\(695\) | −4.24264 | − | 12.7279i | −0.160933 | − | 0.482798i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0000 | − | 24.0000i | 0.909065 | − | 0.909065i | ||||
\(698\) | 28.2843i | 1.07058i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −14.0000 | − | 2.00000i | −0.529150 | − | 0.0755929i | ||||
\(701\) | − | 1.41421i | − | 0.0534141i | −0.999643 | − | 0.0267071i | \(-0.991498\pi\) | ||
0.999643 | − | 0.0267071i | \(-0.00850213\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 48.0000 | − | 48.0000i | 1.81035 | − | 1.81035i | ||||
\(704\) | −33.9411 | −1.27920 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.00000 | + | 8.00000i | −0.301084 | + | 0.301084i | ||||
\(707\) | 1.41421 | − | 1.41421i | 0.0531870 | − | 0.0531870i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.0000 | −0.600893 | −0.300446 | − | 0.953799i | \(-0.597136\pi\) | ||||
−0.300446 | + | 0.953799i | \(0.597136\pi\) | |||||||
\(710\) | 42.4264 | − | 14.1421i | 1.59223 | − | 0.530745i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.00000 | 0.299813 | ||||||||
\(713\) | −8.48528 | − | 8.48528i | −0.317776 | − | 0.317776i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | + | 24.0000i | −0.448775 | + | 0.897549i | ||||
\(716\) | 19.7990i | 0.739923i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.0000i | 0.447836i | ||||||||
\(719\) | −16.9706 | −0.632895 | −0.316448 | − | 0.948610i | \(-0.602490\pi\) | ||||
−0.316448 | + | 0.948610i | \(0.602490\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0000 | −0.372419 | ||||||||
\(722\) | − | 24.0416i | − | 0.894737i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 48.0000i | − | 1.78391i | ||||||
\(725\) | −16.9706 | + | 12.7279i | −0.630271 | + | 0.472703i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.0000 | + | 31.0000i | 1.14973 | + | 1.14973i | 0.986606 | + | 0.163120i | \(0.0521558\pi\) |
0.163120 | + | 0.986606i | \(0.447844\pi\) | |||||||
\(728\) | 11.3137i | 0.419314i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.0000 | − | 20.0000i | 0.370117 | − | 0.740233i | ||||
\(731\) | −11.3137 | −0.418453 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.0000 | − | 28.0000i | 1.03420 | − | 1.03420i | 0.0348096 | − | 0.999394i | \(-0.488918\pi\) |
0.999394 | − | 0.0348096i | \(-0.0110825\pi\) | |||||||
\(734\) | 7.07107 | − | 7.07107i | 0.260998 | − | 0.260998i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.00000 | − | 8.00000i | −0.294884 | − | 0.294884i | ||||
\(737\) | −33.9411 | + | 33.9411i | −1.25024 | + | 1.25024i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 6.00000i | − | 0.220714i | −0.993892 | − | 0.110357i | \(-0.964801\pi\) | ||
0.993892 | − | 0.110357i | \(-0.0351994\pi\) | |||||||
\(740\) | 45.2548 | + | 22.6274i | 1.66360 | + | 0.831800i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 4.00000i | − | 0.146845i | ||||||
\(743\) | −9.89949 | + | 9.89949i | −0.363177 | + | 0.363177i | −0.864981 | − | 0.501804i | \(-0.832670\pi\) |
0.501804 | + | 0.864981i | \(0.332670\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.0000 | + | 9.00000i | −0.989203 | + | 0.329734i | ||||
\(746\) | 22.6274 | + | 22.6274i | 0.828449 | + | 0.828449i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −24.0000 | + | 24.0000i | −0.877527 | + | 0.877527i | ||||
\(749\) | −19.7990 | −0.723439 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.0000i | 0.656829i | 0.944534 | + | 0.328415i | \(0.106514\pi\) | ||||
−0.944534 | + | 0.328415i | \(0.893486\pi\) | |||||||
\(752\) | 5.65685 | + | 5.65685i | 0.206284 | + | 0.206284i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.0000 | + | 12.0000i | 0.437014 | + | 0.437014i | ||||
\(755\) | 8.48528 | + | 25.4558i | 0.308811 | + | 0.926433i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.00000 | − | 8.00000i | −0.290765 | − | 0.290765i | 0.546617 | − | 0.837382i | \(-0.315915\pi\) |
−0.837382 | + | 0.546617i | \(0.815915\pi\) | |||||||
\(758\) | −25.4558 | −0.924598 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 36.0000 | − | 12.0000i | 1.30586 | − | 0.435286i | ||||
\(761\) | 16.9706 | 0.615182 | 0.307591 | − | 0.951519i | \(-0.400477\pi\) | ||||
0.307591 | + | 0.951519i | \(0.400477\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.00000 | − | 4.00000i | −0.144810 | − | 0.144810i | ||||
\(764\) | − | 22.6274i | − | 0.818631i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.0000 | − | 26.0000i | −0.939418 | − | 0.939418i | ||||
\(767\) | 19.7990 | + | 19.7990i | 0.714900 | + | 0.714900i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 6.00000i | − | 0.216366i | −0.994131 | − | 0.108183i | \(-0.965497\pi\) | ||
0.994131 | − | 0.108183i | \(-0.0345032\pi\) | |||||||
\(770\) | −8.48528 | + | 16.9706i | −0.305788 | + | 0.611577i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −26.0000 | − | 26.0000i | −0.935760 | − | 0.935760i | ||||
\(773\) | 28.2843 | − | 28.2843i | 1.01731 | − | 1.01731i | 0.0174671 | − | 0.999847i | \(-0.494440\pi\) |
0.999847 | − | 0.0174671i | \(-0.00556023\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.0000 | + | 24.0000i | 0.646579 | + | 0.862105i | ||||
\(776\) | −19.7990 | − | 19.7990i | −0.710742 | − | 0.710742i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.00000i | 0.215110i | ||||||||
\(779\) | 50.9117i | 1.82410i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 60.0000i | − | 2.14697i | ||||||
\(782\) | −11.3137 | −0.404577 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 20.0000i | − | 0.714286i | ||||||
\(785\) | −22.6274 | − | 11.3137i | −0.807607 | − | 0.403804i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.0000 | + | 20.0000i | −0.712923 | + | 0.712923i | −0.967146 | − | 0.254223i | \(-0.918180\pi\) |
0.254223 | + | 0.967146i | \(0.418180\pi\) | |||||||
\(788\) | −19.7990 | − | 19.7990i | −0.705310 | − | 0.705310i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 14.0000 | + | 42.0000i | 0.498098 | + | 1.49429i | ||||
\(791\) | − | 22.6274i | − | 0.804538i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −14.1421 | + | 14.1421i | −0.501886 | + | 0.501886i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.00000 | 0.283552 | ||||||||
\(797\) | −11.3137 | − | 11.3137i | −0.400752 | − | 0.400752i | 0.477746 | − | 0.878498i | \(-0.341454\pi\) |
−0.878498 | + | 0.477746i | \(0.841454\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000 | 0.283020 | ||||||||
\(800\) | 16.9706 | + | 22.6274i | 0.600000 | + | 0.800000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.0000i | 0.423735i | ||||||||
\(803\) | −21.2132 | − | 21.2132i | −0.748598 | − | 0.748598i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.00000 | + | 2.00000i | −0.211472 | + | 0.0704907i | ||||
\(806\) | 16.9706 | − | 16.9706i | 0.597763 | − | 0.597763i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.00000 | −0.140720 | ||||||||
\(809\) | − | 39.5980i | − | 1.39219i | −0.717949 | − | 0.696095i | \(-0.754919\pi\) | ||
0.717949 | − | 0.696095i | \(-0.245081\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.0000 | −0.772524 | −0.386262 | − | 0.922389i | \(-0.626234\pi\) | ||||
−0.386262 | + | 0.922389i | \(0.626234\pi\) | |||||||
\(812\) | 8.48528 | + | 8.48528i | 0.297775 | + | 0.297775i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 48.0000 | − | 48.0000i | 1.68240 | − | 1.68240i | ||||
\(815\) | 28.2843 | + | 14.1421i | 0.990755 | + | 0.495377i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0000 | − | 12.0000i | 0.419827 | − | 0.419827i | ||||
\(818\) | −16.9706 | −0.593362 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −36.0000 | + | 12.0000i | −1.25717 | + | 0.419058i | ||||
\(821\) | − | 26.8701i | − | 0.937771i | −0.883259 | − | 0.468886i | \(-0.844656\pi\) | ||
0.883259 | − | 0.468886i | \(-0.155344\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.00000 | + | 5.00000i | −0.174289 | + | 0.174289i | −0.788861 | − | 0.614572i | \(-0.789329\pi\) |
0.614572 | + | 0.788861i | \(0.289329\pi\) | |||||||
\(824\) | 14.1421 | + | 14.1421i | 0.492665 | + | 0.492665i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.0000 | + | 14.0000i | 0.487122 | + | 0.487122i | ||||
\(827\) | −5.65685 | + | 5.65685i | −0.196708 | + | 0.196708i | −0.798587 | − | 0.601879i | \(-0.794419\pi\) |
0.601879 | + | 0.798587i | \(0.294419\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.0000 | −0.972480 | −0.486240 | − | 0.873825i | \(-0.661632\pi\) | ||||
−0.486240 | + | 0.873825i | \(0.661632\pi\) | |||||||
\(830\) | −2.82843 | + | 5.65685i | −0.0981761 | + | 0.196352i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 16.0000 | − | 16.0000i | 0.554700 | − | 0.554700i | ||||
\(833\) | −14.1421 | − | 14.1421i | −0.489996 | − | 0.489996i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −44.0000 | − | 22.0000i | −1.52268 | − | 0.761341i | ||||
\(836\) | − | 50.9117i | − | 1.76082i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.0000 | 0.483622 | ||||||||
\(839\) | −8.48528 | −0.292944 | −0.146472 | − | 0.989215i | \(-0.546792\pi\) | ||||
−0.146472 | + | 0.989215i | \(0.546792\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.0000 | −0.379310 | ||||||||
\(842\) | 16.9706 | 0.584844 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.00000 | −0.137686 | ||||||||
\(845\) | 3.53553 | + | 10.6066i | 0.121626 | + | 0.364878i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.00000 | + | 7.00000i | 0.240523 | + | 0.240523i | ||||
\(848\) | −5.65685 | + | 5.65685i | −0.194257 | + | 0.194257i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 28.0000 | + | 4.00000i | 0.960392 | + | 0.137199i | ||||
\(851\) | 22.6274 | 0.775658 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.0000 | + | 14.0000i | −0.479351 | + | 0.479351i | −0.904924 | − | 0.425573i | \(-0.860073\pi\) |
0.425573 | + | 0.904924i | \(0.360073\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 28.0000 | + | 28.0000i | 0.957020 | + | 0.957020i | ||||
\(857\) | 19.7990 | − | 19.7990i | 0.676321 | − | 0.676321i | −0.282845 | − | 0.959166i | \(-0.591278\pi\) |
0.959166 | + | 0.282845i | \(0.0912782\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.00000i | 0.204717i | 0.994748 | + | 0.102359i | \(0.0326389\pi\) | ||||
−0.994748 | + | 0.102359i | \(0.967361\pi\) | |||||||
\(860\) | 11.3137 | + | 5.65685i | 0.385794 | + | 0.192897i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −52.0000 | −1.77113 | ||||||||
\(863\) | −18.3848 | + | 18.3848i | −0.625825 | + | 0.625825i | −0.947015 | − | 0.321190i | \(-0.895917\pi\) |
0.321190 | + | 0.947015i | \(0.395917\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.00000 | − | 8.00000i | 0.136004 | − | 0.272008i | ||||
\(866\) | 32.5269 | − | 32.5269i | 1.10531 | − | 1.10531i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.0000 | − | 12.0000i | 0.407307 | − | 0.407307i | ||||
\(869\) | 59.3970 | 2.01490 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 32.0000i | − | 1.08428i | ||||||
\(872\) | 11.3137i | 0.383131i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.0000 | − | 12.0000i | 0.405906 | − | 0.405906i | ||||
\(875\) | 15.5563 | − | 2.82843i | 0.525901 | − | 0.0956183i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.00000 | + | 4.00000i | 0.135070 | + | 0.135070i | 0.771409 | − | 0.636339i | \(-0.219552\pi\) |
−0.636339 | + | 0.771409i | \(0.719552\pi\) | |||||||
\(878\) | − | 5.65685i | − | 0.190910i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 36.0000 | − | 12.0000i | 1.21356 | − | 0.404520i | ||||
\(881\) | 25.4558 | 0.857629 | 0.428815 | − | 0.903393i | \(-0.358931\pi\) | ||||
0.428815 | + | 0.903393i | \(0.358931\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.0000 | + | 34.0000i | 1.14419 | + | 1.14419i | 0.987675 | + | 0.156516i | \(0.0500262\pi\) |
0.156516 | + | 0.987675i | \(0.449974\pi\) | |||||||
\(884\) | − | 22.6274i | − | 0.761042i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.0000 | + | 32.0000i | −1.07506 | + | 1.07506i | ||||
\(887\) | 1.41421 | + | 1.41421i | 0.0474846 | + | 0.0474846i | 0.730450 | − | 0.682966i | \(-0.239310\pi\) |
−0.682966 | + | 0.730450i | \(0.739310\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 22.0000i | − | 0.737856i | ||||||
\(890\) | −8.48528 | + | 2.82843i | −0.284427 | + | 0.0948091i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 22.0000 | − | 22.0000i | 0.736614 | − | 0.736614i | ||||
\(893\) | −8.48528 | + | 8.48528i | −0.283949 | + | 0.283949i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.00000 | − | 21.0000i | −0.233984 | − | 0.701953i | ||||
\(896\) | 11.3137 | − | 11.3137i | 0.377964 | − | 0.377964i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16.0000 | −0.533927 | ||||||||
\(899\) | − | 25.4558i | − | 0.849000i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.00000i | 0.266519i | ||||||||
\(902\) | 50.9117i | 1.69517i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −32.0000 | + | 32.0000i | −1.06430 | + | 1.06430i | ||||
\(905\) | 16.9706 | + | 50.9117i | 0.564121 | + | 1.69236i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.0000 | − | 28.0000i | 0.929725 | − | 0.929725i | −0.0679631 | − | 0.997688i | \(-0.521650\pi\) |
0.997688 | + | 0.0679631i | \(0.0216500\pi\) | |||||||
\(908\) | 11.3137 | − | 11.3137i | 0.375459 | − | 0.375459i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.00000 | − | 12.0000i | −0.132599 | − | 0.397796i | ||||
\(911\) | 19.7990i | 0.655970i | 0.944683 | + | 0.327985i | \(0.106370\pi\) | ||||
−0.944683 | + | 0.327985i | \(0.893630\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.00000 | + | 6.00000i | 0.198571 | + | 0.198571i | ||||
\(914\) | 1.41421 | + | 1.41421i | 0.0467780 | + | 0.0467780i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −40.0000 | −1.32164 | ||||||||
\(917\) | −12.7279 | − | 12.7279i | −0.420313 | − | 0.420313i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.0000 | −0.329870 | −0.164935 | − | 0.986304i | \(-0.552741\pi\) | ||||
−0.164935 | + | 0.986304i | \(0.552741\pi\) | |||||||
\(920\) | 11.3137 | + | 5.65685i | 0.373002 | + | 0.186501i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.0000 | −0.329332 | ||||||||
\(923\) | 28.2843 | + | 28.2843i | 0.930988 | + | 0.930988i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −56.0000 | − | 8.00000i | −1.84127 | − | 0.263038i | ||||
\(926\) | −7.07107 | − | 7.07107i | −0.232370 | − | 0.232370i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 24.0000i | − | 0.787839i | ||||||
\(929\) | − | 39.5980i | − | 1.29917i | −0.760290 | − | 0.649584i | \(-0.774943\pi\) | ||
0.760290 | − | 0.649584i | \(-0.225057\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.0000 | 0.983210 | ||||||||
\(932\) | −11.3137 | − | 11.3137i | −0.370593 | − | 0.370593i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.0000 | − | 14.0000i | −0.458094 | − | 0.458094i | ||||
\(935\) | 16.9706 | − | 33.9411i | 0.554997 | − | 1.10999i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.00000 | − | 7.00000i | 0.228680 | − | 0.228680i | −0.583461 | − | 0.812141i | \(-0.698302\pi\) |
0.812141 | + | 0.583461i | \(0.198302\pi\) | |||||||
\(938\) | − | 22.6274i | − | 0.738811i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.00000 | − | 4.00000i | −0.260931 | − | 0.130466i | ||||
\(941\) | − | 9.89949i | − | 0.322714i | −0.986896 | − | 0.161357i | \(-0.948413\pi\) | ||
0.986896 | − | 0.161357i | \(-0.0515871\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.0000 | + | 12.0000i | −0.390774 | + | 0.390774i | ||||
\(944\) | − | 39.5980i | − | 1.28880i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.0000 | − | 12.0000i | 0.390154 | − | 0.390154i | ||||
\(947\) | 11.3137 | − | 11.3137i | 0.367646 | − | 0.367646i | −0.498972 | − | 0.866618i | \(-0.666289\pi\) |
0.866618 | + | 0.498972i | \(0.166289\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.0000 | 0.649227 | ||||||||
\(950\) | −33.9411 | + | 25.4558i | −1.10120 | + | 0.825897i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 16.0000i | − | 0.518563i | ||||||
\(953\) | 14.1421 | + | 14.1421i | 0.458109 | + | 0.458109i | 0.898034 | − | 0.439926i | \(-0.144995\pi\) |
−0.439926 | + | 0.898034i | \(0.644995\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.00000 | + | 24.0000i | 0.258874 | + | 0.776622i | ||||
\(956\) | −50.9117 | −1.64660 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 36.0000i | 1.16311i | ||||||||
\(959\) | −11.3137 | −0.365339 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.00000 | −0.161290 | ||||||||
\(962\) | 45.2548i | 1.45907i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 32.0000 | 1.03065 | ||||||||
\(965\) | 36.7696 | + | 18.3848i | 1.18365 | + | 0.591827i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.00000 | + | 7.00000i | 0.225105 | + | 0.225105i | 0.810644 | − | 0.585539i | \(-0.199117\pi\) |
−0.585539 | + | 0.810644i | \(0.699117\pi\) | |||||||
\(968\) | − | 19.7990i | − | 0.636364i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 28.0000 | + | 14.0000i | 0.899026 | + | 0.449513i | ||||
\(971\) | 29.6985 | 0.953070 | 0.476535 | − | 0.879156i | \(-0.341893\pi\) | ||||
0.476535 | + | 0.879156i | \(0.341893\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.00000 | − | 6.00000i | 0.192351 | − | 0.192351i | ||||
\(974\) | −9.89949 | + | 9.89949i | −0.317200 | + | 0.317200i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.6274 | + | 22.6274i | −0.723915 | + | 0.723915i | −0.969400 | − | 0.245485i | \(-0.921053\pi\) |
0.245485 | + | 0.969400i | \(0.421053\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0000i | 0.383522i | ||||||||
\(980\) | 7.07107 | + | 21.2132i | 0.225877 | + | 0.677631i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 18.0000i | − | 0.574403i | ||||||
\(983\) | −9.89949 | + | 9.89949i | −0.315745 | + | 0.315745i | −0.847130 | − | 0.531385i | \(-0.821672\pi\) |
0.531385 | + | 0.847130i | \(0.321672\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.0000 | + | 14.0000i | 0.892154 | + | 0.446077i | ||||
\(986\) | −16.9706 | − | 16.9706i | −0.540453 | − | 0.540453i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 24.0000 | + | 24.0000i | 0.763542 | + | 0.763542i | ||||
\(989\) | 5.65685 | 0.179878 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.0000i | 1.14358i | 0.820401 | + | 0.571789i | \(0.193750\pi\) | ||||
−0.820401 | + | 0.571789i | \(0.806250\pi\) | |||||||
\(992\) | −33.9411 | −1.07763 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 20.0000 | + | 20.0000i | 0.634361 | + | 0.634361i | ||||
\(995\) | −8.48528 | + | 2.82843i | −0.269002 | + | 0.0896672i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.0000 | + | 22.0000i | 0.696747 | + | 0.696747i | 0.963707 | − | 0.266960i | \(-0.0860193\pi\) |
−0.266960 | + | 0.963707i | \(0.586019\pi\) | |||||||
\(998\) | 25.4558 | 0.805791 | ||||||||
\(999\) | 0 | 0 |
(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 | 360.2.w.a.163.2 | yes | 4 | |
3.2 | odd | 2 | inner | 360.2.w.a.163.1 | ✓ | 4 | |
4.3 | odd | 2 | 1440.2.bi.a.1423.2 | 4 | |||
5.2 | odd | 4 | 360.2.w.b.307.1 | yes | 4 | ||
8.3 | odd | 2 | 360.2.w.b.163.1 | yes | 4 | ||
8.5 | even | 2 | 1440.2.bi.b.1423.1 | 4 | |||
12.11 | even | 2 | 1440.2.bi.a.1423.1 | 4 | |||
15.2 | even | 4 | 360.2.w.b.307.2 | yes | 4 | ||
20.7 | even | 4 | 1440.2.bi.b.847.1 | 4 | |||
24.5 | odd | 2 | 1440.2.bi.b.1423.2 | 4 | |||
24.11 | even | 2 | 360.2.w.b.163.2 | yes | 4 | ||
40.27 | even | 4 | inner | 360.2.w.a.307.1 | yes | 4 | |
40.37 | odd | 4 | 1440.2.bi.a.847.2 | 4 | |||
60.47 | odd | 4 | 1440.2.bi.b.847.2 | 4 | |||
120.77 | even | 4 | 1440.2.bi.a.847.1 | 4 | |||
120.107 | odd | 4 | inner | 360.2.w.a.307.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.w.a.163.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
360.2.w.a.163.2 | yes | 4 | 1.1 | even | 1 | trivial | |
360.2.w.a.307.1 | yes | 4 | 40.27 | even | 4 | inner | |
360.2.w.a.307.2 | yes | 4 | 120.107 | odd | 4 | inner | |
360.2.w.b.163.1 | yes | 4 | 8.3 | odd | 2 | ||
360.2.w.b.163.2 | yes | 4 | 24.11 | even | 2 | ||
360.2.w.b.307.1 | yes | 4 | 5.2 | odd | 4 | ||
360.2.w.b.307.2 | yes | 4 | 15.2 | even | 4 | ||
1440.2.bi.a.847.1 | 4 | 120.77 | even | 4 | |||
1440.2.bi.a.847.2 | 4 | 40.37 | odd | 4 | |||
1440.2.bi.a.1423.1 | 4 | 12.11 | even | 2 | |||
1440.2.bi.a.1423.2 | 4 | 4.3 | odd | 2 | |||
1440.2.bi.b.847.1 | 4 | 20.7 | even | 4 | |||
1440.2.bi.b.847.2 | 4 | 60.47 | odd | 4 | |||
1440.2.bi.b.1423.1 | 4 | 8.5 | even | 2 | |||
1440.2.bi.b.1423.2 | 4 | 24.5 | odd | 2 |