Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(114\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.31236 | −1.63508 | −0.817541 | − | 0.575870i | \(-0.804663\pi\) | ||||
−0.817541 | + | 0.575870i | \(0.804663\pi\) | |||||||
\(3\) | 3.26187 | 1.88324 | 0.941622 | − | 0.336672i | \(-0.109301\pi\) | ||||
0.941622 | + | 0.336672i | \(0.109301\pi\) | |||||||
\(4\) | 3.34699 | 1.67349 | ||||||||
\(5\) | −1.15202 | −0.515199 | −0.257599 | − | 0.966252i | \(-0.582931\pi\) | ||||
−0.257599 | + | 0.966252i | \(0.582931\pi\) | |||||||
\(6\) | −7.54261 | −3.07926 | ||||||||
\(7\) | −3.58394 | −1.35460 | −0.677301 | − | 0.735706i | \(-0.736851\pi\) | ||||
−0.677301 | + | 0.735706i | \(0.736851\pi\) | |||||||
\(8\) | −3.11471 | −1.10122 | ||||||||
\(9\) | 7.63982 | 2.54661 | ||||||||
\(10\) | 2.66388 | 0.842392 | ||||||||
\(11\) | 3.98929 | 1.20281 | 0.601407 | − | 0.798943i | \(-0.294607\pi\) | ||||
0.601407 | + | 0.798943i | \(0.294607\pi\) | |||||||
\(12\) | 10.9175 | 3.15160 | ||||||||
\(13\) | −4.27275 | −1.18505 | −0.592523 | − | 0.805553i | \(-0.701868\pi\) | ||||
−0.592523 | + | 0.805553i | \(0.701868\pi\) | |||||||
\(14\) | 8.28735 | 2.21489 | ||||||||
\(15\) | −3.75774 | −0.970245 | ||||||||
\(16\) | 0.508350 | 0.127087 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −17.6660 | −4.16391 | ||||||||
\(19\) | 5.24357 | 1.20296 | 0.601479 | − | 0.798889i | \(-0.294578\pi\) | ||||
0.601479 | + | 0.798889i | \(0.294578\pi\) | |||||||
\(20\) | −3.85579 | −0.862182 | ||||||||
\(21\) | −11.6904 | −2.55105 | ||||||||
\(22\) | −9.22464 | −1.96670 | ||||||||
\(23\) | −1.89550 | −0.395240 | −0.197620 | − | 0.980279i | \(-0.563321\pi\) | ||||
−0.197620 | + | 0.980279i | \(0.563321\pi\) | |||||||
\(24\) | −10.1598 | −2.07386 | ||||||||
\(25\) | −3.67285 | −0.734570 | ||||||||
\(26\) | 9.88011 | 1.93765 | ||||||||
\(27\) | 15.1345 | 2.91264 | ||||||||
\(28\) | −11.9954 | −2.26692 | ||||||||
\(29\) | −0.888851 | −0.165055 | −0.0825277 | − | 0.996589i | \(-0.526299\pi\) | ||||
−0.0825277 | + | 0.996589i | \(0.526299\pi\) | |||||||
\(30\) | 8.68923 | 1.58643 | ||||||||
\(31\) | −9.53721 | −1.71293 | −0.856467 | − | 0.516202i | \(-0.827345\pi\) | ||||
−0.856467 | + | 0.516202i | \(0.827345\pi\) | |||||||
\(32\) | 5.05394 | 0.893419 | ||||||||
\(33\) | 13.0125 | 2.26519 | ||||||||
\(34\) | −2.31236 | −0.396566 | ||||||||
\(35\) | 4.12877 | 0.697889 | ||||||||
\(36\) | 25.5704 | 4.26173 | ||||||||
\(37\) | −5.09602 | −0.837780 | −0.418890 | − | 0.908037i | \(-0.637581\pi\) | ||||
−0.418890 | + | 0.908037i | \(0.637581\pi\) | |||||||
\(38\) | −12.1250 | −1.96693 | ||||||||
\(39\) | −13.9372 | −2.23173 | ||||||||
\(40\) | 3.58821 | 0.567346 | ||||||||
\(41\) | −8.77913 | −1.37107 | −0.685535 | − | 0.728039i | \(-0.740432\pi\) | ||||
−0.685535 | + | 0.728039i | \(0.740432\pi\) | |||||||
\(42\) | 27.0323 | 4.17117 | ||||||||
\(43\) | 7.99375 | 1.21903 | 0.609517 | − | 0.792773i | \(-0.291363\pi\) | ||||
0.609517 | + | 0.792773i | \(0.291363\pi\) | |||||||
\(44\) | 13.3521 | 2.01290 | ||||||||
\(45\) | −8.80122 | −1.31201 | ||||||||
\(46\) | 4.38308 | 0.646249 | ||||||||
\(47\) | 10.3254 | 1.50612 | 0.753060 | − | 0.657952i | \(-0.228577\pi\) | ||||
0.753060 | + | 0.657952i | \(0.228577\pi\) | |||||||
\(48\) | 1.65817 | 0.239337 | ||||||||
\(49\) | 5.84464 | 0.834948 | ||||||||
\(50\) | 8.49294 | 1.20108 | ||||||||
\(51\) | 3.26187 | 0.456754 | ||||||||
\(52\) | −14.3008 | −1.98317 | ||||||||
\(53\) | −4.06792 | −0.558772 | −0.279386 | − | 0.960179i | \(-0.590131\pi\) | ||||
−0.279386 | + | 0.960179i | \(0.590131\pi\) | |||||||
\(54\) | −34.9964 | −4.76240 | ||||||||
\(55\) | −4.59573 | −0.619688 | ||||||||
\(56\) | 11.1630 | 1.49171 | ||||||||
\(57\) | 17.1039 | 2.26546 | ||||||||
\(58\) | 2.05534 | 0.269879 | ||||||||
\(59\) | −11.4318 | −1.48829 | −0.744147 | − | 0.668016i | \(-0.767144\pi\) | ||||
−0.744147 | + | 0.668016i | \(0.767144\pi\) | |||||||
\(60\) | −12.5771 | −1.62370 | ||||||||
\(61\) | −2.07854 | −0.266130 | −0.133065 | − | 0.991107i | \(-0.542482\pi\) | ||||
−0.133065 | + | 0.991107i | \(0.542482\pi\) | |||||||
\(62\) | 22.0534 | 2.80079 | ||||||||
\(63\) | −27.3807 | −3.44964 | ||||||||
\(64\) | −12.7032 | −1.58790 | ||||||||
\(65\) | 4.92228 | 0.610534 | ||||||||
\(66\) | −30.0896 | −3.70378 | ||||||||
\(67\) | −11.4960 | −1.40446 | −0.702229 | − | 0.711952i | \(-0.747812\pi\) | ||||
−0.702229 | + | 0.711952i | \(0.747812\pi\) | |||||||
\(68\) | 3.34699 | 0.405882 | ||||||||
\(69\) | −6.18289 | −0.744333 | ||||||||
\(70\) | −9.54718 | −1.14111 | ||||||||
\(71\) | −5.73616 | −0.680756 | −0.340378 | − | 0.940289i | \(-0.610555\pi\) | ||||
−0.340378 | + | 0.940289i | \(0.610555\pi\) | |||||||
\(72\) | −23.7959 | −2.80437 | ||||||||
\(73\) | −3.58856 | −0.420009 | −0.210004 | − | 0.977700i | \(-0.567348\pi\) | ||||
−0.210004 | + | 0.977700i | \(0.567348\pi\) | |||||||
\(74\) | 11.7838 | 1.36984 | ||||||||
\(75\) | −11.9804 | −1.38338 | ||||||||
\(76\) | 17.5502 | 2.01314 | ||||||||
\(77\) | −14.2974 | −1.62934 | ||||||||
\(78\) | 32.2277 | 3.64906 | ||||||||
\(79\) | −5.05647 | −0.568898 | −0.284449 | − | 0.958691i | \(-0.591811\pi\) | ||||
−0.284449 | + | 0.958691i | \(0.591811\pi\) | |||||||
\(80\) | −0.585629 | −0.0654753 | ||||||||
\(81\) | 26.4474 | 2.93860 | ||||||||
\(82\) | 20.3005 | 2.24181 | ||||||||
\(83\) | 0.365274 | 0.0400940 | 0.0200470 | − | 0.999799i | \(-0.493618\pi\) | ||||
0.0200470 | + | 0.999799i | \(0.493618\pi\) | |||||||
\(84\) | −39.1275 | −4.26916 | ||||||||
\(85\) | −1.15202 | −0.124954 | ||||||||
\(86\) | −18.4844 | −1.99322 | ||||||||
\(87\) | −2.89932 | −0.310840 | ||||||||
\(88\) | −12.4255 | −1.32456 | ||||||||
\(89\) | −10.1520 | −1.07611 | −0.538057 | − | 0.842908i | \(-0.680842\pi\) | ||||
−0.538057 | + | 0.842908i | \(0.680842\pi\) | |||||||
\(90\) | 20.3516 | 2.14524 | ||||||||
\(91\) | 15.3133 | 1.60527 | ||||||||
\(92\) | −6.34422 | −0.661431 | ||||||||
\(93\) | −31.1092 | −3.22587 | ||||||||
\(94\) | −23.8761 | −2.46263 | ||||||||
\(95\) | −6.04069 | −0.619762 | ||||||||
\(96\) | 16.4853 | 1.68253 | ||||||||
\(97\) | 2.81422 | 0.285740 | 0.142870 | − | 0.989741i | \(-0.454367\pi\) | ||||
0.142870 | + | 0.989741i | \(0.454367\pi\) | |||||||
\(98\) | −13.5149 | −1.36521 | ||||||||
\(99\) | 30.4774 | 3.06310 | ||||||||
\(100\) | −12.2930 | −1.22930 | ||||||||
\(101\) | 14.0450 | 1.39753 | 0.698763 | − | 0.715353i | \(-0.253734\pi\) | ||||
0.698763 | + | 0.715353i | \(0.253734\pi\) | |||||||
\(102\) | −7.54261 | −0.746830 | ||||||||
\(103\) | 13.4353 | 1.32382 | 0.661910 | − | 0.749583i | \(-0.269746\pi\) | ||||
0.661910 | + | 0.749583i | \(0.269746\pi\) | |||||||
\(104\) | 13.3084 | 1.30499 | ||||||||
\(105\) | 13.4675 | 1.31430 | ||||||||
\(106\) | 9.40647 | 0.913638 | ||||||||
\(107\) | 3.58337 | 0.346418 | 0.173209 | − | 0.984885i | \(-0.444586\pi\) | ||||
0.173209 | + | 0.984885i | \(0.444586\pi\) | |||||||
\(108\) | 50.6550 | 4.87428 | ||||||||
\(109\) | 1.42208 | 0.136211 | 0.0681054 | − | 0.997678i | \(-0.478305\pi\) | ||||
0.0681054 | + | 0.997678i | \(0.478305\pi\) | |||||||
\(110\) | 10.6270 | 1.01324 | ||||||||
\(111\) | −16.6226 | −1.57774 | ||||||||
\(112\) | −1.82190 | −0.172153 | ||||||||
\(113\) | 1.26745 | 0.119232 | 0.0596160 | − | 0.998221i | \(-0.481012\pi\) | ||||
0.0596160 | + | 0.998221i | \(0.481012\pi\) | |||||||
\(114\) | −39.5502 | −3.70422 | ||||||||
\(115\) | 2.18366 | 0.203627 | ||||||||
\(116\) | −2.97497 | −0.276219 | ||||||||
\(117\) | −32.6430 | −3.01785 | ||||||||
\(118\) | 26.4344 | 2.43348 | ||||||||
\(119\) | −3.58394 | −0.328539 | ||||||||
\(120\) | 11.7043 | 1.06845 | ||||||||
\(121\) | 4.91440 | 0.446763 | ||||||||
\(122\) | 4.80633 | 0.435144 | ||||||||
\(123\) | −28.6364 | −2.58206 | ||||||||
\(124\) | −31.9209 | −2.86658 | ||||||||
\(125\) | 9.99129 | 0.893648 | ||||||||
\(126\) | 63.3139 | 5.64045 | ||||||||
\(127\) | −4.84100 | −0.429569 | −0.214785 | − | 0.976661i | \(-0.568905\pi\) | ||||
−0.214785 | + | 0.976661i | \(0.568905\pi\) | |||||||
\(128\) | 19.2664 | 1.70293 | ||||||||
\(129\) | 26.0746 | 2.29574 | ||||||||
\(130\) | −11.3821 | −0.998274 | ||||||||
\(131\) | 14.6260 | 1.27788 | 0.638939 | − | 0.769258i | \(-0.279374\pi\) | ||||
0.638939 | + | 0.769258i | \(0.279374\pi\) | |||||||
\(132\) | 43.5528 | 3.79079 | ||||||||
\(133\) | −18.7927 | −1.62953 | ||||||||
\(134\) | 26.5828 | 2.29640 | ||||||||
\(135\) | −17.4353 | −1.50059 | ||||||||
\(136\) | −3.11471 | −0.267084 | ||||||||
\(137\) | −11.1706 | −0.954368 | −0.477184 | − | 0.878803i | \(-0.658343\pi\) | ||||
−0.477184 | + | 0.878803i | \(0.658343\pi\) | |||||||
\(138\) | 14.2970 | 1.21705 | ||||||||
\(139\) | −9.26502 | −0.785849 | −0.392925 | − | 0.919571i | \(-0.628537\pi\) | ||||
−0.392925 | + | 0.919571i | \(0.628537\pi\) | |||||||
\(140\) | 13.8189 | 1.16791 | ||||||||
\(141\) | 33.6803 | 2.83639 | ||||||||
\(142\) | 13.2640 | 1.11309 | ||||||||
\(143\) | −17.0452 | −1.42539 | ||||||||
\(144\) | 3.88370 | 0.323642 | ||||||||
\(145\) | 1.02397 | 0.0850363 | ||||||||
\(146\) | 8.29802 | 0.686749 | ||||||||
\(147\) | 19.0645 | 1.57241 | ||||||||
\(148\) | −17.0563 | −1.40202 | ||||||||
\(149\) | −14.9608 | −1.22564 | −0.612820 | − | 0.790223i | \(-0.709965\pi\) | ||||
−0.612820 | + | 0.790223i | \(0.709965\pi\) | |||||||
\(150\) | 27.7029 | 2.26193 | ||||||||
\(151\) | 13.5969 | 1.10650 | 0.553250 | − | 0.833015i | \(-0.313387\pi\) | ||||
0.553250 | + | 0.833015i | \(0.313387\pi\) | |||||||
\(152\) | −16.3322 | −1.32472 | ||||||||
\(153\) | 7.63982 | 0.617643 | ||||||||
\(154\) | 33.0606 | 2.66410 | ||||||||
\(155\) | 10.9870 | 0.882501 | ||||||||
\(156\) | −46.6475 | −3.73479 | ||||||||
\(157\) | 23.0423 | 1.83898 | 0.919488 | − | 0.393118i | \(-0.128604\pi\) | ||||
0.919488 | + | 0.393118i | \(0.128604\pi\) | |||||||
\(158\) | 11.6924 | 0.930194 | ||||||||
\(159\) | −13.2690 | −1.05230 | ||||||||
\(160\) | −5.82224 | −0.460288 | ||||||||
\(161\) | 6.79337 | 0.535393 | ||||||||
\(162\) | −61.1558 | −4.80486 | ||||||||
\(163\) | 7.60787 | 0.595895 | 0.297947 | − | 0.954582i | \(-0.403698\pi\) | ||||
0.297947 | + | 0.954582i | \(0.403698\pi\) | |||||||
\(164\) | −29.3837 | −2.29448 | ||||||||
\(165\) | −14.9907 | −1.16702 | ||||||||
\(166\) | −0.844643 | −0.0655570 | ||||||||
\(167\) | 7.71734 | 0.597185 | 0.298593 | − | 0.954381i | \(-0.403483\pi\) | ||||
0.298593 | + | 0.954381i | \(0.403483\pi\) | |||||||
\(168\) | 36.4121 | 2.80926 | ||||||||
\(169\) | 5.25636 | 0.404335 | ||||||||
\(170\) | 2.66388 | 0.204310 | ||||||||
\(171\) | 40.0599 | 3.06346 | ||||||||
\(172\) | 26.7550 | 2.04005 | ||||||||
\(173\) | −13.1814 | −1.00216 | −0.501080 | − | 0.865401i | \(-0.667064\pi\) | ||||
−0.501080 | + | 0.865401i | \(0.667064\pi\) | |||||||
\(174\) | 6.70426 | 0.508248 | ||||||||
\(175\) | 13.1633 | 0.995051 | ||||||||
\(176\) | 2.02795 | 0.152863 | ||||||||
\(177\) | −37.2891 | −2.80282 | ||||||||
\(178\) | 23.4751 | 1.75953 | ||||||||
\(179\) | −1.00906 | −0.0754205 | −0.0377103 | − | 0.999289i | \(-0.512006\pi\) | ||||
−0.0377103 | + | 0.999289i | \(0.512006\pi\) | |||||||
\(180\) | −29.4576 | −2.19564 | ||||||||
\(181\) | −9.93127 | −0.738185 | −0.369093 | − | 0.929393i | \(-0.620331\pi\) | ||||
−0.369093 | + | 0.929393i | \(0.620331\pi\) | |||||||
\(182\) | −35.4097 | −2.62474 | ||||||||
\(183\) | −6.77994 | −0.501187 | ||||||||
\(184\) | 5.90395 | 0.435245 | ||||||||
\(185\) | 5.87071 | 0.431623 | ||||||||
\(186\) | 71.9355 | 5.27457 | ||||||||
\(187\) | 3.98929 | 0.291725 | ||||||||
\(188\) | 34.5591 | 2.52048 | ||||||||
\(189\) | −54.2412 | −3.94547 | ||||||||
\(190\) | 13.9682 | 1.01336 | ||||||||
\(191\) | −22.4867 | −1.62708 | −0.813540 | − | 0.581509i | \(-0.802462\pi\) | ||||
−0.813540 | + | 0.581509i | \(0.802462\pi\) | |||||||
\(192\) | −41.4363 | −2.99040 | ||||||||
\(193\) | −22.4804 | −1.61818 | −0.809088 | − | 0.587688i | \(-0.800038\pi\) | ||||
−0.809088 | + | 0.587688i | \(0.800038\pi\) | |||||||
\(194\) | −6.50747 | −0.467209 | ||||||||
\(195\) | 16.0559 | 1.14978 | ||||||||
\(196\) | 19.5619 | 1.39728 | ||||||||
\(197\) | −5.91158 | −0.421182 | −0.210591 | − | 0.977574i | \(-0.567539\pi\) | ||||
−0.210591 | + | 0.977574i | \(0.567539\pi\) | |||||||
\(198\) | −70.4746 | −5.00842 | ||||||||
\(199\) | 3.97628 | 0.281871 | 0.140936 | − | 0.990019i | \(-0.454989\pi\) | ||||
0.140936 | + | 0.990019i | \(0.454989\pi\) | |||||||
\(200\) | 11.4399 | 0.808922 | ||||||||
\(201\) | −37.4984 | −2.64494 | ||||||||
\(202\) | −32.4769 | −2.28507 | ||||||||
\(203\) | 3.18559 | 0.223585 | ||||||||
\(204\) | 10.9175 | 0.764374 | ||||||||
\(205\) | 10.1137 | 0.706374 | ||||||||
\(206\) | −31.0672 | −2.16455 | ||||||||
\(207\) | −14.4813 | −1.00652 | ||||||||
\(208\) | −2.17205 | −0.150605 | ||||||||
\(209\) | 20.9181 | 1.44694 | ||||||||
\(210\) | −31.1417 | −2.14898 | ||||||||
\(211\) | −4.31634 | −0.297149 | −0.148574 | − | 0.988901i | \(-0.547468\pi\) | ||||
−0.148574 | + | 0.988901i | \(0.547468\pi\) | |||||||
\(212\) | −13.6153 | −0.935101 | ||||||||
\(213\) | −18.7106 | −1.28203 | ||||||||
\(214\) | −8.28603 | −0.566422 | ||||||||
\(215\) | −9.20895 | −0.628045 | ||||||||
\(216\) | −47.1397 | −3.20745 | ||||||||
\(217\) | 34.1808 | 2.32034 | ||||||||
\(218\) | −3.28836 | −0.222716 | ||||||||
\(219\) | −11.7054 | −0.790979 | ||||||||
\(220\) | −15.3819 | −1.03704 | ||||||||
\(221\) | −4.27275 | −0.287416 | ||||||||
\(222\) | 38.4373 | 2.57974 | ||||||||
\(223\) | 7.42527 | 0.497233 | 0.248617 | − | 0.968602i | \(-0.420024\pi\) | ||||
0.248617 | + | 0.968602i | \(0.420024\pi\) | |||||||
\(224\) | −18.1130 | −1.21023 | ||||||||
\(225\) | −28.0599 | −1.87066 | ||||||||
\(226\) | −2.93080 | −0.194954 | ||||||||
\(227\) | 13.0694 | 0.867445 | 0.433722 | − | 0.901047i | \(-0.357200\pi\) | ||||
0.433722 | + | 0.901047i | \(0.357200\pi\) | |||||||
\(228\) | 57.2464 | 3.79124 | ||||||||
\(229\) | −27.1475 | −1.79395 | −0.896977 | − | 0.442076i | \(-0.854242\pi\) | ||||
−0.896977 | + | 0.442076i | \(0.854242\pi\) | |||||||
\(230\) | −5.04939 | −0.332947 | ||||||||
\(231\) | −46.6362 | −3.06844 | ||||||||
\(232\) | 2.76852 | 0.181762 | ||||||||
\(233\) | −17.0330 | −1.11587 | −0.557934 | − | 0.829885i | \(-0.688406\pi\) | ||||
−0.557934 | + | 0.829885i | \(0.688406\pi\) | |||||||
\(234\) | 75.4823 | 4.93443 | ||||||||
\(235\) | −11.8951 | −0.775951 | ||||||||
\(236\) | −38.2621 | −2.49065 | ||||||||
\(237\) | −16.4936 | −1.07137 | ||||||||
\(238\) | 8.28735 | 0.537189 | ||||||||
\(239\) | −8.43692 | −0.545739 | −0.272869 | − | 0.962051i | \(-0.587973\pi\) | ||||
−0.272869 | + | 0.962051i | \(0.587973\pi\) | |||||||
\(240\) | −1.91025 | −0.123306 | ||||||||
\(241\) | 1.83825 | 0.118412 | 0.0592061 | − | 0.998246i | \(-0.481143\pi\) | ||||
0.0592061 | + | 0.998246i | \(0.481143\pi\) | |||||||
\(242\) | −11.3638 | −0.730495 | ||||||||
\(243\) | 40.8646 | 2.62147 | ||||||||
\(244\) | −6.95685 | −0.445367 | ||||||||
\(245\) | −6.73314 | −0.430164 | ||||||||
\(246\) | 66.2176 | 4.22188 | ||||||||
\(247\) | −22.4044 | −1.42556 | ||||||||
\(248\) | 29.7057 | 1.88631 | ||||||||
\(249\) | 1.19148 | 0.0755068 | ||||||||
\(250\) | −23.1034 | −1.46119 | ||||||||
\(251\) | −28.0184 | −1.76850 | −0.884252 | − | 0.467010i | \(-0.845331\pi\) | ||||
−0.884252 | + | 0.467010i | \(0.845331\pi\) | |||||||
\(252\) | −91.6428 | −5.77295 | ||||||||
\(253\) | −7.56170 | −0.475400 | ||||||||
\(254\) | 11.1941 | 0.702381 | ||||||||
\(255\) | −3.75774 | −0.235319 | ||||||||
\(256\) | −19.1445 | −1.19653 | ||||||||
\(257\) | −2.98989 | −0.186504 | −0.0932520 | − | 0.995643i | \(-0.529726\pi\) | ||||
−0.0932520 | + | 0.995643i | \(0.529726\pi\) | |||||||
\(258\) | −60.2937 | −3.75372 | ||||||||
\(259\) | 18.2638 | 1.13486 | ||||||||
\(260\) | 16.4748 | 1.02173 | ||||||||
\(261\) | −6.79066 | −0.420332 | ||||||||
\(262\) | −33.8205 | −2.08943 | ||||||||
\(263\) | −8.27783 | −0.510433 | −0.255217 | − | 0.966884i | \(-0.582147\pi\) | ||||
−0.255217 | + | 0.966884i | \(0.582147\pi\) | |||||||
\(264\) | −40.5304 | −2.49447 | ||||||||
\(265\) | 4.68632 | 0.287878 | ||||||||
\(266\) | 43.4553 | 2.66441 | ||||||||
\(267\) | −33.1147 | −2.02659 | ||||||||
\(268\) | −38.4769 | −2.35035 | ||||||||
\(269\) | −32.1027 | −1.95733 | −0.978667 | − | 0.205453i | \(-0.934133\pi\) | ||||
−0.978667 | + | 0.205453i | \(0.934133\pi\) | |||||||
\(270\) | 40.3165 | 2.45358 | ||||||||
\(271\) | 27.2641 | 1.65617 | 0.828087 | − | 0.560599i | \(-0.189429\pi\) | ||||
0.828087 | + | 0.560599i | \(0.189429\pi\) | |||||||
\(272\) | 0.508350 | 0.0308232 | ||||||||
\(273\) | 49.9500 | 3.02311 | ||||||||
\(274\) | 25.8304 | 1.56047 | ||||||||
\(275\) | −14.6521 | −0.883552 | ||||||||
\(276\) | −20.6941 | −1.24564 | ||||||||
\(277\) | 0.978675 | 0.0588029 | 0.0294014 | − | 0.999568i | \(-0.490640\pi\) | ||||
0.0294014 | + | 0.999568i | \(0.490640\pi\) | |||||||
\(278\) | 21.4240 | 1.28493 | ||||||||
\(279\) | −72.8626 | −4.36217 | ||||||||
\(280\) | −12.8599 | −0.768528 | ||||||||
\(281\) | −17.5299 | −1.04575 | −0.522873 | − | 0.852411i | \(-0.675140\pi\) | ||||
−0.522873 | + | 0.852411i | \(0.675140\pi\) | |||||||
\(282\) | −77.8808 | −4.63773 | ||||||||
\(283\) | 1.29771 | 0.0771409 | 0.0385704 | − | 0.999256i | \(-0.487720\pi\) | ||||
0.0385704 | + | 0.999256i | \(0.487720\pi\) | |||||||
\(284\) | −19.1988 | −1.13924 | ||||||||
\(285\) | −19.7040 | −1.16716 | ||||||||
\(286\) | 39.4146 | 2.33063 | ||||||||
\(287\) | 31.4639 | 1.85726 | ||||||||
\(288\) | 38.6112 | 2.27519 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −2.36779 | −0.139041 | ||||||||
\(291\) | 9.17962 | 0.538119 | ||||||||
\(292\) | −12.0109 | −0.702882 | ||||||||
\(293\) | 33.2107 | 1.94019 | 0.970094 | − | 0.242730i | \(-0.0780429\pi\) | ||||
0.970094 | + | 0.242730i | \(0.0780429\pi\) | |||||||
\(294\) | −44.0838 | −2.57102 | ||||||||
\(295\) | 13.1697 | 0.766767 | ||||||||
\(296\) | 15.8726 | 0.922579 | ||||||||
\(297\) | 60.3759 | 3.50336 | ||||||||
\(298\) | 34.5948 | 2.00402 | ||||||||
\(299\) | 8.09900 | 0.468377 | ||||||||
\(300\) | −40.0982 | −2.31507 | ||||||||
\(301\) | −28.6491 | −1.65131 | ||||||||
\(302\) | −31.4409 | −1.80922 | ||||||||
\(303\) | 45.8129 | 2.63188 | ||||||||
\(304\) | 2.66557 | 0.152881 | ||||||||
\(305\) | 2.39452 | 0.137110 | ||||||||
\(306\) | −17.6660 | −1.00990 | ||||||||
\(307\) | 15.2836 | 0.872283 | 0.436142 | − | 0.899878i | \(-0.356345\pi\) | ||||
0.436142 | + | 0.899878i | \(0.356345\pi\) | |||||||
\(308\) | −47.8531 | −2.72668 | ||||||||
\(309\) | 43.8243 | 2.49308 | ||||||||
\(310\) | −25.4060 | −1.44296 | ||||||||
\(311\) | −2.08720 | −0.118354 | −0.0591772 | − | 0.998247i | \(-0.518848\pi\) | ||||
−0.0591772 | + | 0.998247i | \(0.518848\pi\) | |||||||
\(312\) | 43.4103 | 2.45762 | ||||||||
\(313\) | −11.0153 | −0.622621 | −0.311311 | − | 0.950308i | \(-0.600768\pi\) | ||||
−0.311311 | + | 0.950308i | \(0.600768\pi\) | |||||||
\(314\) | −53.2820 | −3.00688 | ||||||||
\(315\) | 31.5431 | 1.77725 | ||||||||
\(316\) | −16.9240 | −0.952047 | ||||||||
\(317\) | 2.43821 | 0.136944 | 0.0684719 | − | 0.997653i | \(-0.478188\pi\) | ||||
0.0684719 | + | 0.997653i | \(0.478188\pi\) | |||||||
\(318\) | 30.6827 | 1.72060 | ||||||||
\(319\) | −3.54588 | −0.198531 | ||||||||
\(320\) | 14.6343 | 0.818084 | ||||||||
\(321\) | 11.6885 | 0.652389 | ||||||||
\(322\) | −15.7087 | −0.875411 | ||||||||
\(323\) | 5.24357 | 0.291760 | ||||||||
\(324\) | 88.5192 | 4.91773 | ||||||||
\(325\) | 15.6932 | 0.870500 | ||||||||
\(326\) | −17.5921 | −0.974337 | ||||||||
\(327\) | 4.63866 | 0.256518 | ||||||||
\(328\) | 27.3445 | 1.50985 | ||||||||
\(329\) | −37.0058 | −2.04019 | ||||||||
\(330\) | 34.6638 | 1.90818 | ||||||||
\(331\) | −21.2898 | −1.17020 | −0.585098 | − | 0.810963i | \(-0.698944\pi\) | ||||
−0.585098 | + | 0.810963i | \(0.698944\pi\) | |||||||
\(332\) | 1.22257 | 0.0670971 | ||||||||
\(333\) | −38.9327 | −2.13350 | ||||||||
\(334\) | −17.8452 | −0.976447 | ||||||||
\(335\) | 13.2436 | 0.723574 | ||||||||
\(336\) | −5.94279 | −0.324206 | ||||||||
\(337\) | −12.8010 | −0.697312 | −0.348656 | − | 0.937251i | \(-0.613362\pi\) | ||||
−0.348656 | + | 0.937251i | \(0.613362\pi\) | |||||||
\(338\) | −12.1546 | −0.661121 | ||||||||
\(339\) | 4.13427 | 0.224543 | ||||||||
\(340\) | −3.85579 | −0.209110 | ||||||||
\(341\) | −38.0467 | −2.06034 | ||||||||
\(342\) | −92.6328 | −5.00901 | ||||||||
\(343\) | 4.14075 | 0.223579 | ||||||||
\(344\) | −24.8982 | −1.34242 | ||||||||
\(345\) | 7.12281 | 0.383479 | ||||||||
\(346\) | 30.4800 | 1.63861 | ||||||||
\(347\) | 12.5153 | 0.671855 | 0.335928 | − | 0.941888i | \(-0.390950\pi\) | ||||
0.335928 | + | 0.941888i | \(0.390950\pi\) | |||||||
\(348\) | −9.70399 | −0.520188 | ||||||||
\(349\) | −10.1359 | −0.542562 | −0.271281 | − | 0.962500i | \(-0.587447\pi\) | ||||
−0.271281 | + | 0.962500i | \(0.587447\pi\) | |||||||
\(350\) | −30.4382 | −1.62699 | ||||||||
\(351\) | −64.6659 | −3.45161 | ||||||||
\(352\) | 20.1616 | 1.07462 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | 86.2257 | 4.58284 | ||||||||
\(355\) | 6.60816 | 0.350725 | ||||||||
\(356\) | −33.9788 | −1.80087 | ||||||||
\(357\) | −11.6904 | −0.618720 | ||||||||
\(358\) | 2.33330 | 0.123319 | ||||||||
\(359\) | −6.07354 | −0.320549 | −0.160275 | − | 0.987072i | \(-0.551238\pi\) | ||||
−0.160275 | + | 0.987072i | \(0.551238\pi\) | |||||||
\(360\) | 27.4133 | 1.44481 | ||||||||
\(361\) | 8.49503 | 0.447107 | ||||||||
\(362\) | 22.9646 | 1.20699 | ||||||||
\(363\) | 16.0301 | 0.841364 | ||||||||
\(364\) | 51.2533 | 2.68640 | ||||||||
\(365\) | 4.13409 | 0.216388 | ||||||||
\(366\) | 15.6776 | 0.819483 | ||||||||
\(367\) | −1.73911 | −0.0907807 | −0.0453904 | − | 0.998969i | \(-0.514453\pi\) | ||||
−0.0453904 | + | 0.998969i | \(0.514453\pi\) | |||||||
\(368\) | −0.963578 | −0.0502300 | ||||||||
\(369\) | −67.0710 | −3.49158 | ||||||||
\(370\) | −13.5752 | −0.705740 | ||||||||
\(371\) | 14.5792 | 0.756914 | ||||||||
\(372\) | −104.122 | −5.39848 | ||||||||
\(373\) | −32.9244 | −1.70476 | −0.852381 | − | 0.522921i | \(-0.824842\pi\) | ||||
−0.852381 | + | 0.522921i | \(0.824842\pi\) | |||||||
\(374\) | −9.22464 | −0.476995 | ||||||||
\(375\) | 32.5903 | 1.68296 | ||||||||
\(376\) | −32.1608 | −1.65857 | ||||||||
\(377\) | 3.79783 | 0.195598 | ||||||||
\(378\) | 125.425 | 6.45117 | ||||||||
\(379\) | −8.44074 | −0.433572 | −0.216786 | − | 0.976219i | \(-0.569557\pi\) | ||||
−0.216786 | + | 0.976219i | \(0.569557\pi\) | |||||||
\(380\) | −20.2181 | −1.03717 | ||||||||
\(381\) | −15.7907 | −0.808984 | ||||||||
\(382\) | 51.9972 | 2.66041 | ||||||||
\(383\) | −6.37503 | −0.325749 | −0.162874 | − | 0.986647i | \(-0.552077\pi\) | ||||
−0.162874 | + | 0.986647i | \(0.552077\pi\) | |||||||
\(384\) | 62.8447 | 3.20703 | ||||||||
\(385\) | 16.4708 | 0.839432 | ||||||||
\(386\) | 51.9827 | 2.64585 | ||||||||
\(387\) | 61.0708 | 3.10440 | ||||||||
\(388\) | 9.41915 | 0.478185 | ||||||||
\(389\) | 8.22512 | 0.417030 | 0.208515 | − | 0.978019i | \(-0.433137\pi\) | ||||
0.208515 | + | 0.978019i | \(0.433137\pi\) | |||||||
\(390\) | −37.1269 | −1.87999 | ||||||||
\(391\) | −1.89550 | −0.0958597 | ||||||||
\(392\) | −18.2044 | −0.919460 | ||||||||
\(393\) | 47.7081 | 2.40656 | ||||||||
\(394\) | 13.6697 | 0.688668 | ||||||||
\(395\) | 5.82515 | 0.293095 | ||||||||
\(396\) | 102.008 | 5.12607 | ||||||||
\(397\) | −24.0508 | −1.20708 | −0.603538 | − | 0.797335i | \(-0.706243\pi\) | ||||
−0.603538 | + | 0.797335i | \(0.706243\pi\) | |||||||
\(398\) | −9.19457 | −0.460882 | ||||||||
\(399\) | −61.2993 | −3.06880 | ||||||||
\(400\) | −1.86709 | −0.0933547 | ||||||||
\(401\) | −38.0085 | −1.89805 | −0.949026 | − | 0.315197i | \(-0.897929\pi\) | ||||
−0.949026 | + | 0.315197i | \(0.897929\pi\) | |||||||
\(402\) | 86.7097 | 4.32469 | ||||||||
\(403\) | 40.7501 | 2.02991 | ||||||||
\(404\) | 47.0083 | 2.33875 | ||||||||
\(405\) | −30.4679 | −1.51396 | ||||||||
\(406\) | −7.36622 | −0.365579 | ||||||||
\(407\) | −20.3295 | −1.00769 | ||||||||
\(408\) | −10.1598 | −0.502985 | ||||||||
\(409\) | 33.9260 | 1.67753 | 0.838767 | − | 0.544491i | \(-0.183277\pi\) | ||||
0.838767 | + | 0.544491i | \(0.183277\pi\) | |||||||
\(410\) | −23.3865 | −1.15498 | ||||||||
\(411\) | −36.4371 | −1.79731 | ||||||||
\(412\) | 44.9678 | 2.21540 | ||||||||
\(413\) | 40.9709 | 2.01605 | ||||||||
\(414\) | 33.4859 | 1.64574 | ||||||||
\(415\) | −0.420802 | −0.0206564 | ||||||||
\(416\) | −21.5942 | −1.05874 | ||||||||
\(417\) | −30.2213 | −1.47995 | ||||||||
\(418\) | −48.3701 | −2.36586 | ||||||||
\(419\) | −35.0056 | −1.71014 | −0.855068 | − | 0.518516i | \(-0.826485\pi\) | ||||
−0.855068 | + | 0.518516i | \(0.826485\pi\) | |||||||
\(420\) | 45.0756 | 2.19947 | ||||||||
\(421\) | 20.2970 | 0.989217 | 0.494608 | − | 0.869116i | \(-0.335311\pi\) | ||||
0.494608 | + | 0.869116i | \(0.335311\pi\) | |||||||
\(422\) | 9.98090 | 0.485863 | ||||||||
\(423\) | 78.8845 | 3.83550 | ||||||||
\(424\) | 12.6704 | 0.615329 | ||||||||
\(425\) | −3.67285 | −0.178159 | ||||||||
\(426\) | 43.2656 | 2.09622 | ||||||||
\(427\) | 7.44937 | 0.360500 | ||||||||
\(428\) | 11.9935 | 0.579728 | ||||||||
\(429\) | −55.5993 | −2.68436 | ||||||||
\(430\) | 21.2944 | 1.02691 | ||||||||
\(431\) | −35.8336 | −1.72605 | −0.863023 | − | 0.505165i | \(-0.831432\pi\) | ||||
−0.863023 | + | 0.505165i | \(0.831432\pi\) | |||||||
\(432\) | 7.69363 | 0.370160 | ||||||||
\(433\) | 25.3031 | 1.21599 | 0.607994 | − | 0.793942i | \(-0.291974\pi\) | ||||
0.607994 | + | 0.793942i | \(0.291974\pi\) | |||||||
\(434\) | −79.0382 | −3.79395 | ||||||||
\(435\) | 3.34007 | 0.160144 | ||||||||
\(436\) | 4.75969 | 0.227948 | ||||||||
\(437\) | −9.93920 | −0.475457 | ||||||||
\(438\) | 27.0671 | 1.29332 | ||||||||
\(439\) | 32.0332 | 1.52886 | 0.764430 | − | 0.644706i | \(-0.223020\pi\) | ||||
0.764430 | + | 0.644706i | \(0.223020\pi\) | |||||||
\(440\) | 14.3144 | 0.682412 | ||||||||
\(441\) | 44.6520 | 2.12629 | ||||||||
\(442\) | 9.88011 | 0.469949 | ||||||||
\(443\) | 22.9457 | 1.09018 | 0.545091 | − | 0.838377i | \(-0.316495\pi\) | ||||
0.545091 | + | 0.838377i | \(0.316495\pi\) | |||||||
\(444\) | −55.6355 | −2.64035 | ||||||||
\(445\) | 11.6953 | 0.554412 | ||||||||
\(446\) | −17.1699 | −0.813017 | ||||||||
\(447\) | −48.8004 | −2.30818 | ||||||||
\(448\) | 45.5276 | 2.15098 | ||||||||
\(449\) | −31.2108 | −1.47293 | −0.736465 | − | 0.676475i | \(-0.763507\pi\) | ||||
−0.736465 | + | 0.676475i | \(0.763507\pi\) | |||||||
\(450\) | 64.8845 | 3.05869 | ||||||||
\(451\) | −35.0225 | −1.64914 | ||||||||
\(452\) | 4.24215 | 0.199534 | ||||||||
\(453\) | 44.3514 | 2.08381 | ||||||||
\(454\) | −30.2210 | −1.41834 | ||||||||
\(455\) | −17.6412 | −0.827031 | ||||||||
\(456\) | −53.2736 | −2.49477 | ||||||||
\(457\) | −18.1571 | −0.849351 | −0.424675 | − | 0.905346i | \(-0.639612\pi\) | ||||
−0.424675 | + | 0.905346i | \(0.639612\pi\) | |||||||
\(458\) | 62.7746 | 2.93326 | ||||||||
\(459\) | 15.1345 | 0.706419 | ||||||||
\(460\) | 7.30867 | 0.340768 | ||||||||
\(461\) | −4.07140 | −0.189624 | −0.0948120 | − | 0.995495i | \(-0.530225\pi\) | ||||
−0.0948120 | + | 0.995495i | \(0.530225\pi\) | |||||||
\(462\) | 107.839 | 5.01715 | ||||||||
\(463\) | 0.541809 | 0.0251800 | 0.0125900 | − | 0.999921i | \(-0.495992\pi\) | ||||
0.0125900 | + | 0.999921i | \(0.495992\pi\) | |||||||
\(464\) | −0.451847 | −0.0209765 | ||||||||
\(465\) | 35.8384 | 1.66196 | ||||||||
\(466\) | 39.3863 | 1.82454 | ||||||||
\(467\) | 28.8533 | 1.33517 | 0.667585 | − | 0.744534i | \(-0.267328\pi\) | ||||
0.667585 | + | 0.744534i | \(0.267328\pi\) | |||||||
\(468\) | −109.256 | −5.05035 | ||||||||
\(469\) | 41.2009 | 1.90248 | ||||||||
\(470\) | 27.5057 | 1.26874 | ||||||||
\(471\) | 75.1611 | 3.46324 | ||||||||
\(472\) | 35.6068 | 1.63894 | ||||||||
\(473\) | 31.8893 | 1.46627 | ||||||||
\(474\) | 38.1390 | 1.75178 | ||||||||
\(475\) | −19.2589 | −0.883657 | ||||||||
\(476\) | −11.9954 | −0.549809 | ||||||||
\(477\) | −31.0782 | −1.42297 | ||||||||
\(478\) | 19.5092 | 0.892328 | ||||||||
\(479\) | −16.4647 | −0.752293 | −0.376146 | − | 0.926560i | \(-0.622751\pi\) | ||||
−0.376146 | + | 0.926560i | \(0.622751\pi\) | |||||||
\(480\) | −18.9914 | −0.866835 | ||||||||
\(481\) | 21.7740 | 0.992809 | ||||||||
\(482\) | −4.25069 | −0.193614 | ||||||||
\(483\) | 22.1591 | 1.00828 | ||||||||
\(484\) | 16.4484 | 0.747655 | ||||||||
\(485\) | −3.24203 | −0.147213 | ||||||||
\(486\) | −94.4935 | −4.28631 | ||||||||
\(487\) | 6.67110 | 0.302296 | 0.151148 | − | 0.988511i | \(-0.451703\pi\) | ||||
0.151148 | + | 0.988511i | \(0.451703\pi\) | |||||||
\(488\) | 6.47406 | 0.293067 | ||||||||
\(489\) | 24.8159 | 1.12221 | ||||||||
\(490\) | 15.5694 | 0.703354 | ||||||||
\(491\) | 29.8188 | 1.34570 | 0.672852 | − | 0.739777i | \(-0.265069\pi\) | ||||
0.672852 | + | 0.739777i | \(0.265069\pi\) | |||||||
\(492\) | −95.8458 | −4.32106 | ||||||||
\(493\) | −0.888851 | −0.0400318 | ||||||||
\(494\) | 51.8070 | 2.33091 | ||||||||
\(495\) | −35.1106 | −1.57810 | ||||||||
\(496\) | −4.84824 | −0.217692 | ||||||||
\(497\) | 20.5580 | 0.922154 | ||||||||
\(498\) | −2.75512 | −0.123460 | ||||||||
\(499\) | 36.5895 | 1.63797 | 0.818986 | − | 0.573813i | \(-0.194536\pi\) | ||||
0.818986 | + | 0.573813i | \(0.194536\pi\) | |||||||
\(500\) | 33.4407 | 1.49551 | ||||||||
\(501\) | 25.1730 | 1.12465 | ||||||||
\(502\) | 64.7884 | 2.89165 | ||||||||
\(503\) | 1.09744 | 0.0489326 | 0.0244663 | − | 0.999701i | \(-0.492211\pi\) | ||||
0.0244663 | + | 0.999701i | \(0.492211\pi\) | |||||||
\(504\) | 85.2830 | 3.79881 | ||||||||
\(505\) | −16.1801 | −0.720003 | ||||||||
\(506\) | 17.4853 | 0.777318 | ||||||||
\(507\) | 17.1456 | 0.761462 | ||||||||
\(508\) | −16.2028 | −0.718882 | ||||||||
\(509\) | −12.4961 | −0.553880 | −0.276940 | − | 0.960887i | \(-0.589320\pi\) | ||||
−0.276940 | + | 0.960887i | \(0.589320\pi\) | |||||||
\(510\) | 8.68923 | 0.384766 | ||||||||
\(511\) | 12.8612 | 0.568945 | ||||||||
\(512\) | 5.73590 | 0.253493 | ||||||||
\(513\) | 79.3589 | 3.50378 | ||||||||
\(514\) | 6.91368 | 0.304949 | ||||||||
\(515\) | −15.4777 | −0.682030 | ||||||||
\(516\) | 87.2713 | 3.84191 | ||||||||
\(517\) | 41.1911 | 1.81158 | ||||||||
\(518\) | −42.2325 | −1.85559 | ||||||||
\(519\) | −42.9959 | −1.88731 | ||||||||
\(520\) | −15.3315 | −0.672331 | ||||||||
\(521\) | −12.6025 | −0.552125 | −0.276062 | − | 0.961140i | \(-0.589030\pi\) | ||||
−0.276062 | + | 0.961140i | \(0.589030\pi\) | |||||||
\(522\) | 15.7024 | 0.687277 | ||||||||
\(523\) | −6.36361 | −0.278261 | −0.139131 | − | 0.990274i | \(-0.544431\pi\) | ||||
−0.139131 | + | 0.990274i | \(0.544431\pi\) | |||||||
\(524\) | 48.9530 | 2.13852 | ||||||||
\(525\) | 42.9370 | 1.87392 | ||||||||
\(526\) | 19.1413 | 0.834600 | ||||||||
\(527\) | −9.53721 | −0.415447 | ||||||||
\(528\) | 6.61492 | 0.287878 | ||||||||
\(529\) | −19.4071 | −0.843786 | ||||||||
\(530\) | −10.8364 | −0.470705 | ||||||||
\(531\) | −87.3369 | −3.79010 | ||||||||
\(532\) | −62.8988 | −2.72701 | ||||||||
\(533\) | 37.5110 | 1.62478 | ||||||||
\(534\) | 76.5729 | 3.31363 | ||||||||
\(535\) | −4.12811 | −0.178474 | ||||||||
\(536\) | 35.8067 | 1.54661 | ||||||||
\(537\) | −3.29142 | −0.142035 | ||||||||
\(538\) | 74.2328 | 3.20040 | ||||||||
\(539\) | 23.3159 | 1.00429 | ||||||||
\(540\) | −58.3556 | −2.51122 | ||||||||
\(541\) | 3.05462 | 0.131328 | 0.0656641 | − | 0.997842i | \(-0.479083\pi\) | ||||
0.0656641 | + | 0.997842i | \(0.479083\pi\) | |||||||
\(542\) | −63.0442 | −2.70798 | ||||||||
\(543\) | −32.3945 | −1.39018 | ||||||||
\(544\) | 5.05394 | 0.216686 | ||||||||
\(545\) | −1.63827 | −0.0701756 | ||||||||
\(546\) | −115.502 | −4.94303 | ||||||||
\(547\) | 12.5049 | 0.534670 | 0.267335 | − | 0.963604i | \(-0.413857\pi\) | ||||
0.267335 | + | 0.963604i | \(0.413857\pi\) | |||||||
\(548\) | −37.3878 | −1.59713 | ||||||||
\(549\) | −15.8797 | −0.677728 | ||||||||
\(550\) | 33.8808 | 1.44468 | ||||||||
\(551\) | −4.66075 | −0.198555 | ||||||||
\(552\) | 19.2579 | 0.819672 | ||||||||
\(553\) | 18.1221 | 0.770630 | ||||||||
\(554\) | −2.26304 | −0.0961475 | ||||||||
\(555\) | 19.1495 | 0.812852 | ||||||||
\(556\) | −31.0099 | −1.31511 | ||||||||
\(557\) | 22.6211 | 0.958485 | 0.479242 | − | 0.877683i | \(-0.340911\pi\) | ||||
0.479242 | + | 0.877683i | \(0.340911\pi\) | |||||||
\(558\) | 168.484 | 7.13251 | ||||||||
\(559\) | −34.1552 | −1.44461 | ||||||||
\(560\) | 2.09886 | 0.0886930 | ||||||||
\(561\) | 13.0125 | 0.549390 | ||||||||
\(562\) | 40.5354 | 1.70988 | ||||||||
\(563\) | −3.97719 | −0.167619 | −0.0838093 | − | 0.996482i | \(-0.526709\pi\) | ||||
−0.0838093 | + | 0.996482i | \(0.526709\pi\) | |||||||
\(564\) | 112.727 | 4.74668 | ||||||||
\(565\) | −1.46013 | −0.0614281 | ||||||||
\(566\) | −3.00077 | −0.126132 | ||||||||
\(567\) | −94.7860 | −3.98064 | ||||||||
\(568\) | 17.8665 | 0.749661 | ||||||||
\(569\) | −35.4068 | −1.48433 | −0.742164 | − | 0.670218i | \(-0.766201\pi\) | ||||
−0.742164 | + | 0.670218i | \(0.766201\pi\) | |||||||
\(570\) | 45.5626 | 1.90841 | ||||||||
\(571\) | 14.9937 | 0.627467 | 0.313733 | − | 0.949511i | \(-0.398420\pi\) | ||||
0.313733 | + | 0.949511i | \(0.398420\pi\) | |||||||
\(572\) | −57.0501 | −2.38538 | ||||||||
\(573\) | −73.3487 | −3.06419 | ||||||||
\(574\) | −72.7557 | −3.03677 | ||||||||
\(575\) | 6.96190 | 0.290331 | ||||||||
\(576\) | −97.0503 | −4.04376 | ||||||||
\(577\) | −38.7499 | −1.61318 | −0.806589 | − | 0.591112i | \(-0.798689\pi\) | ||||
−0.806589 | + | 0.591112i | \(0.798689\pi\) | |||||||
\(578\) | −2.31236 | −0.0961813 | ||||||||
\(579\) | −73.3283 | −3.04742 | ||||||||
\(580\) | 3.42723 | 0.142308 | ||||||||
\(581\) | −1.30912 | −0.0543115 | ||||||||
\(582\) | −21.2265 | −0.879868 | ||||||||
\(583\) | −16.2281 | −0.672099 | ||||||||
\(584\) | 11.1773 | 0.462521 | ||||||||
\(585\) | 37.6054 | 1.55479 | ||||||||
\(586\) | −76.7949 | −3.17237 | ||||||||
\(587\) | −10.8143 | −0.446356 | −0.223178 | − | 0.974778i | \(-0.571643\pi\) | ||||
−0.223178 | + | 0.974778i | \(0.571643\pi\) | |||||||
\(588\) | 63.8086 | 2.63142 | ||||||||
\(589\) | −50.0090 | −2.06059 | ||||||||
\(590\) | −30.4529 | −1.25373 | ||||||||
\(591\) | −19.2828 | −0.793189 | ||||||||
\(592\) | −2.59056 | −0.106471 | ||||||||
\(593\) | 16.5566 | 0.679898 | 0.339949 | − | 0.940444i | \(-0.389590\pi\) | ||||
0.339949 | + | 0.940444i | \(0.389590\pi\) | |||||||
\(594\) | −139.611 | −5.72829 | ||||||||
\(595\) | 4.12877 | 0.169263 | ||||||||
\(596\) | −50.0737 | −2.05110 | ||||||||
\(597\) | 12.9701 | 0.530832 | ||||||||
\(598\) | −18.7278 | −0.765836 | ||||||||
\(599\) | 26.6085 | 1.08719 | 0.543597 | − | 0.839347i | \(-0.317062\pi\) | ||||
0.543597 | + | 0.839347i | \(0.317062\pi\) | |||||||
\(600\) | 37.3155 | 1.52340 | ||||||||
\(601\) | 21.9492 | 0.895325 | 0.447662 | − | 0.894203i | \(-0.352257\pi\) | ||||
0.447662 | + | 0.894203i | \(0.352257\pi\) | |||||||
\(602\) | 66.2469 | 2.70002 | ||||||||
\(603\) | −87.8272 | −3.57660 | ||||||||
\(604\) | 45.5087 | 1.85172 | ||||||||
\(605\) | −5.66148 | −0.230172 | ||||||||
\(606\) | −105.936 | −4.30334 | ||||||||
\(607\) | −6.57319 | −0.266798 | −0.133399 | − | 0.991062i | \(-0.542589\pi\) | ||||
−0.133399 | + | 0.991062i | \(0.542589\pi\) | |||||||
\(608\) | 26.5007 | 1.07475 | ||||||||
\(609\) | 10.3910 | 0.421064 | ||||||||
\(610\) | −5.53698 | −0.224186 | ||||||||
\(611\) | −44.1180 | −1.78482 | ||||||||
\(612\) | 25.5704 | 1.03362 | ||||||||
\(613\) | −37.6993 | −1.52266 | −0.761330 | − | 0.648365i | \(-0.775453\pi\) | ||||
−0.761330 | + | 0.648365i | \(0.775453\pi\) | |||||||
\(614\) | −35.3412 | −1.42625 | ||||||||
\(615\) | 32.9897 | 1.33027 | ||||||||
\(616\) | 44.5322 | 1.79425 | ||||||||
\(617\) | −25.7889 | −1.03822 | −0.519112 | − | 0.854706i | \(-0.673737\pi\) | ||||
−0.519112 | + | 0.854706i | \(0.673737\pi\) | |||||||
\(618\) | −101.337 | −4.07638 | ||||||||
\(619\) | −41.2309 | −1.65721 | −0.828604 | − | 0.559835i | \(-0.810865\pi\) | ||||
−0.828604 | + | 0.559835i | \(0.810865\pi\) | |||||||
\(620\) | 36.7735 | 1.47686 | ||||||||
\(621\) | −28.6875 | −1.15119 | ||||||||
\(622\) | 4.82635 | 0.193519 | ||||||||
\(623\) | 36.3843 | 1.45771 | ||||||||
\(624\) | −7.08495 | −0.283625 | ||||||||
\(625\) | 6.85410 | 0.274164 | ||||||||
\(626\) | 25.4713 | 1.01804 | ||||||||
\(627\) | 68.2322 | 2.72493 | ||||||||
\(628\) | 77.1223 | 3.07751 | ||||||||
\(629\) | −5.09602 | −0.203192 | ||||||||
\(630\) | −72.9388 | −2.90595 | ||||||||
\(631\) | 12.1105 | 0.482112 | 0.241056 | − | 0.970511i | \(-0.422506\pi\) | ||||
0.241056 | + | 0.970511i | \(0.422506\pi\) | |||||||
\(632\) | 15.7495 | 0.626480 | ||||||||
\(633\) | −14.0793 | −0.559604 | ||||||||
\(634\) | −5.63802 | −0.223914 | ||||||||
\(635\) | 5.57692 | 0.221314 | ||||||||
\(636\) | −44.4113 | −1.76102 | ||||||||
\(637\) | −24.9727 | −0.989453 | ||||||||
\(638\) | 8.19933 | 0.324615 | ||||||||
\(639\) | −43.8232 | −1.73362 | ||||||||
\(640\) | −22.1953 | −0.877347 | ||||||||
\(641\) | 38.1557 | 1.50706 | 0.753530 | − | 0.657413i | \(-0.228349\pi\) | ||||
0.753530 | + | 0.657413i | \(0.228349\pi\) | |||||||
\(642\) | −27.0280 | −1.06671 | ||||||||
\(643\) | 10.3160 | 0.406821 | 0.203411 | − | 0.979093i | \(-0.434797\pi\) | ||||
0.203411 | + | 0.979093i | \(0.434797\pi\) | |||||||
\(644\) | 22.7373 | 0.895976 | ||||||||
\(645\) | −30.0384 | −1.18276 | ||||||||
\(646\) | −12.1250 | −0.477052 | ||||||||
\(647\) | −11.9820 | −0.471061 | −0.235531 | − | 0.971867i | \(-0.575683\pi\) | ||||
−0.235531 | + | 0.971867i | \(0.575683\pi\) | |||||||
\(648\) | −82.3761 | −3.23604 | ||||||||
\(649\) | −45.6047 | −1.79014 | ||||||||
\(650\) | −36.2882 | −1.42334 | ||||||||
\(651\) | 111.493 | 4.36977 | ||||||||
\(652\) | 25.4635 | 0.997226 | ||||||||
\(653\) | −1.76915 | −0.0692323 | −0.0346161 | − | 0.999401i | \(-0.511021\pi\) | ||||
−0.0346161 | + | 0.999401i | \(0.511021\pi\) | |||||||
\(654\) | −10.7262 | −0.419428 | ||||||||
\(655\) | −16.8494 | −0.658361 | ||||||||
\(656\) | −4.46287 | −0.174246 | ||||||||
\(657\) | −27.4159 | −1.06960 | ||||||||
\(658\) | 85.5705 | 3.33588 | ||||||||
\(659\) | −2.03827 | −0.0793997 | −0.0396999 | − | 0.999212i | \(-0.512640\pi\) | ||||
−0.0396999 | + | 0.999212i | \(0.512640\pi\) | |||||||
\(660\) | −50.1737 | −1.95301 | ||||||||
\(661\) | 14.7410 | 0.573357 | 0.286679 | − | 0.958027i | \(-0.407449\pi\) | ||||
0.286679 | + | 0.958027i | \(0.407449\pi\) | |||||||
\(662\) | 49.2297 | 1.91337 | ||||||||
\(663\) | −13.9372 | −0.541274 | ||||||||
\(664\) | −1.13772 | −0.0441522 | ||||||||
\(665\) | 21.6495 | 0.839531 | ||||||||
\(666\) | 90.0262 | 3.48844 | ||||||||
\(667\) | 1.68482 | 0.0652365 | ||||||||
\(668\) | 25.8298 | 0.999386 | ||||||||
\(669\) | 24.2203 | 0.936411 | ||||||||
\(670\) | −30.6239 | −1.18310 | ||||||||
\(671\) | −8.29189 | −0.320105 | ||||||||
\(672\) | −59.0824 | −2.27915 | ||||||||
\(673\) | 22.5140 | 0.867852 | 0.433926 | − | 0.900948i | \(-0.357128\pi\) | ||||
0.433926 | + | 0.900948i | \(0.357128\pi\) | |||||||
\(674\) | 29.6003 | 1.14016 | ||||||||
\(675\) | −55.5868 | −2.13954 | ||||||||
\(676\) | 17.5930 | 0.676652 | ||||||||
\(677\) | −38.3223 | −1.47285 | −0.736423 | − | 0.676521i | \(-0.763487\pi\) | ||||
−0.736423 | + | 0.676521i | \(0.763487\pi\) | |||||||
\(678\) | −9.55991 | −0.367146 | ||||||||
\(679\) | −10.0860 | −0.387065 | ||||||||
\(680\) | 3.58821 | 0.137602 | ||||||||
\(681\) | 42.6307 | 1.63361 | ||||||||
\(682\) | 87.9774 | 3.36883 | ||||||||
\(683\) | 45.1175 | 1.72637 | 0.863187 | − | 0.504885i | \(-0.168465\pi\) | ||||
0.863187 | + | 0.504885i | \(0.168465\pi\) | |||||||
\(684\) | 134.080 | 5.12668 | ||||||||
\(685\) | 12.8687 | 0.491689 | ||||||||
\(686\) | −9.57488 | −0.365570 | ||||||||
\(687\) | −88.5516 | −3.37845 | ||||||||
\(688\) | 4.06362 | 0.154924 | ||||||||
\(689\) | 17.3812 | 0.662170 | ||||||||
\(690\) | −16.4705 | −0.627020 | ||||||||
\(691\) | 8.83381 | 0.336054 | 0.168027 | − | 0.985782i | \(-0.446260\pi\) | ||||
0.168027 | + | 0.985782i | \(0.446260\pi\) | |||||||
\(692\) | −44.1178 | −1.67711 | ||||||||
\(693\) | −109.229 | −4.14928 | ||||||||
\(694\) | −28.9398 | −1.09854 | ||||||||
\(695\) | 10.6735 | 0.404868 | ||||||||
\(696\) | 9.03055 | 0.342302 | ||||||||
\(697\) | −8.77913 | −0.332533 | ||||||||
\(698\) | 23.4378 | 0.887134 | ||||||||
\(699\) | −55.5595 | −2.10145 | ||||||||
\(700\) | 44.0574 | 1.66521 | ||||||||
\(701\) | −16.1642 | −0.610512 | −0.305256 | − | 0.952270i | \(-0.598742\pi\) | ||||
−0.305256 | + | 0.952270i | \(0.598742\pi\) | |||||||
\(702\) | 149.531 | 5.64367 | ||||||||
\(703\) | −26.7213 | −1.00781 | ||||||||
\(704\) | −50.6767 | −1.90995 | ||||||||
\(705\) | −38.8003 | −1.46130 | ||||||||
\(706\) | −2.31236 | −0.0870266 | ||||||||
\(707\) | −50.3363 | −1.89309 | ||||||||
\(708\) | −124.806 | −4.69050 | ||||||||
\(709\) | 33.3612 | 1.25290 | 0.626452 | − | 0.779460i | \(-0.284506\pi\) | ||||
0.626452 | + | 0.779460i | \(0.284506\pi\) | |||||||
\(710\) | −15.2804 | −0.573464 | ||||||||
\(711\) | −38.6306 | −1.44876 | ||||||||
\(712\) | 31.6207 | 1.18504 | ||||||||
\(713\) | 18.0778 | 0.677019 | ||||||||
\(714\) | 27.0323 | 1.01166 | ||||||||
\(715\) | 19.6364 | 0.734360 | ||||||||
\(716\) | −3.37730 | −0.126216 | ||||||||
\(717\) | −27.5202 | −1.02776 | ||||||||
\(718\) | 14.0442 | 0.524124 | ||||||||
\(719\) | 1.82738 | 0.0681499 | 0.0340750 | − | 0.999419i | \(-0.489152\pi\) | ||||
0.0340750 | + | 0.999419i | \(0.489152\pi\) | |||||||
\(720\) | −4.47410 | −0.166740 | ||||||||
\(721\) | −48.1514 | −1.79325 | ||||||||
\(722\) | −19.6435 | −0.731057 | ||||||||
\(723\) | 5.99614 | 0.222999 | ||||||||
\(724\) | −33.2398 | −1.23535 | ||||||||
\(725\) | 3.26462 | 0.121245 | ||||||||
\(726\) | −37.0674 | −1.37570 | ||||||||
\(727\) | 42.9680 | 1.59359 | 0.796797 | − | 0.604247i | \(-0.206526\pi\) | ||||
0.796797 | + | 0.604247i | \(0.206526\pi\) | |||||||
\(728\) | −47.6965 | −1.76775 | ||||||||
\(729\) | 53.9529 | 1.99826 | ||||||||
\(730\) | −9.55948 | −0.353812 | ||||||||
\(731\) | 7.99375 | 0.295659 | ||||||||
\(732\) | −22.6924 | −0.838734 | ||||||||
\(733\) | −9.21150 | −0.340235 | −0.170117 | − | 0.985424i | \(-0.554415\pi\) | ||||
−0.170117 | + | 0.985424i | \(0.554415\pi\) | |||||||
\(734\) | 4.02144 | 0.148434 | ||||||||
\(735\) | −21.9626 | −0.810104 | ||||||||
\(736\) | −9.57976 | −0.353115 | ||||||||
\(737\) | −45.8607 | −1.68930 | ||||||||
\(738\) | 155.092 | 5.70902 | ||||||||
\(739\) | −9.85307 | −0.362451 | −0.181226 | − | 0.983442i | \(-0.558006\pi\) | ||||
−0.181226 | + | 0.983442i | \(0.558006\pi\) | |||||||
\(740\) | 19.6492 | 0.722319 | ||||||||
\(741\) | −73.0805 | −2.68468 | ||||||||
\(742\) | −33.7123 | −1.23762 | ||||||||
\(743\) | 24.5063 | 0.899048 | 0.449524 | − | 0.893268i | \(-0.351594\pi\) | ||||
0.449524 | + | 0.893268i | \(0.351594\pi\) | |||||||
\(744\) | 96.8962 | 3.55239 | ||||||||
\(745\) | 17.2352 | 0.631448 | ||||||||
\(746\) | 76.1330 | 2.78743 | ||||||||
\(747\) | 2.79063 | 0.102104 | ||||||||
\(748\) | 13.3521 | 0.488201 | ||||||||
\(749\) | −12.8426 | −0.469258 | ||||||||
\(750\) | −75.3604 | −2.75177 | ||||||||
\(751\) | 7.70312 | 0.281091 | 0.140545 | − | 0.990074i | \(-0.455114\pi\) | ||||
0.140545 | + | 0.990074i | \(0.455114\pi\) | |||||||
\(752\) | 5.24893 | 0.191409 | ||||||||
\(753\) | −91.3924 | −3.33053 | ||||||||
\(754\) | −8.78194 | −0.319819 | ||||||||
\(755\) | −15.6639 | −0.570067 | ||||||||
\(756\) | −181.545 | −6.60272 | ||||||||
\(757\) | 41.6208 | 1.51274 | 0.756368 | − | 0.654147i | \(-0.226972\pi\) | ||||
0.756368 | + | 0.654147i | \(0.226972\pi\) | |||||||
\(758\) | 19.5180 | 0.708925 | ||||||||
\(759\) | −24.6653 | −0.895294 | ||||||||
\(760\) | 18.8150 | 0.682493 | ||||||||
\(761\) | 39.6205 | 1.43624 | 0.718121 | − | 0.695918i | \(-0.245002\pi\) | ||||
0.718121 | + | 0.695918i | \(0.245002\pi\) | |||||||
\(762\) | 36.5138 | 1.32276 | ||||||||
\(763\) | −5.09666 | −0.184512 | ||||||||
\(764\) | −75.2627 | −2.72291 | ||||||||
\(765\) | −8.80122 | −0.318209 | ||||||||
\(766\) | 14.7413 | 0.532626 | ||||||||
\(767\) | 48.8452 | 1.76370 | ||||||||
\(768\) | −62.4468 | −2.25336 | ||||||||
\(769\) | 4.09206 | 0.147564 | 0.0737818 | − | 0.997274i | \(-0.476493\pi\) | ||||
0.0737818 | + | 0.997274i | \(0.476493\pi\) | |||||||
\(770\) | −38.0864 | −1.37254 | ||||||||
\(771\) | −9.75263 | −0.351233 | ||||||||
\(772\) | −75.2417 | −2.70801 | ||||||||
\(773\) | −2.54936 | −0.0916942 | −0.0458471 | − | 0.998948i | \(-0.514599\pi\) | ||||
−0.0458471 | + | 0.998948i | \(0.514599\pi\) | |||||||
\(774\) | −141.217 | −5.07595 | ||||||||
\(775\) | 35.0288 | 1.25827 | ||||||||
\(776\) | −8.76548 | −0.314662 | ||||||||
\(777\) | 59.5743 | 2.13722 | ||||||||
\(778\) | −19.0194 | −0.681879 | ||||||||
\(779\) | −46.0340 | −1.64934 | ||||||||
\(780\) | 53.7388 | 1.92416 | ||||||||
\(781\) | −22.8832 | −0.818824 | ||||||||
\(782\) | 4.38308 | 0.156738 | ||||||||
\(783\) | −13.4523 | −0.480747 | ||||||||
\(784\) | 2.97112 | 0.106111 | ||||||||
\(785\) | −26.5452 | −0.947438 | ||||||||
\(786\) | −110.318 | −3.93492 | ||||||||
\(787\) | −0.169565 | −0.00604436 | −0.00302218 | − | 0.999995i | \(-0.500962\pi\) | ||||
−0.00302218 | + | 0.999995i | \(0.500962\pi\) | |||||||
\(788\) | −19.7860 | −0.704846 | ||||||||
\(789\) | −27.0013 | −0.961270 | ||||||||
\(790\) | −13.4698 | −0.479235 | ||||||||
\(791\) | −4.54248 | −0.161512 | ||||||||
\(792\) | −94.9285 | −3.37314 | ||||||||
\(793\) | 8.88108 | 0.315376 | ||||||||
\(794\) | 55.6140 | 1.97367 | ||||||||
\(795\) | 15.2862 | 0.542145 | ||||||||
\(796\) | 13.3086 | 0.471709 | ||||||||
\(797\) | 19.5849 | 0.693732 | 0.346866 | − | 0.937915i | \(-0.387246\pi\) | ||||
0.346866 | + | 0.937915i | \(0.387246\pi\) | |||||||
\(798\) | 141.746 | 5.01774 | ||||||||
\(799\) | 10.3254 | 0.365288 | ||||||||
\(800\) | −18.5624 | −0.656279 | ||||||||
\(801\) | −77.5598 | −2.74044 | ||||||||
\(802\) | 87.8891 | 3.10347 | ||||||||
\(803\) | −14.3158 | −0.505193 | ||||||||
\(804\) | −125.507 | −4.42628 | ||||||||
\(805\) | −7.82609 | −0.275834 | ||||||||
\(806\) | −94.2287 | −3.31906 | ||||||||
\(807\) | −104.715 | −3.68614 | ||||||||
\(808\) | −43.7460 | −1.53898 | ||||||||
\(809\) | 26.8590 | 0.944312 | 0.472156 | − | 0.881515i | \(-0.343476\pi\) | ||||
0.472156 | + | 0.881515i | \(0.343476\pi\) | |||||||
\(810\) | 70.4527 | 2.47545 | ||||||||
\(811\) | −26.7078 | −0.937838 | −0.468919 | − | 0.883241i | \(-0.655356\pi\) | ||||
−0.468919 | + | 0.883241i | \(0.655356\pi\) | |||||||
\(812\) | 10.6621 | 0.374167 | ||||||||
\(813\) | 88.9320 | 3.11898 | ||||||||
\(814\) | 47.0090 | 1.64766 | ||||||||
\(815\) | −8.76441 | −0.307004 | ||||||||
\(816\) | 1.65817 | 0.0580477 | ||||||||
\(817\) | 41.9158 | 1.46645 | ||||||||
\(818\) | −78.4490 | −2.74290 | ||||||||
\(819\) | 116.991 | 4.08799 | ||||||||
\(820\) | 33.8505 | 1.18211 | ||||||||
\(821\) | −45.2479 | −1.57916 | −0.789581 | − | 0.613647i | \(-0.789702\pi\) | ||||
−0.789581 | + | 0.613647i | \(0.789702\pi\) | |||||||
\(822\) | 84.2555 | 2.93875 | ||||||||
\(823\) | −23.8418 | −0.831073 | −0.415537 | − | 0.909576i | \(-0.636406\pi\) | ||||
−0.415537 | + | 0.909576i | \(0.636406\pi\) | |||||||
\(824\) | −41.8471 | −1.45781 | ||||||||
\(825\) | −47.7932 | −1.66394 | ||||||||
\(826\) | −94.7393 | −3.29640 | ||||||||
\(827\) | −14.2975 | −0.497172 | −0.248586 | − | 0.968610i | \(-0.579966\pi\) | ||||
−0.248586 | + | 0.968610i | \(0.579966\pi\) | |||||||
\(828\) | −48.4687 | −1.68441 | ||||||||
\(829\) | 1.97498 | 0.0685937 | 0.0342969 | − | 0.999412i | \(-0.489081\pi\) | ||||
0.0342969 | + | 0.999412i | \(0.489081\pi\) | |||||||
\(830\) | 0.973045 | 0.0337749 | ||||||||
\(831\) | 3.19231 | 0.110740 | ||||||||
\(832\) | 54.2776 | 1.88174 | ||||||||
\(833\) | 5.84464 | 0.202505 | ||||||||
\(834\) | 69.8825 | 2.41983 | ||||||||
\(835\) | −8.89052 | −0.307669 | ||||||||
\(836\) | 70.0126 | 2.42144 | ||||||||
\(837\) | −144.341 | −4.98916 | ||||||||
\(838\) | 80.9454 | 2.79621 | ||||||||
\(839\) | −9.24858 | −0.319296 | −0.159648 | − | 0.987174i | \(-0.551036\pi\) | ||||
−0.159648 | + | 0.987174i | \(0.551036\pi\) | |||||||
\(840\) | −41.9475 | −1.44733 | ||||||||
\(841\) | −28.2099 | −0.972757 | ||||||||
\(842\) | −46.9340 | −1.61745 | ||||||||
\(843\) | −57.1803 | −1.96940 | ||||||||
\(844\) | −14.4467 | −0.497277 | ||||||||
\(845\) | −6.05542 | −0.208313 | ||||||||
\(846\) | −182.409 | −6.27135 | ||||||||
\(847\) | −17.6129 | −0.605187 | ||||||||
\(848\) | −2.06793 | −0.0710129 | ||||||||
\(849\) | 4.23297 | 0.145275 | ||||||||
\(850\) | 8.49294 | 0.291305 | ||||||||
\(851\) | 9.65952 | 0.331124 | ||||||||
\(852\) | −62.6242 | −2.14547 | ||||||||
\(853\) | −37.3539 | −1.27897 | −0.639486 | − | 0.768803i | \(-0.720853\pi\) | ||||
−0.639486 | + | 0.768803i | \(0.720853\pi\) | |||||||
\(854\) | −17.2256 | −0.589448 | ||||||||
\(855\) | −46.1498 | −1.57829 | ||||||||
\(856\) | −11.1612 | −0.381481 | ||||||||
\(857\) | 0.403087 | 0.0137692 | 0.00688459 | − | 0.999976i | \(-0.497809\pi\) | ||||
0.00688459 | + | 0.999976i | \(0.497809\pi\) | |||||||
\(858\) | 128.565 | 4.38915 | ||||||||
\(859\) | 9.88573 | 0.337297 | 0.168648 | − | 0.985676i | \(-0.446060\pi\) | ||||
0.168648 | + | 0.985676i | \(0.446060\pi\) | |||||||
\(860\) | −30.8222 | −1.05103 | ||||||||
\(861\) | 102.631 | 3.49767 | ||||||||
\(862\) | 82.8601 | 2.82223 | ||||||||
\(863\) | −29.8666 | −1.01667 | −0.508335 | − | 0.861159i | \(-0.669739\pi\) | ||||
−0.508335 | + | 0.861159i | \(0.669739\pi\) | |||||||
\(864\) | 76.4890 | 2.60221 | ||||||||
\(865\) | 15.1852 | 0.516312 | ||||||||
\(866\) | −58.5097 | −1.98824 | ||||||||
\(867\) | 3.26187 | 0.110779 | ||||||||
\(868\) | 114.403 | 3.88308 | ||||||||
\(869\) | −20.1717 | −0.684279 | ||||||||
\(870\) | −7.72343 | −0.261849 | ||||||||
\(871\) | 49.1194 | 1.66435 | ||||||||
\(872\) | −4.42938 | −0.149998 | ||||||||
\(873\) | 21.5001 | 0.727669 | ||||||||
\(874\) | 22.9830 | 0.777411 | ||||||||
\(875\) | −35.8082 | −1.21054 | ||||||||
\(876\) | −39.1779 | −1.32370 | ||||||||
\(877\) | −12.5636 | −0.424243 | −0.212122 | − | 0.977243i | \(-0.568037\pi\) | ||||
−0.212122 | + | 0.977243i | \(0.568037\pi\) | |||||||
\(878\) | −74.0721 | −2.49981 | ||||||||
\(879\) | 108.329 | 3.65385 | ||||||||
\(880\) | −2.33624 | −0.0787546 | ||||||||
\(881\) | 39.5541 | 1.33261 | 0.666306 | − | 0.745678i | \(-0.267874\pi\) | ||||
0.666306 | + | 0.745678i | \(0.267874\pi\) | |||||||
\(882\) | −103.251 | −3.47665 | ||||||||
\(883\) | 37.9863 | 1.27834 | 0.639171 | − | 0.769065i | \(-0.279278\pi\) | ||||
0.639171 | + | 0.769065i | \(0.279278\pi\) | |||||||
\(884\) | −14.3008 | −0.480989 | ||||||||
\(885\) | 42.9578 | 1.44401 | ||||||||
\(886\) | −53.0586 | −1.78254 | ||||||||
\(887\) | −59.2432 | −1.98919 | −0.994595 | − | 0.103827i | \(-0.966891\pi\) | ||||
−0.994595 | + | 0.103827i | \(0.966891\pi\) | |||||||
\(888\) | 51.7746 | 1.73744 | ||||||||
\(889\) | 17.3499 | 0.581896 | ||||||||
\(890\) | −27.0438 | −0.906510 | ||||||||
\(891\) | 105.506 | 3.53459 | ||||||||
\(892\) | 24.8523 | 0.832116 | ||||||||
\(893\) | 54.1422 | 1.81180 | ||||||||
\(894\) | 112.844 | 3.77406 | ||||||||
\(895\) | 1.16245 | 0.0388566 | ||||||||
\(896\) | −69.0498 | −2.30679 | ||||||||
\(897\) | 26.4179 | 0.882069 | ||||||||
\(898\) | 72.1706 | 2.40836 | ||||||||
\(899\) | 8.47716 | 0.282729 | ||||||||
\(900\) | −93.9163 | −3.13054 | ||||||||
\(901\) | −4.06792 | −0.135522 | ||||||||
\(902\) | 80.9844 | 2.69649 | ||||||||
\(903\) | −93.4498 | −3.10982 | ||||||||
\(904\) | −3.94775 | −0.131300 | ||||||||
\(905\) | 11.4410 | 0.380312 | ||||||||
\(906\) | −102.556 | −3.40720 | ||||||||
\(907\) | −16.4680 | −0.546810 | −0.273405 | − | 0.961899i | \(-0.588150\pi\) | ||||
−0.273405 | + | 0.961899i | \(0.588150\pi\) | |||||||
\(908\) | 43.7430 | 1.45166 | ||||||||
\(909\) | 107.301 | 3.55895 | ||||||||
\(910\) | 40.7927 | 1.35226 | ||||||||
\(911\) | −29.3614 | −0.972787 | −0.486393 | − | 0.873740i | \(-0.661688\pi\) | ||||
−0.486393 | + | 0.873740i | \(0.661688\pi\) | |||||||
\(912\) | 8.69475 | 0.287912 | ||||||||
\(913\) | 1.45718 | 0.0482257 | ||||||||
\(914\) | 41.9856 | 1.38876 | ||||||||
\(915\) | 7.81062 | 0.258211 | ||||||||
\(916\) | −90.8622 | −3.00217 | ||||||||
\(917\) | −52.4187 | −1.73102 | ||||||||
\(918\) | −34.9964 | −1.15505 | ||||||||
\(919\) | 27.9161 | 0.920867 | 0.460433 | − | 0.887694i | \(-0.347694\pi\) | ||||
0.460433 | + | 0.887694i | \(0.347694\pi\) | |||||||
\(920\) | −6.80146 | −0.224238 | ||||||||
\(921\) | 49.8533 | 1.64272 | ||||||||
\(922\) | 9.41452 | 0.310051 | ||||||||
\(923\) | 24.5091 | 0.806728 | ||||||||
\(924\) | −156.091 | −5.13501 | ||||||||
\(925\) | 18.7169 | 0.615409 | ||||||||
\(926\) | −1.25286 | −0.0411714 | ||||||||
\(927\) | 102.643 | 3.37125 | ||||||||
\(928\) | −4.49220 | −0.147464 | ||||||||
\(929\) | 27.1665 | 0.891304 | 0.445652 | − | 0.895206i | \(-0.352972\pi\) | ||||
0.445652 | + | 0.895206i | \(0.352972\pi\) | |||||||
\(930\) | −82.8710 | −2.71745 | ||||||||
\(931\) | 30.6468 | 1.00441 | ||||||||
\(932\) | −57.0092 | −1.86740 | ||||||||
\(933\) | −6.80819 | −0.222890 | ||||||||
\(934\) | −66.7190 | −2.18311 | ||||||||
\(935\) | −4.59573 | −0.150297 | ||||||||
\(936\) | 101.674 | 3.32331 | ||||||||
\(937\) | 51.5572 | 1.68430 | 0.842150 | − | 0.539244i | \(-0.181290\pi\) | ||||
0.842150 | + | 0.539244i | \(0.181290\pi\) | |||||||
\(938\) | −95.2712 | −3.11071 | ||||||||
\(939\) | −35.9305 | −1.17255 | ||||||||
\(940\) | −39.8127 | −1.29855 | ||||||||
\(941\) | 54.6798 | 1.78251 | 0.891255 | − | 0.453502i | \(-0.149826\pi\) | ||||
0.891255 | + | 0.453502i | \(0.149826\pi\) | |||||||
\(942\) | −173.799 | −5.66268 | ||||||||
\(943\) | 16.6409 | 0.541901 | ||||||||
\(944\) | −5.81135 | −0.189143 | ||||||||
\(945\) | 62.4869 | 2.03270 | ||||||||
\(946\) | −73.7395 | −2.39748 | ||||||||
\(947\) | 31.7075 | 1.03036 | 0.515178 | − | 0.857083i | \(-0.327726\pi\) | ||||
0.515178 | + | 0.857083i | \(0.327726\pi\) | |||||||
\(948\) | −55.2038 | −1.79294 | ||||||||
\(949\) | 15.3330 | 0.497730 | ||||||||
\(950\) | 44.5333 | 1.44485 | ||||||||
\(951\) | 7.95315 | 0.257898 | ||||||||
\(952\) | 11.1630 | 0.361793 | ||||||||
\(953\) | 42.4695 | 1.37572 | 0.687861 | − | 0.725842i | \(-0.258550\pi\) | ||||
0.687861 | + | 0.725842i | \(0.258550\pi\) | |||||||
\(954\) | 71.8638 | 2.32668 | ||||||||
\(955\) | 25.9051 | 0.838269 | ||||||||
\(956\) | −28.2383 | −0.913291 | ||||||||
\(957\) | −11.5662 | −0.373883 | ||||||||
\(958\) | 38.0723 | 1.23006 | ||||||||
\(959\) | 40.0348 | 1.29279 | ||||||||
\(960\) | 47.7354 | 1.54065 | ||||||||
\(961\) | 59.9584 | 1.93414 | ||||||||
\(962\) | −50.3492 | −1.62332 | ||||||||
\(963\) | 27.3763 | 0.882190 | ||||||||
\(964\) | 6.15260 | 0.198162 | ||||||||
\(965\) | 25.8979 | 0.833682 | ||||||||
\(966\) | −51.2398 | −1.64861 | ||||||||
\(967\) | −16.5359 | −0.531757 | −0.265879 | − | 0.964006i | \(-0.585662\pi\) | ||||
−0.265879 | + | 0.964006i | \(0.585662\pi\) | |||||||
\(968\) | −15.3069 | −0.491984 | ||||||||
\(969\) | 17.1039 | 0.549455 | ||||||||
\(970\) | 7.49673 | 0.240705 | ||||||||
\(971\) | −38.5556 | −1.23731 | −0.618654 | − | 0.785663i | \(-0.712322\pi\) | ||||
−0.618654 | + | 0.785663i | \(0.712322\pi\) | |||||||
\(972\) | 136.773 | 4.38701 | ||||||||
\(973\) | 33.2053 | 1.06451 | ||||||||
\(974\) | −15.4260 | −0.494280 | ||||||||
\(975\) | 51.1891 | 1.63936 | ||||||||
\(976\) | −1.05663 | −0.0338218 | ||||||||
\(977\) | −36.7138 | −1.17458 | −0.587289 | − | 0.809377i | \(-0.699805\pi\) | ||||
−0.587289 | + | 0.809377i | \(0.699805\pi\) | |||||||
\(978\) | −57.3832 | −1.83491 | ||||||||
\(979\) | −40.4994 | −1.29437 | ||||||||
\(980\) | −22.5357 | −0.719877 | ||||||||
\(981\) | 10.8645 | 0.346876 | ||||||||
\(982\) | −68.9517 | −2.20034 | ||||||||
\(983\) | −42.7103 | −1.36225 | −0.681123 | − | 0.732169i | \(-0.738508\pi\) | ||||
−0.681123 | + | 0.732169i | \(0.738508\pi\) | |||||||
\(984\) | 89.1943 | 2.84341 | ||||||||
\(985\) | 6.81025 | 0.216993 | ||||||||
\(986\) | 2.05534 | 0.0654553 | ||||||||
\(987\) | −120.708 | −3.84218 | ||||||||
\(988\) | −74.9874 | −2.38567 | ||||||||
\(989\) | −15.1522 | −0.481811 | ||||||||
\(990\) | 81.1881 | 2.58033 | ||||||||
\(991\) | 10.9158 | 0.346751 | 0.173375 | − | 0.984856i | \(-0.444533\pi\) | ||||
0.173375 | + | 0.984856i | \(0.444533\pi\) | |||||||
\(992\) | −48.2005 | −1.53037 | ||||||||
\(993\) | −69.4448 | −2.20376 | ||||||||
\(994\) | −47.5375 | −1.50780 | ||||||||
\(995\) | −4.58075 | −0.145220 | ||||||||
\(996\) | 3.98786 | 0.126360 | ||||||||
\(997\) | 0.555837 | 0.0176035 | 0.00880177 | − | 0.999961i | \(-0.497198\pi\) | ||||
0.00880177 | + | 0.999961i | \(0.497198\pi\) | |||||||
\(998\) | −84.6080 | −2.67822 | ||||||||
\(999\) | −77.1258 | −2.44015 |
(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 | 6001.2.a.b.1.14 | ✓ | 114 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.b.1.14 | ✓ | 114 | 1.1 | even | 1 | trivial |