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 | 53.1 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.53 |
Dual form | 1620.2.x.a.917.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 | −0.297567 | − | 0.954701i | \(-0.596175\pi\) |
−0.735051 | + | 0.678012i | \(0.762842\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.44949 | − | 1.41421i | 0.738549 | − | 0.426401i | −0.0829925 | − | 0.996550i | \(-0.526448\pi\) |
0.821541 | + | 0.570149i | \(0.193114\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.09808 | + | 1.09808i | −1.13660 | + | 0.304552i | −0.777584 | − | 0.628779i | \(-0.783555\pi\) |
−0.359018 | + | 0.933331i | \(0.616888\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.41421 | − | 1.41421i | −0.342997 | − | 0.342997i | 0.514496 | − | 0.857493i | \(-0.327979\pi\) |
−0.857493 | + | 0.514496i | \(0.827979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.07055 | + | 7.72741i | 0.431740 | + | 1.61128i | 0.748749 | + | 0.662853i | \(0.230655\pi\) |
−0.317009 | + | 0.948422i | \(0.602679\pi\) | |||||||
\(24\) | 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 | 0.800717 | + | 0.599043i | \(0.204452\pi\) |
0.118428 | + | 0.992963i | \(0.462214\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | − | 6.92820i | 0.718421 | − | 1.24434i | −0.243204 | − | 0.969975i | \(-0.578198\pi\) |
0.961625 | − | 0.274367i | \(-0.0884683\pi\) | |||||||
\(32\) | 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 | −0.909312 | − | 0.416115i | \(-0.863391\pi\) |
0.416115 | + | 0.909312i | \(0.363391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.22474 | + | 0.707107i | 0.191273 | + | 0.110432i | 0.592578 | − | 0.805513i | \(-0.298110\pi\) |
−0.401305 | + | 0.915944i | \(0.631443\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.10583 | + | 11.5911i | −0.453032 | + | 1.69074i | 0.240779 | + | 0.970580i | \(0.422597\pi\) |
−0.693811 | + | 0.720157i | \(0.744070\pi\) | |||||||
\(48\) | 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 | \(-0.509014\pi\) |
0.999599 | + | 0.0283132i | \(0.00901359\pi\) | |||||||
\(54\) | 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 | \(-0.892275\pi\) |
0.759163 | + | 0.650901i | \(0.225609\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(62\) | 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 | 0.877005 | + | 0.480481i | \(0.159538\pi\) |
−0.519268 | + | 0.854611i | \(0.673795\pi\) | |||||||
\(68\) | 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 | 0.986005 | − | 0.166717i | \(-0.0533166\pi\) |
−0.166717 | + | 0.986005i | \(0.553317\pi\) | |||||||
\(74\) | 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 | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.5911 | + | 3.10583i | 1.27229 | + | 0.340909i | 0.830908 | − | 0.556410i | \(-0.187822\pi\) |
0.441382 | + | 0.897319i | \(0.354488\pi\) | |||||||
\(84\) | 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 | \(-0.476119\pi\) | ||||
0.0749532 | + | 0.997187i | \(0.476119\pi\) | |||||||
\(90\) | 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 | 0.0446959 | − | 0.999001i | \(-0.485768\pi\) |
−0.460793 | + | 0.887508i | \(0.652435\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.22474 | − | 0.707107i | 0.121867 | − | 0.0703598i | −0.437828 | − | 0.899059i | \(-0.644252\pi\) |
0.559694 | + | 0.828699i | \(0.310919\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.73205 | − | 0.732051i | 0.269197 | − | 0.0721311i | −0.121695 | − | 0.992567i | \(-0.538833\pi\) |
0.390892 | + | 0.920436i | \(0.372166\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.82843 | + | 2.82843i | 0.273434 | + | 0.273434i | 0.830481 | − | 0.557047i | \(-0.188066\pi\) |
−0.557047 | + | 0.830481i | \(0.688066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.00000i | − | 0.766261i | −0.923694 | − | 0.383131i | \(-0.874846\pi\) | ||
0.923694 | − | 0.383131i | \(-0.125154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.03528 | + | 3.86370i | 0.0973906 | + | 0.363467i | 0.997371 | − | 0.0724636i | \(-0.0230861\pi\) |
−0.899980 | + | 0.435930i | \(0.856419\pi\) | |||||||
\(114\) | 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 | −0.994268 | − | 0.106912i | \(-0.965904\pi\) |
0.106912 | + | 0.994268i | \(0.465904\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.44949 | − | 1.41421i | −0.214013 | − | 0.123560i | 0.389162 | − | 0.921169i | \(-0.372765\pi\) |
−0.603175 | + | 0.797609i | \(0.706098\pi\) | |||||||
\(132\) | 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 | −0.696688 | − | 0.717375i | \(-0.745344\pi\) |
0.962037 | − | 0.272921i | \(-0.0879897\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.8564 | − | 8.00000i | −1.17529 | − | 0.678551i | −0.220366 | − | 0.975417i | \(-0.570725\pi\) |
−0.954919 | + | 0.296866i | \(0.904058\pi\) | |||||||
\(140\) | 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 | 0.478335 | + | 0.878177i | \(0.341240\pi\) |
−0.999691 | + | 0.0248379i | \(0.992093\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000 | + | 17.3205i | 0.813788 | + | 1.40952i | 0.910195 | + | 0.414181i | \(0.135932\pi\) |
−0.0964061 | + | 0.995342i | \(0.530735\pi\) | |||||||
\(152\) | 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 | −0.963518 | − | 0.267642i | \(-0.913756\pi\) |
0.700610 | − | 0.713544i | \(-0.252911\pi\) | |||||||
\(158\) | 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 | 0.532884 | − | 0.846188i | \(-0.321108\pi\) |
−0.846188 | + | 0.532884i | \(0.821108\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.4548 | − | 4.14110i | 1.19593 | − | 0.320448i | 0.394702 | − | 0.918809i | \(-0.370848\pi\) |
0.801227 | + | 0.598361i | \(0.204181\pi\) | |||||||
\(168\) | 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 | \(-0.368077\pi\) |
−0.108933 | + | 0.994049i | \(0.534744\pi\) | |||||||
\(174\) | 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 | \(-0.322748\pi\) | ||||
0.528516 | + | 0.848923i | \(0.322748\pi\) | |||||||
\(180\) | 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 | \(-0.800899\pi\) |
0.101719 | + | 0.994813i | \(0.467566\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.4904 | − | 5.49038i | 1.47493 | − | 0.395206i | 0.570311 | − | 0.821429i | \(-0.306823\pi\) |
0.904618 | + | 0.426222i | \(0.140156\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.48528 | + | 8.48528i | 0.604551 | + | 0.604551i | 0.941517 | − | 0.336966i | \(-0.109401\pi\) |
−0.336966 | + | 0.941517i | \(0.609401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0000i | 0.850657i | 0.905039 | + | 0.425329i | \(0.139842\pi\) | ||||
−0.905039 | + | 0.425329i | \(0.860158\pi\) | |||||||
\(200\) | 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 | −0.970229 | − | 0.242190i | \(-0.922134\pi\) |
0.694857 | + | 0.719148i | \(0.255467\pi\) | |||||||
\(212\) | 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 | 0.852590 | + | 0.522581i | \(0.175031\pi\) |
−0.999655 | + | 0.0262738i | \(0.991636\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.07055 | − | 7.72741i | 0.137427 | − | 0.512886i | −0.862549 | − | 0.505974i | \(-0.831133\pi\) |
0.999976 | − | 0.00691198i | \(-0.00220017\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.19615 | + | 3.00000i | 0.343371 | + | 0.198246i | 0.661762 | − | 0.749714i | \(-0.269809\pi\) |
−0.318390 | + | 0.947960i | \(0.603142\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.24264 | + | 4.24264i | −0.277945 | + | 0.277945i | −0.832288 | − | 0.554343i | \(-0.812969\pi\) |
0.554343 | + | 0.832288i | \(0.312969\pi\) | |||||||
\(234\) | 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 | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.00000 | − | 8.66025i | −0.322078 | − | 0.557856i | 0.658838 | − | 0.752285i | \(-0.271048\pi\) |
−0.980917 | + | 0.194429i | \(0.937715\pi\) | |||||||
\(242\) | 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 | \(-0.797738\pi\) |
−0.400236 | + | 0.916412i | \(0.631072\pi\) | |||||||
\(258\) | 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 | \(-0.580877\pi\) |
−0.701628 | + | 0.712543i | \(0.747543\pi\) | |||||||
\(264\) | 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 | \(-0.689379\pi\) | ||||
−0.560470 | + | 0.828175i | \(0.689379\pi\) | |||||||
\(270\) | 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 | −0.416121 | − | 0.909309i | \(-0.636611\pi\) |
−0.815026 | + | 0.579424i | \(0.803278\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.0227 | − | 6.36396i | 0.657559 | − | 0.379642i | −0.133787 | − | 0.991010i | \(-0.542714\pi\) |
0.791346 | + | 0.611368i | \(0.209380\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.46410 | − | 1.46410i | 0.324807 | − | 0.0870318i | −0.0927310 | − | 0.995691i | \(-0.529560\pi\) |
0.417538 | + | 0.908659i | \(0.362893\pi\) | |||||||
\(284\) | 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 | −0.995364 | − | 0.0961820i | \(-0.969337\pi\) |
0.813919 | − | 0.580978i | \(-0.197330\pi\) | |||||||
\(294\) | 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 | −0.961095 | − | 0.276219i | \(-0.910919\pi\) |
0.276219 | + | 0.961095i | \(0.410919\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.89898 | − | 2.82843i | −0.277796 | − | 0.160385i | 0.354629 | − | 0.935007i | \(-0.384607\pi\) |
−0.632425 | + | 0.774622i | \(0.717940\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.09808 | − | 4.09808i | 0.0620669 | − | 0.231637i | −0.927924 | − | 0.372770i | \(-0.878408\pi\) |
0.989991 | + | 0.141133i | \(0.0450746\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.55291 | − | 5.79555i | 0.0872204 | − | 0.325511i | −0.908505 | − | 0.417874i | \(-0.862775\pi\) |
0.995725 | + | 0.0923631i | \(0.0294421\pi\) | |||||||
\(318\) | 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 | 0.998298 | + | 0.0583130i | \(0.0185721\pi\) |
−0.448649 | + | 0.893708i | \(0.648095\pi\) | |||||||
\(332\) | 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 | 0.929547 | − | 0.368703i | \(-0.120198\pi\) |
−0.989363 | + | 0.145467i | \(0.953532\pi\) | |||||||
\(338\) | 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 | \(-0.514446\pi\) |
0.460196 | + | 0.887817i | \(0.347779\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.7128 | − | 16.0000i | 1.48343 | − | 0.856460i | 0.483610 | − | 0.875284i | \(-0.339325\pi\) |
0.999823 | + | 0.0188232i | \(0.00599197\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.3867 | − | 4.65874i | −0.925399 | − | 0.247960i | −0.235507 | − | 0.971873i | \(-0.575675\pi\) |
−0.689892 | + | 0.723913i | \(0.742342\pi\) | |||||||
\(354\) | 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 | \(-0.596505\pi\) | ||||
−0.298557 | + | 0.954392i | \(0.596505\pi\) | |||||||
\(360\) | 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 | −0.277557 | − | 0.960709i | \(-0.589525\pi\) |
−0.720726 | + | 0.693220i | \(0.756191\pi\) | |||||||
\(368\) | 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 | −0.0776200 | − | 0.996983i | \(-0.524732\pi\) |
0.431271 | + | 0.902223i | \(0.358065\pi\) | |||||||
\(374\) | 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 | \(-0.865203\pi\) | ||
0.911666 | − | 0.410932i | \(-0.134797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.31749 | + | 34.7733i | 0.476101 | + | 1.77683i | 0.617165 | + | 0.786834i | \(0.288281\pi\) |
−0.141064 | + | 0.990000i | \(0.545052\pi\) | |||||||
\(384\) | 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 | −0.999023 | − | 0.0441839i | \(-0.985931\pi\) |
0.461247 | − | 0.887272i | \(-0.347402\pi\) | |||||||
\(390\) | 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 | −0.990527 | − | 0.137321i | \(-0.956151\pi\) |
0.137321 | + | 0.990527i | \(0.456151\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.3712 | − | 10.6066i | −0.917413 | − | 0.529668i | −0.0346039 | − | 0.999401i | \(-0.511017\pi\) |
−0.882809 | + | 0.469733i | \(0.844350\pi\) | |||||||
\(402\) | 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 | −0.111398 | − | 0.993776i | \(-0.535533\pi\) |
−0.916334 | + | 0.400414i | \(0.868866\pi\) | |||||||
\(410\) | 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 | −0.367351 | − | 0.930082i | \(-0.619735\pi\) |
0.989150 | − | 0.146906i | \(-0.0469315\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0000 | + | 19.0526i | 0.536107 | + | 0.928565i | 0.999109 | + | 0.0422075i | \(0.0134391\pi\) |
−0.463002 | + | 0.886357i | \(0.653228\pi\) | |||||||
\(422\) | 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 | 0.993759 | + | 0.111551i | \(0.0355818\pi\) |
0.111551 | + | 0.993759i | \(0.464418\pi\) | |||||||
\(434\) | 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 | −0.852709 | − | 0.522387i | \(-0.825042\pi\) |
0.0260459 | + | 0.999661i | \(0.491708\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.1822 | − | 6.21166i | −1.10142 | − | 0.295125i | −0.338078 | − | 0.941118i | \(-0.609777\pi\) |
−0.763343 | + | 0.645994i | \(0.776443\pi\) | |||||||
\(444\) | 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 | \(-0.510624\pi\) | ||||
−0.0333704 | + | 0.999443i | \(0.510624\pi\) | |||||||
\(450\) | 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 | −0.254534 | − | 0.967064i | \(-0.581922\pi\) |
−0.703965 | + | 0.710235i | \(0.748589\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.4722 | − | 7.77817i | 0.627463 | − | 0.362266i | −0.152306 | − | 0.988333i | \(-0.548670\pi\) |
0.779769 | + | 0.626068i | \(0.215337\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.5167 | + | 9.51666i | −1.65060 | + | 0.442277i | −0.959781 | − | 0.280751i | \(-0.909416\pi\) |
−0.690819 | + | 0.723028i | \(0.742750\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.7990 | + | 19.7990i | 0.916188 | + | 0.916188i | 0.996750 | − | 0.0805616i | \(-0.0256714\pi\) |
−0.0805616 | + | 0.996750i | \(0.525671\pi\) | |||||||
\(468\) | 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 | 0.821401 | + | 0.570351i | \(0.193193\pi\) |
0.0832378 | + | 0.996530i | \(0.473474\pi\) | |||||||
\(480\) | 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 | −0.557973 | − | 0.829859i | \(-0.688421\pi\) |
0.829859 | + | 0.557973i | \(0.188421\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.8434 | + | 18.3848i | 1.43707 | + | 0.829693i | 0.997645 | − | 0.0685856i | \(-0.0218486\pi\) |
0.439426 | + | 0.898279i | \(0.355182\pi\) | |||||||
\(492\) | 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 | 0.420455 | − | 0.907314i | \(-0.361871\pi\) |
−0.575529 | + | 0.817781i | \(0.695204\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.48528 | − | 8.48528i | 0.378340 | − | 0.378340i | −0.492163 | − | 0.870503i | \(-0.663794\pi\) |
0.870503 | + | 0.492163i | \(0.163794\pi\) | |||||||
\(504\) | 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 | \(-0.823355\pi\) |
0.881271 | + | 0.472611i | \(0.156689\pi\) | |||||||
\(510\) | 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 | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(524\) | 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 | 0.591627 | − | 0.806212i | \(-0.298486\pi\) |
0.109258 | + | 0.994013i | \(0.465153\pi\) | |||||||
\(548\) | 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 | \(-0.374538\pi\) |
−0.923323 | + | 0.384024i | \(0.874538\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.21166 | − | 23.1822i | −0.261790 | − | 0.977014i | −0.964186 | − | 0.265227i | \(-0.914553\pi\) |
0.702396 | − | 0.711787i | \(-0.252114\pi\) | |||||||
\(564\) | 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 | \(-0.0609394\pi\) |
−0.655652 | + | 0.755063i | \(0.727606\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | − | 3.46410i | 0.0836974 | − | 0.144968i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) |
0.904835 | + | 0.425762i | \(0.139994\pi\) | |||||||
\(572\) | 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 | −0.546225 | − | 0.837639i | \(-0.683936\pi\) |
0.837639 | + | 0.546225i | \(0.183936\pi\) | |||||||
\(578\) | 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 | \(-0.996324\pi\) |
0.871742 | + | 0.489965i | \(0.162990\pi\) | |||||||
\(588\) | 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 | \(-0.615302\pi\) |
0.935109 | + | 0.354361i | \(0.115302\pi\) | |||||||
\(594\) | 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 | 0.417896 | + | 0.908495i | \(0.362768\pi\) |
−0.995728 | + | 0.0923393i | \(0.970566\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.0000 | + | 34.6410i | 0.815817 | + | 1.41304i | 0.908740 | + | 0.417363i | \(0.137046\pi\) |
−0.0929227 | + | 0.995673i | \(0.529621\pi\) | |||||||
\(602\) | 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 | 0.960754 | + | 0.277401i | \(0.0894731\pi\) |
−0.693337 | + | 0.720614i | \(0.743860\pi\) | |||||||
\(608\) | 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 | −0.995473 | − | 0.0950469i | \(-0.969700\pi\) |
−0.0950469 | − | 0.995473i | \(-0.530300\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.79555 | − | 1.55291i | 0.233320 | − | 0.0625180i | −0.140264 | − | 0.990114i | \(-0.544795\pi\) |
0.373585 | + | 0.927596i | \(0.378129\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.7846 | − | 12.0000i | 0.835404 | − | 0.482321i | −0.0202954 | − | 0.999794i | \(-0.506461\pi\) |
0.855699 | + | 0.517473i | \(0.173127\pi\) | |||||||
\(620\) | 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 | \(-0.967168\pi\) |
−0.408176 | + | 0.912903i | \(0.633835\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.82843 | − | 2.82843i | −0.111197 | − | 0.111197i | 0.649319 | − | 0.760516i | \(-0.275054\pi\) |
−0.760516 | + | 0.649319i | \(0.775054\pi\) | |||||||
\(648\) | 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 | \(-0.0458777\pi\) |
−0.928861 | + | 0.370428i | \(0.879211\pi\) | |||||||
\(654\) | 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 | \(-0.149122\pi\) |
−0.837165 | + | 0.546950i | \(0.815789\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.00000 | − | 13.8564i | 0.311164 | − | 0.538952i | −0.667451 | − | 0.744654i | \(-0.732615\pi\) |
0.978615 | + | 0.205702i | \(0.0659478\pi\) | |||||||
\(662\) | 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 | 0.590288 | + | 0.807192i | \(0.299014\pi\) |
−0.914801 | + | 0.403905i | \(0.867653\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.62347 | + | 13.5230i | −0.139261 | + | 0.519730i | 0.860683 | + | 0.509142i | \(0.170037\pi\) |
−0.999944 | + | 0.0105881i | \(0.996630\pi\) | |||||||
\(678\) | 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 | \(-0.823736\pi\) |
0.525879 | + | 0.850559i | \(0.323736\pi\) | |||||||
\(684\) | 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 | 0.729039 | − | 0.684472i | \(-0.239967\pi\) |
−0.957290 | + | 0.289130i | \(0.906634\pi\) | |||||||
\(692\) | 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 | −0.653727 | − | 0.756730i | \(-0.726796\pi\) |
0.328484 | + | 0.944509i | \(0.393462\pi\) | |||||||
\(710\) | 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 | \(-0.764408\pi\) | ||||
−0.738378 | + | 0.674387i | \(0.764408\pi\) | |||||||
\(720\) | 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 | 0.407584 | − | 0.913168i | \(-0.366371\pi\) |
−0.103606 | + | 0.994618i | \(0.533038\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.6147 | − | 10.6147i | 1.46320 | − | 0.392064i | 0.562609 | − | 0.826723i | \(-0.309798\pi\) |
0.900595 | + | 0.434659i | \(0.143131\pi\) | |||||||
\(734\) | 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 | \(0.172207\pi\) | ||||
−0.857191 | + | 0.514998i | \(0.827793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.24693 | + | 27.0459i | 0.265864 | + | 0.992219i | 0.961719 | + | 0.274036i | \(0.0883589\pi\) |
−0.695855 | + | 0.718182i | \(0.744974\pi\) | |||||||
\(744\) | 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 | −0.559640 | − | 0.828736i | \(-0.689061\pi\) |
0.997526 | + | 0.0702946i | \(0.0223939\pi\) | |||||||
\(752\) | 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 | −0.524376 | − | 0.851487i | \(-0.675701\pi\) |
0.851487 | + | 0.524376i | \(0.175701\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.2702 | + | 13.4350i | 0.843542 | + | 0.487019i | 0.858467 | − | 0.512869i | \(-0.171417\pi\) |
−0.0149244 | + | 0.999889i | \(0.504751\pi\) | |||||||
\(762\) | 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 | 0.619690 | − | 0.784847i | \(-0.287258\pi\) |
−0.369852 | + | 0.929091i | \(0.620592\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.7279 | + | 12.7279i | −0.457792 | + | 0.457792i | −0.897930 | − | 0.440138i | \(-0.854929\pi\) |
0.440138 | + | 0.897930i | \(0.354929\pi\) | |||||||
\(774\) | 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 | −0.964684 | − | 0.263410i | \(-0.915153\pi\) |
0.703736 | − | 0.710461i | \(-0.251514\pi\) | |||||||
\(788\) | 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 | \(-0.651504\pi\) |
0.0476171 | + | 0.998866i | \(0.484837\pi\) | |||||||
\(798\) | 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 | \(-0.219918\pi\) | ||||
0.770677 | + | 0.637226i | \(0.219918\pi\) | |||||||
\(810\) | 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 | \(-0.579160\pi\) |
0.716316 | + | 0.697776i | \(0.245827\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.5167 | + | 9.51666i | −1.23803 | + | 0.331730i | −0.817702 | − | 0.575641i | \(-0.804753\pi\) |
−0.420331 | + | 0.907371i | \(0.638086\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.9411 | + | 33.9411i | 1.18025 | + | 1.18025i | 0.979680 | + | 0.200569i | \(0.0642791\pi\) |
0.200569 | + | 0.979680i | \(0.435721\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 8.00000i | − | 0.277851i | −0.990303 | − | 0.138926i | \(-0.955635\pi\) | ||
0.990303 | − | 0.138926i | \(-0.0443649\pi\) | |||||||
\(830\) | 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 | \(-0.104100\pi\) |
−0.751701 | + | 0.659504i | \(0.770766\pi\) | |||||||
\(840\) | 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 | −0.990153 | − | 0.139986i | \(-0.955294\pi\) |
0.927491 | + | 0.373845i | \(0.121961\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.8704 | + | 40.5689i | −0.371326 | + | 1.38581i | 0.487314 | + | 0.873227i | \(0.337977\pi\) |
−0.858640 | + | 0.512580i | \(0.828690\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.92820 | + | 4.00000i | 0.236387 | + | 0.136478i | 0.613515 | − | 0.789683i | \(-0.289755\pi\) |
−0.377128 | + | 0.926161i | \(0.623088\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.65685 | − | 5.65685i | 0.192562 | − | 0.192562i | −0.604240 | − | 0.796802i | \(-0.706523\pi\) |
0.796802 | + | 0.604240i | \(0.206523\pi\) | |||||||
\(864\) | 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 | −0.994545 | − | 0.104306i | \(-0.966738\pi\) |
0.809148 | − | 0.587605i | \(-0.199929\pi\) | |||||||
\(878\) | 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 | 0.285365 | − | 0.958419i | \(-0.407885\pi\) |
−0.958419 | + | 0.285365i | \(0.907885\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −46.3644 | + | 12.4233i | −1.55677 | + | 0.417134i | −0.931638 | − | 0.363388i | \(-0.881620\pi\) |
−0.625128 | + | 0.780522i | \(0.714953\pi\) | |||||||
\(888\) | 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 | −0.123003 | − | 0.992406i | \(-0.539253\pi\) |
−0.602727 | + | 0.797948i | \(0.705919\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.4949 | + | 14.1421i | −0.811552 | + | 0.468550i | −0.847495 | − | 0.530804i | \(-0.821890\pi\) |
0.0359424 | + | 0.999354i | \(0.488557\pi\) | |||||||
\(912\) | 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 | \(-0.823020\pi\) | ||
0.849374 | − | 0.527791i | \(-0.176980\pi\) | |||||||
\(920\) | 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 | 0.995480 | + | 0.0949688i | \(0.0302751\pi\) |
−0.415495 | + | 0.909596i | \(0.636392\pi\) | |||||||
\(930\) | 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 | 0.237301 | − | 0.971436i | \(-0.423737\pi\) |
0.971436 | − | 0.237301i | \(-0.0762628\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.0681 | + | 19.0919i | 1.07799 | + | 0.622378i | 0.930353 | − | 0.366664i | \(-0.119500\pi\) |
0.147636 | + | 0.989042i | \(0.452834\pi\) | |||||||
\(942\) | 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 | −0.690535 | − | 0.723299i | \(-0.742625\pi\) |
0.959670 | − | 0.281128i | \(-0.0907087\pi\) | |||||||
\(948\) | 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 | \(-0.948151\pi\) |
0.162168 | + | 0.986763i | \(0.448151\pi\) | |||||||
\(954\) | 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 | 0.953156 | − | 0.302480i | \(-0.0978144\pi\) |
−0.976697 | + | 0.214623i | \(0.931148\pi\) | |||||||
\(968\) | 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 | \(-0.490364\pi\) |
0.525982 | + | 0.850495i | \(0.323698\pi\) | |||||||
\(978\) | 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 | \(-0.313336\pi\) |
0.0627812 | + | 0.998027i | \(0.480003\pi\) | |||||||
\(984\) | 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 | 0.488787 | − | 0.872403i | \(-0.337440\pi\) |
−0.0128998 | + | 0.999917i | \(0.504106\pi\) | |||||||
\(998\) | 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 \(a_p\))