Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, 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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.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: | \(32.0120261703\) |
Analytic rank: | \(0\) |
Dimension: | \(83\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.67158 | −1.88909 | −0.944544 | − | 0.328384i | \(-0.893496\pi\) | ||||
−0.944544 | + | 0.328384i | \(0.893496\pi\) | |||||||
\(3\) | −3.12490 | −1.80416 | −0.902080 | − | 0.431569i | \(-0.857960\pi\) | ||||
−0.902080 | + | 0.431569i | \(0.857960\pi\) | |||||||
\(4\) | 5.13731 | 2.56866 | ||||||||
\(5\) | 1.64338 | 0.734941 | 0.367470 | − | 0.930035i | \(-0.380224\pi\) | ||||
0.367470 | + | 0.930035i | \(0.380224\pi\) | |||||||
\(6\) | 8.34840 | 3.40822 | ||||||||
\(7\) | −0.166545 | −0.0629482 | −0.0314741 | − | 0.999505i | \(-0.510020\pi\) | ||||
−0.0314741 | + | 0.999505i | \(0.510020\pi\) | |||||||
\(8\) | −8.38157 | −2.96333 | ||||||||
\(9\) | 6.76498 | 2.25499 | ||||||||
\(10\) | −4.39041 | −1.38837 | ||||||||
\(11\) | 3.58072 | 1.07963 | 0.539814 | − | 0.841784i | \(-0.318495\pi\) | ||||
0.539814 | + | 0.841784i | \(0.318495\pi\) | |||||||
\(12\) | −16.0536 | −4.63427 | ||||||||
\(13\) | −2.65893 | −0.737454 | −0.368727 | − | 0.929538i | \(-0.620206\pi\) | ||||
−0.368727 | + | 0.929538i | \(0.620206\pi\) | |||||||
\(14\) | 0.444938 | 0.118915 | ||||||||
\(15\) | −5.13539 | −1.32595 | ||||||||
\(16\) | 12.1174 | 3.02934 | ||||||||
\(17\) | −5.38022 | −1.30490 | −0.652448 | − | 0.757834i | \(-0.726258\pi\) | ||||
−0.652448 | + | 0.757834i | \(0.726258\pi\) | |||||||
\(18\) | −18.0732 | −4.25988 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 8.44255 | 1.88781 | ||||||||
\(21\) | 0.520437 | 0.113569 | ||||||||
\(22\) | −9.56617 | −2.03951 | ||||||||
\(23\) | −5.51103 | −1.14913 | −0.574564 | − | 0.818459i | \(-0.694829\pi\) | ||||
−0.574564 | + | 0.818459i | \(0.694829\pi\) | |||||||
\(24\) | 26.1915 | 5.34633 | ||||||||
\(25\) | −2.29931 | −0.459862 | ||||||||
\(26\) | 7.10353 | 1.39312 | ||||||||
\(27\) | −11.7652 | −2.26421 | ||||||||
\(28\) | −0.855596 | −0.161692 | ||||||||
\(29\) | 1.03127 | 0.191502 | 0.0957512 | − | 0.995405i | \(-0.469475\pi\) | ||||
0.0957512 | + | 0.995405i | \(0.469475\pi\) | |||||||
\(30\) | 13.7196 | 2.50484 | ||||||||
\(31\) | −6.29172 | −1.13003 | −0.565013 | − | 0.825082i | \(-0.691129\pi\) | ||||
−0.565013 | + | 0.825082i | \(0.691129\pi\) | |||||||
\(32\) | −15.6093 | −2.75936 | ||||||||
\(33\) | −11.1894 | −1.94782 | ||||||||
\(34\) | 14.3737 | 2.46506 | ||||||||
\(35\) | −0.273697 | −0.0462632 | ||||||||
\(36\) | 34.7538 | 5.79230 | ||||||||
\(37\) | −5.34837 | −0.879267 | −0.439633 | − | 0.898177i | \(-0.644892\pi\) | ||||
−0.439633 | + | 0.898177i | \(0.644892\pi\) | |||||||
\(38\) | 2.67158 | 0.433387 | ||||||||
\(39\) | 8.30888 | 1.33049 | ||||||||
\(40\) | −13.7741 | −2.17787 | ||||||||
\(41\) | −9.81313 | −1.53255 | −0.766277 | − | 0.642510i | \(-0.777893\pi\) | ||||
−0.766277 | + | 0.642510i | \(0.777893\pi\) | |||||||
\(42\) | −1.39039 | −0.214541 | ||||||||
\(43\) | 6.39265 | 0.974869 | 0.487435 | − | 0.873159i | \(-0.337933\pi\) | ||||
0.487435 | + | 0.873159i | \(0.337933\pi\) | |||||||
\(44\) | 18.3953 | 2.77319 | ||||||||
\(45\) | 11.1174 | 1.65729 | ||||||||
\(46\) | 14.7231 | 2.17081 | ||||||||
\(47\) | −0.640569 | −0.0934366 | −0.0467183 | − | 0.998908i | \(-0.514876\pi\) | ||||
−0.0467183 | + | 0.998908i | \(0.514876\pi\) | |||||||
\(48\) | −37.8655 | −5.46542 | ||||||||
\(49\) | −6.97226 | −0.996038 | ||||||||
\(50\) | 6.14278 | 0.868720 | ||||||||
\(51\) | 16.8126 | 2.35424 | ||||||||
\(52\) | −13.6598 | −1.89427 | ||||||||
\(53\) | 13.0990 | 1.79929 | 0.899646 | − | 0.436619i | \(-0.143824\pi\) | ||||
0.899646 | + | 0.436619i | \(0.143824\pi\) | |||||||
\(54\) | 31.4315 | 4.27729 | ||||||||
\(55\) | 5.88448 | 0.793463 | ||||||||
\(56\) | 1.39591 | 0.186536 | ||||||||
\(57\) | 3.12490 | 0.413903 | ||||||||
\(58\) | −2.75512 | −0.361765 | ||||||||
\(59\) | −2.33086 | −0.303452 | −0.151726 | − | 0.988423i | \(-0.548483\pi\) | ||||
−0.151726 | + | 0.988423i | \(0.548483\pi\) | |||||||
\(60\) | −26.3821 | −3.40591 | ||||||||
\(61\) | −3.83664 | −0.491232 | −0.245616 | − | 0.969367i | \(-0.578990\pi\) | ||||
−0.245616 | + | 0.969367i | \(0.578990\pi\) | |||||||
\(62\) | 16.8088 | 2.13472 | ||||||||
\(63\) | −1.12668 | −0.141948 | ||||||||
\(64\) | 17.4667 | 2.18334 | ||||||||
\(65\) | −4.36963 | −0.541985 | ||||||||
\(66\) | 29.8933 | 3.67961 | ||||||||
\(67\) | 5.51744 | 0.674063 | 0.337031 | − | 0.941493i | \(-0.390577\pi\) | ||||
0.337031 | + | 0.941493i | \(0.390577\pi\) | |||||||
\(68\) | −27.6399 | −3.35183 | ||||||||
\(69\) | 17.2214 | 2.07321 | ||||||||
\(70\) | 0.731202 | 0.0873953 | ||||||||
\(71\) | 4.58568 | 0.544220 | 0.272110 | − | 0.962266i | \(-0.412279\pi\) | ||||
0.272110 | + | 0.962266i | \(0.412279\pi\) | |||||||
\(72\) | −56.7011 | −6.68229 | ||||||||
\(73\) | 0.823429 | 0.0963751 | 0.0481876 | − | 0.998838i | \(-0.484655\pi\) | ||||
0.0481876 | + | 0.998838i | \(0.484655\pi\) | |||||||
\(74\) | 14.2886 | 1.66101 | ||||||||
\(75\) | 7.18510 | 0.829664 | ||||||||
\(76\) | −5.13731 | −0.589290 | ||||||||
\(77\) | −0.596352 | −0.0679607 | ||||||||
\(78\) | −22.1978 | −2.51341 | ||||||||
\(79\) | −9.68159 | −1.08926 | −0.544632 | − | 0.838675i | \(-0.683331\pi\) | ||||
−0.544632 | + | 0.838675i | \(0.683331\pi\) | |||||||
\(80\) | 19.9134 | 2.22639 | ||||||||
\(81\) | 16.4700 | 1.83000 | ||||||||
\(82\) | 26.2165 | 2.89513 | ||||||||
\(83\) | 9.69150 | 1.06378 | 0.531890 | − | 0.846813i | \(-0.321482\pi\) | ||||
0.531890 | + | 0.846813i | \(0.321482\pi\) | |||||||
\(84\) | 2.67365 | 0.291719 | ||||||||
\(85\) | −8.84174 | −0.959021 | ||||||||
\(86\) | −17.0784 | −1.84161 | ||||||||
\(87\) | −3.22262 | −0.345501 | ||||||||
\(88\) | −30.0121 | −3.19930 | ||||||||
\(89\) | 13.2518 | 1.40469 | 0.702346 | − | 0.711835i | \(-0.252136\pi\) | ||||
0.702346 | + | 0.711835i | \(0.252136\pi\) | |||||||
\(90\) | −29.7010 | −3.13076 | ||||||||
\(91\) | 0.442832 | 0.0464214 | ||||||||
\(92\) | −28.3119 | −2.95172 | ||||||||
\(93\) | 19.6610 | 2.03875 | ||||||||
\(94\) | 1.71133 | 0.176510 | ||||||||
\(95\) | −1.64338 | −0.168607 | ||||||||
\(96\) | 48.7775 | 4.97833 | ||||||||
\(97\) | −2.16213 | −0.219531 | −0.109766 | − | 0.993957i | \(-0.535010\pi\) | ||||
−0.109766 | + | 0.993957i | \(0.535010\pi\) | |||||||
\(98\) | 18.6269 | 1.88160 | ||||||||
\(99\) | 24.2235 | 2.43455 | ||||||||
\(100\) | −11.8123 | −1.18123 | ||||||||
\(101\) | 9.36880 | 0.932230 | 0.466115 | − | 0.884724i | \(-0.345653\pi\) | ||||
0.466115 | + | 0.884724i | \(0.345653\pi\) | |||||||
\(102\) | −44.9162 | −4.44737 | ||||||||
\(103\) | 8.48833 | 0.836380 | 0.418190 | − | 0.908360i | \(-0.362665\pi\) | ||||
0.418190 | + | 0.908360i | \(0.362665\pi\) | |||||||
\(104\) | 22.2860 | 2.18532 | ||||||||
\(105\) | 0.855274 | 0.0834662 | ||||||||
\(106\) | −34.9951 | −3.39902 | ||||||||
\(107\) | −5.60601 | −0.541953 | −0.270977 | − | 0.962586i | \(-0.587347\pi\) | ||||
−0.270977 | + | 0.962586i | \(0.587347\pi\) | |||||||
\(108\) | −60.4414 | −5.81597 | ||||||||
\(109\) | 12.7494 | 1.22117 | 0.610587 | − | 0.791949i | \(-0.290934\pi\) | ||||
0.610587 | + | 0.791949i | \(0.290934\pi\) | |||||||
\(110\) | −15.7208 | −1.49892 | ||||||||
\(111\) | 16.7131 | 1.58634 | ||||||||
\(112\) | −2.01809 | −0.190692 | ||||||||
\(113\) | −11.8938 | −1.11887 | −0.559437 | − | 0.828873i | \(-0.688982\pi\) | ||||
−0.559437 | + | 0.828873i | \(0.688982\pi\) | |||||||
\(114\) | −8.34840 | −0.781899 | ||||||||
\(115\) | −9.05670 | −0.844542 | ||||||||
\(116\) | 5.29797 | 0.491904 | ||||||||
\(117\) | −17.9876 | −1.66295 | ||||||||
\(118\) | 6.22706 | 0.573247 | ||||||||
\(119\) | 0.896051 | 0.0821408 | ||||||||
\(120\) | 43.0426 | 3.92923 | ||||||||
\(121\) | 1.82157 | 0.165597 | ||||||||
\(122\) | 10.2499 | 0.927980 | ||||||||
\(123\) | 30.6650 | 2.76497 | ||||||||
\(124\) | −32.3225 | −2.90265 | ||||||||
\(125\) | −11.9955 | −1.07291 | ||||||||
\(126\) | 3.01000 | 0.268152 | ||||||||
\(127\) | 6.08771 | 0.540197 | 0.270098 | − | 0.962833i | \(-0.412944\pi\) | ||||
0.270098 | + | 0.962833i | \(0.412944\pi\) | |||||||
\(128\) | −15.4450 | −1.36516 | ||||||||
\(129\) | −19.9764 | −1.75882 | ||||||||
\(130\) | 11.6738 | 1.02386 | ||||||||
\(131\) | 7.99019 | 0.698106 | 0.349053 | − | 0.937103i | \(-0.386503\pi\) | ||||
0.349053 | + | 0.937103i | \(0.386503\pi\) | |||||||
\(132\) | −57.4834 | −5.00329 | ||||||||
\(133\) | 0.166545 | 0.0144413 | ||||||||
\(134\) | −14.7403 | −1.27336 | ||||||||
\(135\) | −19.3346 | −1.66406 | ||||||||
\(136\) | 45.0947 | 3.86684 | ||||||||
\(137\) | −13.7213 | −1.17229 | −0.586144 | − | 0.810207i | \(-0.699355\pi\) | ||||
−0.586144 | + | 0.810207i | \(0.699355\pi\) | |||||||
\(138\) | −46.0082 | −3.91648 | ||||||||
\(139\) | 7.63640 | 0.647711 | 0.323855 | − | 0.946107i | \(-0.395021\pi\) | ||||
0.323855 | + | 0.946107i | \(0.395021\pi\) | |||||||
\(140\) | −1.40607 | −0.118834 | ||||||||
\(141\) | 2.00171 | 0.168575 | ||||||||
\(142\) | −12.2510 | −1.02808 | ||||||||
\(143\) | −9.52089 | −0.796176 | ||||||||
\(144\) | 81.9737 | 6.83114 | ||||||||
\(145\) | 1.69477 | 0.140743 | ||||||||
\(146\) | −2.19985 | −0.182061 | ||||||||
\(147\) | 21.7876 | 1.79701 | ||||||||
\(148\) | −27.4763 | −2.25853 | ||||||||
\(149\) | 6.03014 | 0.494008 | 0.247004 | − | 0.969014i | \(-0.420554\pi\) | ||||
0.247004 | + | 0.969014i | \(0.420554\pi\) | |||||||
\(150\) | −19.1955 | −1.56731 | ||||||||
\(151\) | −22.1234 | −1.80037 | −0.900187 | − | 0.435503i | \(-0.856570\pi\) | ||||
−0.900187 | + | 0.435503i | \(0.856570\pi\) | |||||||
\(152\) | 8.38157 | 0.679835 | ||||||||
\(153\) | −36.3971 | −2.94253 | ||||||||
\(154\) | 1.59320 | 0.128384 | ||||||||
\(155\) | −10.3397 | −0.830502 | ||||||||
\(156\) | 42.6853 | 3.41756 | ||||||||
\(157\) | −21.5678 | −1.72130 | −0.860650 | − | 0.509197i | \(-0.829942\pi\) | ||||
−0.860650 | + | 0.509197i | \(0.829942\pi\) | |||||||
\(158\) | 25.8651 | 2.05772 | ||||||||
\(159\) | −40.9332 | −3.24621 | ||||||||
\(160\) | −25.6520 | −2.02797 | ||||||||
\(161\) | 0.917836 | 0.0723356 | ||||||||
\(162\) | −44.0009 | −3.45703 | ||||||||
\(163\) | −7.27368 | −0.569718 | −0.284859 | − | 0.958569i | \(-0.591947\pi\) | ||||
−0.284859 | + | 0.958569i | \(0.591947\pi\) | |||||||
\(164\) | −50.4131 | −3.93661 | ||||||||
\(165\) | −18.3884 | −1.43153 | ||||||||
\(166\) | −25.8916 | −2.00958 | ||||||||
\(167\) | 19.6431 | 1.52003 | 0.760016 | − | 0.649904i | \(-0.225191\pi\) | ||||
0.760016 | + | 0.649904i | \(0.225191\pi\) | |||||||
\(168\) | −4.36208 | −0.336542 | ||||||||
\(169\) | −5.93009 | −0.456161 | ||||||||
\(170\) | 23.6214 | 1.81168 | ||||||||
\(171\) | −6.76498 | −0.517331 | ||||||||
\(172\) | 32.8410 | 2.50410 | ||||||||
\(173\) | 5.44330 | 0.413847 | 0.206923 | − | 0.978357i | \(-0.433655\pi\) | ||||
0.206923 | + | 0.978357i | \(0.433655\pi\) | |||||||
\(174\) | 8.60947 | 0.652682 | ||||||||
\(175\) | 0.382939 | 0.0289475 | ||||||||
\(176\) | 43.3889 | 3.27056 | ||||||||
\(177\) | 7.28369 | 0.547476 | ||||||||
\(178\) | −35.4033 | −2.65359 | ||||||||
\(179\) | 3.82251 | 0.285708 | 0.142854 | − | 0.989744i | \(-0.454372\pi\) | ||||
0.142854 | + | 0.989744i | \(0.454372\pi\) | |||||||
\(180\) | 57.1137 | 4.25700 | ||||||||
\(181\) | 13.0807 | 0.972283 | 0.486141 | − | 0.873880i | \(-0.338404\pi\) | ||||
0.486141 | + | 0.873880i | \(0.338404\pi\) | |||||||
\(182\) | −1.18306 | −0.0876942 | ||||||||
\(183\) | 11.9891 | 0.886260 | ||||||||
\(184\) | 46.1911 | 3.40525 | ||||||||
\(185\) | −8.78939 | −0.646209 | ||||||||
\(186\) | −52.5257 | −3.85137 | ||||||||
\(187\) | −19.2651 | −1.40880 | ||||||||
\(188\) | −3.29080 | −0.240007 | ||||||||
\(189\) | 1.95943 | 0.142528 | ||||||||
\(190\) | 4.39041 | 0.318514 | ||||||||
\(191\) | 12.9673 | 0.938280 | 0.469140 | − | 0.883124i | \(-0.344564\pi\) | ||||
0.469140 | + | 0.883124i | \(0.344564\pi\) | |||||||
\(192\) | −54.5817 | −3.93910 | ||||||||
\(193\) | 3.01410 | 0.216960 | 0.108480 | − | 0.994099i | \(-0.465402\pi\) | ||||
0.108480 | + | 0.994099i | \(0.465402\pi\) | |||||||
\(194\) | 5.77630 | 0.414714 | ||||||||
\(195\) | 13.6546 | 0.977828 | ||||||||
\(196\) | −35.8187 | −2.55848 | ||||||||
\(197\) | −12.5510 | −0.894224 | −0.447112 | − | 0.894478i | \(-0.647547\pi\) | ||||
−0.447112 | + | 0.894478i | \(0.647547\pi\) | |||||||
\(198\) | −64.7149 | −4.59909 | ||||||||
\(199\) | −8.05425 | −0.570951 | −0.285475 | − | 0.958386i | \(-0.592152\pi\) | ||||
−0.285475 | + | 0.958386i | \(0.592152\pi\) | |||||||
\(200\) | 19.2718 | 1.36272 | ||||||||
\(201\) | −17.2414 | −1.21612 | ||||||||
\(202\) | −25.0294 | −1.76107 | ||||||||
\(203\) | −0.171754 | −0.0120547 | ||||||||
\(204\) | 86.3718 | 6.04724 | ||||||||
\(205\) | −16.1267 | −1.12634 | ||||||||
\(206\) | −22.6772 | −1.58000 | ||||||||
\(207\) | −37.2820 | −2.59128 | ||||||||
\(208\) | −32.2192 | −2.23400 | ||||||||
\(209\) | −3.58072 | −0.247684 | ||||||||
\(210\) | −2.28493 | −0.157675 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | 67.2939 | 4.62177 | ||||||||
\(213\) | −14.3298 | −0.981860 | ||||||||
\(214\) | 14.9769 | 1.02380 | ||||||||
\(215\) | 10.5055 | 0.716471 | ||||||||
\(216\) | 98.6106 | 6.70960 | ||||||||
\(217\) | 1.04786 | 0.0711331 | ||||||||
\(218\) | −34.0611 | −2.30691 | ||||||||
\(219\) | −2.57313 | −0.173876 | ||||||||
\(220\) | 30.2304 | 2.03813 | ||||||||
\(221\) | 14.3056 | 0.962301 | ||||||||
\(222\) | −44.6503 | −2.99673 | ||||||||
\(223\) | 6.72303 | 0.450207 | 0.225104 | − | 0.974335i | \(-0.427728\pi\) | ||||
0.225104 | + | 0.974335i | \(0.427728\pi\) | |||||||
\(224\) | 2.59966 | 0.173697 | ||||||||
\(225\) | −15.5548 | −1.03699 | ||||||||
\(226\) | 31.7751 | 2.11365 | ||||||||
\(227\) | 29.6815 | 1.97003 | 0.985016 | − | 0.172464i | \(-0.0551729\pi\) | ||||
0.985016 | + | 0.172464i | \(0.0551729\pi\) | |||||||
\(228\) | 16.0536 | 1.06317 | ||||||||
\(229\) | 9.42401 | 0.622756 | 0.311378 | − | 0.950286i | \(-0.399209\pi\) | ||||
0.311378 | + | 0.950286i | \(0.399209\pi\) | |||||||
\(230\) | 24.1957 | 1.59541 | ||||||||
\(231\) | 1.86354 | 0.122612 | ||||||||
\(232\) | −8.64368 | −0.567486 | ||||||||
\(233\) | 25.2666 | 1.65527 | 0.827636 | − | 0.561265i | \(-0.189685\pi\) | ||||
0.827636 | + | 0.561265i | \(0.189685\pi\) | |||||||
\(234\) | 48.0552 | 3.14147 | ||||||||
\(235\) | −1.05270 | −0.0686704 | ||||||||
\(236\) | −11.9743 | −0.779464 | ||||||||
\(237\) | 30.2540 | 1.96521 | ||||||||
\(238\) | −2.39387 | −0.155171 | ||||||||
\(239\) | 4.51624 | 0.292131 | 0.146066 | − | 0.989275i | \(-0.453339\pi\) | ||||
0.146066 | + | 0.989275i | \(0.453339\pi\) | |||||||
\(240\) | −62.2274 | −4.01676 | ||||||||
\(241\) | −23.5491 | −1.51693 | −0.758464 | − | 0.651715i | \(-0.774050\pi\) | ||||
−0.758464 | + | 0.651715i | \(0.774050\pi\) | |||||||
\(242\) | −4.86645 | −0.312827 | ||||||||
\(243\) | −16.1716 | −1.03741 | ||||||||
\(244\) | −19.7100 | −1.26181 | ||||||||
\(245\) | −11.4581 | −0.732029 | ||||||||
\(246\) | −81.9239 | −5.22328 | ||||||||
\(247\) | 2.65893 | 0.169184 | ||||||||
\(248\) | 52.7345 | 3.34864 | ||||||||
\(249\) | −30.2849 | −1.91923 | ||||||||
\(250\) | 32.0469 | 2.02683 | ||||||||
\(251\) | −30.0258 | −1.89521 | −0.947606 | − | 0.319441i | \(-0.896505\pi\) | ||||
−0.947606 | + | 0.319441i | \(0.896505\pi\) | |||||||
\(252\) | −5.78809 | −0.364615 | ||||||||
\(253\) | −19.7335 | −1.24063 | ||||||||
\(254\) | −16.2638 | −1.02048 | ||||||||
\(255\) | 27.6295 | 1.73023 | ||||||||
\(256\) | 6.32913 | 0.395571 | ||||||||
\(257\) | 16.5942 | 1.03512 | 0.517558 | − | 0.855648i | \(-0.326841\pi\) | ||||
0.517558 | + | 0.855648i | \(0.326841\pi\) | |||||||
\(258\) | 53.3683 | 3.32257 | ||||||||
\(259\) | 0.890746 | 0.0553483 | ||||||||
\(260\) | −22.4481 | −1.39217 | ||||||||
\(261\) | 6.97654 | 0.431837 | ||||||||
\(262\) | −21.3464 | −1.31879 | ||||||||
\(263\) | 23.7595 | 1.46507 | 0.732536 | − | 0.680728i | \(-0.238336\pi\) | ||||
0.732536 | + | 0.680728i | \(0.238336\pi\) | |||||||
\(264\) | 93.7846 | 5.77204 | ||||||||
\(265\) | 21.5267 | 1.32237 | ||||||||
\(266\) | −0.444938 | −0.0272809 | ||||||||
\(267\) | −41.4107 | −2.53429 | ||||||||
\(268\) | 28.3448 | 1.73144 | ||||||||
\(269\) | −12.6856 | −0.773452 | −0.386726 | − | 0.922195i | \(-0.626394\pi\) | ||||
−0.386726 | + | 0.922195i | \(0.626394\pi\) | |||||||
\(270\) | 51.6539 | 3.14356 | ||||||||
\(271\) | 3.85154 | 0.233964 | 0.116982 | − | 0.993134i | \(-0.462678\pi\) | ||||
0.116982 | + | 0.993134i | \(0.462678\pi\) | |||||||
\(272\) | −65.1941 | −3.95297 | ||||||||
\(273\) | −1.38380 | −0.0837517 | ||||||||
\(274\) | 36.6574 | 2.21456 | ||||||||
\(275\) | −8.23318 | −0.496480 | ||||||||
\(276\) | 88.4717 | 5.32537 | ||||||||
\(277\) | 11.5596 | 0.694547 | 0.347274 | − | 0.937764i | \(-0.387107\pi\) | ||||
0.347274 | + | 0.937764i | \(0.387107\pi\) | |||||||
\(278\) | −20.4012 | −1.22358 | ||||||||
\(279\) | −42.5633 | −2.54820 | ||||||||
\(280\) | 2.29401 | 0.137093 | ||||||||
\(281\) | −3.15560 | −0.188247 | −0.0941237 | − | 0.995561i | \(-0.530005\pi\) | ||||
−0.0941237 | + | 0.995561i | \(0.530005\pi\) | |||||||
\(282\) | −5.34772 | −0.318452 | ||||||||
\(283\) | 10.2909 | 0.611731 | 0.305865 | − | 0.952075i | \(-0.401054\pi\) | ||||
0.305865 | + | 0.952075i | \(0.401054\pi\) | |||||||
\(284\) | 23.5581 | 1.39791 | ||||||||
\(285\) | 5.13539 | 0.304194 | ||||||||
\(286\) | 25.4358 | 1.50405 | ||||||||
\(287\) | 1.63433 | 0.0964715 | ||||||||
\(288\) | −105.597 | −6.22234 | ||||||||
\(289\) | 11.9468 | 0.702753 | ||||||||
\(290\) | −4.52771 | −0.265876 | ||||||||
\(291\) | 6.75644 | 0.396070 | ||||||||
\(292\) | 4.23021 | 0.247555 | ||||||||
\(293\) | −17.9678 | −1.04969 | −0.524846 | − | 0.851197i | \(-0.675877\pi\) | ||||
−0.524846 | + | 0.851197i | \(0.675877\pi\) | |||||||
\(294\) | −58.2072 | −3.39471 | ||||||||
\(295\) | −3.83048 | −0.223019 | ||||||||
\(296\) | 44.8277 | 2.60556 | ||||||||
\(297\) | −42.1278 | −2.44450 | ||||||||
\(298\) | −16.1100 | −0.933225 | ||||||||
\(299\) | 14.6534 | 0.847430 | ||||||||
\(300\) | 36.9121 | 2.13112 | ||||||||
\(301\) | −1.06467 | −0.0613663 | ||||||||
\(302\) | 59.1042 | 3.40107 | ||||||||
\(303\) | −29.2765 | −1.68189 | ||||||||
\(304\) | −12.1174 | −0.694979 | ||||||||
\(305\) | −6.30505 | −0.361026 | ||||||||
\(306\) | 97.2376 | 5.55870 | ||||||||
\(307\) | 28.7590 | 1.64136 | 0.820681 | − | 0.571387i | \(-0.193594\pi\) | ||||
0.820681 | + | 0.571387i | \(0.193594\pi\) | |||||||
\(308\) | −3.06365 | −0.174568 | ||||||||
\(309\) | −26.5252 | −1.50896 | ||||||||
\(310\) | 27.6232 | 1.56889 | ||||||||
\(311\) | −11.0091 | −0.624267 | −0.312133 | − | 0.950038i | \(-0.601044\pi\) | ||||
−0.312133 | + | 0.950038i | \(0.601044\pi\) | |||||||
\(312\) | −69.6415 | −3.94267 | ||||||||
\(313\) | 14.0054 | 0.791630 | 0.395815 | − | 0.918330i | \(-0.370462\pi\) | ||||
0.395815 | + | 0.918330i | \(0.370462\pi\) | |||||||
\(314\) | 57.6201 | 3.25169 | ||||||||
\(315\) | −1.85155 | −0.104323 | ||||||||
\(316\) | −49.7374 | −2.79795 | ||||||||
\(317\) | 22.5695 | 1.26763 | 0.633814 | − | 0.773486i | \(-0.281489\pi\) | ||||
0.633814 | + | 0.773486i | \(0.281489\pi\) | |||||||
\(318\) | 109.356 | 6.13238 | ||||||||
\(319\) | 3.69270 | 0.206751 | ||||||||
\(320\) | 28.7044 | 1.60463 | ||||||||
\(321\) | 17.5182 | 0.977771 | ||||||||
\(322\) | −2.45207 | −0.136648 | ||||||||
\(323\) | 5.38022 | 0.299364 | ||||||||
\(324\) | 84.6116 | 4.70064 | ||||||||
\(325\) | 6.11370 | 0.339127 | ||||||||
\(326\) | 19.4322 | 1.07625 | ||||||||
\(327\) | −39.8406 | −2.20319 | ||||||||
\(328\) | 82.2495 | 4.54147 | ||||||||
\(329\) | 0.106684 | 0.00588167 | ||||||||
\(330\) | 49.1260 | 2.70430 | ||||||||
\(331\) | 19.3140 | 1.06159 | 0.530797 | − | 0.847499i | \(-0.321893\pi\) | ||||
0.530797 | + | 0.847499i | \(0.321893\pi\) | |||||||
\(332\) | 49.7883 | 2.73249 | ||||||||
\(333\) | −36.1816 | −1.98274 | ||||||||
\(334\) | −52.4781 | −2.87148 | ||||||||
\(335\) | 9.06724 | 0.495396 | ||||||||
\(336\) | 6.30632 | 0.344038 | ||||||||
\(337\) | 5.81625 | 0.316831 | 0.158416 | − | 0.987373i | \(-0.449361\pi\) | ||||
0.158416 | + | 0.987373i | \(0.449361\pi\) | |||||||
\(338\) | 15.8427 | 0.861729 | ||||||||
\(339\) | 37.1669 | 2.01863 | ||||||||
\(340\) | −45.4228 | −2.46340 | ||||||||
\(341\) | −22.5289 | −1.22001 | ||||||||
\(342\) | 18.0732 | 0.977284 | ||||||||
\(343\) | 2.32701 | 0.125647 | ||||||||
\(344\) | −53.5804 | −2.88886 | ||||||||
\(345\) | 28.3013 | 1.52369 | ||||||||
\(346\) | −14.5422 | −0.781793 | ||||||||
\(347\) | 15.9540 | 0.856455 | 0.428228 | − | 0.903671i | \(-0.359138\pi\) | ||||
0.428228 | + | 0.903671i | \(0.359138\pi\) | |||||||
\(348\) | −16.5556 | −0.887474 | ||||||||
\(349\) | −35.3986 | −1.89484 | −0.947421 | − | 0.319990i | \(-0.896320\pi\) | ||||
−0.947421 | + | 0.319990i | \(0.896320\pi\) | |||||||
\(350\) | −1.02305 | −0.0546844 | ||||||||
\(351\) | 31.2828 | 1.66975 | ||||||||
\(352\) | −55.8926 | −2.97909 | ||||||||
\(353\) | 17.7615 | 0.945351 | 0.472676 | − | 0.881237i | \(-0.343288\pi\) | ||||
0.472676 | + | 0.881237i | \(0.343288\pi\) | |||||||
\(354\) | −19.4589 | −1.03423 | ||||||||
\(355\) | 7.53600 | 0.399970 | ||||||||
\(356\) | 68.0789 | 3.60817 | ||||||||
\(357\) | −2.80007 | −0.148195 | ||||||||
\(358\) | −10.2121 | −0.539727 | ||||||||
\(359\) | 35.0335 | 1.84900 | 0.924498 | − | 0.381186i | \(-0.124484\pi\) | ||||
0.924498 | + | 0.381186i | \(0.124484\pi\) | |||||||
\(360\) | −93.1814 | −4.91109 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −34.9461 | −1.83673 | ||||||||
\(363\) | −5.69221 | −0.298763 | ||||||||
\(364\) | 2.27497 | 0.119241 | ||||||||
\(365\) | 1.35321 | 0.0708300 | ||||||||
\(366\) | −32.0298 | −1.67422 | ||||||||
\(367\) | 26.2041 | 1.36784 | 0.683921 | − | 0.729556i | \(-0.260273\pi\) | ||||
0.683921 | + | 0.729556i | \(0.260273\pi\) | |||||||
\(368\) | −66.7791 | −3.48110 | ||||||||
\(369\) | −66.3856 | −3.45590 | ||||||||
\(370\) | 23.4815 | 1.22075 | ||||||||
\(371\) | −2.18159 | −0.113262 | ||||||||
\(372\) | 101.005 | 5.23684 | ||||||||
\(373\) | −32.9958 | −1.70846 | −0.854229 | − | 0.519897i | \(-0.825970\pi\) | ||||
−0.854229 | + | 0.519897i | \(0.825970\pi\) | |||||||
\(374\) | 51.4681 | 2.66135 | ||||||||
\(375\) | 37.4848 | 1.93571 | ||||||||
\(376\) | 5.36897 | 0.276884 | ||||||||
\(377\) | −2.74208 | −0.141224 | ||||||||
\(378\) | −5.23478 | −0.269248 | ||||||||
\(379\) | −4.98391 | −0.256006 | −0.128003 | − | 0.991774i | \(-0.540857\pi\) | ||||
−0.128003 | + | 0.991774i | \(0.540857\pi\) | |||||||
\(380\) | −8.44255 | −0.433094 | ||||||||
\(381\) | −19.0235 | −0.974601 | ||||||||
\(382\) | −34.6431 | −1.77249 | ||||||||
\(383\) | −31.4193 | −1.60545 | −0.802727 | − | 0.596347i | \(-0.796618\pi\) | ||||
−0.802727 | + | 0.596347i | \(0.796618\pi\) | |||||||
\(384\) | 48.2642 | 2.46297 | ||||||||
\(385\) | −0.980032 | −0.0499471 | ||||||||
\(386\) | −8.05239 | −0.409856 | ||||||||
\(387\) | 43.2461 | 2.19832 | ||||||||
\(388\) | −11.1076 | −0.563901 | ||||||||
\(389\) | −12.4386 | −0.630663 | −0.315332 | − | 0.948982i | \(-0.602116\pi\) | ||||
−0.315332 | + | 0.948982i | \(0.602116\pi\) | |||||||
\(390\) | −36.4794 | −1.84720 | ||||||||
\(391\) | 29.6506 | 1.49949 | ||||||||
\(392\) | 58.4385 | 2.95159 | ||||||||
\(393\) | −24.9685 | −1.25950 | ||||||||
\(394\) | 33.5310 | 1.68927 | ||||||||
\(395\) | −15.9105 | −0.800545 | ||||||||
\(396\) | 124.444 | 6.25353 | ||||||||
\(397\) | −20.6151 | −1.03464 | −0.517322 | − | 0.855791i | \(-0.673071\pi\) | ||||
−0.517322 | + | 0.855791i | \(0.673071\pi\) | |||||||
\(398\) | 21.5175 | 1.07858 | ||||||||
\(399\) | −0.520437 | −0.0260544 | ||||||||
\(400\) | −27.8616 | −1.39308 | ||||||||
\(401\) | 14.2491 | 0.711565 | 0.355783 | − | 0.934569i | \(-0.384214\pi\) | ||||
0.355783 | + | 0.934569i | \(0.384214\pi\) | |||||||
\(402\) | 46.0618 | 2.29735 | ||||||||
\(403\) | 16.7292 | 0.833342 | ||||||||
\(404\) | 48.1304 | 2.39458 | ||||||||
\(405\) | 27.0664 | 1.34494 | ||||||||
\(406\) | 0.458853 | 0.0227725 | ||||||||
\(407\) | −19.1510 | −0.949281 | ||||||||
\(408\) | −140.916 | −6.97640 | ||||||||
\(409\) | 3.62202 | 0.179098 | 0.0895488 | − | 0.995982i | \(-0.471458\pi\) | ||||
0.0895488 | + | 0.995982i | \(0.471458\pi\) | |||||||
\(410\) | 43.0837 | 2.12775 | ||||||||
\(411\) | 42.8776 | 2.11499 | ||||||||
\(412\) | 43.6072 | 2.14837 | ||||||||
\(413\) | 0.388193 | 0.0191017 | ||||||||
\(414\) | 99.6016 | 4.89515 | ||||||||
\(415\) | 15.9268 | 0.781816 | ||||||||
\(416\) | 41.5041 | 2.03490 | ||||||||
\(417\) | −23.8629 | −1.16857 | ||||||||
\(418\) | 9.56617 | 0.467897 | ||||||||
\(419\) | 4.04751 | 0.197734 | 0.0988668 | − | 0.995101i | \(-0.468478\pi\) | ||||
0.0988668 | + | 0.995101i | \(0.468478\pi\) | |||||||
\(420\) | 4.39381 | 0.214396 | ||||||||
\(421\) | 13.7355 | 0.669429 | 0.334715 | − | 0.942320i | \(-0.391360\pi\) | ||||
0.334715 | + | 0.942320i | \(0.391360\pi\) | |||||||
\(422\) | −2.67158 | −0.130050 | ||||||||
\(423\) | −4.33344 | −0.210699 | ||||||||
\(424\) | −109.791 | −5.33190 | ||||||||
\(425\) | 12.3708 | 0.600072 | ||||||||
\(426\) | 38.2831 | 1.85482 | ||||||||
\(427\) | 0.638975 | 0.0309222 | ||||||||
\(428\) | −28.7998 | −1.39209 | ||||||||
\(429\) | 29.7518 | 1.43643 | ||||||||
\(430\) | −28.0663 | −1.35348 | ||||||||
\(431\) | 37.7988 | 1.82070 | 0.910352 | − | 0.413835i | \(-0.135811\pi\) | ||||
0.910352 | + | 0.413835i | \(0.135811\pi\) | |||||||
\(432\) | −142.563 | −6.85906 | ||||||||
\(433\) | −31.8963 | −1.53284 | −0.766419 | − | 0.642341i | \(-0.777963\pi\) | ||||
−0.766419 | + | 0.642341i | \(0.777963\pi\) | |||||||
\(434\) | −2.79943 | −0.134377 | ||||||||
\(435\) | −5.29598 | −0.253923 | ||||||||
\(436\) | 65.4978 | 3.13678 | ||||||||
\(437\) | 5.51103 | 0.263628 | ||||||||
\(438\) | 6.87431 | 0.328467 | ||||||||
\(439\) | −4.26445 | −0.203531 | −0.101765 | − | 0.994808i | \(-0.532449\pi\) | ||||
−0.101765 | + | 0.994808i | \(0.532449\pi\) | |||||||
\(440\) | −49.3212 | −2.35129 | ||||||||
\(441\) | −47.1672 | −2.24606 | ||||||||
\(442\) | −38.2186 | −1.81787 | ||||||||
\(443\) | −14.8472 | −0.705413 | −0.352706 | − | 0.935734i | \(-0.614739\pi\) | ||||
−0.352706 | + | 0.935734i | \(0.614739\pi\) | |||||||
\(444\) | 85.8605 | 4.07476 | ||||||||
\(445\) | 21.7778 | 1.03237 | ||||||||
\(446\) | −17.9611 | −0.850481 | ||||||||
\(447\) | −18.8435 | −0.891269 | ||||||||
\(448\) | −2.90900 | −0.137437 | ||||||||
\(449\) | 33.7441 | 1.59248 | 0.796240 | − | 0.604980i | \(-0.206819\pi\) | ||||
0.796240 | + | 0.604980i | \(0.206819\pi\) | |||||||
\(450\) | 41.5558 | 1.95896 | ||||||||
\(451\) | −35.1381 | −1.65459 | ||||||||
\(452\) | −61.1021 | −2.87400 | ||||||||
\(453\) | 69.1332 | 3.24816 | ||||||||
\(454\) | −79.2964 | −3.72156 | ||||||||
\(455\) | 0.727741 | 0.0341170 | ||||||||
\(456\) | −26.1915 | −1.22653 | ||||||||
\(457\) | 6.74620 | 0.315574 | 0.157787 | − | 0.987473i | \(-0.449564\pi\) | ||||
0.157787 | + | 0.987473i | \(0.449564\pi\) | |||||||
\(458\) | −25.1769 | −1.17644 | ||||||||
\(459\) | 63.2992 | 2.95456 | ||||||||
\(460\) | −46.5271 | −2.16934 | ||||||||
\(461\) | −12.5703 | −0.585459 | −0.292730 | − | 0.956195i | \(-0.594564\pi\) | ||||
−0.292730 | + | 0.956195i | \(0.594564\pi\) | |||||||
\(462\) | −4.97859 | −0.231625 | ||||||||
\(463\) | 19.3864 | 0.900964 | 0.450482 | − | 0.892785i | \(-0.351252\pi\) | ||||
0.450482 | + | 0.892785i | \(0.351252\pi\) | |||||||
\(464\) | 12.4963 | 0.580126 | ||||||||
\(465\) | 32.3104 | 1.49836 | ||||||||
\(466\) | −67.5017 | −3.12696 | ||||||||
\(467\) | 23.8610 | 1.10416 | 0.552078 | − | 0.833792i | \(-0.313835\pi\) | ||||
0.552078 | + | 0.833792i | \(0.313835\pi\) | |||||||
\(468\) | −92.4080 | −4.27156 | ||||||||
\(469\) | −0.918904 | −0.0424311 | ||||||||
\(470\) | 2.81236 | 0.129724 | ||||||||
\(471\) | 67.3972 | 3.10550 | ||||||||
\(472\) | 19.5362 | 0.899229 | ||||||||
\(473\) | 22.8903 | 1.05250 | ||||||||
\(474\) | −80.8258 | −3.71245 | ||||||||
\(475\) | 2.29931 | 0.105500 | ||||||||
\(476\) | 4.60329 | 0.210992 | ||||||||
\(477\) | 88.6148 | 4.05739 | ||||||||
\(478\) | −12.0655 | −0.551861 | ||||||||
\(479\) | 7.99568 | 0.365332 | 0.182666 | − | 0.983175i | \(-0.441527\pi\) | ||||
0.182666 | + | 0.983175i | \(0.441527\pi\) | |||||||
\(480\) | 80.1599 | 3.65878 | ||||||||
\(481\) | 14.2209 | 0.648419 | ||||||||
\(482\) | 62.9131 | 2.86561 | ||||||||
\(483\) | −2.86814 | −0.130505 | ||||||||
\(484\) | 9.35796 | 0.425362 | ||||||||
\(485\) | −3.55320 | −0.161343 | ||||||||
\(486\) | 43.2035 | 1.95975 | ||||||||
\(487\) | 1.43254 | 0.0649148 | 0.0324574 | − | 0.999473i | \(-0.489667\pi\) | ||||
0.0324574 | + | 0.999473i | \(0.489667\pi\) | |||||||
\(488\) | 32.1571 | 1.45568 | ||||||||
\(489\) | 22.7295 | 1.02786 | ||||||||
\(490\) | 30.6111 | 1.38287 | ||||||||
\(491\) | −6.63121 | −0.299262 | −0.149631 | − | 0.988742i | \(-0.547809\pi\) | ||||
−0.149631 | + | 0.988742i | \(0.547809\pi\) | |||||||
\(492\) | 157.536 | 7.10227 | ||||||||
\(493\) | −5.54848 | −0.249891 | ||||||||
\(494\) | −7.10353 | −0.319603 | ||||||||
\(495\) | 39.8084 | 1.78925 | ||||||||
\(496\) | −76.2390 | −3.42323 | ||||||||
\(497\) | −0.763723 | −0.0342577 | ||||||||
\(498\) | 80.9085 | 3.62559 | ||||||||
\(499\) | 21.4786 | 0.961512 | 0.480756 | − | 0.876854i | \(-0.340362\pi\) | ||||
0.480756 | + | 0.876854i | \(0.340362\pi\) | |||||||
\(500\) | −61.6248 | −2.75594 | ||||||||
\(501\) | −61.3828 | −2.74238 | ||||||||
\(502\) | 80.2162 | 3.58022 | ||||||||
\(503\) | 33.6892 | 1.50213 | 0.751064 | − | 0.660229i | \(-0.229541\pi\) | ||||
0.751064 | + | 0.660229i | \(0.229541\pi\) | |||||||
\(504\) | 9.44331 | 0.420638 | ||||||||
\(505\) | 15.3965 | 0.685134 | ||||||||
\(506\) | 52.7194 | 2.34366 | ||||||||
\(507\) | 18.5309 | 0.822988 | ||||||||
\(508\) | 31.2745 | 1.38758 | ||||||||
\(509\) | −39.6757 | −1.75859 | −0.879297 | − | 0.476273i | \(-0.841987\pi\) | ||||
−0.879297 | + | 0.476273i | \(0.841987\pi\) | |||||||
\(510\) | −73.8143 | −3.26855 | ||||||||
\(511\) | −0.137138 | −0.00606664 | ||||||||
\(512\) | 13.9813 | 0.617893 | ||||||||
\(513\) | 11.7652 | 0.519445 | ||||||||
\(514\) | −44.3326 | −1.95543 | ||||||||
\(515\) | 13.9495 | 0.614690 | ||||||||
\(516\) | −102.625 | −4.51781 | ||||||||
\(517\) | −2.29370 | −0.100877 | ||||||||
\(518\) | −2.37969 | −0.104558 | ||||||||
\(519\) | −17.0098 | −0.746646 | ||||||||
\(520\) | 36.6243 | 1.60608 | ||||||||
\(521\) | 4.14589 | 0.181635 | 0.0908174 | − | 0.995868i | \(-0.471052\pi\) | ||||
0.0908174 | + | 0.995868i | \(0.471052\pi\) | |||||||
\(522\) | −18.6383 | −0.815778 | ||||||||
\(523\) | −9.02330 | −0.394561 | −0.197281 | − | 0.980347i | \(-0.563211\pi\) | ||||
−0.197281 | + | 0.980347i | \(0.563211\pi\) | |||||||
\(524\) | 41.0481 | 1.79320 | ||||||||
\(525\) | −1.19665 | −0.0522259 | ||||||||
\(526\) | −63.4752 | −2.76765 | ||||||||
\(527\) | 33.8508 | 1.47457 | ||||||||
\(528\) | −135.586 | −5.90062 | ||||||||
\(529\) | 7.37143 | 0.320497 | ||||||||
\(530\) | −57.5102 | −2.49808 | ||||||||
\(531\) | −15.7682 | −0.684282 | ||||||||
\(532\) | 0.855596 | 0.0370948 | ||||||||
\(533\) | 26.0924 | 1.13019 | ||||||||
\(534\) | 110.632 | 4.78750 | ||||||||
\(535\) | −9.21279 | −0.398304 | ||||||||
\(536\) | −46.2448 | −1.99747 | ||||||||
\(537\) | −11.9449 | −0.515462 | ||||||||
\(538\) | 33.8904 | 1.46112 | ||||||||
\(539\) | −24.9657 | −1.07535 | ||||||||
\(540\) | −99.3280 | −4.27440 | ||||||||
\(541\) | −16.2230 | −0.697483 | −0.348742 | − | 0.937219i | \(-0.613391\pi\) | ||||
−0.348742 | + | 0.937219i | \(0.613391\pi\) | |||||||
\(542\) | −10.2897 | −0.441979 | ||||||||
\(543\) | −40.8759 | −1.75415 | ||||||||
\(544\) | 83.9816 | 3.60068 | ||||||||
\(545\) | 20.9521 | 0.897491 | ||||||||
\(546\) | 3.69694 | 0.158214 | ||||||||
\(547\) | −1.14322 | −0.0488807 | −0.0244404 | − | 0.999701i | \(-0.507780\pi\) | ||||
−0.0244404 | + | 0.999701i | \(0.507780\pi\) | |||||||
\(548\) | −70.4905 | −3.01120 | ||||||||
\(549\) | −25.9548 | −1.10772 | ||||||||
\(550\) | 21.9956 | 0.937894 | ||||||||
\(551\) | −1.03127 | −0.0439337 | ||||||||
\(552\) | −144.342 | −6.14362 | ||||||||
\(553\) | 1.61242 | 0.0685673 | ||||||||
\(554\) | −30.8823 | −1.31206 | ||||||||
\(555\) | 27.4659 | 1.16586 | ||||||||
\(556\) | 39.2306 | 1.66375 | ||||||||
\(557\) | 15.6208 | 0.661877 | 0.330938 | − | 0.943652i | \(-0.392635\pi\) | ||||
0.330938 | + | 0.943652i | \(0.392635\pi\) | |||||||
\(558\) | 113.711 | 4.81378 | ||||||||
\(559\) | −16.9976 | −0.718922 | ||||||||
\(560\) | −3.31649 | −0.140147 | ||||||||
\(561\) | 60.2014 | 2.54170 | ||||||||
\(562\) | 8.43043 | 0.355616 | ||||||||
\(563\) | −28.0081 | −1.18040 | −0.590200 | − | 0.807257i | \(-0.700951\pi\) | ||||
−0.590200 | + | 0.807257i | \(0.700951\pi\) | |||||||
\(564\) | 10.2834 | 0.433010 | ||||||||
\(565\) | −19.5460 | −0.822306 | ||||||||
\(566\) | −27.4929 | −1.15561 | ||||||||
\(567\) | −2.74300 | −0.115195 | ||||||||
\(568\) | −38.4352 | −1.61270 | ||||||||
\(569\) | 11.0611 | 0.463704 | 0.231852 | − | 0.972751i | \(-0.425521\pi\) | ||||
0.231852 | + | 0.972751i | \(0.425521\pi\) | |||||||
\(570\) | −13.7196 | −0.574650 | ||||||||
\(571\) | 1.48061 | 0.0619616 | 0.0309808 | − | 0.999520i | \(-0.490137\pi\) | ||||
0.0309808 | + | 0.999520i | \(0.490137\pi\) | |||||||
\(572\) | −48.9118 | −2.04510 | ||||||||
\(573\) | −40.5214 | −1.69281 | ||||||||
\(574\) | −4.36624 | −0.182243 | ||||||||
\(575\) | 12.6716 | 0.528440 | ||||||||
\(576\) | 118.162 | 4.92342 | ||||||||
\(577\) | −1.75687 | −0.0731396 | −0.0365698 | − | 0.999331i | \(-0.511643\pi\) | ||||
−0.0365698 | + | 0.999331i | \(0.511643\pi\) | |||||||
\(578\) | −31.9168 | −1.32756 | ||||||||
\(579\) | −9.41874 | −0.391430 | ||||||||
\(580\) | 8.70657 | 0.361521 | ||||||||
\(581\) | −1.61407 | −0.0669631 | ||||||||
\(582\) | −18.0503 | −0.748211 | ||||||||
\(583\) | 46.9040 | 1.94257 | ||||||||
\(584\) | −6.90163 | −0.285591 | ||||||||
\(585\) | −29.5604 | −1.22217 | ||||||||
\(586\) | 48.0024 | 1.98296 | ||||||||
\(587\) | −32.3949 | −1.33708 | −0.668541 | − | 0.743675i | \(-0.733081\pi\) | ||||
−0.668541 | + | 0.743675i | \(0.733081\pi\) | |||||||
\(588\) | 111.930 | 4.61590 | ||||||||
\(589\) | 6.29172 | 0.259246 | ||||||||
\(590\) | 10.2334 | 0.421303 | ||||||||
\(591\) | 39.2207 | 1.61332 | ||||||||
\(592\) | −64.8082 | −2.66360 | ||||||||
\(593\) | −41.8615 | −1.71905 | −0.859523 | − | 0.511098i | \(-0.829239\pi\) | ||||
−0.859523 | + | 0.511098i | \(0.829239\pi\) | |||||||
\(594\) | 112.548 | 4.61788 | ||||||||
\(595\) | 1.47255 | 0.0603687 | ||||||||
\(596\) | 30.9787 | 1.26894 | ||||||||
\(597\) | 25.1687 | 1.03009 | ||||||||
\(598\) | −39.1477 | −1.60087 | ||||||||
\(599\) | 22.6866 | 0.926949 | 0.463475 | − | 0.886110i | \(-0.346603\pi\) | ||||
0.463475 | + | 0.886110i | \(0.346603\pi\) | |||||||
\(600\) | −60.2224 | −2.45857 | ||||||||
\(601\) | 23.7668 | 0.969470 | 0.484735 | − | 0.874661i | \(-0.338916\pi\) | ||||
0.484735 | + | 0.874661i | \(0.338916\pi\) | |||||||
\(602\) | 2.84433 | 0.115926 | ||||||||
\(603\) | 37.3254 | 1.52001 | ||||||||
\(604\) | −113.655 | −4.62454 | ||||||||
\(605\) | 2.99352 | 0.121704 | ||||||||
\(606\) | 78.2144 | 3.17724 | ||||||||
\(607\) | −47.3201 | −1.92066 | −0.960331 | − | 0.278862i | \(-0.910043\pi\) | ||||
−0.960331 | + | 0.278862i | \(0.910043\pi\) | |||||||
\(608\) | 15.6093 | 0.633041 | ||||||||
\(609\) | 0.536712 | 0.0217487 | ||||||||
\(610\) | 16.8444 | 0.682011 | ||||||||
\(611\) | 1.70323 | 0.0689052 | ||||||||
\(612\) | −186.983 | −7.55835 | ||||||||
\(613\) | −1.62158 | −0.0654949 | −0.0327474 | − | 0.999464i | \(-0.510426\pi\) | ||||
−0.0327474 | + | 0.999464i | \(0.510426\pi\) | |||||||
\(614\) | −76.8318 | −3.10068 | ||||||||
\(615\) | 50.3942 | 2.03209 | ||||||||
\(616\) | 4.99837 | 0.201390 | ||||||||
\(617\) | 14.7052 | 0.592010 | 0.296005 | − | 0.955186i | \(-0.404345\pi\) | ||||
0.296005 | + | 0.955186i | \(0.404345\pi\) | |||||||
\(618\) | 70.8640 | 2.85057 | ||||||||
\(619\) | −25.3831 | −1.02023 | −0.510117 | − | 0.860105i | \(-0.670398\pi\) | ||||
−0.510117 | + | 0.860105i | \(0.670398\pi\) | |||||||
\(620\) | −53.1181 | −2.13328 | ||||||||
\(621\) | 64.8382 | 2.60187 | ||||||||
\(622\) | 29.4116 | 1.17930 | ||||||||
\(623\) | −2.20703 | −0.0884229 | ||||||||
\(624\) | 100.682 | 4.03049 | ||||||||
\(625\) | −8.21663 | −0.328665 | ||||||||
\(626\) | −37.4164 | −1.49546 | ||||||||
\(627\) | 11.1894 | 0.446861 | ||||||||
\(628\) | −110.801 | −4.42143 | ||||||||
\(629\) | 28.7754 | 1.14735 | ||||||||
\(630\) | 4.94657 | 0.197076 | ||||||||
\(631\) | −8.23487 | −0.327825 | −0.163912 | − | 0.986475i | \(-0.552411\pi\) | ||||
−0.163912 | + | 0.986475i | \(0.552411\pi\) | |||||||
\(632\) | 81.1470 | 3.22785 | ||||||||
\(633\) | −3.12490 | −0.124203 | ||||||||
\(634\) | −60.2960 | −2.39466 | ||||||||
\(635\) | 10.0044 | 0.397013 | ||||||||
\(636\) | −210.287 | −8.33840 | ||||||||
\(637\) | 18.5388 | 0.734532 | ||||||||
\(638\) | −9.86532 | −0.390572 | ||||||||
\(639\) | 31.0220 | 1.22721 | ||||||||
\(640\) | −25.3820 | −1.00331 | ||||||||
\(641\) | 11.8794 | 0.469206 | 0.234603 | − | 0.972091i | \(-0.424621\pi\) | ||||
0.234603 | + | 0.972091i | \(0.424621\pi\) | |||||||
\(642\) | −46.8012 | −1.84710 | ||||||||
\(643\) | −14.9957 | −0.591373 | −0.295687 | − | 0.955285i | \(-0.595548\pi\) | ||||
−0.295687 | + | 0.955285i | \(0.595548\pi\) | |||||||
\(644\) | 4.71521 | 0.185805 | ||||||||
\(645\) | −32.8287 | −1.29263 | ||||||||
\(646\) | −14.3737 | −0.565524 | ||||||||
\(647\) | −19.6440 | −0.772286 | −0.386143 | − | 0.922439i | \(-0.626193\pi\) | ||||
−0.386143 | + | 0.922439i | \(0.626193\pi\) | |||||||
\(648\) | −138.045 | −5.42290 | ||||||||
\(649\) | −8.34615 | −0.327615 | ||||||||
\(650\) | −16.3332 | −0.640641 | ||||||||
\(651\) | −3.27444 | −0.128335 | ||||||||
\(652\) | −37.3672 | −1.46341 | ||||||||
\(653\) | −2.21179 | −0.0865539 | −0.0432770 | − | 0.999063i | \(-0.513780\pi\) | ||||
−0.0432770 | + | 0.999063i | \(0.513780\pi\) | |||||||
\(654\) | 106.437 | 4.16203 | ||||||||
\(655\) | 13.1309 | 0.513067 | ||||||||
\(656\) | −118.909 | −4.64263 | ||||||||
\(657\) | 5.57048 | 0.217325 | ||||||||
\(658\) | −0.285014 | −0.0111110 | ||||||||
\(659\) | 25.3835 | 0.988799 | 0.494400 | − | 0.869235i | \(-0.335388\pi\) | ||||
0.494400 | + | 0.869235i | \(0.335388\pi\) | |||||||
\(660\) | −94.4669 | −3.67712 | ||||||||
\(661\) | −38.6692 | −1.50406 | −0.752029 | − | 0.659130i | \(-0.770925\pi\) | ||||
−0.752029 | + | 0.659130i | \(0.770925\pi\) | |||||||
\(662\) | −51.5988 | −2.00544 | ||||||||
\(663\) | −44.7036 | −1.73614 | ||||||||
\(664\) | −81.2300 | −3.15233 | ||||||||
\(665\) | 0.273697 | 0.0106135 | ||||||||
\(666\) | 96.6619 | 3.74557 | ||||||||
\(667\) | −5.68337 | −0.220061 | ||||||||
\(668\) | 100.913 | 3.90444 | ||||||||
\(669\) | −21.0088 | −0.812246 | ||||||||
\(670\) | −24.2238 | −0.935848 | ||||||||
\(671\) | −13.7379 | −0.530348 | ||||||||
\(672\) | −8.12366 | −0.313377 | ||||||||
\(673\) | −27.4794 | −1.05925 | −0.529627 | − | 0.848231i | \(-0.677668\pi\) | ||||
−0.529627 | + | 0.848231i | \(0.677668\pi\) | |||||||
\(674\) | −15.5386 | −0.598523 | ||||||||
\(675\) | 27.0518 | 1.04122 | ||||||||
\(676\) | −30.4648 | −1.17172 | ||||||||
\(677\) | −10.5375 | −0.404989 | −0.202495 | − | 0.979283i | \(-0.564905\pi\) | ||||
−0.202495 | + | 0.979283i | \(0.564905\pi\) | |||||||
\(678\) | −99.2940 | −3.81336 | ||||||||
\(679\) | 0.360093 | 0.0138191 | ||||||||
\(680\) | 74.1077 | 2.84190 | ||||||||
\(681\) | −92.7517 | −3.55425 | ||||||||
\(682\) | 60.1876 | 2.30470 | ||||||||
\(683\) | 15.2453 | 0.583345 | 0.291673 | − | 0.956518i | \(-0.405788\pi\) | ||||
0.291673 | + | 0.956518i | \(0.405788\pi\) | |||||||
\(684\) | −34.7538 | −1.32885 | ||||||||
\(685\) | −22.5492 | −0.861562 | ||||||||
\(686\) | −6.21679 | −0.237358 | ||||||||
\(687\) | −29.4490 | −1.12355 | ||||||||
\(688\) | 77.4620 | 2.95321 | ||||||||
\(689\) | −34.8294 | −1.32690 | ||||||||
\(690\) | −75.6089 | −2.87838 | ||||||||
\(691\) | 45.9577 | 1.74831 | 0.874157 | − | 0.485644i | \(-0.161415\pi\) | ||||
0.874157 | + | 0.485644i | \(0.161415\pi\) | |||||||
\(692\) | 27.9640 | 1.06303 | ||||||||
\(693\) | −4.03431 | −0.153251 | ||||||||
\(694\) | −42.6223 | −1.61792 | ||||||||
\(695\) | 12.5495 | 0.476029 | ||||||||
\(696\) | 27.0106 | 1.02383 | ||||||||
\(697\) | 52.7968 | 1.99982 | ||||||||
\(698\) | 94.5699 | 3.57952 | ||||||||
\(699\) | −78.9556 | −2.98638 | ||||||||
\(700\) | 1.96728 | 0.0743561 | ||||||||
\(701\) | 35.0263 | 1.32292 | 0.661462 | − | 0.749979i | \(-0.269936\pi\) | ||||
0.661462 | + | 0.749979i | \(0.269936\pi\) | |||||||
\(702\) | −83.5742 | −3.15431 | ||||||||
\(703\) | 5.34837 | 0.201718 | ||||||||
\(704\) | 62.5435 | 2.35720 | ||||||||
\(705\) | 3.28957 | 0.123892 | ||||||||
\(706\) | −47.4513 | −1.78585 | ||||||||
\(707\) | −1.56033 | −0.0586822 | ||||||||
\(708\) | 37.4186 | 1.40628 | ||||||||
\(709\) | −3.24133 | −0.121731 | −0.0608653 | − | 0.998146i | \(-0.519386\pi\) | ||||
−0.0608653 | + | 0.998146i | \(0.519386\pi\) | |||||||
\(710\) | −20.1330 | −0.755578 | ||||||||
\(711\) | −65.4958 | −2.45628 | ||||||||
\(712\) | −111.071 | −4.16257 | ||||||||
\(713\) | 34.6738 | 1.29854 | ||||||||
\(714\) | 7.48059 | 0.279954 | ||||||||
\(715\) | −15.6464 | −0.585143 | ||||||||
\(716\) | 19.6374 | 0.733885 | ||||||||
\(717\) | −14.1128 | −0.527051 | ||||||||
\(718\) | −93.5946 | −3.49292 | ||||||||
\(719\) | 9.58408 | 0.357426 | 0.178713 | − | 0.983901i | \(-0.442807\pi\) | ||||
0.178713 | + | 0.983901i | \(0.442807\pi\) | |||||||
\(720\) | 134.714 | 5.02049 | ||||||||
\(721\) | −1.41369 | −0.0526486 | ||||||||
\(722\) | −2.67158 | −0.0994257 | ||||||||
\(723\) | 73.5884 | 2.73678 | ||||||||
\(724\) | 67.1998 | 2.49746 | ||||||||
\(725\) | −2.37121 | −0.0880647 | ||||||||
\(726\) | 15.2072 | 0.564391 | ||||||||
\(727\) | −13.2950 | −0.493083 | −0.246542 | − | 0.969132i | \(-0.579294\pi\) | ||||
−0.246542 | + | 0.969132i | \(0.579294\pi\) | |||||||
\(728\) | −3.71163 | −0.137562 | ||||||||
\(729\) | 1.12442 | 0.0416450 | ||||||||
\(730\) | −3.61519 | −0.133804 | ||||||||
\(731\) | −34.3939 | −1.27210 | ||||||||
\(732\) | 61.5918 | 2.27650 | ||||||||
\(733\) | −15.1404 | −0.559224 | −0.279612 | − | 0.960113i | \(-0.590206\pi\) | ||||
−0.279612 | + | 0.960113i | \(0.590206\pi\) | |||||||
\(734\) | −70.0061 | −2.58397 | ||||||||
\(735\) | 35.8053 | 1.32070 | ||||||||
\(736\) | 86.0234 | 3.17086 | ||||||||
\(737\) | 19.7564 | 0.727737 | ||||||||
\(738\) | 177.354 | 6.52850 | ||||||||
\(739\) | 23.0991 | 0.849712 | 0.424856 | − | 0.905261i | \(-0.360325\pi\) | ||||
0.424856 | + | 0.905261i | \(0.360325\pi\) | |||||||
\(740\) | −45.1539 | −1.65989 | ||||||||
\(741\) | −8.30888 | −0.305234 | ||||||||
\(742\) | 5.82827 | 0.213962 | ||||||||
\(743\) | −35.6640 | −1.30838 | −0.654192 | − | 0.756329i | \(-0.726991\pi\) | ||||
−0.654192 | + | 0.756329i | \(0.726991\pi\) | |||||||
\(744\) | −164.790 | −6.04149 | ||||||||
\(745\) | 9.90979 | 0.363067 | ||||||||
\(746\) | 88.1507 | 3.22743 | ||||||||
\(747\) | 65.5628 | 2.39882 | ||||||||
\(748\) | −98.9708 | −3.61873 | ||||||||
\(749\) | 0.933655 | 0.0341150 | ||||||||
\(750\) | −100.143 | −3.65672 | ||||||||
\(751\) | 10.8134 | 0.394585 | 0.197293 | − | 0.980345i | \(-0.436785\pi\) | ||||
0.197293 | + | 0.980345i | \(0.436785\pi\) | |||||||
\(752\) | −7.76201 | −0.283051 | ||||||||
\(753\) | 93.8275 | 3.41927 | ||||||||
\(754\) | 7.32567 | 0.266785 | ||||||||
\(755\) | −36.3571 | −1.32317 | ||||||||
\(756\) | 10.0662 | 0.366105 | ||||||||
\(757\) | 47.4641 | 1.72511 | 0.862557 | − | 0.505960i | \(-0.168862\pi\) | ||||
0.862557 | + | 0.505960i | \(0.168862\pi\) | |||||||
\(758\) | 13.3149 | 0.483619 | ||||||||
\(759\) | 61.6650 | 2.23830 | ||||||||
\(760\) | 13.7741 | 0.499639 | ||||||||
\(761\) | −0.160414 | −0.00581500 | −0.00290750 | − | 0.999996i | \(-0.500925\pi\) | ||||
−0.00290750 | + | 0.999996i | \(0.500925\pi\) | |||||||
\(762\) | 50.8226 | 1.84111 | ||||||||
\(763\) | −2.12336 | −0.0768707 | ||||||||
\(764\) | 66.6170 | 2.41012 | ||||||||
\(765\) | −59.8142 | −2.16259 | ||||||||
\(766\) | 83.9391 | 3.03284 | ||||||||
\(767\) | 6.19759 | 0.223782 | ||||||||
\(768\) | −19.7779 | −0.713673 | ||||||||
\(769\) | 12.0948 | 0.436148 | 0.218074 | − | 0.975932i | \(-0.430023\pi\) | ||||
0.218074 | + | 0.975932i | \(0.430023\pi\) | |||||||
\(770\) | 2.61823 | 0.0943545 | ||||||||
\(771\) | −51.8551 | −1.86751 | ||||||||
\(772\) | 15.4844 | 0.557295 | ||||||||
\(773\) | −10.3243 | −0.371339 | −0.185670 | − | 0.982612i | \(-0.559445\pi\) | ||||
−0.185670 | + | 0.982612i | \(0.559445\pi\) | |||||||
\(774\) | −115.535 | −4.15283 | ||||||||
\(775\) | 14.4666 | 0.519656 | ||||||||
\(776\) | 18.1221 | 0.650544 | ||||||||
\(777\) | −2.78349 | −0.0998571 | ||||||||
\(778\) | 33.2307 | 1.19138 | ||||||||
\(779\) | 9.81313 | 0.351592 | ||||||||
\(780\) | 70.1481 | 2.51171 | ||||||||
\(781\) | 16.4200 | 0.587555 | ||||||||
\(782\) | −79.2137 | −2.83268 | ||||||||
\(783\) | −12.1331 | −0.433602 | ||||||||
\(784\) | −84.4855 | −3.01734 | ||||||||
\(785\) | −35.4441 | −1.26505 | ||||||||
\(786\) | 66.7053 | 2.37930 | ||||||||
\(787\) | −33.2274 | −1.18443 | −0.592215 | − | 0.805780i | \(-0.701747\pi\) | ||||
−0.592215 | + | 0.805780i | \(0.701747\pi\) | |||||||
\(788\) | −64.4786 | −2.29695 | ||||||||
\(789\) | −74.2459 | −2.64322 | ||||||||
\(790\) | 42.5061 | 1.51230 | ||||||||
\(791\) | 1.98085 | 0.0704311 | ||||||||
\(792\) | −203.031 | −7.21439 | ||||||||
\(793\) | 10.2014 | 0.362261 | ||||||||
\(794\) | 55.0748 | 1.95453 | ||||||||
\(795\) | −67.2687 | −2.38577 | ||||||||
\(796\) | −41.3772 | −1.46658 | ||||||||
\(797\) | 45.4304 | 1.60923 | 0.804613 | − | 0.593799i | \(-0.202373\pi\) | ||||
0.804613 | + | 0.593799i | \(0.202373\pi\) | |||||||
\(798\) | 1.39039 | 0.0492191 | ||||||||
\(799\) | 3.44640 | 0.121925 | ||||||||
\(800\) | 35.8906 | 1.26893 | ||||||||
\(801\) | 89.6485 | 3.16757 | ||||||||
\(802\) | −38.0675 | −1.34421 | ||||||||
\(803\) | 2.94847 | 0.104049 | ||||||||
\(804\) | −88.5747 | −3.12379 | ||||||||
\(805\) | 1.50835 | 0.0531624 | ||||||||
\(806\) | −44.6934 | −1.57426 | ||||||||
\(807\) | 39.6411 | 1.39543 | ||||||||
\(808\) | −78.5252 | −2.76251 | ||||||||
\(809\) | 26.5444 | 0.933252 | 0.466626 | − | 0.884455i | \(-0.345469\pi\) | ||||
0.466626 | + | 0.884455i | \(0.345469\pi\) | |||||||
\(810\) | −72.3100 | −2.54072 | ||||||||
\(811\) | 36.0025 | 1.26422 | 0.632109 | − | 0.774880i | \(-0.282190\pi\) | ||||
0.632109 | + | 0.774880i | \(0.282190\pi\) | |||||||
\(812\) | −0.882352 | −0.0309645 | ||||||||
\(813\) | −12.0357 | −0.422109 | ||||||||
\(814\) | 51.1634 | 1.79328 | ||||||||
\(815\) | −11.9534 | −0.418709 | ||||||||
\(816\) | 203.725 | 7.13180 | ||||||||
\(817\) | −6.39265 | −0.223650 | ||||||||
\(818\) | −9.67651 | −0.338331 | ||||||||
\(819\) | 2.99575 | 0.104680 | ||||||||
\(820\) | −82.8479 | −2.89317 | ||||||||
\(821\) | −25.9523 | −0.905743 | −0.452871 | − | 0.891576i | \(-0.649600\pi\) | ||||
−0.452871 | + | 0.891576i | \(0.649600\pi\) | |||||||
\(822\) | −114.551 | −3.99541 | ||||||||
\(823\) | −33.8569 | −1.18018 | −0.590088 | − | 0.807339i | \(-0.700907\pi\) | ||||
−0.590088 | + | 0.807339i | \(0.700907\pi\) | |||||||
\(824\) | −71.1456 | −2.47847 | ||||||||
\(825\) | 25.7279 | 0.895729 | ||||||||
\(826\) | −1.03709 | −0.0360849 | ||||||||
\(827\) | −12.7569 | −0.443600 | −0.221800 | − | 0.975092i | \(-0.571193\pi\) | ||||
−0.221800 | + | 0.975092i | \(0.571193\pi\) | |||||||
\(828\) | −191.529 | −6.65610 | ||||||||
\(829\) | −12.4453 | −0.432244 | −0.216122 | − | 0.976366i | \(-0.569341\pi\) | ||||
−0.216122 | + | 0.976366i | \(0.569341\pi\) | |||||||
\(830\) | −42.5496 | −1.47692 | ||||||||
\(831\) | −36.1225 | −1.25307 | ||||||||
\(832\) | −46.4428 | −1.61011 | ||||||||
\(833\) | 37.5123 | 1.29973 | ||||||||
\(834\) | 63.7517 | 2.20754 | ||||||||
\(835\) | 32.2811 | 1.11713 | ||||||||
\(836\) | −18.3953 | −0.636214 | ||||||||
\(837\) | 74.0231 | 2.55861 | ||||||||
\(838\) | −10.8132 | −0.373536 | ||||||||
\(839\) | −30.6781 | −1.05912 | −0.529562 | − | 0.848271i | \(-0.677644\pi\) | ||||
−0.529562 | + | 0.848271i | \(0.677644\pi\) | |||||||
\(840\) | −7.16854 | −0.247338 | ||||||||
\(841\) | −27.9365 | −0.963327 | ||||||||
\(842\) | −36.6955 | −1.26461 | ||||||||
\(843\) | 9.86093 | 0.339628 | ||||||||
\(844\) | 5.13731 | 0.176834 | ||||||||
\(845\) | −9.74539 | −0.335252 | ||||||||
\(846\) | 11.5771 | 0.398029 | ||||||||
\(847\) | −0.303373 | −0.0104240 | ||||||||
\(848\) | 158.726 | 5.45067 | ||||||||
\(849\) | −32.1580 | −1.10366 | ||||||||
\(850\) | −33.0495 | −1.13359 | ||||||||
\(851\) | 29.4750 | 1.01039 | ||||||||
\(852\) | −73.6165 | −2.52206 | ||||||||
\(853\) | 53.2139 | 1.82201 | 0.911004 | − | 0.412397i | \(-0.135308\pi\) | ||||
0.911004 | + | 0.412397i | \(0.135308\pi\) | |||||||
\(854\) | −1.70707 | −0.0584147 | ||||||||
\(855\) | −11.1174 | −0.380208 | ||||||||
\(856\) | 46.9872 | 1.60599 | ||||||||
\(857\) | 32.4027 | 1.10685 | 0.553427 | − | 0.832897i | \(-0.313320\pi\) | ||||
0.553427 | + | 0.832897i | \(0.313320\pi\) | |||||||
\(858\) | −79.4841 | −2.71354 | ||||||||
\(859\) | 29.5708 | 1.00894 | 0.504471 | − | 0.863429i | \(-0.331688\pi\) | ||||
0.504471 | + | 0.863429i | \(0.331688\pi\) | |||||||
\(860\) | 53.9702 | 1.84037 | ||||||||
\(861\) | −5.10712 | −0.174050 | ||||||||
\(862\) | −100.982 | −3.43947 | ||||||||
\(863\) | −12.9991 | −0.442494 | −0.221247 | − | 0.975218i | \(-0.571013\pi\) | ||||
−0.221247 | + | 0.975218i | \(0.571013\pi\) | |||||||
\(864\) | 183.646 | 6.24777 | ||||||||
\(865\) | 8.94541 | 0.304153 | ||||||||
\(866\) | 85.2133 | 2.89567 | ||||||||
\(867\) | −37.3325 | −1.26788 | ||||||||
\(868\) | 5.38316 | 0.182717 | ||||||||
\(869\) | −34.6671 | −1.17600 | ||||||||
\(870\) | 14.1486 | 0.479683 | ||||||||
\(871\) | −14.6705 | −0.497091 | ||||||||
\(872\) | −106.860 | −3.61874 | ||||||||
\(873\) | −14.6268 | −0.495042 | ||||||||
\(874\) | −14.7231 | −0.498017 | ||||||||
\(875\) | 1.99780 | 0.0675379 | ||||||||
\(876\) | −13.2190 | −0.446628 | ||||||||
\(877\) | 52.6144 | 1.77666 | 0.888330 | − | 0.459205i | \(-0.151866\pi\) | ||||
0.888330 | + | 0.459205i | \(0.151866\pi\) | |||||||
\(878\) | 11.3928 | 0.384488 | ||||||||
\(879\) | 56.1476 | 1.89381 | ||||||||
\(880\) | 71.3044 | 2.40367 | ||||||||
\(881\) | −8.55802 | −0.288327 | −0.144164 | − | 0.989554i | \(-0.546049\pi\) | ||||
−0.144164 | + | 0.989554i | \(0.546049\pi\) | |||||||
\(882\) | 126.011 | 4.24300 | ||||||||
\(883\) | −22.4962 | −0.757057 | −0.378528 | − | 0.925590i | \(-0.623570\pi\) | ||||
−0.378528 | + | 0.925590i | \(0.623570\pi\) | |||||||
\(884\) | 73.4925 | 2.47182 | ||||||||
\(885\) | 11.9699 | 0.402362 | ||||||||
\(886\) | 39.6655 | 1.33259 | ||||||||
\(887\) | 7.77461 | 0.261046 | 0.130523 | − | 0.991445i | \(-0.458334\pi\) | ||||
0.130523 | + | 0.991445i | \(0.458334\pi\) | |||||||
\(888\) | −140.082 | −4.70085 | ||||||||
\(889\) | −1.01388 | −0.0340044 | ||||||||
\(890\) | −58.1810 | −1.95023 | ||||||||
\(891\) | 58.9745 | 1.97572 | ||||||||
\(892\) | 34.5383 | 1.15643 | ||||||||
\(893\) | 0.640569 | 0.0214358 | ||||||||
\(894\) | 50.3420 | 1.68369 | ||||||||
\(895\) | 6.28182 | 0.209978 | ||||||||
\(896\) | 2.57230 | 0.0859345 | ||||||||
\(897\) | −45.7905 | −1.52890 | ||||||||
\(898\) | −90.1498 | −3.00834 | ||||||||
\(899\) | −6.48847 | −0.216403 | ||||||||
\(900\) | −79.9098 | −2.66366 | ||||||||
\(901\) | −70.4758 | −2.34789 | ||||||||
\(902\) | 93.8741 | 3.12566 | ||||||||
\(903\) | 3.32697 | 0.110715 | ||||||||
\(904\) | 99.6886 | 3.31559 | ||||||||
\(905\) | 21.4966 | 0.714570 | ||||||||
\(906\) | −184.695 | −6.13607 | ||||||||
\(907\) | −10.3233 | −0.342780 | −0.171390 | − | 0.985203i | \(-0.554826\pi\) | ||||
−0.171390 | + | 0.985203i | \(0.554826\pi\) | |||||||
\(908\) | 152.483 | 5.06034 | ||||||||
\(909\) | 63.3797 | 2.10217 | ||||||||
\(910\) | −1.94421 | −0.0644501 | ||||||||
\(911\) | −7.22473 | −0.239366 | −0.119683 | − | 0.992812i | \(-0.538188\pi\) | ||||
−0.119683 | + | 0.992812i | \(0.538188\pi\) | |||||||
\(912\) | 37.8655 | 1.25385 | ||||||||
\(913\) | 34.7026 | 1.14849 | ||||||||
\(914\) | −18.0230 | −0.596147 | ||||||||
\(915\) | 19.7026 | 0.651349 | ||||||||
\(916\) | 48.4141 | 1.59965 | ||||||||
\(917\) | −1.33073 | −0.0439446 | ||||||||
\(918\) | −169.109 | −5.58142 | ||||||||
\(919\) | 29.7836 | 0.982470 | 0.491235 | − | 0.871027i | \(-0.336546\pi\) | ||||
0.491235 | + | 0.871027i | \(0.336546\pi\) | |||||||
\(920\) | 75.9094 | 2.50266 | ||||||||
\(921\) | −89.8689 | −2.96128 | ||||||||
\(922\) | 33.5826 | 1.10598 | ||||||||
\(923\) | −12.1930 | −0.401337 | ||||||||
\(924\) | 9.57359 | 0.314948 | ||||||||
\(925\) | 12.2976 | 0.404341 | ||||||||
\(926\) | −51.7923 | −1.70200 | ||||||||
\(927\) | 57.4234 | 1.88603 | ||||||||
\(928\) | −16.0975 | −0.528425 | ||||||||
\(929\) | −29.8516 | −0.979398 | −0.489699 | − | 0.871891i | \(-0.662893\pi\) | ||||
−0.489699 | + | 0.871891i | \(0.662893\pi\) | |||||||
\(930\) | −86.3196 | −2.83053 | ||||||||
\(931\) | 6.97226 | 0.228507 | ||||||||
\(932\) | 129.803 | 4.25183 | ||||||||
\(933\) | 34.4022 | 1.12628 | ||||||||
\(934\) | −63.7465 | −2.08585 | ||||||||
\(935\) | −31.6598 | −1.03539 | ||||||||
\(936\) | 150.764 | 4.92789 | ||||||||
\(937\) | −12.4308 | −0.406098 | −0.203049 | − | 0.979169i | \(-0.565085\pi\) | ||||
−0.203049 | + | 0.979169i | \(0.565085\pi\) | |||||||
\(938\) | 2.45492 | 0.0801560 | ||||||||
\(939\) | −43.7653 | −1.42823 | ||||||||
\(940\) | −5.40803 | −0.176391 | ||||||||
\(941\) | 57.7787 | 1.88353 | 0.941765 | − | 0.336271i | \(-0.109166\pi\) | ||||
0.941765 | + | 0.336271i | \(0.109166\pi\) | |||||||
\(942\) | −180.057 | −5.86657 | ||||||||
\(943\) | 54.0805 | 1.76110 | ||||||||
\(944\) | −28.2439 | −0.919259 | ||||||||
\(945\) | 3.22009 | 0.104750 | ||||||||
\(946\) | −61.1531 | −1.98826 | ||||||||
\(947\) | −12.0844 | −0.392689 | −0.196344 | − | 0.980535i | \(-0.562907\pi\) | ||||
−0.196344 | + | 0.980535i | \(0.562907\pi\) | |||||||
\(948\) | 155.424 | 5.04794 | ||||||||
\(949\) | −2.18944 | −0.0710722 | ||||||||
\(950\) | −6.14278 | −0.199298 | ||||||||
\(951\) | −70.5273 | −2.28700 | ||||||||
\(952\) | −7.51031 | −0.243411 | ||||||||
\(953\) | −1.63488 | −0.0529590 | −0.0264795 | − | 0.999649i | \(-0.508430\pi\) | ||||
−0.0264795 | + | 0.999649i | \(0.508430\pi\) | |||||||
\(954\) | −236.741 | −7.66478 | ||||||||
\(955\) | 21.3102 | 0.689580 | ||||||||
\(956\) | 23.2013 | 0.750384 | ||||||||
\(957\) | −11.5393 | −0.373013 | ||||||||
\(958\) | −21.3611 | −0.690144 | ||||||||
\(959\) | 2.28521 | 0.0737934 | ||||||||
\(960\) | −89.6984 | −2.89500 | ||||||||
\(961\) | 8.58570 | 0.276958 | ||||||||
\(962\) | −37.9923 | −1.22492 | ||||||||
\(963\) | −37.9245 | −1.22210 | ||||||||
\(964\) | −120.979 | −3.89647 | ||||||||
\(965\) | 4.95330 | 0.159452 | ||||||||
\(966\) | 7.66246 | 0.246536 | ||||||||
\(967\) | −30.2353 | −0.972303 | −0.486151 | − | 0.873875i | \(-0.661600\pi\) | ||||
−0.486151 | + | 0.873875i | \(0.661600\pi\) | |||||||
\(968\) | −15.2676 | −0.490719 | ||||||||
\(969\) | −16.8126 | −0.540100 | ||||||||
\(970\) | 9.49265 | 0.304791 | ||||||||
\(971\) | −51.5756 | −1.65514 | −0.827570 | − | 0.561362i | \(-0.810277\pi\) | ||||
−0.827570 | + | 0.561362i | \(0.810277\pi\) | |||||||
\(972\) | −83.0783 | −2.66474 | ||||||||
\(973\) | −1.27181 | −0.0407722 | ||||||||
\(974\) | −3.82715 | −0.122630 | ||||||||
\(975\) | −19.1047 | −0.611839 | ||||||||
\(976\) | −46.4900 | −1.48811 | ||||||||
\(977\) | −37.1261 | −1.18777 | −0.593884 | − | 0.804550i | \(-0.702406\pi\) | ||||
−0.593884 | + | 0.804550i | \(0.702406\pi\) | |||||||
\(978\) | −60.7235 | −1.94172 | ||||||||
\(979\) | 47.4512 | 1.51655 | ||||||||
\(980\) | −58.8637 | −1.88033 | ||||||||
\(981\) | 86.2496 | 2.75374 | ||||||||
\(982\) | 17.7158 | 0.565333 | ||||||||
\(983\) | 4.98940 | 0.159137 | 0.0795686 | − | 0.996829i | \(-0.474646\pi\) | ||||
0.0795686 | + | 0.996829i | \(0.474646\pi\) | |||||||
\(984\) | −257.021 | −8.19353 | ||||||||
\(985\) | −20.6261 | −0.657202 | ||||||||
\(986\) | 14.8232 | 0.472066 | ||||||||
\(987\) | −0.333376 | −0.0106115 | ||||||||
\(988\) | 13.6598 | 0.434575 | ||||||||
\(989\) | −35.2300 | −1.12025 | ||||||||
\(990\) | −106.351 | −3.38006 | ||||||||
\(991\) | 50.1098 | 1.59179 | 0.795895 | − | 0.605434i | \(-0.207000\pi\) | ||||
0.795895 | + | 0.605434i | \(0.207000\pi\) | |||||||
\(992\) | 98.2094 | 3.11815 | ||||||||
\(993\) | −60.3543 | −1.91528 | ||||||||
\(994\) | 2.04034 | 0.0647158 | ||||||||
\(995\) | −13.2362 | −0.419615 | ||||||||
\(996\) | −155.583 | −4.92984 | ||||||||
\(997\) | −16.8805 | −0.534609 | −0.267305 | − | 0.963612i | \(-0.586133\pi\) | ||||
−0.267305 | + | 0.963612i | \(0.586133\pi\) | |||||||
\(998\) | −57.3816 | −1.81638 | ||||||||
\(999\) | 62.9245 | 1.99084 |
(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 | 4009.2.a.f.1.3 | ✓ | 83 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.f.1.3 | ✓ | 83 | 1.1 | even | 1 | trivial |