Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(1,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("403.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 11x^{6} + 10x^{5} + 37x^{4} - 33x^{3} - 36x^{2} + 33x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.656875\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 403.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.656875 | −0.464481 | −0.232240 | − | 0.972658i | \(-0.574606\pi\) | ||||
−0.232240 | + | 0.972658i | \(0.574606\pi\) | |||||||
\(3\) | 2.67827 | 1.54630 | 0.773150 | − | 0.634223i | \(-0.218680\pi\) | ||||
0.773150 | + | 0.634223i | \(0.218680\pi\) | |||||||
\(4\) | −1.56852 | −0.784258 | ||||||||
\(5\) | −1.55873 | −0.697087 | −0.348544 | − | 0.937293i | \(-0.613324\pi\) | ||||
−0.348544 | + | 0.937293i | \(0.613324\pi\) | |||||||
\(6\) | −1.75929 | −0.718226 | ||||||||
\(7\) | 2.17607 | 0.822477 | 0.411239 | − | 0.911528i | \(-0.365096\pi\) | ||||
0.411239 | + | 0.911528i | \(0.365096\pi\) | |||||||
\(8\) | 2.34407 | 0.828753 | ||||||||
\(9\) | 4.17313 | 1.39104 | ||||||||
\(10\) | 1.02389 | 0.323784 | ||||||||
\(11\) | 0.877966 | 0.264717 | 0.132358 | − | 0.991202i | \(-0.457745\pi\) | ||||
0.132358 | + | 0.991202i | \(0.457745\pi\) | |||||||
\(12\) | −4.20091 | −1.21270 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −1.42941 | −0.382025 | ||||||||
\(15\) | −4.17471 | −1.07791 | ||||||||
\(16\) | 1.59727 | 0.399318 | ||||||||
\(17\) | 4.00763 | 0.971993 | 0.485996 | − | 0.873961i | \(-0.338457\pi\) | ||||
0.485996 | + | 0.873961i | \(0.338457\pi\) | |||||||
\(18\) | −2.74122 | −0.646112 | ||||||||
\(19\) | −0.601130 | −0.137909 | −0.0689543 | − | 0.997620i | \(-0.521966\pi\) | ||||
−0.0689543 | + | 0.997620i | \(0.521966\pi\) | |||||||
\(20\) | 2.44490 | 0.546696 | ||||||||
\(21\) | 5.82810 | 1.27180 | ||||||||
\(22\) | −0.576714 | −0.122956 | ||||||||
\(23\) | 7.74079 | 1.61407 | 0.807033 | − | 0.590507i | \(-0.201072\pi\) | ||||
0.807033 | + | 0.590507i | \(0.201072\pi\) | |||||||
\(24\) | 6.27805 | 1.28150 | ||||||||
\(25\) | −2.57035 | −0.514070 | ||||||||
\(26\) | −0.656875 | −0.128824 | ||||||||
\(27\) | 3.14195 | 0.604669 | ||||||||
\(28\) | −3.41320 | −0.645034 | ||||||||
\(29\) | 4.35321 | 0.808371 | 0.404185 | − | 0.914677i | \(-0.367555\pi\) | ||||
0.404185 | + | 0.914677i | \(0.367555\pi\) | |||||||
\(30\) | 2.74226 | 0.500666 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | −5.73734 | −1.01423 | ||||||||
\(33\) | 2.35143 | 0.409331 | ||||||||
\(34\) | −2.63251 | −0.451472 | ||||||||
\(35\) | −3.39192 | −0.573338 | ||||||||
\(36\) | −6.54561 | −1.09094 | ||||||||
\(37\) | −2.60850 | −0.428834 | −0.214417 | − | 0.976742i | \(-0.568785\pi\) | ||||
−0.214417 | + | 0.976742i | \(0.568785\pi\) | |||||||
\(38\) | 0.394867 | 0.0640559 | ||||||||
\(39\) | 2.67827 | 0.428866 | ||||||||
\(40\) | −3.65378 | −0.577713 | ||||||||
\(41\) | −5.00956 | −0.782361 | −0.391181 | − | 0.920314i | \(-0.627933\pi\) | ||||
−0.391181 | + | 0.920314i | \(0.627933\pi\) | |||||||
\(42\) | −3.82833 | −0.590725 | ||||||||
\(43\) | −2.25813 | −0.344362 | −0.172181 | − | 0.985065i | \(-0.555081\pi\) | ||||
−0.172181 | + | 0.985065i | \(0.555081\pi\) | |||||||
\(44\) | −1.37710 | −0.207606 | ||||||||
\(45\) | −6.50480 | −0.969678 | ||||||||
\(46\) | −5.08473 | −0.749702 | ||||||||
\(47\) | −1.99049 | −0.290342 | −0.145171 | − | 0.989407i | \(-0.546373\pi\) | ||||
−0.145171 | + | 0.989407i | \(0.546373\pi\) | |||||||
\(48\) | 4.27792 | 0.617465 | ||||||||
\(49\) | −2.26472 | −0.323531 | ||||||||
\(50\) | 1.68840 | 0.238775 | ||||||||
\(51\) | 10.7335 | 1.50299 | ||||||||
\(52\) | −1.56852 | −0.217514 | ||||||||
\(53\) | −3.22380 | −0.442823 | −0.221411 | − | 0.975180i | \(-0.571066\pi\) | ||||
−0.221411 | + | 0.975180i | \(0.571066\pi\) | |||||||
\(54\) | −2.06387 | −0.280857 | ||||||||
\(55\) | −1.36852 | −0.184531 | ||||||||
\(56\) | 5.10086 | 0.681631 | ||||||||
\(57\) | −1.60999 | −0.213248 | ||||||||
\(58\) | −2.85951 | −0.375473 | ||||||||
\(59\) | 6.18276 | 0.804927 | 0.402464 | − | 0.915436i | \(-0.368154\pi\) | ||||
0.402464 | + | 0.915436i | \(0.368154\pi\) | |||||||
\(60\) | 6.54810 | 0.845356 | ||||||||
\(61\) | 2.46585 | 0.315720 | 0.157860 | − | 0.987462i | \(-0.449541\pi\) | ||||
0.157860 | + | 0.987462i | \(0.449541\pi\) | |||||||
\(62\) | 0.656875 | 0.0834232 | ||||||||
\(63\) | 9.08102 | 1.14410 | ||||||||
\(64\) | 0.574175 | 0.0717718 | ||||||||
\(65\) | −1.55873 | −0.193337 | ||||||||
\(66\) | −1.54459 | −0.190126 | ||||||||
\(67\) | −6.59746 | −0.806007 | −0.403004 | − | 0.915198i | \(-0.632034\pi\) | ||||
−0.403004 | + | 0.915198i | \(0.632034\pi\) | |||||||
\(68\) | −6.28603 | −0.762293 | ||||||||
\(69\) | 20.7319 | 2.49583 | ||||||||
\(70\) | 2.22806 | 0.266305 | ||||||||
\(71\) | −0.570087 | −0.0676569 | −0.0338284 | − | 0.999428i | \(-0.510770\pi\) | ||||
−0.0338284 | + | 0.999428i | \(0.510770\pi\) | |||||||
\(72\) | 9.78210 | 1.15283 | ||||||||
\(73\) | −6.17960 | −0.723267 | −0.361633 | − | 0.932320i | \(-0.617781\pi\) | ||||
−0.361633 | + | 0.932320i | \(0.617781\pi\) | |||||||
\(74\) | 1.71346 | 0.199185 | ||||||||
\(75\) | −6.88408 | −0.794906 | ||||||||
\(76\) | 0.942882 | 0.108156 | ||||||||
\(77\) | 1.91052 | 0.217723 | ||||||||
\(78\) | −1.75929 | −0.199200 | ||||||||
\(79\) | 9.85609 | 1.10890 | 0.554448 | − | 0.832218i | \(-0.312929\pi\) | ||||
0.554448 | + | 0.832218i | \(0.312929\pi\) | |||||||
\(80\) | −2.48972 | −0.278359 | ||||||||
\(81\) | −4.10439 | −0.456043 | ||||||||
\(82\) | 3.29065 | 0.363392 | ||||||||
\(83\) | 7.25438 | 0.796272 | 0.398136 | − | 0.917326i | \(-0.369657\pi\) | ||||
0.398136 | + | 0.917326i | \(0.369657\pi\) | |||||||
\(84\) | −9.14147 | −0.997416 | ||||||||
\(85\) | −6.24683 | −0.677564 | ||||||||
\(86\) | 1.48331 | 0.159949 | ||||||||
\(87\) | 11.6591 | 1.24998 | ||||||||
\(88\) | 2.05801 | 0.219385 | ||||||||
\(89\) | −16.2492 | −1.72242 | −0.861208 | − | 0.508252i | \(-0.830292\pi\) | ||||
−0.861208 | + | 0.508252i | \(0.830292\pi\) | |||||||
\(90\) | 4.27284 | 0.450397 | ||||||||
\(91\) | 2.17607 | 0.228114 | ||||||||
\(92\) | −12.1415 | −1.26584 | ||||||||
\(93\) | −2.67827 | −0.277724 | ||||||||
\(94\) | 1.30750 | 0.134858 | ||||||||
\(95\) | 0.937002 | 0.0961344 | ||||||||
\(96\) | −15.3662 | −1.56830 | ||||||||
\(97\) | −15.9725 | −1.62176 | −0.810882 | − | 0.585210i | \(-0.801012\pi\) | ||||
−0.810882 | + | 0.585210i | \(0.801012\pi\) | |||||||
\(98\) | 1.48764 | 0.150274 | ||||||||
\(99\) | 3.66386 | 0.368232 | ||||||||
\(100\) | 4.03163 | 0.403163 | ||||||||
\(101\) | 0.816483 | 0.0812431 | 0.0406215 | − | 0.999175i | \(-0.487066\pi\) | ||||
0.0406215 | + | 0.999175i | \(0.487066\pi\) | |||||||
\(102\) | −7.05057 | −0.698111 | ||||||||
\(103\) | −0.363514 | −0.0358181 | −0.0179090 | − | 0.999840i | \(-0.505701\pi\) | ||||
−0.0179090 | + | 0.999840i | \(0.505701\pi\) | |||||||
\(104\) | 2.34407 | 0.229855 | ||||||||
\(105\) | −9.08446 | −0.886553 | ||||||||
\(106\) | 2.11763 | 0.205683 | ||||||||
\(107\) | −17.8288 | −1.72357 | −0.861787 | − | 0.507270i | \(-0.830655\pi\) | ||||
−0.861787 | + | 0.507270i | \(0.830655\pi\) | |||||||
\(108\) | −4.92820 | −0.474216 | ||||||||
\(109\) | −10.3157 | −0.988069 | −0.494034 | − | 0.869442i | \(-0.664478\pi\) | ||||
−0.494034 | + | 0.869442i | \(0.664478\pi\) | |||||||
\(110\) | 0.898944 | 0.0857109 | ||||||||
\(111\) | −6.98626 | −0.663107 | ||||||||
\(112\) | 3.47577 | 0.328430 | ||||||||
\(113\) | 15.5910 | 1.46668 | 0.733339 | − | 0.679863i | \(-0.237961\pi\) | ||||
0.733339 | + | 0.679863i | \(0.237961\pi\) | |||||||
\(114\) | 1.05756 | 0.0990497 | ||||||||
\(115\) | −12.0658 | −1.12514 | ||||||||
\(116\) | −6.82808 | −0.633971 | ||||||||
\(117\) | 4.17313 | 0.385806 | ||||||||
\(118\) | −4.06130 | −0.373873 | ||||||||
\(119\) | 8.72088 | 0.799442 | ||||||||
\(120\) | −9.78581 | −0.893318 | ||||||||
\(121\) | −10.2292 | −0.929925 | ||||||||
\(122\) | −1.61975 | −0.146646 | ||||||||
\(123\) | −13.4169 | −1.20976 | ||||||||
\(124\) | 1.56852 | 0.140857 | ||||||||
\(125\) | 11.8002 | 1.05544 | ||||||||
\(126\) | −5.96509 | −0.531413 | ||||||||
\(127\) | −9.71552 | −0.862113 | −0.431057 | − | 0.902325i | \(-0.641859\pi\) | ||||
−0.431057 | + | 0.902325i | \(0.641859\pi\) | |||||||
\(128\) | 11.0975 | 0.980892 | ||||||||
\(129\) | −6.04788 | −0.532486 | ||||||||
\(130\) | 1.02389 | 0.0898014 | ||||||||
\(131\) | 13.5147 | 1.18078 | 0.590392 | − | 0.807117i | \(-0.298973\pi\) | ||||
0.590392 | + | 0.807117i | \(0.298973\pi\) | |||||||
\(132\) | −3.68825 | −0.321021 | ||||||||
\(133\) | −1.30810 | −0.113427 | ||||||||
\(134\) | 4.33370 | 0.374375 | ||||||||
\(135\) | −4.89747 | −0.421507 | ||||||||
\(136\) | 9.39415 | 0.805542 | ||||||||
\(137\) | −5.15662 | −0.440560 | −0.220280 | − | 0.975437i | \(-0.570697\pi\) | ||||
−0.220280 | + | 0.975437i | \(0.570697\pi\) | |||||||
\(138\) | −13.6183 | −1.15926 | ||||||||
\(139\) | 22.2319 | 1.88568 | 0.942842 | − | 0.333241i | \(-0.108142\pi\) | ||||
0.942842 | + | 0.333241i | \(0.108142\pi\) | |||||||
\(140\) | 5.32027 | 0.449645 | ||||||||
\(141\) | −5.33106 | −0.448956 | ||||||||
\(142\) | 0.374476 | 0.0314253 | ||||||||
\(143\) | 0.877966 | 0.0734192 | ||||||||
\(144\) | 6.66562 | 0.555468 | ||||||||
\(145\) | −6.78550 | −0.563505 | ||||||||
\(146\) | 4.05922 | 0.335944 | ||||||||
\(147\) | −6.06552 | −0.500276 | ||||||||
\(148\) | 4.09147 | 0.336317 | ||||||||
\(149\) | 4.62898 | 0.379221 | 0.189611 | − | 0.981859i | \(-0.439277\pi\) | ||||
0.189611 | + | 0.981859i | \(0.439277\pi\) | |||||||
\(150\) | 4.52198 | 0.369218 | ||||||||
\(151\) | −4.33901 | −0.353104 | −0.176552 | − | 0.984291i | \(-0.556494\pi\) | ||||
−0.176552 | + | 0.984291i | \(0.556494\pi\) | |||||||
\(152\) | −1.40909 | −0.114292 | ||||||||
\(153\) | 16.7243 | 1.35208 | ||||||||
\(154\) | −1.25497 | −0.101128 | ||||||||
\(155\) | 1.55873 | 0.125201 | ||||||||
\(156\) | −4.20091 | −0.336342 | ||||||||
\(157\) | −12.7698 | −1.01914 | −0.509572 | − | 0.860428i | \(-0.670196\pi\) | ||||
−0.509572 | + | 0.860428i | \(0.670196\pi\) | |||||||
\(158\) | −6.47422 | −0.515061 | ||||||||
\(159\) | −8.63420 | −0.684737 | ||||||||
\(160\) | 8.94299 | 0.707006 | ||||||||
\(161\) | 16.8445 | 1.32753 | ||||||||
\(162\) | 2.69607 | 0.211823 | ||||||||
\(163\) | −19.4359 | −1.52234 | −0.761168 | − | 0.648554i | \(-0.775374\pi\) | ||||
−0.761168 | + | 0.648554i | \(0.775374\pi\) | |||||||
\(164\) | 7.85756 | 0.613573 | ||||||||
\(165\) | −3.66525 | −0.285340 | ||||||||
\(166\) | −4.76522 | −0.369853 | ||||||||
\(167\) | −11.6238 | −0.899476 | −0.449738 | − | 0.893160i | \(-0.648483\pi\) | ||||
−0.449738 | + | 0.893160i | \(0.648483\pi\) | |||||||
\(168\) | 13.6615 | 1.05401 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 4.10338 | 0.314715 | ||||||||
\(171\) | −2.50859 | −0.191837 | ||||||||
\(172\) | 3.54191 | 0.270068 | ||||||||
\(173\) | 5.18733 | 0.394385 | 0.197193 | − | 0.980365i | \(-0.436818\pi\) | ||||
0.197193 | + | 0.980365i | \(0.436818\pi\) | |||||||
\(174\) | −7.65855 | −0.580593 | ||||||||
\(175\) | −5.59326 | −0.422811 | ||||||||
\(176\) | 1.40235 | 0.105706 | ||||||||
\(177\) | 16.5591 | 1.24466 | ||||||||
\(178\) | 10.6737 | 0.800029 | ||||||||
\(179\) | 20.0692 | 1.50005 | 0.750023 | − | 0.661412i | \(-0.230042\pi\) | ||||
0.750023 | + | 0.661412i | \(0.230042\pi\) | |||||||
\(180\) | 10.2029 | 0.760477 | ||||||||
\(181\) | 17.1393 | 1.27395 | 0.636976 | − | 0.770883i | \(-0.280185\pi\) | ||||
0.636976 | + | 0.770883i | \(0.280185\pi\) | |||||||
\(182\) | −1.42941 | −0.105955 | ||||||||
\(183\) | 6.60421 | 0.488197 | ||||||||
\(184\) | 18.1449 | 1.33766 | ||||||||
\(185\) | 4.06596 | 0.298935 | ||||||||
\(186\) | 1.75929 | 0.128997 | ||||||||
\(187\) | 3.51856 | 0.257303 | ||||||||
\(188\) | 3.12211 | 0.227703 | ||||||||
\(189\) | 6.83711 | 0.497326 | ||||||||
\(190\) | −0.615493 | −0.0446526 | ||||||||
\(191\) | 0.321161 | 0.0232384 | 0.0116192 | − | 0.999932i | \(-0.496301\pi\) | ||||
0.0116192 | + | 0.999932i | \(0.496301\pi\) | |||||||
\(192\) | 1.53779 | 0.110981 | ||||||||
\(193\) | −4.54684 | −0.327289 | −0.163644 | − | 0.986519i | \(-0.552325\pi\) | ||||
−0.163644 | + | 0.986519i | \(0.552325\pi\) | |||||||
\(194\) | 10.4920 | 0.753278 | ||||||||
\(195\) | −4.17471 | −0.298957 | ||||||||
\(196\) | 3.55224 | 0.253732 | ||||||||
\(197\) | 9.75213 | 0.694811 | 0.347405 | − | 0.937715i | \(-0.387063\pi\) | ||||
0.347405 | + | 0.937715i | \(0.387063\pi\) | |||||||
\(198\) | −2.40670 | −0.171037 | ||||||||
\(199\) | −7.30281 | −0.517683 | −0.258841 | − | 0.965920i | \(-0.583341\pi\) | ||||
−0.258841 | + | 0.965920i | \(0.583341\pi\) | |||||||
\(200\) | −6.02507 | −0.426037 | ||||||||
\(201\) | −17.6698 | −1.24633 | ||||||||
\(202\) | −0.536327 | −0.0377358 | ||||||||
\(203\) | 9.47289 | 0.664867 | ||||||||
\(204\) | −16.8357 | −1.17873 | ||||||||
\(205\) | 7.80856 | 0.545374 | ||||||||
\(206\) | 0.238783 | 0.0166368 | ||||||||
\(207\) | 32.3033 | 2.24523 | ||||||||
\(208\) | 1.59727 | 0.110751 | ||||||||
\(209\) | −0.527772 | −0.0365067 | ||||||||
\(210\) | 5.96736 | 0.411787 | ||||||||
\(211\) | −14.7678 | −1.01666 | −0.508330 | − | 0.861162i | \(-0.669737\pi\) | ||||
−0.508330 | + | 0.861162i | \(0.669737\pi\) | |||||||
\(212\) | 5.05658 | 0.347287 | ||||||||
\(213\) | −1.52685 | −0.104618 | ||||||||
\(214\) | 11.7113 | 0.800567 | ||||||||
\(215\) | 3.51983 | 0.240050 | ||||||||
\(216\) | 7.36495 | 0.501121 | ||||||||
\(217\) | −2.17607 | −0.147721 | ||||||||
\(218\) | 6.77615 | 0.458939 | ||||||||
\(219\) | −16.5506 | −1.11839 | ||||||||
\(220\) | 2.14654 | 0.144720 | ||||||||
\(221\) | 4.00763 | 0.269582 | ||||||||
\(222\) | 4.58910 | 0.308000 | ||||||||
\(223\) | 24.6628 | 1.65155 | 0.825773 | − | 0.564003i | \(-0.190739\pi\) | ||||
0.825773 | + | 0.564003i | \(0.190739\pi\) | |||||||
\(224\) | −12.4849 | −0.834180 | ||||||||
\(225\) | −10.7264 | −0.715093 | ||||||||
\(226\) | −10.2413 | −0.681244 | ||||||||
\(227\) | 1.39159 | 0.0923628 | 0.0461814 | − | 0.998933i | \(-0.485295\pi\) | ||||
0.0461814 | + | 0.998933i | \(0.485295\pi\) | |||||||
\(228\) | 2.52529 | 0.167242 | ||||||||
\(229\) | 24.9011 | 1.64551 | 0.822756 | − | 0.568394i | \(-0.192435\pi\) | ||||
0.822756 | + | 0.568394i | \(0.192435\pi\) | |||||||
\(230\) | 7.92574 | 0.522608 | ||||||||
\(231\) | 5.11688 | 0.336666 | ||||||||
\(232\) | 10.2042 | 0.669940 | ||||||||
\(233\) | −22.4331 | −1.46964 | −0.734820 | − | 0.678263i | \(-0.762733\pi\) | ||||
−0.734820 | + | 0.678263i | \(0.762733\pi\) | |||||||
\(234\) | −2.74122 | −0.179199 | ||||||||
\(235\) | 3.10264 | 0.202394 | ||||||||
\(236\) | −9.69776 | −0.631270 | ||||||||
\(237\) | 26.3973 | 1.71469 | ||||||||
\(238\) | −5.72853 | −0.371325 | ||||||||
\(239\) | 9.04754 | 0.585237 | 0.292618 | − | 0.956229i | \(-0.405473\pi\) | ||||
0.292618 | + | 0.956229i | \(0.405473\pi\) | |||||||
\(240\) | −6.66814 | −0.430427 | ||||||||
\(241\) | 4.46843 | 0.287837 | 0.143918 | − | 0.989590i | \(-0.454030\pi\) | ||||
0.143918 | + | 0.989590i | \(0.454030\pi\) | |||||||
\(242\) | 6.71929 | 0.431932 | ||||||||
\(243\) | −20.4185 | −1.30985 | ||||||||
\(244\) | −3.86772 | −0.247606 | ||||||||
\(245\) | 3.53009 | 0.225529 | ||||||||
\(246\) | 8.81325 | 0.561912 | ||||||||
\(247\) | −0.601130 | −0.0382490 | ||||||||
\(248\) | −2.34407 | −0.148848 | ||||||||
\(249\) | 19.4292 | 1.23127 | ||||||||
\(250\) | −7.75123 | −0.490231 | ||||||||
\(251\) | −16.7302 | −1.05600 | −0.528001 | − | 0.849244i | \(-0.677058\pi\) | ||||
−0.528001 | + | 0.849244i | \(0.677058\pi\) | |||||||
\(252\) | −14.2437 | −0.897270 | ||||||||
\(253\) | 6.79615 | 0.427270 | ||||||||
\(254\) | 6.38188 | 0.400435 | ||||||||
\(255\) | −16.7307 | −1.04772 | ||||||||
\(256\) | −8.43804 | −0.527377 | ||||||||
\(257\) | 13.0642 | 0.814921 | 0.407461 | − | 0.913223i | \(-0.366414\pi\) | ||||
0.407461 | + | 0.913223i | \(0.366414\pi\) | |||||||
\(258\) | 3.97270 | 0.247330 | ||||||||
\(259\) | −5.67628 | −0.352707 | ||||||||
\(260\) | 2.44490 | 0.151626 | ||||||||
\(261\) | 18.1665 | 1.12448 | ||||||||
\(262\) | −8.87746 | −0.548451 | ||||||||
\(263\) | 18.6866 | 1.15227 | 0.576134 | − | 0.817355i | \(-0.304561\pi\) | ||||
0.576134 | + | 0.817355i | \(0.304561\pi\) | |||||||
\(264\) | 5.51191 | 0.339235 | ||||||||
\(265\) | 5.02505 | 0.308686 | ||||||||
\(266\) | 0.859259 | 0.0526845 | ||||||||
\(267\) | −43.5199 | −2.66337 | ||||||||
\(268\) | 10.3482 | 0.632118 | ||||||||
\(269\) | −3.71975 | −0.226797 | −0.113398 | − | 0.993550i | \(-0.536174\pi\) | ||||
−0.113398 | + | 0.993550i | \(0.536174\pi\) | |||||||
\(270\) | 3.21702 | 0.195782 | ||||||||
\(271\) | −25.4488 | −1.54591 | −0.772953 | − | 0.634464i | \(-0.781221\pi\) | ||||
−0.772953 | + | 0.634464i | \(0.781221\pi\) | |||||||
\(272\) | 6.40127 | 0.388134 | ||||||||
\(273\) | 5.82810 | 0.352733 | ||||||||
\(274\) | 3.38726 | 0.204632 | ||||||||
\(275\) | −2.25668 | −0.136083 | ||||||||
\(276\) | −32.5183 | −1.95737 | ||||||||
\(277\) | 16.2270 | 0.974986 | 0.487493 | − | 0.873127i | \(-0.337911\pi\) | ||||
0.487493 | + | 0.873127i | \(0.337911\pi\) | |||||||
\(278\) | −14.6036 | −0.875864 | ||||||||
\(279\) | −4.17313 | −0.249839 | ||||||||
\(280\) | −7.95088 | −0.475156 | ||||||||
\(281\) | −10.9457 | −0.652966 | −0.326483 | − | 0.945203i | \(-0.605864\pi\) | ||||
−0.326483 | + | 0.945203i | \(0.605864\pi\) | |||||||
\(282\) | 3.50184 | 0.208531 | ||||||||
\(283\) | −27.2032 | −1.61706 | −0.808532 | − | 0.588452i | \(-0.799738\pi\) | ||||
−0.808532 | + | 0.588452i | \(0.799738\pi\) | |||||||
\(284\) | 0.894190 | 0.0530604 | ||||||||
\(285\) | 2.50954 | 0.148653 | ||||||||
\(286\) | −0.576714 | −0.0341018 | ||||||||
\(287\) | −10.9011 | −0.643474 | ||||||||
\(288\) | −23.9427 | −1.41084 | ||||||||
\(289\) | −0.938913 | −0.0552302 | ||||||||
\(290\) | 4.45722 | 0.261737 | ||||||||
\(291\) | −42.7787 | −2.50773 | ||||||||
\(292\) | 9.69279 | 0.567228 | ||||||||
\(293\) | 32.5419 | 1.90112 | 0.950559 | − | 0.310544i | \(-0.100511\pi\) | ||||
0.950559 | + | 0.310544i | \(0.100511\pi\) | |||||||
\(294\) | 3.98429 | 0.232369 | ||||||||
\(295\) | −9.63728 | −0.561104 | ||||||||
\(296\) | −6.11450 | −0.355398 | ||||||||
\(297\) | 2.75853 | 0.160066 | ||||||||
\(298\) | −3.04066 | −0.176141 | ||||||||
\(299\) | 7.74079 | 0.447661 | ||||||||
\(300\) | 10.7978 | 0.623411 | ||||||||
\(301\) | −4.91385 | −0.283230 | ||||||||
\(302\) | 2.85019 | 0.164010 | ||||||||
\(303\) | 2.18676 | 0.125626 | ||||||||
\(304\) | −0.960168 | −0.0550694 | ||||||||
\(305\) | −3.84360 | −0.220084 | ||||||||
\(306\) | −10.9858 | −0.628017 | ||||||||
\(307\) | 27.5404 | 1.57181 | 0.785906 | − | 0.618346i | \(-0.212197\pi\) | ||||
0.785906 | + | 0.618346i | \(0.212197\pi\) | |||||||
\(308\) | −2.99667 | −0.170751 | ||||||||
\(309\) | −0.973588 | −0.0553855 | ||||||||
\(310\) | −1.02389 | −0.0581532 | ||||||||
\(311\) | −27.8161 | −1.57731 | −0.788653 | − | 0.614838i | \(-0.789221\pi\) | ||||
−0.788653 | + | 0.614838i | \(0.789221\pi\) | |||||||
\(312\) | 6.27805 | 0.355424 | ||||||||
\(313\) | 13.7900 | 0.779458 | 0.389729 | − | 0.920930i | \(-0.372569\pi\) | ||||
0.389729 | + | 0.920930i | \(0.372569\pi\) | |||||||
\(314\) | 8.38818 | 0.473372 | ||||||||
\(315\) | −14.1549 | −0.797538 | ||||||||
\(316\) | −15.4594 | −0.869661 | ||||||||
\(317\) | 5.05640 | 0.283995 | 0.141998 | − | 0.989867i | \(-0.454647\pi\) | ||||
0.141998 | + | 0.989867i | \(0.454647\pi\) | |||||||
\(318\) | 5.67159 | 0.318047 | ||||||||
\(319\) | 3.82197 | 0.213989 | ||||||||
\(320\) | −0.894986 | −0.0500312 | ||||||||
\(321\) | −47.7503 | −2.66516 | ||||||||
\(322\) | −11.0647 | −0.616613 | ||||||||
\(323\) | −2.40911 | −0.134046 | ||||||||
\(324\) | 6.43780 | 0.357655 | ||||||||
\(325\) | −2.57035 | −0.142577 | ||||||||
\(326\) | 12.7670 | 0.707096 | ||||||||
\(327\) | −27.6283 | −1.52785 | ||||||||
\(328\) | −11.7427 | −0.648384 | ||||||||
\(329\) | −4.33144 | −0.238800 | ||||||||
\(330\) | 2.40761 | 0.132535 | ||||||||
\(331\) | 31.5996 | 1.73687 | 0.868436 | − | 0.495801i | \(-0.165125\pi\) | ||||
0.868436 | + | 0.495801i | \(0.165125\pi\) | |||||||
\(332\) | −11.3786 | −0.624482 | ||||||||
\(333\) | −10.8856 | −0.596527 | ||||||||
\(334\) | 7.63538 | 0.417789 | ||||||||
\(335\) | 10.2837 | 0.561857 | ||||||||
\(336\) | 9.30906 | 0.507851 | ||||||||
\(337\) | 17.6494 | 0.961425 | 0.480713 | − | 0.876878i | \(-0.340378\pi\) | ||||
0.480713 | + | 0.876878i | \(0.340378\pi\) | |||||||
\(338\) | −0.656875 | −0.0357293 | ||||||||
\(339\) | 41.7569 | 2.26792 | ||||||||
\(340\) | 9.79825 | 0.531384 | ||||||||
\(341\) | −0.877966 | −0.0475445 | ||||||||
\(342\) | 1.64783 | 0.0891045 | ||||||||
\(343\) | −20.1607 | −1.08857 | ||||||||
\(344\) | −5.29321 | −0.285391 | ||||||||
\(345\) | −32.3155 | −1.73981 | ||||||||
\(346\) | −3.40743 | −0.183184 | ||||||||
\(347\) | −6.21085 | −0.333416 | −0.166708 | − | 0.986006i | \(-0.553314\pi\) | ||||
−0.166708 | + | 0.986006i | \(0.553314\pi\) | |||||||
\(348\) | −18.2874 | −0.980309 | ||||||||
\(349\) | −28.3495 | −1.51752 | −0.758758 | − | 0.651373i | \(-0.774193\pi\) | ||||
−0.758758 | + | 0.651373i | \(0.774193\pi\) | |||||||
\(350\) | 3.67407 | 0.196387 | ||||||||
\(351\) | 3.14195 | 0.167705 | ||||||||
\(352\) | −5.03719 | −0.268483 | ||||||||
\(353\) | 29.8862 | 1.59068 | 0.795341 | − | 0.606162i | \(-0.207292\pi\) | ||||
0.795341 | + | 0.606162i | \(0.207292\pi\) | |||||||
\(354\) | −10.8773 | −0.578120 | ||||||||
\(355\) | 0.888614 | 0.0471627 | ||||||||
\(356\) | 25.4872 | 1.35082 | ||||||||
\(357\) | 23.3569 | 1.23618 | ||||||||
\(358\) | −13.1830 | −0.696742 | ||||||||
\(359\) | 12.6922 | 0.669869 | 0.334934 | − | 0.942241i | \(-0.391286\pi\) | ||||
0.334934 | + | 0.942241i | \(0.391286\pi\) | |||||||
\(360\) | −15.2477 | −0.803624 | ||||||||
\(361\) | −18.6386 | −0.980981 | ||||||||
\(362\) | −11.2584 | −0.591727 | ||||||||
\(363\) | −27.3965 | −1.43794 | ||||||||
\(364\) | −3.41320 | −0.178900 | ||||||||
\(365\) | 9.63235 | 0.504180 | ||||||||
\(366\) | −4.33814 | −0.226758 | ||||||||
\(367\) | 6.55762 | 0.342305 | 0.171152 | − | 0.985245i | \(-0.445251\pi\) | ||||
0.171152 | + | 0.985245i | \(0.445251\pi\) | |||||||
\(368\) | 12.3641 | 0.644525 | ||||||||
\(369\) | −20.9055 | −1.08830 | ||||||||
\(370\) | −2.67082 | −0.138850 | ||||||||
\(371\) | −7.01521 | −0.364212 | ||||||||
\(372\) | 4.20091 | 0.217807 | ||||||||
\(373\) | 2.47432 | 0.128115 | 0.0640577 | − | 0.997946i | \(-0.479596\pi\) | ||||
0.0640577 | + | 0.997946i | \(0.479596\pi\) | |||||||
\(374\) | −2.31125 | −0.119512 | ||||||||
\(375\) | 31.6040 | 1.63202 | ||||||||
\(376\) | −4.66584 | −0.240622 | ||||||||
\(377\) | 4.35321 | 0.224202 | ||||||||
\(378\) | −4.49112 | −0.230999 | ||||||||
\(379\) | 19.7360 | 1.01377 | 0.506885 | − | 0.862014i | \(-0.330797\pi\) | ||||
0.506885 | + | 0.862014i | \(0.330797\pi\) | |||||||
\(380\) | −1.46970 | −0.0753941 | ||||||||
\(381\) | −26.0208 | −1.33309 | ||||||||
\(382\) | −0.210962 | −0.0107938 | ||||||||
\(383\) | −19.3671 | −0.989614 | −0.494807 | − | 0.869003i | \(-0.664761\pi\) | ||||
−0.494807 | + | 0.869003i | \(0.664761\pi\) | |||||||
\(384\) | 29.7222 | 1.51675 | ||||||||
\(385\) | −2.97799 | −0.151772 | ||||||||
\(386\) | 2.98671 | 0.152019 | ||||||||
\(387\) | −9.42347 | −0.479022 | ||||||||
\(388\) | 25.0532 | 1.27188 | ||||||||
\(389\) | −31.2291 | −1.58338 | −0.791688 | − | 0.610925i | \(-0.790798\pi\) | ||||
−0.791688 | + | 0.610925i | \(0.790798\pi\) | |||||||
\(390\) | 2.74226 | 0.138860 | ||||||||
\(391\) | 31.0222 | 1.56886 | ||||||||
\(392\) | −5.30865 | −0.268127 | ||||||||
\(393\) | 36.1960 | 1.82585 | ||||||||
\(394\) | −6.40593 | −0.322726 | ||||||||
\(395\) | −15.3630 | −0.772998 | ||||||||
\(396\) | −5.74683 | −0.288789 | ||||||||
\(397\) | 8.14879 | 0.408976 | 0.204488 | − | 0.978869i | \(-0.434447\pi\) | ||||
0.204488 | + | 0.978869i | \(0.434447\pi\) | |||||||
\(398\) | 4.79704 | 0.240454 | ||||||||
\(399\) | −3.50345 | −0.175392 | ||||||||
\(400\) | −4.10554 | −0.205277 | ||||||||
\(401\) | 6.37211 | 0.318208 | 0.159104 | − | 0.987262i | \(-0.449139\pi\) | ||||
0.159104 | + | 0.987262i | \(0.449139\pi\) | |||||||
\(402\) | 11.6068 | 0.578896 | ||||||||
\(403\) | −1.00000 | −0.0498135 | ||||||||
\(404\) | −1.28067 | −0.0637155 | ||||||||
\(405\) | 6.39765 | 0.317902 | ||||||||
\(406\) | −6.22250 | −0.308818 | ||||||||
\(407\) | −2.29017 | −0.113520 | ||||||||
\(408\) | 25.1601 | 1.24561 | ||||||||
\(409\) | −9.57256 | −0.473332 | −0.236666 | − | 0.971591i | \(-0.576055\pi\) | ||||
−0.236666 | + | 0.971591i | \(0.576055\pi\) | |||||||
\(410\) | −5.12925 | −0.253316 | ||||||||
\(411\) | −13.8108 | −0.681238 | ||||||||
\(412\) | 0.570177 | 0.0280906 | ||||||||
\(413\) | 13.4541 | 0.662034 | ||||||||
\(414\) | −21.2192 | −1.04287 | ||||||||
\(415\) | −11.3077 | −0.555071 | ||||||||
\(416\) | −5.73734 | −0.281296 | ||||||||
\(417\) | 59.5430 | 2.91583 | ||||||||
\(418\) | 0.346680 | 0.0169567 | ||||||||
\(419\) | −22.4308 | −1.09582 | −0.547908 | − | 0.836538i | \(-0.684576\pi\) | ||||
−0.547908 | + | 0.836538i | \(0.684576\pi\) | |||||||
\(420\) | 14.2491 | 0.695286 | ||||||||
\(421\) | 27.5293 | 1.34169 | 0.670847 | − | 0.741596i | \(-0.265931\pi\) | ||||
0.670847 | + | 0.741596i | \(0.265931\pi\) | |||||||
\(422\) | 9.70062 | 0.472219 | ||||||||
\(423\) | −8.30655 | −0.403878 | ||||||||
\(424\) | −7.55680 | −0.366991 | ||||||||
\(425\) | −10.3010 | −0.499672 | ||||||||
\(426\) | 1.00295 | 0.0485929 | ||||||||
\(427\) | 5.36586 | 0.259672 | ||||||||
\(428\) | 27.9647 | 1.35173 | ||||||||
\(429\) | 2.35143 | 0.113528 | ||||||||
\(430\) | −2.31209 | −0.111499 | ||||||||
\(431\) | 14.2990 | 0.688759 | 0.344379 | − | 0.938831i | \(-0.388089\pi\) | ||||
0.344379 | + | 0.938831i | \(0.388089\pi\) | |||||||
\(432\) | 5.01855 | 0.241455 | ||||||||
\(433\) | −6.73207 | −0.323523 | −0.161761 | − | 0.986830i | \(-0.551717\pi\) | ||||
−0.161761 | + | 0.986830i | \(0.551717\pi\) | |||||||
\(434\) | 1.42941 | 0.0686137 | ||||||||
\(435\) | −18.1734 | −0.871347 | ||||||||
\(436\) | 16.1804 | 0.774901 | ||||||||
\(437\) | −4.65322 | −0.222594 | ||||||||
\(438\) | 10.8717 | 0.519469 | ||||||||
\(439\) | −20.3619 | −0.971819 | −0.485910 | − | 0.874009i | \(-0.661512\pi\) | ||||
−0.485910 | + | 0.874009i | \(0.661512\pi\) | |||||||
\(440\) | −3.20789 | −0.152930 | ||||||||
\(441\) | −9.45096 | −0.450045 | ||||||||
\(442\) | −2.63251 | −0.125216 | ||||||||
\(443\) | 17.6424 | 0.838216 | 0.419108 | − | 0.907936i | \(-0.362343\pi\) | ||||
0.419108 | + | 0.907936i | \(0.362343\pi\) | |||||||
\(444\) | 10.9581 | 0.520046 | ||||||||
\(445\) | 25.3283 | 1.20067 | ||||||||
\(446\) | −16.2004 | −0.767111 | ||||||||
\(447\) | 12.3977 | 0.586389 | ||||||||
\(448\) | 1.24944 | 0.0590307 | ||||||||
\(449\) | 19.1462 | 0.903565 | 0.451782 | − | 0.892128i | \(-0.350788\pi\) | ||||
0.451782 | + | 0.892128i | \(0.350788\pi\) | |||||||
\(450\) | 7.04590 | 0.332147 | ||||||||
\(451\) | −4.39822 | −0.207104 | ||||||||
\(452\) | −24.4547 | −1.15025 | ||||||||
\(453\) | −11.6210 | −0.546004 | ||||||||
\(454\) | −0.914097 | −0.0429007 | ||||||||
\(455\) | −3.39192 | −0.159015 | ||||||||
\(456\) | −3.77392 | −0.176730 | ||||||||
\(457\) | −26.0477 | −1.21846 | −0.609230 | − | 0.792994i | \(-0.708521\pi\) | ||||
−0.609230 | + | 0.792994i | \(0.708521\pi\) | |||||||
\(458\) | −16.3569 | −0.764309 | ||||||||
\(459\) | 12.5918 | 0.587734 | ||||||||
\(460\) | 18.9254 | 0.882403 | ||||||||
\(461\) | 4.57637 | 0.213143 | 0.106571 | − | 0.994305i | \(-0.466013\pi\) | ||||
0.106571 | + | 0.994305i | \(0.466013\pi\) | |||||||
\(462\) | −3.36115 | −0.156375 | ||||||||
\(463\) | 10.6466 | 0.494790 | 0.247395 | − | 0.968915i | \(-0.420426\pi\) | ||||
0.247395 | + | 0.968915i | \(0.420426\pi\) | |||||||
\(464\) | 6.95326 | 0.322797 | ||||||||
\(465\) | 4.17471 | 0.193598 | ||||||||
\(466\) | 14.7357 | 0.682619 | ||||||||
\(467\) | −15.0034 | −0.694275 | −0.347138 | − | 0.937814i | \(-0.612846\pi\) | ||||
−0.347138 | + | 0.937814i | \(0.612846\pi\) | |||||||
\(468\) | −6.54561 | −0.302571 | ||||||||
\(469\) | −14.3565 | −0.662923 | ||||||||
\(470\) | −2.03805 | −0.0940080 | ||||||||
\(471\) | −34.2010 | −1.57590 | ||||||||
\(472\) | 14.4928 | 0.667086 | ||||||||
\(473\) | −1.98256 | −0.0911583 | ||||||||
\(474\) | −17.3397 | −0.796439 | ||||||||
\(475\) | 1.54511 | 0.0708947 | ||||||||
\(476\) | −13.6788 | −0.626968 | ||||||||
\(477\) | −13.4533 | −0.615985 | ||||||||
\(478\) | −5.94310 | −0.271831 | ||||||||
\(479\) | −37.1477 | −1.69732 | −0.848661 | − | 0.528937i | \(-0.822591\pi\) | ||||
−0.848661 | + | 0.528937i | \(0.822591\pi\) | |||||||
\(480\) | 23.9517 | 1.09324 | ||||||||
\(481\) | −2.60850 | −0.118937 | ||||||||
\(482\) | −2.93520 | −0.133695 | ||||||||
\(483\) | 45.1141 | 2.05276 | ||||||||
\(484\) | 16.0446 | 0.729301 | ||||||||
\(485\) | 24.8969 | 1.13051 | ||||||||
\(486\) | 13.4124 | 0.608399 | ||||||||
\(487\) | −23.1824 | −1.05049 | −0.525247 | − | 0.850950i | \(-0.676027\pi\) | ||||
−0.525247 | + | 0.850950i | \(0.676027\pi\) | |||||||
\(488\) | 5.78012 | 0.261654 | ||||||||
\(489\) | −52.0546 | −2.35399 | ||||||||
\(490\) | −2.31883 | −0.104754 | ||||||||
\(491\) | −26.1739 | −1.18121 | −0.590606 | − | 0.806960i | \(-0.701111\pi\) | ||||
−0.590606 | + | 0.806960i | \(0.701111\pi\) | |||||||
\(492\) | 21.0447 | 0.948767 | ||||||||
\(493\) | 17.4460 | 0.785730 | ||||||||
\(494\) | 0.394867 | 0.0177659 | ||||||||
\(495\) | −5.71099 | −0.256690 | ||||||||
\(496\) | −1.59727 | −0.0717196 | ||||||||
\(497\) | −1.24055 | −0.0556462 | ||||||||
\(498\) | −12.7625 | −0.571903 | ||||||||
\(499\) | −38.5295 | −1.72482 | −0.862408 | − | 0.506215i | \(-0.831044\pi\) | ||||
−0.862408 | + | 0.506215i | \(0.831044\pi\) | |||||||
\(500\) | −18.5087 | −0.827736 | ||||||||
\(501\) | −31.1317 | −1.39086 | ||||||||
\(502\) | 10.9897 | 0.490492 | ||||||||
\(503\) | −23.8172 | −1.06195 | −0.530977 | − | 0.847386i | \(-0.678175\pi\) | ||||
−0.530977 | + | 0.847386i | \(0.678175\pi\) | |||||||
\(504\) | 21.2865 | 0.948177 | ||||||||
\(505\) | −1.27268 | −0.0566335 | ||||||||
\(506\) | −4.46422 | −0.198459 | ||||||||
\(507\) | 2.67827 | 0.118946 | ||||||||
\(508\) | 15.2389 | 0.676119 | ||||||||
\(509\) | −10.5621 | −0.468156 | −0.234078 | − | 0.972218i | \(-0.575207\pi\) | ||||
−0.234078 | + | 0.972218i | \(0.575207\pi\) | |||||||
\(510\) | 10.9900 | 0.486644 | ||||||||
\(511\) | −13.4472 | −0.594871 | ||||||||
\(512\) | −16.6523 | −0.735935 | ||||||||
\(513\) | −1.88872 | −0.0833891 | ||||||||
\(514\) | −8.58153 | −0.378515 | ||||||||
\(515\) | 0.566621 | 0.0249683 | ||||||||
\(516\) | 9.48620 | 0.417607 | ||||||||
\(517\) | −1.74758 | −0.0768584 | ||||||||
\(518\) | 3.72860 | 0.163825 | ||||||||
\(519\) | 13.8931 | 0.609838 | ||||||||
\(520\) | −3.65378 | −0.160229 | ||||||||
\(521\) | −28.8357 | −1.26331 | −0.631657 | − | 0.775248i | \(-0.717625\pi\) | ||||
−0.631657 | + | 0.775248i | \(0.717625\pi\) | |||||||
\(522\) | −11.9331 | −0.522298 | ||||||||
\(523\) | −13.2684 | −0.580188 | −0.290094 | − | 0.956998i | \(-0.593687\pi\) | ||||
−0.290094 | + | 0.956998i | \(0.593687\pi\) | |||||||
\(524\) | −21.1980 | −0.926039 | ||||||||
\(525\) | −14.9803 | −0.653792 | ||||||||
\(526\) | −12.2748 | −0.535206 | ||||||||
\(527\) | −4.00763 | −0.174575 | ||||||||
\(528\) | 3.75587 | 0.163453 | ||||||||
\(529\) | 36.9198 | 1.60521 | ||||||||
\(530\) | −3.30083 | −0.143379 | ||||||||
\(531\) | 25.8015 | 1.11969 | ||||||||
\(532\) | 2.05178 | 0.0889558 | ||||||||
\(533\) | −5.00956 | −0.216988 | ||||||||
\(534\) | 28.5871 | 1.23708 | ||||||||
\(535\) | 27.7903 | 1.20148 | ||||||||
\(536\) | −15.4649 | −0.667981 | ||||||||
\(537\) | 53.7508 | 2.31952 | ||||||||
\(538\) | 2.44341 | 0.105343 | ||||||||
\(539\) | −1.98834 | −0.0856441 | ||||||||
\(540\) | 7.68175 | 0.330570 | ||||||||
\(541\) | −7.22402 | −0.310585 | −0.155292 | − | 0.987869i | \(-0.549632\pi\) | ||||
−0.155292 | + | 0.987869i | \(0.549632\pi\) | |||||||
\(542\) | 16.7167 | 0.718043 | ||||||||
\(543\) | 45.9036 | 1.96991 | ||||||||
\(544\) | −22.9931 | −0.985823 | ||||||||
\(545\) | 16.0795 | 0.688770 | ||||||||
\(546\) | −3.82833 | −0.163838 | ||||||||
\(547\) | −10.7901 | −0.461352 | −0.230676 | − | 0.973031i | \(-0.574094\pi\) | ||||
−0.230676 | + | 0.973031i | \(0.574094\pi\) | |||||||
\(548\) | 8.08824 | 0.345513 | ||||||||
\(549\) | 10.2903 | 0.439179 | ||||||||
\(550\) | 1.48235 | 0.0632078 | ||||||||
\(551\) | −2.61685 | −0.111481 | ||||||||
\(552\) | 48.5970 | 2.06843 | ||||||||
\(553\) | 21.4475 | 0.912042 | ||||||||
\(554\) | −10.6591 | −0.452862 | ||||||||
\(555\) | 10.8897 | 0.462243 | ||||||||
\(556\) | −34.8710 | −1.47886 | ||||||||
\(557\) | −12.8194 | −0.543175 | −0.271588 | − | 0.962414i | \(-0.587549\pi\) | ||||
−0.271588 | + | 0.962414i | \(0.587549\pi\) | |||||||
\(558\) | 2.74122 | 0.116045 | ||||||||
\(559\) | −2.25813 | −0.0955088 | ||||||||
\(560\) | −5.41781 | −0.228944 | ||||||||
\(561\) | 9.42366 | 0.397867 | ||||||||
\(562\) | 7.18996 | 0.303290 | ||||||||
\(563\) | −33.1561 | −1.39736 | −0.698680 | − | 0.715434i | \(-0.746229\pi\) | ||||
−0.698680 | + | 0.715434i | \(0.746229\pi\) | |||||||
\(564\) | 8.36185 | 0.352097 | ||||||||
\(565\) | −24.3022 | −1.02240 | ||||||||
\(566\) | 17.8691 | 0.751095 | ||||||||
\(567\) | −8.93144 | −0.375085 | ||||||||
\(568\) | −1.33632 | −0.0560709 | ||||||||
\(569\) | −14.1575 | −0.593512 | −0.296756 | − | 0.954953i | \(-0.595905\pi\) | ||||
−0.296756 | + | 0.954953i | \(0.595905\pi\) | |||||||
\(570\) | −1.64846 | −0.0690462 | ||||||||
\(571\) | −5.28503 | −0.221172 | −0.110586 | − | 0.993867i | \(-0.535273\pi\) | ||||
−0.110586 | + | 0.993867i | \(0.535273\pi\) | |||||||
\(572\) | −1.37710 | −0.0575796 | ||||||||
\(573\) | 0.860155 | 0.0359335 | ||||||||
\(574\) | 7.16069 | 0.298881 | ||||||||
\(575\) | −19.8965 | −0.829742 | ||||||||
\(576\) | 2.39610 | 0.0998377 | ||||||||
\(577\) | −4.65661 | −0.193857 | −0.0969286 | − | 0.995291i | \(-0.530902\pi\) | ||||
−0.0969286 | + | 0.995291i | \(0.530902\pi\) | |||||||
\(578\) | 0.616748 | 0.0256534 | ||||||||
\(579\) | −12.1777 | −0.506086 | ||||||||
\(580\) | 10.6432 | 0.441933 | ||||||||
\(581\) | 15.7860 | 0.654916 | ||||||||
\(582\) | 28.1003 | 1.16479 | ||||||||
\(583\) | −2.83039 | −0.117223 | ||||||||
\(584\) | −14.4854 | −0.599410 | ||||||||
\(585\) | −6.50480 | −0.268940 | ||||||||
\(586\) | −21.3760 | −0.883033 | ||||||||
\(587\) | −7.30288 | −0.301422 | −0.150711 | − | 0.988578i | \(-0.548156\pi\) | ||||
−0.150711 | + | 0.988578i | \(0.548156\pi\) | |||||||
\(588\) | 9.51387 | 0.392345 | ||||||||
\(589\) | 0.601130 | 0.0247691 | ||||||||
\(590\) | 6.33049 | 0.260622 | ||||||||
\(591\) | 26.1188 | 1.07439 | ||||||||
\(592\) | −4.16648 | −0.171241 | ||||||||
\(593\) | 11.8112 | 0.485030 | 0.242515 | − | 0.970148i | \(-0.422028\pi\) | ||||
0.242515 | + | 0.970148i | \(0.422028\pi\) | |||||||
\(594\) | −1.81201 | −0.0743475 | ||||||||
\(595\) | −13.5935 | −0.557281 | ||||||||
\(596\) | −7.26063 | −0.297407 | ||||||||
\(597\) | −19.5589 | −0.800493 | ||||||||
\(598\) | −5.08473 | −0.207930 | ||||||||
\(599\) | −20.1734 | −0.824262 | −0.412131 | − | 0.911125i | \(-0.635215\pi\) | ||||
−0.412131 | + | 0.911125i | \(0.635215\pi\) | |||||||
\(600\) | −16.1368 | −0.658781 | ||||||||
\(601\) | 35.7716 | 1.45916 | 0.729578 | − | 0.683898i | \(-0.239717\pi\) | ||||
0.729578 | + | 0.683898i | \(0.239717\pi\) | |||||||
\(602\) | 3.22779 | 0.131555 | ||||||||
\(603\) | −27.5320 | −1.12119 | ||||||||
\(604\) | 6.80580 | 0.276924 | ||||||||
\(605\) | 15.9446 | 0.648239 | ||||||||
\(606\) | −1.43643 | −0.0583509 | ||||||||
\(607\) | 29.9711 | 1.21649 | 0.608245 | − | 0.793750i | \(-0.291874\pi\) | ||||
0.608245 | + | 0.793750i | \(0.291874\pi\) | |||||||
\(608\) | 3.44889 | 0.139871 | ||||||||
\(609\) | 25.3710 | 1.02808 | ||||||||
\(610\) | 2.52477 | 0.102225 | ||||||||
\(611\) | −1.99049 | −0.0805265 | ||||||||
\(612\) | −26.2324 | −1.06038 | ||||||||
\(613\) | −15.7324 | −0.635425 | −0.317713 | − | 0.948187i | \(-0.602915\pi\) | ||||
−0.317713 | + | 0.948187i | \(0.602915\pi\) | |||||||
\(614\) | −18.0906 | −0.730076 | ||||||||
\(615\) | 20.9134 | 0.843311 | ||||||||
\(616\) | 4.47838 | 0.180439 | ||||||||
\(617\) | 46.9097 | 1.88851 | 0.944257 | − | 0.329209i | \(-0.106782\pi\) | ||||
0.944257 | + | 0.329209i | \(0.106782\pi\) | |||||||
\(618\) | 0.639525 | 0.0257255 | ||||||||
\(619\) | 23.5719 | 0.947436 | 0.473718 | − | 0.880677i | \(-0.342912\pi\) | ||||
0.473718 | + | 0.880677i | \(0.342912\pi\) | |||||||
\(620\) | −2.44490 | −0.0981895 | ||||||||
\(621\) | 24.3212 | 0.975975 | ||||||||
\(622\) | 18.2717 | 0.732628 | ||||||||
\(623\) | −35.3595 | −1.41665 | ||||||||
\(624\) | 4.27792 | 0.171254 | ||||||||
\(625\) | −5.54157 | −0.221663 | ||||||||
\(626\) | −9.05832 | −0.362043 | ||||||||
\(627\) | −1.41351 | −0.0564503 | ||||||||
\(628\) | 20.0297 | 0.799271 | ||||||||
\(629\) | −10.4539 | −0.416824 | ||||||||
\(630\) | 9.29800 | 0.370441 | ||||||||
\(631\) | 35.1311 | 1.39855 | 0.699274 | − | 0.714854i | \(-0.253507\pi\) | ||||
0.699274 | + | 0.714854i | \(0.253507\pi\) | |||||||
\(632\) | 23.1033 | 0.919002 | ||||||||
\(633\) | −39.5522 | −1.57206 | ||||||||
\(634\) | −3.32142 | −0.131910 | ||||||||
\(635\) | 15.1439 | 0.600968 | ||||||||
\(636\) | 13.5429 | 0.537010 | ||||||||
\(637\) | −2.26472 | −0.0897314 | ||||||||
\(638\) | −2.51056 | −0.0993939 | ||||||||
\(639\) | −2.37905 | −0.0941136 | ||||||||
\(640\) | −17.2981 | −0.683767 | ||||||||
\(641\) | 17.3741 | 0.686235 | 0.343118 | − | 0.939292i | \(-0.388517\pi\) | ||||
0.343118 | + | 0.939292i | \(0.388517\pi\) | |||||||
\(642\) | 31.3660 | 1.23792 | ||||||||
\(643\) | 43.7159 | 1.72399 | 0.861993 | − | 0.506920i | \(-0.169216\pi\) | ||||
0.861993 | + | 0.506920i | \(0.169216\pi\) | |||||||
\(644\) | −26.4208 | −1.04113 | ||||||||
\(645\) | 9.42704 | 0.371189 | ||||||||
\(646\) | 1.58248 | 0.0622619 | ||||||||
\(647\) | 31.6896 | 1.24585 | 0.622924 | − | 0.782283i | \(-0.285945\pi\) | ||||
0.622924 | + | 0.782283i | \(0.285945\pi\) | |||||||
\(648\) | −9.62097 | −0.377947 | ||||||||
\(649\) | 5.42826 | 0.213078 | ||||||||
\(650\) | 1.68840 | 0.0662244 | ||||||||
\(651\) | −5.82810 | −0.228421 | ||||||||
\(652\) | 30.4855 | 1.19390 | ||||||||
\(653\) | 1.10032 | 0.0430587 | 0.0215293 | − | 0.999768i | \(-0.493146\pi\) | ||||
0.0215293 | + | 0.999768i | \(0.493146\pi\) | |||||||
\(654\) | 18.1484 | 0.709657 | ||||||||
\(655\) | −21.0658 | −0.823109 | ||||||||
\(656\) | −8.00162 | −0.312411 | ||||||||
\(657\) | −25.7882 | −1.00610 | ||||||||
\(658\) | 2.84521 | 0.110918 | ||||||||
\(659\) | 26.0015 | 1.01288 | 0.506438 | − | 0.862277i | \(-0.330962\pi\) | ||||
0.506438 | + | 0.862277i | \(0.330962\pi\) | |||||||
\(660\) | 5.74901 | 0.223780 | ||||||||
\(661\) | 9.05504 | 0.352200 | 0.176100 | − | 0.984372i | \(-0.443652\pi\) | ||||
0.176100 | + | 0.984372i | \(0.443652\pi\) | |||||||
\(662\) | −20.7570 | −0.806744 | ||||||||
\(663\) | 10.7335 | 0.416855 | ||||||||
\(664\) | 17.0048 | 0.659913 | ||||||||
\(665\) | 2.03898 | 0.0790683 | ||||||||
\(666\) | 7.15047 | 0.277075 | ||||||||
\(667\) | 33.6973 | 1.30476 | ||||||||
\(668\) | 18.2321 | 0.705421 | ||||||||
\(669\) | 66.0537 | 2.55378 | ||||||||
\(670\) | −6.75509 | −0.260972 | ||||||||
\(671\) | 2.16493 | 0.0835763 | ||||||||
\(672\) | −33.4378 | −1.28989 | ||||||||
\(673\) | 32.2884 | 1.24463 | 0.622313 | − | 0.782769i | \(-0.286193\pi\) | ||||
0.622313 | + | 0.782769i | \(0.286193\pi\) | |||||||
\(674\) | −11.5935 | −0.446564 | ||||||||
\(675\) | −8.07591 | −0.310842 | ||||||||
\(676\) | −1.56852 | −0.0603275 | ||||||||
\(677\) | −45.1998 | −1.73717 | −0.868585 | − | 0.495540i | \(-0.834970\pi\) | ||||
−0.868585 | + | 0.495540i | \(0.834970\pi\) | |||||||
\(678\) | −27.4291 | −1.05341 | ||||||||
\(679\) | −34.7573 | −1.33386 | ||||||||
\(680\) | −14.6430 | −0.561533 | ||||||||
\(681\) | 3.72704 | 0.142820 | ||||||||
\(682\) | 0.576714 | 0.0220835 | ||||||||
\(683\) | 13.3857 | 0.512189 | 0.256094 | − | 0.966652i | \(-0.417564\pi\) | ||||
0.256094 | + | 0.966652i | \(0.417564\pi\) | |||||||
\(684\) | 3.93477 | 0.150450 | ||||||||
\(685\) | 8.03780 | 0.307109 | ||||||||
\(686\) | 13.2430 | 0.505622 | ||||||||
\(687\) | 66.6919 | 2.54446 | ||||||||
\(688\) | −3.60685 | −0.137510 | ||||||||
\(689\) | −3.22380 | −0.122817 | ||||||||
\(690\) | 21.2273 | 0.808108 | ||||||||
\(691\) | −0.244786 | −0.00931211 | −0.00465605 | − | 0.999989i | \(-0.501482\pi\) | ||||
−0.00465605 | + | 0.999989i | \(0.501482\pi\) | |||||||
\(692\) | −8.13641 | −0.309300 | ||||||||
\(693\) | 7.97283 | 0.302863 | ||||||||
\(694\) | 4.07975 | 0.154865 | ||||||||
\(695\) | −34.6536 | −1.31449 | ||||||||
\(696\) | 27.3297 | 1.03593 | ||||||||
\(697\) | −20.0764 | −0.760449 | ||||||||
\(698\) | 18.6221 | 0.704857 | ||||||||
\(699\) | −60.0818 | −2.27250 | ||||||||
\(700\) | 8.77311 | 0.331592 | ||||||||
\(701\) | 21.6400 | 0.817330 | 0.408665 | − | 0.912684i | \(-0.365994\pi\) | ||||
0.408665 | + | 0.912684i | \(0.365994\pi\) | |||||||
\(702\) | −2.06387 | −0.0778957 | ||||||||
\(703\) | 1.56805 | 0.0591400 | ||||||||
\(704\) | 0.504106 | 0.0189992 | ||||||||
\(705\) | 8.30970 | 0.312962 | ||||||||
\(706\) | −19.6315 | −0.738841 | ||||||||
\(707\) | 1.77672 | 0.0668206 | ||||||||
\(708\) | −25.9732 | −0.976133 | ||||||||
\(709\) | 3.51683 | 0.132077 | 0.0660387 | − | 0.997817i | \(-0.478964\pi\) | ||||
0.0660387 | + | 0.997817i | \(0.478964\pi\) | |||||||
\(710\) | −0.583708 | −0.0219062 | ||||||||
\(711\) | 41.1307 | 1.54252 | ||||||||
\(712\) | −38.0893 | −1.42746 | ||||||||
\(713\) | −7.74079 | −0.289895 | ||||||||
\(714\) | −15.3425 | −0.574180 | ||||||||
\(715\) | −1.36852 | −0.0511796 | ||||||||
\(716\) | −31.4789 | −1.17642 | ||||||||
\(717\) | 24.2318 | 0.904951 | ||||||||
\(718\) | −8.33719 | −0.311141 | ||||||||
\(719\) | 3.98915 | 0.148770 | 0.0743852 | − | 0.997230i | \(-0.476301\pi\) | ||||
0.0743852 | + | 0.997230i | \(0.476301\pi\) | |||||||
\(720\) | −10.3899 | −0.387210 | ||||||||
\(721\) | −0.791031 | −0.0294596 | ||||||||
\(722\) | 12.2433 | 0.455647 | ||||||||
\(723\) | 11.9677 | 0.445082 | ||||||||
\(724\) | −26.8832 | −0.999107 | ||||||||
\(725\) | −11.1893 | −0.415559 | ||||||||
\(726\) | 17.9961 | 0.667897 | ||||||||
\(727\) | −2.47671 | −0.0918562 | −0.0459281 | − | 0.998945i | \(-0.514625\pi\) | ||||
−0.0459281 | + | 0.998945i | \(0.514625\pi\) | |||||||
\(728\) | 5.10086 | 0.189050 | ||||||||
\(729\) | −42.3731 | −1.56937 | ||||||||
\(730\) | −6.32725 | −0.234182 | ||||||||
\(731\) | −9.04975 | −0.334717 | ||||||||
\(732\) | −10.3588 | −0.382872 | ||||||||
\(733\) | 25.9259 | 0.957593 | 0.478797 | − | 0.877926i | \(-0.341073\pi\) | ||||
0.478797 | + | 0.877926i | \(0.341073\pi\) | |||||||
\(734\) | −4.30753 | −0.158994 | ||||||||
\(735\) | 9.45454 | 0.348736 | ||||||||
\(736\) | −44.4115 | −1.63703 | ||||||||
\(737\) | −5.79234 | −0.213364 | ||||||||
\(738\) | 13.7323 | 0.505493 | ||||||||
\(739\) | −43.5409 | −1.60168 | −0.800840 | − | 0.598879i | \(-0.795613\pi\) | ||||
−0.800840 | + | 0.598879i | \(0.795613\pi\) | |||||||
\(740\) | −6.37751 | −0.234442 | ||||||||
\(741\) | −1.60999 | −0.0591444 | ||||||||
\(742\) | 4.60812 | 0.169169 | ||||||||
\(743\) | 16.0866 | 0.590161 | 0.295081 | − | 0.955472i | \(-0.404653\pi\) | ||||
0.295081 | + | 0.955472i | \(0.404653\pi\) | |||||||
\(744\) | −6.27805 | −0.230164 | ||||||||
\(745\) | −7.21535 | −0.264350 | ||||||||
\(746\) | −1.62532 | −0.0595072 | ||||||||
\(747\) | 30.2735 | 1.10765 | ||||||||
\(748\) | −5.51892 | −0.201792 | ||||||||
\(749\) | −38.7967 | −1.41760 | ||||||||
\(750\) | −20.7599 | −0.758044 | ||||||||
\(751\) | 37.4826 | 1.36776 | 0.683879 | − | 0.729595i | \(-0.260292\pi\) | ||||
0.683879 | + | 0.729595i | \(0.260292\pi\) | |||||||
\(752\) | −3.17935 | −0.115939 | ||||||||
\(753\) | −44.8080 | −1.63290 | ||||||||
\(754\) | −2.85951 | −0.104137 | ||||||||
\(755\) | 6.76336 | 0.246144 | ||||||||
\(756\) | −10.7241 | −0.390032 | ||||||||
\(757\) | 10.6822 | 0.388253 | 0.194126 | − | 0.980977i | \(-0.437813\pi\) | ||||
0.194126 | + | 0.980977i | \(0.437813\pi\) | |||||||
\(758\) | −12.9641 | −0.470877 | ||||||||
\(759\) | 18.2019 | 0.660687 | ||||||||
\(760\) | 2.19640 | 0.0796717 | ||||||||
\(761\) | 16.4984 | 0.598068 | 0.299034 | − | 0.954242i | \(-0.403336\pi\) | ||||
0.299034 | + | 0.954242i | \(0.403336\pi\) | |||||||
\(762\) | 17.0924 | 0.619193 | ||||||||
\(763\) | −22.4478 | −0.812664 | ||||||||
\(764\) | −0.503745 | −0.0182249 | ||||||||
\(765\) | −26.0688 | −0.942520 | ||||||||
\(766\) | 12.7218 | 0.459657 | ||||||||
\(767\) | 6.18276 | 0.223247 | ||||||||
\(768\) | −22.5993 | −0.815483 | ||||||||
\(769\) | −38.3588 | −1.38325 | −0.691627 | − | 0.722255i | \(-0.743106\pi\) | ||||
−0.691627 | + | 0.722255i | \(0.743106\pi\) | |||||||
\(770\) | 1.95616 | 0.0704953 | ||||||||
\(771\) | 34.9894 | 1.26011 | ||||||||
\(772\) | 7.13179 | 0.256679 | ||||||||
\(773\) | −10.2453 | −0.368498 | −0.184249 | − | 0.982880i | \(-0.558985\pi\) | ||||
−0.184249 | + | 0.982880i | \(0.558985\pi\) | |||||||
\(774\) | 6.19004 | 0.222496 | ||||||||
\(775\) | 2.57035 | 0.0923296 | ||||||||
\(776\) | −37.4407 | −1.34404 | ||||||||
\(777\) | −15.2026 | −0.545390 | ||||||||
\(778\) | 20.5136 | 0.735448 | ||||||||
\(779\) | 3.01139 | 0.107894 | ||||||||
\(780\) | 6.54810 | 0.234459 | ||||||||
\(781\) | −0.500517 | −0.0179099 | ||||||||
\(782\) | −20.3777 | −0.728705 | ||||||||
\(783\) | 13.6776 | 0.488797 | ||||||||
\(784\) | −3.61737 | −0.129192 | ||||||||
\(785\) | 19.9048 | 0.710432 | ||||||||
\(786\) | −23.7762 | −0.848070 | ||||||||
\(787\) | 21.3288 | 0.760291 | 0.380145 | − | 0.924927i | \(-0.375874\pi\) | ||||
0.380145 | + | 0.924927i | \(0.375874\pi\) | |||||||
\(788\) | −15.2964 | −0.544911 | ||||||||
\(789\) | 50.0479 | 1.78175 | ||||||||
\(790\) | 10.0916 | 0.359042 | ||||||||
\(791\) | 33.9271 | 1.20631 | ||||||||
\(792\) | 8.58835 | 0.305174 | ||||||||
\(793\) | 2.46585 | 0.0875649 | ||||||||
\(794\) | −5.35274 | −0.189962 | ||||||||
\(795\) | 13.4584 | 0.477321 | ||||||||
\(796\) | 11.4546 | 0.405997 | ||||||||
\(797\) | 52.2408 | 1.85046 | 0.925231 | − | 0.379403i | \(-0.123871\pi\) | ||||
0.925231 | + | 0.379403i | \(0.123871\pi\) | |||||||
\(798\) | 2.30133 | 0.0814661 | ||||||||
\(799\) | −7.97713 | −0.282211 | ||||||||
\(800\) | 14.7470 | 0.521384 | ||||||||
\(801\) | −67.8102 | −2.39595 | ||||||||
\(802\) | −4.18568 | −0.147802 | ||||||||
\(803\) | −5.42547 | −0.191461 | ||||||||
\(804\) | 27.7153 | 0.977443 | ||||||||
\(805\) | −26.2561 | −0.925406 | ||||||||
\(806\) | 0.656875 | 0.0231374 | ||||||||
\(807\) | −9.96248 | −0.350696 | ||||||||
\(808\) | 1.91389 | 0.0673305 | ||||||||
\(809\) | 41.0611 | 1.44363 | 0.721815 | − | 0.692086i | \(-0.243308\pi\) | ||||
0.721815 | + | 0.692086i | \(0.243308\pi\) | |||||||
\(810\) | −4.20246 | −0.147659 | ||||||||
\(811\) | −12.9575 | −0.455001 | −0.227500 | − | 0.973778i | \(-0.573055\pi\) | ||||
−0.227500 | + | 0.973778i | \(0.573055\pi\) | |||||||
\(812\) | −14.8584 | −0.521427 | ||||||||
\(813\) | −68.1588 | −2.39043 | ||||||||
\(814\) | 1.50436 | 0.0527277 | ||||||||
\(815\) | 30.2954 | 1.06120 | ||||||||
\(816\) | 17.1443 | 0.600171 | ||||||||
\(817\) | 1.35743 | 0.0474905 | ||||||||
\(818\) | 6.28797 | 0.219854 | ||||||||
\(819\) | 9.08102 | 0.317317 | ||||||||
\(820\) | −12.2479 | −0.427714 | ||||||||
\(821\) | −21.9928 | −0.767554 | −0.383777 | − | 0.923426i | \(-0.625377\pi\) | ||||
−0.383777 | + | 0.923426i | \(0.625377\pi\) | |||||||
\(822\) | 9.07198 | 0.316422 | ||||||||
\(823\) | 2.80755 | 0.0978650 | 0.0489325 | − | 0.998802i | \(-0.484418\pi\) | ||||
0.0489325 | + | 0.998802i | \(0.484418\pi\) | |||||||
\(824\) | −0.852101 | −0.0296843 | ||||||||
\(825\) | −6.04399 | −0.210425 | ||||||||
\(826\) | −8.83768 | −0.307502 | ||||||||
\(827\) | −33.6672 | −1.17072 | −0.585362 | − | 0.810772i | \(-0.699048\pi\) | ||||
−0.585362 | + | 0.810772i | \(0.699048\pi\) | |||||||
\(828\) | −50.6682 | −1.76084 | ||||||||
\(829\) | 31.8293 | 1.10548 | 0.552738 | − | 0.833355i | \(-0.313583\pi\) | ||||
0.552738 | + | 0.833355i | \(0.313583\pi\) | |||||||
\(830\) | 7.42771 | 0.257820 | ||||||||
\(831\) | 43.4603 | 1.50762 | ||||||||
\(832\) | 0.574175 | 0.0199059 | ||||||||
\(833\) | −9.07615 | −0.314470 | ||||||||
\(834\) | −39.1123 | −1.35435 | ||||||||
\(835\) | 18.1184 | 0.627013 | ||||||||
\(836\) | 0.827818 | 0.0286307 | ||||||||
\(837\) | −3.14195 | −0.108602 | ||||||||
\(838\) | 14.7342 | 0.508986 | ||||||||
\(839\) | 5.70452 | 0.196942 | 0.0984709 | − | 0.995140i | \(-0.468605\pi\) | ||||
0.0984709 | + | 0.995140i | \(0.468605\pi\) | |||||||
\(840\) | −21.2946 | −0.734734 | ||||||||
\(841\) | −10.0496 | −0.346537 | ||||||||
\(842\) | −18.0833 | −0.623191 | ||||||||
\(843\) | −29.3155 | −1.00968 | ||||||||
\(844\) | 23.1636 | 0.797323 | ||||||||
\(845\) | −1.55873 | −0.0536221 | ||||||||
\(846\) | 5.45637 | 0.187594 | ||||||||
\(847\) | −22.2594 | −0.764842 | ||||||||
\(848\) | −5.14928 | −0.176827 | ||||||||
\(849\) | −72.8576 | −2.50047 | ||||||||
\(850\) | 6.76647 | 0.232088 | ||||||||
\(851\) | −20.1918 | −0.692167 | ||||||||
\(852\) | 2.39488 | 0.0820473 | ||||||||
\(853\) | −5.83724 | −0.199863 | −0.0999316 | − | 0.994994i | \(-0.531862\pi\) | ||||
−0.0999316 | + | 0.994994i | \(0.531862\pi\) | |||||||
\(854\) | −3.52470 | −0.120613 | ||||||||
\(855\) | 3.91023 | 0.133727 | ||||||||
\(856\) | −41.7919 | −1.42842 | ||||||||
\(857\) | −1.10228 | −0.0376530 | −0.0188265 | − | 0.999823i | \(-0.505993\pi\) | ||||
−0.0188265 | + | 0.999823i | \(0.505993\pi\) | |||||||
\(858\) | −1.54459 | −0.0527316 | ||||||||
\(859\) | 13.0961 | 0.446834 | 0.223417 | − | 0.974723i | \(-0.428279\pi\) | ||||
0.223417 | + | 0.974723i | \(0.428279\pi\) | |||||||
\(860\) | −5.52090 | −0.188261 | ||||||||
\(861\) | −29.1962 | −0.995004 | ||||||||
\(862\) | −9.39266 | −0.319915 | ||||||||
\(863\) | −0.0939544 | −0.00319824 | −0.00159912 | − | 0.999999i | \(-0.500509\pi\) | ||||
−0.00159912 | + | 0.999999i | \(0.500509\pi\) | |||||||
\(864\) | −18.0265 | −0.613273 | ||||||||
\(865\) | −8.08567 | −0.274921 | ||||||||
\(866\) | 4.42213 | 0.150270 | ||||||||
\(867\) | −2.51466 | −0.0854024 | ||||||||
\(868\) | 3.41320 | 0.115852 | ||||||||
\(869\) | 8.65331 | 0.293543 | ||||||||
\(870\) | 11.9376 | 0.404724 | ||||||||
\(871\) | −6.59746 | −0.223546 | ||||||||
\(872\) | −24.1808 | −0.818865 | ||||||||
\(873\) | −66.6554 | −2.25594 | ||||||||
\(874\) | 3.05658 | 0.103390 | ||||||||
\(875\) | 25.6780 | 0.868074 | ||||||||
\(876\) | 25.9599 | 0.877104 | ||||||||
\(877\) | 52.5489 | 1.77445 | 0.887226 | − | 0.461335i | \(-0.152629\pi\) | ||||
0.887226 | + | 0.461335i | \(0.152629\pi\) | |||||||
\(878\) | 13.3752 | 0.451391 | ||||||||
\(879\) | 87.1560 | 2.93970 | ||||||||
\(880\) | −2.18589 | −0.0736864 | ||||||||
\(881\) | 58.3414 | 1.96557 | 0.982786 | − | 0.184746i | \(-0.0591463\pi\) | ||||
0.982786 | + | 0.184746i | \(0.0591463\pi\) | |||||||
\(882\) | 6.20810 | 0.209037 | ||||||||
\(883\) | −38.7524 | −1.30412 | −0.652061 | − | 0.758166i | \(-0.726095\pi\) | ||||
−0.652061 | + | 0.758166i | \(0.726095\pi\) | |||||||
\(884\) | −6.28603 | −0.211422 | ||||||||
\(885\) | −25.8112 | −0.867635 | ||||||||
\(886\) | −11.5888 | −0.389335 | ||||||||
\(887\) | −16.4399 | −0.551998 | −0.275999 | − | 0.961158i | \(-0.589009\pi\) | ||||
−0.275999 | + | 0.961158i | \(0.589009\pi\) | |||||||
\(888\) | −16.3763 | −0.549552 | ||||||||
\(889\) | −21.1417 | −0.709069 | ||||||||
\(890\) | −16.6375 | −0.557690 | ||||||||
\(891\) | −3.60351 | −0.120722 | ||||||||
\(892\) | −38.6840 | −1.29524 | ||||||||
\(893\) | 1.19654 | 0.0400407 | ||||||||
\(894\) | −8.14371 | −0.272367 | ||||||||
\(895\) | −31.2826 | −1.04566 | ||||||||
\(896\) | 24.1490 | 0.806761 | ||||||||
\(897\) | 20.7319 | 0.692218 | ||||||||
\(898\) | −12.5767 | −0.419688 | ||||||||
\(899\) | −4.35321 | −0.145188 | ||||||||
\(900\) | 16.8245 | 0.560817 | ||||||||
\(901\) | −12.9198 | −0.430421 | ||||||||
\(902\) | 2.88908 | 0.0961958 | ||||||||
\(903\) | −13.1606 | −0.437958 | ||||||||
\(904\) | 36.5464 | 1.21551 | ||||||||
\(905\) | −26.7156 | −0.888056 | ||||||||
\(906\) | 7.63357 | 0.253608 | ||||||||
\(907\) | 40.2105 | 1.33517 | 0.667584 | − | 0.744534i | \(-0.267328\pi\) | ||||
0.667584 | + | 0.744534i | \(0.267328\pi\) | |||||||
\(908\) | −2.18272 | −0.0724362 | ||||||||
\(909\) | 3.40729 | 0.113013 | ||||||||
\(910\) | 2.22806 | 0.0738596 | ||||||||
\(911\) | −24.4143 | −0.808881 | −0.404441 | − | 0.914564i | \(-0.632534\pi\) | ||||
−0.404441 | + | 0.914564i | \(0.632534\pi\) | |||||||
\(912\) | −2.57159 | −0.0851538 | ||||||||
\(913\) | 6.36910 | 0.210786 | ||||||||
\(914\) | 17.1101 | 0.565951 | ||||||||
\(915\) | −10.2942 | −0.340316 | ||||||||
\(916\) | −39.0578 | −1.29051 | ||||||||
\(917\) | 29.4089 | 0.971168 | ||||||||
\(918\) | −8.27122 | −0.272991 | ||||||||
\(919\) | −2.91104 | −0.0960264 | −0.0480132 | − | 0.998847i | \(-0.515289\pi\) | ||||
−0.0480132 | + | 0.998847i | \(0.515289\pi\) | |||||||
\(920\) | −28.2831 | −0.932467 | ||||||||
\(921\) | 73.7606 | 2.43049 | ||||||||
\(922\) | −3.00610 | −0.0990007 | ||||||||
\(923\) | −0.570087 | −0.0187646 | ||||||||
\(924\) | −8.02590 | −0.264033 | ||||||||
\(925\) | 6.70475 | 0.220451 | ||||||||
\(926\) | −6.99349 | −0.229820 | ||||||||
\(927\) | −1.51699 | −0.0498245 | ||||||||
\(928\) | −24.9759 | −0.819873 | ||||||||
\(929\) | −23.9908 | −0.787112 | −0.393556 | − | 0.919301i | \(-0.628755\pi\) | ||||
−0.393556 | + | 0.919301i | \(0.628755\pi\) | |||||||
\(930\) | −2.74226 | −0.0899223 | ||||||||
\(931\) | 1.36139 | 0.0446177 | ||||||||
\(932\) | 35.1866 | 1.15258 | ||||||||
\(933\) | −74.4990 | −2.43899 | ||||||||
\(934\) | 9.85537 | 0.322478 | ||||||||
\(935\) | −5.48450 | −0.179362 | ||||||||
\(936\) | 9.78210 | 0.319738 | ||||||||
\(937\) | 31.4017 | 1.02585 | 0.512924 | − | 0.858434i | \(-0.328562\pi\) | ||||
0.512924 | + | 0.858434i | \(0.328562\pi\) | |||||||
\(938\) | 9.43044 | 0.307915 | ||||||||
\(939\) | 36.9334 | 1.20528 | ||||||||
\(940\) | −4.86654 | −0.158729 | ||||||||
\(941\) | 33.3661 | 1.08771 | 0.543853 | − | 0.839181i | \(-0.316965\pi\) | ||||
0.543853 | + | 0.839181i | \(0.316965\pi\) | |||||||
\(942\) | 22.4658 | 0.731976 | ||||||||
\(943\) | −38.7779 | −1.26278 | ||||||||
\(944\) | 9.87555 | 0.321422 | ||||||||
\(945\) | −10.6572 | −0.346680 | ||||||||
\(946\) | 1.30230 | 0.0423413 | ||||||||
\(947\) | −47.4687 | −1.54253 | −0.771263 | − | 0.636517i | \(-0.780375\pi\) | ||||
−0.771263 | + | 0.636517i | \(0.780375\pi\) | |||||||
\(948\) | −41.4045 | −1.34476 | ||||||||
\(949\) | −6.17960 | −0.200598 | ||||||||
\(950\) | −1.01495 | −0.0329292 | ||||||||
\(951\) | 13.5424 | 0.439142 | ||||||||
\(952\) | 20.4423 | 0.662540 | ||||||||
\(953\) | −22.1379 | −0.717118 | −0.358559 | − | 0.933507i | \(-0.616732\pi\) | ||||
−0.358559 | + | 0.933507i | \(0.616732\pi\) | |||||||
\(954\) | 8.83715 | 0.286113 | ||||||||
\(955\) | −0.500604 | −0.0161992 | ||||||||
\(956\) | −14.1912 | −0.458976 | ||||||||
\(957\) | 10.2363 | 0.330891 | ||||||||
\(958\) | 24.4014 | 0.788373 | ||||||||
\(959\) | −11.2212 | −0.362351 | ||||||||
\(960\) | −2.39701 | −0.0773633 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 1.71346 | 0.0552441 | ||||||||
\(963\) | −74.4018 | −2.39757 | ||||||||
\(964\) | −7.00880 | −0.225738 | ||||||||
\(965\) | 7.08732 | 0.228149 | ||||||||
\(966\) | −29.6343 | −0.953469 | ||||||||
\(967\) | 25.1227 | 0.807891 | 0.403946 | − | 0.914783i | \(-0.367638\pi\) | ||||
0.403946 | + | 0.914783i | \(0.367638\pi\) | |||||||
\(968\) | −23.9779 | −0.770678 | ||||||||
\(969\) | −6.45224 | −0.207276 | ||||||||
\(970\) | −16.3542 | −0.525101 | ||||||||
\(971\) | 51.4528 | 1.65120 | 0.825600 | − | 0.564256i | \(-0.190837\pi\) | ||||
0.825600 | + | 0.564256i | \(0.190837\pi\) | |||||||
\(972\) | 32.0268 | 1.02726 | ||||||||
\(973\) | 48.3781 | 1.55093 | ||||||||
\(974\) | 15.2279 | 0.487934 | ||||||||
\(975\) | −6.88408 | −0.220467 | ||||||||
\(976\) | 3.93863 | 0.126072 | ||||||||
\(977\) | −14.7721 | −0.472601 | −0.236300 | − | 0.971680i | \(-0.575935\pi\) | ||||
−0.236300 | + | 0.971680i | \(0.575935\pi\) | |||||||
\(978\) | 34.1933 | 1.09338 | ||||||||
\(979\) | −14.2663 | −0.455952 | ||||||||
\(980\) | −5.53700 | −0.176873 | ||||||||
\(981\) | −43.0489 | −1.37445 | ||||||||
\(982\) | 17.1930 | 0.548650 | ||||||||
\(983\) | 47.9404 | 1.52906 | 0.764530 | − | 0.644588i | \(-0.222971\pi\) | ||||
0.764530 | + | 0.644588i | \(0.222971\pi\) | |||||||
\(984\) | −31.4502 | −1.00260 | ||||||||
\(985\) | −15.2010 | −0.484344 | ||||||||
\(986\) | −11.4599 | −0.364957 | ||||||||
\(987\) | −11.6008 | −0.369256 | ||||||||
\(988\) | 0.942882 | 0.0299971 | ||||||||
\(989\) | −17.4797 | −0.555822 | ||||||||
\(990\) | 3.75141 | 0.119228 | ||||||||
\(991\) | −9.92275 | −0.315206 | −0.157603 | − | 0.987503i | \(-0.550377\pi\) | ||||
−0.157603 | + | 0.987503i | \(0.550377\pi\) | |||||||
\(992\) | 5.73734 | 0.182161 | ||||||||
\(993\) | 84.6323 | 2.68573 | ||||||||
\(994\) | 0.814886 | 0.0258466 | ||||||||
\(995\) | 11.3831 | 0.360870 | ||||||||
\(996\) | −30.4750 | −0.965637 | ||||||||
\(997\) | 8.72610 | 0.276358 | 0.138179 | − | 0.990407i | \(-0.455875\pi\) | ||||
0.138179 | + | 0.990407i | \(0.455875\pi\) | |||||||
\(998\) | 25.3090 | 0.801143 | ||||||||
\(999\) | −8.19578 | −0.259303 |
(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 | 403.2.a.e.1.4 | ✓ | 8 | |
3.2 | odd | 2 | 3627.2.a.p.1.5 | 8 | |||
4.3 | odd | 2 | 6448.2.a.bd.1.2 | 8 | |||
13.12 | even | 2 | 5239.2.a.i.1.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.a.e.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
3627.2.a.p.1.5 | 8 | 3.2 | odd | 2 | |||
5239.2.a.i.1.5 | 8 | 13.12 | even | 2 | |||
6448.2.a.bd.1.2 | 8 | 4.3 | odd | 2 |