Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,2,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(2.30767661842\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{16})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.765367\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.414214 | −0.292893 | −0.146447 | − | 0.989219i | \(-0.546784\pi\) | ||||
−0.146447 | + | 0.989219i | \(0.546784\pi\) | |||||||
\(3\) | −2.61313 | −1.50869 | −0.754344 | − | 0.656479i | \(-0.772045\pi\) | ||||
−0.754344 | + | 0.656479i | \(0.772045\pi\) | |||||||
\(4\) | −1.82843 | −0.914214 | ||||||||
\(5\) | −1.84776 | −0.826343 | −0.413171 | − | 0.910653i | \(-0.635579\pi\) | ||||
−0.413171 | + | 0.910653i | \(0.635579\pi\) | |||||||
\(6\) | 1.08239 | 0.441885 | ||||||||
\(7\) | −1.08239 | −0.409106 | −0.204553 | − | 0.978856i | \(-0.565574\pi\) | ||||
−0.204553 | + | 0.978856i | \(0.565574\pi\) | |||||||
\(8\) | 1.58579 | 0.560660 | ||||||||
\(9\) | 3.82843 | 1.27614 | ||||||||
\(10\) | 0.765367 | 0.242030 | ||||||||
\(11\) | 1.08239 | 0.326354 | 0.163177 | − | 0.986597i | \(-0.447826\pi\) | ||||
0.163177 | + | 0.986597i | \(0.447826\pi\) | |||||||
\(12\) | 4.77791 | 1.37926 | ||||||||
\(13\) | −1.41421 | −0.392232 | −0.196116 | − | 0.980581i | \(-0.562833\pi\) | ||||
−0.196116 | + | 0.980581i | \(0.562833\pi\) | |||||||
\(14\) | 0.448342 | 0.119824 | ||||||||
\(15\) | 4.82843 | 1.24669 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −1.58579 | −0.373773 | ||||||||
\(19\) | 4.82843 | 1.10772 | 0.553859 | − | 0.832611i | \(-0.313155\pi\) | ||||
0.553859 | + | 0.832611i | \(0.313155\pi\) | |||||||
\(20\) | 3.37849 | 0.755454 | ||||||||
\(21\) | 2.82843 | 0.617213 | ||||||||
\(22\) | −0.448342 | −0.0955867 | ||||||||
\(23\) | 4.14386 | 0.864054 | 0.432027 | − | 0.901861i | \(-0.357798\pi\) | ||||
0.432027 | + | 0.901861i | \(0.357798\pi\) | |||||||
\(24\) | −4.14386 | −0.845862 | ||||||||
\(25\) | −1.58579 | −0.317157 | ||||||||
\(26\) | 0.585786 | 0.114882 | ||||||||
\(27\) | −2.16478 | −0.416613 | ||||||||
\(28\) | 1.97908 | 0.374010 | ||||||||
\(29\) | −4.46088 | −0.828366 | −0.414183 | − | 0.910194i | \(-0.635933\pi\) | ||||
−0.414183 | + | 0.910194i | \(0.635933\pi\) | |||||||
\(30\) | −2.00000 | −0.365148 | ||||||||
\(31\) | 3.24718 | 0.583210 | 0.291605 | − | 0.956539i | \(-0.405811\pi\) | ||||
0.291605 | + | 0.956539i | \(0.405811\pi\) | |||||||
\(32\) | −4.41421 | −0.780330 | ||||||||
\(33\) | −2.82843 | −0.492366 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | 0.338062 | ||||||||
\(36\) | −7.00000 | −1.16667 | ||||||||
\(37\) | −3.82683 | −0.629128 | −0.314564 | − | 0.949236i | \(-0.601858\pi\) | ||||
−0.314564 | + | 0.949236i | \(0.601858\pi\) | |||||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | 3.69552 | 0.591756 | ||||||||
\(40\) | −2.93015 | −0.463298 | ||||||||
\(41\) | 8.15640 | 1.27382 | 0.636908 | − | 0.770940i | \(-0.280213\pi\) | ||||
0.636908 | + | 0.770940i | \(0.280213\pi\) | |||||||
\(42\) | −1.17157 | −0.180778 | ||||||||
\(43\) | −4.82843 | −0.736328 | −0.368164 | − | 0.929761i | \(-0.620014\pi\) | ||||
−0.368164 | + | 0.929761i | \(0.620014\pi\) | |||||||
\(44\) | −1.97908 | −0.298357 | ||||||||
\(45\) | −7.07401 | −1.05453 | ||||||||
\(46\) | −1.71644 | −0.253076 | ||||||||
\(47\) | 10.8284 | 1.57949 | 0.789744 | − | 0.613436i | \(-0.210213\pi\) | ||||
0.789744 | + | 0.613436i | \(0.210213\pi\) | |||||||
\(48\) | −7.83938 | −1.13152 | ||||||||
\(49\) | −5.82843 | −0.832632 | ||||||||
\(50\) | 0.656854 | 0.0928932 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.58579 | 0.358584 | ||||||||
\(53\) | −1.41421 | −0.194257 | −0.0971286 | − | 0.995272i | \(-0.530966\pi\) | ||||
−0.0971286 | + | 0.995272i | \(0.530966\pi\) | |||||||
\(54\) | 0.896683 | 0.122023 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | −1.71644 | −0.229369 | ||||||||
\(57\) | −12.6173 | −1.67120 | ||||||||
\(58\) | 1.84776 | 0.242623 | ||||||||
\(59\) | 6.00000 | 0.781133 | 0.390567 | − | 0.920575i | \(-0.372279\pi\) | ||||
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | −8.82843 | −1.13975 | ||||||||
\(61\) | 9.23880 | 1.18291 | 0.591453 | − | 0.806339i | \(-0.298554\pi\) | ||||
0.591453 | + | 0.806339i | \(0.298554\pi\) | |||||||
\(62\) | −1.34502 | −0.170818 | ||||||||
\(63\) | −4.14386 | −0.522077 | ||||||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | 2.61313 | 0.324118 | ||||||||
\(66\) | 1.17157 | 0.144211 | ||||||||
\(67\) | −6.82843 | −0.834225 | −0.417113 | − | 0.908855i | \(-0.636958\pi\) | ||||
−0.417113 | + | 0.908855i | \(0.636958\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.8284 | −1.30359 | ||||||||
\(70\) | −0.828427 | −0.0990160 | ||||||||
\(71\) | 13.0656 | 1.55060 | 0.775302 | − | 0.631590i | \(-0.217597\pi\) | ||||
0.775302 | + | 0.631590i | \(0.217597\pi\) | |||||||
\(72\) | 6.07107 | 0.715482 | ||||||||
\(73\) | 5.35757 | 0.627056 | 0.313528 | − | 0.949579i | \(-0.398489\pi\) | ||||
0.313528 | + | 0.949579i | \(0.398489\pi\) | |||||||
\(74\) | 1.58513 | 0.184267 | ||||||||
\(75\) | 4.14386 | 0.478492 | ||||||||
\(76\) | −8.82843 | −1.01269 | ||||||||
\(77\) | −1.17157 | −0.133513 | ||||||||
\(78\) | −1.53073 | −0.173321 | ||||||||
\(79\) | 4.14386 | 0.466221 | 0.233110 | − | 0.972450i | \(-0.425110\pi\) | ||||
0.233110 | + | 0.972450i | \(0.425110\pi\) | |||||||
\(80\) | −5.54328 | −0.619757 | ||||||||
\(81\) | −5.82843 | −0.647603 | ||||||||
\(82\) | −3.37849 | −0.373092 | ||||||||
\(83\) | 0.343146 | 0.0376651 | 0.0188326 | − | 0.999823i | \(-0.494005\pi\) | ||||
0.0188326 | + | 0.999823i | \(0.494005\pi\) | |||||||
\(84\) | −5.17157 | −0.564265 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.00000 | 0.215666 | ||||||||
\(87\) | 11.6569 | 1.24975 | ||||||||
\(88\) | 1.71644 | 0.182973 | ||||||||
\(89\) | 9.41421 | 0.997905 | 0.498952 | − | 0.866629i | \(-0.333718\pi\) | ||||
0.498952 | + | 0.866629i | \(0.333718\pi\) | |||||||
\(90\) | 2.93015 | 0.308865 | ||||||||
\(91\) | 1.53073 | 0.160464 | ||||||||
\(92\) | −7.57675 | −0.789930 | ||||||||
\(93\) | −8.48528 | −0.879883 | ||||||||
\(94\) | −4.48528 | −0.462621 | ||||||||
\(95\) | −8.92177 | −0.915354 | ||||||||
\(96\) | 11.5349 | 1.17728 | ||||||||
\(97\) | 6.43996 | 0.653879 | 0.326939 | − | 0.945045i | \(-0.393983\pi\) | ||||
0.326939 | + | 0.945045i | \(0.393983\pi\) | |||||||
\(98\) | 2.41421 | 0.243872 | ||||||||
\(99\) | 4.14386 | 0.416474 | ||||||||
\(100\) | 2.89949 | 0.289949 | ||||||||
\(101\) | 13.4142 | 1.33476 | 0.667382 | − | 0.744715i | \(-0.267415\pi\) | ||||
0.667382 | + | 0.744715i | \(0.267415\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.48528 | −0.441948 | −0.220974 | − | 0.975280i | \(-0.570924\pi\) | ||||
−0.220974 | + | 0.975280i | \(0.570924\pi\) | |||||||
\(104\) | −2.24264 | −0.219909 | ||||||||
\(105\) | −5.22625 | −0.510030 | ||||||||
\(106\) | 0.585786 | 0.0568966 | ||||||||
\(107\) | 6.30864 | 0.609880 | 0.304940 | − | 0.952372i | \(-0.401364\pi\) | ||||
0.304940 | + | 0.952372i | \(0.401364\pi\) | |||||||
\(108\) | 3.95815 | 0.380873 | ||||||||
\(109\) | −4.27518 | −0.409488 | −0.204744 | − | 0.978816i | \(-0.565636\pi\) | ||||
−0.204744 | + | 0.978816i | \(0.565636\pi\) | |||||||
\(110\) | 0.828427 | 0.0789874 | ||||||||
\(111\) | 10.0000 | 0.949158 | ||||||||
\(112\) | −3.24718 | −0.306829 | ||||||||
\(113\) | −16.1815 | −1.52223 | −0.761113 | − | 0.648619i | \(-0.775347\pi\) | ||||
−0.761113 | + | 0.648619i | \(0.775347\pi\) | |||||||
\(114\) | 5.22625 | 0.489483 | ||||||||
\(115\) | −7.65685 | −0.714005 | ||||||||
\(116\) | 8.15640 | 0.757303 | ||||||||
\(117\) | −5.41421 | −0.500544 | ||||||||
\(118\) | −2.48528 | −0.228789 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 7.65685 | 0.698972 | ||||||||
\(121\) | −9.82843 | −0.893493 | ||||||||
\(122\) | −3.82683 | −0.346465 | ||||||||
\(123\) | −21.3137 | −1.92179 | ||||||||
\(124\) | −5.93723 | −0.533179 | ||||||||
\(125\) | 12.1689 | 1.08842 | ||||||||
\(126\) | 1.71644 | 0.152913 | ||||||||
\(127\) | 17.3137 | 1.53634 | 0.768172 | − | 0.640244i | \(-0.221167\pi\) | ||||
0.768172 | + | 0.640244i | \(0.221167\pi\) | |||||||
\(128\) | 10.5563 | 0.933058 | ||||||||
\(129\) | 12.6173 | 1.11089 | ||||||||
\(130\) | −1.08239 | −0.0949321 | ||||||||
\(131\) | 0.185709 | 0.0162255 | 0.00811274 | − | 0.999967i | \(-0.497418\pi\) | ||||
0.00811274 | + | 0.999967i | \(0.497418\pi\) | |||||||
\(132\) | 5.17157 | 0.450128 | ||||||||
\(133\) | −5.22625 | −0.453174 | ||||||||
\(134\) | 2.82843 | 0.244339 | ||||||||
\(135\) | 4.00000 | 0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.72792 | 0.745677 | 0.372838 | − | 0.927896i | \(-0.378385\pi\) | ||||
0.372838 | + | 0.927896i | \(0.378385\pi\) | |||||||
\(138\) | 4.48528 | 0.381813 | ||||||||
\(139\) | −14.9678 | −1.26955 | −0.634775 | − | 0.772697i | \(-0.718907\pi\) | ||||
−0.634775 | + | 0.772697i | \(0.718907\pi\) | |||||||
\(140\) | −3.65685 | −0.309061 | ||||||||
\(141\) | −28.2960 | −2.38296 | ||||||||
\(142\) | −5.41196 | −0.454162 | ||||||||
\(143\) | −1.53073 | −0.128006 | ||||||||
\(144\) | 11.4853 | 0.957107 | ||||||||
\(145\) | 8.24264 | 0.684514 | ||||||||
\(146\) | −2.21918 | −0.183660 | ||||||||
\(147\) | 15.2304 | 1.25618 | ||||||||
\(148\) | 6.99709 | 0.575157 | ||||||||
\(149\) | 16.9706 | 1.39028 | 0.695141 | − | 0.718873i | \(-0.255342\pi\) | ||||
0.695141 | + | 0.718873i | \(0.255342\pi\) | |||||||
\(150\) | −1.71644 | −0.140147 | ||||||||
\(151\) | 12.8284 | 1.04396 | 0.521981 | − | 0.852957i | \(-0.325193\pi\) | ||||
0.521981 | + | 0.852957i | \(0.325193\pi\) | |||||||
\(152\) | 7.65685 | 0.621053 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.485281 | 0.0391051 | ||||||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | −6.75699 | −0.540992 | ||||||||
\(157\) | 1.65685 | 0.132231 | 0.0661157 | − | 0.997812i | \(-0.478939\pi\) | ||||
0.0661157 | + | 0.997812i | \(0.478939\pi\) | |||||||
\(158\) | −1.71644 | −0.136553 | ||||||||
\(159\) | 3.69552 | 0.293074 | ||||||||
\(160\) | 8.15640 | 0.644820 | ||||||||
\(161\) | −4.48528 | −0.353490 | ||||||||
\(162\) | 2.41421 | 0.189679 | ||||||||
\(163\) | −5.67459 | −0.444468 | −0.222234 | − | 0.974993i | \(-0.571335\pi\) | ||||
−0.222234 | + | 0.974993i | \(0.571335\pi\) | |||||||
\(164\) | −14.9134 | −1.16454 | ||||||||
\(165\) | 5.22625 | 0.406863 | ||||||||
\(166\) | −0.142136 | −0.0110319 | ||||||||
\(167\) | −10.0042 | −0.774145 | −0.387073 | − | 0.922049i | \(-0.626514\pi\) | ||||
−0.387073 | + | 0.922049i | \(0.626514\pi\) | |||||||
\(168\) | 4.48528 | 0.346047 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.4853 | 1.41360 | ||||||||
\(172\) | 8.82843 | 0.673161 | ||||||||
\(173\) | −3.37849 | −0.256862 | −0.128431 | − | 0.991718i | \(-0.540994\pi\) | ||||
−0.128431 | + | 0.991718i | \(0.540994\pi\) | |||||||
\(174\) | −4.82843 | −0.366042 | ||||||||
\(175\) | 1.71644 | 0.129751 | ||||||||
\(176\) | 3.24718 | 0.244765 | ||||||||
\(177\) | −15.6788 | −1.17849 | ||||||||
\(178\) | −3.89949 | −0.292280 | ||||||||
\(179\) | 6.00000 | 0.448461 | 0.224231 | − | 0.974536i | \(-0.428013\pi\) | ||||
0.224231 | + | 0.974536i | \(0.428013\pi\) | |||||||
\(180\) | 12.9343 | 0.964067 | ||||||||
\(181\) | 12.4860 | 0.928075 | 0.464037 | − | 0.885816i | \(-0.346400\pi\) | ||||
0.464037 | + | 0.885816i | \(0.346400\pi\) | |||||||
\(182\) | −0.634051 | −0.0469990 | ||||||||
\(183\) | −24.1421 | −1.78464 | ||||||||
\(184\) | 6.57128 | 0.484441 | ||||||||
\(185\) | 7.07107 | 0.519875 | ||||||||
\(186\) | 3.51472 | 0.257712 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −19.7990 | −1.44399 | ||||||||
\(189\) | 2.34315 | 0.170439 | ||||||||
\(190\) | 3.69552 | 0.268101 | ||||||||
\(191\) | 20.0000 | 1.44715 | 0.723575 | − | 0.690246i | \(-0.242498\pi\) | ||||
0.723575 | + | 0.690246i | \(0.242498\pi\) | |||||||
\(192\) | 10.9008 | 0.786701 | ||||||||
\(193\) | 5.54328 | 0.399014 | 0.199507 | − | 0.979896i | \(-0.436066\pi\) | ||||
0.199507 | + | 0.979896i | \(0.436066\pi\) | |||||||
\(194\) | −2.66752 | −0.191517 | ||||||||
\(195\) | −6.82843 | −0.488994 | ||||||||
\(196\) | 10.6569 | 0.761204 | ||||||||
\(197\) | −14.9134 | −1.06253 | −0.531267 | − | 0.847204i | \(-0.678284\pi\) | ||||
−0.531267 | + | 0.847204i | \(0.678284\pi\) | |||||||
\(198\) | −1.71644 | −0.121982 | ||||||||
\(199\) | −1.71644 | −0.121675 | −0.0608377 | − | 0.998148i | \(-0.519377\pi\) | ||||
−0.0608377 | + | 0.998148i | \(0.519377\pi\) | |||||||
\(200\) | −2.51472 | −0.177817 | ||||||||
\(201\) | 17.8435 | 1.25859 | ||||||||
\(202\) | −5.55635 | −0.390943 | ||||||||
\(203\) | 4.82843 | 0.338889 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.0711 | −1.05261 | ||||||||
\(206\) | 1.85786 | 0.129444 | ||||||||
\(207\) | 15.8645 | 1.10266 | ||||||||
\(208\) | −4.24264 | −0.294174 | ||||||||
\(209\) | 5.22625 | 0.361507 | ||||||||
\(210\) | 2.16478 | 0.149384 | ||||||||
\(211\) | −14.9678 | −1.03042 | −0.515212 | − | 0.857063i | \(-0.672287\pi\) | ||||
−0.515212 | + | 0.857063i | \(0.672287\pi\) | |||||||
\(212\) | 2.58579 | 0.177593 | ||||||||
\(213\) | −34.1421 | −2.33938 | ||||||||
\(214\) | −2.61313 | −0.178630 | ||||||||
\(215\) | 8.92177 | 0.608460 | ||||||||
\(216\) | −3.43289 | −0.233578 | ||||||||
\(217\) | −3.51472 | −0.238595 | ||||||||
\(218\) | 1.77084 | 0.119936 | ||||||||
\(219\) | −14.0000 | −0.946032 | ||||||||
\(220\) | 3.65685 | 0.246545 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.14214 | −0.278002 | ||||||||
\(223\) | 0.828427 | 0.0554756 | 0.0277378 | − | 0.999615i | \(-0.491170\pi\) | ||||
0.0277378 | + | 0.999615i | \(0.491170\pi\) | |||||||
\(224\) | 4.77791 | 0.319238 | ||||||||
\(225\) | −6.07107 | −0.404738 | ||||||||
\(226\) | 6.70259 | 0.445850 | ||||||||
\(227\) | −5.04054 | −0.334553 | −0.167276 | − | 0.985910i | \(-0.553497\pi\) | ||||
−0.167276 | + | 0.985910i | \(0.553497\pi\) | |||||||
\(228\) | 23.0698 | 1.52783 | ||||||||
\(229\) | −22.8284 | −1.50854 | −0.754272 | − | 0.656562i | \(-0.772010\pi\) | ||||
−0.754272 | + | 0.656562i | \(0.772010\pi\) | |||||||
\(230\) | 3.17157 | 0.209127 | ||||||||
\(231\) | 3.06147 | 0.201430 | ||||||||
\(232\) | −7.07401 | −0.464432 | ||||||||
\(233\) | 10.1355 | 0.663997 | 0.331999 | − | 0.943280i | \(-0.392277\pi\) | ||||
0.331999 | + | 0.943280i | \(0.392277\pi\) | |||||||
\(234\) | 2.24264 | 0.146606 | ||||||||
\(235\) | −20.0083 | −1.30520 | ||||||||
\(236\) | −10.9706 | −0.714123 | ||||||||
\(237\) | −10.8284 | −0.703382 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.17157 | 0.593260 | 0.296630 | − | 0.954993i | \(-0.404137\pi\) | ||||
0.296630 | + | 0.954993i | \(0.404137\pi\) | |||||||
\(240\) | 14.4853 | 0.935021 | ||||||||
\(241\) | 12.3003 | 0.792330 | 0.396165 | − | 0.918179i | \(-0.370341\pi\) | ||||
0.396165 | + | 0.918179i | \(0.370341\pi\) | |||||||
\(242\) | 4.07107 | 0.261698 | ||||||||
\(243\) | 21.7248 | 1.39364 | ||||||||
\(244\) | −16.8925 | −1.08143 | ||||||||
\(245\) | 10.7695 | 0.688040 | ||||||||
\(246\) | 8.82843 | 0.562880 | ||||||||
\(247\) | −6.82843 | −0.434482 | ||||||||
\(248\) | 5.14933 | 0.326983 | ||||||||
\(249\) | −0.896683 | −0.0568250 | ||||||||
\(250\) | −5.04054 | −0.318792 | ||||||||
\(251\) | 3.51472 | 0.221847 | 0.110924 | − | 0.993829i | \(-0.464619\pi\) | ||||
0.110924 | + | 0.993829i | \(0.464619\pi\) | |||||||
\(252\) | 7.57675 | 0.477290 | ||||||||
\(253\) | 4.48528 | 0.281987 | ||||||||
\(254\) | −7.17157 | −0.449985 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | −22.1421 | −1.38119 | −0.690594 | − | 0.723242i | \(-0.742651\pi\) | ||||
−0.690594 | + | 0.723242i | \(0.742651\pi\) | |||||||
\(258\) | −5.22625 | −0.325372 | ||||||||
\(259\) | 4.14214 | 0.257380 | ||||||||
\(260\) | −4.77791 | −0.296313 | ||||||||
\(261\) | −17.0782 | −1.05711 | ||||||||
\(262\) | −0.0769232 | −0.00475233 | ||||||||
\(263\) | 6.48528 | 0.399900 | 0.199950 | − | 0.979806i | \(-0.435922\pi\) | ||||
0.199950 | + | 0.979806i | \(0.435922\pi\) | |||||||
\(264\) | −4.48528 | −0.276050 | ||||||||
\(265\) | 2.61313 | 0.160523 | ||||||||
\(266\) | 2.16478 | 0.132731 | ||||||||
\(267\) | −24.6005 | −1.50553 | ||||||||
\(268\) | 12.4853 | 0.762660 | ||||||||
\(269\) | −6.36304 | −0.387961 | −0.193981 | − | 0.981005i | \(-0.562140\pi\) | ||||
−0.193981 | + | 0.981005i | \(0.562140\pi\) | |||||||
\(270\) | −1.65685 | −0.100833 | ||||||||
\(271\) | 6.14214 | 0.373108 | 0.186554 | − | 0.982445i | \(-0.440268\pi\) | ||||
0.186554 | + | 0.982445i | \(0.440268\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.00000 | −0.242091 | ||||||||
\(274\) | −3.61522 | −0.218404 | ||||||||
\(275\) | −1.71644 | −0.103505 | ||||||||
\(276\) | 19.7990 | 1.19176 | ||||||||
\(277\) | −22.0418 | −1.32436 | −0.662181 | − | 0.749344i | \(-0.730369\pi\) | ||||
−0.662181 | + | 0.749344i | \(0.730369\pi\) | |||||||
\(278\) | 6.19986 | 0.371843 | ||||||||
\(279\) | 12.4316 | 0.744259 | ||||||||
\(280\) | 3.17157 | 0.189538 | ||||||||
\(281\) | −17.8995 | −1.06779 | −0.533897 | − | 0.845549i | \(-0.679273\pi\) | ||||
−0.533897 | + | 0.845549i | \(0.679273\pi\) | |||||||
\(282\) | 11.7206 | 0.697952 | ||||||||
\(283\) | −22.8841 | −1.36032 | −0.680159 | − | 0.733065i | \(-0.738089\pi\) | ||||
−0.680159 | + | 0.733065i | \(0.738089\pi\) | |||||||
\(284\) | −23.8896 | −1.41758 | ||||||||
\(285\) | 23.3137 | 1.38098 | ||||||||
\(286\) | 0.634051 | 0.0374922 | ||||||||
\(287\) | −8.82843 | −0.521126 | ||||||||
\(288\) | −16.8995 | −0.995812 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −3.41421 | −0.200490 | ||||||||
\(291\) | −16.8284 | −0.986500 | ||||||||
\(292\) | −9.79592 | −0.573263 | ||||||||
\(293\) | −23.6569 | −1.38205 | −0.691024 | − | 0.722832i | \(-0.742840\pi\) | ||||
−0.691024 | + | 0.722832i | \(0.742840\pi\) | |||||||
\(294\) | −6.30864 | −0.367928 | ||||||||
\(295\) | −11.0866 | −0.645484 | ||||||||
\(296\) | −6.06854 | −0.352727 | ||||||||
\(297\) | −2.34315 | −0.135963 | ||||||||
\(298\) | −7.02944 | −0.407204 | ||||||||
\(299\) | −5.86030 | −0.338910 | ||||||||
\(300\) | −7.57675 | −0.437444 | ||||||||
\(301\) | 5.22625 | 0.301236 | ||||||||
\(302\) | −5.31371 | −0.305770 | ||||||||
\(303\) | −35.0530 | −2.01374 | ||||||||
\(304\) | 14.4853 | 0.830788 | ||||||||
\(305\) | −17.0711 | −0.977486 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.14214 | 0.122258 | 0.0611291 | − | 0.998130i | \(-0.480530\pi\) | ||||
0.0611291 | + | 0.998130i | \(0.480530\pi\) | |||||||
\(308\) | 2.14214 | 0.122060 | ||||||||
\(309\) | 11.7206 | 0.666762 | ||||||||
\(310\) | 2.48528 | 0.141154 | ||||||||
\(311\) | 4.51528 | 0.256038 | 0.128019 | − | 0.991772i | \(-0.459138\pi\) | ||||
0.128019 | + | 0.991772i | \(0.459138\pi\) | |||||||
\(312\) | 5.86030 | 0.331774 | ||||||||
\(313\) | 12.7486 | 0.720594 | 0.360297 | − | 0.932838i | \(-0.382675\pi\) | ||||
0.360297 | + | 0.932838i | \(0.382675\pi\) | |||||||
\(314\) | −0.686292 | −0.0387297 | ||||||||
\(315\) | 7.65685 | 0.431415 | ||||||||
\(316\) | −7.57675 | −0.426225 | ||||||||
\(317\) | 5.80591 | 0.326092 | 0.163046 | − | 0.986618i | \(-0.447868\pi\) | ||||
0.163046 | + | 0.986618i | \(0.447868\pi\) | |||||||
\(318\) | −1.53073 | −0.0858393 | ||||||||
\(319\) | −4.82843 | −0.270340 | ||||||||
\(320\) | 7.70806 | 0.430894 | ||||||||
\(321\) | −16.4853 | −0.920119 | ||||||||
\(322\) | 1.85786 | 0.103535 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 10.6569 | 0.592047 | ||||||||
\(325\) | 2.24264 | 0.124399 | ||||||||
\(326\) | 2.35049 | 0.130182 | ||||||||
\(327\) | 11.1716 | 0.617789 | ||||||||
\(328\) | 12.9343 | 0.714178 | ||||||||
\(329\) | −11.7206 | −0.646178 | ||||||||
\(330\) | −2.16478 | −0.119167 | ||||||||
\(331\) | 17.7990 | 0.978321 | 0.489160 | − | 0.872194i | \(-0.337303\pi\) | ||||
0.489160 | + | 0.872194i | \(0.337303\pi\) | |||||||
\(332\) | −0.627417 | −0.0344340 | ||||||||
\(333\) | −14.6508 | −0.802857 | ||||||||
\(334\) | 4.14386 | 0.226742 | ||||||||
\(335\) | 12.6173 | 0.689356 | ||||||||
\(336\) | 8.48528 | 0.462910 | ||||||||
\(337\) | 34.4734 | 1.87788 | 0.938942 | − | 0.344075i | \(-0.111808\pi\) | ||||
0.938942 | + | 0.344075i | \(0.111808\pi\) | |||||||
\(338\) | 4.55635 | 0.247833 | ||||||||
\(339\) | 42.2843 | 2.29657 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.51472 | 0.190333 | ||||||||
\(342\) | −7.65685 | −0.414035 | ||||||||
\(343\) | 13.8854 | 0.749741 | ||||||||
\(344\) | −7.65685 | −0.412830 | ||||||||
\(345\) | 20.0083 | 1.07721 | ||||||||
\(346\) | 1.39942 | 0.0752332 | ||||||||
\(347\) | 3.88123 | 0.208355 | 0.104178 | − | 0.994559i | \(-0.466779\pi\) | ||||
0.104178 | + | 0.994559i | \(0.466779\pi\) | |||||||
\(348\) | −21.3137 | −1.14253 | ||||||||
\(349\) | 4.24264 | 0.227103 | 0.113552 | − | 0.993532i | \(-0.463777\pi\) | ||||
0.113552 | + | 0.993532i | \(0.463777\pi\) | |||||||
\(350\) | −0.710974 | −0.0380032 | ||||||||
\(351\) | 3.06147 | 0.163409 | ||||||||
\(352\) | −4.77791 | −0.254663 | ||||||||
\(353\) | −14.0000 | −0.745145 | −0.372572 | − | 0.928003i | \(-0.621524\pi\) | ||||
−0.372572 | + | 0.928003i | \(0.621524\pi\) | |||||||
\(354\) | 6.49435 | 0.345171 | ||||||||
\(355\) | −24.1421 | −1.28133 | ||||||||
\(356\) | −17.2132 | −0.912298 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.48528 | −0.131351 | ||||||||
\(359\) | 23.1716 | 1.22295 | 0.611474 | − | 0.791264i | \(-0.290577\pi\) | ||||
0.611474 | + | 0.791264i | \(0.290577\pi\) | |||||||
\(360\) | −11.2179 | −0.591234 | ||||||||
\(361\) | 4.31371 | 0.227037 | ||||||||
\(362\) | −5.17186 | −0.271827 | ||||||||
\(363\) | 25.6829 | 1.34800 | ||||||||
\(364\) | −2.79884 | −0.146699 | ||||||||
\(365\) | −9.89949 | −0.518163 | ||||||||
\(366\) | 10.0000 | 0.522708 | ||||||||
\(367\) | 26.3170 | 1.37373 | 0.686867 | − | 0.726783i | \(-0.258985\pi\) | ||||
0.686867 | + | 0.726783i | \(0.258985\pi\) | |||||||
\(368\) | 12.4316 | 0.648041 | ||||||||
\(369\) | 31.2262 | 1.62557 | ||||||||
\(370\) | −2.92893 | −0.152268 | ||||||||
\(371\) | 1.53073 | 0.0794717 | ||||||||
\(372\) | 15.5147 | 0.804401 | ||||||||
\(373\) | 19.5563 | 1.01259 | 0.506295 | − | 0.862361i | \(-0.331015\pi\) | ||||
0.506295 | + | 0.862361i | \(0.331015\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −31.7990 | −1.64209 | ||||||||
\(376\) | 17.1716 | 0.885556 | ||||||||
\(377\) | 6.30864 | 0.324912 | ||||||||
\(378\) | −0.970563 | −0.0499204 | ||||||||
\(379\) | −1.08239 | −0.0555988 | −0.0277994 | − | 0.999614i | \(-0.508850\pi\) | ||||
−0.0277994 | + | 0.999614i | \(0.508850\pi\) | |||||||
\(380\) | 16.3128 | 0.836829 | ||||||||
\(381\) | −45.2429 | −2.31786 | ||||||||
\(382\) | −8.28427 | −0.423860 | ||||||||
\(383\) | 5.51472 | 0.281789 | 0.140894 | − | 0.990025i | \(-0.455002\pi\) | ||||
0.140894 | + | 0.990025i | \(0.455002\pi\) | |||||||
\(384\) | −27.5851 | −1.40769 | ||||||||
\(385\) | 2.16478 | 0.110328 | ||||||||
\(386\) | −2.29610 | −0.116868 | ||||||||
\(387\) | −18.4853 | −0.939660 | ||||||||
\(388\) | −11.7750 | −0.597785 | ||||||||
\(389\) | 16.1421 | 0.818439 | 0.409219 | − | 0.912436i | \(-0.365801\pi\) | ||||
0.409219 | + | 0.912436i | \(0.365801\pi\) | |||||||
\(390\) | 2.82843 | 0.143223 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −9.24264 | −0.466824 | ||||||||
\(393\) | −0.485281 | −0.0244792 | ||||||||
\(394\) | 6.17733 | 0.311209 | ||||||||
\(395\) | −7.65685 | −0.385258 | ||||||||
\(396\) | −7.57675 | −0.380746 | ||||||||
\(397\) | 27.2680 | 1.36854 | 0.684272 | − | 0.729227i | \(-0.260120\pi\) | ||||
0.684272 | + | 0.729227i | \(0.260120\pi\) | |||||||
\(398\) | 0.710974 | 0.0356379 | ||||||||
\(399\) | 13.6569 | 0.683698 | ||||||||
\(400\) | −4.75736 | −0.237868 | ||||||||
\(401\) | 17.0782 | 0.852843 | 0.426422 | − | 0.904525i | \(-0.359774\pi\) | ||||
0.426422 | + | 0.904525i | \(0.359774\pi\) | |||||||
\(402\) | −7.39104 | −0.368631 | ||||||||
\(403\) | −4.59220 | −0.228754 | ||||||||
\(404\) | −24.5269 | −1.22026 | ||||||||
\(405\) | 10.7695 | 0.535142 | ||||||||
\(406\) | −2.00000 | −0.0992583 | ||||||||
\(407\) | −4.14214 | −0.205318 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.3137 | 0.955001 | 0.477501 | − | 0.878631i | \(-0.341543\pi\) | ||||
0.477501 | + | 0.878631i | \(0.341543\pi\) | |||||||
\(410\) | 6.24264 | 0.308302 | ||||||||
\(411\) | −22.8072 | −1.12499 | ||||||||
\(412\) | 8.20101 | 0.404035 | ||||||||
\(413\) | −6.49435 | −0.319566 | ||||||||
\(414\) | −6.57128 | −0.322961 | ||||||||
\(415\) | −0.634051 | −0.0311243 | ||||||||
\(416\) | 6.24264 | 0.306071 | ||||||||
\(417\) | 39.1127 | 1.91536 | ||||||||
\(418\) | −2.16478 | −0.105883 | ||||||||
\(419\) | 26.9510 | 1.31664 | 0.658322 | − | 0.752737i | \(-0.271267\pi\) | ||||
0.658322 | + | 0.752737i | \(0.271267\pi\) | |||||||
\(420\) | 9.55582 | 0.466276 | ||||||||
\(421\) | 17.4142 | 0.848717 | 0.424358 | − | 0.905494i | \(-0.360500\pi\) | ||||
0.424358 | + | 0.905494i | \(0.360500\pi\) | |||||||
\(422\) | 6.19986 | 0.301804 | ||||||||
\(423\) | 41.4558 | 2.01565 | ||||||||
\(424\) | −2.24264 | −0.108912 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 14.1421 | 0.685189 | ||||||||
\(427\) | −10.0000 | −0.483934 | ||||||||
\(428\) | −11.5349 | −0.557560 | ||||||||
\(429\) | 4.00000 | 0.193122 | ||||||||
\(430\) | −3.69552 | −0.178214 | ||||||||
\(431\) | −39.8309 | −1.91859 | −0.959294 | − | 0.282408i | \(-0.908867\pi\) | ||||
−0.959294 | + | 0.282408i | \(0.908867\pi\) | |||||||
\(432\) | −6.49435 | −0.312460 | ||||||||
\(433\) | 15.1716 | 0.729099 | 0.364550 | − | 0.931184i | \(-0.381223\pi\) | ||||
0.364550 | + | 0.931184i | \(0.381223\pi\) | |||||||
\(434\) | 1.45584 | 0.0698828 | ||||||||
\(435\) | −21.5391 | −1.03272 | ||||||||
\(436\) | 7.81685 | 0.374359 | ||||||||
\(437\) | 20.0083 | 0.957128 | ||||||||
\(438\) | 5.79899 | 0.277086 | ||||||||
\(439\) | −10.9008 | −0.520269 | −0.260134 | − | 0.965572i | \(-0.583767\pi\) | ||||
−0.260134 | + | 0.965572i | \(0.583767\pi\) | |||||||
\(440\) | −3.17157 | −0.151199 | ||||||||
\(441\) | −22.3137 | −1.06256 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.7990 | 0.750633 | 0.375316 | − | 0.926897i | \(-0.377534\pi\) | ||||
0.375316 | + | 0.926897i | \(0.377534\pi\) | |||||||
\(444\) | −18.2843 | −0.867733 | ||||||||
\(445\) | −17.3952 | −0.824611 | ||||||||
\(446\) | −0.343146 | −0.0162484 | ||||||||
\(447\) | −44.3462 | −2.09750 | ||||||||
\(448\) | 4.51528 | 0.213327 | ||||||||
\(449\) | 18.7946 | 0.886973 | 0.443486 | − | 0.896281i | \(-0.353741\pi\) | ||||
0.443486 | + | 0.896281i | \(0.353741\pi\) | |||||||
\(450\) | 2.51472 | 0.118545 | ||||||||
\(451\) | 8.82843 | 0.415714 | ||||||||
\(452\) | 29.5867 | 1.39164 | ||||||||
\(453\) | −33.5223 | −1.57501 | ||||||||
\(454\) | 2.08786 | 0.0979882 | ||||||||
\(455\) | −2.82843 | −0.132599 | ||||||||
\(456\) | −20.0083 | −0.936976 | ||||||||
\(457\) | 18.8284 | 0.880757 | 0.440378 | − | 0.897812i | \(-0.354844\pi\) | ||||
0.440378 | + | 0.897812i | \(0.354844\pi\) | |||||||
\(458\) | 9.45584 | 0.441843 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.0000 | 0.652753 | ||||||||
\(461\) | 24.0416 | 1.11973 | 0.559865 | − | 0.828584i | \(-0.310853\pi\) | ||||
0.559865 | + | 0.828584i | \(0.310853\pi\) | |||||||
\(462\) | −1.26810 | −0.0589974 | ||||||||
\(463\) | −30.6274 | −1.42338 | −0.711688 | − | 0.702495i | \(-0.752069\pi\) | ||||
−0.711688 | + | 0.702495i | \(0.752069\pi\) | |||||||
\(464\) | −13.3827 | −0.621274 | ||||||||
\(465\) | 15.6788 | 0.727085 | ||||||||
\(466\) | −4.19825 | −0.194480 | ||||||||
\(467\) | −12.6274 | −0.584327 | −0.292164 | − | 0.956368i | \(-0.594375\pi\) | ||||
−0.292164 | + | 0.956368i | \(0.594375\pi\) | |||||||
\(468\) | 9.89949 | 0.457604 | ||||||||
\(469\) | 7.39104 | 0.341286 | ||||||||
\(470\) | 8.28772 | 0.382284 | ||||||||
\(471\) | −4.32957 | −0.199496 | ||||||||
\(472\) | 9.51472 | 0.437950 | ||||||||
\(473\) | −5.22625 | −0.240303 | ||||||||
\(474\) | 4.48528 | 0.206016 | ||||||||
\(475\) | −7.65685 | −0.351321 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.41421 | −0.247900 | ||||||||
\(478\) | −3.79899 | −0.173762 | ||||||||
\(479\) | −34.6047 | −1.58113 | −0.790564 | − | 0.612379i | \(-0.790213\pi\) | ||||
−0.790564 | + | 0.612379i | \(0.790213\pi\) | |||||||
\(480\) | −21.3137 | −0.972833 | ||||||||
\(481\) | 5.41196 | 0.246764 | ||||||||
\(482\) | −5.09494 | −0.232068 | ||||||||
\(483\) | 11.7206 | 0.533306 | ||||||||
\(484\) | 17.9706 | 0.816844 | ||||||||
\(485\) | −11.8995 | −0.540328 | ||||||||
\(486\) | −8.99869 | −0.408189 | ||||||||
\(487\) | 4.40649 | 0.199677 | 0.0998386 | − | 0.995004i | \(-0.468167\pi\) | ||||
0.0998386 | + | 0.995004i | \(0.468167\pi\) | |||||||
\(488\) | 14.6508 | 0.663209 | ||||||||
\(489\) | 14.8284 | 0.670565 | ||||||||
\(490\) | −4.46088 | −0.201522 | ||||||||
\(491\) | −25.1127 | −1.13332 | −0.566660 | − | 0.823952i | \(-0.691765\pi\) | ||||
−0.566660 | + | 0.823952i | \(0.691765\pi\) | |||||||
\(492\) | 38.9706 | 1.75693 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 2.82843 | 0.127257 | ||||||||
\(495\) | −7.65685 | −0.344150 | ||||||||
\(496\) | 9.74153 | 0.437408 | ||||||||
\(497\) | −14.1421 | −0.634361 | ||||||||
\(498\) | 0.371418 | 0.0166437 | ||||||||
\(499\) | 37.0321 | 1.65778 | 0.828892 | − | 0.559408i | \(-0.188972\pi\) | ||||
0.828892 | + | 0.559408i | \(0.188972\pi\) | |||||||
\(500\) | −22.2500 | −0.995052 | ||||||||
\(501\) | 26.1421 | 1.16794 | ||||||||
\(502\) | −1.45584 | −0.0649775 | ||||||||
\(503\) | 14.9678 | 0.667380 | 0.333690 | − | 0.942683i | \(-0.391706\pi\) | ||||
0.333690 | + | 0.942683i | \(0.391706\pi\) | |||||||
\(504\) | −6.57128 | −0.292708 | ||||||||
\(505\) | −24.7862 | −1.10297 | ||||||||
\(506\) | −1.85786 | −0.0825921 | ||||||||
\(507\) | 28.7444 | 1.27658 | ||||||||
\(508\) | −31.6569 | −1.40455 | ||||||||
\(509\) | 3.02944 | 0.134277 | 0.0671387 | − | 0.997744i | \(-0.478613\pi\) | ||||
0.0671387 | + | 0.997744i | \(0.478613\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.79899 | −0.256532 | ||||||||
\(512\) | −22.7574 | −1.00574 | ||||||||
\(513\) | −10.4525 | −0.461489 | ||||||||
\(514\) | 9.17157 | 0.404541 | ||||||||
\(515\) | 8.28772 | 0.365201 | ||||||||
\(516\) | −23.0698 | −1.01559 | ||||||||
\(517\) | 11.7206 | 0.515472 | ||||||||
\(518\) | −1.71573 | −0.0753848 | ||||||||
\(519\) | 8.82843 | 0.387525 | ||||||||
\(520\) | 4.14386 | 0.181720 | ||||||||
\(521\) | −3.11586 | −0.136508 | −0.0682542 | − | 0.997668i | \(-0.521743\pi\) | ||||
−0.0682542 | + | 0.997668i | \(0.521743\pi\) | |||||||
\(522\) | 7.07401 | 0.309621 | ||||||||
\(523\) | 6.82843 | 0.298586 | 0.149293 | − | 0.988793i | \(-0.452300\pi\) | ||||
0.149293 | + | 0.988793i | \(0.452300\pi\) | |||||||
\(524\) | −0.339556 | −0.0148336 | ||||||||
\(525\) | −4.48528 | −0.195754 | ||||||||
\(526\) | −2.68629 | −0.117128 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −8.48528 | −0.369274 | ||||||||
\(529\) | −5.82843 | −0.253410 | ||||||||
\(530\) | −1.08239 | −0.0470161 | ||||||||
\(531\) | 22.9706 | 0.996838 | ||||||||
\(532\) | 9.55582 | 0.414297 | ||||||||
\(533\) | −11.5349 | −0.499632 | ||||||||
\(534\) | 10.1899 | 0.440959 | ||||||||
\(535\) | −11.6569 | −0.503970 | ||||||||
\(536\) | −10.8284 | −0.467717 | ||||||||
\(537\) | −15.6788 | −0.676588 | ||||||||
\(538\) | 2.63566 | 0.113631 | ||||||||
\(539\) | −6.30864 | −0.271733 | ||||||||
\(540\) | −7.31371 | −0.314732 | ||||||||
\(541\) | 18.3463 | 0.788768 | 0.394384 | − | 0.918946i | \(-0.370958\pi\) | ||||
0.394384 | + | 0.918946i | \(0.370958\pi\) | |||||||
\(542\) | −2.54416 | −0.109281 | ||||||||
\(543\) | −32.6274 | −1.40018 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.89949 | 0.338377 | ||||||||
\(546\) | 1.65685 | 0.0709068 | ||||||||
\(547\) | 24.7862 | 1.05978 | 0.529891 | − | 0.848065i | \(-0.322233\pi\) | ||||
0.529891 | + | 0.848065i | \(0.322233\pi\) | |||||||
\(548\) | −15.9584 | −0.681708 | ||||||||
\(549\) | 35.3701 | 1.50956 | ||||||||
\(550\) | 0.710974 | 0.0303160 | ||||||||
\(551\) | −21.5391 | −0.917595 | ||||||||
\(552\) | −17.1716 | −0.730871 | ||||||||
\(553\) | −4.48528 | −0.190734 | ||||||||
\(554\) | 9.13001 | 0.387897 | ||||||||
\(555\) | −18.4776 | −0.784330 | ||||||||
\(556\) | 27.3675 | 1.16064 | ||||||||
\(557\) | −28.2426 | −1.19668 | −0.598340 | − | 0.801243i | \(-0.704173\pi\) | ||||
−0.598340 | + | 0.801243i | \(0.704173\pi\) | |||||||
\(558\) | −5.14933 | −0.217988 | ||||||||
\(559\) | 6.82843 | 0.288812 | ||||||||
\(560\) | 6.00000 | 0.253546 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.41421 | 0.312750 | ||||||||
\(563\) | 38.7696 | 1.63394 | 0.816971 | − | 0.576679i | \(-0.195652\pi\) | ||||
0.816971 | + | 0.576679i | \(0.195652\pi\) | |||||||
\(564\) | 51.7373 | 2.17853 | ||||||||
\(565\) | 29.8995 | 1.25788 | ||||||||
\(566\) | 9.47890 | 0.398428 | ||||||||
\(567\) | 6.30864 | 0.264938 | ||||||||
\(568\) | 20.7193 | 0.869362 | ||||||||
\(569\) | −36.0416 | −1.51094 | −0.755472 | − | 0.655181i | \(-0.772592\pi\) | ||||
−0.755472 | + | 0.655181i | \(0.772592\pi\) | |||||||
\(570\) | −9.65685 | −0.404481 | ||||||||
\(571\) | −47.2220 | −1.97618 | −0.988089 | − | 0.153883i | \(-0.950822\pi\) | ||||
−0.988089 | + | 0.153883i | \(0.950822\pi\) | |||||||
\(572\) | 2.79884 | 0.117025 | ||||||||
\(573\) | −52.2625 | −2.18330 | ||||||||
\(574\) | 3.65685 | 0.152634 | ||||||||
\(575\) | −6.57128 | −0.274041 | ||||||||
\(576\) | −15.9706 | −0.665440 | ||||||||
\(577\) | 12.9289 | 0.538238 | 0.269119 | − | 0.963107i | \(-0.413267\pi\) | ||||
0.269119 | + | 0.963107i | \(0.413267\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.4853 | −0.601988 | ||||||||
\(580\) | −15.0711 | −0.625792 | ||||||||
\(581\) | −0.371418 | −0.0154090 | ||||||||
\(582\) | 6.97056 | 0.288939 | ||||||||
\(583\) | −1.53073 | −0.0633965 | ||||||||
\(584\) | 8.49596 | 0.351565 | ||||||||
\(585\) | 10.0042 | 0.413621 | ||||||||
\(586\) | 9.79899 | 0.404793 | ||||||||
\(587\) | −22.6863 | −0.936363 | −0.468182 | − | 0.883632i | \(-0.655091\pi\) | ||||
−0.468182 | + | 0.883632i | \(0.655091\pi\) | |||||||
\(588\) | −27.8477 | −1.14842 | ||||||||
\(589\) | 15.6788 | 0.646032 | ||||||||
\(590\) | 4.59220 | 0.189058 | ||||||||
\(591\) | 38.9706 | 1.60303 | ||||||||
\(592\) | −11.4805 | −0.471846 | ||||||||
\(593\) | 27.0711 | 1.11168 | 0.555838 | − | 0.831291i | \(-0.312398\pi\) | ||||
0.555838 | + | 0.831291i | \(0.312398\pi\) | |||||||
\(594\) | 0.970563 | 0.0398227 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −31.0294 | −1.27102 | ||||||||
\(597\) | 4.48528 | 0.183570 | ||||||||
\(598\) | 2.42742 | 0.0992645 | ||||||||
\(599\) | 34.6274 | 1.41484 | 0.707419 | − | 0.706794i | \(-0.249859\pi\) | ||||
0.707419 | + | 0.706794i | \(0.249859\pi\) | |||||||
\(600\) | 6.57128 | 0.268271 | ||||||||
\(601\) | −20.3253 | −0.829088 | −0.414544 | − | 0.910029i | \(-0.636059\pi\) | ||||
−0.414544 | + | 0.910029i | \(0.636059\pi\) | |||||||
\(602\) | −2.16478 | −0.0882300 | ||||||||
\(603\) | −26.1421 | −1.06459 | ||||||||
\(604\) | −23.4558 | −0.954405 | ||||||||
\(605\) | 18.1606 | 0.738332 | ||||||||
\(606\) | 14.5194 | 0.589812 | ||||||||
\(607\) | −34.3421 | −1.39390 | −0.696951 | − | 0.717119i | \(-0.745460\pi\) | ||||
−0.696951 | + | 0.717119i | \(0.745460\pi\) | |||||||
\(608\) | −21.3137 | −0.864385 | ||||||||
\(609\) | −12.6173 | −0.511278 | ||||||||
\(610\) | 7.07107 | 0.286299 | ||||||||
\(611\) | −15.3137 | −0.619526 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.3137 | −0.699294 | −0.349647 | − | 0.936881i | \(-0.613698\pi\) | ||||
−0.349647 | + | 0.936881i | \(0.613698\pi\) | |||||||
\(614\) | −0.887302 | −0.0358086 | ||||||||
\(615\) | 39.3826 | 1.58806 | ||||||||
\(616\) | −1.85786 | −0.0748555 | ||||||||
\(617\) | 3.37849 | 0.136013 | 0.0680065 | − | 0.997685i | \(-0.478336\pi\) | ||||
0.0680065 | + | 0.997685i | \(0.478336\pi\) | |||||||
\(618\) | −4.85483 | −0.195290 | ||||||||
\(619\) | −9.63274 | −0.387173 | −0.193586 | − | 0.981083i | \(-0.562012\pi\) | ||||
−0.193586 | + | 0.981083i | \(0.562012\pi\) | |||||||
\(620\) | 10.9706 | 0.440588 | ||||||||
\(621\) | −8.97056 | −0.359976 | ||||||||
\(622\) | −1.87029 | −0.0749918 | ||||||||
\(623\) | −10.1899 | −0.408249 | ||||||||
\(624\) | 11.0866 | 0.443817 | ||||||||
\(625\) | −14.5563 | −0.582254 | ||||||||
\(626\) | −5.28064 | −0.211057 | ||||||||
\(627\) | −13.6569 | −0.545402 | ||||||||
\(628\) | −3.02944 | −0.120888 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −3.17157 | −0.126358 | ||||||||
\(631\) | 6.68629 | 0.266177 | 0.133089 | − | 0.991104i | \(-0.457511\pi\) | ||||
0.133089 | + | 0.991104i | \(0.457511\pi\) | |||||||
\(632\) | 6.57128 | 0.261391 | ||||||||
\(633\) | 39.1127 | 1.55459 | ||||||||
\(634\) | −2.40489 | −0.0955102 | ||||||||
\(635\) | −31.9916 | −1.26955 | ||||||||
\(636\) | −6.75699 | −0.267932 | ||||||||
\(637\) | 8.24264 | 0.326585 | ||||||||
\(638\) | 2.00000 | 0.0791808 | ||||||||
\(639\) | 50.0208 | 1.97879 | ||||||||
\(640\) | −19.5056 | −0.771026 | ||||||||
\(641\) | −14.9903 | −0.592082 | −0.296041 | − | 0.955175i | \(-0.595666\pi\) | ||||
−0.296041 | + | 0.955175i | \(0.595666\pi\) | |||||||
\(642\) | 6.82843 | 0.269497 | ||||||||
\(643\) | 40.0936 | 1.58114 | 0.790568 | − | 0.612374i | \(-0.209785\pi\) | ||||
0.790568 | + | 0.612374i | \(0.209785\pi\) | |||||||
\(644\) | 8.20101 | 0.323165 | ||||||||
\(645\) | −23.3137 | −0.917976 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.82843 | 0.111197 | 0.0555985 | − | 0.998453i | \(-0.482293\pi\) | ||||
0.0555985 | + | 0.998453i | \(0.482293\pi\) | |||||||
\(648\) | −9.24264 | −0.363085 | ||||||||
\(649\) | 6.49435 | 0.254926 | ||||||||
\(650\) | −0.928932 | −0.0364357 | ||||||||
\(651\) | 9.18440 | 0.359965 | ||||||||
\(652\) | 10.3756 | 0.406339 | ||||||||
\(653\) | 17.7122 | 0.693133 | 0.346566 | − | 0.938025i | \(-0.387348\pi\) | ||||
0.346566 | + | 0.938025i | \(0.387348\pi\) | |||||||
\(654\) | −4.62742 | −0.180946 | ||||||||
\(655\) | −0.343146 | −0.0134078 | ||||||||
\(656\) | 24.4692 | 0.955362 | ||||||||
\(657\) | 20.5111 | 0.800213 | ||||||||
\(658\) | 4.85483 | 0.189261 | ||||||||
\(659\) | 8.48528 | 0.330540 | 0.165270 | − | 0.986248i | \(-0.447151\pi\) | ||||
0.165270 | + | 0.986248i | \(0.447151\pi\) | |||||||
\(660\) | −9.55582 | −0.371960 | ||||||||
\(661\) | −41.2132 | −1.60301 | −0.801504 | − | 0.597990i | \(-0.795966\pi\) | ||||
−0.801504 | + | 0.597990i | \(0.795966\pi\) | |||||||
\(662\) | −7.37258 | −0.286544 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.544156 | 0.0211173 | ||||||||
\(665\) | 9.65685 | 0.374477 | ||||||||
\(666\) | 6.06854 | 0.235151 | ||||||||
\(667\) | −18.4853 | −0.715753 | ||||||||
\(668\) | 18.2919 | 0.707734 | ||||||||
\(669\) | −2.16478 | −0.0836954 | ||||||||
\(670\) | −5.22625 | −0.201908 | ||||||||
\(671\) | 10.0000 | 0.386046 | ||||||||
\(672\) | −12.4853 | −0.481630 | ||||||||
\(673\) | −0.317025 | −0.0122204 | −0.00611021 | − | 0.999981i | \(-0.501945\pi\) | ||||
−0.00611021 | + | 0.999981i | \(0.501945\pi\) | |||||||
\(674\) | −14.2793 | −0.550020 | ||||||||
\(675\) | 3.43289 | 0.132132 | ||||||||
\(676\) | 20.1127 | 0.773565 | ||||||||
\(677\) | −43.9204 | −1.68800 | −0.843999 | − | 0.536344i | \(-0.819805\pi\) | ||||
−0.843999 | + | 0.536344i | \(0.819805\pi\) | |||||||
\(678\) | −17.5147 | −0.672649 | ||||||||
\(679\) | −6.97056 | −0.267506 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.1716 | 0.504736 | ||||||||
\(682\) | −1.45584 | −0.0557472 | ||||||||
\(683\) | −31.2806 | −1.19692 | −0.598459 | − | 0.801153i | \(-0.704220\pi\) | ||||
−0.598459 | + | 0.801153i | \(0.704220\pi\) | |||||||
\(684\) | −33.7990 | −1.29234 | ||||||||
\(685\) | −16.1271 | −0.616185 | ||||||||
\(686\) | −5.75152 | −0.219594 | ||||||||
\(687\) | 59.6536 | 2.27593 | ||||||||
\(688\) | −14.4853 | −0.552246 | ||||||||
\(689\) | 2.00000 | 0.0761939 | ||||||||
\(690\) | −8.28772 | −0.315508 | ||||||||
\(691\) | −40.7276 | −1.54935 | −0.774676 | − | 0.632358i | \(-0.782087\pi\) | ||||
−0.774676 | + | 0.632358i | \(0.782087\pi\) | |||||||
\(692\) | 6.17733 | 0.234827 | ||||||||
\(693\) | −4.48528 | −0.170382 | ||||||||
\(694\) | −1.60766 | −0.0610258 | ||||||||
\(695\) | 27.6569 | 1.04908 | ||||||||
\(696\) | 18.4853 | 0.700683 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −1.75736 | −0.0665170 | ||||||||
\(699\) | −26.4853 | −1.00177 | ||||||||
\(700\) | −3.13839 | −0.118620 | ||||||||
\(701\) | −21.6985 | −0.819540 | −0.409770 | − | 0.912189i | \(-0.634391\pi\) | ||||
−0.409770 | + | 0.912189i | \(0.634391\pi\) | |||||||
\(702\) | −1.26810 | −0.0478614 | ||||||||
\(703\) | −18.4776 | −0.696896 | ||||||||
\(704\) | −4.51528 | −0.170176 | ||||||||
\(705\) | 52.2843 | 1.96914 | ||||||||
\(706\) | 5.79899 | 0.218248 | ||||||||
\(707\) | −14.5194 | −0.546060 | ||||||||
\(708\) | 28.6675 | 1.07739 | ||||||||
\(709\) | −11.5893 | −0.435245 | −0.217622 | − | 0.976033i | \(-0.569830\pi\) | ||||
−0.217622 | + | 0.976033i | \(0.569830\pi\) | |||||||
\(710\) | 10.0000 | 0.375293 | ||||||||
\(711\) | 15.8645 | 0.594964 | ||||||||
\(712\) | 14.9289 | 0.559485 | ||||||||
\(713\) | 13.4558 | 0.503925 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.82843 | 0.105777 | ||||||||
\(716\) | −10.9706 | −0.409989 | ||||||||
\(717\) | −23.9665 | −0.895044 | ||||||||
\(718\) | −9.59798 | −0.358193 | ||||||||
\(719\) | −14.0711 | −0.524763 | −0.262382 | − | 0.964964i | \(-0.584508\pi\) | ||||
−0.262382 | + | 0.964964i | \(0.584508\pi\) | |||||||
\(720\) | −21.2220 | −0.790898 | ||||||||
\(721\) | 4.85483 | 0.180803 | ||||||||
\(722\) | −1.78680 | −0.0664977 | ||||||||
\(723\) | −32.1421 | −1.19538 | ||||||||
\(724\) | −22.8297 | −0.848459 | ||||||||
\(725\) | 7.07401 | 0.262722 | ||||||||
\(726\) | −10.6382 | −0.394821 | ||||||||
\(727\) | 19.1127 | 0.708851 | 0.354425 | − | 0.935084i | \(-0.384676\pi\) | ||||
0.354425 | + | 0.935084i | \(0.384676\pi\) | |||||||
\(728\) | 2.42742 | 0.0899661 | ||||||||
\(729\) | −39.2843 | −1.45497 | ||||||||
\(730\) | 4.10051 | 0.151767 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 44.1421 | 1.63154 | ||||||||
\(733\) | −12.0416 | −0.444768 | −0.222384 | − | 0.974959i | \(-0.571384\pi\) | ||||
−0.222384 | + | 0.974959i | \(0.571384\pi\) | |||||||
\(734\) | −10.9008 | −0.402358 | ||||||||
\(735\) | −28.1421 | −1.03804 | ||||||||
\(736\) | −18.2919 | −0.674248 | ||||||||
\(737\) | −7.39104 | −0.272252 | ||||||||
\(738\) | −12.9343 | −0.476119 | ||||||||
\(739\) | −34.2843 | −1.26117 | −0.630584 | − | 0.776121i | \(-0.717184\pi\) | ||||
−0.630584 | + | 0.776121i | \(0.717184\pi\) | |||||||
\(740\) | −12.9289 | −0.475277 | ||||||||
\(741\) | 17.8435 | 0.655499 | ||||||||
\(742\) | −0.634051 | −0.0232767 | ||||||||
\(743\) | 49.2780 | 1.80783 | 0.903917 | − | 0.427708i | \(-0.140679\pi\) | ||||
0.903917 | + | 0.427708i | \(0.140679\pi\) | |||||||
\(744\) | −13.4558 | −0.493315 | ||||||||
\(745\) | −31.3575 | −1.14885 | ||||||||
\(746\) | −8.10051 | −0.296581 | ||||||||
\(747\) | 1.31371 | 0.0480661 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.82843 | −0.249505 | ||||||||
\(750\) | 13.1716 | 0.480958 | ||||||||
\(751\) | −26.2082 | −0.956350 | −0.478175 | − | 0.878265i | \(-0.658702\pi\) | ||||
−0.478175 | + | 0.878265i | \(0.658702\pi\) | |||||||
\(752\) | 32.4853 | 1.18462 | ||||||||
\(753\) | −9.18440 | −0.334698 | ||||||||
\(754\) | −2.61313 | −0.0951644 | ||||||||
\(755\) | −23.7038 | −0.862671 | ||||||||
\(756\) | −4.28427 | −0.155817 | ||||||||
\(757\) | 53.4558 | 1.94289 | 0.971443 | − | 0.237274i | \(-0.0762538\pi\) | ||||
0.971443 | + | 0.237274i | \(0.0762538\pi\) | |||||||
\(758\) | 0.448342 | 0.0162845 | ||||||||
\(759\) | −11.7206 | −0.425431 | ||||||||
\(760\) | −14.1480 | −0.513203 | ||||||||
\(761\) | −21.6985 | −0.786569 | −0.393285 | − | 0.919417i | \(-0.628661\pi\) | ||||
−0.393285 | + | 0.919417i | \(0.628661\pi\) | |||||||
\(762\) | 18.7402 | 0.678887 | ||||||||
\(763\) | 4.62742 | 0.167524 | ||||||||
\(764\) | −36.5685 | −1.32300 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.28427 | −0.0825341 | ||||||||
\(767\) | −8.48528 | −0.306386 | ||||||||
\(768\) | −10.3756 | −0.374397 | ||||||||
\(769\) | −12.7279 | −0.458981 | −0.229490 | − | 0.973311i | \(-0.573706\pi\) | ||||
−0.229490 | + | 0.973311i | \(0.573706\pi\) | |||||||
\(770\) | −0.896683 | −0.0323142 | ||||||||
\(771\) | 57.8602 | 2.08378 | ||||||||
\(772\) | −10.1355 | −0.364784 | ||||||||
\(773\) | 4.82843 | 0.173666 | 0.0868332 | − | 0.996223i | \(-0.472325\pi\) | ||||
0.0868332 | + | 0.996223i | \(0.472325\pi\) | |||||||
\(774\) | 7.65685 | 0.275220 | ||||||||
\(775\) | −5.14933 | −0.184969 | ||||||||
\(776\) | 10.2124 | 0.366604 | ||||||||
\(777\) | −10.8239 | −0.388306 | ||||||||
\(778\) | −6.68629 | −0.239715 | ||||||||
\(779\) | 39.3826 | 1.41103 | ||||||||
\(780\) | 12.4853 | 0.447045 | ||||||||
\(781\) | 14.1421 | 0.506045 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.65685 | 0.345108 | ||||||||
\(784\) | −17.4853 | −0.624474 | ||||||||
\(785\) | −3.06147 | −0.109268 | ||||||||
\(786\) | 0.201010 | 0.00716979 | ||||||||
\(787\) | 49.6494 | 1.76981 | 0.884905 | − | 0.465772i | \(-0.154223\pi\) | ||||
0.884905 | + | 0.465772i | \(0.154223\pi\) | |||||||
\(788\) | 27.2680 | 0.971384 | ||||||||
\(789\) | −16.9469 | −0.603324 | ||||||||
\(790\) | 3.17157 | 0.112839 | ||||||||
\(791\) | 17.5147 | 0.622752 | ||||||||
\(792\) | 6.57128 | 0.233500 | ||||||||
\(793\) | −13.0656 | −0.463974 | ||||||||
\(794\) | −11.2948 | −0.400837 | ||||||||
\(795\) | −6.82843 | −0.242179 | ||||||||
\(796\) | 3.13839 | 0.111237 | ||||||||
\(797\) | 17.2132 | 0.609723 | 0.304861 | − | 0.952397i | \(-0.401390\pi\) | ||||
0.304861 | + | 0.952397i | \(0.401390\pi\) | |||||||
\(798\) | −5.65685 | −0.200250 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 7.00000 | 0.247487 | ||||||||
\(801\) | 36.0416 | 1.27347 | ||||||||
\(802\) | −7.07401 | −0.249792 | ||||||||
\(803\) | 5.79899 | 0.204642 | ||||||||
\(804\) | −32.6256 | −1.15062 | ||||||||
\(805\) | 8.28772 | 0.292104 | ||||||||
\(806\) | 1.90215 | 0.0670004 | ||||||||
\(807\) | 16.6274 | 0.585313 | ||||||||
\(808\) | 21.2721 | 0.748349 | ||||||||
\(809\) | −29.7724 | −1.04674 | −0.523371 | − | 0.852105i | \(-0.675326\pi\) | ||||
−0.523371 | + | 0.852105i | \(0.675326\pi\) | |||||||
\(810\) | −4.46088 | −0.156740 | ||||||||
\(811\) | 44.2693 | 1.55451 | 0.777253 | − | 0.629189i | \(-0.216613\pi\) | ||||
0.777253 | + | 0.629189i | \(0.216613\pi\) | |||||||
\(812\) | −8.82843 | −0.309817 | ||||||||
\(813\) | −16.0502 | −0.562904 | ||||||||
\(814\) | 1.71573 | 0.0601363 | ||||||||
\(815\) | 10.4853 | 0.367283 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.3137 | −0.815643 | ||||||||
\(818\) | −8.00000 | −0.279713 | ||||||||
\(819\) | 5.86030 | 0.204776 | ||||||||
\(820\) | 27.5563 | 0.962309 | ||||||||
\(821\) | 14.3881 | 0.502149 | 0.251074 | − | 0.967968i | \(-0.419216\pi\) | ||||
0.251074 | + | 0.967968i | \(0.419216\pi\) | |||||||
\(822\) | 9.44703 | 0.329503 | ||||||||
\(823\) | −23.5181 | −0.819791 | −0.409895 | − | 0.912133i | \(-0.634435\pi\) | ||||
−0.409895 | + | 0.912133i | \(0.634435\pi\) | |||||||
\(824\) | −7.11270 | −0.247783 | ||||||||
\(825\) | 4.48528 | 0.156157 | ||||||||
\(826\) | 2.69005 | 0.0935988 | ||||||||
\(827\) | 34.7135 | 1.20711 | 0.603553 | − | 0.797323i | \(-0.293751\pi\) | ||||
0.603553 | + | 0.797323i | \(0.293751\pi\) | |||||||
\(828\) | −29.0070 | −1.00806 | ||||||||
\(829\) | −13.9411 | −0.484195 | −0.242098 | − | 0.970252i | \(-0.577835\pi\) | ||||
−0.242098 | + | 0.970252i | \(0.577835\pi\) | |||||||
\(830\) | 0.262632 | 0.00911610 | ||||||||
\(831\) | 57.5980 | 1.99805 | ||||||||
\(832\) | 5.89949 | 0.204528 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −16.2010 | −0.560995 | ||||||||
\(835\) | 18.4853 | 0.639710 | ||||||||
\(836\) | −9.55582 | −0.330495 | ||||||||
\(837\) | −7.02944 | −0.242973 | ||||||||
\(838\) | −11.1635 | −0.385636 | ||||||||
\(839\) | −3.88123 | −0.133995 | −0.0669974 | − | 0.997753i | \(-0.521342\pi\) | ||||
−0.0669974 | + | 0.997753i | \(0.521342\pi\) | |||||||
\(840\) | −8.28772 | −0.285953 | ||||||||
\(841\) | −9.10051 | −0.313811 | ||||||||
\(842\) | −7.21320 | −0.248583 | ||||||||
\(843\) | 46.7736 | 1.61097 | ||||||||
\(844\) | 27.3675 | 0.942028 | ||||||||
\(845\) | 20.3253 | 0.699213 | ||||||||
\(846\) | −17.1716 | −0.590371 | ||||||||
\(847\) | 10.6382 | 0.365533 | ||||||||
\(848\) | −4.24264 | −0.145693 | ||||||||
\(849\) | 59.7990 | 2.05230 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.8579 | −0.543601 | ||||||||
\(852\) | 62.4264 | 2.13869 | ||||||||
\(853\) | 42.5754 | 1.45775 | 0.728877 | − | 0.684645i | \(-0.240043\pi\) | ||||
0.728877 | + | 0.684645i | \(0.240043\pi\) | |||||||
\(854\) | 4.14214 | 0.141741 | ||||||||
\(855\) | −34.1563 | −1.16812 | ||||||||
\(856\) | 10.0042 | 0.341935 | ||||||||
\(857\) | 3.82683 | 0.130722 | 0.0653611 | − | 0.997862i | \(-0.479180\pi\) | ||||
0.0653611 | + | 0.997862i | \(0.479180\pi\) | |||||||
\(858\) | −1.65685 | −0.0565641 | ||||||||
\(859\) | −1.02944 | −0.0351239 | −0.0175620 | − | 0.999846i | \(-0.505590\pi\) | ||||
−0.0175620 | + | 0.999846i | \(0.505590\pi\) | |||||||
\(860\) | −16.3128 | −0.556262 | ||||||||
\(861\) | 23.0698 | 0.786216 | ||||||||
\(862\) | 16.4985 | 0.561942 | ||||||||
\(863\) | 34.6274 | 1.17873 | 0.589365 | − | 0.807867i | \(-0.299378\pi\) | ||||
0.589365 | + | 0.807867i | \(0.299378\pi\) | |||||||
\(864\) | 9.55582 | 0.325096 | ||||||||
\(865\) | 6.24264 | 0.212256 | ||||||||
\(866\) | −6.28427 | −0.213548 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.42641 | 0.218126 | ||||||||
\(869\) | 4.48528 | 0.152153 | ||||||||
\(870\) | 8.92177 | 0.302476 | ||||||||
\(871\) | 9.65685 | 0.327210 | ||||||||
\(872\) | −6.77952 | −0.229583 | ||||||||
\(873\) | 24.6549 | 0.834443 | ||||||||
\(874\) | −8.28772 | −0.280336 | ||||||||
\(875\) | −13.1716 | −0.445280 | ||||||||
\(876\) | 25.5980 | 0.864876 | ||||||||
\(877\) | −37.6436 | −1.27113 | −0.635567 | − | 0.772045i | \(-0.719234\pi\) | ||||
−0.635567 | + | 0.772045i | \(0.719234\pi\) | |||||||
\(878\) | 4.51528 | 0.152383 | ||||||||
\(879\) | 61.8183 | 2.08508 | ||||||||
\(880\) | −6.00000 | −0.202260 | ||||||||
\(881\) | −18.5320 | −0.624358 | −0.312179 | − | 0.950023i | \(-0.601059\pi\) | ||||
−0.312179 | + | 0.950023i | \(0.601059\pi\) | |||||||
\(882\) | 9.24264 | 0.311216 | ||||||||
\(883\) | −8.00000 | −0.269221 | −0.134611 | − | 0.990899i | \(-0.542978\pi\) | ||||
−0.134611 | + | 0.990899i | \(0.542978\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28.9706 | 0.973835 | ||||||||
\(886\) | −6.54416 | −0.219855 | ||||||||
\(887\) | 48.8615 | 1.64061 | 0.820304 | − | 0.571927i | \(-0.193804\pi\) | ||||
0.820304 | + | 0.571927i | \(0.193804\pi\) | |||||||
\(888\) | 15.8579 | 0.532155 | ||||||||
\(889\) | −18.7402 | −0.628527 | ||||||||
\(890\) | 7.20533 | 0.241523 | ||||||||
\(891\) | −6.30864 | −0.211348 | ||||||||
\(892\) | −1.51472 | −0.0507165 | ||||||||
\(893\) | 52.2843 | 1.74963 | ||||||||
\(894\) | 18.3688 | 0.614345 | ||||||||
\(895\) | −11.0866 | −0.370583 | ||||||||
\(896\) | −11.4261 | −0.381720 | ||||||||
\(897\) | 15.3137 | 0.511310 | ||||||||
\(898\) | −7.78498 | −0.259788 | ||||||||
\(899\) | −14.4853 | −0.483111 | ||||||||
\(900\) | 11.1005 | 0.370017 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −3.65685 | −0.121760 | ||||||||
\(903\) | −13.6569 | −0.454472 | ||||||||
\(904\) | −25.6604 | −0.853452 | ||||||||
\(905\) | −23.0711 | −0.766908 | ||||||||
\(906\) | 13.8854 | 0.461311 | ||||||||
\(907\) | −25.0489 | −0.831734 | −0.415867 | − | 0.909425i | \(-0.636522\pi\) | ||||
−0.415867 | + | 0.909425i | \(0.636522\pi\) | |||||||
\(908\) | 9.21627 | 0.305852 | ||||||||
\(909\) | 51.3553 | 1.70335 | ||||||||
\(910\) | 1.17157 | 0.0388373 | ||||||||
\(911\) | −8.47343 | −0.280737 | −0.140369 | − | 0.990099i | \(-0.544829\pi\) | ||||
−0.140369 | + | 0.990099i | \(0.544829\pi\) | |||||||
\(912\) | −37.8519 | −1.25340 | ||||||||
\(913\) | 0.371418 | 0.0122922 | ||||||||
\(914\) | −7.79899 | −0.257968 | ||||||||
\(915\) | 44.6088 | 1.47472 | ||||||||
\(916\) | 41.7401 | 1.37913 | ||||||||
\(917\) | −0.201010 | −0.00663794 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.31371 | −0.109309 | −0.0546546 | − | 0.998505i | \(-0.517406\pi\) | ||||
−0.0546546 | + | 0.998505i | \(0.517406\pi\) | |||||||
\(920\) | −12.1421 | −0.400314 | ||||||||
\(921\) | −5.59767 | −0.184450 | ||||||||
\(922\) | −9.95837 | −0.327961 | ||||||||
\(923\) | −18.4776 | −0.608197 | ||||||||
\(924\) | −5.59767 | −0.184150 | ||||||||
\(925\) | 6.06854 | 0.199532 | ||||||||
\(926\) | 12.6863 | 0.416897 | ||||||||
\(927\) | −17.1716 | −0.563988 | ||||||||
\(928\) | 19.6913 | 0.646399 | ||||||||
\(929\) | −20.9594 | −0.687656 | −0.343828 | − | 0.939033i | \(-0.611724\pi\) | ||||
−0.343828 | + | 0.939033i | \(0.611724\pi\) | |||||||
\(930\) | −6.49435 | −0.212958 | ||||||||
\(931\) | −28.1421 | −0.922321 | ||||||||
\(932\) | −18.5320 | −0.607035 | ||||||||
\(933\) | −11.7990 | −0.386282 | ||||||||
\(934\) | 5.23045 | 0.171145 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.58579 | −0.280635 | ||||||||
\(937\) | 3.55635 | 0.116181 | 0.0580904 | − | 0.998311i | \(-0.481499\pi\) | ||||
0.0580904 | + | 0.998311i | \(0.481499\pi\) | |||||||
\(938\) | −3.06147 | −0.0999605 | ||||||||
\(939\) | −33.3137 | −1.08715 | ||||||||
\(940\) | 36.5838 | 1.19323 | ||||||||
\(941\) | 18.6858 | 0.609141 | 0.304570 | − | 0.952490i | \(-0.401487\pi\) | ||||
0.304570 | + | 0.952490i | \(0.401487\pi\) | |||||||
\(942\) | 1.79337 | 0.0584310 | ||||||||
\(943\) | 33.7990 | 1.10065 | ||||||||
\(944\) | 18.0000 | 0.585850 | ||||||||
\(945\) | −4.32957 | −0.140841 | ||||||||
\(946\) | 2.16478 | 0.0703832 | ||||||||
\(947\) | 14.8590 | 0.482852 | 0.241426 | − | 0.970419i | \(-0.422385\pi\) | ||||
0.241426 | + | 0.970419i | \(0.422385\pi\) | |||||||
\(948\) | 19.7990 | 0.643041 | ||||||||
\(949\) | −7.57675 | −0.245952 | ||||||||
\(950\) | 3.17157 | 0.102899 | ||||||||
\(951\) | −15.1716 | −0.491972 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.69848 | −0.314165 | −0.157082 | − | 0.987586i | \(-0.550209\pi\) | ||||
−0.157082 | + | 0.987586i | \(0.550209\pi\) | |||||||
\(954\) | 2.24264 | 0.0726082 | ||||||||
\(955\) | −36.9552 | −1.19584 | ||||||||
\(956\) | −16.7696 | −0.542366 | ||||||||
\(957\) | 12.6173 | 0.407859 | ||||||||
\(958\) | 14.3337 | 0.463102 | ||||||||
\(959\) | −9.44703 | −0.305061 | ||||||||
\(960\) | −20.1421 | −0.650085 | ||||||||
\(961\) | −20.4558 | −0.659866 | ||||||||
\(962\) | −2.24171 | −0.0722756 | ||||||||
\(963\) | 24.1522 | 0.778293 | ||||||||
\(964\) | −22.4901 | −0.724358 | ||||||||
\(965\) | −10.2426 | −0.329722 | ||||||||
\(966\) | −4.85483 | −0.156202 | ||||||||
\(967\) | −32.3431 | −1.04009 | −0.520043 | − | 0.854140i | \(-0.674084\pi\) | ||||
−0.520043 | + | 0.854140i | \(0.674084\pi\) | |||||||
\(968\) | −15.5858 | −0.500946 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.92893 | 0.158258 | ||||||||
\(971\) | −55.7401 | −1.78879 | −0.894393 | − | 0.447283i | \(-0.852392\pi\) | ||||
−0.894393 | + | 0.447283i | \(0.852392\pi\) | |||||||
\(972\) | −39.7222 | −1.27409 | ||||||||
\(973\) | 16.2010 | 0.519381 | ||||||||
\(974\) | −1.82523 | −0.0584841 | ||||||||
\(975\) | −5.86030 | −0.187680 | ||||||||
\(976\) | 27.7164 | 0.887180 | ||||||||
\(977\) | −1.61522 | −0.0516756 | −0.0258378 | − | 0.999666i | \(-0.508225\pi\) | ||||
−0.0258378 | + | 0.999666i | \(0.508225\pi\) | |||||||
\(978\) | −6.14214 | −0.196404 | ||||||||
\(979\) | 10.1899 | 0.325670 | ||||||||
\(980\) | −19.6913 | −0.629015 | ||||||||
\(981\) | −16.3672 | −0.522564 | ||||||||
\(982\) | 10.4020 | 0.331942 | ||||||||
\(983\) | 23.5181 | 0.750112 | 0.375056 | − | 0.927002i | \(-0.377623\pi\) | ||||
0.375056 | + | 0.927002i | \(0.377623\pi\) | |||||||
\(984\) | −33.7990 | −1.07747 | ||||||||
\(985\) | 27.5563 | 0.878018 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 30.6274 | 0.974881 | ||||||||
\(988\) | 12.4853 | 0.397210 | ||||||||
\(989\) | −20.0083 | −0.636228 | ||||||||
\(990\) | 3.17157 | 0.100799 | ||||||||
\(991\) | −32.0685 | −1.01869 | −0.509345 | − | 0.860563i | \(-0.670112\pi\) | ||||
−0.509345 | + | 0.860563i | \(0.670112\pi\) | |||||||
\(992\) | −14.3337 | −0.455096 | ||||||||
\(993\) | −46.5110 | −1.47598 | ||||||||
\(994\) | 5.85786 | 0.185800 | ||||||||
\(995\) | 3.17157 | 0.100546 | ||||||||
\(996\) | 1.63952 | 0.0519502 | ||||||||
\(997\) | 7.70806 | 0.244117 | 0.122058 | − | 0.992523i | \(-0.461050\pi\) | ||||
0.122058 | + | 0.992523i | \(0.461050\pi\) | |||||||
\(998\) | −15.3392 | −0.485554 | ||||||||
\(999\) | 8.28427 | 0.262103 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))