Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(1,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3234.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.a (trivial) |
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: | yes |
Analytic conductor: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.621.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 462) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.66908\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.454904 | 0.203439 | 0.101720 | − | 0.994813i | \(-0.467566\pi\) | ||||
0.101720 | + | 0.994813i | \(0.467566\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.454904 | 0.143853 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0.909808 | 0.252335 | 0.126168 | − | 0.992009i | \(-0.459732\pi\) | ||||
0.126168 | + | 0.992009i | \(0.459732\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.454904 | 0.117456 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | 0.121268 | − | 0.992620i | \(-0.461304\pi\) | ||||
0.121268 | + | 0.992620i | \(0.461304\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 3.88325 | 0.890880 | 0.445440 | − | 0.895312i | \(-0.353047\pi\) | ||||
0.445440 | + | 0.895312i | \(0.353047\pi\) | |||||||
\(20\) | 0.454904 | 0.101720 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 8.33816 | 1.73863 | 0.869313 | − | 0.494262i | \(-0.164562\pi\) | ||||
0.869313 | + | 0.494262i | \(0.164562\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.79306 | −0.958612 | ||||||||
\(26\) | 0.909808 | 0.178428 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.79306 | −0.518659 | −0.259329 | − | 0.965789i | \(-0.583502\pi\) | ||||
−0.259329 | + | 0.965789i | \(0.583502\pi\) | |||||||
\(30\) | 0.454904 | 0.0830537 | ||||||||
\(31\) | −9.58612 | −1.72172 | −0.860859 | − | 0.508843i | \(-0.830073\pi\) | ||||
−0.860859 | + | 0.508843i | \(0.830073\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 7.88325 | 1.29600 | 0.647999 | − | 0.761641i | \(-0.275606\pi\) | ||||
0.647999 | + | 0.761641i | \(0.275606\pi\) | |||||||
\(38\) | 3.88325 | 0.629947 | ||||||||
\(39\) | 0.909808 | 0.145686 | ||||||||
\(40\) | 0.454904 | 0.0719267 | ||||||||
\(41\) | −1.79306 | −0.280029 | −0.140015 | − | 0.990149i | \(-0.544715\pi\) | ||||
−0.140015 | + | 0.990149i | \(0.544715\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.88325 | 1.20218 | 0.601092 | − | 0.799179i | \(-0.294732\pi\) | ||||
0.601092 | + | 0.799179i | \(0.294732\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0.454904 | 0.0678131 | ||||||||
\(46\) | 8.33816 | 1.22939 | ||||||||
\(47\) | 0.338158 | 0.0493254 | 0.0246627 | − | 0.999696i | \(-0.492149\pi\) | ||||
0.0246627 | + | 0.999696i | \(0.492149\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.79306 | −0.677841 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 0.909808 | 0.126168 | ||||||||
\(53\) | 0.909808 | 0.124972 | 0.0624859 | − | 0.998046i | \(-0.480097\pi\) | ||||
0.0624859 | + | 0.998046i | \(0.480097\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.454904 | 0.0613393 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.88325 | 0.514350 | ||||||||
\(58\) | −2.79306 | −0.366747 | ||||||||
\(59\) | 6.97345 | 0.907865 | 0.453933 | − | 0.891036i | \(-0.350021\pi\) | ||||
0.453933 | + | 0.891036i | \(0.350021\pi\) | |||||||
\(60\) | 0.454904 | 0.0587279 | ||||||||
\(61\) | −14.0410 | −1.79777 | −0.898885 | − | 0.438185i | \(-0.855621\pi\) | ||||
−0.898885 | + | 0.438185i | \(0.855621\pi\) | |||||||
\(62\) | −9.58612 | −1.21744 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.413875 | 0.0513349 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | −3.79306 | −0.463396 | −0.231698 | − | 0.972788i | \(-0.574428\pi\) | ||||
−0.231698 | + | 0.972788i | \(0.574428\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | 8.33816 | 1.00380 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.79306 | −0.568832 | −0.284416 | − | 0.958701i | \(-0.591800\pi\) | ||||
−0.284416 | + | 0.958701i | \(0.591800\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 10.6763 | 1.24957 | 0.624784 | − | 0.780798i | \(-0.285187\pi\) | ||||
0.624784 | + | 0.780798i | \(0.285187\pi\) | |||||||
\(74\) | 7.88325 | 0.916410 | ||||||||
\(75\) | −4.79306 | −0.553455 | ||||||||
\(76\) | 3.88325 | 0.445440 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.909808 | 0.103015 | ||||||||
\(79\) | 5.36471 | 0.603577 | 0.301789 | − | 0.953375i | \(-0.402416\pi\) | ||||
0.301789 | + | 0.953375i | \(0.402416\pi\) | |||||||
\(80\) | 0.454904 | 0.0508598 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.79306 | −0.198011 | ||||||||
\(83\) | 1.97345 | 0.216614 | 0.108307 | − | 0.994118i | \(-0.465457\pi\) | ||||
0.108307 | + | 0.994118i | \(0.465457\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.454904 | 0.0493413 | ||||||||
\(86\) | 7.88325 | 0.850073 | ||||||||
\(87\) | −2.79306 | −0.299448 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −11.0902 | −1.17556 | −0.587779 | − | 0.809022i | \(-0.699998\pi\) | ||||
−0.587779 | + | 0.809022i | \(0.699998\pi\) | |||||||
\(90\) | 0.454904 | 0.0479511 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.33816 | 0.869313 | ||||||||
\(93\) | −9.58612 | −0.994035 | ||||||||
\(94\) | 0.338158 | 0.0348784 | ||||||||
\(95\) | 1.76651 | 0.181240 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 14.5861 | 1.48100 | 0.740498 | − | 0.672058i | \(-0.234590\pi\) | ||||
0.740498 | + | 0.672058i | \(0.234590\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −4.79306 | −0.479306 | ||||||||
\(101\) | −8.06364 | −0.802362 | −0.401181 | − | 0.915999i | \(-0.631400\pi\) | ||||
−0.401181 | + | 0.915999i | \(0.631400\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 5.76651 | 0.568191 | 0.284095 | − | 0.958796i | \(-0.408307\pi\) | ||||
0.284095 | + | 0.958796i | \(0.408307\pi\) | |||||||
\(104\) | 0.909808 | 0.0892140 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.909808 | 0.0883684 | ||||||||
\(107\) | 15.6127 | 1.50933 | 0.754667 | − | 0.656108i | \(-0.227798\pi\) | ||||
0.754667 | + | 0.656108i | \(0.227798\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 14.0410 | 1.34489 | 0.672443 | − | 0.740149i | \(-0.265245\pi\) | ||||
0.672443 | + | 0.740149i | \(0.265245\pi\) | |||||||
\(110\) | 0.454904 | 0.0433734 | ||||||||
\(111\) | 7.88325 | 0.748245 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.58612 | 0.713643 | 0.356821 | − | 0.934173i | \(-0.383861\pi\) | ||||
0.356821 | + | 0.934173i | \(0.383861\pi\) | |||||||
\(114\) | 3.88325 | 0.363700 | ||||||||
\(115\) | 3.79306 | 0.353705 | ||||||||
\(116\) | −2.79306 | −0.259329 | ||||||||
\(117\) | 0.909808 | 0.0841118 | ||||||||
\(118\) | 6.97345 | 0.641958 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.454904 | 0.0415269 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −14.0410 | −1.27122 | ||||||||
\(123\) | −1.79306 | −0.161675 | ||||||||
\(124\) | −9.58612 | −0.860859 | ||||||||
\(125\) | −4.45490 | −0.398459 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.42835 | 0.659159 | 0.329580 | − | 0.944128i | \(-0.393093\pi\) | ||||
0.329580 | + | 0.944128i | \(0.393093\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 7.88325 | 0.694082 | ||||||||
\(130\) | 0.413875 | 0.0362993 | ||||||||
\(131\) | −19.4057 | −1.69549 | −0.847744 | − | 0.530406i | \(-0.822039\pi\) | ||||
−0.847744 | + | 0.530406i | \(0.822039\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.79306 | −0.327671 | ||||||||
\(135\) | 0.454904 | 0.0391519 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | 0.909808 | 0.0777302 | 0.0388651 | − | 0.999244i | \(-0.487626\pi\) | ||||
0.0388651 | + | 0.999244i | \(0.487626\pi\) | |||||||
\(138\) | 8.33816 | 0.709791 | ||||||||
\(139\) | −8.37919 | −0.710713 | −0.355357 | − | 0.934731i | \(-0.615641\pi\) | ||||
−0.355357 | + | 0.934731i | \(0.615641\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.338158 | 0.0284781 | ||||||||
\(142\) | −4.79306 | −0.402225 | ||||||||
\(143\) | 0.909808 | 0.0760820 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.27058 | −0.105516 | ||||||||
\(146\) | 10.6763 | 0.883578 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.88325 | 0.647999 | ||||||||
\(149\) | 4.11675 | 0.337257 | 0.168628 | − | 0.985680i | \(-0.446066\pi\) | ||||
0.168628 | + | 0.985680i | \(0.446066\pi\) | |||||||
\(150\) | −4.79306 | −0.391352 | ||||||||
\(151\) | −6.15777 | −0.501113 | −0.250556 | − | 0.968102i | \(-0.580614\pi\) | ||||
−0.250556 | + | 0.968102i | \(0.580614\pi\) | |||||||
\(152\) | 3.88325 | 0.314973 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.36077 | −0.350265 | ||||||||
\(156\) | 0.909808 | 0.0728430 | ||||||||
\(157\) | −17.6498 | −1.40860 | −0.704302 | − | 0.709900i | \(-0.748740\pi\) | ||||
−0.704302 | + | 0.709900i | \(0.748740\pi\) | |||||||
\(158\) | 5.36471 | 0.426794 | ||||||||
\(159\) | 0.909808 | 0.0721525 | ||||||||
\(160\) | 0.454904 | 0.0359633 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −11.6127 | −0.909575 | −0.454788 | − | 0.890600i | \(-0.650285\pi\) | ||||
−0.454788 | + | 0.890600i | \(0.650285\pi\) | |||||||
\(164\) | −1.79306 | −0.140015 | ||||||||
\(165\) | 0.454904 | 0.0354142 | ||||||||
\(166\) | 1.97345 | 0.153169 | ||||||||
\(167\) | −4.85670 | −0.375823 | −0.187911 | − | 0.982186i | \(-0.560172\pi\) | ||||
−0.187911 | + | 0.982186i | \(0.560172\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.1722 | −0.936327 | ||||||||
\(170\) | 0.454904 | 0.0348896 | ||||||||
\(171\) | 3.88325 | 0.296960 | ||||||||
\(172\) | 7.88325 | 0.601092 | ||||||||
\(173\) | −25.5861 | −1.94528 | −0.972639 | − | 0.232324i | \(-0.925367\pi\) | ||||
−0.972639 | + | 0.232324i | \(0.925367\pi\) | |||||||
\(174\) | −2.79306 | −0.211742 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 6.97345 | 0.524156 | ||||||||
\(178\) | −11.0902 | −0.831245 | ||||||||
\(179\) | −15.7029 | −1.17369 | −0.586844 | − | 0.809700i | \(-0.699630\pi\) | ||||
−0.586844 | + | 0.809700i | \(0.699630\pi\) | |||||||
\(180\) | 0.454904 | 0.0339065 | ||||||||
\(181\) | −2.49593 | −0.185521 | −0.0927606 | − | 0.995688i | \(-0.529569\pi\) | ||||
−0.0927606 | + | 0.995688i | \(0.529569\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.0410 | −1.03794 | ||||||||
\(184\) | 8.33816 | 0.614697 | ||||||||
\(185\) | 3.58612 | 0.263657 | ||||||||
\(186\) | −9.58612 | −0.702889 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 0.338158 | 0.0246627 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.76651 | 0.128156 | ||||||||
\(191\) | 9.81962 | 0.710523 | 0.355261 | − | 0.934767i | \(-0.384392\pi\) | ||||
0.355261 | + | 0.934767i | \(0.384392\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 6.85670 | 0.493556 | 0.246778 | − | 0.969072i | \(-0.420628\pi\) | ||||
0.246778 | + | 0.969072i | \(0.420628\pi\) | |||||||
\(194\) | 14.5861 | 1.04722 | ||||||||
\(195\) | 0.413875 | 0.0296382 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.4694 | 1.67212 | 0.836062 | − | 0.548635i | \(-0.184852\pi\) | ||||
0.836062 | + | 0.548635i | \(0.184852\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | −2.23349 | −0.158328 | −0.0791640 | − | 0.996862i | \(-0.525225\pi\) | ||||
−0.0791640 | + | 0.996862i | \(0.525225\pi\) | |||||||
\(200\) | −4.79306 | −0.338921 | ||||||||
\(201\) | −3.79306 | −0.267542 | ||||||||
\(202\) | −8.06364 | −0.567356 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | −0.815671 | −0.0569690 | ||||||||
\(206\) | 5.76651 | 0.401772 | ||||||||
\(207\) | 8.33816 | 0.579542 | ||||||||
\(208\) | 0.909808 | 0.0630838 | ||||||||
\(209\) | 3.88325 | 0.268610 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.2624 | −1.25724 | −0.628619 | − | 0.777713i | \(-0.716380\pi\) | ||||
−0.628619 | + | 0.777713i | \(0.716380\pi\) | |||||||
\(212\) | 0.909808 | 0.0624859 | ||||||||
\(213\) | −4.79306 | −0.328415 | ||||||||
\(214\) | 15.6127 | 1.06726 | ||||||||
\(215\) | 3.58612 | 0.244572 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 14.0410 | 0.950978 | ||||||||
\(219\) | 10.6763 | 0.721439 | ||||||||
\(220\) | 0.454904 | 0.0306696 | ||||||||
\(221\) | 0.909808 | 0.0612003 | ||||||||
\(222\) | 7.88325 | 0.529089 | ||||||||
\(223\) | 12.4959 | 0.836790 | 0.418395 | − | 0.908265i | \(-0.362593\pi\) | ||||
0.418395 | + | 0.908265i | \(0.362593\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.79306 | −0.319537 | ||||||||
\(226\) | 7.58612 | 0.504621 | ||||||||
\(227\) | 9.79306 | 0.649988 | 0.324994 | − | 0.945716i | \(-0.394638\pi\) | ||||
0.324994 | + | 0.945716i | \(0.394638\pi\) | |||||||
\(228\) | 3.88325 | 0.257175 | ||||||||
\(229\) | 8.67632 | 0.573347 | 0.286674 | − | 0.958028i | \(-0.407450\pi\) | ||||
0.286674 | + | 0.958028i | \(0.407450\pi\) | |||||||
\(230\) | 3.79306 | 0.250107 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.79306 | −0.183374 | ||||||||
\(233\) | 16.7665 | 1.09841 | 0.549205 | − | 0.835688i | \(-0.314931\pi\) | ||||
0.549205 | + | 0.835688i | \(0.314931\pi\) | |||||||
\(234\) | 0.909808 | 0.0594760 | ||||||||
\(235\) | 0.153830 | 0.0100347 | ||||||||
\(236\) | 6.97345 | 0.453933 | ||||||||
\(237\) | 5.36471 | 0.348476 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.2624 | −1.69878 | −0.849388 | − | 0.527769i | \(-0.823029\pi\) | ||||
−0.849388 | + | 0.527769i | \(0.823029\pi\) | |||||||
\(240\) | 0.454904 | 0.0293639 | ||||||||
\(241\) | 7.94689 | 0.511904 | 0.255952 | − | 0.966689i | \(-0.417611\pi\) | ||||
0.255952 | + | 0.966689i | \(0.417611\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −14.0410 | −0.898885 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.79306 | −0.114321 | ||||||||
\(247\) | 3.53302 | 0.224800 | ||||||||
\(248\) | −9.58612 | −0.608720 | ||||||||
\(249\) | 1.97345 | 0.125062 | ||||||||
\(250\) | −4.45490 | −0.281753 | ||||||||
\(251\) | −3.93636 | −0.248461 | −0.124230 | − | 0.992253i | \(-0.539646\pi\) | ||||
−0.124230 | + | 0.992253i | \(0.539646\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.33816 | 0.524216 | ||||||||
\(254\) | 7.42835 | 0.466096 | ||||||||
\(255\) | 0.454904 | 0.0284872 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.0902 | −0.941300 | −0.470650 | − | 0.882320i | \(-0.655981\pi\) | ||||
−0.470650 | + | 0.882320i | \(0.655981\pi\) | |||||||
\(258\) | 7.88325 | 0.490790 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.413875 | 0.0256675 | ||||||||
\(261\) | −2.79306 | −0.172886 | ||||||||
\(262\) | −19.4057 | −1.19889 | ||||||||
\(263\) | −28.6232 | −1.76498 | −0.882491 | − | 0.470329i | \(-0.844135\pi\) | ||||
−0.882491 | + | 0.470329i | \(0.844135\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | 0.413875 | 0.0254242 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.0902 | −0.678709 | ||||||||
\(268\) | −3.79306 | −0.231698 | ||||||||
\(269\) | −22.9508 | −1.39934 | −0.699669 | − | 0.714468i | \(-0.746669\pi\) | ||||
−0.699669 | + | 0.714468i | \(0.746669\pi\) | |||||||
\(270\) | 0.454904 | 0.0276846 | ||||||||
\(271\) | 9.81962 | 0.596499 | 0.298250 | − | 0.954488i | \(-0.403597\pi\) | ||||
0.298250 | + | 0.954488i | \(0.403597\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.909808 | 0.0549635 | ||||||||
\(275\) | −4.79306 | −0.289033 | ||||||||
\(276\) | 8.33816 | 0.501898 | ||||||||
\(277\) | 10.7294 | 0.644669 | 0.322334 | − | 0.946626i | \(-0.395532\pi\) | ||||
0.322334 | + | 0.946626i | \(0.395532\pi\) | |||||||
\(278\) | −8.37919 | −0.502550 | ||||||||
\(279\) | −9.58612 | −0.573906 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.58612 | 0.154275 | 0.0771376 | − | 0.997020i | \(-0.475422\pi\) | ||||
0.0771376 | + | 0.997020i | \(0.475422\pi\) | |||||||
\(282\) | 0.338158 | 0.0201370 | ||||||||
\(283\) | −20.0821 | −1.19375 | −0.596877 | − | 0.802333i | \(-0.703592\pi\) | ||||
−0.596877 | + | 0.802333i | \(0.703592\pi\) | |||||||
\(284\) | −4.79306 | −0.284416 | ||||||||
\(285\) | 1.76651 | 0.104639 | ||||||||
\(286\) | 0.909808 | 0.0537981 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | −1.27058 | −0.0746108 | ||||||||
\(291\) | 14.5861 | 0.855054 | ||||||||
\(292\) | 10.6763 | 0.624784 | ||||||||
\(293\) | 10.3792 | 0.606359 | 0.303179 | − | 0.952934i | \(-0.401952\pi\) | ||||
0.303179 | + | 0.952934i | \(0.401952\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.17225 | 0.184695 | ||||||||
\(296\) | 7.88325 | 0.458205 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 4.11675 | 0.238477 | ||||||||
\(299\) | 7.58612 | 0.438717 | ||||||||
\(300\) | −4.79306 | −0.276728 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.15777 | −0.354340 | ||||||||
\(303\) | −8.06364 | −0.463244 | ||||||||
\(304\) | 3.88325 | 0.222720 | ||||||||
\(305\) | −6.38732 | −0.365737 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 9.76651 | 0.557404 | 0.278702 | − | 0.960378i | \(-0.410096\pi\) | ||||
0.278702 | + | 0.960378i | \(0.410096\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.76651 | 0.328045 | ||||||||
\(310\) | −4.36077 | −0.247675 | ||||||||
\(311\) | −6.51854 | −0.369633 | −0.184816 | − | 0.982773i | \(-0.559169\pi\) | ||||
−0.184816 | + | 0.982773i | \(0.559169\pi\) | |||||||
\(312\) | 0.909808 | 0.0515077 | ||||||||
\(313\) | 30.7931 | 1.74053 | 0.870263 | − | 0.492587i | \(-0.163949\pi\) | ||||
0.870263 | + | 0.492587i | \(0.163949\pi\) | |||||||
\(314\) | −17.6498 | −0.996034 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.36471 | 0.301789 | ||||||||
\(317\) | −27.6272 | −1.55170 | −0.775848 | − | 0.630920i | \(-0.782678\pi\) | ||||
−0.775848 | + | 0.630920i | \(0.782678\pi\) | |||||||
\(318\) | 0.909808 | 0.0510195 | ||||||||
\(319\) | −2.79306 | −0.156381 | ||||||||
\(320\) | 0.454904 | 0.0254299 | ||||||||
\(321\) | 15.6127 | 0.871415 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.88325 | 0.216070 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.36077 | −0.241892 | ||||||||
\(326\) | −11.6127 | −0.643167 | ||||||||
\(327\) | 14.0410 | 0.776471 | ||||||||
\(328\) | −1.79306 | −0.0990053 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.454904 | 0.0250416 | ||||||||
\(331\) | −28.9653 | −1.59208 | −0.796039 | − | 0.605246i | \(-0.793075\pi\) | ||||
−0.796039 | + | 0.605246i | \(0.793075\pi\) | |||||||
\(332\) | 1.97345 | 0.108307 | ||||||||
\(333\) | 7.88325 | 0.432000 | ||||||||
\(334\) | −4.85670 | −0.265747 | ||||||||
\(335\) | −1.72548 | −0.0942730 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.03708 | −0.492281 | −0.246141 | − | 0.969234i | \(-0.579163\pi\) | ||||
−0.246141 | + | 0.969234i | \(0.579163\pi\) | |||||||
\(338\) | −12.1722 | −0.662083 | ||||||||
\(339\) | 7.58612 | 0.412022 | ||||||||
\(340\) | 0.454904 | 0.0246706 | ||||||||
\(341\) | −9.58612 | −0.519118 | ||||||||
\(342\) | 3.88325 | 0.209982 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7.88325 | 0.425037 | ||||||||
\(345\) | 3.79306 | 0.204212 | ||||||||
\(346\) | −25.5861 | −1.37552 | ||||||||
\(347\) | −21.6127 | −1.16023 | −0.580115 | − | 0.814535i | \(-0.696992\pi\) | ||||
−0.580115 | + | 0.814535i | \(0.696992\pi\) | |||||||
\(348\) | −2.79306 | −0.149724 | ||||||||
\(349\) | 14.2745 | 0.764098 | 0.382049 | − | 0.924142i | \(-0.375219\pi\) | ||||
0.382049 | + | 0.924142i | \(0.375219\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.909808 | 0.0485620 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −28.4959 | −1.51669 | −0.758343 | − | 0.651856i | \(-0.773991\pi\) | ||||
−0.758343 | + | 0.651856i | \(0.773991\pi\) | |||||||
\(354\) | 6.97345 | 0.370634 | ||||||||
\(355\) | −2.18038 | −0.115723 | ||||||||
\(356\) | −11.0902 | −0.587779 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.7029 | −0.829922 | ||||||||
\(359\) | −13.6392 | −0.719851 | −0.359926 | − | 0.932981i | \(-0.617198\pi\) | ||||
−0.359926 | + | 0.932981i | \(0.617198\pi\) | |||||||
\(360\) | 0.454904 | 0.0239756 | ||||||||
\(361\) | −3.92034 | −0.206334 | ||||||||
\(362\) | −2.49593 | −0.131183 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.85670 | 0.254211 | ||||||||
\(366\) | −14.0410 | −0.733936 | ||||||||
\(367\) | 22.7294 | 1.18647 | 0.593233 | − | 0.805031i | \(-0.297851\pi\) | ||||
0.593233 | + | 0.805031i | \(0.297851\pi\) | |||||||
\(368\) | 8.33816 | 0.434657 | ||||||||
\(369\) | −1.79306 | −0.0933431 | ||||||||
\(370\) | 3.58612 | 0.186434 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −9.58612 | −0.497017 | ||||||||
\(373\) | 10.4018 | 0.538585 | 0.269292 | − | 0.963058i | \(-0.413210\pi\) | ||||
0.269292 | + | 0.963058i | \(0.413210\pi\) | |||||||
\(374\) | 1.00000 | 0.0517088 | ||||||||
\(375\) | −4.45490 | −0.230050 | ||||||||
\(376\) | 0.338158 | 0.0174392 | ||||||||
\(377\) | −2.54115 | −0.130876 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.61268 | 0.391037 | 0.195519 | − | 0.980700i | \(-0.437361\pi\) | ||||
0.195519 | + | 0.980700i | \(0.437361\pi\) | |||||||
\(380\) | 1.76651 | 0.0906200 | ||||||||
\(381\) | 7.42835 | 0.380566 | ||||||||
\(382\) | 9.81962 | 0.502415 | ||||||||
\(383\) | −22.1457 | −1.13159 | −0.565796 | − | 0.824545i | \(-0.691431\pi\) | ||||
−0.565796 | + | 0.824545i | \(0.691431\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.85670 | 0.348997 | ||||||||
\(387\) | 7.88325 | 0.400728 | ||||||||
\(388\) | 14.5861 | 0.740498 | ||||||||
\(389\) | −3.54510 | −0.179743 | −0.0898717 | − | 0.995953i | \(-0.528646\pi\) | ||||
−0.0898717 | + | 0.995953i | \(0.528646\pi\) | |||||||
\(390\) | 0.413875 | 0.0209574 | ||||||||
\(391\) | 8.33816 | 0.421679 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.4057 | −0.978890 | ||||||||
\(394\) | 23.4694 | 1.18237 | ||||||||
\(395\) | 2.44043 | 0.122791 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | −2.55957 | −0.128461 | −0.0642306 | − | 0.997935i | \(-0.520459\pi\) | ||||
−0.0642306 | + | 0.997935i | \(0.520459\pi\) | |||||||
\(398\) | −2.23349 | −0.111955 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.79306 | −0.239653 | ||||||||
\(401\) | 10.4959 | 0.524142 | 0.262071 | − | 0.965049i | \(-0.415595\pi\) | ||||
0.262071 | + | 0.965049i | \(0.415595\pi\) | |||||||
\(402\) | −3.79306 | −0.189181 | ||||||||
\(403\) | −8.72153 | −0.434451 | ||||||||
\(404\) | −8.06364 | −0.401181 | ||||||||
\(405\) | 0.454904 | 0.0226044 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.88325 | 0.390758 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 15.8486 | 0.783661 | 0.391831 | − | 0.920037i | \(-0.371842\pi\) | ||||
0.391831 | + | 0.920037i | \(0.371842\pi\) | |||||||
\(410\) | −0.815671 | −0.0402831 | ||||||||
\(411\) | 0.909808 | 0.0448775 | ||||||||
\(412\) | 5.76651 | 0.284095 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8.33816 | 0.409798 | ||||||||
\(415\) | 0.897729 | 0.0440678 | ||||||||
\(416\) | 0.909808 | 0.0446070 | ||||||||
\(417\) | −8.37919 | −0.410331 | ||||||||
\(418\) | 3.88325 | 0.189936 | ||||||||
\(419\) | −9.52249 | −0.465204 | −0.232602 | − | 0.972572i | \(-0.574724\pi\) | ||||
−0.232602 | + | 0.972572i | \(0.574724\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.530621 | −0.0258609 | −0.0129305 | − | 0.999916i | \(-0.504116\pi\) | ||||
−0.0129305 | + | 0.999916i | \(0.504116\pi\) | |||||||
\(422\) | −18.2624 | −0.889002 | ||||||||
\(423\) | 0.338158 | 0.0164418 | ||||||||
\(424\) | 0.909808 | 0.0441842 | ||||||||
\(425\) | −4.79306 | −0.232498 | ||||||||
\(426\) | −4.79306 | −0.232225 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 15.6127 | 0.754667 | ||||||||
\(429\) | 0.909808 | 0.0439260 | ||||||||
\(430\) | 3.58612 | 0.172938 | ||||||||
\(431\) | 20.8036 | 1.00207 | 0.501037 | − | 0.865426i | \(-0.332952\pi\) | ||||
0.501037 | + | 0.865426i | \(0.332952\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −4.40574 | −0.211726 | −0.105863 | − | 0.994381i | \(-0.533761\pi\) | ||||
−0.105863 | + | 0.994381i | \(0.533761\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.27058 | −0.0609194 | ||||||||
\(436\) | 14.0410 | 0.672443 | ||||||||
\(437\) | 32.3792 | 1.54891 | ||||||||
\(438\) | 10.6763 | 0.510134 | ||||||||
\(439\) | −15.1949 | −0.725211 | −0.362606 | − | 0.931943i | \(-0.618113\pi\) | ||||
−0.362606 | + | 0.931943i | \(0.618113\pi\) | |||||||
\(440\) | 0.454904 | 0.0216867 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.909808 | 0.0432752 | ||||||||
\(443\) | −11.3873 | −0.541028 | −0.270514 | − | 0.962716i | \(-0.587194\pi\) | ||||
−0.270514 | + | 0.962716i | \(0.587194\pi\) | |||||||
\(444\) | 7.88325 | 0.374123 | ||||||||
\(445\) | −5.04497 | −0.239155 | ||||||||
\(446\) | 12.4959 | 0.591700 | ||||||||
\(447\) | 4.11675 | 0.194715 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.0821 | −1.13650 | −0.568251 | − | 0.822855i | \(-0.692380\pi\) | ||||
−0.568251 | + | 0.822855i | \(0.692380\pi\) | |||||||
\(450\) | −4.79306 | −0.225947 | ||||||||
\(451\) | −1.79306 | −0.0844320 | ||||||||
\(452\) | 7.58612 | 0.356821 | ||||||||
\(453\) | −6.15777 | −0.289317 | ||||||||
\(454\) | 9.79306 | 0.459611 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.88325 | 0.181850 | ||||||||
\(457\) | −29.5330 | −1.38150 | −0.690748 | − | 0.723095i | \(-0.742719\pi\) | ||||
−0.690748 | + | 0.723095i | \(0.742719\pi\) | |||||||
\(458\) | 8.67632 | 0.405418 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 3.79306 | 0.176852 | ||||||||
\(461\) | 4.14569 | 0.193084 | 0.0965421 | − | 0.995329i | \(-0.469222\pi\) | ||||
0.0965421 | + | 0.995329i | \(0.469222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.32368 | −0.433308 | −0.216654 | − | 0.976248i | \(-0.569514\pi\) | ||||
−0.216654 | + | 0.976248i | \(0.569514\pi\) | |||||||
\(464\) | −2.79306 | −0.129665 | ||||||||
\(465\) | −4.36077 | −0.202226 | ||||||||
\(466\) | 16.7665 | 0.776693 | ||||||||
\(467\) | 36.5596 | 1.69178 | 0.845888 | − | 0.533361i | \(-0.179071\pi\) | ||||
0.845888 | + | 0.533361i | \(0.179071\pi\) | |||||||
\(468\) | 0.909808 | 0.0420559 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.153830 | 0.00709563 | ||||||||
\(471\) | −17.6498 | −0.813258 | ||||||||
\(472\) | 6.97345 | 0.320979 | ||||||||
\(473\) | 7.88325 | 0.362472 | ||||||||
\(474\) | 5.36471 | 0.246409 | ||||||||
\(475\) | −18.6127 | −0.854008 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.909808 | 0.0416573 | ||||||||
\(478\) | −26.2624 | −1.20122 | ||||||||
\(479\) | 0.729425 | 0.0333283 | 0.0166641 | − | 0.999861i | \(-0.494695\pi\) | ||||
0.0166641 | + | 0.999861i | \(0.494695\pi\) | |||||||
\(480\) | 0.454904 | 0.0207634 | ||||||||
\(481\) | 7.17225 | 0.327026 | ||||||||
\(482\) | 7.94689 | 0.361971 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 6.63529 | 0.301293 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −36.8567 | −1.67014 | −0.835068 | − | 0.550146i | \(-0.814572\pi\) | ||||
−0.835068 | + | 0.550146i | \(0.814572\pi\) | |||||||
\(488\) | −14.0410 | −0.635608 | ||||||||
\(489\) | −11.6127 | −0.525143 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.5065 | 1.15109 | 0.575545 | − | 0.817770i | \(-0.304790\pi\) | ||||
0.575545 | + | 0.817770i | \(0.304790\pi\) | |||||||
\(492\) | −1.79306 | −0.0808375 | ||||||||
\(493\) | −2.79306 | −0.125793 | ||||||||
\(494\) | 3.53302 | 0.158958 | ||||||||
\(495\) | 0.454904 | 0.0204464 | ||||||||
\(496\) | −9.58612 | −0.430430 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.97345 | 0.0884322 | ||||||||
\(499\) | −4.12728 | −0.184762 | −0.0923811 | − | 0.995724i | \(-0.529448\pi\) | ||||
−0.0923811 | + | 0.995724i | \(0.529448\pi\) | |||||||
\(500\) | −4.45490 | −0.199229 | ||||||||
\(501\) | −4.85670 | −0.216981 | ||||||||
\(502\) | −3.93636 | −0.175688 | ||||||||
\(503\) | −6.85670 | −0.305725 | −0.152863 | − | 0.988247i | \(-0.548849\pi\) | ||||
−0.152863 | + | 0.988247i | \(0.548849\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.66818 | −0.163232 | ||||||||
\(506\) | 8.33816 | 0.370676 | ||||||||
\(507\) | −12.1722 | −0.540589 | ||||||||
\(508\) | 7.42835 | 0.329580 | ||||||||
\(509\) | 16.4428 | 0.728815 | 0.364408 | − | 0.931240i | \(-0.381271\pi\) | ||||
0.364408 | + | 0.931240i | \(0.381271\pi\) | |||||||
\(510\) | 0.454904 | 0.0201435 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.88325 | 0.171450 | ||||||||
\(514\) | −15.0902 | −0.665600 | ||||||||
\(515\) | 2.62321 | 0.115592 | ||||||||
\(516\) | 7.88325 | 0.347041 | ||||||||
\(517\) | 0.338158 | 0.0148722 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.5861 | −1.12311 | ||||||||
\(520\) | 0.413875 | 0.0181496 | ||||||||
\(521\) | −5.63923 | −0.247059 | −0.123530 | − | 0.992341i | \(-0.539421\pi\) | ||||
−0.123530 | + | 0.992341i | \(0.539421\pi\) | |||||||
\(522\) | −2.79306 | −0.122249 | ||||||||
\(523\) | −4.08206 | −0.178496 | −0.0892480 | − | 0.996009i | \(-0.528446\pi\) | ||||
−0.0892480 | + | 0.996009i | \(0.528446\pi\) | |||||||
\(524\) | −19.4057 | −0.847744 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.6232 | −1.24803 | ||||||||
\(527\) | −9.58612 | −0.417578 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | 46.5249 | 2.02282 | ||||||||
\(530\) | 0.413875 | 0.0179776 | ||||||||
\(531\) | 6.97345 | 0.302622 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.63134 | −0.0706613 | ||||||||
\(534\) | −11.0902 | −0.479920 | ||||||||
\(535\) | 7.10227 | 0.307058 | ||||||||
\(536\) | −3.79306 | −0.163835 | ||||||||
\(537\) | −15.7029 | −0.677629 | ||||||||
\(538\) | −22.9508 | −0.989481 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.454904 | 0.0195760 | ||||||||
\(541\) | −4.89773 | −0.210570 | −0.105285 | − | 0.994442i | \(-0.533575\pi\) | ||||
−0.105285 | + | 0.994442i | \(0.533575\pi\) | |||||||
\(542\) | 9.81962 | 0.421789 | ||||||||
\(543\) | −2.49593 | −0.107111 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 6.38732 | 0.273603 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.4694 | 0.917964 | 0.458982 | − | 0.888445i | \(-0.348214\pi\) | ||||
0.458982 | + | 0.888445i | \(0.348214\pi\) | |||||||
\(548\) | 0.909808 | 0.0388651 | ||||||||
\(549\) | −14.0410 | −0.599256 | ||||||||
\(550\) | −4.79306 | −0.204377 | ||||||||
\(551\) | −10.8462 | −0.462062 | ||||||||
\(552\) | 8.33816 | 0.354896 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10.7294 | 0.455850 | ||||||||
\(555\) | 3.58612 | 0.152223 | ||||||||
\(556\) | −8.37919 | −0.355357 | ||||||||
\(557\) | −39.4694 | −1.67237 | −0.836186 | − | 0.548447i | \(-0.815219\pi\) | ||||
−0.836186 | + | 0.548447i | \(0.815219\pi\) | |||||||
\(558\) | −9.58612 | −0.405813 | ||||||||
\(559\) | 7.17225 | 0.303354 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.00000 | 0.0422200 | ||||||||
\(562\) | 2.58612 | 0.109089 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0.338158 | 0.0142390 | ||||||||
\(565\) | 3.45096 | 0.145183 | ||||||||
\(566\) | −20.0821 | −0.844112 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.79306 | −0.201112 | ||||||||
\(569\) | 34.1988 | 1.43369 | 0.716844 | − | 0.697233i | \(-0.245586\pi\) | ||||
0.716844 | + | 0.697233i | \(0.245586\pi\) | |||||||
\(570\) | 1.76651 | 0.0739909 | ||||||||
\(571\) | 14.7931 | 0.619070 | 0.309535 | − | 0.950888i | \(-0.399827\pi\) | ||||
0.309535 | + | 0.950888i | \(0.399827\pi\) | |||||||
\(572\) | 0.909808 | 0.0380410 | ||||||||
\(573\) | 9.81962 | 0.410220 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −39.9653 | −1.66667 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −7.19880 | −0.299690 | −0.149845 | − | 0.988709i | \(-0.547877\pi\) | ||||
−0.149845 | + | 0.988709i | \(0.547877\pi\) | |||||||
\(578\) | −16.0000 | −0.665512 | ||||||||
\(579\) | 6.85670 | 0.284955 | ||||||||
\(580\) | −1.27058 | −0.0527578 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 14.5861 | 0.604614 | ||||||||
\(583\) | 0.909808 | 0.0376804 | ||||||||
\(584\) | 10.6763 | 0.441789 | ||||||||
\(585\) | 0.413875 | 0.0171116 | ||||||||
\(586\) | 10.3792 | 0.428760 | ||||||||
\(587\) | −44.4959 | −1.83654 | −0.918272 | − | 0.395951i | \(-0.870415\pi\) | ||||
−0.918272 | + | 0.395951i | \(0.870415\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −37.2254 | −1.53384 | ||||||||
\(590\) | 3.17225 | 0.130599 | ||||||||
\(591\) | 23.4694 | 0.965401 | ||||||||
\(592\) | 7.88325 | 0.324000 | ||||||||
\(593\) | 17.9653 | 0.737747 | 0.368873 | − | 0.929480i | \(-0.379744\pi\) | ||||
0.368873 | + | 0.929480i | \(0.379744\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.11675 | 0.168628 | ||||||||
\(597\) | −2.23349 | −0.0914107 | ||||||||
\(598\) | 7.58612 | 0.310220 | ||||||||
\(599\) | −25.8075 | −1.05447 | −0.527234 | − | 0.849720i | \(-0.676771\pi\) | ||||
−0.527234 | + | 0.849720i | \(0.676771\pi\) | |||||||
\(600\) | −4.79306 | −0.195676 | ||||||||
\(601\) | 10.4139 | 0.424791 | 0.212395 | − | 0.977184i | \(-0.431874\pi\) | ||||
0.212395 | + | 0.977184i | \(0.431874\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.79306 | −0.154465 | ||||||||
\(604\) | −6.15777 | −0.250556 | ||||||||
\(605\) | 0.454904 | 0.0184945 | ||||||||
\(606\) | −8.06364 | −0.327563 | ||||||||
\(607\) | −8.89773 | −0.361148 | −0.180574 | − | 0.983561i | \(-0.557795\pi\) | ||||
−0.180574 | + | 0.983561i | \(0.557795\pi\) | |||||||
\(608\) | 3.88325 | 0.157487 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.38732 | −0.258615 | ||||||||
\(611\) | 0.307659 | 0.0124466 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | −23.6272 | −0.954292 | −0.477146 | − | 0.878824i | \(-0.658329\pi\) | ||||
−0.477146 | + | 0.878824i | \(0.658329\pi\) | |||||||
\(614\) | 9.76651 | 0.394144 | ||||||||
\(615\) | −0.815671 | −0.0328910 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.8486 | −1.44321 | −0.721604 | − | 0.692306i | \(-0.756595\pi\) | ||||
−0.721604 | + | 0.692306i | \(0.756595\pi\) | |||||||
\(618\) | 5.76651 | 0.231963 | ||||||||
\(619\) | 27.9203 | 1.12221 | 0.561107 | − | 0.827744i | \(-0.310376\pi\) | ||||
0.561107 | + | 0.827744i | \(0.310376\pi\) | |||||||
\(620\) | −4.36077 | −0.175133 | ||||||||
\(621\) | 8.33816 | 0.334599 | ||||||||
\(622\) | −6.51854 | −0.261370 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.909808 | 0.0364215 | ||||||||
\(625\) | 21.9388 | 0.877550 | ||||||||
\(626\) | 30.7931 | 1.23074 | ||||||||
\(627\) | 3.88325 | 0.155082 | ||||||||
\(628\) | −17.6498 | −0.704302 | ||||||||
\(629\) | 7.88325 | 0.314326 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.6682 | 1.73840 | 0.869201 | − | 0.494458i | \(-0.164633\pi\) | ||||
0.869201 | + | 0.494458i | \(0.164633\pi\) | |||||||
\(632\) | 5.36471 | 0.213397 | ||||||||
\(633\) | −18.2624 | −0.725867 | ||||||||
\(634\) | −27.6272 | −1.09721 | ||||||||
\(635\) | 3.37919 | 0.134099 | ||||||||
\(636\) | 0.909808 | 0.0360762 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.79306 | −0.110578 | ||||||||
\(639\) | −4.79306 | −0.189611 | ||||||||
\(640\) | 0.454904 | 0.0179817 | ||||||||
\(641\) | −19.7665 | −0.780730 | −0.390365 | − | 0.920660i | \(-0.627651\pi\) | ||||
−0.390365 | + | 0.920660i | \(0.627651\pi\) | |||||||
\(642\) | 15.6127 | 0.616183 | ||||||||
\(643\) | 24.7584 | 0.976375 | 0.488187 | − | 0.872739i | \(-0.337658\pi\) | ||||
0.488187 | + | 0.872739i | \(0.337658\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.58612 | 0.141204 | ||||||||
\(646\) | 3.88325 | 0.152785 | ||||||||
\(647\) | 31.0781 | 1.22181 | 0.610903 | − | 0.791705i | \(-0.290806\pi\) | ||||
0.610903 | + | 0.791705i | \(0.290806\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 6.97345 | 0.273732 | ||||||||
\(650\) | −4.36077 | −0.171043 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.6127 | −0.454788 | ||||||||
\(653\) | 22.7173 | 0.888998 | 0.444499 | − | 0.895779i | \(-0.353382\pi\) | ||||
0.444499 | + | 0.895779i | \(0.353382\pi\) | |||||||
\(654\) | 14.0410 | 0.549048 | ||||||||
\(655\) | −8.82775 | −0.344929 | ||||||||
\(656\) | −1.79306 | −0.0700073 | ||||||||
\(657\) | 10.6763 | 0.416523 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.6127 | 1.69891 | 0.849454 | − | 0.527662i | \(-0.176931\pi\) | ||||
0.849454 | + | 0.527662i | \(0.176931\pi\) | |||||||
\(660\) | 0.454904 | 0.0177071 | ||||||||
\(661\) | −7.93636 | −0.308689 | −0.154344 | − | 0.988017i | \(-0.549327\pi\) | ||||
−0.154344 | + | 0.988017i | \(0.549327\pi\) | |||||||
\(662\) | −28.9653 | −1.12577 | ||||||||
\(663\) | 0.909808 | 0.0353340 | ||||||||
\(664\) | 1.97345 | 0.0765846 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.88325 | 0.305470 | ||||||||
\(667\) | −23.2890 | −0.901753 | ||||||||
\(668\) | −4.85670 | −0.187911 | ||||||||
\(669\) | 12.4959 | 0.483121 | ||||||||
\(670\) | −1.72548 | −0.0666611 | ||||||||
\(671\) | −14.0410 | −0.542048 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.9388 | 1.42388 | 0.711942 | − | 0.702238i | \(-0.247816\pi\) | ||||
0.711942 | + | 0.702238i | \(0.247816\pi\) | |||||||
\(674\) | −9.03708 | −0.348095 | ||||||||
\(675\) | −4.79306 | −0.184485 | ||||||||
\(676\) | −12.1722 | −0.468163 | ||||||||
\(677\) | −39.6498 | −1.52386 | −0.761932 | − | 0.647657i | \(-0.775749\pi\) | ||||
−0.761932 | + | 0.647657i | \(0.775749\pi\) | |||||||
\(678\) | 7.58612 | 0.291343 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.454904 | 0.0174448 | ||||||||
\(681\) | 9.79306 | 0.375271 | ||||||||
\(682\) | −9.58612 | −0.367072 | ||||||||
\(683\) | −45.5514 | −1.74298 | −0.871489 | − | 0.490416i | \(-0.836845\pi\) | ||||
−0.871489 | + | 0.490416i | \(0.836845\pi\) | |||||||
\(684\) | 3.88325 | 0.148480 | ||||||||
\(685\) | 0.413875 | 0.0158134 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.67632 | 0.331022 | ||||||||
\(688\) | 7.88325 | 0.300546 | ||||||||
\(689\) | 0.827751 | 0.0315348 | ||||||||
\(690\) | 3.79306 | 0.144399 | ||||||||
\(691\) | −19.1988 | −0.730357 | −0.365178 | − | 0.930938i | \(-0.618992\pi\) | ||||
−0.365178 | + | 0.930938i | \(0.618992\pi\) | |||||||
\(692\) | −25.5861 | −0.972639 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.6127 | −0.820406 | ||||||||
\(695\) | −3.81173 | −0.144587 | ||||||||
\(696\) | −2.79306 | −0.105871 | ||||||||
\(697\) | −1.79306 | −0.0679171 | ||||||||
\(698\) | 14.2745 | 0.540299 | ||||||||
\(699\) | 16.7665 | 0.634168 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.2890 | 0.879613 | 0.439807 | − | 0.898093i | \(-0.355047\pi\) | ||||
0.439807 | + | 0.898093i | \(0.355047\pi\) | |||||||
\(702\) | 0.909808 | 0.0343385 | ||||||||
\(703\) | 30.6127 | 1.15458 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0.153830 | 0.00579356 | ||||||||
\(706\) | −28.4959 | −1.07246 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6.97345 | 0.262078 | ||||||||
\(709\) | −20.7931 | −0.780900 | −0.390450 | − | 0.920624i | \(-0.627681\pi\) | ||||
−0.390450 | + | 0.920624i | \(0.627681\pi\) | |||||||
\(710\) | −2.18038 | −0.0818283 | ||||||||
\(711\) | 5.36471 | 0.201192 | ||||||||
\(712\) | −11.0902 | −0.415623 | ||||||||
\(713\) | −79.9306 | −2.99343 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.413875 | 0.0154781 | ||||||||
\(716\) | −15.7029 | −0.586844 | ||||||||
\(717\) | −26.2624 | −0.980789 | ||||||||
\(718\) | −13.6392 | −0.509012 | ||||||||
\(719\) | −5.48146 | −0.204424 | −0.102212 | − | 0.994763i | \(-0.532592\pi\) | ||||
−0.102212 | + | 0.994763i | \(0.532592\pi\) | |||||||
\(720\) | 0.454904 | 0.0169533 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.92034 | −0.145900 | ||||||||
\(723\) | 7.94689 | 0.295548 | ||||||||
\(724\) | −2.49593 | −0.0927606 | ||||||||
\(725\) | 13.3873 | 0.497193 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | 25.5330 | 0.946967 | 0.473484 | − | 0.880803i | \(-0.342996\pi\) | ||||
0.473484 | + | 0.880803i | \(0.342996\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.85670 | 0.179755 | ||||||||
\(731\) | 7.88325 | 0.291573 | ||||||||
\(732\) | −14.0410 | −0.518971 | ||||||||
\(733\) | 16.2214 | 0.599152 | 0.299576 | − | 0.954073i | \(-0.403155\pi\) | ||||
0.299576 | + | 0.954073i | \(0.403155\pi\) | |||||||
\(734\) | 22.7294 | 0.838958 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.33816 | 0.307349 | ||||||||
\(737\) | −3.79306 | −0.139719 | ||||||||
\(738\) | −1.79306 | −0.0660035 | ||||||||
\(739\) | 18.7584 | 0.690038 | 0.345019 | − | 0.938596i | \(-0.387872\pi\) | ||||
0.345019 | + | 0.938596i | \(0.387872\pi\) | |||||||
\(740\) | 3.58612 | 0.131829 | ||||||||
\(741\) | 3.53302 | 0.129789 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.6763 | −1.63902 | −0.819508 | − | 0.573068i | \(-0.805753\pi\) | ||||
−0.819508 | + | 0.573068i | \(0.805753\pi\) | |||||||
\(744\) | −9.58612 | −0.351444 | ||||||||
\(745\) | 1.87272 | 0.0686113 | ||||||||
\(746\) | 10.4018 | 0.380837 | ||||||||
\(747\) | 1.97345 | 0.0722046 | ||||||||
\(748\) | 1.00000 | 0.0365636 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −4.45490 | −0.162670 | ||||||||
\(751\) | −2.96292 | −0.108118 | −0.0540592 | − | 0.998538i | \(-0.517216\pi\) | ||||
−0.0540592 | + | 0.998538i | \(0.517216\pi\) | |||||||
\(752\) | 0.338158 | 0.0123314 | ||||||||
\(753\) | −3.93636 | −0.143449 | ||||||||
\(754\) | −2.54115 | −0.0925433 | ||||||||
\(755\) | −2.80120 | −0.101946 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.1988 | 0.952212 | 0.476106 | − | 0.879388i | \(-0.342048\pi\) | ||||
0.476106 | + | 0.879388i | \(0.342048\pi\) | |||||||
\(758\) | 7.61268 | 0.276505 | ||||||||
\(759\) | 8.33816 | 0.302656 | ||||||||
\(760\) | 1.76651 | 0.0640780 | ||||||||
\(761\) | 25.7931 | 0.934998 | 0.467499 | − | 0.883994i | \(-0.345155\pi\) | ||||
0.467499 | + | 0.883994i | \(0.345155\pi\) | |||||||
\(762\) | 7.42835 | 0.269101 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 9.81962 | 0.355261 | ||||||||
\(765\) | 0.454904 | 0.0164471 | ||||||||
\(766\) | −22.1457 | −0.800156 | ||||||||
\(767\) | 6.34450 | 0.229087 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −37.2012 | −1.34151 | −0.670755 | − | 0.741679i | \(-0.734030\pi\) | ||||
−0.670755 | + | 0.741679i | \(0.734030\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.0902 | −0.543460 | ||||||||
\(772\) | 6.85670 | 0.246778 | ||||||||
\(773\) | −40.7705 | −1.46641 | −0.733206 | − | 0.680007i | \(-0.761977\pi\) | ||||
−0.733206 | + | 0.680007i | \(0.761977\pi\) | |||||||
\(774\) | 7.88325 | 0.283358 | ||||||||
\(775\) | 45.9469 | 1.65046 | ||||||||
\(776\) | 14.5861 | 0.523611 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.54510 | −0.127098 | ||||||||
\(779\) | −6.96292 | −0.249472 | ||||||||
\(780\) | 0.413875 | 0.0148191 | ||||||||
\(781\) | −4.79306 | −0.171509 | ||||||||
\(782\) | 8.33816 | 0.298172 | ||||||||
\(783\) | −2.79306 | −0.0998159 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.02895 | −0.286565 | ||||||||
\(786\) | −19.4057 | −0.692180 | ||||||||
\(787\) | 54.5885 | 1.94587 | 0.972935 | − | 0.231078i | \(-0.0742252\pi\) | ||||
0.972935 | + | 0.231078i | \(0.0742252\pi\) | |||||||
\(788\) | 23.4694 | 0.836062 | ||||||||
\(789\) | −28.6232 | −1.01901 | ||||||||
\(790\) | 2.44043 | 0.0868266 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | −12.7746 | −0.453641 | ||||||||
\(794\) | −2.55957 | −0.0908358 | ||||||||
\(795\) | 0.413875 | 0.0146787 | ||||||||
\(796\) | −2.23349 | −0.0791640 | ||||||||
\(797\) | −16.7705 | −0.594040 | −0.297020 | − | 0.954871i | \(-0.595993\pi\) | ||||
−0.297020 | + | 0.954871i | \(0.595993\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.338158 | 0.0119632 | ||||||||
\(800\) | −4.79306 | −0.169460 | ||||||||
\(801\) | −11.0902 | −0.391853 | ||||||||
\(802\) | 10.4959 | 0.370624 | ||||||||
\(803\) | 10.6763 | 0.376759 | ||||||||
\(804\) | −3.79306 | −0.133771 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.72153 | −0.307203 | ||||||||
\(807\) | −22.9508 | −0.807908 | ||||||||
\(808\) | −8.06364 | −0.283678 | ||||||||
\(809\) | −10.2069 | −0.358857 | −0.179428 | − | 0.983771i | \(-0.557425\pi\) | ||||
−0.179428 | + | 0.983771i | \(0.557425\pi\) | |||||||
\(810\) | 0.454904 | 0.0159837 | ||||||||
\(811\) | −28.4139 | −0.997746 | −0.498873 | − | 0.866675i | \(-0.666253\pi\) | ||||
−0.498873 | + | 0.866675i | \(0.666253\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.81962 | 0.344389 | ||||||||
\(814\) | 7.88325 | 0.276308 | ||||||||
\(815\) | −5.28266 | −0.185043 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | 30.6127 | 1.07100 | ||||||||
\(818\) | 15.8486 | 0.554132 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.815671 | −0.0284845 | ||||||||
\(821\) | −3.40574 | −0.118861 | −0.0594306 | − | 0.998232i | \(-0.518928\pi\) | ||||
−0.0594306 | + | 0.998232i | \(0.518928\pi\) | |||||||
\(822\) | 0.909808 | 0.0317332 | ||||||||
\(823\) | −38.0289 | −1.32561 | −0.662803 | − | 0.748794i | \(-0.730633\pi\) | ||||
−0.662803 | + | 0.748794i | \(0.730633\pi\) | |||||||
\(824\) | 5.76651 | 0.200886 | ||||||||
\(825\) | −4.79306 | −0.166873 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.9653 | −0.450848 | −0.225424 | − | 0.974261i | \(-0.572377\pi\) | ||||
−0.225424 | + | 0.974261i | \(0.572377\pi\) | |||||||
\(828\) | 8.33816 | 0.289771 | ||||||||
\(829\) | 51.8833 | 1.80198 | 0.900990 | − | 0.433840i | \(-0.142842\pi\) | ||||
0.900990 | + | 0.433840i | \(0.142842\pi\) | |||||||
\(830\) | 0.897729 | 0.0311606 | ||||||||
\(831\) | 10.7294 | 0.372200 | ||||||||
\(832\) | 0.909808 | 0.0315419 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.37919 | −0.290148 | ||||||||
\(835\) | −2.20933 | −0.0764571 | ||||||||
\(836\) | 3.88325 | 0.134305 | ||||||||
\(837\) | −9.58612 | −0.331345 | ||||||||
\(838\) | −9.52249 | −0.328949 | ||||||||
\(839\) | −50.2504 | −1.73484 | −0.867418 | − | 0.497581i | \(-0.834222\pi\) | ||||
−0.867418 | + | 0.497581i | \(0.834222\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.1988 | −0.730993 | ||||||||
\(842\) | −0.530621 | −0.0182864 | ||||||||
\(843\) | 2.58612 | 0.0890709 | ||||||||
\(844\) | −18.2624 | −0.628619 | ||||||||
\(845\) | −5.53721 | −0.190486 | ||||||||
\(846\) | 0.338158 | 0.0116261 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.909808 | 0.0312429 | ||||||||
\(849\) | −20.0821 | −0.689214 | ||||||||
\(850\) | −4.79306 | −0.164401 | ||||||||
\(851\) | 65.7318 | 2.25326 | ||||||||
\(852\) | −4.79306 | −0.164208 | ||||||||
\(853\) | 13.3647 | 0.457599 | 0.228800 | − | 0.973474i | \(-0.426520\pi\) | ||||
0.228800 | + | 0.973474i | \(0.426520\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.76651 | 0.0604133 | ||||||||
\(856\) | 15.6127 | 0.533630 | ||||||||
\(857\) | 26.3526 | 0.900189 | 0.450094 | − | 0.892981i | \(-0.351390\pi\) | ||||
0.450094 | + | 0.892981i | \(0.351390\pi\) | |||||||
\(858\) | 0.909808 | 0.0310603 | ||||||||
\(859\) | 1.97345 | 0.0673331 | 0.0336666 | − | 0.999433i | \(-0.489282\pi\) | ||||
0.0336666 | + | 0.999433i | \(0.489282\pi\) | |||||||
\(860\) | 3.58612 | 0.122286 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.8036 | 0.708573 | ||||||||
\(863\) | −49.8075 | −1.69547 | −0.847734 | − | 0.530421i | \(-0.822034\pi\) | ||||
−0.847734 | + | 0.530421i | \(0.822034\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −11.6392 | −0.395746 | ||||||||
\(866\) | −4.40574 | −0.149713 | ||||||||
\(867\) | −16.0000 | −0.543388 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.36471 | 0.181985 | ||||||||
\(870\) | −1.27058 | −0.0430765 | ||||||||
\(871\) | −3.45096 | −0.116931 | ||||||||
\(872\) | 14.0410 | 0.475489 | ||||||||
\(873\) | 14.5861 | 0.493666 | ||||||||
\(874\) | 32.3792 | 1.09524 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.6763 | 0.360719 | ||||||||
\(877\) | −24.5370 | −0.828554 | −0.414277 | − | 0.910151i | \(-0.635966\pi\) | ||||
−0.414277 | + | 0.910151i | \(0.635966\pi\) | |||||||
\(878\) | −15.1949 | −0.512802 | ||||||||
\(879\) | 10.3792 | 0.350081 | ||||||||
\(880\) | 0.454904 | 0.0153348 | ||||||||
\(881\) | 11.5861 | 0.390346 | 0.195173 | − | 0.980769i | \(-0.437473\pi\) | ||||
0.195173 | + | 0.980769i | \(0.437473\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.1376 | −1.48535 | −0.742674 | − | 0.669654i | \(-0.766443\pi\) | ||||
−0.742674 | + | 0.669654i | \(0.766443\pi\) | |||||||
\(884\) | 0.909808 | 0.0306002 | ||||||||
\(885\) | 3.17225 | 0.106634 | ||||||||
\(886\) | −11.3873 | −0.382565 | ||||||||
\(887\) | −20.0289 | −0.672506 | −0.336253 | − | 0.941772i | \(-0.609160\pi\) | ||||
−0.336253 | + | 0.941772i | \(0.609160\pi\) | |||||||
\(888\) | 7.88325 | 0.264545 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −5.04497 | −0.169108 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 12.4959 | 0.418395 | ||||||||
\(893\) | 1.31315 | 0.0439430 | ||||||||
\(894\) | 4.11675 | 0.137685 | ||||||||
\(895\) | −7.14330 | −0.238774 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.58612 | 0.253293 | ||||||||
\(898\) | −24.0821 | −0.803629 | ||||||||
\(899\) | 26.7746 | 0.892984 | ||||||||
\(900\) | −4.79306 | −0.159769 | ||||||||
\(901\) | 0.909808 | 0.0303101 | ||||||||
\(902\) | −1.79306 | −0.0597024 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.58612 | 0.252311 | ||||||||
\(905\) | −1.13541 | −0.0377423 | ||||||||
\(906\) | −6.15777 | −0.204578 | ||||||||
\(907\) | −17.9203 | −0.595035 | −0.297518 | − | 0.954716i | \(-0.596159\pi\) | ||||
−0.297518 | + | 0.954716i | \(0.596159\pi\) | |||||||
\(908\) | 9.79306 | 0.324994 | ||||||||
\(909\) | −8.06364 | −0.267454 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.9695 | 0.462830 | 0.231415 | − | 0.972855i | \(-0.425664\pi\) | ||||
0.231415 | + | 0.972855i | \(0.425664\pi\) | |||||||
\(912\) | 3.88325 | 0.128587 | ||||||||
\(913\) | 1.97345 | 0.0653115 | ||||||||
\(914\) | −29.5330 | −0.976865 | ||||||||
\(915\) | −6.38732 | −0.211158 | ||||||||
\(916\) | 8.67632 | 0.286674 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −42.9614 | −1.41716 | −0.708582 | − | 0.705628i | \(-0.750665\pi\) | ||||
−0.708582 | + | 0.705628i | \(0.750665\pi\) | |||||||
\(920\) | 3.79306 | 0.125054 | ||||||||
\(921\) | 9.76651 | 0.321817 | ||||||||
\(922\) | 4.14569 | 0.136531 | ||||||||
\(923\) | −4.36077 | −0.143536 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −37.7849 | −1.24236 | ||||||||
\(926\) | −9.32368 | −0.306395 | ||||||||
\(927\) | 5.76651 | 0.189397 | ||||||||
\(928\) | −2.79306 | −0.0916868 | ||||||||
\(929\) | −25.6682 | −0.842146 | −0.421073 | − | 0.907027i | \(-0.638346\pi\) | ||||
−0.421073 | + | 0.907027i | \(0.638346\pi\) | |||||||
\(930\) | −4.36077 | −0.142995 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 16.7665 | 0.549205 | ||||||||
\(933\) | −6.51854 | −0.213407 | ||||||||
\(934\) | 36.5596 | 1.19627 | ||||||||
\(935\) | 0.454904 | 0.0148770 | ||||||||
\(936\) | 0.909808 | 0.0297380 | ||||||||
\(937\) | 26.7584 | 0.874158 | 0.437079 | − | 0.899423i | \(-0.356013\pi\) | ||||
0.437079 | + | 0.899423i | \(0.356013\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.7931 | 1.00489 | ||||||||
\(940\) | 0.153830 | 0.00501737 | ||||||||
\(941\) | −15.6208 | −0.509224 | −0.254612 | − | 0.967043i | \(-0.581948\pi\) | ||||
−0.254612 | + | 0.967043i | \(0.581948\pi\) | |||||||
\(942\) | −17.6498 | −0.575060 | ||||||||
\(943\) | −14.9508 | −0.486866 | ||||||||
\(944\) | 6.97345 | 0.226966 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.88325 | 0.256307 | ||||||||
\(947\) | 19.7849 | 0.642924 | 0.321462 | − | 0.946923i | \(-0.395826\pi\) | ||||
0.321462 | + | 0.946923i | \(0.395826\pi\) | |||||||
\(948\) | 5.36471 | 0.174238 | ||||||||
\(949\) | 9.71340 | 0.315310 | ||||||||
\(950\) | −18.6127 | −0.603875 | ||||||||
\(951\) | −27.6272 | −0.895872 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.5065 | 1.40931 | 0.704656 | − | 0.709549i | \(-0.251101\pi\) | ||||
0.704656 | + | 0.709549i | \(0.251101\pi\) | |||||||
\(954\) | 0.909808 | 0.0294561 | ||||||||
\(955\) | 4.46698 | 0.144548 | ||||||||
\(956\) | −26.2624 | −0.849388 | ||||||||
\(957\) | −2.79306 | −0.0902869 | ||||||||
\(958\) | 0.729425 | 0.0235666 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.454904 | 0.0146820 | ||||||||
\(961\) | 60.8938 | 1.96432 | ||||||||
\(962\) | 7.17225 | 0.231243 | ||||||||
\(963\) | 15.6127 | 0.503112 | ||||||||
\(964\) | 7.94689 | 0.255952 | ||||||||
\(965\) | 3.11914 | 0.100409 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.5185 | 1.11004 | 0.555021 | − | 0.831837i | \(-0.312710\pi\) | ||||
0.555021 | + | 0.831837i | \(0.312710\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 3.88325 | 0.124748 | ||||||||
\(970\) | 6.63529 | 0.213046 | ||||||||
\(971\) | −44.9388 | −1.44215 | −0.721077 | − | 0.692855i | \(-0.756352\pi\) | ||||
−0.721077 | + | 0.692855i | \(0.756352\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −36.8567 | −1.18096 | ||||||||
\(975\) | −4.36077 | −0.139656 | ||||||||
\(976\) | −14.0410 | −0.449442 | ||||||||
\(977\) | 32.5249 | 1.04056 | 0.520282 | − | 0.853995i | \(-0.325827\pi\) | ||||
0.520282 | + | 0.853995i | \(0.325827\pi\) | |||||||
\(978\) | −11.6127 | −0.371333 | ||||||||
\(979\) | −11.0902 | −0.354444 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0410 | 0.448296 | ||||||||
\(982\) | 25.5065 | 0.813944 | ||||||||
\(983\) | −47.1949 | −1.50528 | −0.752641 | − | 0.658431i | \(-0.771220\pi\) | ||||
−0.752641 | + | 0.658431i | \(0.771220\pi\) | |||||||
\(984\) | −1.79306 | −0.0571607 | ||||||||
\(985\) | 10.6763 | 0.340176 | ||||||||
\(986\) | −2.79306 | −0.0889492 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.53302 | 0.112400 | ||||||||
\(989\) | 65.7318 | 2.09015 | ||||||||
\(990\) | 0.454904 | 0.0144578 | ||||||||
\(991\) | 12.5490 | 0.398633 | 0.199317 | − | 0.979935i | \(-0.436128\pi\) | ||||
0.199317 | + | 0.979935i | \(0.436128\pi\) | |||||||
\(992\) | −9.58612 | −0.304360 | ||||||||
\(993\) | −28.9653 | −0.919186 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.01602 | −0.0322101 | ||||||||
\(996\) | 1.97345 | 0.0625310 | ||||||||
\(997\) | 40.9098 | 1.29563 | 0.647813 | − | 0.761799i | \(-0.275684\pi\) | ||||
0.647813 | + | 0.761799i | \(0.275684\pi\) | |||||||
\(998\) | −4.12728 | −0.130647 | ||||||||
\(999\) | 7.88325 | 0.249415 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3234.2.a.bi.1.2 | 3 | ||
3.2 | odd | 2 | 9702.2.a.dt.1.2 | 3 | |||
7.2 | even | 3 | 462.2.i.f.67.2 | ✓ | 6 | ||
7.4 | even | 3 | 462.2.i.f.331.2 | yes | 6 | ||
7.6 | odd | 2 | 3234.2.a.bg.1.2 | 3 | |||
21.2 | odd | 6 | 1386.2.k.w.991.2 | 6 | |||
21.11 | odd | 6 | 1386.2.k.w.793.2 | 6 | |||
21.20 | even | 2 | 9702.2.a.du.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.f.67.2 | ✓ | 6 | 7.2 | even | 3 | ||
462.2.i.f.331.2 | yes | 6 | 7.4 | even | 3 | ||
1386.2.k.w.793.2 | 6 | 21.11 | odd | 6 | |||
1386.2.k.w.991.2 | 6 | 21.2 | odd | 6 | |||
3234.2.a.bg.1.2 | 3 | 7.6 | odd | 2 | |||
3234.2.a.bi.1.2 | 3 | 1.1 | even | 1 | trivial | ||
9702.2.a.dt.1.2 | 3 | 3.2 | odd | 2 | |||
9702.2.a.du.1.2 | 3 | 21.20 | even | 2 |