Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2645,2,Mod(1,2645)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2645, 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("2645.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2645 = 5 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2645.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: | \(21.1204313346\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 18 x^{14} + 88 x^{13} + 93 x^{12} - 728 x^{11} + 58 x^{10} + 2760 x^{9} - 1764 x^{8} + \cdots - 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.113281\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2645.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.113281 | 0.0801018 | 0.0400509 | − | 0.999198i | \(-0.487248\pi\) | ||||
0.0400509 | + | 0.999198i | \(0.487248\pi\) | |||||||
\(3\) | 2.52529 | 1.45798 | 0.728989 | − | 0.684526i | \(-0.239991\pi\) | ||||
0.728989 | + | 0.684526i | \(0.239991\pi\) | |||||||
\(4\) | −1.98717 | −0.993584 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.286068 | 0.116787 | ||||||||
\(7\) | −0.501381 | −0.189504 | −0.0947522 | − | 0.995501i | \(-0.530206\pi\) | ||||
−0.0947522 | + | 0.995501i | \(0.530206\pi\) | |||||||
\(8\) | −0.451671 | −0.159690 | ||||||||
\(9\) | 3.37710 | 1.12570 | ||||||||
\(10\) | −0.113281 | −0.0358226 | ||||||||
\(11\) | −6.19977 | −1.86930 | −0.934650 | − | 0.355568i | \(-0.884287\pi\) | ||||
−0.934650 | + | 0.355568i | \(0.884287\pi\) | |||||||
\(12\) | −5.01818 | −1.44862 | ||||||||
\(13\) | 3.05313 | 0.846786 | 0.423393 | − | 0.905946i | \(-0.360839\pi\) | ||||
0.423393 | + | 0.905946i | \(0.360839\pi\) | |||||||
\(14\) | −0.0567970 | −0.0151796 | ||||||||
\(15\) | −2.52529 | −0.652027 | ||||||||
\(16\) | 3.92317 | 0.980792 | ||||||||
\(17\) | 6.98061 | 1.69305 | 0.846523 | − | 0.532352i | \(-0.178692\pi\) | ||||
0.846523 | + | 0.532352i | \(0.178692\pi\) | |||||||
\(18\) | 0.382561 | 0.0901705 | ||||||||
\(19\) | −3.54142 | −0.812458 | −0.406229 | − | 0.913771i | \(-0.633156\pi\) | ||||
−0.406229 | + | 0.913771i | \(0.633156\pi\) | |||||||
\(20\) | 1.98717 | 0.444344 | ||||||||
\(21\) | −1.26613 | −0.276293 | ||||||||
\(22\) | −0.702317 | −0.149734 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | −1.14060 | −0.232824 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.345862 | 0.0678291 | ||||||||
\(27\) | 0.952279 | 0.183266 | ||||||||
\(28\) | 0.996329 | 0.188288 | ||||||||
\(29\) | −8.35422 | −1.55134 | −0.775670 | − | 0.631138i | \(-0.782588\pi\) | ||||
−0.775670 | + | 0.631138i | \(0.782588\pi\) | |||||||
\(30\) | −0.286068 | −0.0522286 | ||||||||
\(31\) | 3.59669 | 0.645984 | 0.322992 | − | 0.946402i | \(-0.395311\pi\) | ||||
0.322992 | + | 0.946402i | \(0.395311\pi\) | |||||||
\(32\) | 1.34776 | 0.238253 | ||||||||
\(33\) | −15.6562 | −2.72540 | ||||||||
\(34\) | 0.790771 | 0.135616 | ||||||||
\(35\) | 0.501381 | 0.0847489 | ||||||||
\(36\) | −6.71086 | −1.11848 | ||||||||
\(37\) | −6.85247 | −1.12654 | −0.563269 | − | 0.826273i | \(-0.690457\pi\) | ||||
−0.563269 | + | 0.826273i | \(0.690457\pi\) | |||||||
\(38\) | −0.401176 | −0.0650793 | ||||||||
\(39\) | 7.71005 | 1.23460 | ||||||||
\(40\) | 0.451671 | 0.0714154 | ||||||||
\(41\) | 3.05506 | 0.477121 | 0.238560 | − | 0.971128i | \(-0.423325\pi\) | ||||
0.238560 | + | 0.971128i | \(0.423325\pi\) | |||||||
\(42\) | −0.143429 | −0.0221316 | ||||||||
\(43\) | −5.28782 | −0.806384 | −0.403192 | − | 0.915115i | \(-0.632099\pi\) | ||||
−0.403192 | + | 0.915115i | \(0.632099\pi\) | |||||||
\(44\) | 12.3200 | 1.85731 | ||||||||
\(45\) | −3.37710 | −0.503428 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.71570 | −0.687855 | −0.343928 | − | 0.938996i | \(-0.611758\pi\) | ||||
−0.343928 | + | 0.938996i | \(0.611758\pi\) | |||||||
\(48\) | 9.90715 | 1.42997 | ||||||||
\(49\) | −6.74862 | −0.964088 | ||||||||
\(50\) | 0.113281 | 0.0160204 | ||||||||
\(51\) | 17.6281 | 2.46842 | ||||||||
\(52\) | −6.06708 | −0.841353 | ||||||||
\(53\) | −6.35870 | −0.873434 | −0.436717 | − | 0.899599i | \(-0.643859\pi\) | ||||
−0.436717 | + | 0.899599i | \(0.643859\pi\) | |||||||
\(54\) | 0.107875 | 0.0146800 | ||||||||
\(55\) | 6.19977 | 0.835977 | ||||||||
\(56\) | 0.226459 | 0.0302619 | ||||||||
\(57\) | −8.94312 | −1.18454 | ||||||||
\(58\) | −0.946376 | −0.124265 | ||||||||
\(59\) | −5.33690 | −0.694805 | −0.347403 | − | 0.937716i | \(-0.612936\pi\) | ||||
−0.347403 | + | 0.937716i | \(0.612936\pi\) | |||||||
\(60\) | 5.01818 | 0.647844 | ||||||||
\(61\) | −2.34975 | −0.300854 | −0.150427 | − | 0.988621i | \(-0.548065\pi\) | ||||
−0.150427 | + | 0.988621i | \(0.548065\pi\) | |||||||
\(62\) | 0.407437 | 0.0517445 | ||||||||
\(63\) | −1.69321 | −0.213325 | ||||||||
\(64\) | −7.69366 | −0.961708 | ||||||||
\(65\) | −3.05313 | −0.378694 | ||||||||
\(66\) | −1.77355 | −0.218309 | ||||||||
\(67\) | −12.9019 | −1.57622 | −0.788110 | − | 0.615535i | \(-0.788940\pi\) | ||||
−0.788110 | + | 0.615535i | \(0.788940\pi\) | |||||||
\(68\) | −13.8716 | −1.68218 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0567970 | 0.00678854 | ||||||||
\(71\) | −6.85230 | −0.813219 | −0.406609 | − | 0.913602i | \(-0.633289\pi\) | ||||
−0.406609 | + | 0.913602i | \(0.633289\pi\) | |||||||
\(72\) | −1.52534 | −0.179763 | ||||||||
\(73\) | −3.29471 | −0.385617 | −0.192808 | − | 0.981236i | \(-0.561760\pi\) | ||||
−0.192808 | + | 0.981236i | \(0.561760\pi\) | |||||||
\(74\) | −0.776255 | −0.0902378 | ||||||||
\(75\) | 2.52529 | 0.291596 | ||||||||
\(76\) | 7.03739 | 0.807245 | ||||||||
\(77\) | 3.10845 | 0.354241 | ||||||||
\(78\) | 0.873403 | 0.0988934 | ||||||||
\(79\) | −6.07749 | −0.683771 | −0.341885 | − | 0.939742i | \(-0.611065\pi\) | ||||
−0.341885 | + | 0.939742i | \(0.611065\pi\) | |||||||
\(80\) | −3.92317 | −0.438624 | ||||||||
\(81\) | −7.72651 | −0.858501 | ||||||||
\(82\) | 0.346081 | 0.0382182 | ||||||||
\(83\) | 3.53631 | 0.388160 | 0.194080 | − | 0.980986i | \(-0.437828\pi\) | ||||
0.194080 | + | 0.980986i | \(0.437828\pi\) | |||||||
\(84\) | 2.51602 | 0.274520 | ||||||||
\(85\) | −6.98061 | −0.757153 | ||||||||
\(86\) | −0.599010 | −0.0645929 | ||||||||
\(87\) | −21.0968 | −2.26182 | ||||||||
\(88\) | 2.80025 | 0.298508 | ||||||||
\(89\) | −1.94781 | −0.206468 | −0.103234 | − | 0.994657i | \(-0.532919\pi\) | ||||
−0.103234 | + | 0.994657i | \(0.532919\pi\) | |||||||
\(90\) | −0.382561 | −0.0403255 | ||||||||
\(91\) | −1.53078 | −0.160470 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.08268 | 0.941830 | ||||||||
\(94\) | −0.534200 | −0.0550985 | ||||||||
\(95\) | 3.54142 | 0.363342 | ||||||||
\(96\) | 3.40349 | 0.347368 | ||||||||
\(97\) | −13.4025 | −1.36082 | −0.680410 | − | 0.732832i | \(-0.738198\pi\) | ||||
−0.680410 | + | 0.732832i | \(0.738198\pi\) | |||||||
\(98\) | −0.764491 | −0.0772252 | ||||||||
\(99\) | −20.9372 | −2.10427 | ||||||||
\(100\) | −1.98717 | −0.198717 | ||||||||
\(101\) | 16.8703 | 1.67866 | 0.839330 | − | 0.543622i | \(-0.182948\pi\) | ||||
0.839330 | + | 0.543622i | \(0.182948\pi\) | |||||||
\(102\) | 1.99693 | 0.197725 | ||||||||
\(103\) | 1.72738 | 0.170203 | 0.0851017 | − | 0.996372i | \(-0.472878\pi\) | ||||
0.0851017 | + | 0.996372i | \(0.472878\pi\) | |||||||
\(104\) | −1.37901 | −0.135223 | ||||||||
\(105\) | 1.26613 | 0.123562 | ||||||||
\(106\) | −0.720320 | −0.0699637 | ||||||||
\(107\) | 12.4577 | 1.20433 | 0.602165 | − | 0.798371i | \(-0.294305\pi\) | ||||
0.602165 | + | 0.798371i | \(0.294305\pi\) | |||||||
\(108\) | −1.89234 | −0.182090 | ||||||||
\(109\) | −2.36457 | −0.226485 | −0.113243 | − | 0.993567i | \(-0.536124\pi\) | ||||
−0.113243 | + | 0.993567i | \(0.536124\pi\) | |||||||
\(110\) | 0.702317 | 0.0669633 | ||||||||
\(111\) | −17.3045 | −1.64247 | ||||||||
\(112\) | −1.96700 | −0.185864 | ||||||||
\(113\) | 9.70650 | 0.913111 | 0.456555 | − | 0.889695i | \(-0.349083\pi\) | ||||
0.456555 | + | 0.889695i | \(0.349083\pi\) | |||||||
\(114\) | −1.01309 | −0.0948842 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 16.6012 | 1.54139 | ||||||||
\(117\) | 10.3107 | 0.953226 | ||||||||
\(118\) | −0.604570 | −0.0556552 | ||||||||
\(119\) | −3.49995 | −0.320840 | ||||||||
\(120\) | 1.14060 | 0.104122 | ||||||||
\(121\) | 27.4371 | 2.49429 | ||||||||
\(122\) | −0.266182 | −0.0240990 | ||||||||
\(123\) | 7.71492 | 0.695631 | ||||||||
\(124\) | −7.14722 | −0.641839 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.191809 | −0.0170877 | ||||||||
\(127\) | 3.74546 | 0.332355 | 0.166178 | − | 0.986096i | \(-0.446857\pi\) | ||||
0.166178 | + | 0.986096i | \(0.446857\pi\) | |||||||
\(128\) | −3.56707 | −0.315288 | ||||||||
\(129\) | −13.3533 | −1.17569 | ||||||||
\(130\) | −0.345862 | −0.0303341 | ||||||||
\(131\) | 1.51981 | 0.132786 | 0.0663930 | − | 0.997794i | \(-0.478851\pi\) | ||||
0.0663930 | + | 0.997794i | \(0.478851\pi\) | |||||||
\(132\) | 31.1115 | 2.70791 | ||||||||
\(133\) | 1.77560 | 0.153964 | ||||||||
\(134\) | −1.46154 | −0.126258 | ||||||||
\(135\) | −0.952279 | −0.0819592 | ||||||||
\(136\) | −3.15294 | −0.270362 | ||||||||
\(137\) | −9.21062 | −0.786917 | −0.393458 | − | 0.919342i | \(-0.628721\pi\) | ||||
−0.393458 | + | 0.919342i | \(0.628721\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.2045 | 1.28963 | 0.644816 | − | 0.764338i | \(-0.276934\pi\) | ||||
0.644816 | + | 0.764338i | \(0.276934\pi\) | |||||||
\(140\) | −0.996329 | −0.0842051 | ||||||||
\(141\) | −11.9085 | −1.00288 | ||||||||
\(142\) | −0.776236 | −0.0651403 | ||||||||
\(143\) | −18.9287 | −1.58290 | ||||||||
\(144\) | 13.2489 | 1.10408 | ||||||||
\(145\) | 8.35422 | 0.693780 | ||||||||
\(146\) | −0.373228 | −0.0308886 | ||||||||
\(147\) | −17.0422 | −1.40562 | ||||||||
\(148\) | 13.6170 | 1.11931 | ||||||||
\(149\) | 5.57800 | 0.456968 | 0.228484 | − | 0.973548i | \(-0.426623\pi\) | ||||
0.228484 | + | 0.973548i | \(0.426623\pi\) | |||||||
\(150\) | 0.286068 | 0.0233573 | ||||||||
\(151\) | −18.0280 | −1.46710 | −0.733551 | − | 0.679635i | \(-0.762138\pi\) | ||||
−0.733551 | + | 0.679635i | \(0.762138\pi\) | |||||||
\(152\) | 1.59956 | 0.129741 | ||||||||
\(153\) | 23.5742 | 1.90586 | ||||||||
\(154\) | 0.352128 | 0.0283753 | ||||||||
\(155\) | −3.59669 | −0.288893 | ||||||||
\(156\) | −15.3212 | −1.22667 | ||||||||
\(157\) | −10.8804 | −0.868347 | −0.434173 | − | 0.900829i | \(-0.642959\pi\) | ||||
−0.434173 | + | 0.900829i | \(0.642959\pi\) | |||||||
\(158\) | −0.688464 | −0.0547713 | ||||||||
\(159\) | −16.0576 | −1.27345 | ||||||||
\(160\) | −1.34776 | −0.106550 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.875267 | −0.0687675 | ||||||||
\(163\) | −19.2284 | −1.50608 | −0.753042 | − | 0.657973i | \(-0.771414\pi\) | ||||
−0.753042 | + | 0.657973i | \(0.771414\pi\) | |||||||
\(164\) | −6.07092 | −0.474059 | ||||||||
\(165\) | 15.6562 | 1.21884 | ||||||||
\(166\) | 0.400597 | 0.0310924 | ||||||||
\(167\) | −0.792333 | −0.0613126 | −0.0306563 | − | 0.999530i | \(-0.509760\pi\) | ||||
−0.0306563 | + | 0.999530i | \(0.509760\pi\) | |||||||
\(168\) | 0.571876 | 0.0441212 | ||||||||
\(169\) | −3.67839 | −0.282953 | ||||||||
\(170\) | −0.790771 | −0.0606494 | ||||||||
\(171\) | −11.9597 | −0.914583 | ||||||||
\(172\) | 10.5078 | 0.801210 | ||||||||
\(173\) | 8.64911 | 0.657580 | 0.328790 | − | 0.944403i | \(-0.393359\pi\) | ||||
0.328790 | + | 0.944403i | \(0.393359\pi\) | |||||||
\(174\) | −2.38987 | −0.181176 | ||||||||
\(175\) | −0.501381 | −0.0379009 | ||||||||
\(176\) | −24.3227 | −1.83340 | ||||||||
\(177\) | −13.4772 | −1.01301 | ||||||||
\(178\) | −0.220650 | −0.0165384 | ||||||||
\(179\) | 8.20533 | 0.613295 | 0.306648 | − | 0.951823i | \(-0.400793\pi\) | ||||
0.306648 | + | 0.951823i | \(0.400793\pi\) | |||||||
\(180\) | 6.71086 | 0.500198 | ||||||||
\(181\) | 16.8443 | 1.25203 | 0.626015 | − | 0.779811i | \(-0.284685\pi\) | ||||
0.626015 | + | 0.779811i | \(0.284685\pi\) | |||||||
\(182\) | −0.173409 | −0.0128539 | ||||||||
\(183\) | −5.93379 | −0.438639 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.85247 | 0.503803 | ||||||||
\(186\) | 1.02890 | 0.0754423 | ||||||||
\(187\) | −43.2782 | −3.16481 | ||||||||
\(188\) | 9.37088 | 0.683442 | ||||||||
\(189\) | −0.477455 | −0.0347297 | ||||||||
\(190\) | 0.401176 | 0.0291044 | ||||||||
\(191\) | 13.9177 | 1.00705 | 0.503524 | − | 0.863981i | \(-0.332036\pi\) | ||||
0.503524 | + | 0.863981i | \(0.332036\pi\) | |||||||
\(192\) | −19.4287 | −1.40215 | ||||||||
\(193\) | 26.8599 | 1.93342 | 0.966708 | − | 0.255883i | \(-0.0823661\pi\) | ||||
0.966708 | + | 0.255883i | \(0.0823661\pi\) | |||||||
\(194\) | −1.51825 | −0.109004 | ||||||||
\(195\) | −7.71005 | −0.552128 | ||||||||
\(196\) | 13.4106 | 0.957902 | ||||||||
\(197\) | 22.8883 | 1.63072 | 0.815361 | − | 0.578953i | \(-0.196539\pi\) | ||||
0.815361 | + | 0.578953i | \(0.196539\pi\) | |||||||
\(198\) | −2.37179 | −0.168556 | ||||||||
\(199\) | 26.4627 | 1.87589 | 0.937945 | − | 0.346784i | \(-0.112726\pi\) | ||||
0.937945 | + | 0.346784i | \(0.112726\pi\) | |||||||
\(200\) | −0.451671 | −0.0319379 | ||||||||
\(201\) | −32.5811 | −2.29809 | ||||||||
\(202\) | 1.91109 | 0.134464 | ||||||||
\(203\) | 4.18865 | 0.293986 | ||||||||
\(204\) | −35.0299 | −2.45259 | ||||||||
\(205\) | −3.05506 | −0.213375 | ||||||||
\(206\) | 0.195679 | 0.0136336 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 11.9780 | 0.830521 | ||||||||
\(209\) | 21.9560 | 1.51873 | ||||||||
\(210\) | 0.143429 | 0.00989754 | ||||||||
\(211\) | −10.9026 | −0.750564 | −0.375282 | − | 0.926911i | \(-0.622454\pi\) | ||||
−0.375282 | + | 0.926911i | \(0.622454\pi\) | |||||||
\(212\) | 12.6358 | 0.867830 | ||||||||
\(213\) | −17.3041 | −1.18565 | ||||||||
\(214\) | 1.41122 | 0.0964691 | ||||||||
\(215\) | 5.28782 | 0.360626 | ||||||||
\(216\) | −0.430117 | −0.0292657 | ||||||||
\(217\) | −1.80331 | −0.122417 | ||||||||
\(218\) | −0.267862 | −0.0181419 | ||||||||
\(219\) | −8.32010 | −0.562220 | ||||||||
\(220\) | −12.3200 | −0.830613 | ||||||||
\(221\) | 21.3127 | 1.43365 | ||||||||
\(222\) | −1.96027 | −0.131565 | ||||||||
\(223\) | −1.06241 | −0.0711441 | −0.0355720 | − | 0.999367i | \(-0.511325\pi\) | ||||
−0.0355720 | + | 0.999367i | \(0.511325\pi\) | |||||||
\(224\) | −0.675743 | −0.0451500 | ||||||||
\(225\) | 3.37710 | 0.225140 | ||||||||
\(226\) | 1.09956 | 0.0731418 | ||||||||
\(227\) | −3.87761 | −0.257366 | −0.128683 | − | 0.991686i | \(-0.541075\pi\) | ||||
−0.128683 | + | 0.991686i | \(0.541075\pi\) | |||||||
\(228\) | 17.7715 | 1.17694 | ||||||||
\(229\) | 8.37271 | 0.553284 | 0.276642 | − | 0.960973i | \(-0.410778\pi\) | ||||
0.276642 | + | 0.960973i | \(0.410778\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.84974 | 0.516475 | ||||||||
\(232\) | 3.77336 | 0.247733 | ||||||||
\(233\) | −13.5701 | −0.889010 | −0.444505 | − | 0.895776i | \(-0.646620\pi\) | ||||
−0.444505 | + | 0.895776i | \(0.646620\pi\) | |||||||
\(234\) | 1.16801 | 0.0763552 | ||||||||
\(235\) | 4.71570 | 0.307618 | ||||||||
\(236\) | 10.6053 | 0.690347 | ||||||||
\(237\) | −15.3474 | −0.996922 | ||||||||
\(238\) | −0.396478 | −0.0256998 | ||||||||
\(239\) | −2.42699 | −0.156989 | −0.0784944 | − | 0.996915i | \(-0.525011\pi\) | ||||
−0.0784944 | + | 0.996915i | \(0.525011\pi\) | |||||||
\(240\) | −9.90715 | −0.639503 | ||||||||
\(241\) | 16.1605 | 1.04099 | 0.520494 | − | 0.853865i | \(-0.325748\pi\) | ||||
0.520494 | + | 0.853865i | \(0.325748\pi\) | |||||||
\(242\) | 3.10811 | 0.199797 | ||||||||
\(243\) | −22.3685 | −1.43494 | ||||||||
\(244\) | 4.66934 | 0.298924 | ||||||||
\(245\) | 6.74862 | 0.431153 | ||||||||
\(246\) | 0.873955 | 0.0557213 | ||||||||
\(247\) | −10.8124 | −0.687978 | ||||||||
\(248\) | −1.62452 | −0.103157 | ||||||||
\(249\) | 8.93021 | 0.565929 | ||||||||
\(250\) | −0.113281 | −0.00716453 | ||||||||
\(251\) | −17.9361 | −1.13211 | −0.566057 | − | 0.824366i | \(-0.691532\pi\) | ||||
−0.566057 | + | 0.824366i | \(0.691532\pi\) | |||||||
\(252\) | 3.36470 | 0.211956 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.424289 | 0.0266223 | ||||||||
\(255\) | −17.6281 | −1.10391 | ||||||||
\(256\) | 14.9832 | 0.936453 | ||||||||
\(257\) | −16.1250 | −1.00585 | −0.502925 | − | 0.864330i | \(-0.667743\pi\) | ||||
−0.502925 | + | 0.864330i | \(0.667743\pi\) | |||||||
\(258\) | −1.51267 | −0.0941750 | ||||||||
\(259\) | 3.43570 | 0.213484 | ||||||||
\(260\) | 6.06708 | 0.376265 | ||||||||
\(261\) | −28.2130 | −1.74634 | ||||||||
\(262\) | 0.172165 | 0.0106364 | ||||||||
\(263\) | 10.3450 | 0.637898 | 0.318949 | − | 0.947772i | \(-0.396670\pi\) | ||||
0.318949 | + | 0.947772i | \(0.396670\pi\) | |||||||
\(264\) | 7.07146 | 0.435218 | ||||||||
\(265\) | 6.35870 | 0.390612 | ||||||||
\(266\) | 0.201142 | 0.0123328 | ||||||||
\(267\) | −4.91879 | −0.301025 | ||||||||
\(268\) | 25.6383 | 1.56611 | ||||||||
\(269\) | 14.6854 | 0.895384 | 0.447692 | − | 0.894188i | \(-0.352246\pi\) | ||||
0.447692 | + | 0.894188i | \(0.352246\pi\) | |||||||
\(270\) | −0.107875 | −0.00656508 | ||||||||
\(271\) | −10.9413 | −0.664635 | −0.332318 | − | 0.943168i | \(-0.607831\pi\) | ||||
−0.332318 | + | 0.943168i | \(0.607831\pi\) | |||||||
\(272\) | 27.3861 | 1.66053 | ||||||||
\(273\) | −3.86567 | −0.233961 | ||||||||
\(274\) | −1.04339 | −0.0630335 | ||||||||
\(275\) | −6.19977 | −0.373860 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.1983 | −1.57410 | −0.787051 | − | 0.616887i | \(-0.788393\pi\) | ||||
−0.787051 | + | 0.616887i | \(0.788393\pi\) | |||||||
\(278\) | 1.72239 | 0.103302 | ||||||||
\(279\) | 12.1464 | 0.727184 | ||||||||
\(280\) | −0.226459 | −0.0135335 | ||||||||
\(281\) | 13.6076 | 0.811761 | 0.405880 | − | 0.913926i | \(-0.366965\pi\) | ||||
0.405880 | + | 0.913926i | \(0.366965\pi\) | |||||||
\(282\) | −1.34901 | −0.0803323 | ||||||||
\(283\) | −16.3451 | −0.971616 | −0.485808 | − | 0.874066i | \(-0.661475\pi\) | ||||
−0.485808 | + | 0.874066i | \(0.661475\pi\) | |||||||
\(284\) | 13.6167 | 0.808001 | ||||||||
\(285\) | 8.94312 | 0.529745 | ||||||||
\(286\) | −2.14427 | −0.126793 | ||||||||
\(287\) | −1.53175 | −0.0904164 | ||||||||
\(288\) | 4.55152 | 0.268201 | ||||||||
\(289\) | 31.7289 | 1.86641 | ||||||||
\(290\) | 0.946376 | 0.0555731 | ||||||||
\(291\) | −33.8453 | −1.98404 | ||||||||
\(292\) | 6.54714 | 0.383142 | ||||||||
\(293\) | 22.3129 | 1.30354 | 0.651768 | − | 0.758418i | \(-0.274028\pi\) | ||||
0.651768 | + | 0.758418i | \(0.274028\pi\) | |||||||
\(294\) | −1.93056 | −0.112593 | ||||||||
\(295\) | 5.33690 | 0.310726 | ||||||||
\(296\) | 3.09506 | 0.179897 | ||||||||
\(297\) | −5.90391 | −0.342580 | ||||||||
\(298\) | 0.631882 | 0.0366039 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5.01818 | −0.289725 | ||||||||
\(301\) | 2.65121 | 0.152813 | ||||||||
\(302\) | −2.04224 | −0.117518 | ||||||||
\(303\) | 42.6025 | 2.44745 | ||||||||
\(304\) | −13.8936 | −0.796852 | ||||||||
\(305\) | 2.34975 | 0.134546 | ||||||||
\(306\) | 2.67051 | 0.152663 | ||||||||
\(307\) | −11.8483 | −0.676220 | −0.338110 | − | 0.941107i | \(-0.609788\pi\) | ||||
−0.338110 | + | 0.941107i | \(0.609788\pi\) | |||||||
\(308\) | −6.17701 | −0.351968 | ||||||||
\(309\) | 4.36213 | 0.248153 | ||||||||
\(310\) | −0.407437 | −0.0231408 | ||||||||
\(311\) | −30.4520 | −1.72678 | −0.863389 | − | 0.504540i | \(-0.831662\pi\) | ||||
−0.863389 | + | 0.504540i | \(0.831662\pi\) | |||||||
\(312\) | −3.48240 | −0.197152 | ||||||||
\(313\) | 13.3111 | 0.752389 | 0.376194 | − | 0.926541i | \(-0.377232\pi\) | ||||
0.376194 | + | 0.926541i | \(0.377232\pi\) | |||||||
\(314\) | −1.23254 | −0.0695562 | ||||||||
\(315\) | 1.69321 | 0.0954018 | ||||||||
\(316\) | 12.0770 | 0.679383 | ||||||||
\(317\) | −22.5735 | −1.26785 | −0.633927 | − | 0.773393i | \(-0.718558\pi\) | ||||
−0.633927 | + | 0.773393i | \(0.718558\pi\) | |||||||
\(318\) | −1.81902 | −0.102006 | ||||||||
\(319\) | 51.7943 | 2.89992 | ||||||||
\(320\) | 7.69366 | 0.430089 | ||||||||
\(321\) | 31.4593 | 1.75589 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.7213 | −1.37553 | ||||||||
\(324\) | 15.3539 | 0.852992 | ||||||||
\(325\) | 3.05313 | 0.169357 | ||||||||
\(326\) | −2.17821 | −0.120640 | ||||||||
\(327\) | −5.97124 | −0.330210 | ||||||||
\(328\) | −1.37988 | −0.0761913 | ||||||||
\(329\) | 2.36436 | 0.130352 | ||||||||
\(330\) | 1.77355 | 0.0976310 | ||||||||
\(331\) | 17.3256 | 0.952301 | 0.476151 | − | 0.879364i | \(-0.342032\pi\) | ||||
0.476151 | + | 0.879364i | \(0.342032\pi\) | |||||||
\(332\) | −7.02724 | −0.385670 | ||||||||
\(333\) | −23.1414 | −1.26814 | ||||||||
\(334\) | −0.0897563 | −0.00491125 | ||||||||
\(335\) | 12.9019 | 0.704907 | ||||||||
\(336\) | −4.96726 | −0.270986 | ||||||||
\(337\) | −3.08625 | −0.168119 | −0.0840594 | − | 0.996461i | \(-0.526789\pi\) | ||||
−0.0840594 | + | 0.996461i | \(0.526789\pi\) | |||||||
\(338\) | −0.416692 | −0.0226650 | ||||||||
\(339\) | 24.5117 | 1.33130 | ||||||||
\(340\) | 13.8716 | 0.752295 | ||||||||
\(341\) | −22.2986 | −1.20754 | ||||||||
\(342\) | −1.35481 | −0.0732597 | ||||||||
\(343\) | 6.89330 | 0.372203 | ||||||||
\(344\) | 2.38835 | 0.128771 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.979781 | 0.0526734 | ||||||||
\(347\) | −9.90897 | −0.531942 | −0.265971 | − | 0.963981i | \(-0.585692\pi\) | ||||
−0.265971 | + | 0.963981i | \(0.585692\pi\) | |||||||
\(348\) | 41.9230 | 2.24731 | ||||||||
\(349\) | −17.3731 | −0.929961 | −0.464980 | − | 0.885321i | \(-0.653939\pi\) | ||||
−0.464980 | + | 0.885321i | \(0.653939\pi\) | |||||||
\(350\) | −0.0567970 | −0.00303593 | ||||||||
\(351\) | 2.90743 | 0.155187 | ||||||||
\(352\) | −8.35582 | −0.445366 | ||||||||
\(353\) | 24.9109 | 1.32588 | 0.662938 | − | 0.748675i | \(-0.269309\pi\) | ||||
0.662938 | + | 0.748675i | \(0.269309\pi\) | |||||||
\(354\) | −1.52672 | −0.0811440 | ||||||||
\(355\) | 6.85230 | 0.363683 | ||||||||
\(356\) | 3.87063 | 0.205143 | ||||||||
\(357\) | −8.83839 | −0.467777 | ||||||||
\(358\) | 0.929509 | 0.0491261 | ||||||||
\(359\) | −5.74833 | −0.303385 | −0.151693 | − | 0.988428i | \(-0.548472\pi\) | ||||
−0.151693 | + | 0.988428i | \(0.548472\pi\) | |||||||
\(360\) | 1.52534 | 0.0803922 | ||||||||
\(361\) | −6.45834 | −0.339913 | ||||||||
\(362\) | 1.90815 | 0.100290 | ||||||||
\(363\) | 69.2868 | 3.63661 | ||||||||
\(364\) | 3.04192 | 0.159440 | ||||||||
\(365\) | 3.29471 | 0.172453 | ||||||||
\(366\) | −0.672187 | −0.0351358 | ||||||||
\(367\) | 7.49151 | 0.391054 | 0.195527 | − | 0.980698i | \(-0.437358\pi\) | ||||
0.195527 | + | 0.980698i | \(0.437358\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.3172 | 0.537094 | ||||||||
\(370\) | 0.776255 | 0.0403556 | ||||||||
\(371\) | 3.18813 | 0.165520 | ||||||||
\(372\) | −18.0488 | −0.935787 | ||||||||
\(373\) | −19.9803 | −1.03454 | −0.517271 | − | 0.855821i | \(-0.673052\pi\) | ||||
−0.517271 | + | 0.855821i | \(0.673052\pi\) | |||||||
\(374\) | −4.90260 | −0.253507 | ||||||||
\(375\) | −2.52529 | −0.130405 | ||||||||
\(376\) | 2.12994 | 0.109843 | ||||||||
\(377\) | −25.5065 | −1.31365 | ||||||||
\(378\) | −0.0540866 | −0.00278192 | ||||||||
\(379\) | −8.88450 | −0.456366 | −0.228183 | − | 0.973618i | \(-0.573278\pi\) | ||||
−0.228183 | + | 0.973618i | \(0.573278\pi\) | |||||||
\(380\) | −7.03739 | −0.361011 | ||||||||
\(381\) | 9.45837 | 0.484567 | ||||||||
\(382\) | 1.57661 | 0.0806664 | ||||||||
\(383\) | −5.38561 | −0.275192 | −0.137596 | − | 0.990488i | \(-0.543938\pi\) | ||||
−0.137596 | + | 0.990488i | \(0.543938\pi\) | |||||||
\(384\) | −9.00789 | −0.459682 | ||||||||
\(385\) | −3.10845 | −0.158421 | ||||||||
\(386\) | 3.04272 | 0.154870 | ||||||||
\(387\) | −17.8575 | −0.907746 | ||||||||
\(388\) | 26.6331 | 1.35209 | ||||||||
\(389\) | 4.79365 | 0.243048 | 0.121524 | − | 0.992589i | \(-0.461222\pi\) | ||||
0.121524 | + | 0.992589i | \(0.461222\pi\) | |||||||
\(390\) | −0.873403 | −0.0442265 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 3.04815 | 0.153955 | ||||||||
\(393\) | 3.83795 | 0.193599 | ||||||||
\(394\) | 2.59281 | 0.130624 | ||||||||
\(395\) | 6.07749 | 0.305792 | ||||||||
\(396\) | 41.6058 | 2.09077 | ||||||||
\(397\) | −29.1751 | −1.46426 | −0.732128 | − | 0.681168i | \(-0.761473\pi\) | ||||
−0.732128 | + | 0.681168i | \(0.761473\pi\) | |||||||
\(398\) | 2.99772 | 0.150262 | ||||||||
\(399\) | 4.48391 | 0.224476 | ||||||||
\(400\) | 3.92317 | 0.196158 | ||||||||
\(401\) | 13.3918 | 0.668753 | 0.334376 | − | 0.942440i | \(-0.391474\pi\) | ||||
0.334376 | + | 0.942440i | \(0.391474\pi\) | |||||||
\(402\) | −3.69082 | −0.184081 | ||||||||
\(403\) | 10.9812 | 0.547010 | ||||||||
\(404\) | −33.5242 | −1.66789 | ||||||||
\(405\) | 7.72651 | 0.383933 | ||||||||
\(406\) | 0.474495 | 0.0235488 | ||||||||
\(407\) | 42.4837 | 2.10584 | ||||||||
\(408\) | −7.96208 | −0.394182 | ||||||||
\(409\) | 1.92003 | 0.0949392 | 0.0474696 | − | 0.998873i | \(-0.484884\pi\) | ||||
0.0474696 | + | 0.998873i | \(0.484884\pi\) | |||||||
\(410\) | −0.346081 | −0.0170917 | ||||||||
\(411\) | −23.2595 | −1.14731 | ||||||||
\(412\) | −3.43259 | −0.169111 | ||||||||
\(413\) | 2.67582 | 0.131669 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.53631 | −0.173591 | ||||||||
\(416\) | 4.11490 | 0.201749 | ||||||||
\(417\) | 38.3959 | 1.88025 | ||||||||
\(418\) | 2.48720 | 0.121653 | ||||||||
\(419\) | 2.14905 | 0.104988 | 0.0524941 | − | 0.998621i | \(-0.483283\pi\) | ||||
0.0524941 | + | 0.998621i | \(0.483283\pi\) | |||||||
\(420\) | −2.51602 | −0.122769 | ||||||||
\(421\) | 1.96986 | 0.0960052 | 0.0480026 | − | 0.998847i | \(-0.484714\pi\) | ||||
0.0480026 | + | 0.998847i | \(0.484714\pi\) | |||||||
\(422\) | −1.23506 | −0.0601216 | ||||||||
\(423\) | −15.9254 | −0.774318 | ||||||||
\(424\) | 2.87204 | 0.139478 | ||||||||
\(425\) | 6.98061 | 0.338609 | ||||||||
\(426\) | −1.96022 | −0.0949731 | ||||||||
\(427\) | 1.17812 | 0.0570132 | ||||||||
\(428\) | −24.7555 | −1.19660 | ||||||||
\(429\) | −47.8005 | −2.30783 | ||||||||
\(430\) | 0.599010 | 0.0288868 | ||||||||
\(431\) | −5.74228 | −0.276596 | −0.138298 | − | 0.990391i | \(-0.544163\pi\) | ||||
−0.138298 | + | 0.990391i | \(0.544163\pi\) | |||||||
\(432\) | 3.73595 | 0.179746 | ||||||||
\(433\) | 14.8410 | 0.713214 | 0.356607 | − | 0.934255i | \(-0.383934\pi\) | ||||
0.356607 | + | 0.934255i | \(0.383934\pi\) | |||||||
\(434\) | −0.204281 | −0.00980581 | ||||||||
\(435\) | 21.0968 | 1.01152 | ||||||||
\(436\) | 4.69881 | 0.225032 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.942510 | −0.0450349 | ||||||||
\(439\) | −32.4246 | −1.54754 | −0.773772 | − | 0.633465i | \(-0.781632\pi\) | ||||
−0.773772 | + | 0.633465i | \(0.781632\pi\) | |||||||
\(440\) | −2.80025 | −0.133497 | ||||||||
\(441\) | −22.7907 | −1.08527 | ||||||||
\(442\) | 2.41433 | 0.114838 | ||||||||
\(443\) | −23.3020 | −1.10711 | −0.553555 | − | 0.832812i | \(-0.686729\pi\) | ||||
−0.553555 | + | 0.832812i | \(0.686729\pi\) | |||||||
\(444\) | 34.3869 | 1.63193 | ||||||||
\(445\) | 1.94781 | 0.0923351 | ||||||||
\(446\) | −0.120351 | −0.00569877 | ||||||||
\(447\) | 14.0861 | 0.666248 | ||||||||
\(448\) | 3.85746 | 0.182248 | ||||||||
\(449\) | −8.21844 | −0.387852 | −0.193926 | − | 0.981016i | \(-0.562122\pi\) | ||||
−0.193926 | + | 0.981016i | \(0.562122\pi\) | |||||||
\(450\) | 0.382561 | 0.0180341 | ||||||||
\(451\) | −18.9407 | −0.891882 | ||||||||
\(452\) | −19.2884 | −0.907252 | ||||||||
\(453\) | −45.5261 | −2.13900 | ||||||||
\(454\) | −0.439260 | −0.0206155 | ||||||||
\(455\) | 1.53078 | 0.0717642 | ||||||||
\(456\) | 4.03934 | 0.189160 | ||||||||
\(457\) | −27.3857 | −1.28105 | −0.640524 | − | 0.767938i | \(-0.721283\pi\) | ||||
−0.640524 | + | 0.767938i | \(0.721283\pi\) | |||||||
\(458\) | 0.948470 | 0.0443191 | ||||||||
\(459\) | 6.64749 | 0.310278 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.3263 | −0.806967 | −0.403483 | − | 0.914987i | \(-0.632201\pi\) | ||||
−0.403483 | + | 0.914987i | \(0.632201\pi\) | |||||||
\(462\) | 0.889227 | 0.0413706 | ||||||||
\(463\) | 27.3662 | 1.27182 | 0.635909 | − | 0.771764i | \(-0.280625\pi\) | ||||
0.635909 | + | 0.771764i | \(0.280625\pi\) | |||||||
\(464\) | −32.7750 | −1.52154 | ||||||||
\(465\) | −9.08268 | −0.421199 | ||||||||
\(466\) | −1.53724 | −0.0712113 | ||||||||
\(467\) | 25.8613 | 1.19672 | 0.598359 | − | 0.801228i | \(-0.295820\pi\) | ||||
0.598359 | + | 0.801228i | \(0.295820\pi\) | |||||||
\(468\) | −20.4891 | −0.947110 | ||||||||
\(469\) | 6.46878 | 0.298700 | ||||||||
\(470\) | 0.534200 | 0.0246408 | ||||||||
\(471\) | −27.4761 | −1.26603 | ||||||||
\(472\) | 2.41052 | 0.110953 | ||||||||
\(473\) | 32.7832 | 1.50738 | ||||||||
\(474\) | −1.73857 | −0.0798553 | ||||||||
\(475\) | −3.54142 | −0.162492 | ||||||||
\(476\) | 6.95498 | 0.318781 | ||||||||
\(477\) | −21.4739 | −0.983224 | ||||||||
\(478\) | −0.274932 | −0.0125751 | ||||||||
\(479\) | −9.64732 | −0.440797 | −0.220399 | − | 0.975410i | \(-0.570736\pi\) | ||||
−0.220399 | + | 0.975410i | \(0.570736\pi\) | |||||||
\(480\) | −3.40349 | −0.155347 | ||||||||
\(481\) | −20.9215 | −0.953938 | ||||||||
\(482\) | 1.83068 | 0.0833851 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −54.5222 | −2.47828 | ||||||||
\(485\) | 13.4025 | 0.608577 | ||||||||
\(486\) | −2.53393 | −0.114941 | ||||||||
\(487\) | 3.97432 | 0.180094 | 0.0900468 | − | 0.995938i | \(-0.471298\pi\) | ||||
0.0900468 | + | 0.995938i | \(0.471298\pi\) | |||||||
\(488\) | 1.06131 | 0.0480433 | ||||||||
\(489\) | −48.5573 | −2.19584 | ||||||||
\(490\) | 0.764491 | 0.0345362 | ||||||||
\(491\) | 25.2364 | 1.13890 | 0.569451 | − | 0.822025i | \(-0.307156\pi\) | ||||
0.569451 | + | 0.822025i | \(0.307156\pi\) | |||||||
\(492\) | −15.3308 | −0.691168 | ||||||||
\(493\) | −58.3176 | −2.62649 | ||||||||
\(494\) | −1.22484 | −0.0551083 | ||||||||
\(495\) | 20.9372 | 0.941058 | ||||||||
\(496\) | 14.1104 | 0.633576 | ||||||||
\(497\) | 3.43562 | 0.154108 | ||||||||
\(498\) | 1.01162 | 0.0453320 | ||||||||
\(499\) | −14.0420 | −0.628608 | −0.314304 | − | 0.949322i | \(-0.601771\pi\) | ||||
−0.314304 | + | 0.949322i | \(0.601771\pi\) | |||||||
\(500\) | 1.98717 | 0.0888688 | ||||||||
\(501\) | −2.00087 | −0.0893923 | ||||||||
\(502\) | −2.03182 | −0.0906844 | ||||||||
\(503\) | −23.9547 | −1.06809 | −0.534044 | − | 0.845456i | \(-0.679328\pi\) | ||||
−0.534044 | + | 0.845456i | \(0.679328\pi\) | |||||||
\(504\) | 0.764775 | 0.0340658 | ||||||||
\(505\) | −16.8703 | −0.750720 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.28900 | −0.412539 | ||||||||
\(508\) | −7.44285 | −0.330223 | ||||||||
\(509\) | −11.5565 | −0.512234 | −0.256117 | − | 0.966646i | \(-0.582443\pi\) | ||||
−0.256117 | + | 0.966646i | \(0.582443\pi\) | |||||||
\(510\) | −1.99693 | −0.0884254 | ||||||||
\(511\) | 1.65191 | 0.0730760 | ||||||||
\(512\) | 8.83146 | 0.390299 | ||||||||
\(513\) | −3.37242 | −0.148896 | ||||||||
\(514\) | −1.82666 | −0.0805704 | ||||||||
\(515\) | −1.72738 | −0.0761173 | ||||||||
\(516\) | 26.5352 | 1.16815 | ||||||||
\(517\) | 29.2362 | 1.28581 | ||||||||
\(518\) | 0.389200 | 0.0171005 | ||||||||
\(519\) | 21.8415 | 0.958737 | ||||||||
\(520\) | 1.37901 | 0.0604736 | ||||||||
\(521\) | −30.9059 | −1.35401 | −0.677006 | − | 0.735978i | \(-0.736723\pi\) | ||||
−0.677006 | + | 0.735978i | \(0.736723\pi\) | |||||||
\(522\) | −3.19600 | −0.139885 | ||||||||
\(523\) | −23.4745 | −1.02647 | −0.513235 | − | 0.858248i | \(-0.671553\pi\) | ||||
−0.513235 | + | 0.858248i | \(0.671553\pi\) | |||||||
\(524\) | −3.02011 | −0.131934 | ||||||||
\(525\) | −1.26613 | −0.0552586 | ||||||||
\(526\) | 1.17189 | 0.0510968 | ||||||||
\(527\) | 25.1071 | 1.09368 | ||||||||
\(528\) | −61.4220 | −2.67305 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 0.720320 | 0.0312887 | ||||||||
\(531\) | −18.0232 | −0.782142 | ||||||||
\(532\) | −3.52842 | −0.152976 | ||||||||
\(533\) | 9.32751 | 0.404019 | ||||||||
\(534\) | −0.557206 | −0.0241127 | ||||||||
\(535\) | −12.4577 | −0.538593 | ||||||||
\(536\) | 5.82741 | 0.251706 | ||||||||
\(537\) | 20.7208 | 0.894170 | ||||||||
\(538\) | 1.66358 | 0.0717219 | ||||||||
\(539\) | 41.8399 | 1.80217 | ||||||||
\(540\) | 1.89234 | 0.0814333 | ||||||||
\(541\) | 15.4160 | 0.662787 | 0.331393 | − | 0.943493i | \(-0.392481\pi\) | ||||
0.331393 | + | 0.943493i | \(0.392481\pi\) | |||||||
\(542\) | −1.23944 | −0.0532385 | ||||||||
\(543\) | 42.5369 | 1.82543 | ||||||||
\(544\) | 9.40820 | 0.403373 | ||||||||
\(545\) | 2.36457 | 0.101287 | ||||||||
\(546\) | −0.437908 | −0.0187407 | ||||||||
\(547\) | 31.2975 | 1.33818 | 0.669091 | − | 0.743180i | \(-0.266684\pi\) | ||||
0.669091 | + | 0.743180i | \(0.266684\pi\) | |||||||
\(548\) | 18.3031 | 0.781868 | ||||||||
\(549\) | −7.93532 | −0.338671 | ||||||||
\(550\) | −0.702317 | −0.0299469 | ||||||||
\(551\) | 29.5858 | 1.26040 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.04714 | 0.129578 | ||||||||
\(554\) | −2.96777 | −0.126089 | ||||||||
\(555\) | 17.3045 | 0.734534 | ||||||||
\(556\) | −30.2139 | −1.28136 | ||||||||
\(557\) | 35.3135 | 1.49628 | 0.748141 | − | 0.663540i | \(-0.230947\pi\) | ||||
0.748141 | + | 0.663540i | \(0.230947\pi\) | |||||||
\(558\) | 1.37595 | 0.0582487 | ||||||||
\(559\) | −16.1444 | −0.682835 | ||||||||
\(560\) | 1.96700 | 0.0831211 | ||||||||
\(561\) | −109.290 | −4.61423 | ||||||||
\(562\) | 1.54148 | 0.0650235 | ||||||||
\(563\) | 12.7665 | 0.538045 | 0.269023 | − | 0.963134i | \(-0.413299\pi\) | ||||
0.269023 | + | 0.963134i | \(0.413299\pi\) | |||||||
\(564\) | 23.6642 | 0.996443 | ||||||||
\(565\) | −9.70650 | −0.408356 | ||||||||
\(566\) | −1.85159 | −0.0778282 | ||||||||
\(567\) | 3.87393 | 0.162690 | ||||||||
\(568\) | 3.09498 | 0.129863 | ||||||||
\(569\) | −33.5566 | −1.40677 | −0.703384 | − | 0.710810i | \(-0.748328\pi\) | ||||
−0.703384 | + | 0.710810i | \(0.748328\pi\) | |||||||
\(570\) | 1.01309 | 0.0424335 | ||||||||
\(571\) | 3.85906 | 0.161497 | 0.0807483 | − | 0.996735i | \(-0.474269\pi\) | ||||
0.0807483 | + | 0.996735i | \(0.474269\pi\) | |||||||
\(572\) | 37.6145 | 1.57274 | ||||||||
\(573\) | 35.1462 | 1.46825 | ||||||||
\(574\) | −0.173519 | −0.00724252 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −25.9822 | −1.08259 | ||||||||
\(577\) | −0.180157 | −0.00750004 | −0.00375002 | − | 0.999993i | \(-0.501194\pi\) | ||||
−0.00375002 | + | 0.999993i | \(0.501194\pi\) | |||||||
\(578\) | 3.59428 | 0.149503 | ||||||||
\(579\) | 67.8290 | 2.81888 | ||||||||
\(580\) | −16.6012 | −0.689329 | ||||||||
\(581\) | −1.77304 | −0.0735581 | ||||||||
\(582\) | −3.83403 | −0.158926 | ||||||||
\(583\) | 39.4225 | 1.63271 | ||||||||
\(584\) | 1.48812 | 0.0615790 | ||||||||
\(585\) | −10.3107 | −0.426296 | ||||||||
\(586\) | 2.52763 | 0.104416 | ||||||||
\(587\) | −24.6763 | −1.01850 | −0.509250 | − | 0.860619i | \(-0.670077\pi\) | ||||
−0.509250 | + | 0.860619i | \(0.670077\pi\) | |||||||
\(588\) | 33.8658 | 1.39660 | ||||||||
\(589\) | −12.7374 | −0.524835 | ||||||||
\(590\) | 0.604570 | 0.0248898 | ||||||||
\(591\) | 57.7996 | 2.37756 | ||||||||
\(592\) | −26.8834 | −1.10490 | ||||||||
\(593\) | −14.8192 | −0.608551 | −0.304276 | − | 0.952584i | \(-0.598414\pi\) | ||||
−0.304276 | + | 0.952584i | \(0.598414\pi\) | |||||||
\(594\) | −0.668802 | −0.0274413 | ||||||||
\(595\) | 3.49995 | 0.143484 | ||||||||
\(596\) | −11.0844 | −0.454035 | ||||||||
\(597\) | 66.8260 | 2.73501 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.8740 | −0.893746 | −0.446873 | − | 0.894598i | \(-0.647462\pi\) | ||||
−0.446873 | + | 0.894598i | \(0.647462\pi\) | |||||||
\(600\) | −1.14060 | −0.0465648 | ||||||||
\(601\) | −20.4481 | −0.834097 | −0.417049 | − | 0.908884i | \(-0.636936\pi\) | ||||
−0.417049 | + | 0.908884i | \(0.636936\pi\) | |||||||
\(602\) | 0.300332 | 0.0122406 | ||||||||
\(603\) | −43.5710 | −1.77435 | ||||||||
\(604\) | 35.8247 | 1.45769 | ||||||||
\(605\) | −27.4371 | −1.11548 | ||||||||
\(606\) | 4.82606 | 0.196045 | ||||||||
\(607\) | 32.5583 | 1.32150 | 0.660751 | − | 0.750606i | \(-0.270238\pi\) | ||||
0.660751 | + | 0.750606i | \(0.270238\pi\) | |||||||
\(608\) | −4.77299 | −0.193570 | ||||||||
\(609\) | 10.5776 | 0.428625 | ||||||||
\(610\) | 0.266182 | 0.0107774 | ||||||||
\(611\) | −14.3976 | −0.582467 | ||||||||
\(612\) | −46.8459 | −1.89363 | ||||||||
\(613\) | −9.62065 | −0.388574 | −0.194287 | − | 0.980945i | \(-0.562239\pi\) | ||||
−0.194287 | + | 0.980945i | \(0.562239\pi\) | |||||||
\(614\) | −1.34219 | −0.0541665 | ||||||||
\(615\) | −7.71492 | −0.311096 | ||||||||
\(616\) | −1.40400 | −0.0565686 | ||||||||
\(617\) | −23.1152 | −0.930583 | −0.465291 | − | 0.885158i | \(-0.654050\pi\) | ||||
−0.465291 | + | 0.885158i | \(0.654050\pi\) | |||||||
\(618\) | 0.494147 | 0.0198775 | ||||||||
\(619\) | 8.36137 | 0.336072 | 0.168036 | − | 0.985781i | \(-0.446258\pi\) | ||||
0.168036 | + | 0.985781i | \(0.446258\pi\) | |||||||
\(620\) | 7.14722 | 0.287039 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.44964 | −0.138318 | ||||||||
\(623\) | 0.976596 | 0.0391265 | ||||||||
\(624\) | 30.2478 | 1.21088 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.50790 | 0.0602677 | ||||||||
\(627\) | 55.4453 | 2.21427 | ||||||||
\(628\) | 21.6211 | 0.862775 | ||||||||
\(629\) | −47.8344 | −1.90728 | ||||||||
\(630\) | 0.191809 | 0.00764186 | ||||||||
\(631\) | 40.9225 | 1.62910 | 0.814550 | − | 0.580093i | \(-0.196984\pi\) | ||||
0.814550 | + | 0.580093i | \(0.196984\pi\) | |||||||
\(632\) | 2.74502 | 0.109191 | ||||||||
\(633\) | −27.5322 | −1.09431 | ||||||||
\(634\) | −2.55715 | −0.101557 | ||||||||
\(635\) | −3.74546 | −0.148634 | ||||||||
\(636\) | 31.9091 | 1.26528 | ||||||||
\(637\) | −20.6044 | −0.816377 | ||||||||
\(638\) | 5.86731 | 0.232289 | ||||||||
\(639\) | −23.1409 | −0.915440 | ||||||||
\(640\) | 3.56707 | 0.141001 | ||||||||
\(641\) | 32.1256 | 1.26888 | 0.634442 | − | 0.772970i | \(-0.281230\pi\) | ||||
0.634442 | + | 0.772970i | \(0.281230\pi\) | |||||||
\(642\) | 3.56375 | 0.140650 | ||||||||
\(643\) | 0.111851 | 0.00441097 | 0.00220548 | − | 0.999998i | \(-0.499298\pi\) | ||||
0.00220548 | + | 0.999998i | \(0.499298\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.3533 | 0.525785 | ||||||||
\(646\) | −2.80045 | −0.110182 | ||||||||
\(647\) | 19.8482 | 0.780313 | 0.390157 | − | 0.920748i | \(-0.372421\pi\) | ||||
0.390157 | + | 0.920748i | \(0.372421\pi\) | |||||||
\(648\) | 3.48984 | 0.137094 | ||||||||
\(649\) | 33.0876 | 1.29880 | ||||||||
\(650\) | 0.345862 | 0.0135658 | ||||||||
\(651\) | −4.55389 | −0.178481 | ||||||||
\(652\) | 38.2100 | 1.49642 | ||||||||
\(653\) | −1.34328 | −0.0525666 | −0.0262833 | − | 0.999655i | \(-0.508367\pi\) | ||||
−0.0262833 | + | 0.999655i | \(0.508367\pi\) | |||||||
\(654\) | −0.676429 | −0.0264505 | ||||||||
\(655\) | −1.51981 | −0.0593837 | ||||||||
\(656\) | 11.9855 | 0.467956 | ||||||||
\(657\) | −11.1266 | −0.434088 | ||||||||
\(658\) | 0.267838 | 0.0104414 | ||||||||
\(659\) | −23.6269 | −0.920375 | −0.460187 | − | 0.887822i | \(-0.652218\pi\) | ||||
−0.460187 | + | 0.887822i | \(0.652218\pi\) | |||||||
\(660\) | −31.1115 | −1.21102 | ||||||||
\(661\) | 24.1333 | 0.938676 | 0.469338 | − | 0.883019i | \(-0.344493\pi\) | ||||
0.469338 | + | 0.883019i | \(0.344493\pi\) | |||||||
\(662\) | 1.96266 | 0.0762811 | ||||||||
\(663\) | 53.8208 | 2.09023 | ||||||||
\(664\) | −1.59725 | −0.0619852 | ||||||||
\(665\) | −1.77560 | −0.0688549 | ||||||||
\(666\) | −2.62149 | −0.101581 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 1.57450 | 0.0609192 | ||||||||
\(669\) | −2.68289 | −0.103726 | ||||||||
\(670\) | 1.46154 | 0.0564643 | ||||||||
\(671\) | 14.5679 | 0.562387 | ||||||||
\(672\) | −1.70645 | −0.0658276 | ||||||||
\(673\) | 16.5575 | 0.638247 | 0.319123 | − | 0.947713i | \(-0.396612\pi\) | ||||
0.319123 | + | 0.947713i | \(0.396612\pi\) | |||||||
\(674\) | −0.349614 | −0.0134666 | ||||||||
\(675\) | 0.952279 | 0.0366532 | ||||||||
\(676\) | 7.30957 | 0.281137 | ||||||||
\(677\) | 37.4176 | 1.43808 | 0.719038 | − | 0.694971i | \(-0.244583\pi\) | ||||
0.719038 | + | 0.694971i | \(0.244583\pi\) | |||||||
\(678\) | 2.77672 | 0.106639 | ||||||||
\(679\) | 6.71977 | 0.257881 | ||||||||
\(680\) | 3.15294 | 0.120910 | ||||||||
\(681\) | −9.79209 | −0.375234 | ||||||||
\(682\) | −2.52601 | −0.0967260 | ||||||||
\(683\) | −42.7978 | −1.63761 | −0.818806 | − | 0.574070i | \(-0.805364\pi\) | ||||
−0.818806 | + | 0.574070i | \(0.805364\pi\) | |||||||
\(684\) | 23.7660 | 0.908714 | ||||||||
\(685\) | 9.21062 | 0.351920 | ||||||||
\(686\) | 0.780881 | 0.0298142 | ||||||||
\(687\) | 21.1435 | 0.806676 | ||||||||
\(688\) | −20.7450 | −0.790896 | ||||||||
\(689\) | −19.4139 | −0.739612 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.3417 | −0.849917 | −0.424959 | − | 0.905213i | \(-0.639711\pi\) | ||||
−0.424959 | + | 0.905213i | \(0.639711\pi\) | |||||||
\(692\) | −17.1872 | −0.653361 | ||||||||
\(693\) | 10.4975 | 0.398768 | ||||||||
\(694\) | −1.12250 | −0.0426095 | ||||||||
\(695\) | −15.2045 | −0.576741 | ||||||||
\(696\) | 9.52883 | 0.361189 | ||||||||
\(697\) | 21.3262 | 0.807787 | ||||||||
\(698\) | −1.96804 | −0.0744915 | ||||||||
\(699\) | −34.2686 | −1.29616 | ||||||||
\(700\) | 0.996329 | 0.0376577 | ||||||||
\(701\) | 7.26364 | 0.274344 | 0.137172 | − | 0.990547i | \(-0.456199\pi\) | ||||
0.137172 | + | 0.990547i | \(0.456199\pi\) | |||||||
\(702\) | 0.329357 | 0.0124308 | ||||||||
\(703\) | 24.2675 | 0.915265 | ||||||||
\(704\) | 47.6989 | 1.79772 | ||||||||
\(705\) | 11.9085 | 0.448501 | ||||||||
\(706\) | 2.82194 | 0.106205 | ||||||||
\(707\) | −8.45847 | −0.318113 | ||||||||
\(708\) | 26.7815 | 1.00651 | ||||||||
\(709\) | 0.612928 | 0.0230190 | 0.0115095 | − | 0.999934i | \(-0.496336\pi\) | ||||
0.0115095 | + | 0.999934i | \(0.496336\pi\) | |||||||
\(710\) | 0.776236 | 0.0291316 | ||||||||
\(711\) | −20.5243 | −0.769720 | ||||||||
\(712\) | 0.879769 | 0.0329707 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −1.00122 | −0.0374698 | ||||||||
\(715\) | 18.9287 | 0.707894 | ||||||||
\(716\) | −16.3054 | −0.609360 | ||||||||
\(717\) | −6.12886 | −0.228886 | ||||||||
\(718\) | −0.651177 | −0.0243017 | ||||||||
\(719\) | 31.8816 | 1.18898 | 0.594492 | − | 0.804101i | \(-0.297353\pi\) | ||||
0.594492 | + | 0.804101i | \(0.297353\pi\) | |||||||
\(720\) | −13.2489 | −0.493758 | ||||||||
\(721\) | −0.866074 | −0.0322543 | ||||||||
\(722\) | −0.731608 | −0.0272276 | ||||||||
\(723\) | 40.8099 | 1.51774 | ||||||||
\(724\) | −33.4725 | −1.24400 | ||||||||
\(725\) | −8.35422 | −0.310268 | ||||||||
\(726\) | 7.84888 | 0.291299 | ||||||||
\(727\) | 6.14210 | 0.227798 | 0.113899 | − | 0.993492i | \(-0.463666\pi\) | ||||
0.113899 | + | 0.993492i | \(0.463666\pi\) | |||||||
\(728\) | 0.691410 | 0.0256254 | ||||||||
\(729\) | −33.3075 | −1.23361 | ||||||||
\(730\) | 0.373228 | 0.0138138 | ||||||||
\(731\) | −36.9122 | −1.36525 | ||||||||
\(732\) | 11.7914 | 0.435824 | ||||||||
\(733\) | 13.2938 | 0.491017 | 0.245508 | − | 0.969394i | \(-0.421045\pi\) | ||||
0.245508 | + | 0.969394i | \(0.421045\pi\) | |||||||
\(734\) | 0.848646 | 0.0313241 | ||||||||
\(735\) | 17.0422 | 0.628612 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 79.9889 | 2.94643 | ||||||||
\(738\) | 1.16875 | 0.0430222 | ||||||||
\(739\) | −15.7842 | −0.580631 | −0.290316 | − | 0.956931i | \(-0.593760\pi\) | ||||
−0.290316 | + | 0.956931i | \(0.593760\pi\) | |||||||
\(740\) | −13.6170 | −0.500571 | ||||||||
\(741\) | −27.3045 | −1.00306 | ||||||||
\(742\) | 0.361155 | 0.0132584 | ||||||||
\(743\) | 21.2530 | 0.779695 | 0.389848 | − | 0.920879i | \(-0.372528\pi\) | ||||
0.389848 | + | 0.920879i | \(0.372528\pi\) | |||||||
\(744\) | −4.10238 | −0.150401 | ||||||||
\(745\) | −5.57800 | −0.204362 | ||||||||
\(746\) | −2.26339 | −0.0828688 | ||||||||
\(747\) | 11.9425 | 0.436952 | ||||||||
\(748\) | 86.0010 | 3.14451 | ||||||||
\(749\) | −6.24606 | −0.228226 | ||||||||
\(750\) | −0.286068 | −0.0104457 | ||||||||
\(751\) | 32.2731 | 1.17766 | 0.588831 | − | 0.808256i | \(-0.299588\pi\) | ||||
0.588831 | + | 0.808256i | \(0.299588\pi\) | |||||||
\(752\) | −18.5005 | −0.674643 | ||||||||
\(753\) | −45.2938 | −1.65060 | ||||||||
\(754\) | −2.88941 | −0.105226 | ||||||||
\(755\) | 18.0280 | 0.656108 | ||||||||
\(756\) | 0.948783 | 0.0345069 | ||||||||
\(757\) | −41.1345 | −1.49506 | −0.747529 | − | 0.664230i | \(-0.768760\pi\) | ||||
−0.747529 | + | 0.664230i | \(0.768760\pi\) | |||||||
\(758\) | −1.00645 | −0.0365558 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.59956 | −0.0580220 | ||||||||
\(761\) | 28.6007 | 1.03678 | 0.518388 | − | 0.855145i | \(-0.326532\pi\) | ||||
0.518388 | + | 0.855145i | \(0.326532\pi\) | |||||||
\(762\) | 1.07145 | 0.0388147 | ||||||||
\(763\) | 1.18555 | 0.0429199 | ||||||||
\(764\) | −27.6568 | −1.00059 | ||||||||
\(765\) | −23.5742 | −0.852327 | ||||||||
\(766\) | −0.610088 | −0.0220434 | ||||||||
\(767\) | −16.2943 | −0.588352 | ||||||||
\(768\) | 37.8371 | 1.36533 | ||||||||
\(769\) | −11.2292 | −0.404934 | −0.202467 | − | 0.979289i | \(-0.564896\pi\) | ||||
−0.202467 | + | 0.979289i | \(0.564896\pi\) | |||||||
\(770\) | −0.352128 | −0.0126898 | ||||||||
\(771\) | −40.7203 | −1.46651 | ||||||||
\(772\) | −53.3751 | −1.92101 | ||||||||
\(773\) | 45.4663 | 1.63531 | 0.817654 | − | 0.575710i | \(-0.195274\pi\) | ||||
0.817654 | + | 0.575710i | \(0.195274\pi\) | |||||||
\(774\) | −2.02291 | −0.0727121 | ||||||||
\(775\) | 3.59669 | 0.129197 | ||||||||
\(776\) | 6.05353 | 0.217309 | ||||||||
\(777\) | 8.67614 | 0.311255 | ||||||||
\(778\) | 0.543030 | 0.0194686 | ||||||||
\(779\) | −10.8193 | −0.387640 | ||||||||
\(780\) | 15.3212 | 0.548585 | ||||||||
\(781\) | 42.4827 | 1.52015 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.95555 | −0.284308 | ||||||||
\(784\) | −26.4760 | −0.945570 | ||||||||
\(785\) | 10.8804 | 0.388336 | ||||||||
\(786\) | 0.434767 | 0.0155076 | ||||||||
\(787\) | −10.3696 | −0.369637 | −0.184818 | − | 0.982773i | \(-0.559170\pi\) | ||||
−0.184818 | + | 0.982773i | \(0.559170\pi\) | |||||||
\(788\) | −45.4828 | −1.62026 | ||||||||
\(789\) | 26.1241 | 0.930041 | ||||||||
\(790\) | 0.688464 | 0.0244945 | ||||||||
\(791\) | −4.86666 | −0.173038 | ||||||||
\(792\) | 9.45673 | 0.336030 | ||||||||
\(793\) | −7.17409 | −0.254759 | ||||||||
\(794\) | −3.30498 | −0.117290 | ||||||||
\(795\) | 16.0576 | 0.569503 | ||||||||
\(796\) | −52.5858 | −1.86385 | ||||||||
\(797\) | −23.5681 | −0.834826 | −0.417413 | − | 0.908717i | \(-0.637063\pi\) | ||||
−0.417413 | + | 0.908717i | \(0.637063\pi\) | |||||||
\(798\) | 0.507943 | 0.0179810 | ||||||||
\(799\) | −32.9184 | −1.16457 | ||||||||
\(800\) | 1.34776 | 0.0476506 | ||||||||
\(801\) | −6.57795 | −0.232420 | ||||||||
\(802\) | 1.51703 | 0.0535683 | ||||||||
\(803\) | 20.4264 | 0.720833 | ||||||||
\(804\) | 64.7441 | 2.28335 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.24396 | 0.0438165 | ||||||||
\(807\) | 37.0849 | 1.30545 | ||||||||
\(808\) | −7.61983 | −0.268065 | ||||||||
\(809\) | 34.1876 | 1.20197 | 0.600986 | − | 0.799260i | \(-0.294775\pi\) | ||||
0.600986 | + | 0.799260i | \(0.294775\pi\) | |||||||
\(810\) | 0.875267 | 0.0307538 | ||||||||
\(811\) | −23.2655 | −0.816964 | −0.408482 | − | 0.912766i | \(-0.633942\pi\) | ||||
−0.408482 | + | 0.912766i | \(0.633942\pi\) | |||||||
\(812\) | −8.32355 | −0.292099 | ||||||||
\(813\) | −27.6299 | −0.969023 | ||||||||
\(814\) | 4.81260 | 0.168682 | ||||||||
\(815\) | 19.2284 | 0.673541 | ||||||||
\(816\) | 69.1579 | 2.42101 | ||||||||
\(817\) | 18.7264 | 0.655153 | ||||||||
\(818\) | 0.217503 | 0.00760480 | ||||||||
\(819\) | −5.16960 | −0.180641 | ||||||||
\(820\) | 6.07092 | 0.212006 | ||||||||
\(821\) | −6.82939 | −0.238347 | −0.119174 | − | 0.992873i | \(-0.538025\pi\) | ||||
−0.119174 | + | 0.992873i | \(0.538025\pi\) | |||||||
\(822\) | −2.63486 | −0.0919014 | ||||||||
\(823\) | 32.4070 | 1.12964 | 0.564819 | − | 0.825215i | \(-0.308946\pi\) | ||||
0.564819 | + | 0.825215i | \(0.308946\pi\) | |||||||
\(824\) | −0.780205 | −0.0271797 | ||||||||
\(825\) | −15.6562 | −0.545080 | ||||||||
\(826\) | 0.303120 | 0.0105469 | ||||||||
\(827\) | 17.1191 | 0.595290 | 0.297645 | − | 0.954677i | \(-0.403799\pi\) | ||||
0.297645 | + | 0.954677i | \(0.403799\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.0835 | 0.940647 | 0.470324 | − | 0.882494i | \(-0.344137\pi\) | ||||
0.470324 | + | 0.882494i | \(0.344137\pi\) | |||||||
\(830\) | −0.400597 | −0.0139049 | ||||||||
\(831\) | −66.1583 | −2.29501 | ||||||||
\(832\) | −23.4898 | −0.814361 | ||||||||
\(833\) | −47.1095 | −1.63225 | ||||||||
\(834\) | 4.34953 | 0.150612 | ||||||||
\(835\) | 0.792333 | 0.0274198 | ||||||||
\(836\) | −43.6302 | −1.50898 | ||||||||
\(837\) | 3.42505 | 0.118387 | ||||||||
\(838\) | 0.243447 | 0.00840975 | ||||||||
\(839\) | 5.81736 | 0.200838 | 0.100419 | − | 0.994945i | \(-0.467982\pi\) | ||||
0.100419 | + | 0.994945i | \(0.467982\pi\) | |||||||
\(840\) | −0.571876 | −0.0197316 | ||||||||
\(841\) | 40.7930 | 1.40666 | ||||||||
\(842\) | 0.223148 | 0.00769019 | ||||||||
\(843\) | 34.3631 | 1.18353 | ||||||||
\(844\) | 21.6652 | 0.745748 | ||||||||
\(845\) | 3.67839 | 0.126540 | ||||||||
\(846\) | −1.80404 | −0.0620243 | ||||||||
\(847\) | −13.7565 | −0.472678 | ||||||||
\(848\) | −24.9463 | −0.856658 | ||||||||
\(849\) | −41.2762 | −1.41659 | ||||||||
\(850\) | 0.790771 | 0.0271232 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 34.3861 | 1.17805 | ||||||||
\(853\) | −24.5624 | −0.841000 | −0.420500 | − | 0.907292i | \(-0.638145\pi\) | ||||
−0.420500 | + | 0.907292i | \(0.638145\pi\) | |||||||
\(854\) | 0.133459 | 0.00456686 | ||||||||
\(855\) | 11.9597 | 0.409014 | ||||||||
\(856\) | −5.62678 | −0.192319 | ||||||||
\(857\) | 14.0873 | 0.481212 | 0.240606 | − | 0.970623i | \(-0.422654\pi\) | ||||
0.240606 | + | 0.970623i | \(0.422654\pi\) | |||||||
\(858\) | −5.41489 | −0.184861 | ||||||||
\(859\) | −23.7290 | −0.809623 | −0.404811 | − | 0.914400i | \(-0.632663\pi\) | ||||
−0.404811 | + | 0.914400i | \(0.632663\pi\) | |||||||
\(860\) | −10.5078 | −0.358312 | ||||||||
\(861\) | −3.86812 | −0.131825 | ||||||||
\(862\) | −0.650491 | −0.0221558 | ||||||||
\(863\) | −0.236102 | −0.00803701 | −0.00401851 | − | 0.999992i | \(-0.501279\pi\) | ||||
−0.00401851 | + | 0.999992i | \(0.501279\pi\) | |||||||
\(864\) | 1.28345 | 0.0436637 | ||||||||
\(865\) | −8.64911 | −0.294079 | ||||||||
\(866\) | 1.68121 | 0.0571297 | ||||||||
\(867\) | 80.1247 | 2.72118 | ||||||||
\(868\) | 3.58348 | 0.121631 | ||||||||
\(869\) | 37.6790 | 1.27817 | ||||||||
\(870\) | 2.38987 | 0.0810243 | ||||||||
\(871\) | −39.3912 | −1.33472 | ||||||||
\(872\) | 1.06801 | 0.0361674 | ||||||||
\(873\) | −45.2616 | −1.53187 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.501381 | 0.0169498 | ||||||||
\(876\) | 16.5334 | 0.558613 | ||||||||
\(877\) | 17.8626 | 0.603176 | 0.301588 | − | 0.953438i | \(-0.402483\pi\) | ||||
0.301588 | + | 0.953438i | \(0.402483\pi\) | |||||||
\(878\) | −3.67310 | −0.123961 | ||||||||
\(879\) | 56.3467 | 1.90053 | ||||||||
\(880\) | 24.3227 | 0.819920 | ||||||||
\(881\) | 6.19555 | 0.208733 | 0.104367 | − | 0.994539i | \(-0.466718\pi\) | ||||
0.104367 | + | 0.994539i | \(0.466718\pi\) | |||||||
\(882\) | −2.58176 | −0.0869324 | ||||||||
\(883\) | 16.9839 | 0.571554 | 0.285777 | − | 0.958296i | \(-0.407748\pi\) | ||||
0.285777 | + | 0.958296i | \(0.407748\pi\) | |||||||
\(884\) | −42.3519 | −1.42445 | ||||||||
\(885\) | 13.4772 | 0.453032 | ||||||||
\(886\) | −2.63967 | −0.0886816 | ||||||||
\(887\) | −1.86877 | −0.0627471 | −0.0313735 | − | 0.999508i | \(-0.509988\pi\) | ||||
−0.0313735 | + | 0.999508i | \(0.509988\pi\) | |||||||
\(888\) | 7.81593 | 0.262285 | ||||||||
\(889\) | −1.87790 | −0.0629828 | ||||||||
\(890\) | 0.220650 | 0.00739621 | ||||||||
\(891\) | 47.9026 | 1.60480 | ||||||||
\(892\) | 2.11118 | 0.0706876 | ||||||||
\(893\) | 16.7003 | 0.558853 | ||||||||
\(894\) | 1.59569 | 0.0533677 | ||||||||
\(895\) | −8.20533 | −0.274274 | ||||||||
\(896\) | 1.78846 | 0.0597484 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.930994 | −0.0310677 | ||||||||
\(899\) | −30.0475 | −1.00214 | ||||||||
\(900\) | −6.71086 | −0.223695 | ||||||||
\(901\) | −44.3876 | −1.47876 | ||||||||
\(902\) | −2.14562 | −0.0714414 | ||||||||
\(903\) | 6.69508 | 0.222798 | ||||||||
\(904\) | −4.38414 | −0.145814 | ||||||||
\(905\) | −16.8443 | −0.559925 | ||||||||
\(906\) | −5.15724 | −0.171338 | ||||||||
\(907\) | −14.9750 | −0.497236 | −0.248618 | − | 0.968602i | \(-0.579976\pi\) | ||||
−0.248618 | + | 0.968602i | \(0.579976\pi\) | |||||||
\(908\) | 7.70545 | 0.255714 | ||||||||
\(909\) | 56.9727 | 1.88967 | ||||||||
\(910\) | 0.173409 | 0.00574845 | ||||||||
\(911\) | 6.38511 | 0.211548 | 0.105774 | − | 0.994390i | \(-0.466268\pi\) | ||||
0.105774 | + | 0.994390i | \(0.466268\pi\) | |||||||
\(912\) | −35.0854 | −1.16179 | ||||||||
\(913\) | −21.9243 | −0.725588 | ||||||||
\(914\) | −3.10228 | −0.102614 | ||||||||
\(915\) | 5.93379 | 0.196165 | ||||||||
\(916\) | −16.6380 | −0.549734 | ||||||||
\(917\) | −0.762002 | −0.0251635 | ||||||||
\(918\) | 0.753035 | 0.0248539 | ||||||||
\(919\) | −59.7346 | −1.97046 | −0.985231 | − | 0.171231i | \(-0.945226\pi\) | ||||
−0.985231 | + | 0.171231i | \(0.945226\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.9205 | −0.985914 | ||||||||
\(922\) | −1.96274 | −0.0646395 | ||||||||
\(923\) | −20.9210 | −0.688623 | ||||||||
\(924\) | −15.5987 | −0.513161 | ||||||||
\(925\) | −6.85247 | −0.225308 | ||||||||
\(926\) | 3.10008 | 0.101875 | ||||||||
\(927\) | 5.83352 | 0.191598 | ||||||||
\(928\) | −11.2595 | −0.369611 | ||||||||
\(929\) | −17.1029 | −0.561127 | −0.280564 | − | 0.959835i | \(-0.590521\pi\) | ||||
−0.280564 | + | 0.959835i | \(0.590521\pi\) | |||||||
\(930\) | −1.02890 | −0.0337388 | ||||||||
\(931\) | 23.8997 | 0.783281 | ||||||||
\(932\) | 26.9662 | 0.883306 | ||||||||
\(933\) | −76.9003 | −2.51760 | ||||||||
\(934\) | 2.92959 | 0.0958592 | ||||||||
\(935\) | 43.2782 | 1.41535 | ||||||||
\(936\) | −4.65705 | −0.152220 | ||||||||
\(937\) | −24.1459 | −0.788813 | −0.394407 | − | 0.918936i | \(-0.629050\pi\) | ||||
−0.394407 | + | 0.918936i | \(0.629050\pi\) | |||||||
\(938\) | 0.732790 | 0.0239264 | ||||||||
\(939\) | 33.6145 | 1.09697 | ||||||||
\(940\) | −9.37088 | −0.305644 | ||||||||
\(941\) | 33.0474 | 1.07732 | 0.538658 | − | 0.842525i | \(-0.318932\pi\) | ||||
0.538658 | + | 0.842525i | \(0.318932\pi\) | |||||||
\(942\) | −3.11252 | −0.101411 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −20.9376 | −0.681460 | ||||||||
\(945\) | 0.477455 | 0.0155316 | ||||||||
\(946\) | 3.71372 | 0.120744 | ||||||||
\(947\) | 48.3069 | 1.56976 | 0.784882 | − | 0.619645i | \(-0.212724\pi\) | ||||
0.784882 | + | 0.619645i | \(0.212724\pi\) | |||||||
\(948\) | 30.4979 | 0.990526 | ||||||||
\(949\) | −10.0592 | −0.326535 | ||||||||
\(950\) | −0.401176 | −0.0130159 | ||||||||
\(951\) | −57.0047 | −1.84850 | ||||||||
\(952\) | 1.58082 | 0.0512348 | ||||||||
\(953\) | −16.2320 | −0.525805 | −0.262902 | − | 0.964822i | \(-0.584680\pi\) | ||||
−0.262902 | + | 0.964822i | \(0.584680\pi\) | |||||||
\(954\) | −2.43259 | −0.0787581 | ||||||||
\(955\) | −13.9177 | −0.450366 | ||||||||
\(956\) | 4.82283 | 0.155982 | ||||||||
\(957\) | 130.796 | 4.22802 | ||||||||
\(958\) | −1.09286 | −0.0353087 | ||||||||
\(959\) | 4.61803 | 0.149124 | ||||||||
\(960\) | 19.4287 | 0.627060 | ||||||||
\(961\) | −18.0638 | −0.582705 | ||||||||
\(962\) | −2.37001 | −0.0764122 | ||||||||
\(963\) | 42.0708 | 1.35571 | ||||||||
\(964\) | −32.1136 | −1.03431 | ||||||||
\(965\) | −26.8599 | −0.864650 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.7729 | −0.828799 | −0.414400 | − | 0.910095i | \(-0.636008\pi\) | ||||
−0.414400 | + | 0.910095i | \(0.636008\pi\) | |||||||
\(968\) | −12.3926 | −0.398312 | ||||||||
\(969\) | −62.4284 | −2.00549 | ||||||||
\(970\) | 1.51825 | 0.0487481 | ||||||||
\(971\) | −24.4811 | −0.785636 | −0.392818 | − | 0.919616i | \(-0.628500\pi\) | ||||
−0.392818 | + | 0.919616i | \(0.628500\pi\) | |||||||
\(972\) | 44.4500 | 1.42573 | ||||||||
\(973\) | −7.62327 | −0.244391 | ||||||||
\(974\) | 0.450215 | 0.0144258 | ||||||||
\(975\) | 7.71005 | 0.246919 | ||||||||
\(976\) | −9.21845 | −0.295075 | ||||||||
\(977\) | −4.35357 | −0.139283 | −0.0696416 | − | 0.997572i | \(-0.522186\pi\) | ||||
−0.0696416 | + | 0.997572i | \(0.522186\pi\) | |||||||
\(978\) | −5.50062 | −0.175891 | ||||||||
\(979\) | 12.0760 | 0.385950 | ||||||||
\(980\) | −13.4106 | −0.428387 | ||||||||
\(981\) | −7.98540 | −0.254954 | ||||||||
\(982\) | 2.85881 | 0.0912281 | ||||||||
\(983\) | 57.7581 | 1.84220 | 0.921099 | − | 0.389328i | \(-0.127293\pi\) | ||||
0.921099 | + | 0.389328i | \(0.127293\pi\) | |||||||
\(984\) | −3.48461 | −0.111085 | ||||||||
\(985\) | −22.8883 | −0.729281 | ||||||||
\(986\) | −6.60628 | −0.210387 | ||||||||
\(987\) | 5.97071 | 0.190050 | ||||||||
\(988\) | 21.4861 | 0.683564 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 2.37179 | 0.0753805 | ||||||||
\(991\) | −4.42302 | −0.140502 | −0.0702509 | − | 0.997529i | \(-0.522380\pi\) | ||||
−0.0702509 | + | 0.997529i | \(0.522380\pi\) | |||||||
\(992\) | 4.84748 | 0.153908 | ||||||||
\(993\) | 43.7522 | 1.38843 | ||||||||
\(994\) | 0.389190 | 0.0123444 | ||||||||
\(995\) | −26.4627 | −0.838923 | ||||||||
\(996\) | −17.7458 | −0.562298 | ||||||||
\(997\) | −11.6089 | −0.367657 | −0.183829 | − | 0.982958i | \(-0.558849\pi\) | ||||
−0.183829 | + | 0.982958i | \(0.558849\pi\) | |||||||
\(998\) | −1.59070 | −0.0503526 | ||||||||
\(999\) | −6.52546 | −0.206457 |
(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 | 2645.2.a.v.1.8 | ✓ | 16 | |
23.22 | odd | 2 | 2645.2.a.w.1.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2645.2.a.v.1.8 | ✓ | 16 | 1.1 | even | 1 | trivial | |
2645.2.a.w.1.8 | yes | 16 | 23.22 | odd | 2 |