Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,2,Mod(18,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.18");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.f (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: | \(2.59513806569\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 111x^{12} + 329x^{8} + 168x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 18.1 | ||
Root | \(0.419746 - 0.419746i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.18 |
Dual form | 325.2.f.d.307.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.38239i | − | 1.68461i | −0.539005 | − | 0.842303i | \(-0.681200\pi\) | ||
0.539005 | − | 0.842303i | \(-0.318800\pi\) | |||||||
\(3\) | 0.648130 | + | 0.648130i | 0.374198 | + | 0.374198i | 0.869004 | − | 0.494805i | \(-0.164761\pi\) |
−0.494805 | + | 0.869004i | \(0.664761\pi\) | |||||||
\(4\) | −3.67579 | −1.83790 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.54410 | − | 1.54410i | 0.630376 | − | 0.630376i | ||||
\(7\) | 2.38239 | 0.900459 | 0.450230 | − | 0.892913i | \(-0.351342\pi\) | ||||
0.450230 | + | 0.892913i | \(0.351342\pi\) | |||||||
\(8\) | 3.99239i | 1.41152i | ||||||||
\(9\) | − | 2.15985i | − | 0.719951i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.88966 | − | 3.88966i | −1.17278 | − | 1.17278i | −0.981545 | − | 0.191231i | \(-0.938752\pi\) |
−0.191231 | − | 0.981545i | \(-0.561248\pi\) | |||||||
\(12\) | −2.38239 | − | 2.38239i | −0.687737 | − | 0.687737i | ||||
\(13\) | 2.76764 | − | 2.31088i | 0.767606 | − | 0.640922i | ||||
\(14\) | − | 5.67579i | − | 1.51692i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.15985 | 0.539963 | ||||||||
\(17\) | 0.262878 | + | 0.262878i | 0.0637573 | + | 0.0637573i | 0.738266 | − | 0.674509i | \(-0.235645\pi\) |
−0.674509 | + | 0.738266i | \(0.735645\pi\) | |||||||
\(18\) | −5.14562 | −1.21283 | ||||||||
\(19\) | 0.587589 | + | 0.587589i | 0.134802 | + | 0.134802i | 0.771288 | − | 0.636486i | \(-0.219613\pi\) |
−0.636486 | + | 0.771288i | \(0.719613\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.54410 | + | 1.54410i | 0.336950 | + | 0.336950i | ||||
\(22\) | −9.26669 | + | 9.26669i | −1.97566 | + | 1.97566i | ||||
\(23\) | −1.98090 | + | 1.98090i | −0.413046 | + | 0.413046i | −0.882798 | − | 0.469752i | \(-0.844343\pi\) |
0.469752 | + | 0.882798i | \(0.344343\pi\) | |||||||
\(24\) | −2.58759 | + | 2.58759i | −0.528189 | + | 0.528189i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.50541 | − | 6.59361i | −1.07970 | − | 1.29311i | ||||
\(27\) | 3.34426 | − | 3.34426i | 0.643603 | − | 0.643603i | ||||
\(28\) | −8.75717 | −1.65495 | ||||||||
\(29\) | 7.92385i | 1.47142i | 0.677296 | + | 0.735711i | \(0.263152\pi\) | ||||
−0.677296 | + | 0.735711i | \(0.736848\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.59361 | − | 6.59361i | 1.18425 | − | 1.18425i | 0.205615 | − | 0.978633i | \(-0.434081\pi\) |
0.978633 | − | 0.205615i | \(-0.0659194\pi\) | |||||||
\(32\) | 2.83916i | 0.501897i | ||||||||
\(33\) | − | 5.04201i | − | 0.877702i | ||||||
\(34\) | 0.626279 | − | 0.626279i | 0.107406 | − | 0.107406i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.93917i | 1.32319i | ||||||||
\(37\) | 10.3366 | 1.69932 | 0.849662 | − | 0.527328i | \(-0.176806\pi\) | ||||
0.849662 | + | 0.527328i | \(0.176806\pi\) | |||||||
\(38\) | 1.39987 | − | 1.39987i | 0.227088 | − | 0.227088i | ||||
\(39\) | 3.29154 | + | 0.296046i | 0.527069 | + | 0.0474052i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.37974 | + | 6.37974i | −0.996349 | + | 0.996349i | −0.999993 | − | 0.00364462i | \(-0.998840\pi\) |
0.00364462 | + | 0.999993i | \(0.498840\pi\) | |||||||
\(42\) | 3.67865 | − | 3.67865i | 0.567628 | − | 0.567628i | ||||
\(43\) | −3.09762 | + | 3.09762i | −0.472383 | + | 0.472383i | −0.902685 | − | 0.430302i | \(-0.858407\pi\) |
0.430302 | + | 0.902685i | \(0.358407\pi\) | |||||||
\(44\) | 14.2976 | + | 14.2976i | 2.15544 | + | 2.15544i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.71928 | + | 4.71928i | 0.695820 | + | 0.695820i | ||||
\(47\) | 5.67137 | 0.827255 | 0.413627 | − | 0.910446i | \(-0.364262\pi\) | ||||
0.413627 | + | 0.910446i | \(0.364262\pi\) | |||||||
\(48\) | 1.39987 | + | 1.39987i | 0.202053 | + | 0.202053i | ||||
\(49\) | −1.32421 | −0.189173 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.340759i | 0.0477158i | ||||||||
\(52\) | −10.1733 | + | 8.49429i | −1.41078 | + | 1.17795i | ||||
\(53\) | −1.54732 | − | 1.54732i | −0.212540 | − | 0.212540i | 0.592805 | − | 0.805346i | \(-0.298020\pi\) |
−0.805346 | + | 0.592805i | \(0.798020\pi\) | |||||||
\(54\) | −7.96733 | − | 7.96733i | −1.08422 | − | 1.08422i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9.51143i | 1.27102i | ||||||||
\(57\) | 0.761669i | 0.100885i | ||||||||
\(58\) | 18.8777 | 2.47876 | ||||||||
\(59\) | −5.49009 | + | 5.49009i | −0.714748 | + | 0.714748i | −0.967525 | − | 0.252776i | \(-0.918656\pi\) |
0.252776 | + | 0.967525i | \(0.418656\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.11885 | 0.527365 | 0.263682 | − | 0.964610i | \(-0.415063\pi\) | ||||
0.263682 | + | 0.964610i | \(0.415063\pi\) | |||||||
\(62\) | −15.7086 | − | 15.7086i | −1.99499 | − | 1.99499i | ||||
\(63\) | − | 5.14562i | − | 0.648287i | ||||||
\(64\) | 11.0837 | 1.38546 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −12.0120 | −1.47858 | ||||||||
\(67\) | 3.74764i | 0.457847i | 0.973444 | + | 0.228924i | \(0.0735206\pi\) | ||||
−0.973444 | + | 0.228924i | \(0.926479\pi\) | |||||||
\(68\) | −0.966285 | − | 0.966285i | −0.117179 | − | 0.117179i | ||||
\(69\) | −2.56776 | −0.309122 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.04349 | + | 2.04349i | −0.242517 | + | 0.242517i | −0.817891 | − | 0.575373i | \(-0.804857\pi\) |
0.575373 | + | 0.817891i | \(0.304857\pi\) | |||||||
\(72\) | 8.62298 | 1.01623 | ||||||||
\(73\) | 7.56049i | 0.884888i | 0.896796 | + | 0.442444i | \(0.145889\pi\) | ||||
−0.896796 | + | 0.442444i | \(0.854111\pi\) | |||||||
\(74\) | − | 24.6258i | − | 2.86269i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.15985 | − | 2.15985i | −0.247752 | − | 0.247752i | ||||
\(77\) | −9.26669 | − | 9.26669i | −1.05604 | − | 1.05604i | ||||
\(78\) | 0.705296 | − | 7.84175i | 0.0798591 | − | 0.887903i | ||||
\(79\) | − | 6.07165i | − | 0.683114i | −0.939861 | − | 0.341557i | \(-0.889046\pi\) | ||
0.939861 | − | 0.341557i | \(-0.110954\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.14453 | −0.238281 | ||||||||
\(82\) | 15.1991 | + | 15.1991i | 1.67845 | + | 1.67845i | ||||
\(83\) | 13.0415 | 1.43150 | 0.715748 | − | 0.698359i | \(-0.246086\pi\) | ||||
0.715748 | + | 0.698359i | \(0.246086\pi\) | |||||||
\(84\) | −5.67579 | − | 5.67579i | −0.619279 | − | 0.619279i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.37974 | + | 7.37974i | 0.795778 | + | 0.795778i | ||||
\(87\) | −5.13569 | + | 5.13569i | −0.550603 | + | 0.550603i | ||||
\(88\) | 15.5290 | − | 15.5290i | 1.65540 | − | 1.65540i | ||||
\(89\) | 2.23522 | − | 2.23522i | 0.236932 | − | 0.236932i | −0.578646 | − | 0.815579i | \(-0.696419\pi\) |
0.815579 | + | 0.578646i | \(0.196419\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.59361 | − | 5.50541i | 0.691198 | − | 0.577124i | ||||
\(92\) | 7.28137 | − | 7.28137i | 0.759135 | − | 0.759135i | ||||
\(93\) | 8.54704 | 0.886287 | ||||||||
\(94\) | − | 13.5114i | − | 1.39360i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.84015 | + | 1.84015i | −0.187809 | + | 0.187809i | ||||
\(97\) | − | 1.88723i | − | 0.191619i | −0.995400 | − | 0.0958094i | \(-0.969456\pi\) | ||
0.995400 | − | 0.0958094i | \(-0.0305439\pi\) | |||||||
\(98\) | 3.15479i | 0.318682i | ||||||||
\(99\) | −8.40109 | + | 8.40109i | −0.844342 | + | 0.844342i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 6.40791i | − | 0.637611i | −0.947820 | − | 0.318805i | \(-0.896718\pi\) | ||
0.947820 | − | 0.318805i | \(-0.103282\pi\) | |||||||
\(102\) | 0.811821 | 0.0803822 | ||||||||
\(103\) | −6.56425 | + | 6.56425i | −0.646795 | + | 0.646795i | −0.952217 | − | 0.305422i | \(-0.901202\pi\) |
0.305422 | + | 0.952217i | \(0.401202\pi\) | |||||||
\(104\) | 9.22591 | + | 11.0495i | 0.904675 | + | 1.08349i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.68632 | + | 3.68632i | −0.358047 | + | 0.358047i | ||||
\(107\) | 1.34459 | − | 1.34459i | 0.129987 | − | 0.129987i | −0.639120 | − | 0.769107i | \(-0.720701\pi\) |
0.769107 | + | 0.639120i | \(0.220701\pi\) | |||||||
\(108\) | −12.2928 | + | 12.2928i | −1.18287 | + | 1.18287i | ||||
\(109\) | 11.7474 | + | 11.7474i | 1.12520 | + | 1.12520i | 0.990947 | + | 0.134254i | \(0.0428638\pi\) |
0.134254 | + | 0.990947i | \(0.457136\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.69945 | + | 6.69945i | 0.635884 | + | 0.635884i | ||||
\(112\) | 5.14562 | 0.486215 | ||||||||
\(113\) | −0.581032 | − | 0.581032i | −0.0546589 | − | 0.0546589i | 0.679249 | − | 0.733908i | \(-0.262306\pi\) |
−0.733908 | + | 0.679249i | \(0.762306\pi\) | |||||||
\(114\) | 1.81459 | 0.169952 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 29.1264i | − | 2.70432i | ||||||
\(117\) | −4.99115 | − | 5.97771i | −0.461432 | − | 0.552639i | ||||
\(118\) | 13.0795 | + | 13.0795i | 1.20407 | + | 1.20407i | ||||
\(119\) | 0.626279 | + | 0.626279i | 0.0574109 | + | 0.0574109i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.2589i | 1.75081i | ||||||||
\(122\) | − | 9.81271i | − | 0.888401i | ||||||
\(123\) | −8.26981 | −0.745664 | ||||||||
\(124\) | −24.2367 | + | 24.2367i | −2.17652 | + | 2.17652i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −12.2589 | −1.09211 | ||||||||
\(127\) | −4.56648 | − | 4.56648i | −0.405209 | − | 0.405209i | 0.474855 | − | 0.880064i | \(-0.342501\pi\) |
−0.880064 | + | 0.474855i | \(0.842501\pi\) | |||||||
\(128\) | − | 20.7274i | − | 1.83206i | ||||||
\(129\) | −4.01532 | −0.353530 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.9085 | 1.30256 | 0.651282 | − | 0.758836i | \(-0.274232\pi\) | ||||
0.651282 | + | 0.758836i | \(0.274232\pi\) | |||||||
\(132\) | 18.5334i | 1.61312i | ||||||||
\(133\) | 1.39987 | + | 1.39987i | 0.121384 | + | 0.121384i | ||||
\(134\) | 8.92835 | 0.771292 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.04951 | + | 1.04951i | −0.0899949 | + | 0.0899949i | ||||
\(137\) | 9.21583 | 0.787362 | 0.393681 | − | 0.919247i | \(-0.371202\pi\) | ||||
0.393681 | + | 0.919247i | \(0.371202\pi\) | |||||||
\(138\) | 6.11742i | 0.520749i | ||||||||
\(139\) | − | 5.87665i | − | 0.498451i | −0.968446 | − | 0.249225i | \(-0.919824\pi\) | ||
0.968446 | − | 0.249225i | \(-0.0801760\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.67579 | + | 3.67579i | 0.309557 | + | 0.309557i | ||||
\(142\) | 4.86839 | + | 4.86839i | 0.408546 | + | 0.408546i | ||||
\(143\) | −19.7537 | − | 1.77667i | −1.65189 | − | 0.148573i | ||||
\(144\) | − | 4.66497i | − | 0.388747i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 18.0120 | 1.49069 | ||||||||
\(147\) | −0.858261 | − | 0.858261i | −0.0707881 | − | 0.0707881i | ||||
\(148\) | −37.9951 | −3.12318 | ||||||||
\(149\) | 5.89568 | + | 5.89568i | 0.482993 | + | 0.482993i | 0.906086 | − | 0.423093i | \(-0.139056\pi\) |
−0.423093 | + | 0.906086i | \(0.639056\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.9452 | − | 12.9452i | −1.05346 | − | 1.05346i | −0.998488 | − | 0.0549773i | \(-0.982491\pi\) |
−0.0549773 | − | 0.998488i | \(-0.517509\pi\) | |||||||
\(152\) | −2.34588 | + | 2.34588i | −0.190276 | + | 0.190276i | ||||
\(153\) | 0.567778 | − | 0.567778i | 0.0459022 | − | 0.0459022i | ||||
\(154\) | −22.0769 | + | 22.0769i | −1.77901 | + | 1.77901i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −12.0990 | − | 1.08820i | −0.968697 | − | 0.0871258i | ||||
\(157\) | −13.8195 | + | 13.8195i | −1.10291 | + | 1.10291i | −0.108855 | + | 0.994058i | \(0.534718\pi\) |
−0.994058 | + | 0.108855i | \(0.965282\pi\) | |||||||
\(158\) | −14.4651 | −1.15078 | ||||||||
\(159\) | − | 2.00573i | − | 0.159064i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.71928 | + | 4.71928i | −0.371931 | + | 0.371931i | ||||
\(162\) | 5.10911i | 0.401410i | ||||||||
\(163\) | − | 3.80590i | − | 0.298101i | −0.988830 | − | 0.149051i | \(-0.952378\pi\) | ||
0.988830 | − | 0.149051i | \(-0.0476217\pi\) | |||||||
\(164\) | 23.4506 | − | 23.4506i | 1.83118 | − | 1.83118i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 31.0701i | − | 2.41150i | ||||||
\(167\) | −18.2483 | −1.41210 | −0.706050 | − | 0.708162i | \(-0.749524\pi\) | ||||
−0.706050 | + | 0.708162i | \(0.749524\pi\) | |||||||
\(168\) | −6.16465 | + | 6.16465i | −0.475613 | + | 0.475613i | ||||
\(169\) | 2.31971 | − | 12.7914i | 0.178439 | − | 0.983951i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.26911 | − | 1.26911i | 0.0970510 | − | 0.0970510i | ||||
\(172\) | 11.3862 | − | 11.3862i | 0.868190 | − | 0.868190i | ||||
\(173\) | −0.00740374 | + | 0.00740374i | −0.000562896 | + | 0.000562896i | −0.707388 | − | 0.706825i | \(-0.750127\pi\) |
0.706825 | + | 0.707388i | \(0.250127\pi\) | |||||||
\(174\) | 12.2352 | + | 12.2352i | 0.927549 | + | 0.927549i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.40109 | − | 8.40109i | −0.633256 | − | 0.633256i | ||||
\(177\) | −7.11659 | −0.534915 | ||||||||
\(178\) | −5.32516 | − | 5.32516i | −0.399137 | − | 0.399137i | ||||
\(179\) | −12.0717 | −0.902278 | −0.451139 | − | 0.892454i | \(-0.648982\pi\) | ||||
−0.451139 | + | 0.892454i | \(0.648982\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.2589i | 1.35717i | 0.734521 | + | 0.678586i | \(0.237407\pi\) | ||||
−0.734521 | + | 0.678586i | \(0.762593\pi\) | |||||||
\(182\) | −13.1160 | − | 15.7086i | −0.972226 | − | 1.16440i | ||||
\(183\) | 2.66955 | + | 2.66955i | 0.197339 | + | 0.197339i | ||||
\(184\) | −7.90852 | − | 7.90852i | −0.583024 | − | 0.583024i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 20.3624i | − | 1.49304i | ||||||
\(187\) | − | 2.04501i | − | 0.149546i | ||||||
\(188\) | −20.8468 | −1.52041 | ||||||||
\(189\) | 7.96733 | − | 7.96733i | 0.579538 | − | 0.579538i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.39878 | −0.462999 | −0.231500 | − | 0.972835i | \(-0.574363\pi\) | ||||
−0.231500 | + | 0.972835i | \(0.574363\pi\) | |||||||
\(192\) | 7.18368 | + | 7.18368i | 0.518438 | + | 0.518438i | ||||
\(193\) | 12.4812i | 0.898414i | 0.893428 | + | 0.449207i | \(0.148293\pi\) | ||||
−0.893428 | + | 0.449207i | \(0.851707\pi\) | |||||||
\(194\) | −4.49611 | −0.322802 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.86752 | 0.347680 | ||||||||
\(197\) | 19.8948i | 1.41745i | 0.705485 | + | 0.708725i | \(0.250729\pi\) | ||||
−0.705485 | + | 0.708725i | \(0.749271\pi\) | |||||||
\(198\) | 20.0147 | + | 20.0147i | 1.42238 | + | 1.42238i | ||||
\(199\) | −13.5740 | −0.962232 | −0.481116 | − | 0.876657i | \(-0.659768\pi\) | ||||
−0.481116 | + | 0.876657i | \(0.659768\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.42896 | + | 2.42896i | −0.171326 | + | 0.171326i | ||||
\(202\) | −15.2661 | −1.07412 | ||||||||
\(203\) | 18.8777i | 1.32496i | ||||||||
\(204\) | − | 1.25256i | − | 0.0876966i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.6386 | + | 15.6386i | 1.08959 | + | 1.08959i | ||||
\(207\) | 4.27845 | + | 4.27845i | 0.297373 | + | 0.297373i | ||||
\(208\) | 5.97771 | − | 4.99115i | 0.414479 | − | 0.346074i | ||||
\(209\) | − | 4.57104i | − | 0.316185i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.6348 | −0.732129 | −0.366064 | − | 0.930590i | \(-0.619295\pi\) | ||||
−0.366064 | + | 0.930590i | \(0.619295\pi\) | |||||||
\(212\) | 5.68761 | + | 5.68761i | 0.390627 | + | 0.390627i | ||||
\(213\) | −2.64889 | −0.181499 | ||||||||
\(214\) | −3.20334 | − | 3.20334i | −0.218976 | − | 0.218976i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 13.3516 | + | 13.3516i | 0.908460 | + | 0.908460i | ||||
\(217\) | 15.7086 | − | 15.7086i | 1.06637 | − | 1.06637i | ||||
\(218\) | 27.9870 | − | 27.9870i | 1.89552 | − | 1.89552i | ||||
\(219\) | −4.90018 | + | 4.90018i | −0.331124 | + | 0.331124i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.33503 | + | 0.120074i | 0.0898039 | + | 0.00807708i | ||||
\(222\) | 15.9607 | − | 15.9607i | 1.07121 | − | 1.07121i | ||||
\(223\) | 10.1659 | 0.680757 | 0.340379 | − | 0.940288i | \(-0.389445\pi\) | ||||
0.340379 | + | 0.940288i | \(0.389445\pi\) | |||||||
\(224\) | 6.76399i | 0.451938i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.38425 | + | 1.38425i | −0.0920787 | + | 0.0920787i | ||||
\(227\) | − | 18.5876i | − | 1.23370i | −0.787080 | − | 0.616852i | \(-0.788408\pi\) | ||
0.787080 | − | 0.616852i | \(-0.211592\pi\) | |||||||
\(228\) | − | 2.79973i | − | 0.185417i | ||||||
\(229\) | 6.29605 | − | 6.29605i | 0.416054 | − | 0.416054i | −0.467787 | − | 0.883841i | \(-0.654949\pi\) |
0.883841 | + | 0.467787i | \(0.154949\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 12.0120i | − | 0.790335i | ||||||
\(232\) | −31.6351 | −2.07694 | ||||||||
\(233\) | 19.7706 | − | 19.7706i | 1.29521 | − | 1.29521i | 0.363696 | − | 0.931518i | \(-0.381515\pi\) |
0.931518 | − | 0.363696i | \(-0.118485\pi\) | |||||||
\(234\) | −14.2412 | + | 11.8909i | −0.930979 | + | 0.777331i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 20.1804 | − | 20.1804i | 1.31363 | − | 1.31363i | ||||
\(237\) | 3.93522 | − | 3.93522i | 0.255620 | − | 0.255620i | ||||
\(238\) | 1.49204 | − | 1.49204i | 0.0967147 | − | 0.0967147i | ||||
\(239\) | −10.0206 | − | 10.0206i | −0.648176 | − | 0.648176i | 0.304376 | − | 0.952552i | \(-0.401552\pi\) |
−0.952552 | + | 0.304376i | \(0.901552\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.79586 | + | 2.79586i | 0.180097 | + | 0.180097i | 0.791398 | − | 0.611301i | \(-0.209353\pi\) |
−0.611301 | + | 0.791398i | \(0.709353\pi\) | |||||||
\(242\) | 45.8822 | 2.94942 | ||||||||
\(243\) | −11.4227 | − | 11.4227i | −0.732767 | − | 0.732767i | ||||
\(244\) | −15.1400 | −0.969241 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 19.7019i | 1.25615i | ||||||||
\(247\) | 2.98408 | + | 0.268392i | 0.189873 | + | 0.0170774i | ||||
\(248\) | 26.3243 | + | 26.3243i | 1.67159 | + | 1.67159i | ||||
\(249\) | 8.45262 | + | 8.45262i | 0.535663 | + | 0.535663i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 22.3744i | − | 1.41226i | −0.708081 | − | 0.706131i | \(-0.750439\pi\) | ||
0.708081 | − | 0.706131i | \(-0.249561\pi\) | |||||||
\(252\) | 18.9142i | 1.19148i | ||||||||
\(253\) | 15.4100 | 0.968821 | ||||||||
\(254\) | −10.8791 | + | 10.8791i | −0.682617 | + | 0.682617i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −27.2134 | −1.70084 | ||||||||
\(257\) | 1.41312 | + | 1.41312i | 0.0881481 | + | 0.0881481i | 0.749806 | − | 0.661658i | \(-0.230147\pi\) |
−0.661658 | + | 0.749806i | \(0.730147\pi\) | |||||||
\(258\) | 9.56607i | 0.595558i | ||||||||
\(259\) | 24.6258 | 1.53017 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.1143 | 1.05935 | ||||||||
\(262\) | − | 35.5179i | − | 2.19431i | ||||||
\(263\) | 3.71113 | + | 3.71113i | 0.228838 | + | 0.228838i | 0.812207 | − | 0.583369i | \(-0.198266\pi\) |
−0.583369 | + | 0.812207i | \(0.698266\pi\) | |||||||
\(264\) | 20.1297 | 1.23890 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.33503 | − | 3.33503i | 0.204484 | − | 0.204484i | ||||
\(267\) | 2.89742 | 0.177319 | ||||||||
\(268\) | − | 13.7755i | − | 0.841475i | ||||||
\(269\) | − | 0.372632i | − | 0.0227198i | −0.999935 | − | 0.0113599i | \(-0.996384\pi\) | ||
0.999935 | − | 0.0113599i | \(-0.00361604\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.10584 | − | 3.10584i | −0.188666 | − | 0.188666i | 0.606453 | − | 0.795119i | \(-0.292592\pi\) |
−0.795119 | + | 0.606453i | \(0.792592\pi\) | |||||||
\(272\) | 0.567778 | + | 0.567778i | 0.0344266 | + | 0.0344266i | ||||
\(273\) | 7.84175 | + | 0.705296i | 0.474604 | + | 0.0426865i | ||||
\(274\) | − | 21.9557i | − | 1.32639i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 9.43856 | 0.568134 | ||||||||
\(277\) | 12.4546 | + | 12.4546i | 0.748324 | + | 0.748324i | 0.974164 | − | 0.225840i | \(-0.0725128\pi\) |
−0.225840 | + | 0.974164i | \(0.572513\pi\) | |||||||
\(278\) | −14.0005 | −0.839693 | ||||||||
\(279\) | −14.2412 | − | 14.2412i | −0.852601 | − | 0.852601i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.18924 | − | 7.18924i | −0.428874 | − | 0.428874i | 0.459370 | − | 0.888245i | \(-0.348075\pi\) |
−0.888245 | + | 0.459370i | \(0.848075\pi\) | |||||||
\(282\) | 8.75717 | − | 8.75717i | 0.521482 | − | 0.521482i | ||||
\(283\) | −21.6211 | + | 21.6211i | −1.28524 | + | 1.28524i | −0.347594 | + | 0.937645i | \(0.613001\pi\) |
−0.937645 | + | 0.347594i | \(0.886999\pi\) | |||||||
\(284\) | 7.51143 | − | 7.51143i | 0.445722 | − | 0.445722i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.23273 | + | 47.0611i | −0.250287 | + | 2.78278i | ||||
\(287\) | −15.1991 | + | 15.1991i | −0.897172 | + | 0.897172i | ||||
\(288\) | 6.13217 | 0.361342 | ||||||||
\(289\) | − | 16.8618i | − | 0.991870i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.22317 | − | 1.22317i | 0.0717034 | − | 0.0717034i | ||||
\(292\) | − | 27.7908i | − | 1.62633i | ||||||
\(293\) | − | 25.7477i | − | 1.50419i | −0.659053 | − | 0.752097i | \(-0.729043\pi\) | ||
0.659053 | − | 0.752097i | \(-0.270957\pi\) | |||||||
\(294\) | −2.04471 | + | 2.04471i | −0.119250 | + | 0.119250i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 41.2676i | 2.39863i | ||||||||
\(297\) | −26.0160 | −1.50960 | ||||||||
\(298\) | 14.0458 | − | 14.0458i | 0.813653 | − | 0.813653i | ||||
\(299\) | −0.904812 | + | 10.0600i | −0.0523267 | + | 0.581787i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.37974 | + | 7.37974i | −0.425361 | + | 0.425361i | ||||
\(302\) | −30.8405 | + | 30.8405i | −1.77467 | + | 1.77467i | ||||
\(303\) | 4.15316 | − | 4.15316i | 0.238593 | − | 0.238593i | ||||
\(304\) | 1.26911 | + | 1.26911i | 0.0727882 | + | 0.0727882i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.35267 | − | 1.35267i | −0.0773270 | − | 0.0773270i | ||||
\(307\) | 1.82202 | 0.103988 | 0.0519940 | − | 0.998647i | \(-0.483442\pi\) | ||||
0.0519940 | + | 0.998647i | \(0.483442\pi\) | |||||||
\(308\) | 34.0624 | + | 34.0624i | 1.94089 | + | 1.94089i | ||||
\(309\) | −8.50898 | −0.484059 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 7.73334i | − | 0.438518i | −0.975667 | − | 0.219259i | \(-0.929636\pi\) | ||
0.975667 | − | 0.219259i | \(-0.0703639\pi\) | |||||||
\(312\) | −1.18193 | + | 13.1411i | −0.0669136 | + | 0.743970i | ||||
\(313\) | −13.6675 | − | 13.6675i | −0.772534 | − | 0.772534i | 0.206015 | − | 0.978549i | \(-0.433950\pi\) |
−0.978549 | + | 0.206015i | \(0.933950\pi\) | |||||||
\(314\) | 32.9233 | + | 32.9233i | 1.85797 | + | 1.85797i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 22.3181i | 1.25549i | ||||||||
\(317\) | 14.3180i | 0.804179i | 0.915600 | + | 0.402089i | \(0.131716\pi\) | ||||
−0.915600 | + | 0.402089i | \(0.868284\pi\) | |||||||
\(318\) | −4.77843 | −0.267961 | ||||||||
\(319\) | 30.8210 | − | 30.8210i | 1.72565 | − | 1.72565i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.74294 | 0.0972815 | ||||||||
\(322\) | 11.2432 | + | 11.2432i | 0.626557 | + | 0.626557i | ||||
\(323\) | 0.308929i | 0.0171892i | ||||||||
\(324\) | 7.88284 | 0.437936 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.06715 | −0.502183 | ||||||||
\(327\) | 15.2278i | 0.842097i | ||||||||
\(328\) | −25.4704 | − | 25.4704i | −1.40637 | − | 1.40637i | ||||
\(329\) | 13.5114 | 0.744909 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.8440 | + | 10.8440i | −0.596039 | + | 0.596039i | −0.939256 | − | 0.343217i | \(-0.888483\pi\) |
0.343217 | + | 0.939256i | \(0.388483\pi\) | |||||||
\(332\) | −47.9380 | −2.63094 | ||||||||
\(333\) | − | 22.3255i | − | 1.22343i | ||||||
\(334\) | 43.4747i | 2.37883i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.33503 | + | 3.33503i | 0.181941 | + | 0.181941i | ||||
\(337\) | 5.26248 | + | 5.26248i | 0.286665 | + | 0.286665i | 0.835760 | − | 0.549095i | \(-0.185027\pi\) |
−0.549095 | + | 0.835760i | \(0.685027\pi\) | |||||||
\(338\) | −30.4740 | − | 5.52645i | −1.65757 | − | 0.300599i | ||||
\(339\) | − | 0.753170i | − | 0.0409066i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −51.2938 | −2.77771 | ||||||||
\(342\) | −3.02351 | − | 3.02351i | −0.163493 | − | 0.163493i | ||||
\(343\) | −19.8315 | −1.07080 | ||||||||
\(344\) | −12.3669 | − | 12.3669i | −0.666779 | − | 0.666779i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.0176386 | + | 0.0176386i | 0.000948257 | + | 0.000948257i | ||||
\(347\) | 7.90775 | − | 7.90775i | 0.424510 | − | 0.424510i | −0.462243 | − | 0.886753i | \(-0.652955\pi\) |
0.886753 | + | 0.462243i | \(0.152955\pi\) | |||||||
\(348\) | 18.8777 | − | 18.8777i | 1.01195 | − | 1.01195i | ||||
\(349\) | 1.59130 | − | 1.59130i | 0.0851802 | − | 0.0851802i | −0.663233 | − | 0.748413i | \(-0.730816\pi\) |
0.748413 | + | 0.663233i | \(0.230816\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.52755 | − | 16.9839i | 0.0815347 | − | 0.906533i | ||||
\(352\) | 11.0434 | − | 11.0434i | 0.588613 | − | 0.588613i | ||||
\(353\) | 19.3600 | 1.03043 | 0.515215 | − | 0.857061i | \(-0.327712\pi\) | ||||
0.515215 | + | 0.857061i | \(0.327712\pi\) | |||||||
\(354\) | 16.9545i | 0.901121i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.21618 | + | 8.21618i | −0.435457 | + | 0.435457i | ||||
\(357\) | 0.811821i | 0.0429661i | ||||||||
\(358\) | 28.7594i | 1.51998i | ||||||||
\(359\) | −3.46070 | + | 3.46070i | −0.182649 | + | 0.182649i | −0.792509 | − | 0.609860i | \(-0.791226\pi\) |
0.609860 | + | 0.792509i | \(0.291226\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.3095i | − | 0.963657i | ||||||
\(362\) | 43.4998 | 2.28630 | ||||||||
\(363\) | −12.4823 | + | 12.4823i | −0.655149 | + | 0.655149i | ||||
\(364\) | −24.2367 | + | 20.2367i | −1.27035 | + | 1.06069i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.35992 | − | 6.35992i | 0.332438 | − | 0.332438i | ||||
\(367\) | 7.68286 | − | 7.68286i | 0.401042 | − | 0.401042i | −0.477558 | − | 0.878600i | \(-0.658478\pi\) |
0.878600 | + | 0.477558i | \(0.158478\pi\) | |||||||
\(368\) | −4.27845 | + | 4.27845i | −0.223030 | + | 0.223030i | ||||
\(369\) | 13.7793 | + | 13.7793i | 0.717323 | + | 0.717323i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.68632 | − | 3.68632i | −0.191384 | − | 0.191384i | ||||
\(372\) | −31.4171 | −1.62890 | ||||||||
\(373\) | −6.30515 | − | 6.30515i | −0.326469 | − | 0.326469i | 0.524773 | − | 0.851242i | \(-0.324150\pi\) |
−0.851242 | + | 0.524773i | \(0.824150\pi\) | |||||||
\(374\) | −4.87202 | −0.251926 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.6423i | 1.16769i | ||||||||
\(377\) | 18.3110 | + | 21.9304i | 0.943066 | + | 1.12947i | ||||
\(378\) | −18.9813 | − | 18.9813i | −0.976293 | − | 0.976293i | ||||
\(379\) | −0.333942 | − | 0.333942i | −0.0171534 | − | 0.0171534i | 0.698478 | − | 0.715631i | \(-0.253861\pi\) |
−0.715631 | + | 0.698478i | \(0.753861\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 5.91934i | − | 0.303257i | ||||||
\(382\) | 15.2444i | 0.779971i | ||||||||
\(383\) | 5.09138 | 0.260158 | 0.130079 | − | 0.991504i | \(-0.458477\pi\) | ||||
0.130079 | + | 0.991504i | \(0.458477\pi\) | |||||||
\(384\) | 13.4341 | − | 13.4341i | 0.685554 | − | 0.685554i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 29.7350 | 1.51347 | ||||||||
\(387\) | 6.69041 | + | 6.69041i | 0.340092 | + | 0.340092i | ||||
\(388\) | 6.93704i | 0.352175i | ||||||||
\(389\) | −33.6544 | −1.70634 | −0.853172 | − | 0.521629i | \(-0.825324\pi\) | ||||
−0.853172 | + | 0.521629i | \(0.825324\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.04147 | −0.0526694 | ||||||||
\(392\) | − | 5.28676i | − | 0.267022i | ||||||
\(393\) | 9.66267 | + | 9.66267i | 0.487417 | + | 0.487417i | ||||
\(394\) | 47.3973 | 2.38784 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 30.8807 | − | 30.8807i | 1.55181 | − | 1.55181i | ||||
\(397\) | 11.6763 | 0.586019 | 0.293010 | − | 0.956110i | \(-0.405343\pi\) | ||||
0.293010 | + | 0.956110i | \(0.405343\pi\) | |||||||
\(398\) | 32.3385i | 1.62098i | ||||||||
\(399\) | 1.81459i | 0.0908433i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.30809 | + | 6.30809i | 0.315011 | + | 0.315011i | 0.846847 | − | 0.531836i | \(-0.178498\pi\) |
−0.531836 | + | 0.846847i | \(0.678498\pi\) | |||||||
\(402\) | 5.78673 | + | 5.78673i | 0.288616 | + | 0.288616i | ||||
\(403\) | 3.01175 | − | 33.4858i | 0.150026 | − | 1.66805i | ||||
\(404\) | 23.5541i | 1.17186i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 44.9741 | 2.23203 | ||||||||
\(407\) | −40.2058 | − | 40.2058i | −1.99293 | − | 1.99293i | ||||
\(408\) | −1.36044 | −0.0673519 | ||||||||
\(409\) | 12.8746 | + | 12.8746i | 0.636609 | + | 0.636609i | 0.949718 | − | 0.313108i | \(-0.101370\pi\) |
−0.313108 | + | 0.949718i | \(0.601370\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.97306 | + | 5.97306i | 0.294629 | + | 0.294629i | ||||
\(412\) | 24.1288 | − | 24.1288i | 1.18874 | − | 1.18874i | ||||
\(413\) | −13.0795 | + | 13.0795i | −0.643602 | + | 0.643602i | ||||
\(414\) | 10.1930 | − | 10.1930i | 0.500956 | − | 0.500956i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.56095 | + | 7.85778i | 0.321677 | + | 0.385260i | ||||
\(417\) | 3.80883 | − | 3.80883i | 0.186519 | − | 0.186519i | ||||
\(418\) | −10.8900 | −0.532648 | ||||||||
\(419\) | 31.0270i | 1.51577i | 0.652389 | + | 0.757884i | \(0.273767\pi\) | ||||
−0.652389 | + | 0.757884i | \(0.726233\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.82280 | + | 6.82280i | −0.332523 | + | 0.332523i | −0.853544 | − | 0.521021i | \(-0.825551\pi\) |
0.521021 | + | 0.853544i | \(0.325551\pi\) | |||||||
\(422\) | 25.3362i | 1.23335i | ||||||||
\(423\) | − | 12.2493i | − | 0.595583i | ||||||
\(424\) | 6.17749 | − | 6.17749i | 0.300006 | − | 0.300006i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.31070i | 0.305755i | ||||||||
\(427\) | 9.81271 | 0.474870 | ||||||||
\(428\) | −4.94243 | + | 4.94243i | −0.238902 | + | 0.238902i | ||||
\(429\) | −11.6515 | − | 13.9545i | −0.562538 | − | 0.673729i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.95943 | + | 8.95943i | −0.431560 | + | 0.431560i | −0.889159 | − | 0.457599i | \(-0.848710\pi\) |
0.457599 | + | 0.889159i | \(0.348710\pi\) | |||||||
\(432\) | 7.22311 | − | 7.22311i | 0.347522 | − | 0.347522i | ||||
\(433\) | −15.4575 | + | 15.4575i | −0.742841 | + | 0.742841i | −0.973124 | − | 0.230283i | \(-0.926035\pi\) |
0.230283 | + | 0.973124i | \(0.426035\pi\) | |||||||
\(434\) | −37.4240 | − | 37.4240i | −1.79641 | − | 1.79641i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −43.1811 | − | 43.1811i | −2.06800 | − | 2.06800i | ||||
\(437\) | −2.32791 | −0.111359 | ||||||||
\(438\) | 11.6742 | + | 11.6742i | 0.557813 | + | 0.557813i | ||||
\(439\) | −24.6942 | −1.17859 | −0.589294 | − | 0.807919i | \(-0.700594\pi\) | ||||
−0.589294 | + | 0.807919i | \(0.700594\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.86010i | 0.136195i | ||||||||
\(442\) | 0.286064 | − | 3.18057i | 0.0136067 | − | 0.151284i | ||||
\(443\) | 22.0612 | + | 22.0612i | 1.04816 | + | 1.04816i | 0.998780 | + | 0.0493786i | \(0.0157241\pi\) |
0.0493786 | + | 0.998780i | \(0.484276\pi\) | |||||||
\(444\) | −24.6258 | − | 24.6258i | −1.16869 | − | 1.16869i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 24.2191i | − | 1.14681i | ||||||
\(447\) | 7.64234i | 0.361470i | ||||||||
\(448\) | 26.4057 | 1.24755 | ||||||||
\(449\) | −0.902668 | + | 0.902668i | −0.0425995 | + | 0.0425995i | −0.728086 | − | 0.685486i | \(-0.759590\pi\) |
0.685486 | + | 0.728086i | \(0.259590\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 49.6300 | 2.33699 | ||||||||
\(452\) | 2.13575 | + | 2.13575i | 0.100457 | + | 0.100457i | ||||
\(453\) | − | 16.7803i | − | 0.788410i | ||||||
\(454\) | −44.2830 | −2.07830 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.04088 | −0.142402 | ||||||||
\(457\) | − | 31.9104i | − | 1.49271i | −0.665550 | − | 0.746353i | \(-0.731803\pi\) | ||
0.665550 | − | 0.746353i | \(-0.268197\pi\) | |||||||
\(458\) | −14.9996 | − | 14.9996i | −0.700887 | − | 0.700887i | ||||
\(459\) | 1.75826 | 0.0820688 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.65292 | + | 1.65292i | −0.0769842 | + | 0.0769842i | −0.744550 | − | 0.667566i | \(-0.767336\pi\) |
0.667566 | + | 0.744550i | \(0.267336\pi\) | |||||||
\(462\) | −28.6174 | −1.33140 | ||||||||
\(463\) | − | 3.04132i | − | 0.141342i | −0.997500 | − | 0.0706710i | \(-0.977486\pi\) | ||
0.997500 | − | 0.0706710i | \(-0.0225140\pi\) | |||||||
\(464\) | 17.1143i | 0.794514i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −47.1013 | − | 47.1013i | −2.18192 | − | 2.18192i | ||||
\(467\) | 14.5459 | + | 14.5459i | 0.673102 | + | 0.673102i | 0.958430 | − | 0.285328i | \(-0.0921024\pi\) |
−0.285328 | + | 0.958430i | \(0.592102\pi\) | |||||||
\(468\) | 18.3464 | + | 21.9728i | 0.848064 | + | 1.01569i | ||||
\(469\) | 8.92835i | 0.412273i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.9136 | −0.825416 | ||||||||
\(472\) | −21.9186 | − | 21.9186i | −1.00888 | − | 1.00888i | ||||
\(473\) | 24.0974 | 1.10800 | ||||||||
\(474\) | −9.37524 | − | 9.37524i | −0.430619 | − | 0.430619i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.30207 | − | 2.30207i | −0.105515 | − | 0.105515i | ||||
\(477\) | −3.34198 | + | 3.34198i | −0.153019 | + | 0.153019i | ||||
\(478\) | −23.8729 | + | 23.8729i | −1.09192 | + | 1.09192i | ||||
\(479\) | 25.2765 | − | 25.2765i | 1.15491 | − | 1.15491i | 0.169359 | − | 0.985554i | \(-0.445830\pi\) |
0.985554 | − | 0.169359i | \(-0.0541698\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.6080 | − | 23.8866i | 1.30441 | − | 1.08913i | ||||
\(482\) | 6.66084 | − | 6.66084i | 0.303393 | − | 0.303393i | ||||
\(483\) | −6.11742 | −0.278352 | ||||||||
\(484\) | − | 70.7916i | − | 3.21780i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −27.2134 | + | 27.2134i | −1.23442 | + | 1.23442i | ||||
\(487\) | 20.4552i | 0.926915i | 0.886119 | + | 0.463457i | \(0.153391\pi\) | ||||
−0.886119 | + | 0.463457i | \(0.846609\pi\) | |||||||
\(488\) | 16.4440i | 0.744387i | ||||||||
\(489\) | 2.46672 | − | 2.46672i | 0.111549 | − | 0.111549i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.81787i | 0.352816i | 0.984317 | + | 0.176408i | \(0.0564477\pi\) | ||||
−0.984317 | + | 0.176408i | \(0.943552\pi\) | |||||||
\(492\) | 30.3981 | 1.37045 | ||||||||
\(493\) | −2.08301 | + | 2.08301i | −0.0938139 | + | 0.0938139i | ||||
\(494\) | 0.639415 | − | 7.10925i | 0.0287686 | − | 0.319860i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.2412 | − | 14.2412i | 0.639450 | − | 0.639450i | ||||
\(497\) | −4.86839 | + | 4.86839i | −0.218377 | + | 0.218377i | ||||
\(498\) | 20.1375 | − | 20.1375i | 0.902381 | − | 0.902381i | ||||
\(499\) | −19.1295 | − | 19.1295i | −0.856354 | − | 0.856354i | 0.134552 | − | 0.990906i | \(-0.457040\pi\) |
−0.990906 | + | 0.134552i | \(0.957040\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.8273 | − | 11.8273i | −0.528405 | − | 0.528405i | ||||
\(502\) | −53.3047 | −2.37911 | ||||||||
\(503\) | 1.20851 | + | 1.20851i | 0.0538846 | + | 0.0538846i | 0.733536 | − | 0.679651i | \(-0.237869\pi\) |
−0.679651 | + | 0.733536i | \(0.737869\pi\) | |||||||
\(504\) | 20.5433 | 0.915072 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 36.7128i | − | 1.63208i | ||||||
\(507\) | 9.79395 | − | 6.78700i | 0.434964 | − | 0.301421i | ||||
\(508\) | 16.7854 | + | 16.7854i | 0.744732 | + | 0.744732i | ||||
\(509\) | 10.5094 | + | 10.5094i | 0.465822 | + | 0.465822i | 0.900558 | − | 0.434736i | \(-0.143158\pi\) |
−0.434736 | + | 0.900558i | \(0.643158\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.0120i | 0.796806i | ||||||||
\(512\) | 23.3781i | 1.03318i | ||||||||
\(513\) | 3.93010 | 0.173518 | ||||||||
\(514\) | 3.36661 | − | 3.36661i | 0.148495 | − | 0.148495i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 14.7595 | 0.649750 | ||||||||
\(517\) | −22.0597 | − | 22.0597i | −0.970185 | − | 0.970185i | ||||
\(518\) | − | 58.6683i | − | 2.57774i | ||||||
\(519\) | −0.00959718 | −0.000421269 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.86424 | −0.388349 | −0.194175 | − | 0.980967i | \(-0.562203\pi\) | ||||
−0.194175 | + | 0.980967i | \(0.562203\pi\) | |||||||
\(522\) | − | 40.7731i | − | 1.78459i | ||||||
\(523\) | 2.10327 | + | 2.10327i | 0.0919697 | + | 0.0919697i | 0.751595 | − | 0.659625i | \(-0.229285\pi\) |
−0.659625 | + | 0.751595i | \(0.729285\pi\) | |||||||
\(524\) | −54.8006 | −2.39398 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.84137 | − | 8.84137i | 0.385502 | − | 0.385502i | ||||
\(527\) | 3.46663 | 0.151009 | ||||||||
\(528\) | − | 10.8900i | − | 0.473927i | ||||||
\(529\) | 15.1521i | 0.658786i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.8578 | + | 11.8578i | 0.514584 | + | 0.514584i | ||||
\(532\) | −5.14562 | − | 5.14562i | −0.223091 | − | 0.223091i | ||||
\(533\) | −2.91407 | + | 32.3997i | −0.126222 | + | 1.40339i | ||||
\(534\) | − | 6.90279i | − | 0.298713i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14.9620 | −0.646262 | ||||||||
\(537\) | −7.82401 | − | 7.82401i | −0.337631 | − | 0.337631i | ||||
\(538\) | −0.887755 | −0.0382738 | ||||||||
\(539\) | 5.15072 | + | 5.15072i | 0.221857 | + | 0.221857i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.31137 | + | 4.31137i | 0.185360 | + | 0.185360i | 0.793687 | − | 0.608327i | \(-0.208159\pi\) |
−0.608327 | + | 0.793687i | \(0.708159\pi\) | |||||||
\(542\) | −7.39933 | + | 7.39933i | −0.317828 | + | 0.317828i | ||||
\(543\) | −11.8341 | + | 11.8341i | −0.507851 | + | 0.507851i | ||||
\(544\) | −0.746353 | + | 0.746353i | −0.0319996 | + | 0.0319996i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.68029 | − | 18.6821i | 0.0719099 | − | 0.799521i | ||||
\(547\) | 12.6865 | − | 12.6865i | 0.542435 | − | 0.542435i | −0.381807 | − | 0.924242i | \(-0.624698\pi\) |
0.924242 | + | 0.381807i | \(0.124698\pi\) | |||||||
\(548\) | −33.8755 | −1.44709 | ||||||||
\(549\) | − | 8.89611i | − | 0.379677i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.65596 | + | 4.65596i | −0.198351 | + | 0.198351i | ||||
\(552\) | − | 10.2515i | − | 0.436333i | ||||||
\(553\) | − | 14.4651i | − | 0.615117i | ||||||
\(554\) | 29.6717 | − | 29.6717i | 1.26063 | − | 1.26063i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21.6013i | 0.916100i | ||||||||
\(557\) | −1.92751 | −0.0816713 | −0.0408357 | − | 0.999166i | \(-0.513002\pi\) | ||||
−0.0408357 | + | 0.999166i | \(0.513002\pi\) | |||||||
\(558\) | −33.9282 | + | 33.9282i | −1.43630 | + | 1.43630i | ||||
\(559\) | −1.41490 | + | 15.7313i | −0.0598437 | + | 0.665364i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.32543 | − | 1.32543i | 0.0559599 | − | 0.0559599i | ||||
\(562\) | −17.1276 | + | 17.1276i | −0.722484 | + | 0.722484i | ||||
\(563\) | −10.3956 | + | 10.3956i | −0.438124 | + | 0.438124i | −0.891380 | − | 0.453256i | \(-0.850262\pi\) |
0.453256 | + | 0.891380i | \(0.350262\pi\) | |||||||
\(564\) | −13.5114 | − | 13.5114i | −0.568934 | − | 0.568934i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 51.5098 | + | 51.5098i | 2.16512 | + | 2.16512i | ||||
\(567\) | −5.10911 | −0.214562 | ||||||||
\(568\) | −8.15840 | − | 8.15840i | −0.342319 | − | 0.342319i | ||||
\(569\) | −25.2005 | −1.05646 | −0.528230 | − | 0.849101i | \(-0.677144\pi\) | ||||
−0.528230 | + | 0.849101i | \(0.677144\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.7839i | 0.911630i | 0.890075 | + | 0.455815i | \(0.150652\pi\) | ||||
−0.890075 | + | 0.455815i | \(0.849348\pi\) | |||||||
\(572\) | 72.6105 | + | 6.53068i | 3.03600 | + | 0.273061i | ||||
\(573\) | −4.14724 | − | 4.14724i | −0.173254 | − | 0.173254i | ||||
\(574\) | 36.2101 | + | 36.2101i | 1.51138 | + | 1.51138i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | − | 23.9392i | − | 0.997465i | ||||||
\(577\) | 36.6110i | 1.52414i | 0.647497 | + | 0.762068i | \(0.275816\pi\) | ||||
−0.647497 | + | 0.762068i | \(0.724184\pi\) | |||||||
\(578\) | −40.1714 | −1.67091 | ||||||||
\(579\) | −8.08943 | + | 8.08943i | −0.336185 | + | 0.336185i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.0701 | 1.28900 | ||||||||
\(582\) | −2.91407 | − | 2.91407i | −0.120792 | − | 0.120792i | ||||
\(583\) | 12.0371i | 0.498524i | ||||||||
\(584\) | −30.1844 | −1.24904 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −61.3410 | −2.53397 | ||||||||
\(587\) | − | 5.27384i | − | 0.217675i | −0.994060 | − | 0.108837i | \(-0.965287\pi\) | ||
0.994060 | − | 0.108837i | \(-0.0347128\pi\) | |||||||
\(588\) | 3.15479 | + | 3.15479i | 0.130101 | + | 0.130101i | ||||
\(589\) | 7.74867 | 0.319278 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.8945 | + | 12.8945i | −0.530407 | + | 0.530407i | ||||
\(592\) | 22.3255 | 0.917572 | ||||||||
\(593\) | 22.9283i | 0.941552i | 0.882253 | + | 0.470776i | \(0.156026\pi\) | ||||
−0.882253 | + | 0.470776i | \(0.843974\pi\) | |||||||
\(594\) | 61.9804i | 2.54309i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.6713 | − | 21.6713i | −0.887691 | − | 0.887691i | ||||
\(597\) | −8.79769 | − | 8.79769i | −0.360066 | − | 0.360066i | ||||
\(598\) | 23.9669 | + | 2.15562i | 0.980081 | + | 0.0881498i | ||||
\(599\) | − | 2.73954i | − | 0.111934i | −0.998433 | − | 0.0559672i | \(-0.982176\pi\) | ||
0.998433 | − | 0.0559672i | \(-0.0178242\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.4400 | 1.73116 | 0.865582 | − | 0.500767i | \(-0.166949\pi\) | ||||
0.865582 | + | 0.500767i | \(0.166949\pi\) | |||||||
\(602\) | 17.5814 | + | 17.5814i | 0.716566 | + | 0.716566i | ||||
\(603\) | 8.09436 | 0.329628 | ||||||||
\(604\) | 47.5838 | + | 47.5838i | 1.93616 | + | 1.93616i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.89446 | − | 9.89446i | −0.401935 | − | 0.401935i | ||||
\(607\) | −17.7698 | + | 17.7698i | −0.721255 | + | 0.721255i | −0.968861 | − | 0.247606i | \(-0.920356\pi\) |
0.247606 | + | 0.968861i | \(0.420356\pi\) | |||||||
\(608\) | −1.66826 | + | 1.66826i | −0.0676568 | + | 0.0676568i | ||||
\(609\) | −12.2352 | + | 12.2352i | −0.495796 | + | 0.495796i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.6963 | − | 13.1058i | 0.635006 | − | 0.530206i | ||||
\(612\) | −2.08703 | + | 2.08703i | −0.0843633 | + | 0.0843633i | ||||
\(613\) | 25.4815 | 1.02919 | 0.514593 | − | 0.857435i | \(-0.327943\pi\) | ||||
0.514593 | + | 0.857435i | \(0.327943\pi\) | |||||||
\(614\) | − | 4.34076i | − | 0.175179i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 36.9962 | − | 36.9962i | 1.49062 | − | 1.49062i | ||||
\(617\) | − | 17.0369i | − | 0.685880i | −0.939357 | − | 0.342940i | \(-0.888577\pi\) | ||
0.939357 | − | 0.342940i | \(-0.111423\pi\) | |||||||
\(618\) | 20.2717i | 0.815449i | ||||||||
\(619\) | −26.5396 | + | 26.5396i | −1.06672 | + | 1.06672i | −0.0691073 | + | 0.997609i | \(0.522015\pi\) |
−0.997609 | + | 0.0691073i | \(0.977985\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.2493i | 0.531675i | ||||||||
\(622\) | −18.4239 | −0.738729 | ||||||||
\(623\) | 5.32516 | − | 5.32516i | 0.213348 | − | 0.213348i | ||||
\(624\) | 7.10925 | + | 0.639415i | 0.284598 | + | 0.0255971i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −32.5614 | + | 32.5614i | −1.30141 | + | 1.30141i | ||||
\(627\) | 2.96263 | − | 2.96263i | 0.118316 | − | 0.118316i | ||||
\(628\) | 50.7974 | − | 50.7974i | 2.02704 | − | 2.02704i | ||||
\(629\) | 2.71726 | + | 2.71726i | 0.108344 | + | 0.108344i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.89770 | − | 8.89770i | −0.354212 | − | 0.354212i | 0.507462 | − | 0.861674i | \(-0.330584\pi\) |
−0.861674 | + | 0.507462i | \(0.830584\pi\) | |||||||
\(632\) | 24.2404 | 0.964231 | ||||||||
\(633\) | −6.89273 | − | 6.89273i | −0.273961 | − | 0.273961i | ||||
\(634\) | 34.1111 | 1.35472 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.37263i | 0.292344i | ||||||||
\(637\) | −3.66494 | + | 3.06008i | −0.145210 | + | 0.121245i | ||||
\(638\) | −73.4278 | − | 73.4278i | −2.90703 | − | 2.90703i | ||||
\(639\) | 4.41364 | + | 4.41364i | 0.174601 | + | 0.174601i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.6332i | 1.56542i | 0.622388 | + | 0.782709i | \(0.286162\pi\) | ||||
−0.622388 | + | 0.782709i | \(0.713838\pi\) | |||||||
\(642\) | − | 4.15237i | − | 0.163881i | ||||||
\(643\) | −2.08560 | −0.0822481 | −0.0411240 | − | 0.999154i | \(-0.513094\pi\) | ||||
−0.0411240 | + | 0.999154i | \(0.513094\pi\) | |||||||
\(644\) | 17.3471 | − | 17.3471i | 0.683571 | − | 0.683571i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.735989 | 0.0289571 | ||||||||
\(647\) | −9.45363 | − | 9.45363i | −0.371661 | − | 0.371661i | 0.496421 | − | 0.868082i | \(-0.334647\pi\) |
−0.868082 | + | 0.496421i | \(0.834647\pi\) | |||||||
\(648\) | − | 8.56180i | − | 0.336339i | ||||||
\(649\) | 42.7091 | 1.67648 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.3624 | 0.798065 | ||||||||
\(652\) | 13.9897i | 0.547879i | ||||||||
\(653\) | −7.46934 | − | 7.46934i | −0.292298 | − | 0.292298i | 0.545689 | − | 0.837987i | \(-0.316268\pi\) |
−0.837987 | + | 0.545689i | \(0.816268\pi\) | |||||||
\(654\) | 36.2785 | 1.41860 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −13.7793 | + | 13.7793i | −0.537992 | + | 0.537992i | ||||
\(657\) | 16.3296 | 0.637076 | ||||||||
\(658\) | − | 32.1895i | − | 1.25488i | ||||||
\(659\) | 13.0165i | 0.507053i | 0.967328 | + | 0.253526i | \(0.0815905\pi\) | ||||
−0.967328 | + | 0.253526i | \(0.918410\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.1615 | − | 10.1615i | −0.395238 | − | 0.395238i | 0.481311 | − | 0.876550i | \(-0.340161\pi\) |
−0.876550 | + | 0.481311i | \(0.840161\pi\) | |||||||
\(662\) | 25.8346 | + | 25.8346i | 1.00409 | + | 1.00409i | ||||
\(663\) | 0.787451 | + | 0.943099i | 0.0305821 | + | 0.0366269i | ||||
\(664\) | 52.0669i | 2.02059i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −53.1881 | −2.06100 | ||||||||
\(667\) | −15.6963 | − | 15.6963i | −0.607765 | − | 0.607765i | ||||
\(668\) | 67.0771 | 2.59529 | ||||||||
\(669\) | 6.58881 | + | 6.58881i | 0.254738 | + | 0.254738i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.0209 | − | 16.0209i | −0.618481 | − | 0.618481i | ||||
\(672\) | −4.38395 | + | 4.38395i | −0.169115 | + | 0.169115i | ||||
\(673\) | −21.0987 | + | 21.0987i | −0.813295 | + | 0.813295i | −0.985126 | − | 0.171832i | \(-0.945031\pi\) |
0.171832 | + | 0.985126i | \(0.445031\pi\) | |||||||
\(674\) | 12.5373 | − | 12.5373i | 0.482918 | − | 0.482918i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.52676 | + | 47.0184i | −0.327952 | + | 1.80840i | ||||
\(677\) | 2.76719 | − | 2.76719i | 0.106352 | − | 0.106352i | −0.651929 | − | 0.758280i | \(-0.726040\pi\) |
0.758280 | + | 0.651929i | \(0.226040\pi\) | |||||||
\(678\) | −1.79435 | −0.0689114 | ||||||||
\(679\) | − | 4.49611i | − | 0.172545i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0472 | − | 12.0472i | 0.461650 | − | 0.461650i | ||||
\(682\) | 122.202i | 4.67935i | ||||||||
\(683\) | − | 43.9664i | − | 1.68233i | −0.540780 | − | 0.841164i | \(-0.681871\pi\) | ||
0.540780 | − | 0.841164i | \(-0.318129\pi\) | |||||||
\(684\) | −4.66497 | + | 4.66497i | −0.178370 | + | 0.178370i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 47.2465i | 1.80388i | ||||||||
\(687\) | 8.16132 | 0.311374 | ||||||||
\(688\) | −6.69041 | + | 6.69041i | −0.255069 | + | 0.255069i | ||||
\(689\) | −7.85808 | − | 0.706766i | −0.299369 | − | 0.0269256i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.17085 | − | 3.17085i | 0.120625 | − | 0.120625i | −0.644218 | − | 0.764842i | \(-0.722817\pi\) |
0.764842 | + | 0.644218i | \(0.222817\pi\) | |||||||
\(692\) | 0.0272146 | − | 0.0272146i | 0.00103454 | − | 0.00103454i | ||||
\(693\) | −20.0147 | + | 20.0147i | −0.760295 | + | 0.760295i | ||||
\(694\) | −18.8394 | − | 18.8394i | −0.715132 | − | 0.715132i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −20.5037 | − | 20.5037i | −0.777189 | − | 0.777189i | ||||
\(697\) | −3.35419 | −0.127049 | ||||||||
\(698\) | −3.79109 | − | 3.79109i | −0.143495 | − | 0.143495i | ||||
\(699\) | 25.6278 | 0.969334 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.6817i | 1.08329i | 0.840606 | + | 0.541647i | \(0.182199\pi\) | ||||
−0.840606 | + | 0.541647i | \(0.817801\pi\) | |||||||
\(702\) | −40.4623 | − | 3.63923i | −1.52715 | − | 0.137354i | ||||
\(703\) | 6.07366 | + | 6.07366i | 0.229072 | + | 0.229072i | ||||
\(704\) | −43.1118 | − | 43.1118i | −1.62484 | − | 1.62484i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 46.1231i | − | 1.73587i | ||||||
\(707\) | − | 15.2661i | − | 0.574143i | ||||||
\(708\) | 26.1591 | 0.983118 | ||||||||
\(709\) | 10.9424 | − | 10.9424i | 0.410952 | − | 0.410952i | −0.471118 | − | 0.882070i | \(-0.656149\pi\) |
0.882070 | + | 0.471118i | \(0.156149\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.1139 | −0.491809 | ||||||||
\(712\) | 8.92385 | + | 8.92385i | 0.334435 | + | 0.334435i | ||||
\(713\) | 26.1226i | 0.978298i | ||||||||
\(714\) | 1.93407 | 0.0723809 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 44.3729 | 1.65829 | ||||||||
\(717\) | − | 12.9893i | − | 0.485093i | ||||||
\(718\) | 8.24474 | + | 8.24474i | 0.307691 | + | 0.307691i | ||||
\(719\) | −1.67615 | −0.0625099 | −0.0312550 | − | 0.999511i | \(-0.509950\pi\) | ||||
−0.0312550 | + | 0.999511i | \(0.509950\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.6386 | + | 15.6386i | −0.582413 | + | 0.582413i | ||||
\(722\) | −43.6203 | −1.62338 | ||||||||
\(723\) | 3.62417i | 0.134784i | ||||||||
\(724\) | − | 67.1158i | − | 2.49434i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 29.7376 | + | 29.7376i | 1.10367 | + | 1.10367i | ||||
\(727\) | −9.40127 | − | 9.40127i | −0.348674 | − | 0.348674i | 0.510942 | − | 0.859615i | \(-0.329297\pi\) |
−0.859615 | + | 0.510942i | \(0.829297\pi\) | |||||||
\(728\) | 21.9797 | + | 26.3243i | 0.814623 | + | 0.975642i | ||||
\(729\) | − | 8.37322i | − | 0.310119i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.62859 | −0.0602357 | ||||||||
\(732\) | −9.81271 | − | 9.81271i | −0.362688 | − | 0.362688i | ||||
\(733\) | 17.2489 | 0.637104 | 0.318552 | − | 0.947905i | \(-0.396804\pi\) | ||||
0.318552 | + | 0.947905i | \(0.396804\pi\) | |||||||
\(734\) | −18.3036 | − | 18.3036i | −0.675598 | − | 0.675598i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.62409 | − | 5.62409i | −0.207307 | − | 0.207307i | ||||
\(737\) | 14.5770 | − | 14.5770i | 0.536952 | − | 0.536952i | ||||
\(738\) | 32.8277 | − | 32.8277i | 1.20841 | − | 1.20841i | ||||
\(739\) | −17.3014 | + | 17.3014i | −0.636442 | + | 0.636442i | −0.949676 | − | 0.313234i | \(-0.898588\pi\) |
0.313234 | + | 0.949676i | \(0.398588\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.76012 | + | 2.10803i | 0.0646597 | + | 0.0774403i | ||||
\(742\) | −8.78225 | + | 8.78225i | −0.322406 | + | 0.322406i | ||||
\(743\) | −19.0572 | −0.699142 | −0.349571 | − | 0.936910i | \(-0.613673\pi\) | ||||
−0.349571 | + | 0.936910i | \(0.613673\pi\) | |||||||
\(744\) | 34.1231i | 1.25101i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.0213 | + | 15.0213i | −0.549971 | + | 0.549971i | ||||
\(747\) | − | 28.1678i | − | 1.03061i | ||||||
\(748\) | 7.51703i | 0.274850i | ||||||||
\(749\) | 3.20334 | − | 3.20334i | 0.117048 | − | 0.117048i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 6.28578i | − | 0.229371i | −0.993402 | − | 0.114686i | \(-0.963414\pi\) | ||
0.993402 | − | 0.114686i | \(-0.0365861\pi\) | |||||||
\(752\) | 12.2493 | 0.446687 | ||||||||
\(753\) | 14.5016 | − | 14.5016i | 0.528466 | − | 0.528466i | ||||
\(754\) | 52.2468 | − | 43.6240i | 1.90271 | − | 1.58869i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −29.2862 | + | 29.2862i | −1.06513 | + | 1.06513i | ||||
\(757\) | 1.17728 | − | 1.17728i | 0.0427888 | − | 0.0427888i | −0.685389 | − | 0.728177i | \(-0.740368\pi\) |
0.728177 | + | 0.685389i | \(0.240368\pi\) | |||||||
\(758\) | −0.795581 | + | 0.795581i | −0.0288968 | + | 0.0288968i | ||||
\(759\) | 9.98772 | + | 9.98772i | 0.362531 | + | 0.362531i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.23399 | + | 8.23399i | 0.298482 | + | 0.298482i | 0.840419 | − | 0.541937i | \(-0.182309\pi\) |
−0.541937 | + | 0.840419i | \(0.682309\pi\) | |||||||
\(762\) | −14.1022 | −0.510869 | ||||||||
\(763\) | 27.9870 | + | 27.9870i | 1.01320 | + | 1.01320i | ||||
\(764\) | 23.5206 | 0.850944 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 12.1297i | − | 0.438263i | ||||||
\(767\) | −2.50770 | + | 27.8815i | −0.0905477 | + | 1.00674i | ||||
\(768\) | −17.6378 | − | 17.6378i | −0.636450 | − | 0.636450i | ||||
\(769\) | −33.1546 | − | 33.1546i | −1.19558 | − | 1.19558i | −0.975475 | − | 0.220109i | \(-0.929359\pi\) |
−0.220109 | − | 0.975475i | \(-0.570641\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.83177i | 0.0659697i | ||||||||
\(772\) | − | 45.8782i | − | 1.65119i | ||||||
\(773\) | −53.2581 | −1.91556 | −0.957780 | − | 0.287502i | \(-0.907175\pi\) | ||||
−0.957780 | + | 0.287502i | \(0.907175\pi\) | |||||||
\(774\) | 15.9392 | − | 15.9392i | 0.572922 | − | 0.572922i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.53454 | 0.270474 | ||||||||
\(777\) | 15.9607 | + | 15.9607i | 0.572588 | + | 0.572588i | ||||
\(778\) | 80.1779i | 2.87452i | ||||||||
\(779\) | −7.49734 | −0.268620 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.8969 | 0.568837 | ||||||||
\(782\) | 2.48119i | 0.0887272i | ||||||||
\(783\) | 26.4994 | + | 26.4994i | 0.947011 | + | 0.947011i | ||||
\(784\) | −2.86010 | −0.102146 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 23.0203 | − | 23.0203i | 0.821105 | − | 0.821105i | ||||
\(787\) | 39.5579 | 1.41009 | 0.705043 | − | 0.709165i | \(-0.250928\pi\) | ||||
0.705043 | + | 0.709165i | \(0.250928\pi\) | |||||||
\(788\) | − | 73.1293i | − | 2.60512i | ||||||
\(789\) | 4.81060i | 0.171262i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.38425 | − | 1.38425i | −0.0492182 | − | 0.0492182i | ||||
\(792\) | −33.5404 | − | 33.5404i | −1.19181 | − | 1.19181i | ||||
\(793\) | 11.3995 | − | 9.51815i | 0.404808 | − | 0.337999i | ||||
\(794\) | − | 27.8176i | − | 0.987211i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 49.8950 | 1.76848 | ||||||||
\(797\) | 17.6570 | + | 17.6570i | 0.625443 | + | 0.625443i | 0.946918 | − | 0.321475i | \(-0.104179\pi\) |
−0.321475 | + | 0.946918i | \(0.604179\pi\) | |||||||
\(798\) | 4.32307 | 0.153035 | ||||||||
\(799\) | 1.49088 | + | 1.49088i | 0.0527435 | + | 0.0527435i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.82774 | − | 4.82774i | −0.170580 | − | 0.170580i | ||||
\(802\) | 15.0283 | − | 15.0283i | 0.530669 | − | 0.530669i | ||||
\(803\) | 29.4077 | − | 29.4077i | 1.03778 | − | 1.03778i | ||||
\(804\) | 8.92835 | − | 8.92835i | 0.314879 | − | 0.314879i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −79.7763 | − | 7.17518i | −2.81000 | − | 0.252735i | ||||
\(807\) | 0.241514 | − | 0.241514i | 0.00850169 | − | 0.00850169i | ||||
\(808\) | 25.5829 | 0.900002 | ||||||||
\(809\) | 26.8465i | 0.943871i | 0.881633 | + | 0.471936i | \(0.156445\pi\) | ||||
−0.881633 | + | 0.471936i | \(0.843555\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.1320 | − | 22.1320i | 0.777159 | − | 0.777159i | −0.202188 | − | 0.979347i | \(-0.564805\pi\) |
0.979347 | + | 0.202188i | \(0.0648051\pi\) | |||||||
\(812\) | − | 69.3905i | − | 2.43513i | ||||||
\(813\) | − | 4.02598i | − | 0.141197i | ||||||
\(814\) | −95.7859 | + | 95.7859i | −3.35729 | + | 3.35729i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.735989i | 0.0257648i | ||||||||
\(817\) | −3.64025 | −0.127356 | ||||||||
\(818\) | 30.6724 | − | 30.6724i | 1.07244 | − | 1.07244i | ||||
\(819\) | −11.8909 | − | 14.2412i | −0.415501 | − | 0.497629i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.5151 | − | 32.5151i | 1.13479 | − | 1.13479i | 0.145416 | − | 0.989371i | \(-0.453548\pi\) |
0.989371 | − | 0.145416i | \(-0.0464519\pi\) | |||||||
\(822\) | 14.2302 | − | 14.2302i | 0.496334 | − | 0.496334i | ||||
\(823\) | 14.6543 | − | 14.6543i | 0.510816 | − | 0.510816i | −0.403960 | − | 0.914776i | \(-0.632367\pi\) |
0.914776 | + | 0.403960i | \(0.132367\pi\) | |||||||
\(824\) | −26.2071 | − | 26.2071i | −0.912966 | − | 0.912966i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 31.1606 | + | 31.1606i | 1.08422 | + | 1.08422i | ||||
\(827\) | 2.99000 | 0.103972 | 0.0519862 | − | 0.998648i | \(-0.483445\pi\) | ||||
0.0519862 | + | 0.998648i | \(0.483445\pi\) | |||||||
\(828\) | −15.7267 | − | 15.7267i | −0.546541 | − | 0.546541i | ||||
\(829\) | 1.29806 | 0.0450836 | 0.0225418 | − | 0.999746i | \(-0.492824\pi\) | ||||
0.0225418 | + | 0.999746i | \(0.492824\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.1444i | 0.560043i | ||||||||
\(832\) | 30.6757 | − | 25.6131i | 1.06349 | − | 0.887973i | ||||
\(833\) | −0.348106 | − | 0.348106i | −0.0120611 | − | 0.0120611i | ||||
\(834\) | −9.07414 | − | 9.07414i | −0.314212 | − | 0.314212i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 16.8022i | 0.581116i | ||||||||
\(837\) | − | 44.1015i | − | 1.52437i | ||||||
\(838\) | 73.9185 | 2.55347 | ||||||||
\(839\) | −3.30809 | + | 3.30809i | −0.114208 | + | 0.114208i | −0.761901 | − | 0.647693i | \(-0.775734\pi\) |
0.647693 | + | 0.761901i | \(0.275734\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −33.7873 | −1.16508 | ||||||||
\(842\) | 16.2546 | + | 16.2546i | 0.560170 | + | 0.560170i | ||||
\(843\) | − | 9.31913i | − | 0.320968i | ||||||
\(844\) | 39.0912 | 1.34558 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −29.1827 | −1.00332 | ||||||||
\(847\) | 45.8822i | 1.57653i | ||||||||
\(848\) | −3.34198 | − | 3.34198i | −0.114764 | − | 0.114764i | ||||
\(849\) | −28.0265 | −0.961868 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.4757 | + | 20.4757i | −0.701899 | + | 0.701899i | ||||
\(852\) | 9.73678 | 0.333577 | ||||||||
\(853\) | 23.1640i | 0.793119i | 0.918009 | + | 0.396560i | \(0.129796\pi\) | ||||
−0.918009 | + | 0.396560i | \(0.870204\pi\) | |||||||
\(854\) | − | 23.3777i | − | 0.799969i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.36813 | + | 5.36813i | 0.183479 | + | 0.183479i | ||||
\(857\) | 0.287160 | + | 0.287160i | 0.00980921 | + | 0.00980921i | 0.711994 | − | 0.702185i | \(-0.247792\pi\) |
−0.702185 | + | 0.711994i | \(0.747792\pi\) | |||||||
\(858\) | −33.2451 | + | 27.7583i | −1.13497 | + | 0.947654i | ||||
\(859\) | 34.3061i | 1.17051i | 0.810850 | + | 0.585254i | \(0.199005\pi\) | ||||
−0.810850 | + | 0.585254i | \(0.800995\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.7019 | −0.671440 | ||||||||
\(862\) | 21.3449 | + | 21.3449i | 0.727009 | + | 0.727009i | ||||
\(863\) | 13.0838 | 0.445377 | 0.222688 | − | 0.974890i | \(-0.428517\pi\) | ||||
0.222688 | + | 0.974890i | \(0.428517\pi\) | |||||||
\(864\) | 9.49489 | + | 9.49489i | 0.323023 | + | 0.323023i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 36.8258 | + | 36.8258i | 1.25139 | + | 1.25139i | ||||
\(867\) | 10.9286 | − | 10.9286i | 0.371156 | − | 0.371156i | ||||
\(868\) | −57.7414 | + | 57.7414i | −1.95987 | + | 1.95987i | ||||
\(869\) | −23.6167 | + | 23.6167i | −0.801140 | + | 0.801140i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.66033 | + | 10.3721i | 0.293444 | + | 0.351446i | ||||
\(872\) | −46.9004 | + | 46.9004i | −1.58825 | + | 1.58825i | ||||
\(873\) | −4.07613 | −0.137956 | ||||||||
\(874\) | 5.54599i | 0.187596i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 18.0120 | − | 18.0120i | 0.608571 | − | 0.608571i | ||||
\(877\) | − | 43.5876i | − | 1.47185i | −0.677064 | − | 0.735924i | \(-0.736748\pi\) | ||
0.677064 | − | 0.735924i | \(-0.263252\pi\) | |||||||
\(878\) | 58.8312i | 1.98546i | ||||||||
\(879\) | 16.6878 | − | 16.6878i | 0.562867 | − | 0.562867i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 53.6106i | − | 1.80619i | −0.429445 | − | 0.903093i | \(-0.641291\pi\) | ||
0.429445 | − | 0.903093i | \(-0.358709\pi\) | |||||||
\(882\) | 6.81388 | 0.229435 | ||||||||
\(883\) | 13.4449 | − | 13.4449i | 0.452458 | − | 0.452458i | −0.443712 | − | 0.896170i | \(-0.646339\pi\) |
0.896170 | + | 0.443712i | \(0.146339\pi\) | |||||||
\(884\) | −4.90730 | − | 0.441368i | −0.165050 | − | 0.0148448i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 52.5584 | − | 52.5584i | 1.76573 | − | 1.76573i | ||||
\(887\) | −16.8456 | + | 16.8456i | −0.565618 | + | 0.565618i | −0.930898 | − | 0.365279i | \(-0.880973\pi\) |
0.365279 | + | 0.930898i | \(0.380973\pi\) | |||||||
\(888\) | −26.7468 | + | 26.7468i | −0.897564 | + | 0.897564i | ||||
\(889\) | −10.8791 | − | 10.8791i | −0.364874 | − | 0.364874i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.34149 | + | 8.34149i | 0.279450 | + | 0.279450i | ||||
\(892\) | −37.3676 | −1.25116 | ||||||||
\(893\) | 3.33244 | + | 3.33244i | 0.111516 | + | 0.111516i | ||||
\(894\) | 18.2071 | 0.608935 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 49.3808i | − | 1.64970i | ||||||
\(897\) | −7.10665 | + | 5.93378i | −0.237284 | + | 0.198123i | ||||
\(898\) | 2.15051 | + | 2.15051i | 0.0717634 | + | 0.0717634i | ||||
\(899\) | 52.2468 | + | 52.2468i | 1.74253 | + | 1.74253i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 0.813512i | − | 0.0271020i | ||||||
\(902\) | − | 118.238i | − | 3.93690i | ||||||
\(903\) | −9.56607 | −0.318339 | ||||||||
\(904\) | 2.31971 | − | 2.31971i | 0.0771523 | − | 0.0771523i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −39.9774 | −1.32816 | ||||||||
\(907\) | 18.6035 | + | 18.6035i | 0.617718 | + | 0.617718i | 0.944946 | − | 0.327228i | \(-0.106114\pi\) |
−0.327228 | + | 0.944946i | \(0.606114\pi\) | |||||||
\(908\) | 68.3242i | 2.26742i | ||||||||
\(909\) | −13.8401 | −0.459049 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.7993 | 0.589716 | 0.294858 | − | 0.955541i | \(-0.404728\pi\) | ||||
0.294858 | + | 0.955541i | \(0.404728\pi\) | |||||||
\(912\) | 1.64509i | 0.0544745i | ||||||||
\(913\) | −50.7271 | − | 50.7271i | −1.67882 | − | 1.67882i | ||||
\(914\) | −76.0231 | −2.51462 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −23.1429 | + | 23.1429i | −0.764664 | + | 0.764664i | ||||
\(917\) | 35.5179 | 1.17291 | ||||||||
\(918\) | − | 4.18888i | − | 0.138253i | ||||||
\(919\) | − | 55.5174i | − | 1.83135i | −0.401920 | − | 0.915675i | \(-0.631657\pi\) | ||
0.401920 | − | 0.915675i | \(-0.368343\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.18090 | + | 1.18090i | 0.0389121 | + | 0.0389121i | ||||
\(922\) | 3.93791 | + | 3.93791i | 0.129688 | + | 0.129688i | ||||
\(923\) | −0.933401 | + | 10.3779i | −0.0307233 | + | 0.341593i | ||||
\(924\) | 44.1538i | 1.45255i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −7.24561 | −0.238105 | ||||||||
\(927\) | 14.1778 | + | 14.1778i | 0.465661 | + | 0.465661i | ||||
\(928\) | −22.4971 | −0.738502 | ||||||||
\(929\) | −26.7318 | − | 26.7318i | −0.877040 | − | 0.877040i | 0.116187 | − | 0.993227i | \(-0.462933\pi\) |
−0.993227 | + | 0.116187i | \(0.962933\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.778091 | − | 0.778091i | −0.0255009 | − | 0.0255009i | ||||
\(932\) | −72.6725 | + | 72.6725i | −2.38047 | + | 2.38047i | ||||
\(933\) | 5.01222 | − | 5.01222i | 0.164093 | − | 0.164093i | ||||
\(934\) | 34.6539 | − | 34.6539i | 1.13391 | − | 1.13391i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 23.8653 | − | 19.9266i | 0.780063 | − | 0.651322i | ||||
\(937\) | −43.2141 | + | 43.2141i | −1.41174 | + | 1.41174i | −0.664101 | + | 0.747643i | \(0.731185\pi\) |
−0.747643 | + | 0.664101i | \(0.768815\pi\) | |||||||
\(938\) | 21.2708 | 0.694517 | ||||||||
\(939\) | − | 17.7167i | − | 0.578162i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.7446 | + | 16.7446i | −0.545859 | + | 0.545859i | −0.925240 | − | 0.379381i | \(-0.876137\pi\) |
0.379381 | + | 0.925240i | \(0.376137\pi\) | |||||||
\(942\) | 42.6773i | 1.39050i | ||||||||
\(943\) | − | 25.2753i | − | 0.823076i | ||||||
\(944\) | −11.8578 | + | 11.8578i | −0.385938 | + | 0.385938i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 57.4094i | − | 1.86654i | ||||||
\(947\) | 5.66954 | 0.184235 | 0.0921176 | − | 0.995748i | \(-0.470636\pi\) | ||||
0.0921176 | + | 0.995748i | \(0.470636\pi\) | |||||||
\(948\) | −14.4651 | + | 14.4651i | −0.469803 | + | 0.469803i | ||||
\(949\) | 17.4714 | + | 20.9247i | 0.567144 | + | 0.679246i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.27993 | + | 9.27993i | −0.300922 | + | 0.300922i | ||||
\(952\) | −2.50035 | + | 2.50035i | −0.0810367 | + | 0.0810367i | ||||
\(953\) | −8.52197 | + | 8.52197i | −0.276054 | + | 0.276054i | −0.831531 | − | 0.555478i | \(-0.812535\pi\) |
0.555478 | + | 0.831531i | \(0.312535\pi\) | |||||||
\(954\) | 7.96190 | + | 7.96190i | 0.257776 | + | 0.257776i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 36.8335 | + | 36.8335i | 1.19128 | + | 1.19128i | ||||
\(957\) | 39.9521 | 1.29147 | ||||||||
\(958\) | −60.2186 | − | 60.2186i | −1.94557 | − | 1.94557i | ||||
\(959\) | 21.9557 | 0.708987 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 55.9514i | − | 1.80489i | ||||||
\(962\) | −56.9071 | − | 68.1554i | −1.83476 | − | 2.19742i | ||||
\(963\) | −2.90412 | − | 2.90412i | −0.0935839 | − | 0.0935839i | ||||
\(964\) | −10.2770 | − | 10.2770i | −0.331000 | − | 0.331000i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 14.5741i | 0.468913i | ||||||||
\(967\) | 14.0855i | 0.452959i | 0.974016 | + | 0.226480i | \(0.0727216\pi\) | ||||
−0.974016 | + | 0.226480i | \(0.927278\pi\) | |||||||
\(968\) | −76.8889 | −2.47130 | ||||||||
\(969\) | −0.200226 | + | 0.200226i | −0.00643219 | + | 0.00643219i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.4963 | −1.33168 | −0.665840 | − | 0.746094i | \(-0.731927\pi\) | ||||
−0.665840 | + | 0.746094i | \(0.731927\pi\) | |||||||
\(972\) | 41.9875 | + | 41.9875i | 1.34675 | + | 1.34675i | ||||
\(973\) | − | 14.0005i | − | 0.448835i | ||||||
\(974\) | 48.7323 | 1.56149 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.89611 | 0.284758 | ||||||||
\(977\) | 7.91854i | 0.253337i | 0.991945 | + | 0.126668i | \(0.0404284\pi\) | ||||
−0.991945 | + | 0.126668i | \(0.959572\pi\) | |||||||
\(978\) | −5.87670 | − | 5.87670i | −0.187916 | − | 0.187916i | ||||
\(979\) | −17.3884 | −0.555737 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.3728 | − | 25.3728i | 0.810090 | − | 0.810090i | ||||
\(982\) | 18.6252 | 0.594355 | ||||||||
\(983\) | − | 55.0656i | − | 1.75632i | −0.478367 | − | 0.878160i | \(-0.658771\pi\) | ||
0.478367 | − | 0.878160i | \(-0.341229\pi\) | |||||||
\(984\) | − | 33.0163i | − | 1.05252i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.96254 | + | 4.96254i | 0.158039 | + | 0.158039i | ||||
\(987\) | 8.75717 | + | 8.75717i | 0.278744 | + | 0.278744i | ||||
\(988\) | −10.9689 | − | 0.986553i | −0.348966 | − | 0.0313864i | ||||
\(989\) | − | 12.2721i | − | 0.390232i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.92894 | 0.251871 | 0.125936 | − | 0.992038i | \(-0.459807\pi\) | ||||
0.125936 | + | 0.992038i | \(0.459807\pi\) | |||||||
\(992\) | 18.7203 | + | 18.7203i | 0.594371 | + | 0.594371i | ||||
\(993\) | −14.0566 | −0.446074 | ||||||||
\(994\) | 11.5984 | + | 11.5984i | 0.367879 | + | 0.367879i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −31.0701 | − | 31.0701i | −0.984493 | − | 0.984493i | ||||
\(997\) | −20.5699 | + | 20.5699i | −0.651457 | + | 0.651457i | −0.953344 | − | 0.301887i | \(-0.902383\pi\) |
0.301887 | + | 0.953344i | \(0.402383\pi\) | |||||||
\(998\) | −45.5740 | + | 45.5740i | −1.44262 | + | 1.44262i | ||||
\(999\) | 34.5682 | − | 34.5682i | 1.09369 | − | 1.09369i |
(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 | 325.2.f.d.18.1 | ✓ | 16 | |
5.2 | odd | 4 | 325.2.k.d.57.8 | yes | 16 | ||
5.3 | odd | 4 | 325.2.k.d.57.1 | yes | 16 | ||
5.4 | even | 2 | inner | 325.2.f.d.18.8 | yes | 16 | |
13.8 | odd | 4 | 325.2.k.d.268.8 | yes | 16 | ||
65.8 | even | 4 | inner | 325.2.f.d.307.1 | yes | 16 | |
65.34 | odd | 4 | 325.2.k.d.268.1 | yes | 16 | ||
65.47 | even | 4 | inner | 325.2.f.d.307.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
325.2.f.d.18.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
325.2.f.d.18.8 | yes | 16 | 5.4 | even | 2 | inner | |
325.2.f.d.307.1 | yes | 16 | 65.8 | even | 4 | inner | |
325.2.f.d.307.8 | yes | 16 | 65.47 | even | 4 | inner | |
325.2.k.d.57.1 | yes | 16 | 5.3 | odd | 4 | ||
325.2.k.d.57.8 | yes | 16 | 5.2 | odd | 4 | ||
325.2.k.d.268.1 | yes | 16 | 65.34 | odd | 4 | ||
325.2.k.d.268.8 | yes | 16 | 13.8 | odd | 4 |