Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8619,2,Mod(1,8619)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8619, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8619.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8619 = 3 \cdot 13^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8619.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: | \(68.8230615021\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 51) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8619.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.56155 | −1.10418 | −0.552092 | − | 0.833783i | \(-0.686170\pi\) | ||||
−0.552092 | + | 0.833783i | \(0.686170\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.438447 | 0.219224 | ||||||||
\(5\) | 0.561553 | 0.251134 | 0.125567 | − | 0.992085i | \(-0.459925\pi\) | ||||
0.125567 | + | 0.992085i | \(0.459925\pi\) | |||||||
\(6\) | 1.56155 | 0.637501 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 2.43845 | 0.862121 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.876894 | −0.277298 | ||||||||
\(11\) | 2.56155 | 0.772337 | 0.386169 | − | 0.922428i | \(-0.373798\pi\) | ||||
0.386169 | + | 0.922428i | \(0.373798\pi\) | |||||||
\(12\) | −0.438447 | −0.126569 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.561553 | −0.144992 | ||||||||
\(16\) | −4.68466 | −1.17116 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.56155 | −0.368062 | ||||||||
\(19\) | −7.68466 | −1.76298 | −0.881491 | − | 0.472201i | \(-0.843460\pi\) | ||||
−0.881491 | + | 0.472201i | \(0.843460\pi\) | |||||||
\(20\) | 0.246211 | 0.0550545 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.00000 | −0.852803 | ||||||||
\(23\) | −6.56155 | −1.36818 | −0.684089 | − | 0.729398i | \(-0.739800\pi\) | ||||
−0.684089 | + | 0.729398i | \(0.739800\pi\) | |||||||
\(24\) | −2.43845 | −0.497746 | ||||||||
\(25\) | −4.68466 | −0.936932 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.24621 | 1.53128 | 0.765641 | − | 0.643268i | \(-0.222422\pi\) | ||||
0.765641 | + | 0.643268i | \(0.222422\pi\) | |||||||
\(30\) | 0.876894 | 0.160098 | ||||||||
\(31\) | 5.12311 | 0.920137 | 0.460068 | − | 0.887883i | \(-0.347825\pi\) | ||||
0.460068 | + | 0.887883i | \(0.347825\pi\) | |||||||
\(32\) | 2.43845 | 0.431061 | ||||||||
\(33\) | −2.56155 | −0.445909 | ||||||||
\(34\) | −1.56155 | −0.267804 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.438447 | 0.0730745 | ||||||||
\(37\) | −3.12311 | −0.513435 | −0.256718 | − | 0.966486i | \(-0.582641\pi\) | ||||
−0.256718 | + | 0.966486i | \(0.582641\pi\) | |||||||
\(38\) | 12.0000 | 1.94666 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.36932 | 0.216508 | ||||||||
\(41\) | −0.561553 | −0.0876998 | −0.0438499 | − | 0.999038i | \(-0.513962\pi\) | ||||
−0.0438499 | + | 0.999038i | \(0.513962\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.68466 | −1.17190 | −0.585950 | − | 0.810347i | \(-0.699278\pi\) | ||||
−0.585950 | + | 0.810347i | \(0.699278\pi\) | |||||||
\(44\) | 1.12311 | 0.169315 | ||||||||
\(45\) | 0.561553 | 0.0837114 | ||||||||
\(46\) | 10.2462 | 1.51072 | ||||||||
\(47\) | 2.87689 | 0.419638 | 0.209819 | − | 0.977740i | \(-0.432712\pi\) | ||||
0.209819 | + | 0.977740i | \(0.432712\pi\) | |||||||
\(48\) | 4.68466 | 0.676172 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 7.31534 | 1.03455 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.24621 | −0.583262 | −0.291631 | − | 0.956531i | \(-0.594198\pi\) | ||||
−0.291631 | + | 0.956531i | \(0.594198\pi\) | |||||||
\(54\) | 1.56155 | 0.212500 | ||||||||
\(55\) | 1.43845 | 0.193960 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.68466 | 1.01786 | ||||||||
\(58\) | −12.8769 | −1.69082 | ||||||||
\(59\) | 1.12311 | 0.146216 | 0.0731079 | − | 0.997324i | \(-0.476708\pi\) | ||||
0.0731079 | + | 0.997324i | \(0.476708\pi\) | |||||||
\(60\) | −0.246211 | −0.0317857 | ||||||||
\(61\) | 0.876894 | 0.112275 | 0.0561374 | − | 0.998423i | \(-0.482122\pi\) | ||||
0.0561374 | + | 0.998423i | \(0.482122\pi\) | |||||||
\(62\) | −8.00000 | −1.01600 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.56155 | 0.695194 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.00000 | 0.492366 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0.438447 | 0.0531695 | ||||||||
\(69\) | 6.56155 | 0.789918 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.2462 | −1.21600 | −0.608001 | − | 0.793936i | \(-0.708028\pi\) | ||||
−0.608001 | + | 0.793936i | \(0.708028\pi\) | |||||||
\(72\) | 2.43845 | 0.287374 | ||||||||
\(73\) | −4.24621 | −0.496981 | −0.248491 | − | 0.968634i | \(-0.579935\pi\) | ||||
−0.248491 | + | 0.968634i | \(0.579935\pi\) | |||||||
\(74\) | 4.87689 | 0.566927 | ||||||||
\(75\) | 4.68466 | 0.540938 | ||||||||
\(76\) | −3.36932 | −0.386487 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.3693 | 1.72918 | 0.864592 | − | 0.502475i | \(-0.167577\pi\) | ||||
0.864592 | + | 0.502475i | \(0.167577\pi\) | |||||||
\(80\) | −2.63068 | −0.294119 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.876894 | 0.0968368 | ||||||||
\(83\) | 9.12311 | 1.00139 | 0.500695 | − | 0.865624i | \(-0.333078\pi\) | ||||
0.500695 | + | 0.865624i | \(0.333078\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.561553 | 0.0609090 | ||||||||
\(86\) | 12.0000 | 1.29399 | ||||||||
\(87\) | −8.24621 | −0.884087 | ||||||||
\(88\) | 6.24621 | 0.665848 | ||||||||
\(89\) | −7.12311 | −0.755048 | −0.377524 | − | 0.926000i | \(-0.623224\pi\) | ||||
−0.377524 | + | 0.926000i | \(0.623224\pi\) | |||||||
\(90\) | −0.876894 | −0.0924328 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.87689 | −0.299937 | ||||||||
\(93\) | −5.12311 | −0.531241 | ||||||||
\(94\) | −4.49242 | −0.463358 | ||||||||
\(95\) | −4.31534 | −0.442745 | ||||||||
\(96\) | −2.43845 | −0.248873 | ||||||||
\(97\) | 11.1231 | 1.12938 | 0.564690 | − | 0.825303i | \(-0.308996\pi\) | ||||
0.564690 | + | 0.825303i | \(0.308996\pi\) | |||||||
\(98\) | 10.9309 | 1.10418 | ||||||||
\(99\) | 2.56155 | 0.257446 | ||||||||
\(100\) | −2.05398 | −0.205398 | ||||||||
\(101\) | 19.1231 | 1.90282 | 0.951410 | − | 0.307927i | \(-0.0996352\pi\) | ||||
0.951410 | + | 0.307927i | \(0.0996352\pi\) | |||||||
\(102\) | 1.56155 | 0.154617 | ||||||||
\(103\) | 4.31534 | 0.425203 | 0.212602 | − | 0.977139i | \(-0.431806\pi\) | ||||
0.212602 | + | 0.977139i | \(0.431806\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.63068 | 0.644029 | ||||||||
\(107\) | 7.68466 | 0.742904 | 0.371452 | − | 0.928452i | \(-0.378860\pi\) | ||||
0.371452 | + | 0.928452i | \(0.378860\pi\) | |||||||
\(108\) | −0.438447 | −0.0421896 | ||||||||
\(109\) | 15.1231 | 1.44853 | 0.724265 | − | 0.689521i | \(-0.242179\pi\) | ||||
0.724265 | + | 0.689521i | \(0.242179\pi\) | |||||||
\(110\) | −2.24621 | −0.214168 | ||||||||
\(111\) | 3.12311 | 0.296432 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.56155 | −0.429115 | −0.214557 | − | 0.976711i | \(-0.568831\pi\) | ||||
−0.214557 | + | 0.976711i | \(0.568831\pi\) | |||||||
\(114\) | −12.0000 | −1.12390 | ||||||||
\(115\) | −3.68466 | −0.343596 | ||||||||
\(116\) | 3.61553 | 0.335693 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.75379 | −0.161449 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.36932 | −0.125001 | ||||||||
\(121\) | −4.43845 | −0.403495 | ||||||||
\(122\) | −1.36932 | −0.123972 | ||||||||
\(123\) | 0.561553 | 0.0506335 | ||||||||
\(124\) | 2.24621 | 0.201716 | ||||||||
\(125\) | −5.43845 | −0.486430 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.807764 | −0.0716775 | −0.0358387 | − | 0.999358i | \(-0.511410\pi\) | ||||
−0.0358387 | + | 0.999358i | \(0.511410\pi\) | |||||||
\(128\) | −13.5616 | −1.19868 | ||||||||
\(129\) | 7.68466 | 0.676596 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.5616 | 1.62173 | 0.810865 | − | 0.585233i | \(-0.198997\pi\) | ||||
0.810865 | + | 0.585233i | \(0.198997\pi\) | |||||||
\(132\) | −1.12311 | −0.0977538 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.24621 | 0.539590 | ||||||||
\(135\) | −0.561553 | −0.0483308 | ||||||||
\(136\) | 2.43845 | 0.209095 | ||||||||
\(137\) | 16.2462 | 1.38801 | 0.694004 | − | 0.719971i | \(-0.255845\pi\) | ||||
0.694004 | + | 0.719971i | \(0.255845\pi\) | |||||||
\(138\) | −10.2462 | −0.872215 | ||||||||
\(139\) | −9.12311 | −0.773812 | −0.386906 | − | 0.922119i | \(-0.626456\pi\) | ||||
−0.386906 | + | 0.922119i | \(0.626456\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.87689 | −0.242278 | ||||||||
\(142\) | 16.0000 | 1.34269 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.68466 | −0.390388 | ||||||||
\(145\) | 4.63068 | 0.384557 | ||||||||
\(146\) | 6.63068 | 0.548759 | ||||||||
\(147\) | 7.00000 | 0.577350 | ||||||||
\(148\) | −1.36932 | −0.112557 | ||||||||
\(149\) | 4.24621 | 0.347863 | 0.173932 | − | 0.984758i | \(-0.444353\pi\) | ||||
0.173932 | + | 0.984758i | \(0.444353\pi\) | |||||||
\(150\) | −7.31534 | −0.597295 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | −18.7386 | −1.51990 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.87689 | 0.231078 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.68466 | −0.453685 | −0.226843 | − | 0.973931i | \(-0.572840\pi\) | ||||
−0.226843 | + | 0.973931i | \(0.572840\pi\) | |||||||
\(158\) | −24.0000 | −1.90934 | ||||||||
\(159\) | 4.24621 | 0.336746 | ||||||||
\(160\) | 1.36932 | 0.108254 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.56155 | −0.122687 | ||||||||
\(163\) | 6.87689 | 0.538640 | 0.269320 | − | 0.963051i | \(-0.413201\pi\) | ||||
0.269320 | + | 0.963051i | \(0.413201\pi\) | |||||||
\(164\) | −0.246211 | −0.0192259 | ||||||||
\(165\) | −1.43845 | −0.111983 | ||||||||
\(166\) | −14.2462 | −1.10572 | ||||||||
\(167\) | 0.807764 | 0.0625067 | 0.0312533 | − | 0.999511i | \(-0.490050\pi\) | ||||
0.0312533 | + | 0.999511i | \(0.490050\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.876894 | −0.0672547 | ||||||||
\(171\) | −7.68466 | −0.587661 | ||||||||
\(172\) | −3.36932 | −0.256908 | ||||||||
\(173\) | −18.8078 | −1.42993 | −0.714964 | − | 0.699161i | \(-0.753557\pi\) | ||||
−0.714964 | + | 0.699161i | \(0.753557\pi\) | |||||||
\(174\) | 12.8769 | 0.976195 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.0000 | −0.904534 | ||||||||
\(177\) | −1.12311 | −0.0844178 | ||||||||
\(178\) | 11.1231 | 0.833712 | ||||||||
\(179\) | −9.12311 | −0.681893 | −0.340946 | − | 0.940083i | \(-0.610747\pi\) | ||||
−0.340946 | + | 0.940083i | \(0.610747\pi\) | |||||||
\(180\) | 0.246211 | 0.0183515 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.876894 | −0.0648219 | ||||||||
\(184\) | −16.0000 | −1.17954 | ||||||||
\(185\) | −1.75379 | −0.128941 | ||||||||
\(186\) | 8.00000 | 0.586588 | ||||||||
\(187\) | 2.56155 | 0.187319 | ||||||||
\(188\) | 1.26137 | 0.0919946 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.73863 | 0.488872 | ||||||||
\(191\) | −13.1231 | −0.949555 | −0.474777 | − | 0.880106i | \(-0.657471\pi\) | ||||
−0.474777 | + | 0.880106i | \(0.657471\pi\) | |||||||
\(192\) | −5.56155 | −0.401371 | ||||||||
\(193\) | 24.2462 | 1.74528 | 0.872640 | − | 0.488364i | \(-0.162406\pi\) | ||||
0.872640 | + | 0.488364i | \(0.162406\pi\) | |||||||
\(194\) | −17.3693 | −1.24704 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.06913 | −0.219224 | ||||||||
\(197\) | −19.9309 | −1.42002 | −0.710008 | − | 0.704194i | \(-0.751309\pi\) | ||||
−0.710008 | + | 0.704194i | \(0.751309\pi\) | |||||||
\(198\) | −4.00000 | −0.284268 | ||||||||
\(199\) | 16.0000 | 1.13421 | 0.567105 | − | 0.823646i | \(-0.308063\pi\) | ||||
0.567105 | + | 0.823646i | \(0.308063\pi\) | |||||||
\(200\) | −11.4233 | −0.807749 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | −29.8617 | −2.10106 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.438447 | −0.0306974 | ||||||||
\(205\) | −0.315342 | −0.0220244 | ||||||||
\(206\) | −6.73863 | −0.469503 | ||||||||
\(207\) | −6.56155 | −0.456059 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −19.6847 | −1.36162 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.3693 | −0.782696 | −0.391348 | − | 0.920243i | \(-0.627991\pi\) | ||||
−0.391348 | + | 0.920243i | \(0.627991\pi\) | |||||||
\(212\) | −1.86174 | −0.127865 | ||||||||
\(213\) | 10.2462 | 0.702059 | ||||||||
\(214\) | −12.0000 | −0.820303 | ||||||||
\(215\) | −4.31534 | −0.294304 | ||||||||
\(216\) | −2.43845 | −0.165915 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −23.6155 | −1.59945 | ||||||||
\(219\) | 4.24621 | 0.286932 | ||||||||
\(220\) | 0.630683 | 0.0425206 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.87689 | −0.327316 | ||||||||
\(223\) | −13.9309 | −0.932880 | −0.466440 | − | 0.884553i | \(-0.654464\pi\) | ||||
−0.466440 | + | 0.884553i | \(0.654464\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.68466 | −0.312311 | ||||||||
\(226\) | 7.12311 | 0.473822 | ||||||||
\(227\) | −23.0540 | −1.53015 | −0.765073 | − | 0.643944i | \(-0.777297\pi\) | ||||
−0.765073 | + | 0.643944i | \(0.777297\pi\) | |||||||
\(228\) | 3.36932 | 0.223138 | ||||||||
\(229\) | −6.00000 | −0.396491 | −0.198246 | − | 0.980152i | \(-0.563524\pi\) | ||||
−0.198246 | + | 0.980152i | \(0.563524\pi\) | |||||||
\(230\) | 5.75379 | 0.379394 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 20.1080 | 1.32015 | ||||||||
\(233\) | 0.561553 | 0.0367885 | 0.0183943 | − | 0.999831i | \(-0.494145\pi\) | ||||
0.0183943 | + | 0.999831i | \(0.494145\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.61553 | 0.105385 | ||||||||
\(236\) | 0.492423 | 0.0320540 | ||||||||
\(237\) | −15.3693 | −0.998344 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.2462 | −0.662772 | −0.331386 | − | 0.943495i | \(-0.607516\pi\) | ||||
−0.331386 | + | 0.943495i | \(0.607516\pi\) | |||||||
\(240\) | 2.63068 | 0.169810 | ||||||||
\(241\) | 21.3693 | 1.37652 | 0.688259 | − | 0.725465i | \(-0.258375\pi\) | ||||
0.688259 | + | 0.725465i | \(0.258375\pi\) | |||||||
\(242\) | 6.93087 | 0.445533 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.384472 | 0.0246133 | ||||||||
\(245\) | −3.93087 | −0.251134 | ||||||||
\(246\) | −0.876894 | −0.0559087 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 12.4924 | 0.793270 | ||||||||
\(249\) | −9.12311 | −0.578153 | ||||||||
\(250\) | 8.49242 | 0.537108 | ||||||||
\(251\) | −24.4924 | −1.54595 | −0.772974 | − | 0.634438i | \(-0.781232\pi\) | ||||
−0.772974 | + | 0.634438i | \(0.781232\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.8078 | −1.05670 | ||||||||
\(254\) | 1.26137 | 0.0791452 | ||||||||
\(255\) | −0.561553 | −0.0351658 | ||||||||
\(256\) | 10.0540 | 0.628373 | ||||||||
\(257\) | 9.36932 | 0.584442 | 0.292221 | − | 0.956351i | \(-0.405606\pi\) | ||||
0.292221 | + | 0.956351i | \(0.405606\pi\) | |||||||
\(258\) | −12.0000 | −0.747087 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.24621 | 0.510428 | ||||||||
\(262\) | −28.9848 | −1.79069 | ||||||||
\(263\) | 12.4924 | 0.770316 | 0.385158 | − | 0.922851i | \(-0.374147\pi\) | ||||
0.385158 | + | 0.922851i | \(0.374147\pi\) | |||||||
\(264\) | −6.24621 | −0.384428 | ||||||||
\(265\) | −2.38447 | −0.146477 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.12311 | 0.435927 | ||||||||
\(268\) | −1.75379 | −0.107130 | ||||||||
\(269\) | 20.5616 | 1.25366 | 0.626830 | − | 0.779156i | \(-0.284352\pi\) | ||||
0.626830 | + | 0.779156i | \(0.284352\pi\) | |||||||
\(270\) | 0.876894 | 0.0533661 | ||||||||
\(271\) | 0.807764 | 0.0490682 | 0.0245341 | − | 0.999699i | \(-0.492190\pi\) | ||||
0.0245341 | + | 0.999699i | \(0.492190\pi\) | |||||||
\(272\) | −4.68466 | −0.284049 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −25.3693 | −1.53262 | ||||||||
\(275\) | −12.0000 | −0.723627 | ||||||||
\(276\) | 2.87689 | 0.173169 | ||||||||
\(277\) | 6.00000 | 0.360505 | 0.180253 | − | 0.983620i | \(-0.442309\pi\) | ||||
0.180253 | + | 0.983620i | \(0.442309\pi\) | |||||||
\(278\) | 14.2462 | 0.854431 | ||||||||
\(279\) | 5.12311 | 0.306712 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.1231 | 1.14079 | 0.570394 | − | 0.821371i | \(-0.306790\pi\) | ||||
0.570394 | + | 0.821371i | \(0.306790\pi\) | |||||||
\(282\) | 4.49242 | 0.267520 | ||||||||
\(283\) | −3.36932 | −0.200285 | −0.100143 | − | 0.994973i | \(-0.531930\pi\) | ||||
−0.100143 | + | 0.994973i | \(0.531930\pi\) | |||||||
\(284\) | −4.49242 | −0.266576 | ||||||||
\(285\) | 4.31534 | 0.255619 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.43845 | 0.143687 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −7.23106 | −0.424622 | ||||||||
\(291\) | −11.1231 | −0.652048 | ||||||||
\(292\) | −1.86174 | −0.108950 | ||||||||
\(293\) | 7.12311 | 0.416136 | 0.208068 | − | 0.978114i | \(-0.433282\pi\) | ||||
0.208068 | + | 0.978114i | \(0.433282\pi\) | |||||||
\(294\) | −10.9309 | −0.637501 | ||||||||
\(295\) | 0.630683 | 0.0367198 | ||||||||
\(296\) | −7.61553 | −0.442644 | ||||||||
\(297\) | −2.56155 | −0.148636 | ||||||||
\(298\) | −6.63068 | −0.384105 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.05398 | 0.118586 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12.4924 | 0.718858 | ||||||||
\(303\) | −19.1231 | −1.09859 | ||||||||
\(304\) | 36.0000 | 2.06474 | ||||||||
\(305\) | 0.492423 | 0.0281960 | ||||||||
\(306\) | −1.56155 | −0.0892680 | ||||||||
\(307\) | 0.492423 | 0.0281040 | 0.0140520 | − | 0.999901i | \(-0.495527\pi\) | ||||
0.0140520 | + | 0.999901i | \(0.495527\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.31534 | −0.245491 | ||||||||
\(310\) | −4.49242 | −0.255152 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.61553 | −0.430455 | −0.215228 | − | 0.976564i | \(-0.569049\pi\) | ||||
−0.215228 | + | 0.976564i | \(0.569049\pi\) | |||||||
\(314\) | 8.87689 | 0.500952 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.73863 | 0.379078 | ||||||||
\(317\) | 18.0000 | 1.01098 | 0.505490 | − | 0.862832i | \(-0.331312\pi\) | ||||
0.505490 | + | 0.862832i | \(0.331312\pi\) | |||||||
\(318\) | −6.63068 | −0.371830 | ||||||||
\(319\) | 21.1231 | 1.18267 | ||||||||
\(320\) | 3.12311 | 0.174587 | ||||||||
\(321\) | −7.68466 | −0.428916 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.68466 | −0.427586 | ||||||||
\(324\) | 0.438447 | 0.0243582 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.7386 | −0.594758 | ||||||||
\(327\) | −15.1231 | −0.836310 | ||||||||
\(328\) | −1.36932 | −0.0756079 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.24621 | 0.123650 | ||||||||
\(331\) | 6.06913 | 0.333590 | 0.166795 | − | 0.985992i | \(-0.446658\pi\) | ||||
0.166795 | + | 0.985992i | \(0.446658\pi\) | |||||||
\(332\) | 4.00000 | 0.219529 | ||||||||
\(333\) | −3.12311 | −0.171145 | ||||||||
\(334\) | −1.26137 | −0.0690189 | ||||||||
\(335\) | −2.24621 | −0.122724 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.7386 | 1.78339 | 0.891694 | − | 0.452640i | \(-0.149518\pi\) | ||||
0.891694 | + | 0.452640i | \(0.149518\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.56155 | 0.247750 | ||||||||
\(340\) | 0.246211 | 0.0133527 | ||||||||
\(341\) | 13.1231 | 0.710656 | ||||||||
\(342\) | 12.0000 | 0.648886 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −18.7386 | −1.01032 | ||||||||
\(345\) | 3.68466 | 0.198375 | ||||||||
\(346\) | 29.3693 | 1.57890 | ||||||||
\(347\) | 24.4924 | 1.31482 | 0.657411 | − | 0.753532i | \(-0.271652\pi\) | ||||
0.657411 | + | 0.753532i | \(0.271652\pi\) | |||||||
\(348\) | −3.61553 | −0.193813 | ||||||||
\(349\) | −7.43845 | −0.398171 | −0.199085 | − | 0.979982i | \(-0.563797\pi\) | ||||
−0.199085 | + | 0.979982i | \(0.563797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.24621 | 0.332924 | ||||||||
\(353\) | −22.4924 | −1.19715 | −0.598575 | − | 0.801066i | \(-0.704266\pi\) | ||||
−0.598575 | + | 0.801066i | \(0.704266\pi\) | |||||||
\(354\) | 1.75379 | 0.0932128 | ||||||||
\(355\) | −5.75379 | −0.305379 | ||||||||
\(356\) | −3.12311 | −0.165524 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.2462 | 0.752936 | ||||||||
\(359\) | 2.24621 | 0.118550 | 0.0592752 | − | 0.998242i | \(-0.481121\pi\) | ||||
0.0592752 | + | 0.998242i | \(0.481121\pi\) | |||||||
\(360\) | 1.36932 | 0.0721693 | ||||||||
\(361\) | 40.0540 | 2.10810 | ||||||||
\(362\) | −9.36932 | −0.492440 | ||||||||
\(363\) | 4.43845 | 0.232958 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.38447 | −0.124809 | ||||||||
\(366\) | 1.36932 | 0.0715753 | ||||||||
\(367\) | −18.2462 | −0.952444 | −0.476222 | − | 0.879325i | \(-0.657994\pi\) | ||||
−0.476222 | + | 0.879325i | \(0.657994\pi\) | |||||||
\(368\) | 30.7386 | 1.60236 | ||||||||
\(369\) | −0.561553 | −0.0292333 | ||||||||
\(370\) | 2.73863 | 0.142375 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.24621 | −0.116461 | ||||||||
\(373\) | 16.2462 | 0.841197 | 0.420598 | − | 0.907247i | \(-0.361820\pi\) | ||||
0.420598 | + | 0.907247i | \(0.361820\pi\) | |||||||
\(374\) | −4.00000 | −0.206835 | ||||||||
\(375\) | 5.43845 | 0.280840 | ||||||||
\(376\) | 7.01515 | 0.361779 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000 | 0.616399 | 0.308199 | − | 0.951322i | \(-0.400274\pi\) | ||||
0.308199 | + | 0.951322i | \(0.400274\pi\) | |||||||
\(380\) | −1.89205 | −0.0970601 | ||||||||
\(381\) | 0.807764 | 0.0413830 | ||||||||
\(382\) | 20.4924 | 1.04848 | ||||||||
\(383\) | 10.2462 | 0.523557 | 0.261778 | − | 0.965128i | \(-0.415691\pi\) | ||||
0.261778 | + | 0.965128i | \(0.415691\pi\) | |||||||
\(384\) | 13.5616 | 0.692060 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −37.8617 | −1.92711 | ||||||||
\(387\) | −7.68466 | −0.390633 | ||||||||
\(388\) | 4.87689 | 0.247587 | ||||||||
\(389\) | −21.8617 | −1.10843 | −0.554217 | − | 0.832372i | \(-0.686982\pi\) | ||||
−0.554217 | + | 0.832372i | \(0.686982\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.56155 | −0.331832 | ||||||||
\(392\) | −17.0691 | −0.862121 | ||||||||
\(393\) | −18.5616 | −0.936306 | ||||||||
\(394\) | 31.1231 | 1.56796 | ||||||||
\(395\) | 8.63068 | 0.434257 | ||||||||
\(396\) | 1.12311 | 0.0564382 | ||||||||
\(397\) | −5.36932 | −0.269478 | −0.134739 | − | 0.990881i | \(-0.543020\pi\) | ||||
−0.134739 | + | 0.990881i | \(0.543020\pi\) | |||||||
\(398\) | −24.9848 | −1.25238 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 21.9460 | 1.09730 | ||||||||
\(401\) | 6.17708 | 0.308469 | 0.154234 | − | 0.988034i | \(-0.450709\pi\) | ||||
0.154234 | + | 0.988034i | \(0.450709\pi\) | |||||||
\(402\) | −6.24621 | −0.311533 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 8.38447 | 0.417143 | ||||||||
\(405\) | 0.561553 | 0.0279038 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | −2.43845 | −0.120721 | ||||||||
\(409\) | 2.31534 | 0.114486 | 0.0572431 | − | 0.998360i | \(-0.481769\pi\) | ||||
0.0572431 | + | 0.998360i | \(0.481769\pi\) | |||||||
\(410\) | 0.492423 | 0.0243190 | ||||||||
\(411\) | −16.2462 | −0.801367 | ||||||||
\(412\) | 1.89205 | 0.0932146 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 10.2462 | 0.503574 | ||||||||
\(415\) | 5.12311 | 0.251483 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.12311 | 0.446760 | ||||||||
\(418\) | 30.7386 | 1.50348 | ||||||||
\(419\) | 32.4924 | 1.58736 | 0.793679 | − | 0.608336i | \(-0.208163\pi\) | ||||
0.793679 | + | 0.608336i | \(0.208163\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.5616 | −1.39200 | −0.696002 | − | 0.718039i | \(-0.745040\pi\) | ||||
−0.696002 | + | 0.718039i | \(0.745040\pi\) | |||||||
\(422\) | 17.7538 | 0.864241 | ||||||||
\(423\) | 2.87689 | 0.139879 | ||||||||
\(424\) | −10.3542 | −0.502843 | ||||||||
\(425\) | −4.68466 | −0.227239 | ||||||||
\(426\) | −16.0000 | −0.775203 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.36932 | 0.162862 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.73863 | 0.324966 | ||||||||
\(431\) | 24.0000 | 1.15604 | 0.578020 | − | 0.816023i | \(-0.303826\pi\) | ||||
0.578020 | + | 0.816023i | \(0.303826\pi\) | |||||||
\(432\) | 4.68466 | 0.225391 | ||||||||
\(433\) | 14.3153 | 0.687951 | 0.343976 | − | 0.938979i | \(-0.388226\pi\) | ||||
0.343976 | + | 0.938979i | \(0.388226\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.63068 | −0.222024 | ||||||||
\(436\) | 6.63068 | 0.317552 | ||||||||
\(437\) | 50.4233 | 2.41207 | ||||||||
\(438\) | −6.63068 | −0.316826 | ||||||||
\(439\) | −5.75379 | −0.274613 | −0.137307 | − | 0.990529i | \(-0.543845\pi\) | ||||
−0.137307 | + | 0.990529i | \(0.543845\pi\) | |||||||
\(440\) | 3.50758 | 0.167217 | ||||||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.8769 | −1.08691 | −0.543457 | − | 0.839437i | \(-0.682885\pi\) | ||||
−0.543457 | + | 0.839437i | \(0.682885\pi\) | |||||||
\(444\) | 1.36932 | 0.0649849 | ||||||||
\(445\) | −4.00000 | −0.189618 | ||||||||
\(446\) | 21.7538 | 1.03007 | ||||||||
\(447\) | −4.24621 | −0.200839 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.7386 | 0.601173 | 0.300587 | − | 0.953755i | \(-0.402818\pi\) | ||||
0.300587 | + | 0.953755i | \(0.402818\pi\) | |||||||
\(450\) | 7.31534 | 0.344849 | ||||||||
\(451\) | −1.43845 | −0.0677338 | ||||||||
\(452\) | −2.00000 | −0.0940721 | ||||||||
\(453\) | 8.00000 | 0.375873 | ||||||||
\(454\) | 36.0000 | 1.68956 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 18.7386 | 0.877517 | ||||||||
\(457\) | 6.80776 | 0.318454 | 0.159227 | − | 0.987242i | \(-0.449100\pi\) | ||||
0.159227 | + | 0.987242i | \(0.449100\pi\) | |||||||
\(458\) | 9.36932 | 0.437799 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −1.61553 | −0.0753244 | ||||||||
\(461\) | −8.24621 | −0.384064 | −0.192032 | − | 0.981389i | \(-0.561508\pi\) | ||||
−0.192032 | + | 0.981389i | \(0.561508\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.9848 | −1.16114 | −0.580572 | − | 0.814209i | \(-0.697171\pi\) | ||||
−0.580572 | + | 0.814209i | \(0.697171\pi\) | |||||||
\(464\) | −38.6307 | −1.79338 | ||||||||
\(465\) | −2.87689 | −0.133413 | ||||||||
\(466\) | −0.876894 | −0.0406213 | ||||||||
\(467\) | −3.36932 | −0.155913 | −0.0779567 | − | 0.996957i | \(-0.524840\pi\) | ||||
−0.0779567 | + | 0.996957i | \(0.524840\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.52273 | −0.116365 | ||||||||
\(471\) | 5.68466 | 0.261935 | ||||||||
\(472\) | 2.73863 | 0.126056 | ||||||||
\(473\) | −19.6847 | −0.905102 | ||||||||
\(474\) | 24.0000 | 1.10236 | ||||||||
\(475\) | 36.0000 | 1.65179 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.24621 | −0.194421 | ||||||||
\(478\) | 16.0000 | 0.731823 | ||||||||
\(479\) | 29.3002 | 1.33876 | 0.669380 | − | 0.742920i | \(-0.266560\pi\) | ||||
0.669380 | + | 0.742920i | \(0.266560\pi\) | |||||||
\(480\) | −1.36932 | −0.0625005 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −33.3693 | −1.51993 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.94602 | −0.0884557 | ||||||||
\(485\) | 6.24621 | 0.283626 | ||||||||
\(486\) | 1.56155 | 0.0708335 | ||||||||
\(487\) | 7.36932 | 0.333936 | 0.166968 | − | 0.985962i | \(-0.446602\pi\) | ||||
0.166968 | + | 0.985962i | \(0.446602\pi\) | |||||||
\(488\) | 2.13826 | 0.0967945 | ||||||||
\(489\) | −6.87689 | −0.310984 | ||||||||
\(490\) | 6.13826 | 0.277298 | ||||||||
\(491\) | 3.36932 | 0.152055 | 0.0760276 | − | 0.997106i | \(-0.475776\pi\) | ||||
0.0760276 | + | 0.997106i | \(0.475776\pi\) | |||||||
\(492\) | 0.246211 | 0.0111001 | ||||||||
\(493\) | 8.24621 | 0.371391 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.43845 | 0.0646534 | ||||||||
\(496\) | −24.0000 | −1.07763 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 14.2462 | 0.638388 | ||||||||
\(499\) | 11.3693 | 0.508961 | 0.254480 | − | 0.967078i | \(-0.418096\pi\) | ||||
0.254480 | + | 0.967078i | \(0.418096\pi\) | |||||||
\(500\) | −2.38447 | −0.106637 | ||||||||
\(501\) | −0.807764 | −0.0360882 | ||||||||
\(502\) | 38.2462 | 1.70701 | ||||||||
\(503\) | −25.4384 | −1.13424 | −0.567122 | − | 0.823634i | \(-0.691943\pi\) | ||||
−0.567122 | + | 0.823634i | \(0.691943\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.7386 | 0.477863 | ||||||||
\(506\) | 26.2462 | 1.16679 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.354162 | −0.0157134 | ||||||||
\(509\) | −16.8769 | −0.748055 | −0.374028 | − | 0.927418i | \(-0.622023\pi\) | ||||
−0.374028 | + | 0.927418i | \(0.622023\pi\) | |||||||
\(510\) | 0.876894 | 0.0388295 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11.4233 | 0.504843 | ||||||||
\(513\) | 7.68466 | 0.339286 | ||||||||
\(514\) | −14.6307 | −0.645332 | ||||||||
\(515\) | 2.42329 | 0.106783 | ||||||||
\(516\) | 3.36932 | 0.148326 | ||||||||
\(517\) | 7.36932 | 0.324102 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.8078 | 0.825569 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.4384 | −1.37734 | −0.688672 | − | 0.725073i | \(-0.741806\pi\) | ||||
−0.688672 | + | 0.725073i | \(0.741806\pi\) | |||||||
\(522\) | −12.8769 | −0.563606 | ||||||||
\(523\) | −20.0000 | −0.874539 | −0.437269 | − | 0.899331i | \(-0.644054\pi\) | ||||
−0.437269 | + | 0.899331i | \(0.644054\pi\) | |||||||
\(524\) | 8.13826 | 0.355522 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.5076 | −0.850571 | ||||||||
\(527\) | 5.12311 | 0.223166 | ||||||||
\(528\) | 12.0000 | 0.522233 | ||||||||
\(529\) | 20.0540 | 0.871912 | ||||||||
\(530\) | 3.72348 | 0.161738 | ||||||||
\(531\) | 1.12311 | 0.0487386 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −11.1231 | −0.481344 | ||||||||
\(535\) | 4.31534 | 0.186568 | ||||||||
\(536\) | −9.75379 | −0.421300 | ||||||||
\(537\) | 9.12311 | 0.393691 | ||||||||
\(538\) | −32.1080 | −1.38427 | ||||||||
\(539\) | −17.9309 | −0.772337 | ||||||||
\(540\) | −0.246211 | −0.0105952 | ||||||||
\(541\) | 40.1080 | 1.72438 | 0.862188 | − | 0.506589i | \(-0.169094\pi\) | ||||
0.862188 | + | 0.506589i | \(0.169094\pi\) | |||||||
\(542\) | −1.26137 | −0.0541803 | ||||||||
\(543\) | −6.00000 | −0.257485 | ||||||||
\(544\) | 2.43845 | 0.104548 | ||||||||
\(545\) | 8.49242 | 0.363775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0000 | 1.19719 | 0.598597 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598597 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(548\) | 7.12311 | 0.304284 | ||||||||
\(549\) | 0.876894 | 0.0374249 | ||||||||
\(550\) | 18.7386 | 0.799018 | ||||||||
\(551\) | −63.3693 | −2.69962 | ||||||||
\(552\) | 16.0000 | 0.681005 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −9.36932 | −0.398064 | ||||||||
\(555\) | 1.75379 | 0.0744442 | ||||||||
\(556\) | −4.00000 | −0.169638 | ||||||||
\(557\) | 6.49242 | 0.275093 | 0.137546 | − | 0.990495i | \(-0.456078\pi\) | ||||
0.137546 | + | 0.990495i | \(0.456078\pi\) | |||||||
\(558\) | −8.00000 | −0.338667 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.56155 | −0.108149 | ||||||||
\(562\) | −29.8617 | −1.25964 | ||||||||
\(563\) | 22.8769 | 0.964146 | 0.482073 | − | 0.876131i | \(-0.339884\pi\) | ||||
0.482073 | + | 0.876131i | \(0.339884\pi\) | |||||||
\(564\) | −1.26137 | −0.0531131 | ||||||||
\(565\) | −2.56155 | −0.107765 | ||||||||
\(566\) | 5.26137 | 0.221152 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24.9848 | −1.04834 | ||||||||
\(569\) | 12.8769 | 0.539827 | 0.269914 | − | 0.962885i | \(-0.413005\pi\) | ||||
0.269914 | + | 0.962885i | \(0.413005\pi\) | |||||||
\(570\) | −6.73863 | −0.282250 | ||||||||
\(571\) | 18.7386 | 0.784187 | 0.392094 | − | 0.919925i | \(-0.371751\pi\) | ||||
0.392094 | + | 0.919925i | \(0.371751\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.1231 | 0.548226 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.7386 | 1.28189 | ||||||||
\(576\) | 5.56155 | 0.231731 | ||||||||
\(577\) | 41.0540 | 1.70910 | 0.854550 | − | 0.519370i | \(-0.173833\pi\) | ||||
0.854550 | + | 0.519370i | \(0.173833\pi\) | |||||||
\(578\) | −1.56155 | −0.0649520 | ||||||||
\(579\) | −24.2462 | −1.00764 | ||||||||
\(580\) | 2.03031 | 0.0843040 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 17.3693 | 0.719981 | ||||||||
\(583\) | −10.8769 | −0.450475 | ||||||||
\(584\) | −10.3542 | −0.428458 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.1231 | −0.459491 | ||||||||
\(587\) | −36.9848 | −1.52653 | −0.763264 | − | 0.646087i | \(-0.776404\pi\) | ||||
−0.763264 | + | 0.646087i | \(0.776404\pi\) | |||||||
\(588\) | 3.06913 | 0.126569 | ||||||||
\(589\) | −39.3693 | −1.62218 | ||||||||
\(590\) | −0.984845 | −0.0405454 | ||||||||
\(591\) | 19.9309 | 0.819846 | ||||||||
\(592\) | 14.6307 | 0.601317 | ||||||||
\(593\) | −44.2462 | −1.81697 | −0.908487 | − | 0.417913i | \(-0.862762\pi\) | ||||
−0.908487 | + | 0.417913i | \(0.862762\pi\) | |||||||
\(594\) | 4.00000 | 0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.86174 | 0.0762598 | ||||||||
\(597\) | −16.0000 | −0.654836 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −41.6155 | −1.70036 | −0.850182 | − | 0.526489i | \(-0.823508\pi\) | ||||
−0.850182 | + | 0.526489i | \(0.823508\pi\) | |||||||
\(600\) | 11.4233 | 0.466354 | ||||||||
\(601\) | 34.9848 | 1.42706 | 0.713531 | − | 0.700624i | \(-0.247095\pi\) | ||||
0.713531 | + | 0.700624i | \(0.247095\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | −3.50758 | −0.142721 | ||||||||
\(605\) | −2.49242 | −0.101331 | ||||||||
\(606\) | 29.8617 | 1.21305 | ||||||||
\(607\) | 15.3693 | 0.623821 | 0.311911 | − | 0.950111i | \(-0.399031\pi\) | ||||
0.311911 | + | 0.950111i | \(0.399031\pi\) | |||||||
\(608\) | −18.7386 | −0.759952 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.768944 | −0.0311336 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.438447 | 0.0177232 | ||||||||
\(613\) | −2.31534 | −0.0935158 | −0.0467579 | − | 0.998906i | \(-0.514889\pi\) | ||||
−0.0467579 | + | 0.998906i | \(0.514889\pi\) | |||||||
\(614\) | −0.768944 | −0.0310320 | ||||||||
\(615\) | 0.315342 | 0.0127158 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.7538 | 1.11733 | 0.558663 | − | 0.829395i | \(-0.311315\pi\) | ||||
0.558663 | + | 0.829395i | \(0.311315\pi\) | |||||||
\(618\) | 6.73863 | 0.271068 | ||||||||
\(619\) | 19.3693 | 0.778519 | 0.389259 | − | 0.921128i | \(-0.372731\pi\) | ||||
0.389259 | + | 0.921128i | \(0.372731\pi\) | |||||||
\(620\) | 1.26137 | 0.0506577 | ||||||||
\(621\) | 6.56155 | 0.263306 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.3693 | 0.814773 | ||||||||
\(626\) | 11.8920 | 0.475302 | ||||||||
\(627\) | 19.6847 | 0.786130 | ||||||||
\(628\) | −2.49242 | −0.0994585 | ||||||||
\(629\) | −3.12311 | −0.124526 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.6847 | −0.465159 | −0.232579 | − | 0.972577i | \(-0.574717\pi\) | ||||
−0.232579 | + | 0.972577i | \(0.574717\pi\) | |||||||
\(632\) | 37.4773 | 1.49077 | ||||||||
\(633\) | 11.3693 | 0.451890 | ||||||||
\(634\) | −28.1080 | −1.11631 | ||||||||
\(635\) | −0.453602 | −0.0180007 | ||||||||
\(636\) | 1.86174 | 0.0738228 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −32.9848 | −1.30588 | ||||||||
\(639\) | −10.2462 | −0.405334 | ||||||||
\(640\) | −7.61553 | −0.301030 | ||||||||
\(641\) | −0.0691303 | −0.00273048 | −0.00136524 | − | 0.999999i | \(-0.500435\pi\) | ||||
−0.00136524 | + | 0.999999i | \(0.500435\pi\) | |||||||
\(642\) | 12.0000 | 0.473602 | ||||||||
\(643\) | 30.2462 | 1.19279 | 0.596397 | − | 0.802690i | \(-0.296598\pi\) | ||||
0.596397 | + | 0.802690i | \(0.296598\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.31534 | 0.169916 | ||||||||
\(646\) | 12.0000 | 0.472134 | ||||||||
\(647\) | 15.3693 | 0.604230 | 0.302115 | − | 0.953271i | \(-0.402307\pi\) | ||||
0.302115 | + | 0.953271i | \(0.402307\pi\) | |||||||
\(648\) | 2.43845 | 0.0957913 | ||||||||
\(649\) | 2.87689 | 0.112928 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.01515 | 0.118083 | ||||||||
\(653\) | −4.06913 | −0.159237 | −0.0796187 | − | 0.996825i | \(-0.525370\pi\) | ||||
−0.0796187 | + | 0.996825i | \(0.525370\pi\) | |||||||
\(654\) | 23.6155 | 0.923440 | ||||||||
\(655\) | 10.4233 | 0.407272 | ||||||||
\(656\) | 2.63068 | 0.102711 | ||||||||
\(657\) | −4.24621 | −0.165660 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 47.8617 | 1.86443 | 0.932214 | − | 0.361907i | \(-0.117874\pi\) | ||||
0.932214 | + | 0.361907i | \(0.117874\pi\) | |||||||
\(660\) | −0.630683 | −0.0245493 | ||||||||
\(661\) | −25.6847 | −0.999017 | −0.499509 | − | 0.866309i | \(-0.666486\pi\) | ||||
−0.499509 | + | 0.866309i | \(0.666486\pi\) | |||||||
\(662\) | −9.47727 | −0.368344 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 22.2462 | 0.863320 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.87689 | 0.188976 | ||||||||
\(667\) | −54.1080 | −2.09507 | ||||||||
\(668\) | 0.354162 | 0.0137029 | ||||||||
\(669\) | 13.9309 | 0.538599 | ||||||||
\(670\) | 3.50758 | 0.135510 | ||||||||
\(671\) | 2.24621 | 0.0867140 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.7386 | 1.87874 | 0.939368 | − | 0.342910i | \(-0.111413\pi\) | ||||
0.939368 | + | 0.342910i | \(0.111413\pi\) | |||||||
\(674\) | −51.1231 | −1.96919 | ||||||||
\(675\) | 4.68466 | 0.180313 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.6847 | −0.525944 | −0.262972 | − | 0.964803i | \(-0.584703\pi\) | ||||
−0.262972 | + | 0.964803i | \(0.584703\pi\) | |||||||
\(678\) | −7.12311 | −0.273561 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.36932 | 0.0525109 | ||||||||
\(681\) | 23.0540 | 0.883430 | ||||||||
\(682\) | −20.4924 | −0.784695 | ||||||||
\(683\) | 5.43845 | 0.208096 | 0.104048 | − | 0.994572i | \(-0.466820\pi\) | ||||
0.104048 | + | 0.994572i | \(0.466820\pi\) | |||||||
\(684\) | −3.36932 | −0.128829 | ||||||||
\(685\) | 9.12311 | 0.348576 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.00000 | 0.228914 | ||||||||
\(688\) | 36.0000 | 1.37249 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −5.75379 | −0.219043 | ||||||||
\(691\) | −36.9848 | −1.40697 | −0.703485 | − | 0.710710i | \(-0.748374\pi\) | ||||
−0.703485 | + | 0.710710i | \(0.748374\pi\) | |||||||
\(692\) | −8.24621 | −0.313474 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −38.2462 | −1.45181 | ||||||||
\(695\) | −5.12311 | −0.194330 | ||||||||
\(696\) | −20.1080 | −0.762190 | ||||||||
\(697\) | −0.561553 | −0.0212703 | ||||||||
\(698\) | 11.6155 | 0.439654 | ||||||||
\(699\) | −0.561553 | −0.0212399 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.36932 | −0.353874 | −0.176937 | − | 0.984222i | \(-0.556619\pi\) | ||||
−0.176937 | + | 0.984222i | \(0.556619\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0000 | 0.905177 | ||||||||
\(704\) | 14.2462 | 0.536924 | ||||||||
\(705\) | −1.61553 | −0.0608443 | ||||||||
\(706\) | 35.1231 | 1.32188 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.492423 | −0.0185064 | ||||||||
\(709\) | −4.73863 | −0.177963 | −0.0889816 | − | 0.996033i | \(-0.528361\pi\) | ||||
−0.0889816 | + | 0.996033i | \(0.528361\pi\) | |||||||
\(710\) | 8.98485 | 0.337195 | ||||||||
\(711\) | 15.3693 | 0.576394 | ||||||||
\(712\) | −17.3693 | −0.650943 | ||||||||
\(713\) | −33.6155 | −1.25891 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.00000 | −0.149487 | ||||||||
\(717\) | 10.2462 | 0.382652 | ||||||||
\(718\) | −3.50758 | −0.130902 | ||||||||
\(719\) | 8.80776 | 0.328474 | 0.164237 | − | 0.986421i | \(-0.447484\pi\) | ||||
0.164237 | + | 0.986421i | \(0.447484\pi\) | |||||||
\(720\) | −2.63068 | −0.0980398 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −62.5464 | −2.32774 | ||||||||
\(723\) | −21.3693 | −0.794733 | ||||||||
\(724\) | 2.63068 | 0.0977686 | ||||||||
\(725\) | −38.6307 | −1.43471 | ||||||||
\(726\) | −6.93087 | −0.257229 | ||||||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.72348 | 0.137812 | ||||||||
\(731\) | −7.68466 | −0.284227 | ||||||||
\(732\) | −0.384472 | −0.0142105 | ||||||||
\(733\) | 28.2462 | 1.04330 | 0.521649 | − | 0.853160i | \(-0.325317\pi\) | ||||
0.521649 | + | 0.853160i | \(0.325317\pi\) | |||||||
\(734\) | 28.4924 | 1.05167 | ||||||||
\(735\) | 3.93087 | 0.144992 | ||||||||
\(736\) | −16.0000 | −0.589768 | ||||||||
\(737\) | −10.2462 | −0.377424 | ||||||||
\(738\) | 0.876894 | 0.0322789 | ||||||||
\(739\) | 8.31534 | 0.305885 | 0.152942 | − | 0.988235i | \(-0.451125\pi\) | ||||
0.152942 | + | 0.988235i | \(0.451125\pi\) | |||||||
\(740\) | −0.768944 | −0.0282669 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.49242 | 0.164811 | 0.0824055 | − | 0.996599i | \(-0.473740\pi\) | ||||
0.0824055 | + | 0.996599i | \(0.473740\pi\) | |||||||
\(744\) | −12.4924 | −0.457994 | ||||||||
\(745\) | 2.38447 | 0.0873603 | ||||||||
\(746\) | −25.3693 | −0.928837 | ||||||||
\(747\) | 9.12311 | 0.333797 | ||||||||
\(748\) | 1.12311 | 0.0410648 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −8.49242 | −0.310099 | ||||||||
\(751\) | −0.630683 | −0.0230140 | −0.0115070 | − | 0.999934i | \(-0.503663\pi\) | ||||
−0.0115070 | + | 0.999934i | \(0.503663\pi\) | |||||||
\(752\) | −13.4773 | −0.491465 | ||||||||
\(753\) | 24.4924 | 0.892553 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.49242 | −0.163496 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.0540 | −0.765220 | −0.382610 | − | 0.923910i | \(-0.624975\pi\) | ||||
−0.382610 | + | 0.923910i | \(0.624975\pi\) | |||||||
\(758\) | −18.7386 | −0.680618 | ||||||||
\(759\) | 16.8078 | 0.610083 | ||||||||
\(760\) | −10.5227 | −0.381700 | ||||||||
\(761\) | 32.2462 | 1.16892 | 0.584462 | − | 0.811421i | \(-0.301306\pi\) | ||||
0.584462 | + | 0.811421i | \(0.301306\pi\) | |||||||
\(762\) | −1.26137 | −0.0456945 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.75379 | −0.208165 | ||||||||
\(765\) | 0.561553 | 0.0203030 | ||||||||
\(766\) | −16.0000 | −0.578103 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −10.0540 | −0.362792 | ||||||||
\(769\) | 29.5464 | 1.06547 | 0.532735 | − | 0.846282i | \(-0.321164\pi\) | ||||
0.532735 | + | 0.846282i | \(0.321164\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.36932 | −0.337428 | ||||||||
\(772\) | 10.6307 | 0.382607 | ||||||||
\(773\) | 33.3693 | 1.20021 | 0.600105 | − | 0.799921i | \(-0.295125\pi\) | ||||
0.600105 | + | 0.799921i | \(0.295125\pi\) | |||||||
\(774\) | 12.0000 | 0.431331 | ||||||||
\(775\) | −24.0000 | −0.862105 | ||||||||
\(776\) | 27.1231 | 0.973663 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.1383 | 1.22392 | ||||||||
\(779\) | 4.31534 | 0.154613 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.2462 | −0.939163 | ||||||||
\(782\) | 10.2462 | 0.366404 | ||||||||
\(783\) | −8.24621 | −0.294696 | ||||||||
\(784\) | 32.7926 | 1.17116 | ||||||||
\(785\) | −3.19224 | −0.113936 | ||||||||
\(786\) | 28.9848 | 1.03386 | ||||||||
\(787\) | −6.24621 | −0.222653 | −0.111327 | − | 0.993784i | \(-0.535510\pi\) | ||||
−0.111327 | + | 0.993784i | \(0.535510\pi\) | |||||||
\(788\) | −8.73863 | −0.311301 | ||||||||
\(789\) | −12.4924 | −0.444742 | ||||||||
\(790\) | −13.4773 | −0.479500 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.24621 | 0.221949 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 8.38447 | 0.297554 | ||||||||
\(795\) | 2.38447 | 0.0845685 | ||||||||
\(796\) | 7.01515 | 0.248646 | ||||||||
\(797\) | 31.6155 | 1.11988 | 0.559940 | − | 0.828533i | \(-0.310824\pi\) | ||||
0.559940 | + | 0.828533i | \(0.310824\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.87689 | 0.101777 | ||||||||
\(800\) | −11.4233 | −0.403874 | ||||||||
\(801\) | −7.12311 | −0.251683 | ||||||||
\(802\) | −9.64584 | −0.340606 | ||||||||
\(803\) | −10.8769 | −0.383837 | ||||||||
\(804\) | 1.75379 | 0.0618514 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.5616 | −0.723801 | ||||||||
\(808\) | 46.6307 | 1.64046 | ||||||||
\(809\) | 53.0540 | 1.86528 | 0.932639 | − | 0.360810i | \(-0.117500\pi\) | ||||
0.932639 | + | 0.360810i | \(0.117500\pi\) | |||||||
\(810\) | −0.876894 | −0.0308109 | ||||||||
\(811\) | 20.6307 | 0.724441 | 0.362221 | − | 0.932092i | \(-0.382019\pi\) | ||||
0.362221 | + | 0.932092i | \(0.382019\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.807764 | −0.0283295 | ||||||||
\(814\) | 12.4924 | 0.437859 | ||||||||
\(815\) | 3.86174 | 0.135271 | ||||||||
\(816\) | 4.68466 | 0.163996 | ||||||||
\(817\) | 59.0540 | 2.06604 | ||||||||
\(818\) | −3.61553 | −0.126414 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.138261 | −0.00482827 | ||||||||
\(821\) | 16.5616 | 0.578002 | 0.289001 | − | 0.957329i | \(-0.406677\pi\) | ||||
0.289001 | + | 0.957329i | \(0.406677\pi\) | |||||||
\(822\) | 25.3693 | 0.884857 | ||||||||
\(823\) | 36.4924 | 1.27205 | 0.636023 | − | 0.771670i | \(-0.280578\pi\) | ||||
0.636023 | + | 0.771670i | \(0.280578\pi\) | |||||||
\(824\) | 10.5227 | 0.366577 | ||||||||
\(825\) | 12.0000 | 0.417786 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.4233 | 0.501547 | 0.250774 | − | 0.968046i | \(-0.419315\pi\) | ||||
0.250774 | + | 0.968046i | \(0.419315\pi\) | |||||||
\(828\) | −2.87689 | −0.0999790 | ||||||||
\(829\) | 50.4924 | 1.75367 | 0.876837 | − | 0.480787i | \(-0.159649\pi\) | ||||
0.876837 | + | 0.480787i | \(0.159649\pi\) | |||||||
\(830\) | −8.00000 | −0.277684 | ||||||||
\(831\) | −6.00000 | −0.208138 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.00000 | −0.242536 | ||||||||
\(834\) | −14.2462 | −0.493306 | ||||||||
\(835\) | 0.453602 | 0.0156976 | ||||||||
\(836\) | −8.63068 | −0.298498 | ||||||||
\(837\) | −5.12311 | −0.177080 | ||||||||
\(838\) | −50.7386 | −1.75274 | ||||||||
\(839\) | −11.0540 | −0.381626 | −0.190813 | − | 0.981626i | \(-0.561112\pi\) | ||||
−0.190813 | + | 0.981626i | \(0.561112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.0000 | 1.34483 | ||||||||
\(842\) | 44.6004 | 1.53703 | ||||||||
\(843\) | −19.1231 | −0.658635 | ||||||||
\(844\) | −4.98485 | −0.171585 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.49242 | −0.154453 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 19.8920 | 0.683096 | ||||||||
\(849\) | 3.36932 | 0.115635 | ||||||||
\(850\) | 7.31534 | 0.250914 | ||||||||
\(851\) | 20.4924 | 0.702471 | ||||||||
\(852\) | 4.49242 | 0.153908 | ||||||||
\(853\) | −20.7386 | −0.710077 | −0.355039 | − | 0.934852i | \(-0.615532\pi\) | ||||
−0.355039 | + | 0.934852i | \(0.615532\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.31534 | −0.147582 | ||||||||
\(856\) | 18.7386 | 0.640473 | ||||||||
\(857\) | −6.00000 | −0.204956 | −0.102478 | − | 0.994735i | \(-0.532677\pi\) | ||||
−0.102478 | + | 0.994735i | \(0.532677\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.0000 | 0.409435 | 0.204717 | − | 0.978821i | \(-0.434372\pi\) | ||||
0.204717 | + | 0.978821i | \(0.434372\pi\) | |||||||
\(860\) | −1.89205 | −0.0645183 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −37.4773 | −1.27648 | ||||||||
\(863\) | 26.2462 | 0.893431 | 0.446716 | − | 0.894676i | \(-0.352594\pi\) | ||||
0.446716 | + | 0.894676i | \(0.352594\pi\) | |||||||
\(864\) | −2.43845 | −0.0829577 | ||||||||
\(865\) | −10.5616 | −0.359104 | ||||||||
\(866\) | −22.3542 | −0.759625 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 39.3693 | 1.33551 | ||||||||
\(870\) | 7.23106 | 0.245156 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 36.8769 | 1.24881 | ||||||||
\(873\) | 11.1231 | 0.376460 | ||||||||
\(874\) | −78.7386 | −2.66337 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.86174 | 0.0629023 | ||||||||
\(877\) | 34.0000 | 1.14810 | 0.574049 | − | 0.818821i | \(-0.305372\pi\) | ||||
0.574049 | + | 0.818821i | \(0.305372\pi\) | |||||||
\(878\) | 8.98485 | 0.303224 | ||||||||
\(879\) | −7.12311 | −0.240256 | ||||||||
\(880\) | −6.73863 | −0.227159 | ||||||||
\(881\) | 23.7538 | 0.800285 | 0.400143 | − | 0.916453i | \(-0.368961\pi\) | ||||
0.400143 | + | 0.916453i | \(0.368961\pi\) | |||||||
\(882\) | 10.9309 | 0.368062 | ||||||||
\(883\) | 38.4233 | 1.29305 | 0.646523 | − | 0.762894i | \(-0.276222\pi\) | ||||
0.646523 | + | 0.762894i | \(0.276222\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.630683 | −0.0212002 | ||||||||
\(886\) | 35.7235 | 1.20015 | ||||||||
\(887\) | 22.5616 | 0.757543 | 0.378771 | − | 0.925490i | \(-0.376347\pi\) | ||||
0.378771 | + | 0.925490i | \(0.376347\pi\) | |||||||
\(888\) | 7.61553 | 0.255560 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.24621 | 0.209373 | ||||||||
\(891\) | 2.56155 | 0.0858152 | ||||||||
\(892\) | −6.10795 | −0.204509 | ||||||||
\(893\) | −22.1080 | −0.739814 | ||||||||
\(894\) | 6.63068 | 0.221763 | ||||||||
\(895\) | −5.12311 | −0.171247 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.8920 | −0.663806 | ||||||||
\(899\) | 42.2462 | 1.40899 | ||||||||
\(900\) | −2.05398 | −0.0684658 | ||||||||
\(901\) | −4.24621 | −0.141462 | ||||||||
\(902\) | 2.24621 | 0.0747907 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.1231 | −0.369949 | ||||||||
\(905\) | 3.36932 | 0.112000 | ||||||||
\(906\) | −12.4924 | −0.415033 | ||||||||
\(907\) | 47.8617 | 1.58922 | 0.794611 | − | 0.607118i | \(-0.207675\pi\) | ||||
0.794611 | + | 0.607118i | \(0.207675\pi\) | |||||||
\(908\) | −10.1080 | −0.335444 | ||||||||
\(909\) | 19.1231 | 0.634273 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.3002 | −0.970758 | −0.485379 | − | 0.874304i | \(-0.661318\pi\) | ||||
−0.485379 | + | 0.874304i | \(0.661318\pi\) | |||||||
\(912\) | −36.0000 | −1.19208 | ||||||||
\(913\) | 23.3693 | 0.773412 | ||||||||
\(914\) | −10.6307 | −0.351632 | ||||||||
\(915\) | −0.492423 | −0.0162790 | ||||||||
\(916\) | −2.63068 | −0.0869202 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.56155 | 0.0515389 | ||||||||
\(919\) | −4.31534 | −0.142350 | −0.0711750 | − | 0.997464i | \(-0.522675\pi\) | ||||
−0.0711750 | + | 0.997464i | \(0.522675\pi\) | |||||||
\(920\) | −8.98485 | −0.296222 | ||||||||
\(921\) | −0.492423 | −0.0162259 | ||||||||
\(922\) | 12.8769 | 0.424078 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.6307 | 0.481054 | ||||||||
\(926\) | 39.0152 | 1.28212 | ||||||||
\(927\) | 4.31534 | 0.141734 | ||||||||
\(928\) | 20.1080 | 0.660076 | ||||||||
\(929\) | −31.9309 | −1.04762 | −0.523809 | − | 0.851836i | \(-0.675489\pi\) | ||||
−0.523809 | + | 0.851836i | \(0.675489\pi\) | |||||||
\(930\) | 4.49242 | 0.147312 | ||||||||
\(931\) | 53.7926 | 1.76298 | ||||||||
\(932\) | 0.246211 | 0.00806492 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.26137 | 0.172157 | ||||||||
\(935\) | 1.43845 | 0.0470423 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.0000 | −0.718709 | −0.359354 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359354 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.61553 | 0.248523 | ||||||||
\(940\) | 0.708324 | 0.0231030 | ||||||||
\(941\) | −30.0000 | −0.977972 | −0.488986 | − | 0.872292i | \(-0.662633\pi\) | ||||
−0.488986 | + | 0.872292i | \(0.662633\pi\) | |||||||
\(942\) | −8.87689 | −0.289225 | ||||||||
\(943\) | 3.68466 | 0.119989 | ||||||||
\(944\) | −5.26137 | −0.171243 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 30.7386 | 0.999399 | ||||||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | −6.73863 | −0.218861 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −56.2159 | −1.82388 | ||||||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −54.3542 | −1.76070 | −0.880352 | − | 0.474321i | \(-0.842694\pi\) | ||||
−0.880352 | + | 0.474321i | \(0.842694\pi\) | |||||||
\(954\) | 6.63068 | 0.214676 | ||||||||
\(955\) | −7.36932 | −0.238465 | ||||||||
\(956\) | −4.49242 | −0.145295 | ||||||||
\(957\) | −21.1231 | −0.682813 | ||||||||
\(958\) | −45.7538 | −1.47824 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.12311 | −0.100798 | ||||||||
\(961\) | −4.75379 | −0.153348 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.68466 | 0.247635 | ||||||||
\(964\) | 9.36932 | 0.301765 | ||||||||
\(965\) | 13.6155 | 0.438299 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.5616 | −1.49732 | −0.748659 | − | 0.662955i | \(-0.769302\pi\) | ||||
−0.748659 | + | 0.662955i | \(0.769302\pi\) | |||||||
\(968\) | −10.8229 | −0.347862 | ||||||||
\(969\) | 7.68466 | 0.246867 | ||||||||
\(970\) | −9.75379 | −0.313175 | ||||||||
\(971\) | −2.38447 | −0.0765213 | −0.0382607 | − | 0.999268i | \(-0.512182\pi\) | ||||
−0.0382607 | + | 0.999268i | \(0.512182\pi\) | |||||||
\(972\) | −0.438447 | −0.0140632 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −11.5076 | −0.368727 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.10795 | −0.131492 | ||||||||
\(977\) | 8.24621 | 0.263820 | 0.131910 | − | 0.991262i | \(-0.457889\pi\) | ||||
0.131910 | + | 0.991262i | \(0.457889\pi\) | |||||||
\(978\) | 10.7386 | 0.343384 | ||||||||
\(979\) | −18.2462 | −0.583151 | ||||||||
\(980\) | −1.72348 | −0.0550545 | ||||||||
\(981\) | 15.1231 | 0.482844 | ||||||||
\(982\) | −5.26137 | −0.167897 | ||||||||
\(983\) | −2.06913 | −0.0659950 | −0.0329975 | − | 0.999455i | \(-0.510505\pi\) | ||||
−0.0329975 | + | 0.999455i | \(0.510505\pi\) | |||||||
\(984\) | 1.36932 | 0.0436522 | ||||||||
\(985\) | −11.1922 | −0.356614 | ||||||||
\(986\) | −12.8769 | −0.410084 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 50.4233 | 1.60337 | ||||||||
\(990\) | −2.24621 | −0.0713893 | ||||||||
\(991\) | −6.73863 | −0.214060 | −0.107030 | − | 0.994256i | \(-0.534134\pi\) | ||||
−0.107030 | + | 0.994256i | \(0.534134\pi\) | |||||||
\(992\) | 12.4924 | 0.396635 | ||||||||
\(993\) | −6.06913 | −0.192598 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.98485 | 0.284839 | ||||||||
\(996\) | −4.00000 | −0.126745 | ||||||||
\(997\) | −10.0000 | −0.316703 | −0.158352 | − | 0.987383i | \(-0.550618\pi\) | ||||
−0.158352 | + | 0.987383i | \(0.550618\pi\) | |||||||
\(998\) | −17.7538 | −0.561986 | ||||||||
\(999\) | 3.12311 | 0.0988107 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))