Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,2,Mod(53,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 10, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.x (of order \(12\), degree \(4\), not 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: | \(12.9357651274\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 917.2 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.917 |
Dual form | 1620.2.x.a.53.2 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.19067 | − | 0.448288i | 0.979698 | − | 0.200480i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.73205 | + | 0.732051i | −1.03262 | + | 0.276689i | −0.735051 | − | 0.678012i | \(-0.762842\pi\) |
−0.297567 | + | 0.954701i | \(0.596175\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.44949 | − | 1.41421i | −0.738549 | − | 0.426401i | 0.0829925 | − | 0.996550i | \(-0.473552\pi\) |
−0.821541 | + | 0.570149i | \(0.806886\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.09808 | − | 1.09808i | −1.13660 | − | 0.304552i | −0.359018 | − | 0.933331i | \(-0.616888\pi\) |
−0.777584 | + | 0.628779i | \(0.783555\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.41421 | − | 1.41421i | 0.342997 | − | 0.342997i | −0.514496 | − | 0.857493i | \(-0.672021\pi\) |
0.857493 | + | 0.514496i | \(0.172021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.07055 | + | 7.72741i | −0.431740 | + | 1.61128i | 0.317009 | + | 0.948422i | \(0.397321\pi\) |
−0.748749 | + | 0.662853i | \(0.769345\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.59808 | − | 1.96410i | 0.919615 | − | 0.392820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.94975 | + | 8.57321i | −0.919145 | + | 1.59201i | −0.118428 | + | 0.992963i | \(0.537786\pi\) |
−0.800717 | + | 0.599043i | \(0.795548\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | + | 6.92820i | 0.718421 | + | 1.24434i | 0.961625 | + | 0.274367i | \(0.0884683\pi\) |
−0.243204 | + | 0.969975i | \(0.578198\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.65685 | + | 2.82843i | −0.956183 | + | 0.478091i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | − | 3.00000i | −0.493197 | − | 0.493197i | 0.416115 | − | 0.909312i | \(-0.363391\pi\) |
−0.909312 | + | 0.416115i | \(0.863391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.22474 | + | 0.707107i | −0.191273 | + | 0.110432i | −0.592578 | − | 0.805513i | \(-0.701890\pi\) |
0.401305 | + | 0.915944i | \(0.368557\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.10583 | + | 11.5911i | 0.453032 | + | 1.69074i | 0.693811 | + | 0.720157i | \(0.255930\pi\) |
−0.240779 | + | 0.970580i | \(0.577403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.866025 | − | 0.500000i | 0.123718 | − | 0.0714286i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.07107 | − | 7.07107i | −0.971286 | − | 0.971286i | 0.0283132 | − | 0.999599i | \(-0.490986\pi\) |
−0.999599 | + | 0.0283132i | \(0.990986\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | − | 2.00000i | −0.809040 | − | 0.269680i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.41421 | + | 2.44949i | 0.184115 | + | 0.318896i | 0.943278 | − | 0.332004i | \(-0.107725\pi\) |
−0.759163 | + | 0.650901i | \(0.774391\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.46979 | − | 0.568406i | −1.17458 | − | 0.0705021i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.92820 | − | 10.9282i | 0.357737 | − | 1.33509i | −0.519268 | − | 0.854611i | \(-0.673795\pi\) |
0.877005 | − | 0.480481i | \(-0.159538\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.65685i | 0.671345i | 0.941979 | + | 0.335673i | \(0.108964\pi\) | ||||
−0.941979 | + | 0.335673i | \(0.891036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.00000 | − | 7.00000i | 0.819288 | − | 0.819288i | −0.166717 | − | 0.986005i | \(-0.553317\pi\) |
0.986005 | + | 0.166717i | \(0.0533166\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.72741 | + | 2.07055i | 0.880620 | + | 0.235961i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.5911 | + | 3.10583i | −1.27229 | + | 0.340909i | −0.830908 | − | 0.556410i | \(-0.812178\pi\) |
−0.441382 | + | 0.897319i | \(0.645512\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.46410 | − | 3.73205i | 0.267269 | − | 0.404798i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.41421 | −0.149906 | −0.0749532 | − | 0.997187i | \(-0.523881\pi\) | ||||
−0.0749532 | + | 0.997187i | \(0.523881\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | 1.25794 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.79315 | + | 8.76268i | 0.183973 | + | 0.899032i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.09808 | + | 1.09808i | −0.416097 | + | 0.111493i | −0.460793 | − | 0.887508i | \(-0.652435\pi\) |
0.0446959 | + | 0.999001i | \(0.485768\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.22474 | − | 0.707107i | −0.121867 | − | 0.0703598i | 0.437828 | − | 0.899059i | \(-0.355748\pi\) |
−0.559694 | + | 0.828699i | \(0.689081\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.73205 | + | 0.732051i | 0.269197 | + | 0.0721311i | 0.390892 | − | 0.920436i | \(-0.372166\pi\) |
−0.121695 | + | 0.992567i | \(0.538833\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.82843 | + | 2.82843i | −0.273434 | + | 0.273434i | −0.830481 | − | 0.557047i | \(-0.811934\pi\) |
0.557047 | + | 0.830481i | \(0.311934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000i | 0.766261i | 0.923694 | + | 0.383131i | \(0.125154\pi\) | ||||
−0.923694 | + | 0.383131i | \(0.874846\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.03528 | + | 3.86370i | −0.0973906 | + | 0.363467i | −0.997371 | − | 0.0724636i | \(-0.976914\pi\) |
0.899980 | + | 0.435930i | \(0.143581\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.07180 | + | 17.8564i | −0.0999456 | + | 1.66512i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.82843 | + | 4.89898i | −0.259281 | + | 0.449089i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.50000 | − | 2.59808i | −0.136364 | − | 0.236189i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.19239 | − | 6.36396i | 0.822192 | − | 0.569210i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0000 | − | 10.0000i | −0.887357 | − | 0.887357i | 0.106912 | − | 0.994268i | \(-0.465904\pi\) |
−0.994268 | + | 0.106912i | \(0.965904\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.44949 | − | 1.41421i | 0.214013 | − | 0.123560i | −0.389162 | − | 0.921169i | \(-0.627235\pi\) |
0.603175 | + | 0.797609i | \(0.293902\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.92820 | − | 10.9282i | −0.253907 | − | 0.947595i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.10583 | − | 11.5911i | −0.265349 | − | 0.990295i | −0.962037 | − | 0.272921i | \(-0.912010\pi\) |
0.696688 | − | 0.717375i | \(-0.254656\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.8564 | + | 8.00000i | −1.17529 | + | 0.678551i | −0.954919 | − | 0.296866i | \(-0.904058\pi\) |
−0.220366 | + | 0.975417i | \(0.570725\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.48528 | + | 8.48528i | 0.709575 | + | 0.709575i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.00000 | + | 21.0000i | −0.581318 | + | 1.74396i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.36396 | + | 11.0227i | 0.521356 | + | 0.903015i | 0.999691 | + | 0.0248379i | \(0.00790696\pi\) |
−0.478335 | + | 0.878177i | \(0.658760\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000 | − | 17.3205i | 0.813788 | − | 1.40952i | −0.0964061 | − | 0.995342i | \(-0.530735\pi\) |
0.910195 | − | 0.414181i | \(-0.135932\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.8685 | + | 13.3843i | 0.953302 | + | 1.07505i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.29423 | + | 12.2942i | −0.262908 | + | 0.981186i | 0.700610 | + | 0.713544i | \(0.252911\pi\) |
−0.963518 | + | 0.267642i | \(0.913756\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 22.6274i | − | 1.78329i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | + | 4.00000i | −0.313304 | + | 0.313304i | −0.846188 | − | 0.532884i | \(-0.821108\pi\) |
0.532884 | + | 0.846188i | \(0.321108\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.4548 | − | 4.14110i | −1.19593 | − | 0.320448i | −0.394702 | − | 0.918809i | \(-0.629152\pi\) |
−0.801227 | + | 0.598361i | \(0.795819\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.33013 | + | 2.50000i | 0.333087 | + | 0.192308i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.86370 | + | 1.03528i | −0.293752 | + | 0.0787106i | −0.402685 | − | 0.915338i | \(-0.631923\pi\) |
0.108933 | + | 0.994049i | \(0.465256\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.1244 | + | 8.73205i | −0.840922 | + | 0.660081i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.1421 | −1.05703 | −0.528516 | − | 0.848923i | \(-0.677252\pi\) | ||||
−0.528516 | + | 0.848923i | \(0.677252\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.91688 | − | 5.22715i | −0.582060 | − | 0.384308i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.46410 | + | 1.46410i | −0.399575 | + | 0.107066i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.79796 | + | 5.65685i | 0.708955 | + | 0.409316i | 0.810674 | − | 0.585498i | \(-0.199101\pi\) |
−0.101719 | + | 0.994813i | \(0.532434\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.4904 | + | 5.49038i | 1.47493 | + | 0.395206i | 0.904618 | − | 0.426222i | \(-0.140156\pi\) |
0.570311 | + | 0.821429i | \(0.306823\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.48528 | + | 8.48528i | −0.604551 | + | 0.604551i | −0.941517 | − | 0.336966i | \(-0.890599\pi\) |
0.336966 | + | 0.941517i | \(0.390599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 12.0000i | − | 0.850657i | −0.905039 | − | 0.425329i | \(-0.860158\pi\) | ||
0.905039 | − | 0.425329i | \(-0.139842\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.24693 | − | 27.0459i | 0.508635 | − | 1.89825i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.36603 | + | 2.09808i | −0.165250 | + | 0.146536i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.65685 | − | 9.79796i | 0.391293 | − | 0.677739i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | − | 6.92820i | −0.275371 | − | 0.476957i | 0.694857 | − | 0.719148i | \(-0.255467\pi\) |
−0.970229 | + | 0.242190i | \(0.922134\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.0000 | − | 16.0000i | −1.08615 | − | 1.08615i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.34847 | + | 4.24264i | −0.494312 | + | 0.285391i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.19615 | − | 8.19615i | −0.147065 | − | 0.548855i | −0.999655 | − | 0.0262738i | \(-0.991636\pi\) |
0.852590 | − | 0.522581i | \(-0.175031\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.07055 | − | 7.72741i | −0.137427 | − | 0.512886i | −0.999976 | − | 0.00691198i | \(-0.997800\pi\) |
0.862549 | − | 0.505974i | \(-0.168867\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.19615 | − | 3.00000i | 0.343371 | − | 0.198246i | −0.318390 | − | 0.947960i | \(-0.603142\pi\) |
0.661762 | + | 0.749714i | \(0.269809\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.24264 | + | 4.24264i | 0.277945 | + | 0.277945i | 0.832288 | − | 0.554343i | \(-0.187031\pi\) |
−0.554343 | + | 0.832288i | \(0.687031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0000 | + | 24.0000i | 0.782794 | + | 1.56559i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.00000 | + | 8.66025i | −0.322078 | + | 0.557856i | −0.980917 | − | 0.194429i | \(-0.937715\pi\) |
0.658838 | + | 0.752285i | \(0.271048\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.67303 | − | 1.48356i | 0.106886 | − | 0.0947814i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.39230 | − | 16.3923i | 0.279476 | − | 1.04302i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.4558i | 1.60676i | 0.595468 | + | 0.803379i | \(0.296967\pi\) | ||||
−0.595468 | + | 0.803379i | \(0.703033\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0000 | − | 16.0000i | 1.00591 | − | 1.00591i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.3185 | + | 5.17638i | 1.20506 | + | 0.322894i | 0.804820 | − | 0.593519i | \(-0.202262\pi\) |
0.400236 | + | 0.916412i | \(0.368928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.3923 | + | 6.00000i | 0.645746 | + | 0.372822i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.4548 | − | 4.14110i | 0.952985 | − | 0.255351i | 0.251356 | − | 0.967895i | \(-0.419123\pi\) |
0.701628 | + | 0.712543i | \(0.252457\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.6603 | − | 12.3205i | −1.14629 | − | 0.756843i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.3848 | 1.12094 | 0.560470 | − | 0.828175i | \(-0.310621\pi\) | ||||
0.560470 | + | 0.828175i | \(0.310621\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | 0.728948 | 0.364474 | − | 0.931214i | \(-0.381249\pi\) | ||||
0.364474 | + | 0.931214i | \(0.381249\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.0406 | − | 1.69161i | −0.846680 | − | 0.102008i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.4904 | + | 5.49038i | −1.23115 | + | 0.329885i | −0.815026 | − | 0.579424i | \(-0.803278\pi\) |
−0.416121 | + | 0.909309i | \(0.636611\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.0227 | − | 6.36396i | −0.657559 | − | 0.379642i | 0.133787 | − | 0.991010i | \(-0.457286\pi\) |
−0.791346 | + | 0.611368i | \(0.790620\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.46410 | + | 1.46410i | 0.324807 | + | 0.0870318i | 0.417538 | − | 0.908659i | \(-0.362893\pi\) |
−0.0927310 | + | 0.995691i | \(0.529560\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.82843 | − | 2.82843i | 0.166957 | − | 0.166957i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000i | 0.764706i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.10583 | − | 11.5911i | 0.181444 | − | 0.677160i | −0.813919 | − | 0.580978i | \(-0.802670\pi\) |
0.995364 | − | 0.0961820i | \(-0.0306631\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.19615 | + | 4.73205i | 0.244309 | + | 0.275511i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.9706 | − | 29.3939i | 0.981433 | − | 1.69989i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.0000 | − | 12.0000i | −0.684876 | − | 0.684876i | 0.276219 | − | 0.961095i | \(-0.410919\pi\) |
−0.961095 | + | 0.276219i | \(0.910919\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.89898 | − | 2.82843i | 0.277796 | − | 0.160385i | −0.354629 | − | 0.935007i | \(-0.615393\pi\) |
0.632425 | + | 0.774622i | \(0.282060\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.09808 | + | 4.09808i | 0.0620669 | + | 0.231637i | 0.989991 | − | 0.141133i | \(-0.0450746\pi\) |
−0.927924 | + | 0.372770i | \(0.878408\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.55291 | − | 5.79555i | −0.0872204 | − | 0.325511i | 0.908505 | − | 0.417874i | \(-0.137225\pi\) |
−0.995725 | + | 0.0923631i | \(0.970558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.2487 | − | 14.0000i | 1.35767 | − | 0.783850i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.65685 | + | 5.65685i | 0.314756 | + | 0.314756i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.0000 | + | 3.00000i | −1.16487 | + | 0.166410i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.9706 | − | 29.3939i | −0.935617 | − | 1.62054i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000 | − | 17.3205i | 0.549650 | − | 0.952021i | −0.448649 | − | 0.893708i | \(-0.648095\pi\) |
0.998298 | − | 0.0583130i | \(-0.0185721\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.51575 | − | 25.2528i | 0.0828142 | − | 1.37971i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.09808 | + | 4.09808i | −0.0598160 | + | 0.223236i | −0.989363 | − | 0.145467i | \(-0.953532\pi\) |
0.929547 | + | 0.368703i | \(0.120198\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 22.6274i | − | 1.22534i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | − | 12.0000i | 0.647939 | − | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.72741 | − | 2.07055i | −0.414829 | − | 0.111153i | 0.0453672 | − | 0.998970i | \(-0.485554\pi\) |
−0.460196 | + | 0.887817i | \(0.652221\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.7128 | + | 16.0000i | 1.48343 | + | 0.856460i | 0.999823 | − | 0.0188232i | \(-0.00599197\pi\) |
0.483610 | + | 0.875284i | \(0.339325\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.3867 | − | 4.65874i | 0.925399 | − | 0.247960i | 0.235507 | − | 0.971873i | \(-0.424325\pi\) |
0.689892 | + | 0.723913i | \(0.257658\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.53590 | + | 12.3923i | 0.134592 | + | 0.657715i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.3137 | 0.597115 | 0.298557 | − | 0.954392i | \(-0.403495\pi\) | ||||
0.298557 | + | 0.954392i | \(0.403495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.1967 | − | 18.4727i | 0.638403 | − | 0.966906i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.1244 | + | 5.12436i | −0.998283 | + | 0.267489i | −0.720726 | − | 0.693220i | \(-0.756191\pi\) |
−0.277557 | + | 0.960709i | \(0.589525\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.4949 | + | 14.1421i | 1.27171 | + | 0.734223i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.83013 | + | 1.83013i | 0.353651 | + | 0.0947604i | 0.431271 | − | 0.902223i | \(-0.358065\pi\) |
−0.0776200 | + | 0.996983i | \(0.524732\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.6985 | − | 29.6985i | 1.52955 | − | 1.52955i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000i | 0.821865i | 0.911666 | + | 0.410932i | \(0.134797\pi\) | ||||
−0.911666 | + | 0.410932i | \(0.865203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.31749 | + | 34.7733i | −0.476101 | + | 1.77683i | 0.141064 | + | 0.990000i | \(0.454948\pi\) |
−0.617165 | + | 0.786834i | \(0.711719\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.8564 | + | 1.07180i | 0.910047 | + | 0.0546238i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.6066 | − | 18.3712i | 0.537776 | − | 0.931455i | −0.461247 | − | 0.887272i | \(-0.652598\pi\) |
0.999023 | − | 0.0441839i | \(-0.0140687\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | + | 13.8564i | 0.404577 | + | 0.700749i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.0000 | − | 17.0000i | −0.853206 | − | 0.853206i | 0.137321 | − | 0.990527i | \(-0.456151\pi\) |
−0.990527 | + | 0.137321i | \(0.956151\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.3712 | − | 10.6066i | 0.917413 | − | 0.529668i | 0.0346039 | − | 0.999401i | \(-0.488983\pi\) |
0.882809 | + | 0.469733i | \(0.155650\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.78461 | − | 32.7846i | −0.437593 | − | 1.63312i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.10583 | + | 11.5911i | 0.153950 | + | 0.574550i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.7846 | + | 12.0000i | −1.02773 | + | 0.593362i | −0.916334 | − | 0.400414i | \(-0.868866\pi\) |
−0.111398 | + | 0.993776i | \(0.535533\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.65685 | − | 5.65685i | −0.278356 | − | 0.278356i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.0000 | + | 12.0000i | −1.17811 | + | 0.589057i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.7279 | − | 22.0454i | −0.621800 | − | 1.07699i | −0.989150 | − | 0.146906i | \(-0.953068\pi\) |
0.367351 | − | 0.930082i | \(-0.380265\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0000 | − | 19.0526i | 0.536107 | − | 0.928565i | −0.463002 | − | 0.886357i | \(-0.653228\pi\) |
0.999109 | − | 0.0422075i | \(-0.0134391\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.72500 | − | 9.28032i | 0.180689 | − | 0.450162i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.2843i | 1.36241i | 0.732095 | + | 0.681203i | \(0.238543\pi\) | ||||
−0.732095 | + | 0.681203i | \(0.761457\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.0000 | − | 23.0000i | 1.10531 | − | 1.10531i | 0.111551 | − | 0.993759i | \(-0.464418\pi\) |
0.993759 | − | 0.111551i | \(-0.0355818\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −30.9096 | − | 8.28221i | −1.47861 | − | 0.396192i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.3205 | − | 10.0000i | −0.826663 | − | 0.477274i | 0.0260459 | − | 0.999661i | \(-0.491708\pi\) |
−0.852709 | + | 0.522387i | \(0.825042\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.1822 | − | 6.21166i | 1.10142 | − | 0.295125i | 0.338078 | − | 0.941118i | \(-0.390223\pi\) |
0.763343 | + | 0.645994i | \(0.223557\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.09808 | + | 0.633975i | −0.146863 | + | 0.0300533i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.41421 | 0.0667409 | 0.0333704 | − | 0.999443i | \(-0.489376\pi\) | ||||
0.0333704 | + | 0.999443i | \(0.489376\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 26.2880 | − | 5.37945i | 1.23240 | − | 0.252193i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.4904 | + | 5.49038i | −0.958500 | + | 0.256829i | −0.703965 | − | 0.710235i | \(-0.748589\pi\) |
−0.254534 | + | 0.967064i | \(0.581922\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.4722 | − | 7.77817i | −0.627463 | − | 0.362266i | 0.152306 | − | 0.988333i | \(-0.451330\pi\) |
−0.779769 | + | 0.626068i | \(0.784663\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.5167 | − | 9.51666i | −1.65060 | − | 0.442277i | −0.690819 | − | 0.723028i | \(-0.742750\pi\) |
−0.959781 | + | 0.280751i | \(0.909416\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.7990 | + | 19.7990i | −0.916188 | + | 0.916188i | −0.996750 | − | 0.0805616i | \(-0.974329\pi\) |
0.0805616 | + | 0.996750i | \(0.474329\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.0000i | 1.47762i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.85641 | + | 18.3923i | 0.360477 | + | 0.843897i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.7990 | + | 34.2929i | −0.904639 | + | 1.56688i | −0.0832378 | + | 0.996530i | \(0.526526\pi\) |
−0.821401 | + | 0.570351i | \(0.806807\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.00000 | + | 15.5885i | 0.410365 | + | 0.710772i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.48528 | + | 4.24264i | −0.385297 | + | 0.192648i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.00000 | + | 6.00000i | 0.271886 | + | 0.271886i | 0.829859 | − | 0.557973i | \(-0.188421\pi\) |
−0.557973 | + | 0.829859i | \(0.688421\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.8434 | + | 18.3848i | −1.43707 | + | 0.829693i | −0.997645 | − | 0.0685856i | \(-0.978151\pi\) |
−0.439426 | + | 0.898279i | \(0.644818\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.12436 | + | 19.1244i | 0.230789 | + | 0.861318i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.14110 | − | 15.4548i | −0.185754 | − | 0.693243i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.46410 | + | 2.00000i | −0.155074 | + | 0.0895323i | −0.575529 | − | 0.817781i | \(-0.695204\pi\) |
0.420455 | + | 0.907314i | \(0.361871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.48528 | − | 8.48528i | −0.378340 | − | 0.378340i | 0.492163 | − | 0.870503i | \(-0.336206\pi\) |
−0.870503 | + | 0.492163i | \(0.836206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.00000 | − | 1.00000i | −0.133498 | − | 0.0444994i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.707107 | − | 1.22474i | −0.0313420 | − | 0.0542859i | 0.849929 | − | 0.526897i | \(-0.176645\pi\) |
−0.881271 | + | 0.472611i | \(0.843311\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.0000 | + | 24.2487i | −0.619324 | + | 1.07270i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.31319 | + | 0.378937i | 0.278193 | + | 0.0166980i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.78461 | − | 32.7846i | 0.386347 | − | 1.44187i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.6985i | 1.30111i | 0.759457 | + | 0.650557i | \(0.225465\pi\) | ||||
−0.759457 | + | 0.650557i | \(0.774535\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.4548 | + | 4.14110i | 0.673222 | + | 0.180389i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −35.5070 | − | 20.5000i | −1.54378 | − | 0.891304i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.79555 | − | 1.55291i | 0.251033 | − | 0.0672642i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.92820 | + | 7.46410i | −0.213065 | + | 0.322701i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.82843 | −0.121829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.0000 | 1.71973 | 0.859867 | − | 0.510518i | \(-0.170546\pi\) | ||||
0.859867 | + | 0.510518i | \(0.170546\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.58630 | + | 17.5254i | 0.153620 | + | 0.750704i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.3923 | − | 4.39230i | 0.700884 | − | 0.187801i | 0.109258 | − | 0.994013i | \(-0.465153\pi\) |
0.591627 | + | 0.806212i | \(0.298486\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.2929 | − | 19.7990i | −1.46092 | − | 0.843465i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.7279 | − | 12.7279i | 0.539299 | − | 0.539299i | −0.384024 | − | 0.923323i | \(-0.625462\pi\) |
0.923323 | + | 0.384024i | \(0.125462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.21166 | − | 23.1822i | 0.261790 | − | 0.977014i | −0.702396 | − | 0.711787i | \(-0.747886\pi\) |
0.964186 | − | 0.265227i | \(-0.0854470\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.535898 | + | 8.92820i | −0.0225454 | + | 0.375612i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.77817 | + | 13.4722i | −0.326078 | + | 0.564784i | −0.981730 | − | 0.190280i | \(-0.939061\pi\) |
0.655652 | + | 0.755063i | \(0.272394\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | + | 3.46410i | 0.0836974 | + | 0.144968i | 0.904835 | − | 0.425762i | \(-0.139994\pi\) |
−0.821138 | + | 0.570730i | \(0.806660\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.65685 | + | 39.5980i | 0.235907 | + | 1.65135i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.00000 | + | 7.00000i | 0.291414 | + | 0.291414i | 0.837639 | − | 0.546225i | \(-0.183936\pi\) |
−0.546225 | + | 0.837639i | \(0.683936\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.3939 | − | 16.9706i | 1.21946 | − | 0.704058i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.32051 | + | 27.3205i | 0.303184 | + | 1.13150i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.10583 | + | 11.5911i | 0.128191 | + | 0.478416i | 0.999933 | − | 0.0115488i | \(-0.00367618\pi\) |
−0.871742 | + | 0.489965i | \(0.837010\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.7128 | + | 16.0000i | −1.14189 | + | 0.659269i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.1421 | − | 14.1421i | −0.580748 | − | 0.580748i | 0.354361 | − | 0.935109i | \(-0.384698\pi\) |
−0.935109 | + | 0.354361i | \(0.884698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.00000 | + | 12.0000i | −0.163984 | + | 0.491952i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.1421 | + | 24.4949i | 0.577832 | + | 1.00083i | 0.995728 | + | 0.0923393i | \(0.0294344\pi\) |
−0.417896 | + | 0.908495i | \(0.637232\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.0000 | − | 34.6410i | 0.815817 | − | 1.41304i | −0.0929227 | − | 0.995673i | \(-0.529621\pi\) |
0.908740 | − | 0.417363i | \(-0.137046\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.45069 | − | 5.01910i | −0.180946 | − | 0.204055i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.58846 | − | 24.5885i | 0.267417 | − | 0.998015i | −0.693337 | − | 0.720614i | \(-0.743860\pi\) |
0.960754 | − | 0.277401i | \(-0.0894731\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 50.9117i | − | 2.05967i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.0000 | + | 27.0000i | −1.09052 | + | 1.09052i | −0.0950469 | + | 0.995473i | \(0.530300\pi\) |
−0.995473 | + | 0.0950469i | \(0.969700\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.79555 | − | 1.55291i | −0.233320 | − | 0.0625180i | 0.140264 | − | 0.990114i | \(-0.455205\pi\) |
−0.373585 | + | 0.927596i | \(0.621871\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.7846 | + | 12.0000i | 0.835404 | + | 0.482321i | 0.855699 | − | 0.517473i | \(-0.173127\pi\) |
−0.0202954 | + | 0.999794i | \(0.506461\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.86370 | − | 1.03528i | 0.154796 | − | 0.0414775i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.2846 | − | 18.0622i | 0.691384 | − | 0.722487i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.48528 | −0.338330 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −26.3896 | − | 17.4238i | −1.04724 | − | 0.691444i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.09808 | + | 1.09808i | −0.162372 | + | 0.0435074i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.5176 | + | 20.5061i | 1.40286 | + | 0.809942i | 0.994685 | − | 0.102961i | \(-0.0328318\pi\) |
0.408176 | + | 0.912903i | \(0.366165\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.82843 | − | 2.82843i | 0.111197 | − | 0.111197i | −0.649319 | − | 0.760516i | \(-0.724946\pi\) |
0.760516 | + | 0.649319i | \(0.224946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 8.00000i | − | 0.314027i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.55291 | + | 5.79555i | −0.0607702 | + | 0.226798i | −0.989631 | − | 0.143630i | \(-0.954122\pi\) |
0.928861 | + | 0.370428i | \(0.120789\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.73205 | − | 4.19615i | 0.184897 | − | 0.163957i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.41421 | + | 2.44949i | −0.0550899 | + | 0.0954186i | −0.892255 | − | 0.451531i | \(-0.850878\pi\) |
0.837165 | + | 0.546950i | \(0.184211\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.00000 | + | 13.8564i | 0.311164 | + | 0.538952i | 0.978615 | − | 0.205702i | \(-0.0659478\pi\) |
−0.667451 | + | 0.744654i | \(0.732615\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.3137 | − | 22.6274i | −0.438727 | − | 0.877454i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −56.0000 | − | 56.0000i | −2.16833 | − | 2.16833i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.41858 | − | 31.4186i | −0.324513 | − | 1.21110i | −0.914801 | − | 0.403905i | \(-0.867653\pi\) |
0.590288 | − | 0.807192i | \(-0.299014\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.62347 | + | 13.5230i | 0.139261 | + | 0.519730i | 0.999944 | + | 0.0105881i | \(0.00337036\pi\) |
−0.860683 | + | 0.509142i | \(0.829963\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.3923 | − | 6.00000i | 0.398820 | − | 0.230259i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.48528 | + | 8.48528i | 0.324680 | + | 0.324680i | 0.850559 | − | 0.525879i | \(-0.176264\pi\) |
−0.525879 | + | 0.850559i | \(0.676264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | − | 24.0000i | −0.458496 | − | 0.916993i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.2132 | + | 36.7423i | 0.808159 | + | 1.39977i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.00000 | + | 10.3923i | −0.228251 | + | 0.395342i | −0.957290 | − | 0.289130i | \(-0.906634\pi\) |
0.729039 | + | 0.684472i | \(0.239967\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26.7685 | + | 23.7370i | −1.01539 | + | 0.900397i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.732051 | + | 2.73205i | −0.0277284 | + | 0.103484i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 9.89949i | − | 0.373899i | −0.982370 | − | 0.186949i | \(-0.940140\pi\) | ||
0.982370 | − | 0.186949i | \(-0.0598600\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000 | − | 12.0000i | 0.452589 | − | 0.452589i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.86370 | + | 1.03528i | 0.145310 | + | 0.0389356i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.66025 | − | 5.00000i | −0.325243 | − | 0.187779i | 0.328484 | − | 0.944509i | \(-0.393462\pi\) |
−0.653727 | + | 0.756730i | \(0.726796\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −61.8193 | + | 16.5644i | −2.31515 | + | 0.620342i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.3923 | + | 14.7846i | 0.837425 | + | 0.552913i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 39.5980 | 1.47676 | 0.738378 | − | 0.674387i | \(-0.235592\pi\) | ||||
0.738378 | + | 0.674387i | \(0.235592\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.92065 | + | 49.1421i | −0.219888 | + | 1.82509i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.19615 | − | 2.19615i | 0.303978 | − | 0.0814508i | −0.103606 | − | 0.994618i | \(-0.533038\pi\) |
0.407584 | + | 0.913168i | \(0.366371\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.6147 | + | 10.6147i | 1.46320 | + | 0.392064i | 0.900595 | − | 0.434659i | \(-0.143131\pi\) |
0.562609 | + | 0.826723i | \(0.309798\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.6274 | + | 22.6274i | −0.833492 | + | 0.833492i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 28.0000i | − | 1.03000i | −0.857191 | − | 0.514998i | \(-0.827793\pi\) | ||
0.857191 | − | 0.514998i | \(-0.172207\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.24693 | + | 27.0459i | −0.265864 | + | 0.992219i | 0.695855 | + | 0.718182i | \(0.255026\pi\) |
−0.961719 | + | 0.274036i | \(0.911641\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.8827 | + | 21.2942i | 0.691808 | + | 0.780160i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.65685 | − | 9.79796i | 0.206697 | − | 0.358010i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.0000 | + | 20.7846i | 0.437886 | + | 0.758441i | 0.997526 | − | 0.0702946i | \(-0.0223939\pi\) |
−0.559640 | + | 0.828736i | \(0.689061\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.1421 | − | 42.4264i | 0.514685 | − | 1.54406i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.00000 | + | 9.00000i | 0.327111 | + | 0.327111i | 0.851487 | − | 0.524376i | \(-0.175701\pi\) |
−0.524376 | + | 0.851487i | \(0.675701\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.2702 | + | 13.4350i | −0.843542 | + | 0.487019i | −0.858467 | − | 0.512869i | \(-0.828583\pi\) |
0.0149244 | + | 0.999889i | \(0.495249\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.85641 | − | 21.8564i | −0.212016 | − | 0.791255i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.10583 | − | 11.5911i | −0.112145 | − | 0.418531i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.92820 | − | 4.00000i | 0.249837 | − | 0.144244i | −0.369852 | − | 0.929091i | \(-0.620592\pi\) |
0.619690 | + | 0.784847i | \(0.287258\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.7279 | + | 12.7279i | 0.457792 | + | 0.457792i | 0.897930 | − | 0.440138i | \(-0.145071\pi\) |
−0.440138 | + | 0.897930i | \(0.645071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.0000 | + | 24.0000i | 1.14947 | + | 0.862105i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.82843 | − | 4.89898i | −0.101339 | − | 0.175524i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | − | 13.8564i | 0.286263 | − | 0.495821i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.70522 | + | 28.4094i | −0.0608618 | + | 1.01397i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.32051 | + | 27.3205i | −0.260948 | + | 0.973871i | 0.703736 | + | 0.710461i | \(0.251514\pi\) |
−0.964684 | + | 0.263410i | \(0.915153\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 11.3137i | − | 0.402269i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.5911 | + | 3.10583i | 0.410578 | + | 0.110014i | 0.458195 | − | 0.888852i | \(-0.348496\pi\) |
−0.0476171 | + | 0.998866i | \(0.515163\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.7846 | + | 12.0000i | 0.735307 | + | 0.424529i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27.0459 | + | 7.24693i | −0.954430 | + | 0.255739i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.1436 | − | 49.5692i | −0.357515 | − | 1.74709i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.8406 | −1.54135 | −0.770677 | − | 0.637226i | \(-0.780082\pi\) | ||||
−0.770677 | + | 0.637226i | \(0.780082\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.00000 | 0.280918 | 0.140459 | − | 0.990086i | \(-0.455142\pi\) | ||||
0.140459 | + | 0.990086i | \(0.455142\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.96953 | + | 10.5558i | −0.244132 | + | 0.369755i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.4722 | − | 7.77817i | −0.470183 | − | 0.271460i | 0.246133 | − | 0.969236i | \(-0.420840\pi\) |
−0.716316 | + | 0.697776i | \(0.754173\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.5167 | − | 9.51666i | −1.23803 | − | 0.331730i | −0.420331 | − | 0.907371i | \(-0.638086\pi\) |
−0.817702 | + | 0.575641i | \(0.804753\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.9411 | + | 33.9411i | −1.18025 | + | 1.18025i | −0.200569 | + | 0.979680i | \(0.564279\pi\) |
−0.979680 | + | 0.200569i | \(0.935721\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.00000i | 0.277851i | 0.990303 | + | 0.138926i | \(0.0443649\pi\) | ||||
−0.990303 | + | 0.138926i | \(0.955635\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.517638 | − | 1.93185i | 0.0179351 | − | 0.0669347i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.7128 | − | 2.14359i | −1.23589 | − | 0.0741821i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.65685 | + | 9.79796i | −0.195296 | + | 0.338263i | −0.946998 | − | 0.321241i | \(-0.895900\pi\) |
0.751701 | + | 0.659504i | \(0.229234\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.5000 | − | 59.7558i | −1.18966 | − | 2.06054i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.6066 | + | 3.53553i | 0.364878 | + | 0.121626i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.00000 | + | 6.00000i | 0.206162 | + | 0.206162i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.3939 | − | 16.9706i | 1.00761 | − | 0.581743i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.83013 | − | 6.83013i | −0.0626624 | − | 0.233859i | 0.927491 | − | 0.373845i | \(-0.121961\pi\) |
−0.990153 | + | 0.139986i | \(0.955294\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.8704 | + | 40.5689i | 0.371326 | + | 1.38581i | 0.858640 | + | 0.512580i | \(0.171310\pi\) |
−0.487314 | + | 0.873227i | \(0.662023\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.92820 | − | 4.00000i | 0.236387 | − | 0.136478i | −0.377128 | − | 0.926161i | \(-0.623088\pi\) |
0.613515 | + | 0.789683i | \(0.289755\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.65685 | − | 5.65685i | −0.192562 | − | 0.192562i | 0.604240 | − | 0.796802i | \(-0.293477\pi\) |
−0.796802 | + | 0.604240i | \(0.793477\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.00000 | + | 4.00000i | −0.272008 | + | 0.136004i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.0000 | + | 41.5692i | −0.813209 | + | 1.40852i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −20.4553 | + | 24.1160i | −0.691516 | + | 0.815268i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.49038 | + | 20.4904i | −0.185397 | + | 0.691911i | 0.809148 | + | 0.587605i | \(0.199929\pi\) |
−0.994545 | + | 0.104306i | \(0.966738\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.0122i | 1.38174i | 0.722981 | + | 0.690868i | \(0.242771\pi\) | ||||
−0.722981 | + | 0.690868i | \(0.757229\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.0000 | + | 20.0000i | −0.673054 | + | 0.673054i | −0.958419 | − | 0.285365i | \(-0.907885\pi\) |
0.285365 | + | 0.958419i | \(0.407885\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.3644 | + | 12.4233i | 1.55677 | + | 0.417134i | 0.931638 | − | 0.363388i | \(-0.118380\pi\) |
0.625128 | + | 0.780522i | \(0.285047\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34.6410 | + | 20.0000i | 1.16182 | + | 0.670778i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −46.3644 | + | 12.4233i | −1.55153 | + | 0.415730i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.9808 | + | 6.33975i | −1.03557 | + | 0.211914i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −79.1960 | −2.64133 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.0000 | −0.666297 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.5254 | − | 3.58630i | 0.582563 | − | 0.119213i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.8564 | + | 5.85641i | −0.725730 | + | 0.194459i | −0.602727 | − | 0.797948i | \(-0.705919\pi\) |
−0.123003 | + | 0.992406i | \(0.539253\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.4949 | + | 14.1421i | 0.811552 | + | 0.468550i | 0.847495 | − | 0.530804i | \(-0.178110\pi\) |
−0.0359424 | + | 0.999354i | \(0.511443\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.7846 | + | 8.78461i | 1.08501 | + | 0.290728i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.65685 | + | 5.65685i | −0.186806 | + | 0.186806i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.0000i | 1.05558i | 0.849374 | + | 0.527791i | \(0.176980\pi\) | ||||
−0.849374 | + | 0.527791i | \(0.823020\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.21166 | − | 23.1822i | 0.204459 | − | 0.763052i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.6865 | − | 7.90192i | −0.647289 | − | 0.259814i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.6777 | + | 30.6186i | −0.579986 | + | 1.00456i | 0.415495 | + | 0.909596i | \(0.363608\pi\) |
−0.995480 | + | 0.0949688i | \(0.969725\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | + | 3.46410i | 0.0655474 | + | 0.113531i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.3137 | + | 5.65685i | −0.369998 | + | 0.184999i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.0000 | + | 37.0000i | 1.20874 | + | 1.20874i | 0.971436 | + | 0.237301i | \(0.0762628\pi\) |
0.237301 | + | 0.971436i | \(0.423737\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.0681 | + | 19.0919i | −1.07799 | + | 0.622378i | −0.930353 | − | 0.366664i | \(-0.880500\pi\) |
−0.147636 | + | 0.989042i | \(0.547166\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.92820 | − | 10.9282i | −0.0953554 | − | 0.355871i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.28221 | − | 30.9096i | −0.269136 | − | 1.00443i | −0.959670 | − | 0.281128i | \(-0.909291\pi\) |
0.690535 | − | 0.723299i | \(-0.257375\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −36.3731 | + | 21.0000i | −1.18072 | + | 0.681689i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.4558 | + | 25.4558i | 0.824596 | + | 0.824596i | 0.986763 | − | 0.162168i | \(-0.0518485\pi\) |
−0.162168 | + | 0.986763i | \(0.551849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.0000 | + | 8.00000i | 0.776622 | + | 0.258874i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.9706 | + | 29.3939i | 0.548008 | + | 0.949178i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | + | 28.5788i | −0.532258 | + | 0.921898i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 47.3489 | + | 2.84203i | 1.52422 | + | 0.0914882i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.732051 | + | 2.73205i | −0.0235412 | + | 0.0878568i | −0.976697 | − | 0.214623i | \(-0.931148\pi\) |
0.953156 | + | 0.302480i | \(0.0978144\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 53.7401i | − | 1.72460i | −0.506396 | − | 0.862301i | \(-0.669022\pi\) | ||
0.506396 | − | 0.862301i | \(-0.330978\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.0000 | − | 32.0000i | 1.02587 | − | 1.02587i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.3867 | − | 4.65874i | −0.556249 | − | 0.149046i | −0.0302663 | − | 0.999542i | \(-0.509636\pi\) |
−0.525982 | + | 0.850495i | \(0.676302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.46410 | + | 2.00000i | 0.110713 | + | 0.0639203i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.3185 | + | 5.17638i | −0.616165 | + | 0.165101i | −0.553384 | − | 0.832926i | \(-0.686664\pi\) |
−0.0627812 | + | 0.998027i | \(0.519997\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.7846 | + | 22.3923i | −0.471077 | + | 0.713478i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.00000 | 0.127064 | 0.0635321 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635321 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.37945 | − | 26.2880i | −0.170540 | − | 0.833387i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.0263 | − | 4.02628i | 0.475887 | − | 0.127514i | −0.0128998 | − | 0.999917i | \(-0.504106\pi\) |
0.488787 | + | 0.872403i | \(0.337440\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))