Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, 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("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.33134 | −1.64850 | −0.824252 | − | 0.566223i | \(-0.808404\pi\) | ||||
−0.824252 | + | 0.566223i | \(0.808404\pi\) | |||||||
\(3\) | −0.785356 | −0.453426 | −0.226713 | − | 0.973962i | \(-0.572798\pi\) | ||||
−0.226713 | + | 0.973962i | \(0.572798\pi\) | |||||||
\(4\) | 3.43514 | 1.71757 | ||||||||
\(5\) | 0.539311 | 0.241187 | 0.120593 | − | 0.992702i | \(-0.461520\pi\) | ||||
0.120593 | + | 0.992702i | \(0.461520\pi\) | |||||||
\(6\) | 1.83093 | 0.747475 | ||||||||
\(7\) | −3.00025 | −1.13399 | −0.566993 | − | 0.823722i | \(-0.691894\pi\) | ||||
−0.566993 | + | 0.823722i | \(0.691894\pi\) | |||||||
\(8\) | −3.34579 | −1.18291 | ||||||||
\(9\) | −2.38322 | −0.794405 | ||||||||
\(10\) | −1.25731 | −0.397598 | ||||||||
\(11\) | −0.795769 | −0.239933 | −0.119967 | − | 0.992778i | \(-0.538279\pi\) | ||||
−0.119967 | + | 0.992778i | \(0.538279\pi\) | |||||||
\(12\) | −2.69781 | −0.778789 | ||||||||
\(13\) | −0.649389 | −0.180108 | −0.0900541 | − | 0.995937i | \(-0.528704\pi\) | ||||
−0.0900541 | + | 0.995937i | \(0.528704\pi\) | |||||||
\(14\) | 6.99459 | 1.86938 | ||||||||
\(15\) | −0.423551 | −0.109360 | ||||||||
\(16\) | 0.929885 | 0.232471 | ||||||||
\(17\) | −3.23621 | −0.784897 | −0.392448 | − | 0.919774i | \(-0.628372\pi\) | ||||
−0.392448 | + | 0.919774i | \(0.628372\pi\) | |||||||
\(18\) | 5.55608 | 1.30958 | ||||||||
\(19\) | −6.59290 | −1.51251 | −0.756257 | − | 0.654274i | \(-0.772974\pi\) | ||||
−0.756257 | + | 0.654274i | \(0.772974\pi\) | |||||||
\(20\) | 1.85260 | 0.414255 | ||||||||
\(21\) | 2.35626 | 0.514179 | ||||||||
\(22\) | 1.85521 | 0.395531 | ||||||||
\(23\) | −2.44607 | −0.510041 | −0.255021 | − | 0.966936i | \(-0.582082\pi\) | ||||
−0.255021 | + | 0.966936i | \(0.582082\pi\) | |||||||
\(24\) | 2.62763 | 0.536364 | ||||||||
\(25\) | −4.70914 | −0.941829 | ||||||||
\(26\) | 1.51395 | 0.296909 | ||||||||
\(27\) | 4.22774 | 0.813629 | ||||||||
\(28\) | −10.3063 | −1.94770 | ||||||||
\(29\) | −7.21868 | −1.34047 | −0.670237 | − | 0.742147i | \(-0.733808\pi\) | ||||
−0.670237 | + | 0.742147i | \(0.733808\pi\) | |||||||
\(30\) | 0.987440 | 0.180281 | ||||||||
\(31\) | 7.30019 | 1.31115 | 0.655577 | − | 0.755128i | \(-0.272426\pi\) | ||||
0.655577 | + | 0.755128i | \(0.272426\pi\) | |||||||
\(32\) | 4.52369 | 0.799684 | ||||||||
\(33\) | 0.624962 | 0.108792 | ||||||||
\(34\) | 7.54471 | 1.29391 | ||||||||
\(35\) | −1.61806 | −0.273503 | ||||||||
\(36\) | −8.18667 | −1.36444 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 15.3703 | 2.49339 | ||||||||
\(39\) | 0.510002 | 0.0816657 | ||||||||
\(40\) | −1.80442 | −0.285303 | ||||||||
\(41\) | −10.9274 | −1.70657 | −0.853287 | − | 0.521442i | \(-0.825394\pi\) | ||||
−0.853287 | + | 0.521442i | \(0.825394\pi\) | |||||||
\(42\) | −5.49325 | −0.847626 | ||||||||
\(43\) | −7.88053 | −1.20177 | −0.600885 | − | 0.799335i | \(-0.705185\pi\) | ||||
−0.600885 | + | 0.799335i | \(0.705185\pi\) | |||||||
\(44\) | −2.73357 | −0.412102 | ||||||||
\(45\) | −1.28529 | −0.191600 | ||||||||
\(46\) | 5.70262 | 0.840806 | ||||||||
\(47\) | −12.9550 | −1.88967 | −0.944837 | − | 0.327539i | \(-0.893781\pi\) | ||||
−0.944837 | + | 0.327539i | \(0.893781\pi\) | |||||||
\(48\) | −0.730292 | −0.105408 | ||||||||
\(49\) | 2.00148 | 0.285926 | ||||||||
\(50\) | 10.9786 | 1.55261 | ||||||||
\(51\) | 2.54158 | 0.355893 | ||||||||
\(52\) | −2.23074 | −0.309348 | ||||||||
\(53\) | 6.49773 | 0.892532 | 0.446266 | − | 0.894900i | \(-0.352754\pi\) | ||||
0.446266 | + | 0.894900i | \(0.352754\pi\) | |||||||
\(54\) | −9.85630 | −1.34127 | ||||||||
\(55\) | −0.429166 | −0.0578688 | ||||||||
\(56\) | 10.0382 | 1.34141 | ||||||||
\(57\) | 5.17777 | 0.685813 | ||||||||
\(58\) | 16.8292 | 2.20978 | ||||||||
\(59\) | −4.15850 | −0.541391 | −0.270695 | − | 0.962665i | \(-0.587254\pi\) | ||||
−0.270695 | + | 0.962665i | \(0.587254\pi\) | |||||||
\(60\) | −1.45496 | −0.187834 | ||||||||
\(61\) | 1.90087 | 0.243382 | 0.121691 | − | 0.992568i | \(-0.461168\pi\) | ||||
0.121691 | + | 0.992568i | \(0.461168\pi\) | |||||||
\(62\) | −17.0192 | −2.16144 | ||||||||
\(63\) | 7.15023 | 0.900845 | ||||||||
\(64\) | −12.4060 | −1.55075 | ||||||||
\(65\) | −0.350222 | −0.0434397 | ||||||||
\(66\) | −1.45700 | −0.179344 | ||||||||
\(67\) | 2.59315 | 0.316804 | 0.158402 | − | 0.987375i | \(-0.449366\pi\) | ||||
0.158402 | + | 0.987375i | \(0.449366\pi\) | |||||||
\(68\) | −11.1168 | −1.34811 | ||||||||
\(69\) | 1.92104 | 0.231266 | ||||||||
\(70\) | 3.77226 | 0.450871 | ||||||||
\(71\) | 2.45964 | 0.291905 | 0.145953 | − | 0.989292i | \(-0.453375\pi\) | ||||
0.145953 | + | 0.989292i | \(0.453375\pi\) | |||||||
\(72\) | 7.97373 | 0.939713 | ||||||||
\(73\) | 3.05908 | 0.358039 | 0.179019 | − | 0.983846i | \(-0.442708\pi\) | ||||
0.179019 | + | 0.983846i | \(0.442708\pi\) | |||||||
\(74\) | 2.33134 | 0.271013 | ||||||||
\(75\) | 3.69836 | 0.427049 | ||||||||
\(76\) | −22.6475 | −2.59785 | ||||||||
\(77\) | 2.38750 | 0.272081 | ||||||||
\(78\) | −1.18899 | −0.134626 | ||||||||
\(79\) | −10.3354 | −1.16282 | −0.581412 | − | 0.813609i | \(-0.697500\pi\) | ||||
−0.581412 | + | 0.813609i | \(0.697500\pi\) | |||||||
\(80\) | 0.501497 | 0.0560691 | ||||||||
\(81\) | 3.82936 | 0.425485 | ||||||||
\(82\) | 25.4755 | 2.81329 | ||||||||
\(83\) | 11.9288 | 1.30936 | 0.654681 | − | 0.755906i | \(-0.272803\pi\) | ||||
0.654681 | + | 0.755906i | \(0.272803\pi\) | |||||||
\(84\) | 8.09408 | 0.883137 | ||||||||
\(85\) | −1.74532 | −0.189307 | ||||||||
\(86\) | 18.3722 | 1.98112 | ||||||||
\(87\) | 5.66923 | 0.607806 | ||||||||
\(88\) | 2.66247 | 0.283820 | ||||||||
\(89\) | 12.9884 | 1.37677 | 0.688384 | − | 0.725346i | \(-0.258320\pi\) | ||||
0.688384 | + | 0.725346i | \(0.258320\pi\) | |||||||
\(90\) | 2.99645 | 0.315854 | ||||||||
\(91\) | 1.94833 | 0.204240 | ||||||||
\(92\) | −8.40259 | −0.876031 | ||||||||
\(93\) | −5.73326 | −0.594511 | ||||||||
\(94\) | 30.2024 | 3.11514 | ||||||||
\(95\) | −3.55562 | −0.364799 | ||||||||
\(96\) | −3.55271 | −0.362597 | ||||||||
\(97\) | −8.94380 | −0.908105 | −0.454052 | − | 0.890975i | \(-0.650022\pi\) | ||||
−0.454052 | + | 0.890975i | \(0.650022\pi\) | |||||||
\(98\) | −4.66613 | −0.471350 | ||||||||
\(99\) | 1.89649 | 0.190604 | ||||||||
\(100\) | −16.1765 | −1.61765 | ||||||||
\(101\) | −17.1608 | −1.70757 | −0.853783 | − | 0.520629i | \(-0.825698\pi\) | ||||
−0.853783 | + | 0.520629i | \(0.825698\pi\) | |||||||
\(102\) | −5.92528 | −0.586690 | ||||||||
\(103\) | 1.22033 | 0.120243 | 0.0601215 | − | 0.998191i | \(-0.480851\pi\) | ||||
0.0601215 | + | 0.998191i | \(0.480851\pi\) | |||||||
\(104\) | 2.17272 | 0.213052 | ||||||||
\(105\) | 1.27076 | 0.124013 | ||||||||
\(106\) | −15.1484 | −1.47134 | ||||||||
\(107\) | −5.50039 | −0.531743 | −0.265871 | − | 0.964008i | \(-0.585660\pi\) | ||||
−0.265871 | + | 0.964008i | \(0.585660\pi\) | |||||||
\(108\) | 14.5229 | 1.39746 | ||||||||
\(109\) | 1.00000 | 0.0957826 | ||||||||
\(110\) | 1.00053 | 0.0953970 | ||||||||
\(111\) | 0.785356 | 0.0745427 | ||||||||
\(112\) | −2.78989 | −0.263619 | ||||||||
\(113\) | −7.67104 | −0.721631 | −0.360816 | − | 0.932637i | \(-0.617502\pi\) | ||||
−0.360816 | + | 0.932637i | \(0.617502\pi\) | |||||||
\(114\) | −12.0711 | −1.13057 | ||||||||
\(115\) | −1.31919 | −0.123015 | ||||||||
\(116\) | −24.7971 | −2.30236 | ||||||||
\(117\) | 1.54763 | 0.143079 | ||||||||
\(118\) | 9.69487 | 0.892485 | ||||||||
\(119\) | 9.70944 | 0.890063 | ||||||||
\(120\) | 1.41711 | 0.129364 | ||||||||
\(121\) | −10.3668 | −0.942432 | ||||||||
\(122\) | −4.43157 | −0.401216 | ||||||||
\(123\) | 8.58190 | 0.773804 | ||||||||
\(124\) | 25.0772 | 2.25200 | ||||||||
\(125\) | −5.23624 | −0.468344 | ||||||||
\(126\) | −16.6696 | −1.48505 | ||||||||
\(127\) | −4.06695 | −0.360884 | −0.180442 | − | 0.983586i | \(-0.557753\pi\) | ||||
−0.180442 | + | 0.983586i | \(0.557753\pi\) | |||||||
\(128\) | 19.8753 | 1.75674 | ||||||||
\(129\) | 6.18903 | 0.544913 | ||||||||
\(130\) | 0.816487 | 0.0716106 | ||||||||
\(131\) | 12.8962 | 1.12675 | 0.563373 | − | 0.826203i | \(-0.309503\pi\) | ||||
0.563373 | + | 0.826203i | \(0.309503\pi\) | |||||||
\(132\) | 2.14683 | 0.186858 | ||||||||
\(133\) | 19.7803 | 1.71517 | ||||||||
\(134\) | −6.04551 | −0.522253 | ||||||||
\(135\) | 2.28007 | 0.196237 | ||||||||
\(136\) | 10.8277 | 0.928466 | ||||||||
\(137\) | 11.6034 | 0.991348 | 0.495674 | − | 0.868509i | \(-0.334921\pi\) | ||||
0.495674 | + | 0.868509i | \(0.334921\pi\) | |||||||
\(138\) | −4.47859 | −0.381243 | ||||||||
\(139\) | −12.4435 | −1.05544 | −0.527720 | − | 0.849418i | \(-0.676953\pi\) | ||||
−0.527720 | + | 0.849418i | \(0.676953\pi\) | |||||||
\(140\) | −5.55827 | −0.469760 | ||||||||
\(141\) | 10.1743 | 0.856827 | ||||||||
\(142\) | −5.73425 | −0.481207 | ||||||||
\(143\) | 0.516763 | 0.0432139 | ||||||||
\(144\) | −2.21612 | −0.184676 | ||||||||
\(145\) | −3.89311 | −0.323305 | ||||||||
\(146\) | −7.13176 | −0.590229 | ||||||||
\(147\) | −1.57188 | −0.129646 | ||||||||
\(148\) | −3.43514 | −0.282366 | ||||||||
\(149\) | 22.3239 | 1.82884 | 0.914421 | − | 0.404765i | \(-0.132647\pi\) | ||||
0.914421 | + | 0.404765i | \(0.132647\pi\) | |||||||
\(150\) | −8.62212 | −0.703993 | ||||||||
\(151\) | −0.434227 | −0.0353369 | −0.0176685 | − | 0.999844i | \(-0.505624\pi\) | ||||
−0.0176685 | + | 0.999844i | \(0.505624\pi\) | |||||||
\(152\) | 22.0584 | 1.78917 | ||||||||
\(153\) | 7.71259 | 0.623526 | ||||||||
\(154\) | −5.56607 | −0.448527 | ||||||||
\(155\) | 3.93707 | 0.316233 | ||||||||
\(156\) | 1.75193 | 0.140266 | ||||||||
\(157\) | 16.6221 | 1.32659 | 0.663296 | − | 0.748357i | \(-0.269157\pi\) | ||||
0.663296 | + | 0.748357i | \(0.269157\pi\) | |||||||
\(158\) | 24.0953 | 1.91692 | ||||||||
\(159\) | −5.10303 | −0.404697 | ||||||||
\(160\) | 2.43968 | 0.192873 | ||||||||
\(161\) | 7.33882 | 0.578380 | ||||||||
\(162\) | −8.92753 | −0.701413 | ||||||||
\(163\) | −0.309575 | −0.0242478 | −0.0121239 | − | 0.999927i | \(-0.503859\pi\) | ||||
−0.0121239 | + | 0.999927i | \(0.503859\pi\) | |||||||
\(164\) | −37.5371 | −2.93116 | ||||||||
\(165\) | 0.337049 | 0.0262392 | ||||||||
\(166\) | −27.8102 | −2.15849 | ||||||||
\(167\) | −1.37567 | −0.106453 | −0.0532263 | − | 0.998582i | \(-0.516950\pi\) | ||||
−0.0532263 | + | 0.998582i | \(0.516950\pi\) | |||||||
\(168\) | −7.88355 | −0.608229 | ||||||||
\(169\) | −12.5783 | −0.967561 | ||||||||
\(170\) | 4.06894 | 0.312073 | ||||||||
\(171\) | 15.7123 | 1.20155 | ||||||||
\(172\) | −27.0707 | −2.06412 | ||||||||
\(173\) | −17.6238 | −1.33991 | −0.669955 | − | 0.742402i | \(-0.733686\pi\) | ||||
−0.669955 | + | 0.742402i | \(0.733686\pi\) | |||||||
\(174\) | −13.2169 | −1.00197 | ||||||||
\(175\) | 14.1286 | 1.06802 | ||||||||
\(176\) | −0.739974 | −0.0557776 | ||||||||
\(177\) | 3.26591 | 0.245480 | ||||||||
\(178\) | −30.2804 | −2.26961 | ||||||||
\(179\) | −0.167386 | −0.0125110 | −0.00625552 | − | 0.999980i | \(-0.501991\pi\) | ||||
−0.00625552 | + | 0.999980i | \(0.501991\pi\) | |||||||
\(180\) | −4.41516 | −0.329086 | ||||||||
\(181\) | −17.0999 | −1.27103 | −0.635513 | − | 0.772090i | \(-0.719211\pi\) | ||||
−0.635513 | + | 0.772090i | \(0.719211\pi\) | |||||||
\(182\) | −4.54221 | −0.336691 | ||||||||
\(183\) | −1.49286 | −0.110356 | ||||||||
\(184\) | 8.18403 | 0.603335 | ||||||||
\(185\) | −0.539311 | −0.0396509 | ||||||||
\(186\) | 13.3662 | 0.980054 | ||||||||
\(187\) | 2.57528 | 0.188323 | ||||||||
\(188\) | −44.5020 | −3.24564 | ||||||||
\(189\) | −12.6843 | −0.922645 | ||||||||
\(190\) | 8.28935 | 0.601373 | ||||||||
\(191\) | −14.4227 | −1.04359 | −0.521796 | − | 0.853070i | \(-0.674738\pi\) | ||||
−0.521796 | + | 0.853070i | \(0.674738\pi\) | |||||||
\(192\) | 9.74316 | 0.703152 | ||||||||
\(193\) | −5.74160 | −0.413289 | −0.206645 | − | 0.978416i | \(-0.566254\pi\) | ||||
−0.206645 | + | 0.978416i | \(0.566254\pi\) | |||||||
\(194\) | 20.8510 | 1.49702 | ||||||||
\(195\) | 0.275049 | 0.0196967 | ||||||||
\(196\) | 6.87536 | 0.491097 | ||||||||
\(197\) | −0.439451 | −0.0313096 | −0.0156548 | − | 0.999877i | \(-0.504983\pi\) | ||||
−0.0156548 | + | 0.999877i | \(0.504983\pi\) | |||||||
\(198\) | −4.42135 | −0.314212 | ||||||||
\(199\) | −14.5105 | −1.02862 | −0.514311 | − | 0.857604i | \(-0.671952\pi\) | ||||
−0.514311 | + | 0.857604i | \(0.671952\pi\) | |||||||
\(200\) | 15.7558 | 1.11410 | ||||||||
\(201\) | −2.03655 | −0.143647 | ||||||||
\(202\) | 40.0077 | 2.81493 | ||||||||
\(203\) | 21.6578 | 1.52008 | ||||||||
\(204\) | 8.73067 | 0.611270 | ||||||||
\(205\) | −5.89326 | −0.411603 | ||||||||
\(206\) | −2.84501 | −0.198221 | ||||||||
\(207\) | 5.82952 | 0.405179 | ||||||||
\(208\) | −0.603857 | −0.0418700 | ||||||||
\(209\) | 5.24642 | 0.362902 | ||||||||
\(210\) | −2.96257 | −0.204436 | ||||||||
\(211\) | −12.2480 | −0.843188 | −0.421594 | − | 0.906785i | \(-0.638529\pi\) | ||||
−0.421594 | + | 0.906785i | \(0.638529\pi\) | |||||||
\(212\) | 22.3206 | 1.53298 | ||||||||
\(213\) | −1.93169 | −0.132357 | ||||||||
\(214\) | 12.8233 | 0.876581 | ||||||||
\(215\) | −4.25005 | −0.289851 | ||||||||
\(216\) | −14.1451 | −0.962454 | ||||||||
\(217\) | −21.9024 | −1.48683 | ||||||||
\(218\) | −2.33134 | −0.157898 | ||||||||
\(219\) | −2.40247 | −0.162344 | ||||||||
\(220\) | −1.47424 | −0.0993936 | ||||||||
\(221\) | 2.10156 | 0.141366 | ||||||||
\(222\) | −1.83093 | −0.122884 | ||||||||
\(223\) | 6.60184 | 0.442092 | 0.221046 | − | 0.975263i | \(-0.429053\pi\) | ||||
0.221046 | + | 0.975263i | \(0.429053\pi\) | |||||||
\(224\) | −13.5722 | −0.906831 | ||||||||
\(225\) | 11.2229 | 0.748194 | ||||||||
\(226\) | 17.8838 | 1.18961 | ||||||||
\(227\) | −3.89368 | −0.258432 | −0.129216 | − | 0.991616i | \(-0.541246\pi\) | ||||
−0.129216 | + | 0.991616i | \(0.541246\pi\) | |||||||
\(228\) | 17.7864 | 1.17793 | ||||||||
\(229\) | −23.3583 | −1.54356 | −0.771781 | − | 0.635889i | \(-0.780634\pi\) | ||||
−0.771781 | + | 0.635889i | \(0.780634\pi\) | |||||||
\(230\) | 3.07548 | 0.202791 | ||||||||
\(231\) | −1.87504 | −0.123369 | ||||||||
\(232\) | 24.1521 | 1.58567 | ||||||||
\(233\) | 24.6770 | 1.61664 | 0.808321 | − | 0.588742i | \(-0.200376\pi\) | ||||
0.808321 | + | 0.588742i | \(0.200376\pi\) | |||||||
\(234\) | −3.60806 | −0.235866 | ||||||||
\(235\) | −6.98675 | −0.455765 | ||||||||
\(236\) | −14.2850 | −0.929875 | ||||||||
\(237\) | 8.11698 | 0.527254 | ||||||||
\(238\) | −22.6360 | −1.46727 | ||||||||
\(239\) | −17.5349 | −1.13424 | −0.567121 | − | 0.823635i | \(-0.691943\pi\) | ||||
−0.567121 | + | 0.823635i | \(0.691943\pi\) | |||||||
\(240\) | −0.393854 | −0.0254232 | ||||||||
\(241\) | −22.1761 | −1.42849 | −0.714245 | − | 0.699896i | \(-0.753230\pi\) | ||||
−0.714245 | + | 0.699896i | \(0.753230\pi\) | |||||||
\(242\) | 24.1684 | 1.55360 | ||||||||
\(243\) | −15.6906 | −1.00656 | ||||||||
\(244\) | 6.52975 | 0.418025 | ||||||||
\(245\) | 1.07942 | 0.0689616 | ||||||||
\(246\) | −20.0073 | −1.27562 | ||||||||
\(247\) | 4.28136 | 0.272416 | ||||||||
\(248\) | −24.4249 | −1.55098 | ||||||||
\(249\) | −9.36840 | −0.593698 | ||||||||
\(250\) | 12.2075 | 0.772067 | ||||||||
\(251\) | 20.2005 | 1.27504 | 0.637522 | − | 0.770432i | \(-0.279959\pi\) | ||||
0.637522 | + | 0.770432i | \(0.279959\pi\) | |||||||
\(252\) | 24.5620 | 1.54726 | ||||||||
\(253\) | 1.94651 | 0.122376 | ||||||||
\(254\) | 9.48144 | 0.594919 | ||||||||
\(255\) | 1.37070 | 0.0858366 | ||||||||
\(256\) | −21.5239 | −1.34524 | ||||||||
\(257\) | −1.24949 | −0.0779411 | −0.0389705 | − | 0.999240i | \(-0.512408\pi\) | ||||
−0.0389705 | + | 0.999240i | \(0.512408\pi\) | |||||||
\(258\) | −14.4287 | −0.898292 | ||||||||
\(259\) | 3.00025 | 0.186426 | ||||||||
\(260\) | −1.20306 | −0.0746107 | ||||||||
\(261\) | 17.2037 | 1.06488 | ||||||||
\(262\) | −30.0654 | −1.85745 | ||||||||
\(263\) | 5.30809 | 0.327311 | 0.163656 | − | 0.986518i | \(-0.447671\pi\) | ||||
0.163656 | + | 0.986518i | \(0.447671\pi\) | |||||||
\(264\) | −2.09099 | −0.128691 | ||||||||
\(265\) | 3.50429 | 0.215267 | ||||||||
\(266\) | −46.1146 | −2.82747 | ||||||||
\(267\) | −10.2005 | −0.624262 | ||||||||
\(268\) | 8.90783 | 0.544132 | ||||||||
\(269\) | 12.7805 | 0.779240 | 0.389620 | − | 0.920976i | \(-0.372606\pi\) | ||||
0.389620 | + | 0.920976i | \(0.372606\pi\) | |||||||
\(270\) | −5.31560 | −0.323497 | ||||||||
\(271\) | 7.20552 | 0.437704 | 0.218852 | − | 0.975758i | \(-0.429769\pi\) | ||||
0.218852 | + | 0.975758i | \(0.429769\pi\) | |||||||
\(272\) | −3.00931 | −0.182466 | ||||||||
\(273\) | −1.53013 | −0.0926078 | ||||||||
\(274\) | −27.0515 | −1.63424 | ||||||||
\(275\) | 3.74739 | 0.225976 | ||||||||
\(276\) | 6.59903 | 0.397215 | ||||||||
\(277\) | −10.7882 | −0.648202 | −0.324101 | − | 0.946022i | \(-0.605062\pi\) | ||||
−0.324101 | + | 0.946022i | \(0.605062\pi\) | |||||||
\(278\) | 29.0099 | 1.73990 | ||||||||
\(279\) | −17.3979 | −1.04159 | ||||||||
\(280\) | 5.41370 | 0.323530 | ||||||||
\(281\) | −30.0396 | −1.79201 | −0.896007 | − | 0.444041i | \(-0.853545\pi\) | ||||
−0.896007 | + | 0.444041i | \(0.853545\pi\) | |||||||
\(282\) | −23.7196 | −1.41248 | ||||||||
\(283\) | −17.3914 | −1.03381 | −0.516905 | − | 0.856042i | \(-0.672916\pi\) | ||||
−0.516905 | + | 0.856042i | \(0.672916\pi\) | |||||||
\(284\) | 8.44919 | 0.501367 | ||||||||
\(285\) | 2.79243 | 0.165409 | ||||||||
\(286\) | −1.20475 | −0.0712384 | ||||||||
\(287\) | 32.7849 | 1.93523 | ||||||||
\(288\) | −10.7809 | −0.635273 | ||||||||
\(289\) | −6.52693 | −0.383937 | ||||||||
\(290\) | 9.07615 | 0.532970 | ||||||||
\(291\) | 7.02407 | 0.411758 | ||||||||
\(292\) | 10.5084 | 0.614956 | ||||||||
\(293\) | −15.9269 | −0.930458 | −0.465229 | − | 0.885190i | \(-0.654028\pi\) | ||||
−0.465229 | + | 0.885190i | \(0.654028\pi\) | |||||||
\(294\) | 3.66458 | 0.213722 | ||||||||
\(295\) | −2.24272 | −0.130576 | ||||||||
\(296\) | 3.34579 | 0.194470 | ||||||||
\(297\) | −3.36431 | −0.195217 | ||||||||
\(298\) | −52.0445 | −3.01485 | ||||||||
\(299\) | 1.58845 | 0.0918626 | ||||||||
\(300\) | 12.7044 | 0.733486 | ||||||||
\(301\) | 23.6435 | 1.36279 | ||||||||
\(302\) | 1.01233 | 0.0582531 | ||||||||
\(303\) | 13.4774 | 0.774255 | ||||||||
\(304\) | −6.13064 | −0.351616 | ||||||||
\(305\) | 1.02516 | 0.0587005 | ||||||||
\(306\) | −17.9807 | −1.02789 | ||||||||
\(307\) | 3.28079 | 0.187245 | 0.0936224 | − | 0.995608i | \(-0.470155\pi\) | ||||
0.0936224 | + | 0.995608i | \(0.470155\pi\) | |||||||
\(308\) | 8.20139 | 0.467318 | ||||||||
\(309\) | −0.958397 | −0.0545213 | ||||||||
\(310\) | −9.17864 | −0.521312 | ||||||||
\(311\) | 14.3857 | 0.815738 | 0.407869 | − | 0.913040i | \(-0.366272\pi\) | ||||
0.407869 | + | 0.913040i | \(0.366272\pi\) | |||||||
\(312\) | −1.70636 | −0.0966034 | ||||||||
\(313\) | 17.8657 | 1.00983 | 0.504914 | − | 0.863170i | \(-0.331524\pi\) | ||||
0.504914 | + | 0.863170i | \(0.331524\pi\) | |||||||
\(314\) | −38.7518 | −2.18689 | ||||||||
\(315\) | 3.85620 | 0.217272 | ||||||||
\(316\) | −35.5035 | −1.99723 | ||||||||
\(317\) | 4.28569 | 0.240708 | 0.120354 | − | 0.992731i | \(-0.461597\pi\) | ||||
0.120354 | + | 0.992731i | \(0.461597\pi\) | |||||||
\(318\) | 11.8969 | 0.667145 | ||||||||
\(319\) | 5.74440 | 0.321624 | ||||||||
\(320\) | −6.69070 | −0.374022 | ||||||||
\(321\) | 4.31977 | 0.241106 | ||||||||
\(322\) | −17.1093 | −0.953462 | ||||||||
\(323\) | 21.3360 | 1.18717 | ||||||||
\(324\) | 13.1544 | 0.730798 | ||||||||
\(325\) | 3.05807 | 0.169631 | ||||||||
\(326\) | 0.721725 | 0.0399726 | ||||||||
\(327\) | −0.785356 | −0.0434303 | ||||||||
\(328\) | 36.5607 | 2.01873 | ||||||||
\(329\) | 38.8681 | 2.14287 | ||||||||
\(330\) | −0.785774 | −0.0432554 | ||||||||
\(331\) | 14.8114 | 0.814107 | 0.407053 | − | 0.913404i | \(-0.366556\pi\) | ||||
0.407053 | + | 0.913404i | \(0.366556\pi\) | |||||||
\(332\) | 40.9772 | 2.24892 | ||||||||
\(333\) | 2.38322 | 0.130599 | ||||||||
\(334\) | 3.20715 | 0.175487 | ||||||||
\(335\) | 1.39851 | 0.0764090 | ||||||||
\(336\) | 2.19105 | 0.119532 | ||||||||
\(337\) | 10.6619 | 0.580793 | 0.290397 | − | 0.956906i | \(-0.406213\pi\) | ||||
0.290397 | + | 0.956906i | \(0.406213\pi\) | |||||||
\(338\) | 29.3243 | 1.59503 | ||||||||
\(339\) | 6.02450 | 0.327206 | ||||||||
\(340\) | −5.99542 | −0.325148 | ||||||||
\(341\) | −5.80927 | −0.314589 | ||||||||
\(342\) | −36.6307 | −1.98076 | ||||||||
\(343\) | 14.9968 | 0.809750 | ||||||||
\(344\) | 26.3666 | 1.42159 | ||||||||
\(345\) | 1.03604 | 0.0557783 | ||||||||
\(346\) | 41.0869 | 2.20885 | ||||||||
\(347\) | 21.3224 | 1.14465 | 0.572323 | − | 0.820028i | \(-0.306042\pi\) | ||||
0.572323 | + | 0.820028i | \(0.306042\pi\) | |||||||
\(348\) | 19.4746 | 1.04395 | ||||||||
\(349\) | 19.0377 | 1.01907 | 0.509533 | − | 0.860451i | \(-0.329818\pi\) | ||||
0.509533 | + | 0.860451i | \(0.329818\pi\) | |||||||
\(350\) | −32.9385 | −1.76064 | ||||||||
\(351\) | −2.74545 | −0.146541 | ||||||||
\(352\) | −3.59981 | −0.191871 | ||||||||
\(353\) | 13.5897 | 0.723308 | 0.361654 | − | 0.932312i | \(-0.382212\pi\) | ||||
0.361654 | + | 0.932312i | \(0.382212\pi\) | |||||||
\(354\) | −7.61393 | −0.404676 | ||||||||
\(355\) | 1.32651 | 0.0704038 | ||||||||
\(356\) | 44.6169 | 2.36469 | ||||||||
\(357\) | −7.62537 | −0.403577 | ||||||||
\(358\) | 0.390234 | 0.0206245 | ||||||||
\(359\) | 18.8696 | 0.995901 | 0.497951 | − | 0.867205i | \(-0.334086\pi\) | ||||
0.497951 | + | 0.867205i | \(0.334086\pi\) | |||||||
\(360\) | 4.30032 | 0.226647 | ||||||||
\(361\) | 24.4663 | 1.28770 | ||||||||
\(362\) | 39.8656 | 2.09529 | ||||||||
\(363\) | 8.14160 | 0.427323 | ||||||||
\(364\) | 6.69277 | 0.350796 | ||||||||
\(365\) | 1.64980 | 0.0863543 | ||||||||
\(366\) | 3.48037 | 0.181922 | ||||||||
\(367\) | 7.02187 | 0.366539 | 0.183269 | − | 0.983063i | \(-0.441332\pi\) | ||||
0.183269 | + | 0.983063i | \(0.441332\pi\) | |||||||
\(368\) | −2.27457 | −0.118570 | ||||||||
\(369\) | 26.0423 | 1.35571 | ||||||||
\(370\) | 1.25731 | 0.0653647 | ||||||||
\(371\) | −19.4948 | −1.01212 | ||||||||
\(372\) | −19.6945 | −1.02111 | ||||||||
\(373\) | 9.72342 | 0.503460 | 0.251730 | − | 0.967798i | \(-0.419001\pi\) | ||||
0.251730 | + | 0.967798i | \(0.419001\pi\) | |||||||
\(374\) | −6.00384 | −0.310451 | ||||||||
\(375\) | 4.11232 | 0.212359 | ||||||||
\(376\) | 43.3445 | 2.23532 | ||||||||
\(377\) | 4.68773 | 0.241430 | ||||||||
\(378\) | 29.5713 | 1.52098 | ||||||||
\(379\) | 8.41766 | 0.432386 | 0.216193 | − | 0.976351i | \(-0.430636\pi\) | ||||
0.216193 | + | 0.976351i | \(0.430636\pi\) | |||||||
\(380\) | −12.2140 | −0.626567 | ||||||||
\(381\) | 3.19401 | 0.163634 | ||||||||
\(382\) | 33.6242 | 1.72037 | ||||||||
\(383\) | 26.3782 | 1.34787 | 0.673933 | − | 0.738793i | \(-0.264604\pi\) | ||||
0.673933 | + | 0.738793i | \(0.264604\pi\) | |||||||
\(384\) | −15.6092 | −0.796552 | ||||||||
\(385\) | 1.28761 | 0.0656224 | ||||||||
\(386\) | 13.3856 | 0.681309 | ||||||||
\(387\) | 18.7810 | 0.954692 | ||||||||
\(388\) | −30.7232 | −1.55973 | ||||||||
\(389\) | −23.5909 | −1.19610 | −0.598052 | − | 0.801457i | \(-0.704058\pi\) | ||||
−0.598052 | + | 0.801457i | \(0.704058\pi\) | |||||||
\(390\) | −0.641233 | −0.0324701 | ||||||||
\(391\) | 7.91601 | 0.400330 | ||||||||
\(392\) | −6.69653 | −0.338226 | ||||||||
\(393\) | −10.1281 | −0.510896 | ||||||||
\(394\) | 1.02451 | 0.0516139 | ||||||||
\(395\) | −5.57399 | −0.280458 | ||||||||
\(396\) | 6.51469 | 0.327376 | ||||||||
\(397\) | −24.3525 | −1.22222 | −0.611109 | − | 0.791546i | \(-0.709276\pi\) | ||||
−0.611109 | + | 0.791546i | \(0.709276\pi\) | |||||||
\(398\) | 33.8289 | 1.69569 | ||||||||
\(399\) | −15.5346 | −0.777703 | ||||||||
\(400\) | −4.37896 | −0.218948 | ||||||||
\(401\) | 21.2851 | 1.06293 | 0.531464 | − | 0.847081i | \(-0.321642\pi\) | ||||
0.531464 | + | 0.847081i | \(0.321642\pi\) | |||||||
\(402\) | 4.74788 | 0.236803 | ||||||||
\(403\) | −4.74067 | −0.236149 | ||||||||
\(404\) | −58.9498 | −2.93286 | ||||||||
\(405\) | 2.06521 | 0.102621 | ||||||||
\(406\) | −50.4917 | −2.50586 | ||||||||
\(407\) | 0.795769 | 0.0394448 | ||||||||
\(408\) | −8.50358 | −0.420990 | ||||||||
\(409\) | −15.6659 | −0.774630 | −0.387315 | − | 0.921948i | \(-0.626597\pi\) | ||||
−0.387315 | + | 0.921948i | \(0.626597\pi\) | |||||||
\(410\) | 13.7392 | 0.678530 | ||||||||
\(411\) | −9.11283 | −0.449503 | ||||||||
\(412\) | 4.19201 | 0.206526 | ||||||||
\(413\) | 12.4765 | 0.613930 | ||||||||
\(414\) | −13.5906 | −0.667940 | ||||||||
\(415\) | 6.43335 | 0.315801 | ||||||||
\(416\) | −2.93764 | −0.144030 | ||||||||
\(417\) | 9.77255 | 0.478564 | ||||||||
\(418\) | −12.2312 | −0.598246 | ||||||||
\(419\) | 22.1978 | 1.08443 | 0.542216 | − | 0.840239i | \(-0.317585\pi\) | ||||
0.542216 | + | 0.840239i | \(0.317585\pi\) | |||||||
\(420\) | 4.36522 | 0.213001 | ||||||||
\(421\) | −10.1692 | −0.495617 | −0.247809 | − | 0.968809i | \(-0.579710\pi\) | ||||
−0.247809 | + | 0.968809i | \(0.579710\pi\) | |||||||
\(422\) | 28.5543 | 1.39000 | ||||||||
\(423\) | 30.8745 | 1.50117 | ||||||||
\(424\) | −21.7400 | −1.05579 | ||||||||
\(425\) | 15.2398 | 0.739239 | ||||||||
\(426\) | 4.50343 | 0.218192 | ||||||||
\(427\) | −5.70308 | −0.275992 | ||||||||
\(428\) | −18.8946 | −0.913304 | ||||||||
\(429\) | −0.405844 | −0.0195943 | ||||||||
\(430\) | 9.90831 | 0.477821 | ||||||||
\(431\) | −23.0489 | −1.11023 | −0.555114 | − | 0.831774i | \(-0.687325\pi\) | ||||
−0.555114 | + | 0.831774i | \(0.687325\pi\) | |||||||
\(432\) | 3.93132 | 0.189146 | ||||||||
\(433\) | −11.3144 | −0.543736 | −0.271868 | − | 0.962335i | \(-0.587641\pi\) | ||||
−0.271868 | + | 0.962335i | \(0.587641\pi\) | |||||||
\(434\) | 51.0619 | 2.45105 | ||||||||
\(435\) | 3.05748 | 0.146595 | ||||||||
\(436\) | 3.43514 | 0.164513 | ||||||||
\(437\) | 16.1267 | 0.771445 | ||||||||
\(438\) | 5.60097 | 0.267625 | ||||||||
\(439\) | −12.2506 | −0.584688 | −0.292344 | − | 0.956313i | \(-0.594435\pi\) | ||||
−0.292344 | + | 0.956313i | \(0.594435\pi\) | |||||||
\(440\) | 1.43590 | 0.0684538 | ||||||||
\(441\) | −4.76996 | −0.227141 | ||||||||
\(442\) | −4.89945 | −0.233043 | ||||||||
\(443\) | 35.3529 | 1.67966 | 0.839832 | − | 0.542846i | \(-0.182653\pi\) | ||||
0.839832 | + | 0.542846i | \(0.182653\pi\) | |||||||
\(444\) | 2.69781 | 0.128032 | ||||||||
\(445\) | 7.00479 | 0.332059 | ||||||||
\(446\) | −15.3911 | −0.728791 | ||||||||
\(447\) | −17.5322 | −0.829244 | ||||||||
\(448\) | 37.2212 | 1.75853 | ||||||||
\(449\) | 16.7119 | 0.788682 | 0.394341 | − | 0.918964i | \(-0.370973\pi\) | ||||
0.394341 | + | 0.918964i | \(0.370973\pi\) | |||||||
\(450\) | −26.1644 | −1.23340 | ||||||||
\(451\) | 8.69568 | 0.409464 | ||||||||
\(452\) | −26.3511 | −1.23945 | ||||||||
\(453\) | 0.341023 | 0.0160227 | ||||||||
\(454\) | 9.07748 | 0.426027 | ||||||||
\(455\) | 1.05075 | 0.0492601 | ||||||||
\(456\) | −17.3237 | −0.811258 | ||||||||
\(457\) | −7.40351 | −0.346322 | −0.173161 | − | 0.984894i | \(-0.555398\pi\) | ||||
−0.173161 | + | 0.984894i | \(0.555398\pi\) | |||||||
\(458\) | 54.4562 | 2.54457 | ||||||||
\(459\) | −13.6819 | −0.638615 | ||||||||
\(460\) | −4.53161 | −0.211287 | ||||||||
\(461\) | −16.9742 | −0.790569 | −0.395284 | − | 0.918559i | \(-0.629354\pi\) | ||||
−0.395284 | + | 0.918559i | \(0.629354\pi\) | |||||||
\(462\) | 4.37135 | 0.203374 | ||||||||
\(463\) | 16.6781 | 0.775097 | 0.387548 | − | 0.921849i | \(-0.373322\pi\) | ||||
0.387548 | + | 0.921849i | \(0.373322\pi\) | |||||||
\(464\) | −6.71254 | −0.311622 | ||||||||
\(465\) | −3.09200 | −0.143388 | ||||||||
\(466\) | −57.5304 | −2.66504 | ||||||||
\(467\) | 33.8684 | 1.56724 | 0.783621 | − | 0.621239i | \(-0.213370\pi\) | ||||
0.783621 | + | 0.621239i | \(0.213370\pi\) | |||||||
\(468\) | 5.31633 | 0.245748 | ||||||||
\(469\) | −7.78010 | −0.359251 | ||||||||
\(470\) | 16.2885 | 0.751331 | ||||||||
\(471\) | −13.0543 | −0.601511 | ||||||||
\(472\) | 13.9135 | 0.640419 | ||||||||
\(473\) | 6.27108 | 0.288345 | ||||||||
\(474\) | −18.9234 | −0.869181 | ||||||||
\(475\) | 31.0469 | 1.42453 | ||||||||
\(476\) | 33.3532 | 1.52874 | ||||||||
\(477\) | −15.4855 | −0.709032 | ||||||||
\(478\) | 40.8799 | 1.86980 | ||||||||
\(479\) | 4.14348 | 0.189321 | 0.0946603 | − | 0.995510i | \(-0.469824\pi\) | ||||
0.0946603 | + | 0.995510i | \(0.469824\pi\) | |||||||
\(480\) | −1.91602 | −0.0874537 | ||||||||
\(481\) | 0.649389 | 0.0296096 | ||||||||
\(482\) | 51.7000 | 2.35487 | ||||||||
\(483\) | −5.76359 | −0.262252 | ||||||||
\(484\) | −35.6112 | −1.61869 | ||||||||
\(485\) | −4.82348 | −0.219023 | ||||||||
\(486\) | 36.5802 | 1.65931 | ||||||||
\(487\) | −36.4013 | −1.64950 | −0.824751 | − | 0.565496i | \(-0.808685\pi\) | ||||
−0.824751 | + | 0.565496i | \(0.808685\pi\) | |||||||
\(488\) | −6.35991 | −0.287900 | ||||||||
\(489\) | 0.243127 | 0.0109946 | ||||||||
\(490\) | −2.51649 | −0.113684 | ||||||||
\(491\) | 33.5646 | 1.51475 | 0.757375 | − | 0.652980i | \(-0.226481\pi\) | ||||
0.757375 | + | 0.652980i | \(0.226481\pi\) | |||||||
\(492\) | 29.4800 | 1.32906 | ||||||||
\(493\) | 23.3612 | 1.05213 | ||||||||
\(494\) | −9.98129 | −0.449079 | ||||||||
\(495\) | 1.02280 | 0.0459713 | ||||||||
\(496\) | 6.78834 | 0.304806 | ||||||||
\(497\) | −7.37952 | −0.331017 | ||||||||
\(498\) | 21.8409 | 0.978714 | ||||||||
\(499\) | −17.1110 | −0.765994 | −0.382997 | − | 0.923750i | \(-0.625108\pi\) | ||||
−0.382997 | + | 0.923750i | \(0.625108\pi\) | |||||||
\(500\) | −17.9872 | −0.804412 | ||||||||
\(501\) | 1.08039 | 0.0482683 | ||||||||
\(502\) | −47.0942 | −2.10192 | ||||||||
\(503\) | 29.1668 | 1.30048 | 0.650241 | − | 0.759728i | \(-0.274668\pi\) | ||||
0.650241 | + | 0.759728i | \(0.274668\pi\) | |||||||
\(504\) | −23.9232 | −1.06562 | ||||||||
\(505\) | −9.25502 | −0.411843 | ||||||||
\(506\) | −4.53797 | −0.201737 | ||||||||
\(507\) | 9.87844 | 0.438717 | ||||||||
\(508\) | −13.9705 | −0.619842 | ||||||||
\(509\) | 14.7919 | 0.655640 | 0.327820 | − | 0.944740i | \(-0.393686\pi\) | ||||
0.327820 | + | 0.944740i | \(0.393686\pi\) | |||||||
\(510\) | −3.19557 | −0.141502 | ||||||||
\(511\) | −9.17801 | −0.406011 | ||||||||
\(512\) | 10.4289 | 0.460897 | ||||||||
\(513\) | −27.8731 | −1.23063 | ||||||||
\(514\) | 2.91298 | 0.128486 | ||||||||
\(515\) | 0.658139 | 0.0290011 | ||||||||
\(516\) | 21.2601 | 0.935926 | ||||||||
\(517\) | 10.3091 | 0.453396 | ||||||||
\(518\) | −6.99459 | −0.307325 | ||||||||
\(519\) | 13.8409 | 0.607549 | ||||||||
\(520\) | 1.17177 | 0.0513855 | ||||||||
\(521\) | −12.6683 | −0.555008 | −0.277504 | − | 0.960724i | \(-0.589507\pi\) | ||||
−0.277504 | + | 0.960724i | \(0.589507\pi\) | |||||||
\(522\) | −40.1075 | −1.75546 | ||||||||
\(523\) | −4.80546 | −0.210128 | −0.105064 | − | 0.994465i | \(-0.533505\pi\) | ||||
−0.105064 | + | 0.994465i | \(0.533505\pi\) | |||||||
\(524\) | 44.3002 | 1.93526 | ||||||||
\(525\) | −11.0960 | −0.484268 | ||||||||
\(526\) | −12.3750 | −0.539574 | ||||||||
\(527\) | −23.6250 | −1.02912 | ||||||||
\(528\) | 0.581143 | 0.0252910 | ||||||||
\(529\) | −17.0167 | −0.739858 | ||||||||
\(530\) | −8.16969 | −0.354869 | ||||||||
\(531\) | 9.91060 | 0.430083 | ||||||||
\(532\) | 67.9481 | 2.94592 | ||||||||
\(533\) | 7.09613 | 0.307368 | ||||||||
\(534\) | 23.7809 | 1.02910 | ||||||||
\(535\) | −2.96642 | −0.128249 | ||||||||
\(536\) | −8.67613 | −0.374752 | ||||||||
\(537\) | 0.131458 | 0.00567283 | ||||||||
\(538\) | −29.7956 | −1.28458 | ||||||||
\(539\) | −1.59272 | −0.0686032 | ||||||||
\(540\) | 7.83234 | 0.337050 | ||||||||
\(541\) | 6.77689 | 0.291361 | 0.145681 | − | 0.989332i | \(-0.453463\pi\) | ||||
0.145681 | + | 0.989332i | \(0.453463\pi\) | |||||||
\(542\) | −16.7985 | −0.721557 | ||||||||
\(543\) | 13.4295 | 0.576316 | ||||||||
\(544\) | −14.6396 | −0.627669 | ||||||||
\(545\) | 0.539311 | 0.0231015 | ||||||||
\(546\) | 3.56725 | 0.152664 | ||||||||
\(547\) | 24.4096 | 1.04368 | 0.521840 | − | 0.853043i | \(-0.325246\pi\) | ||||
0.521840 | + | 0.853043i | \(0.325246\pi\) | |||||||
\(548\) | 39.8594 | 1.70271 | ||||||||
\(549\) | −4.53019 | −0.193344 | ||||||||
\(550\) | −8.73643 | −0.372523 | ||||||||
\(551\) | 47.5920 | 2.02749 | ||||||||
\(552\) | −6.42738 | −0.273568 | ||||||||
\(553\) | 31.0088 | 1.31863 | ||||||||
\(554\) | 25.1510 | 1.06856 | ||||||||
\(555\) | 0.423551 | 0.0179787 | ||||||||
\(556\) | −42.7449 | −1.81279 | ||||||||
\(557\) | −33.8449 | −1.43405 | −0.717027 | − | 0.697046i | \(-0.754497\pi\) | ||||
−0.717027 | + | 0.697046i | \(0.754497\pi\) | |||||||
\(558\) | 40.5605 | 1.71706 | ||||||||
\(559\) | 5.11753 | 0.216449 | ||||||||
\(560\) | −1.50461 | −0.0635816 | ||||||||
\(561\) | −2.02251 | −0.0853904 | ||||||||
\(562\) | 70.0325 | 2.95414 | ||||||||
\(563\) | 10.8104 | 0.455605 | 0.227803 | − | 0.973707i | \(-0.426846\pi\) | ||||
0.227803 | + | 0.973707i | \(0.426846\pi\) | |||||||
\(564\) | 34.9500 | 1.47166 | ||||||||
\(565\) | −4.13707 | −0.174048 | ||||||||
\(566\) | 40.5452 | 1.70424 | ||||||||
\(567\) | −11.4890 | −0.482494 | ||||||||
\(568\) | −8.22942 | −0.345299 | ||||||||
\(569\) | −19.2197 | −0.805731 | −0.402866 | − | 0.915259i | \(-0.631986\pi\) | ||||
−0.402866 | + | 0.915259i | \(0.631986\pi\) | |||||||
\(570\) | −6.51009 | −0.272678 | ||||||||
\(571\) | 9.19600 | 0.384841 | 0.192420 | − | 0.981313i | \(-0.438366\pi\) | ||||
0.192420 | + | 0.981313i | \(0.438366\pi\) | |||||||
\(572\) | 1.77515 | 0.0742229 | ||||||||
\(573\) | 11.3270 | 0.473191 | ||||||||
\(574\) | −76.4327 | −3.19024 | ||||||||
\(575\) | 11.5189 | 0.480372 | ||||||||
\(576\) | 29.5662 | 1.23193 | ||||||||
\(577\) | −6.90358 | −0.287400 | −0.143700 | − | 0.989621i | \(-0.545900\pi\) | ||||
−0.143700 | + | 0.989621i | \(0.545900\pi\) | |||||||
\(578\) | 15.2165 | 0.632922 | ||||||||
\(579\) | 4.50920 | 0.187396 | ||||||||
\(580\) | −13.3734 | −0.555298 | ||||||||
\(581\) | −35.7895 | −1.48480 | ||||||||
\(582\) | −16.3755 | −0.678785 | ||||||||
\(583\) | −5.17069 | −0.214148 | ||||||||
\(584\) | −10.2350 | −0.423529 | ||||||||
\(585\) | 0.834655 | 0.0345087 | ||||||||
\(586\) | 37.1309 | 1.53386 | ||||||||
\(587\) | −29.5311 | −1.21888 | −0.609440 | − | 0.792832i | \(-0.708606\pi\) | ||||
−0.609440 | + | 0.792832i | \(0.708606\pi\) | |||||||
\(588\) | −5.39961 | −0.222676 | ||||||||
\(589\) | −48.1294 | −1.98314 | ||||||||
\(590\) | 5.22854 | 0.215256 | ||||||||
\(591\) | 0.345125 | 0.0141966 | ||||||||
\(592\) | −0.929885 | −0.0382181 | ||||||||
\(593\) | −11.0037 | −0.451869 | −0.225934 | − | 0.974143i | \(-0.572544\pi\) | ||||
−0.225934 | + | 0.974143i | \(0.572544\pi\) | |||||||
\(594\) | 7.84333 | 0.321816 | ||||||||
\(595\) | 5.23640 | 0.214672 | ||||||||
\(596\) | 76.6855 | 3.14116 | ||||||||
\(597\) | 11.3959 | 0.466403 | ||||||||
\(598\) | −3.70322 | −0.151436 | ||||||||
\(599\) | −8.35889 | −0.341535 | −0.170768 | − | 0.985311i | \(-0.554625\pi\) | ||||
−0.170768 | + | 0.985311i | \(0.554625\pi\) | |||||||
\(600\) | −12.3739 | −0.505163 | ||||||||
\(601\) | −2.16462 | −0.0882966 | −0.0441483 | − | 0.999025i | \(-0.514057\pi\) | ||||
−0.0441483 | + | 0.999025i | \(0.514057\pi\) | |||||||
\(602\) | −55.1211 | −2.24657 | ||||||||
\(603\) | −6.18004 | −0.251671 | ||||||||
\(604\) | −1.49163 | −0.0606936 | ||||||||
\(605\) | −5.59090 | −0.227302 | ||||||||
\(606\) | −31.4203 | −1.27636 | ||||||||
\(607\) | 39.6869 | 1.61084 | 0.805421 | − | 0.592703i | \(-0.201939\pi\) | ||||
0.805421 | + | 0.592703i | \(0.201939\pi\) | |||||||
\(608\) | −29.8243 | −1.20953 | ||||||||
\(609\) | −17.0091 | −0.689244 | ||||||||
\(610\) | −2.38999 | −0.0967680 | ||||||||
\(611\) | 8.41281 | 0.340346 | ||||||||
\(612\) | 26.4938 | 1.07095 | ||||||||
\(613\) | 14.7180 | 0.594455 | 0.297228 | − | 0.954807i | \(-0.403938\pi\) | ||||
0.297228 | + | 0.954807i | \(0.403938\pi\) | |||||||
\(614\) | −7.64864 | −0.308674 | ||||||||
\(615\) | 4.62831 | 0.186632 | ||||||||
\(616\) | −7.98807 | −0.321849 | ||||||||
\(617\) | 14.7349 | 0.593207 | 0.296603 | − | 0.955001i | \(-0.404146\pi\) | ||||
0.296603 | + | 0.955001i | \(0.404146\pi\) | |||||||
\(618\) | 2.23435 | 0.0898786 | ||||||||
\(619\) | −30.8137 | −1.23851 | −0.619254 | − | 0.785191i | \(-0.712565\pi\) | ||||
−0.619254 | + | 0.785191i | \(0.712565\pi\) | |||||||
\(620\) | 13.5244 | 0.543152 | ||||||||
\(621\) | −10.3414 | −0.414985 | ||||||||
\(622\) | −33.5379 | −1.34475 | ||||||||
\(623\) | −38.9684 | −1.56124 | ||||||||
\(624\) | 0.474243 | 0.0189849 | ||||||||
\(625\) | 20.7218 | 0.828870 | ||||||||
\(626\) | −41.6509 | −1.66471 | ||||||||
\(627\) | −4.12031 | −0.164549 | ||||||||
\(628\) | 57.0993 | 2.27851 | ||||||||
\(629\) | 3.23621 | 0.129036 | ||||||||
\(630\) | −8.99010 | −0.358174 | ||||||||
\(631\) | 6.71897 | 0.267478 | 0.133739 | − | 0.991017i | \(-0.457302\pi\) | ||||
0.133739 | + | 0.991017i | \(0.457302\pi\) | |||||||
\(632\) | 34.5801 | 1.37552 | ||||||||
\(633\) | 9.61905 | 0.382323 | ||||||||
\(634\) | −9.99139 | −0.396809 | ||||||||
\(635\) | −2.19335 | −0.0870405 | ||||||||
\(636\) | −17.5296 | −0.695094 | ||||||||
\(637\) | −1.29974 | −0.0514976 | ||||||||
\(638\) | −13.3921 | −0.530199 | ||||||||
\(639\) | −5.86185 | −0.231891 | ||||||||
\(640\) | 10.7189 | 0.423703 | ||||||||
\(641\) | 3.79314 | 0.149820 | 0.0749100 | − | 0.997190i | \(-0.476133\pi\) | ||||
0.0749100 | + | 0.997190i | \(0.476133\pi\) | |||||||
\(642\) | −10.0708 | −0.397464 | ||||||||
\(643\) | 36.1832 | 1.42693 | 0.713463 | − | 0.700693i | \(-0.247126\pi\) | ||||
0.713463 | + | 0.700693i | \(0.247126\pi\) | |||||||
\(644\) | 25.2098 | 0.993407 | ||||||||
\(645\) | 3.33781 | 0.131426 | ||||||||
\(646\) | −49.7415 | −1.95705 | ||||||||
\(647\) | −9.03471 | −0.355191 | −0.177596 | − | 0.984104i | \(-0.556832\pi\) | ||||
−0.177596 | + | 0.984104i | \(0.556832\pi\) | |||||||
\(648\) | −12.8122 | −0.503312 | ||||||||
\(649\) | 3.30920 | 0.129898 | ||||||||
\(650\) | −7.12939 | −0.279638 | ||||||||
\(651\) | 17.2012 | 0.674167 | ||||||||
\(652\) | −1.06343 | −0.0416473 | ||||||||
\(653\) | 3.65802 | 0.143149 | 0.0715746 | − | 0.997435i | \(-0.477198\pi\) | ||||
0.0715746 | + | 0.997435i | \(0.477198\pi\) | |||||||
\(654\) | 1.83093 | 0.0715951 | ||||||||
\(655\) | 6.95505 | 0.271756 | ||||||||
\(656\) | −10.1612 | −0.396729 | ||||||||
\(657\) | −7.29046 | −0.284428 | ||||||||
\(658\) | −90.6146 | −3.53253 | ||||||||
\(659\) | −2.70982 | −0.105559 | −0.0527797 | − | 0.998606i | \(-0.516808\pi\) | ||||
−0.0527797 | + | 0.998606i | \(0.516808\pi\) | |||||||
\(660\) | 1.15781 | 0.0450676 | ||||||||
\(661\) | −15.5150 | −0.603463 | −0.301731 | − | 0.953393i | \(-0.597565\pi\) | ||||
−0.301731 | + | 0.953393i | \(0.597565\pi\) | |||||||
\(662\) | −34.5303 | −1.34206 | ||||||||
\(663\) | −1.65047 | −0.0640991 | ||||||||
\(664\) | −39.9114 | −1.54886 | ||||||||
\(665\) | 10.6677 | 0.413677 | ||||||||
\(666\) | −5.55608 | −0.215294 | ||||||||
\(667\) | 17.6574 | 0.683698 | ||||||||
\(668\) | −4.72561 | −0.182839 | ||||||||
\(669\) | −5.18480 | −0.200456 | ||||||||
\(670\) | −3.26041 | −0.125961 | ||||||||
\(671\) | −1.51265 | −0.0583954 | ||||||||
\(672\) | 10.6590 | 0.411180 | ||||||||
\(673\) | −38.7570 | −1.49397 | −0.746986 | − | 0.664839i | \(-0.768500\pi\) | ||||
−0.746986 | + | 0.664839i | \(0.768500\pi\) | |||||||
\(674\) | −24.8566 | −0.957441 | ||||||||
\(675\) | −19.9091 | −0.766300 | ||||||||
\(676\) | −43.2081 | −1.66185 | ||||||||
\(677\) | −38.0659 | −1.46299 | −0.731495 | − | 0.681847i | \(-0.761177\pi\) | ||||
−0.731495 | + | 0.681847i | \(0.761177\pi\) | |||||||
\(678\) | −14.0452 | −0.539401 | ||||||||
\(679\) | 26.8336 | 1.02978 | ||||||||
\(680\) | 5.83948 | 0.223934 | ||||||||
\(681\) | 3.05792 | 0.117180 | ||||||||
\(682\) | 13.5434 | 0.518602 | ||||||||
\(683\) | 43.9239 | 1.68070 | 0.840350 | − | 0.542044i | \(-0.182350\pi\) | ||||
0.840350 | + | 0.542044i | \(0.182350\pi\) | |||||||
\(684\) | 53.9739 | 2.06374 | ||||||||
\(685\) | 6.25785 | 0.239100 | ||||||||
\(686\) | −34.9626 | −1.33488 | ||||||||
\(687\) | 18.3446 | 0.699891 | ||||||||
\(688\) | −7.32799 | −0.279377 | ||||||||
\(689\) | −4.21955 | −0.160752 | ||||||||
\(690\) | −2.41535 | −0.0919508 | ||||||||
\(691\) | 1.59591 | 0.0607113 | 0.0303556 | − | 0.999539i | \(-0.490336\pi\) | ||||
0.0303556 | + | 0.999539i | \(0.490336\pi\) | |||||||
\(692\) | −60.5400 | −2.30139 | ||||||||
\(693\) | −5.68993 | −0.216143 | ||||||||
\(694\) | −49.7097 | −1.88695 | ||||||||
\(695\) | −6.71088 | −0.254558 | ||||||||
\(696\) | −18.9680 | −0.718982 | ||||||||
\(697\) | 35.3634 | 1.33948 | ||||||||
\(698\) | −44.3833 | −1.67993 | ||||||||
\(699\) | −19.3802 | −0.733027 | ||||||||
\(700\) | 48.5336 | 1.83440 | ||||||||
\(701\) | 2.87514 | 0.108593 | 0.0542963 | − | 0.998525i | \(-0.482708\pi\) | ||||
0.0542963 | + | 0.998525i | \(0.482708\pi\) | |||||||
\(702\) | 6.40057 | 0.241574 | ||||||||
\(703\) | 6.59290 | 0.248656 | ||||||||
\(704\) | 9.87233 | 0.372077 | ||||||||
\(705\) | 5.48709 | 0.206656 | ||||||||
\(706\) | −31.6822 | −1.19238 | ||||||||
\(707\) | 51.4867 | 1.93636 | ||||||||
\(708\) | 11.2188 | 0.421629 | ||||||||
\(709\) | −32.3808 | −1.21609 | −0.608043 | − | 0.793904i | \(-0.708045\pi\) | ||||
−0.608043 | + | 0.793904i | \(0.708045\pi\) | |||||||
\(710\) | −3.09254 | −0.116061 | ||||||||
\(711\) | 24.6315 | 0.923753 | ||||||||
\(712\) | −43.4564 | −1.62860 | ||||||||
\(713\) | −17.8568 | −0.668743 | ||||||||
\(714\) | 17.7773 | 0.665299 | ||||||||
\(715\) | 0.278696 | 0.0104226 | ||||||||
\(716\) | −0.574995 | −0.0214886 | ||||||||
\(717\) | 13.7712 | 0.514294 | ||||||||
\(718\) | −43.9915 | −1.64175 | ||||||||
\(719\) | −17.3136 | −0.645686 | −0.322843 | − | 0.946452i | \(-0.604639\pi\) | ||||
−0.322843 | + | 0.946452i | \(0.604639\pi\) | |||||||
\(720\) | −1.19518 | −0.0445416 | ||||||||
\(721\) | −3.66130 | −0.136354 | ||||||||
\(722\) | −57.0392 | −2.12278 | ||||||||
\(723\) | 17.4162 | 0.647714 | ||||||||
\(724\) | −58.7405 | −2.18307 | ||||||||
\(725\) | 33.9938 | 1.26250 | ||||||||
\(726\) | −18.9808 | −0.704444 | ||||||||
\(727\) | −0.538076 | −0.0199562 | −0.00997808 | − | 0.999950i | \(-0.503176\pi\) | ||||
−0.00997808 | + | 0.999950i | \(0.503176\pi\) | |||||||
\(728\) | −6.51869 | −0.241599 | ||||||||
\(729\) | 0.834665 | 0.0309135 | ||||||||
\(730\) | −3.84623 | −0.142355 | ||||||||
\(731\) | 25.5031 | 0.943266 | ||||||||
\(732\) | −5.12818 | −0.189543 | ||||||||
\(733\) | 5.43035 | 0.200575 | 0.100287 | − | 0.994959i | \(-0.468024\pi\) | ||||
0.100287 | + | 0.994959i | \(0.468024\pi\) | |||||||
\(734\) | −16.3704 | −0.604241 | ||||||||
\(735\) | −0.847730 | −0.0312690 | ||||||||
\(736\) | −11.0653 | −0.407872 | ||||||||
\(737\) | −2.06355 | −0.0760118 | ||||||||
\(738\) | −60.7135 | −2.23489 | ||||||||
\(739\) | −27.5295 | −1.01269 | −0.506344 | − | 0.862332i | \(-0.669003\pi\) | ||||
−0.506344 | + | 0.862332i | \(0.669003\pi\) | |||||||
\(740\) | −1.85260 | −0.0681031 | ||||||||
\(741\) | −3.36239 | −0.123520 | ||||||||
\(742\) | 45.4490 | 1.66848 | ||||||||
\(743\) | 23.6459 | 0.867483 | 0.433742 | − | 0.901037i | \(-0.357193\pi\) | ||||
0.433742 | + | 0.901037i | \(0.357193\pi\) | |||||||
\(744\) | 19.1822 | 0.703255 | ||||||||
\(745\) | 12.0395 | 0.441093 | ||||||||
\(746\) | −22.6686 | −0.829956 | ||||||||
\(747\) | −28.4290 | −1.04016 | ||||||||
\(748\) | 8.84642 | 0.323457 | ||||||||
\(749\) | 16.5025 | 0.602989 | ||||||||
\(750\) | −9.58720 | −0.350075 | ||||||||
\(751\) | −3.80026 | −0.138674 | −0.0693368 | − | 0.997593i | \(-0.522088\pi\) | ||||
−0.0693368 | + | 0.997593i | \(0.522088\pi\) | |||||||
\(752\) | −12.0466 | −0.439295 | ||||||||
\(753\) | −15.8646 | −0.578138 | ||||||||
\(754\) | −10.9287 | −0.397999 | ||||||||
\(755\) | −0.234183 | −0.00852280 | ||||||||
\(756\) | −43.5722 | −1.58471 | ||||||||
\(757\) | 40.1975 | 1.46100 | 0.730502 | − | 0.682910i | \(-0.239286\pi\) | ||||
0.730502 | + | 0.682910i | \(0.239286\pi\) | |||||||
\(758\) | −19.6244 | −0.712791 | ||||||||
\(759\) | −1.52870 | −0.0554884 | ||||||||
\(760\) | 11.8963 | 0.431526 | ||||||||
\(761\) | −50.5236 | −1.83148 | −0.915739 | − | 0.401774i | \(-0.868394\pi\) | ||||
−0.915739 | + | 0.401774i | \(0.868394\pi\) | |||||||
\(762\) | −7.44631 | −0.269751 | ||||||||
\(763\) | −3.00025 | −0.108616 | ||||||||
\(764\) | −49.5440 | −1.79244 | ||||||||
\(765\) | 4.15948 | 0.150386 | ||||||||
\(766\) | −61.4966 | −2.22196 | ||||||||
\(767\) | 2.70048 | 0.0975089 | ||||||||
\(768\) | 16.9039 | 0.609968 | ||||||||
\(769\) | −37.9780 | −1.36952 | −0.684760 | − | 0.728769i | \(-0.740093\pi\) | ||||
−0.684760 | + | 0.728769i | \(0.740093\pi\) | |||||||
\(770\) | −3.00184 | −0.108179 | ||||||||
\(771\) | 0.981295 | 0.0353405 | ||||||||
\(772\) | −19.7232 | −0.709852 | ||||||||
\(773\) | −42.7526 | −1.53770 | −0.768851 | − | 0.639427i | \(-0.779171\pi\) | ||||
−0.768851 | + | 0.639427i | \(0.779171\pi\) | |||||||
\(774\) | −43.7849 | −1.57381 | ||||||||
\(775\) | −34.3777 | −1.23488 | ||||||||
\(776\) | 29.9240 | 1.07421 | ||||||||
\(777\) | −2.35626 | −0.0845305 | ||||||||
\(778\) | 54.9983 | 1.97178 | ||||||||
\(779\) | 72.0432 | 2.58122 | ||||||||
\(780\) | 0.944832 | 0.0338304 | ||||||||
\(781\) | −1.95730 | −0.0700378 | ||||||||
\(782\) | −18.4549 | −0.659946 | ||||||||
\(783\) | −30.5187 | −1.09065 | ||||||||
\(784\) | 1.86115 | 0.0664696 | ||||||||
\(785\) | 8.96450 | 0.319957 | ||||||||
\(786\) | 23.6120 | 0.842214 | ||||||||
\(787\) | −17.4328 | −0.621413 | −0.310706 | − | 0.950506i | \(-0.600566\pi\) | ||||
−0.310706 | + | 0.950506i | \(0.600566\pi\) | |||||||
\(788\) | −1.50957 | −0.0537763 | ||||||||
\(789\) | −4.16875 | −0.148411 | ||||||||
\(790\) | 12.9949 | 0.462336 | ||||||||
\(791\) | 23.0150 | 0.818320 | ||||||||
\(792\) | −6.34524 | −0.225468 | ||||||||
\(793\) | −1.23441 | −0.0438350 | ||||||||
\(794\) | 56.7740 | 2.01483 | ||||||||
\(795\) | −2.75212 | −0.0976076 | ||||||||
\(796\) | −49.8455 | −1.76673 | ||||||||
\(797\) | −22.6239 | −0.801380 | −0.400690 | − | 0.916214i | \(-0.631230\pi\) | ||||
−0.400690 | + | 0.916214i | \(0.631230\pi\) | |||||||
\(798\) | 36.2164 | 1.28205 | ||||||||
\(799\) | 41.9250 | 1.48320 | ||||||||
\(800\) | −21.3027 | −0.753165 | ||||||||
\(801\) | −30.9542 | −1.09371 | ||||||||
\(802\) | −49.6228 | −1.75224 | ||||||||
\(803\) | −2.43432 | −0.0859054 | ||||||||
\(804\) | −6.99582 | −0.246724 | ||||||||
\(805\) | 3.95790 | 0.139498 | ||||||||
\(806\) | 11.0521 | 0.389293 | ||||||||
\(807\) | −10.0372 | −0.353327 | ||||||||
\(808\) | 57.4165 | 2.01990 | ||||||||
\(809\) | 36.3020 | 1.27631 | 0.638155 | − | 0.769908i | \(-0.279698\pi\) | ||||
0.638155 | + | 0.769908i | \(0.279698\pi\) | |||||||
\(810\) | −4.81471 | −0.169172 | ||||||||
\(811\) | 47.2757 | 1.66007 | 0.830036 | − | 0.557709i | \(-0.188320\pi\) | ||||
0.830036 | + | 0.557709i | \(0.188320\pi\) | |||||||
\(812\) | 74.3975 | 2.61084 | ||||||||
\(813\) | −5.65890 | −0.198466 | ||||||||
\(814\) | −1.85521 | −0.0650249 | ||||||||
\(815\) | −0.166957 | −0.00584826 | ||||||||
\(816\) | 2.36338 | 0.0827348 | ||||||||
\(817\) | 51.9555 | 1.81769 | ||||||||
\(818\) | 36.5225 | 1.27698 | ||||||||
\(819\) | −4.64328 | −0.162249 | ||||||||
\(820\) | −20.2442 | −0.706957 | ||||||||
\(821\) | −13.7154 | −0.478670 | −0.239335 | − | 0.970937i | \(-0.576929\pi\) | ||||
−0.239335 | + | 0.970937i | \(0.576929\pi\) | |||||||
\(822\) | 21.2451 | 0.741007 | ||||||||
\(823\) | −51.4044 | −1.79185 | −0.895923 | − | 0.444210i | \(-0.853485\pi\) | ||||
−0.895923 | + | 0.444210i | \(0.853485\pi\) | |||||||
\(824\) | −4.08297 | −0.142237 | ||||||||
\(825\) | −2.94304 | −0.102463 | ||||||||
\(826\) | −29.0870 | −1.01207 | ||||||||
\(827\) | −12.0718 | −0.419777 | −0.209888 | − | 0.977725i | \(-0.567310\pi\) | ||||
−0.209888 | + | 0.977725i | \(0.567310\pi\) | |||||||
\(828\) | 20.0252 | 0.695923 | ||||||||
\(829\) | 34.6406 | 1.20312 | 0.601558 | − | 0.798829i | \(-0.294547\pi\) | ||||
0.601558 | + | 0.798829i | \(0.294547\pi\) | |||||||
\(830\) | −14.9983 | −0.520599 | ||||||||
\(831\) | 8.47261 | 0.293912 | ||||||||
\(832\) | 8.05634 | 0.279303 | ||||||||
\(833\) | −6.47722 | −0.224422 | ||||||||
\(834\) | −22.7831 | −0.788914 | ||||||||
\(835\) | −0.741913 | −0.0256750 | ||||||||
\(836\) | 18.0222 | 0.623310 | ||||||||
\(837\) | 30.8633 | 1.06679 | ||||||||
\(838\) | −51.7505 | −1.78769 | ||||||||
\(839\) | −23.2399 | −0.802329 | −0.401164 | − | 0.916006i | \(-0.631394\pi\) | ||||
−0.401164 | + | 0.916006i | \(0.631394\pi\) | |||||||
\(840\) | −4.25168 | −0.146697 | ||||||||
\(841\) | 23.1093 | 0.796873 | ||||||||
\(842\) | 23.7079 | 0.817027 | ||||||||
\(843\) | 23.5918 | 0.812545 | ||||||||
\(844\) | −42.0736 | −1.44823 | ||||||||
\(845\) | −6.78361 | −0.233363 | ||||||||
\(846\) | −71.9788 | −2.47468 | ||||||||
\(847\) | 31.1028 | 1.06871 | ||||||||
\(848\) | 6.04214 | 0.207488 | ||||||||
\(849\) | 13.6584 | 0.468757 | ||||||||
\(850\) | −35.5291 | −1.21864 | ||||||||
\(851\) | 2.44607 | 0.0838503 | ||||||||
\(852\) | −6.63563 | −0.227333 | ||||||||
\(853\) | 13.4371 | 0.460079 | 0.230039 | − | 0.973181i | \(-0.426114\pi\) | ||||
0.230039 | + | 0.973181i | \(0.426114\pi\) | |||||||
\(854\) | 13.2958 | 0.454973 | ||||||||
\(855\) | 8.47380 | 0.289798 | ||||||||
\(856\) | 18.4031 | 0.629006 | ||||||||
\(857\) | 12.0581 | 0.411897 | 0.205949 | − | 0.978563i | \(-0.433972\pi\) | ||||
0.205949 | + | 0.978563i | \(0.433972\pi\) | |||||||
\(858\) | 0.946158 | 0.0323013 | ||||||||
\(859\) | 26.2382 | 0.895236 | 0.447618 | − | 0.894225i | \(-0.352272\pi\) | ||||
0.447618 | + | 0.894225i | \(0.352272\pi\) | |||||||
\(860\) | −14.5995 | −0.497839 | ||||||||
\(861\) | −25.7478 | −0.877484 | ||||||||
\(862\) | 53.7348 | 1.83022 | ||||||||
\(863\) | −14.0937 | −0.479756 | −0.239878 | − | 0.970803i | \(-0.577108\pi\) | ||||
−0.239878 | + | 0.970803i | \(0.577108\pi\) | |||||||
\(864\) | 19.1250 | 0.650646 | ||||||||
\(865\) | −9.50468 | −0.323169 | ||||||||
\(866\) | 26.3777 | 0.896352 | ||||||||
\(867\) | 5.12596 | 0.174087 | ||||||||
\(868\) | −75.2377 | −2.55373 | ||||||||
\(869\) | 8.22459 | 0.279000 | ||||||||
\(870\) | −7.12801 | −0.241662 | ||||||||
\(871\) | −1.68396 | −0.0570590 | ||||||||
\(872\) | −3.34579 | −0.113303 | ||||||||
\(873\) | 21.3150 | 0.721403 | ||||||||
\(874\) | −37.5968 | −1.27173 | ||||||||
\(875\) | 15.7100 | 0.531096 | ||||||||
\(876\) | −8.25282 | −0.278837 | ||||||||
\(877\) | −6.93409 | −0.234148 | −0.117074 | − | 0.993123i | \(-0.537351\pi\) | ||||
−0.117074 | + | 0.993123i | \(0.537351\pi\) | |||||||
\(878\) | 28.5602 | 0.963862 | ||||||||
\(879\) | 12.5083 | 0.421894 | ||||||||
\(880\) | −0.399076 | −0.0134528 | ||||||||
\(881\) | −43.8606 | −1.47770 | −0.738851 | − | 0.673868i | \(-0.764631\pi\) | ||||
−0.738851 | + | 0.673868i | \(0.764631\pi\) | |||||||
\(882\) | 11.1204 | 0.374443 | ||||||||
\(883\) | 12.5169 | 0.421227 | 0.210614 | − | 0.977569i | \(-0.432454\pi\) | ||||
0.210614 | + | 0.977569i | \(0.432454\pi\) | |||||||
\(884\) | 7.21915 | 0.242806 | ||||||||
\(885\) | 1.76134 | 0.0592067 | ||||||||
\(886\) | −82.4195 | −2.76894 | ||||||||
\(887\) | −41.3722 | −1.38914 | −0.694571 | − | 0.719424i | \(-0.744406\pi\) | ||||
−0.694571 | + | 0.719424i | \(0.744406\pi\) | |||||||
\(888\) | −2.62763 | −0.0881776 | ||||||||
\(889\) | 12.2019 | 0.409237 | ||||||||
\(890\) | −16.3305 | −0.547400 | ||||||||
\(891\) | −3.04728 | −0.102088 | ||||||||
\(892\) | 22.6782 | 0.759323 | ||||||||
\(893\) | 85.4107 | 2.85816 | ||||||||
\(894\) | 40.8734 | 1.36701 | ||||||||
\(895\) | −0.0902732 | −0.00301750 | ||||||||
\(896\) | −59.6307 | −1.99212 | ||||||||
\(897\) | −1.24750 | −0.0416529 | ||||||||
\(898\) | −38.9610 | −1.30015 | ||||||||
\(899\) | −52.6978 | −1.75757 | ||||||||
\(900\) | 38.5522 | 1.28507 | ||||||||
\(901\) | −21.0280 | −0.700546 | ||||||||
\(902\) | −20.2726 | −0.675003 | ||||||||
\(903\) | −18.5686 | −0.617925 | ||||||||
\(904\) | 25.6657 | 0.853627 | ||||||||
\(905\) | −9.22216 | −0.306555 | ||||||||
\(906\) | −0.795040 | −0.0264134 | ||||||||
\(907\) | −40.6815 | −1.35081 | −0.675404 | − | 0.737448i | \(-0.736031\pi\) | ||||
−0.675404 | + | 0.737448i | \(0.736031\pi\) | |||||||
\(908\) | −13.3753 | −0.443875 | ||||||||
\(909\) | 40.8980 | 1.35650 | ||||||||
\(910\) | −2.44966 | −0.0812055 | ||||||||
\(911\) | −50.7882 | −1.68269 | −0.841344 | − | 0.540500i | \(-0.818235\pi\) | ||||
−0.841344 | + | 0.540500i | \(0.818235\pi\) | |||||||
\(912\) | 4.81474 | 0.159432 | ||||||||
\(913\) | −9.49260 | −0.314159 | ||||||||
\(914\) | 17.2601 | 0.570913 | ||||||||
\(915\) | −0.805116 | −0.0266163 | ||||||||
\(916\) | −80.2390 | −2.65117 | ||||||||
\(917\) | −38.6918 | −1.27771 | ||||||||
\(918\) | 31.8971 | 1.05276 | ||||||||
\(919\) | 10.6720 | 0.352036 | 0.176018 | − | 0.984387i | \(-0.443678\pi\) | ||||
0.176018 | + | 0.984387i | \(0.443678\pi\) | |||||||
\(920\) | 4.41374 | 0.145517 | ||||||||
\(921\) | −2.57659 | −0.0849016 | ||||||||
\(922\) | 39.5727 | 1.30326 | ||||||||
\(923\) | −1.59726 | −0.0525745 | ||||||||
\(924\) | −6.44102 | −0.211894 | ||||||||
\(925\) | 4.70914 | 0.154836 | ||||||||
\(926\) | −38.8823 | −1.27775 | ||||||||
\(927\) | −2.90832 | −0.0955217 | ||||||||
\(928\) | −32.6551 | −1.07196 | ||||||||
\(929\) | −23.5478 | −0.772580 | −0.386290 | − | 0.922377i | \(-0.626244\pi\) | ||||
−0.386290 | + | 0.922377i | \(0.626244\pi\) | |||||||
\(930\) | 7.20851 | 0.236376 | ||||||||
\(931\) | −13.1956 | −0.432467 | ||||||||
\(932\) | 84.7688 | 2.77669 | ||||||||
\(933\) | −11.2979 | −0.369877 | ||||||||
\(934\) | −78.9587 | −2.58361 | ||||||||
\(935\) | 1.38887 | 0.0454210 | ||||||||
\(936\) | −5.17805 | −0.169250 | ||||||||
\(937\) | −36.1802 | −1.18196 | −0.590979 | − | 0.806687i | \(-0.701258\pi\) | ||||
−0.590979 | + | 0.806687i | \(0.701258\pi\) | |||||||
\(938\) | 18.1380 | 0.592228 | ||||||||
\(939\) | −14.0309 | −0.457882 | ||||||||
\(940\) | −24.0004 | −0.782807 | ||||||||
\(941\) | 31.0330 | 1.01165 | 0.505824 | − | 0.862637i | \(-0.331189\pi\) | ||||
0.505824 | + | 0.862637i | \(0.331189\pi\) | |||||||
\(942\) | 30.4340 | 0.991593 | ||||||||
\(943\) | 26.7292 | 0.870423 | ||||||||
\(944\) | −3.86693 | −0.125858 | ||||||||
\(945\) | −6.84076 | −0.222530 | ||||||||
\(946\) | −14.6200 | −0.475337 | ||||||||
\(947\) | −36.6051 | −1.18950 | −0.594752 | − | 0.803909i | \(-0.702750\pi\) | ||||
−0.594752 | + | 0.803909i | \(0.702750\pi\) | |||||||
\(948\) | 27.8829 | 0.905595 | ||||||||
\(949\) | −1.98654 | −0.0644857 | ||||||||
\(950\) | −72.3808 | −2.34834 | ||||||||
\(951\) | −3.36579 | −0.109143 | ||||||||
\(952\) | −32.4857 | −1.05287 | ||||||||
\(953\) | 15.1993 | 0.492354 | 0.246177 | − | 0.969225i | \(-0.420826\pi\) | ||||
0.246177 | + | 0.969225i | \(0.420826\pi\) | |||||||
\(954\) | 36.1019 | 1.16884 | ||||||||
\(955\) | −7.77832 | −0.251701 | ||||||||
\(956\) | −60.2349 | −1.94814 | ||||||||
\(957\) | −4.51140 | −0.145833 | ||||||||
\(958\) | −9.65986 | −0.312096 | ||||||||
\(959\) | −34.8132 | −1.12418 | ||||||||
\(960\) | 5.25459 | 0.169591 | ||||||||
\(961\) | 22.2928 | 0.719124 | ||||||||
\(962\) | −1.51395 | −0.0488116 | ||||||||
\(963\) | 13.1086 | 0.422419 | ||||||||
\(964\) | −76.1780 | −2.45353 | ||||||||
\(965\) | −3.09650 | −0.0996800 | ||||||||
\(966\) | 13.4369 | 0.432324 | ||||||||
\(967\) | −20.9316 | −0.673115 | −0.336558 | − | 0.941663i | \(-0.609263\pi\) | ||||
−0.336558 | + | 0.941663i | \(0.609263\pi\) | |||||||
\(968\) | 34.6849 | 1.11482 | ||||||||
\(969\) | −16.7564 | −0.538293 | ||||||||
\(970\) | 11.2452 | 0.361061 | ||||||||
\(971\) | 17.3852 | 0.557918 | 0.278959 | − | 0.960303i | \(-0.410011\pi\) | ||||
0.278959 | + | 0.960303i | \(0.410011\pi\) | |||||||
\(972\) | −53.8995 | −1.72883 | ||||||||
\(973\) | 37.3334 | 1.19685 | ||||||||
\(974\) | 84.8638 | 2.71921 | ||||||||
\(975\) | −2.40167 | −0.0769151 | ||||||||
\(976\) | 1.76759 | 0.0565793 | ||||||||
\(977\) | −12.7447 | −0.407739 | −0.203870 | − | 0.978998i | \(-0.565352\pi\) | ||||
−0.203870 | + | 0.978998i | \(0.565352\pi\) | |||||||
\(978\) | −0.566811 | −0.0181246 | ||||||||
\(979\) | −10.3358 | −0.330333 | ||||||||
\(980\) | 3.70795 | 0.118446 | ||||||||
\(981\) | −2.38322 | −0.0760902 | ||||||||
\(982\) | −78.2505 | −2.49707 | ||||||||
\(983\) | 19.6734 | 0.627482 | 0.313741 | − | 0.949509i | \(-0.398418\pi\) | ||||
0.313741 | + | 0.949509i | \(0.398418\pi\) | |||||||
\(984\) | −28.7132 | −0.915344 | ||||||||
\(985\) | −0.237000 | −0.00755146 | ||||||||
\(986\) | −54.4628 | −1.73445 | ||||||||
\(987\) | −30.5253 | −0.971631 | ||||||||
\(988\) | 14.7070 | 0.467893 | ||||||||
\(989\) | 19.2764 | 0.612952 | ||||||||
\(990\) | −2.38448 | −0.0757838 | ||||||||
\(991\) | 22.5825 | 0.717356 | 0.358678 | − | 0.933461i | \(-0.383228\pi\) | ||||
0.358678 | + | 0.933461i | \(0.383228\pi\) | |||||||
\(992\) | 33.0239 | 1.04851 | ||||||||
\(993\) | −11.6322 | −0.369137 | ||||||||
\(994\) | 17.2042 | 0.545683 | ||||||||
\(995\) | −7.82566 | −0.248090 | ||||||||
\(996\) | −32.1817 | −1.01972 | ||||||||
\(997\) | 4.04191 | 0.128008 | 0.0640042 | − | 0.997950i | \(-0.479613\pi\) | ||||
0.0640042 | + | 0.997950i | \(0.479613\pi\) | |||||||
\(998\) | 39.8915 | 1.26274 | ||||||||
\(999\) | −4.22774 | −0.133760 |
(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 | 4033.2.a.e.1.10 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.e.1.10 | ✓ | 82 | 1.1 | even | 1 | trivial |