Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [161,2,Mod(1,161)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(161, 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("161.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 161 = 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 161.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: | \(1.28559147254\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.2147108.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 9x^{3} + 17x^{2} + 16x - 27 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.50216\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 161.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50216 | −1.06219 | −0.531093 | − | 0.847313i | \(-0.678219\pi\) | ||||
−0.531093 | + | 0.847313i | \(0.678219\pi\) | |||||||
\(3\) | −3.04067 | −1.75553 | −0.877766 | − | 0.479090i | \(-0.840967\pi\) | ||||
−0.877766 | + | 0.479090i | \(0.840967\pi\) | |||||||
\(4\) | 0.256481 | 0.128240 | ||||||||
\(5\) | −3.82405 | −1.71017 | −0.855084 | − | 0.518490i | \(-0.826494\pi\) | ||||
−0.855084 | + | 0.518490i | \(0.826494\pi\) | |||||||
\(6\) | 4.56757 | 1.86470 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.61904 | 0.925971 | ||||||||
\(9\) | 6.24568 | 2.08189 | ||||||||
\(10\) | 5.74433 | 1.81652 | ||||||||
\(11\) | −0.542019 | −0.163425 | −0.0817124 | − | 0.996656i | \(-0.526039\pi\) | ||||
−0.0817124 | + | 0.996656i | \(0.526039\pi\) | |||||||
\(12\) | −0.779873 | −0.225130 | ||||||||
\(13\) | −1.21662 | −0.337430 | −0.168715 | − | 0.985665i | \(-0.553962\pi\) | ||||
−0.168715 | + | 0.985665i | \(0.553962\pi\) | |||||||
\(14\) | −1.50216 | −0.401469 | ||||||||
\(15\) | 11.6277 | 3.00225 | ||||||||
\(16\) | −4.44718 | −1.11179 | ||||||||
\(17\) | −3.66299 | −0.888405 | −0.444203 | − | 0.895926i | \(-0.646513\pi\) | ||||
−0.444203 | + | 0.895926i | \(0.646513\pi\) | |||||||
\(18\) | −9.38200 | −2.21136 | ||||||||
\(19\) | 5.00432 | 1.14807 | 0.574035 | − | 0.818831i | \(-0.305378\pi\) | ||||
0.574035 | + | 0.818831i | \(0.305378\pi\) | |||||||
\(20\) | −0.980794 | −0.219312 | ||||||||
\(21\) | −3.04067 | −0.663529 | ||||||||
\(22\) | 0.814198 | 0.173588 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −7.96365 | −1.62557 | ||||||||
\(25\) | 9.62336 | 1.92467 | ||||||||
\(26\) | 1.82756 | 0.358413 | ||||||||
\(27\) | −9.86904 | −1.89930 | ||||||||
\(28\) | 0.256481 | 0.0484703 | ||||||||
\(29\) | 3.72840 | 0.692346 | 0.346173 | − | 0.938171i | \(-0.387481\pi\) | ||||
0.346173 | + | 0.938171i | \(0.387481\pi\) | |||||||
\(30\) | −17.4666 | −3.18895 | ||||||||
\(31\) | 9.04067 | 1.62375 | 0.811876 | − | 0.583830i | \(-0.198446\pi\) | ||||
0.811876 | + | 0.583830i | \(0.198446\pi\) | |||||||
\(32\) | 1.44228 | 0.254962 | ||||||||
\(33\) | 1.64810 | 0.286897 | ||||||||
\(34\) | 5.50239 | 0.943652 | ||||||||
\(35\) | −3.82405 | −0.646382 | ||||||||
\(36\) | 1.60189 | 0.266982 | ||||||||
\(37\) | −9.08566 | −1.49367 | −0.746837 | − | 0.665008i | \(-0.768428\pi\) | ||||
−0.746837 | + | 0.665008i | \(0.768428\pi\) | |||||||
\(38\) | −7.51728 | −1.21946 | ||||||||
\(39\) | 3.69934 | 0.592369 | ||||||||
\(40\) | −10.0154 | −1.58357 | ||||||||
\(41\) | −4.86472 | −0.759742 | −0.379871 | − | 0.925040i | \(-0.624032\pi\) | ||||
−0.379871 | + | 0.925040i | \(0.624032\pi\) | |||||||
\(42\) | 4.56757 | 0.704791 | ||||||||
\(43\) | 3.64810 | 0.556330 | 0.278165 | − | 0.960533i | \(-0.410274\pi\) | ||||
0.278165 | + | 0.960533i | \(0.410274\pi\) | |||||||
\(44\) | −0.139017 | −0.0209576 | ||||||||
\(45\) | −23.8838 | −3.56038 | ||||||||
\(46\) | 1.50216 | 0.221481 | ||||||||
\(47\) | 10.6393 | 1.55190 | 0.775950 | − | 0.630794i | \(-0.217271\pi\) | ||||
0.775950 | + | 0.630794i | \(0.217271\pi\) | |||||||
\(48\) | 13.5224 | 1.95179 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −14.4558 | −2.04436 | ||||||||
\(51\) | 11.1379 | 1.55962 | ||||||||
\(52\) | −0.312039 | −0.0432721 | ||||||||
\(53\) | 7.48704 | 1.02842 | 0.514212 | − | 0.857663i | \(-0.328084\pi\) | ||||
0.514212 | + | 0.857663i | \(0.328084\pi\) | |||||||
\(54\) | 14.8249 | 2.01741 | ||||||||
\(55\) | 2.07271 | 0.279484 | ||||||||
\(56\) | 2.61904 | 0.349984 | ||||||||
\(57\) | −15.2165 | −2.01547 | ||||||||
\(58\) | −5.60065 | −0.735401 | ||||||||
\(59\) | 5.18027 | 0.674413 | 0.337207 | − | 0.941431i | \(-0.390518\pi\) | ||||
0.337207 | + | 0.941431i | \(0.390518\pi\) | |||||||
\(60\) | 2.98227 | 0.385010 | ||||||||
\(61\) | 3.26161 | 0.417606 | 0.208803 | − | 0.977958i | \(-0.433043\pi\) | ||||
0.208803 | + | 0.977958i | \(0.433043\pi\) | |||||||
\(62\) | −13.5805 | −1.72473 | ||||||||
\(63\) | 6.24568 | 0.786881 | ||||||||
\(64\) | 6.72782 | 0.840978 | ||||||||
\(65\) | 4.65242 | 0.577061 | ||||||||
\(66\) | −2.47571 | −0.304739 | ||||||||
\(67\) | −12.0377 | −1.47064 | −0.735319 | − | 0.677721i | \(-0.762968\pi\) | ||||
−0.735319 | + | 0.677721i | \(0.762968\pi\) | |||||||
\(68\) | −0.939485 | −0.113929 | ||||||||
\(69\) | 3.04067 | 0.366054 | ||||||||
\(70\) | 5.74433 | 0.686579 | ||||||||
\(71\) | −5.29796 | −0.628752 | −0.314376 | − | 0.949298i | \(-0.601795\pi\) | ||||
−0.314376 | + | 0.949298i | \(0.601795\pi\) | |||||||
\(72\) | 16.3577 | 1.92777 | ||||||||
\(73\) | 8.19070 | 0.958649 | 0.479324 | − | 0.877638i | \(-0.340882\pi\) | ||||
0.479324 | + | 0.877638i | \(0.340882\pi\) | |||||||
\(74\) | 13.6481 | 1.58656 | ||||||||
\(75\) | −29.2615 | −3.37882 | ||||||||
\(76\) | 1.28351 | 0.147229 | ||||||||
\(77\) | −0.542019 | −0.0617688 | ||||||||
\(78\) | −5.55700 | −0.629206 | ||||||||
\(79\) | 10.0291 | 1.12836 | 0.564179 | − | 0.825653i | \(-0.309193\pi\) | ||||
0.564179 | + | 0.825653i | \(0.309193\pi\) | |||||||
\(80\) | 17.0062 | 1.90135 | ||||||||
\(81\) | 11.2715 | 1.25238 | ||||||||
\(82\) | 7.30758 | 0.806987 | ||||||||
\(83\) | 7.64810 | 0.839488 | 0.419744 | − | 0.907643i | \(-0.362120\pi\) | ||||
0.419744 | + | 0.907643i | \(0.362120\pi\) | |||||||
\(84\) | −0.779873 | −0.0850911 | ||||||||
\(85\) | 14.0075 | 1.51932 | ||||||||
\(86\) | −5.48003 | −0.590926 | ||||||||
\(87\) | −11.3368 | −1.21544 | ||||||||
\(88\) | −1.41957 | −0.151327 | ||||||||
\(89\) | −4.74703 | −0.503184 | −0.251592 | − | 0.967833i | \(-0.580954\pi\) | ||||
−0.251592 | + | 0.967833i | \(0.580954\pi\) | |||||||
\(90\) | 35.8772 | 3.78179 | ||||||||
\(91\) | −1.21662 | −0.127536 | ||||||||
\(92\) | −0.256481 | −0.0267399 | ||||||||
\(93\) | −27.4897 | −2.85055 | ||||||||
\(94\) | −15.9819 | −1.64841 | ||||||||
\(95\) | −19.1368 | −1.96339 | ||||||||
\(96\) | −4.38551 | −0.447594 | ||||||||
\(97\) | −10.9894 | −1.11581 | −0.557904 | − | 0.829906i | \(-0.688394\pi\) | ||||
−0.557904 | + | 0.829906i | \(0.688394\pi\) | |||||||
\(98\) | −1.50216 | −0.151741 | ||||||||
\(99\) | −3.38527 | −0.340233 | ||||||||
\(100\) | 2.46820 | 0.246820 | ||||||||
\(101\) | 3.59862 | 0.358076 | 0.179038 | − | 0.983842i | \(-0.442701\pi\) | ||||
0.179038 | + | 0.983842i | \(0.442701\pi\) | |||||||
\(102\) | −16.7310 | −1.65661 | ||||||||
\(103\) | 9.48704 | 0.934786 | 0.467393 | − | 0.884050i | \(-0.345193\pi\) | ||||
0.467393 | + | 0.884050i | \(0.345193\pi\) | |||||||
\(104\) | −3.18638 | −0.312450 | ||||||||
\(105\) | 11.6277 | 1.13475 | ||||||||
\(106\) | −11.2467 | −1.09238 | ||||||||
\(107\) | 6.60294 | 0.638330 | 0.319165 | − | 0.947699i | \(-0.396598\pi\) | ||||
0.319165 | + | 0.947699i | \(0.396598\pi\) | |||||||
\(108\) | −2.53122 | −0.243566 | ||||||||
\(109\) | 1.10726 | 0.106057 | 0.0530283 | − | 0.998593i | \(-0.483113\pi\) | ||||
0.0530283 | + | 0.998593i | \(0.483113\pi\) | |||||||
\(110\) | −3.11353 | −0.296864 | ||||||||
\(111\) | 27.6265 | 2.62219 | ||||||||
\(112\) | −4.44718 | −0.420219 | ||||||||
\(113\) | 0.433241 | 0.0407559 | 0.0203779 | − | 0.999792i | \(-0.493513\pi\) | ||||
0.0203779 | + | 0.999792i | \(0.493513\pi\) | |||||||
\(114\) | 22.8576 | 2.14081 | ||||||||
\(115\) | 3.82405 | 0.356595 | ||||||||
\(116\) | 0.956262 | 0.0887867 | ||||||||
\(117\) | −7.59862 | −0.702493 | ||||||||
\(118\) | −7.78158 | −0.716353 | ||||||||
\(119\) | −3.66299 | −0.335786 | ||||||||
\(120\) | 30.4534 | 2.78000 | ||||||||
\(121\) | −10.7062 | −0.973292 | ||||||||
\(122\) | −4.89945 | −0.443576 | ||||||||
\(123\) | 14.7920 | 1.33375 | ||||||||
\(124\) | 2.31876 | 0.208230 | ||||||||
\(125\) | −17.6800 | −1.58134 | ||||||||
\(126\) | −9.38200 | −0.835815 | ||||||||
\(127\) | 8.84149 | 0.784556 | 0.392278 | − | 0.919847i | \(-0.371687\pi\) | ||||
0.392278 | + | 0.919847i | \(0.371687\pi\) | |||||||
\(128\) | −12.9908 | −1.14824 | ||||||||
\(129\) | −11.0927 | −0.976655 | ||||||||
\(130\) | −6.98867 | −0.612947 | ||||||||
\(131\) | −2.54931 | −0.222735 | −0.111367 | − | 0.993779i | \(-0.535523\pi\) | ||||
−0.111367 | + | 0.993779i | \(0.535523\pi\) | |||||||
\(132\) | 0.422706 | 0.0367918 | ||||||||
\(133\) | 5.00432 | 0.433929 | ||||||||
\(134\) | 18.0825 | 1.56209 | ||||||||
\(135\) | 37.7397 | 3.24812 | ||||||||
\(136\) | −9.59352 | −0.822638 | ||||||||
\(137\) | 13.6265 | 1.16419 | 0.582095 | − | 0.813121i | \(-0.302233\pi\) | ||||
0.582095 | + | 0.813121i | \(0.302233\pi\) | |||||||
\(138\) | −4.56757 | −0.388817 | ||||||||
\(139\) | −18.0466 | −1.53069 | −0.765347 | − | 0.643618i | \(-0.777432\pi\) | ||||
−0.765347 | + | 0.643618i | \(0.777432\pi\) | |||||||
\(140\) | −0.980794 | −0.0828923 | ||||||||
\(141\) | −32.3506 | −2.72441 | ||||||||
\(142\) | 7.95838 | 0.667852 | ||||||||
\(143\) | 0.659431 | 0.0551444 | ||||||||
\(144\) | −27.7756 | −2.31464 | ||||||||
\(145\) | −14.2576 | −1.18403 | ||||||||
\(146\) | −12.3037 | −1.01826 | ||||||||
\(147\) | −3.04067 | −0.250790 | ||||||||
\(148\) | −2.33029 | −0.191549 | ||||||||
\(149\) | 13.8178 | 1.13200 | 0.565999 | − | 0.824406i | \(-0.308491\pi\) | ||||
0.565999 | + | 0.824406i | \(0.308491\pi\) | |||||||
\(150\) | 43.9554 | 3.58894 | ||||||||
\(151\) | 16.1412 | 1.31355 | 0.656777 | − | 0.754085i | \(-0.271919\pi\) | ||||
0.656777 | + | 0.754085i | \(0.271919\pi\) | |||||||
\(152\) | 13.1065 | 1.06308 | ||||||||
\(153\) | −22.8778 | −1.84956 | ||||||||
\(154\) | 0.814198 | 0.0656100 | ||||||||
\(155\) | −34.5720 | −2.77689 | ||||||||
\(156\) | 0.948809 | 0.0759655 | ||||||||
\(157\) | −15.3111 | −1.22196 | −0.610979 | − | 0.791647i | \(-0.709224\pi\) | ||||
−0.610979 | + | 0.791647i | \(0.709224\pi\) | |||||||
\(158\) | −15.0652 | −1.19853 | ||||||||
\(159\) | −22.7656 | −1.80543 | ||||||||
\(160\) | −5.51536 | −0.436028 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | −16.9315 | −1.33027 | ||||||||
\(163\) | −3.94876 | −0.309291 | −0.154645 | − | 0.987970i | \(-0.549423\pi\) | ||||
−0.154645 | + | 0.987970i | \(0.549423\pi\) | |||||||
\(164\) | −1.24771 | −0.0974295 | ||||||||
\(165\) | −6.30242 | −0.490643 | ||||||||
\(166\) | −11.4887 | −0.891693 | ||||||||
\(167\) | 1.87752 | 0.145287 | 0.0726433 | − | 0.997358i | \(-0.476857\pi\) | ||||
0.0726433 | + | 0.997358i | \(0.476857\pi\) | |||||||
\(168\) | −7.96365 | −0.614409 | ||||||||
\(169\) | −11.5198 | −0.886141 | ||||||||
\(170\) | −21.0414 | −1.61380 | ||||||||
\(171\) | 31.2554 | 2.39016 | ||||||||
\(172\) | 0.935667 | 0.0713439 | ||||||||
\(173\) | 10.9246 | 0.830582 | 0.415291 | − | 0.909689i | \(-0.363680\pi\) | ||||
0.415291 | + | 0.909689i | \(0.363680\pi\) | |||||||
\(174\) | 17.0297 | 1.29102 | ||||||||
\(175\) | 9.62336 | 0.727458 | ||||||||
\(176\) | 2.41045 | 0.181695 | ||||||||
\(177\) | −15.7515 | −1.18395 | ||||||||
\(178\) | 7.13079 | 0.534475 | ||||||||
\(179\) | 4.74253 | 0.354474 | 0.177237 | − | 0.984168i | \(-0.443284\pi\) | ||||
0.177237 | + | 0.984168i | \(0.443284\pi\) | |||||||
\(180\) | −6.12573 | −0.456585 | ||||||||
\(181\) | 2.82837 | 0.210231 | 0.105115 | − | 0.994460i | \(-0.466479\pi\) | ||||
0.105115 | + | 0.994460i | \(0.466479\pi\) | |||||||
\(182\) | 1.82756 | 0.135468 | ||||||||
\(183\) | −9.91748 | −0.733121 | ||||||||
\(184\) | −2.61904 | −0.193078 | ||||||||
\(185\) | 34.7440 | 2.55443 | ||||||||
\(186\) | 41.2939 | 3.02782 | ||||||||
\(187\) | 1.98541 | 0.145187 | ||||||||
\(188\) | 2.72877 | 0.199016 | ||||||||
\(189\) | −9.86904 | −0.717867 | ||||||||
\(190\) | 28.7464 | 2.08549 | ||||||||
\(191\) | −3.56838 | −0.258199 | −0.129099 | − | 0.991632i | \(-0.541209\pi\) | ||||
−0.129099 | + | 0.991632i | \(0.541209\pi\) | |||||||
\(192\) | −20.4571 | −1.47636 | ||||||||
\(193\) | 20.9158 | 1.50555 | 0.752777 | − | 0.658276i | \(-0.228714\pi\) | ||||
0.752777 | + | 0.658276i | \(0.228714\pi\) | |||||||
\(194\) | 16.5079 | 1.18520 | ||||||||
\(195\) | −14.1465 | −1.01305 | ||||||||
\(196\) | 0.256481 | 0.0183200 | ||||||||
\(197\) | 5.54576 | 0.395119 | 0.197559 | − | 0.980291i | \(-0.436698\pi\) | ||||
0.197559 | + | 0.980291i | \(0.436698\pi\) | |||||||
\(198\) | 5.08522 | 0.361391 | ||||||||
\(199\) | −7.73808 | −0.548538 | −0.274269 | − | 0.961653i | \(-0.588436\pi\) | ||||
−0.274269 | + | 0.961653i | \(0.588436\pi\) | |||||||
\(200\) | 25.2040 | 1.78219 | ||||||||
\(201\) | 36.6027 | 2.58175 | ||||||||
\(202\) | −5.40570 | −0.380344 | ||||||||
\(203\) | 3.72840 | 0.261682 | ||||||||
\(204\) | 2.85667 | 0.200007 | ||||||||
\(205\) | 18.6029 | 1.29929 | ||||||||
\(206\) | −14.2510 | −0.992917 | ||||||||
\(207\) | −6.24568 | −0.434105 | ||||||||
\(208\) | 5.41053 | 0.375153 | ||||||||
\(209\) | −2.71243 | −0.187623 | ||||||||
\(210\) | −17.4666 | −1.20531 | ||||||||
\(211\) | 9.43918 | 0.649820 | 0.324910 | − | 0.945745i | \(-0.394666\pi\) | ||||
0.324910 | + | 0.945745i | \(0.394666\pi\) | |||||||
\(212\) | 1.92028 | 0.131885 | ||||||||
\(213\) | 16.1094 | 1.10379 | ||||||||
\(214\) | −9.91866 | −0.678026 | ||||||||
\(215\) | −13.9505 | −0.951418 | ||||||||
\(216\) | −25.8474 | −1.75870 | ||||||||
\(217\) | 9.04067 | 0.613721 | ||||||||
\(218\) | −1.66329 | −0.112652 | ||||||||
\(219\) | −24.9052 | −1.68294 | ||||||||
\(220\) | 0.531609 | 0.0358411 | ||||||||
\(221\) | 4.45647 | 0.299774 | ||||||||
\(222\) | −41.4994 | −2.78526 | ||||||||
\(223\) | 11.1010 | 0.743379 | 0.371689 | − | 0.928357i | \(-0.378779\pi\) | ||||
0.371689 | + | 0.928357i | \(0.378779\pi\) | |||||||
\(224\) | 1.44228 | 0.0963665 | ||||||||
\(225\) | 60.1044 | 4.00696 | ||||||||
\(226\) | −0.650797 | −0.0432903 | ||||||||
\(227\) | 20.9827 | 1.39267 | 0.696336 | − | 0.717716i | \(-0.254812\pi\) | ||||
0.696336 | + | 0.717716i | \(0.254812\pi\) | |||||||
\(228\) | −3.90273 | −0.258465 | ||||||||
\(229\) | 4.63545 | 0.306319 | 0.153159 | − | 0.988201i | \(-0.451055\pi\) | ||||
0.153159 | + | 0.988201i | \(0.451055\pi\) | |||||||
\(230\) | −5.74433 | −0.378770 | ||||||||
\(231\) | 1.64810 | 0.108437 | ||||||||
\(232\) | 9.76484 | 0.641093 | ||||||||
\(233\) | 16.1703 | 1.05935 | 0.529675 | − | 0.848201i | \(-0.322314\pi\) | ||||
0.529675 | + | 0.848201i | \(0.322314\pi\) | |||||||
\(234\) | 11.4143 | 0.746178 | ||||||||
\(235\) | −40.6852 | −2.65401 | ||||||||
\(236\) | 1.32864 | 0.0864869 | ||||||||
\(237\) | −30.4951 | −1.98087 | ||||||||
\(238\) | 5.50239 | 0.356667 | ||||||||
\(239\) | 1.26610 | 0.0818973 | 0.0409486 | − | 0.999161i | \(-0.486962\pi\) | ||||
0.0409486 | + | 0.999161i | \(0.486962\pi\) | |||||||
\(240\) | −51.7104 | −3.33789 | ||||||||
\(241\) | −2.09623 | −0.135030 | −0.0675150 | − | 0.997718i | \(-0.521507\pi\) | ||||
−0.0675150 | + | 0.997718i | \(0.521507\pi\) | |||||||
\(242\) | 16.0824 | 1.03382 | ||||||||
\(243\) | −4.66568 | −0.299304 | ||||||||
\(244\) | 0.836539 | 0.0535539 | ||||||||
\(245\) | −3.82405 | −0.244310 | ||||||||
\(246\) | −22.2200 | −1.41669 | ||||||||
\(247\) | −6.08835 | −0.387393 | ||||||||
\(248\) | 23.6779 | 1.50355 | ||||||||
\(249\) | −23.2554 | −1.47375 | ||||||||
\(250\) | 26.5581 | 1.67968 | ||||||||
\(251\) | 11.5365 | 0.728179 | 0.364089 | − | 0.931364i | \(-0.381380\pi\) | ||||
0.364089 | + | 0.931364i | \(0.381380\pi\) | |||||||
\(252\) | 1.60189 | 0.100910 | ||||||||
\(253\) | 0.542019 | 0.0340764 | ||||||||
\(254\) | −13.2813 | −0.833345 | ||||||||
\(255\) | −42.5921 | −2.66722 | ||||||||
\(256\) | 6.05863 | 0.378664 | ||||||||
\(257\) | 14.6546 | 0.914131 | 0.457066 | − | 0.889433i | \(-0.348900\pi\) | ||||
0.457066 | + | 0.889433i | \(0.348900\pi\) | |||||||
\(258\) | 16.6630 | 1.03739 | ||||||||
\(259\) | −9.08566 | −0.564555 | ||||||||
\(260\) | 1.19325 | 0.0740025 | ||||||||
\(261\) | 23.2864 | 1.44139 | ||||||||
\(262\) | 3.82947 | 0.236586 | ||||||||
\(263\) | −22.7133 | −1.40056 | −0.700282 | − | 0.713866i | \(-0.746942\pi\) | ||||
−0.700282 | + | 0.713866i | \(0.746942\pi\) | |||||||
\(264\) | 4.31645 | 0.265659 | ||||||||
\(265\) | −28.6308 | −1.75878 | ||||||||
\(266\) | −7.51728 | −0.460914 | ||||||||
\(267\) | 14.4341 | 0.883355 | ||||||||
\(268\) | −3.08743 | −0.188595 | ||||||||
\(269\) | 25.0855 | 1.52949 | 0.764746 | − | 0.644332i | \(-0.222865\pi\) | ||||
0.764746 | + | 0.644332i | \(0.222865\pi\) | |||||||
\(270\) | −56.6910 | −3.45011 | ||||||||
\(271\) | −28.0232 | −1.70229 | −0.851145 | − | 0.524930i | \(-0.824091\pi\) | ||||
−0.851145 | + | 0.524930i | \(0.824091\pi\) | |||||||
\(272\) | 16.2900 | 0.987724 | ||||||||
\(273\) | 3.69934 | 0.223894 | ||||||||
\(274\) | −20.4692 | −1.23659 | ||||||||
\(275\) | −5.21604 | −0.314539 | ||||||||
\(276\) | 0.779873 | 0.0469428 | ||||||||
\(277\) | −16.2692 | −0.977524 | −0.488762 | − | 0.872417i | \(-0.662551\pi\) | ||||
−0.488762 | + | 0.872417i | \(0.662551\pi\) | |||||||
\(278\) | 27.1089 | 1.62588 | ||||||||
\(279\) | 56.4651 | 3.38048 | ||||||||
\(280\) | −10.0154 | −0.598532 | ||||||||
\(281\) | −13.4694 | −0.803518 | −0.401759 | − | 0.915745i | \(-0.631601\pi\) | ||||
−0.401759 | + | 0.915745i | \(0.631601\pi\) | |||||||
\(282\) | 48.5957 | 2.89383 | ||||||||
\(283\) | 18.0516 | 1.07305 | 0.536527 | − | 0.843883i | \(-0.319736\pi\) | ||||
0.536527 | + | 0.843883i | \(0.319736\pi\) | |||||||
\(284\) | −1.35882 | −0.0806314 | ||||||||
\(285\) | 58.1886 | 3.44679 | ||||||||
\(286\) | −0.990570 | −0.0585736 | ||||||||
\(287\) | −4.86472 | −0.287155 | ||||||||
\(288\) | 9.00803 | 0.530803 | ||||||||
\(289\) | −3.58251 | −0.210736 | ||||||||
\(290\) | 21.4172 | 1.25766 | ||||||||
\(291\) | 33.4152 | 1.95884 | ||||||||
\(292\) | 2.10075 | 0.122937 | ||||||||
\(293\) | 23.1521 | 1.35256 | 0.676280 | − | 0.736644i | \(-0.263591\pi\) | ||||
0.676280 | + | 0.736644i | \(0.263591\pi\) | |||||||
\(294\) | 4.56757 | 0.266386 | ||||||||
\(295\) | −19.8096 | −1.15336 | ||||||||
\(296\) | −23.7957 | −1.38310 | ||||||||
\(297\) | 5.34920 | 0.310392 | ||||||||
\(298\) | −20.7565 | −1.20239 | ||||||||
\(299\) | 1.21662 | 0.0703590 | ||||||||
\(300\) | −7.50500 | −0.433301 | ||||||||
\(301\) | 3.64810 | 0.210273 | ||||||||
\(302\) | −24.2467 | −1.39524 | ||||||||
\(303\) | −10.9422 | −0.628614 | ||||||||
\(304\) | −22.2551 | −1.27642 | ||||||||
\(305\) | −12.4726 | −0.714176 | ||||||||
\(306\) | 34.3662 | 1.96458 | ||||||||
\(307\) | −1.14301 | −0.0652353 | −0.0326176 | − | 0.999468i | \(-0.510384\pi\) | ||||
−0.0326176 | + | 0.999468i | \(0.510384\pi\) | |||||||
\(308\) | −0.139017 | −0.00792124 | ||||||||
\(309\) | −28.8470 | −1.64105 | ||||||||
\(310\) | 51.9326 | 2.94957 | ||||||||
\(311\) | −19.3196 | −1.09551 | −0.547757 | − | 0.836638i | \(-0.684518\pi\) | ||||
−0.547757 | + | 0.836638i | \(0.684518\pi\) | |||||||
\(312\) | 9.68874 | 0.548517 | ||||||||
\(313\) | −17.4140 | −0.984299 | −0.492150 | − | 0.870511i | \(-0.663789\pi\) | ||||
−0.492150 | + | 0.870511i | \(0.663789\pi\) | |||||||
\(314\) | 22.9997 | 1.29795 | ||||||||
\(315\) | −23.8838 | −1.34570 | ||||||||
\(316\) | 2.57226 | 0.144701 | ||||||||
\(317\) | 1.42612 | 0.0800989 | 0.0400495 | − | 0.999198i | \(-0.487248\pi\) | ||||
0.0400495 | + | 0.999198i | \(0.487248\pi\) | |||||||
\(318\) | 34.1976 | 1.91770 | ||||||||
\(319\) | −2.02086 | −0.113147 | ||||||||
\(320\) | −25.7275 | −1.43821 | ||||||||
\(321\) | −20.0774 | −1.12061 | ||||||||
\(322\) | 1.50216 | 0.0837120 | ||||||||
\(323\) | −18.3308 | −1.01995 | ||||||||
\(324\) | 2.89091 | 0.160606 | ||||||||
\(325\) | −11.7080 | −0.649442 | ||||||||
\(326\) | 5.93166 | 0.328524 | ||||||||
\(327\) | −3.36682 | −0.186186 | ||||||||
\(328\) | −12.7409 | −0.703499 | ||||||||
\(329\) | 10.6393 | 0.586563 | ||||||||
\(330\) | 9.46723 | 0.521154 | ||||||||
\(331\) | 3.91690 | 0.215292 | 0.107646 | − | 0.994189i | \(-0.465669\pi\) | ||||
0.107646 | + | 0.994189i | \(0.465669\pi\) | |||||||
\(332\) | 1.96159 | 0.107656 | ||||||||
\(333\) | −56.7461 | −3.10967 | ||||||||
\(334\) | −2.82033 | −0.154321 | ||||||||
\(335\) | 46.0327 | 2.51504 | ||||||||
\(336\) | 13.5224 | 0.737708 | ||||||||
\(337\) | 7.73646 | 0.421432 | 0.210716 | − | 0.977547i | \(-0.432421\pi\) | ||||
0.210716 | + | 0.977547i | \(0.432421\pi\) | |||||||
\(338\) | 17.3046 | 0.941247 | ||||||||
\(339\) | −1.31734 | −0.0715482 | ||||||||
\(340\) | 3.59264 | 0.194838 | ||||||||
\(341\) | −4.90021 | −0.265361 | ||||||||
\(342\) | −46.9505 | −2.53879 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 9.55453 | 0.515146 | ||||||||
\(345\) | −11.6277 | −0.626013 | ||||||||
\(346\) | −16.4105 | −0.882233 | ||||||||
\(347\) | −32.0316 | −1.71955 | −0.859773 | − | 0.510677i | \(-0.829395\pi\) | ||||
−0.859773 | + | 0.510677i | \(0.829395\pi\) | |||||||
\(348\) | −2.90768 | −0.155868 | ||||||||
\(349\) | 29.0447 | 1.55473 | 0.777363 | − | 0.629052i | \(-0.216557\pi\) | ||||
0.777363 | + | 0.629052i | \(0.216557\pi\) | |||||||
\(350\) | −14.4558 | −0.772696 | ||||||||
\(351\) | 12.0069 | 0.640880 | ||||||||
\(352\) | −0.781744 | −0.0416671 | ||||||||
\(353\) | 14.1412 | 0.752661 | 0.376331 | − | 0.926485i | \(-0.377186\pi\) | ||||
0.376331 | + | 0.926485i | \(0.377186\pi\) | |||||||
\(354\) | 23.6612 | 1.25758 | ||||||||
\(355\) | 20.2597 | 1.07527 | ||||||||
\(356\) | −1.21752 | −0.0645284 | ||||||||
\(357\) | 11.1379 | 0.589482 | ||||||||
\(358\) | −7.12404 | −0.376517 | ||||||||
\(359\) | 7.25851 | 0.383089 | 0.191545 | − | 0.981484i | \(-0.438650\pi\) | ||||
0.191545 | + | 0.981484i | \(0.438650\pi\) | |||||||
\(360\) | −62.5527 | −3.29681 | ||||||||
\(361\) | 6.04319 | 0.318063 | ||||||||
\(362\) | −4.24866 | −0.223304 | ||||||||
\(363\) | 32.5541 | 1.70865 | ||||||||
\(364\) | −0.312039 | −0.0163553 | ||||||||
\(365\) | −31.3216 | −1.63945 | ||||||||
\(366\) | 14.8976 | 0.778711 | ||||||||
\(367\) | −15.7667 | −0.823015 | −0.411507 | − | 0.911406i | \(-0.634998\pi\) | ||||
−0.411507 | + | 0.911406i | \(0.634998\pi\) | |||||||
\(368\) | 4.44718 | 0.231825 | ||||||||
\(369\) | −30.3835 | −1.58170 | ||||||||
\(370\) | −52.1910 | −2.71328 | ||||||||
\(371\) | 7.48704 | 0.388708 | ||||||||
\(372\) | −7.05057 | −0.365555 | ||||||||
\(373\) | 4.16807 | 0.215815 | 0.107907 | − | 0.994161i | \(-0.465585\pi\) | ||||
0.107907 | + | 0.994161i | \(0.465585\pi\) | |||||||
\(374\) | −2.98240 | −0.154216 | ||||||||
\(375\) | 53.7589 | 2.77610 | ||||||||
\(376\) | 27.8648 | 1.43702 | ||||||||
\(377\) | −4.53605 | −0.233618 | ||||||||
\(378\) | 14.8249 | 0.762509 | ||||||||
\(379\) | 18.6572 | 0.958356 | 0.479178 | − | 0.877718i | \(-0.340935\pi\) | ||||
0.479178 | + | 0.877718i | \(0.340935\pi\) | |||||||
\(380\) | −4.90821 | −0.251786 | ||||||||
\(381\) | −26.8841 | −1.37731 | ||||||||
\(382\) | 5.36027 | 0.274255 | ||||||||
\(383\) | −30.2829 | −1.54738 | −0.773692 | − | 0.633562i | \(-0.781592\pi\) | ||||
−0.773692 | + | 0.633562i | \(0.781592\pi\) | |||||||
\(384\) | 39.5008 | 2.01577 | ||||||||
\(385\) | 2.07271 | 0.105635 | ||||||||
\(386\) | −31.4189 | −1.59918 | ||||||||
\(387\) | 22.7849 | 1.15822 | ||||||||
\(388\) | −2.81857 | −0.143091 | ||||||||
\(389\) | −14.0727 | −0.713515 | −0.356757 | − | 0.934197i | \(-0.616118\pi\) | ||||
−0.356757 | + | 0.934197i | \(0.616118\pi\) | |||||||
\(390\) | 21.2502 | 1.07605 | ||||||||
\(391\) | 3.66299 | 0.185245 | ||||||||
\(392\) | 2.61904 | 0.132282 | ||||||||
\(393\) | 7.75163 | 0.391018 | ||||||||
\(394\) | −8.33061 | −0.419690 | ||||||||
\(395\) | −38.3516 | −1.92968 | ||||||||
\(396\) | −0.868257 | −0.0436316 | ||||||||
\(397\) | 30.2423 | 1.51782 | 0.758908 | − | 0.651198i | \(-0.225733\pi\) | ||||
0.758908 | + | 0.651198i | \(0.225733\pi\) | |||||||
\(398\) | 11.6238 | 0.582649 | ||||||||
\(399\) | −15.2165 | −0.761777 | ||||||||
\(400\) | −42.7968 | −2.13984 | ||||||||
\(401\) | −0.668630 | −0.0333898 | −0.0166949 | − | 0.999861i | \(-0.505314\pi\) | ||||
−0.0166949 | + | 0.999861i | \(0.505314\pi\) | |||||||
\(402\) | −54.9830 | −2.74230 | ||||||||
\(403\) | −10.9991 | −0.547902 | ||||||||
\(404\) | 0.922976 | 0.0459198 | ||||||||
\(405\) | −43.1026 | −2.14179 | ||||||||
\(406\) | −5.60065 | −0.277955 | ||||||||
\(407\) | 4.92460 | 0.244103 | ||||||||
\(408\) | 29.1707 | 1.44417 | ||||||||
\(409\) | −9.05602 | −0.447791 | −0.223896 | − | 0.974613i | \(-0.571878\pi\) | ||||
−0.223896 | + | 0.974613i | \(0.571878\pi\) | |||||||
\(410\) | −27.9446 | −1.38008 | ||||||||
\(411\) | −41.4337 | −2.04377 | ||||||||
\(412\) | 2.43324 | 0.119877 | ||||||||
\(413\) | 5.18027 | 0.254904 | ||||||||
\(414\) | 9.38200 | 0.461100 | ||||||||
\(415\) | −29.2467 | −1.43567 | ||||||||
\(416\) | −1.75471 | −0.0860318 | ||||||||
\(417\) | 54.8738 | 2.68718 | ||||||||
\(418\) | 4.07451 | 0.199291 | ||||||||
\(419\) | −19.9592 | −0.975068 | −0.487534 | − | 0.873104i | \(-0.662104\pi\) | ||||
−0.487534 | + | 0.873104i | \(0.662104\pi\) | |||||||
\(420\) | 2.98227 | 0.145520 | ||||||||
\(421\) | −6.86296 | −0.334480 | −0.167240 | − | 0.985916i | \(-0.553486\pi\) | ||||
−0.167240 | + | 0.985916i | \(0.553486\pi\) | |||||||
\(422\) | −14.1791 | −0.690230 | ||||||||
\(423\) | 66.4496 | 3.23089 | ||||||||
\(424\) | 19.6089 | 0.952291 | ||||||||
\(425\) | −35.2503 | −1.70989 | ||||||||
\(426\) | −24.1988 | −1.17244 | ||||||||
\(427\) | 3.26161 | 0.157840 | ||||||||
\(428\) | 1.69352 | 0.0818596 | ||||||||
\(429\) | −2.00511 | −0.0968078 | ||||||||
\(430\) | 20.9559 | 1.01058 | ||||||||
\(431\) | 4.52160 | 0.217798 | 0.108899 | − | 0.994053i | \(-0.465268\pi\) | ||||
0.108899 | + | 0.994053i | \(0.465268\pi\) | |||||||
\(432\) | 43.8894 | 2.11163 | ||||||||
\(433\) | 14.5170 | 0.697641 | 0.348820 | − | 0.937190i | \(-0.386582\pi\) | ||||
0.348820 | + | 0.937190i | \(0.386582\pi\) | |||||||
\(434\) | −13.5805 | −0.651886 | ||||||||
\(435\) | 43.3526 | 2.07860 | ||||||||
\(436\) | 0.283992 | 0.0136007 | ||||||||
\(437\) | −5.00432 | −0.239389 | ||||||||
\(438\) | 37.4116 | 1.78759 | ||||||||
\(439\) | 25.5058 | 1.21732 | 0.608662 | − | 0.793430i | \(-0.291707\pi\) | ||||
0.608662 | + | 0.793430i | \(0.291707\pi\) | |||||||
\(440\) | 5.42851 | 0.258794 | ||||||||
\(441\) | 6.24568 | 0.297413 | ||||||||
\(442\) | −6.69432 | −0.318416 | ||||||||
\(443\) | 13.9434 | 0.662469 | 0.331235 | − | 0.943548i | \(-0.392535\pi\) | ||||
0.331235 | + | 0.943548i | \(0.392535\pi\) | |||||||
\(444\) | 7.08566 | 0.336270 | ||||||||
\(445\) | 18.1529 | 0.860528 | ||||||||
\(446\) | −16.6755 | −0.789607 | ||||||||
\(447\) | −42.0154 | −1.98726 | ||||||||
\(448\) | 6.72782 | 0.317860 | ||||||||
\(449\) | −22.5307 | −1.06329 | −0.531644 | − | 0.846968i | \(-0.678426\pi\) | ||||
−0.531644 | + | 0.846968i | \(0.678426\pi\) | |||||||
\(450\) | −90.2864 | −4.25614 | ||||||||
\(451\) | 2.63677 | 0.124161 | ||||||||
\(452\) | 0.111118 | 0.00522654 | ||||||||
\(453\) | −49.0801 | −2.30599 | ||||||||
\(454\) | −31.5194 | −1.47928 | ||||||||
\(455\) | 4.65242 | 0.218109 | ||||||||
\(456\) | −39.8526 | −1.86627 | ||||||||
\(457\) | −12.9589 | −0.606191 | −0.303096 | − | 0.952960i | \(-0.598020\pi\) | ||||
−0.303096 | + | 0.952960i | \(0.598020\pi\) | |||||||
\(458\) | −6.96317 | −0.325368 | ||||||||
\(459\) | 36.1502 | 1.68735 | ||||||||
\(460\) | 0.980794 | 0.0457298 | ||||||||
\(461\) | 14.9315 | 0.695428 | 0.347714 | − | 0.937601i | \(-0.386958\pi\) | ||||
0.347714 | + | 0.937601i | \(0.386958\pi\) | |||||||
\(462\) | −2.47571 | −0.115180 | ||||||||
\(463\) | 17.4941 | 0.813018 | 0.406509 | − | 0.913647i | \(-0.366746\pi\) | ||||
0.406509 | + | 0.913647i | \(0.366746\pi\) | |||||||
\(464\) | −16.5809 | −0.769747 | ||||||||
\(465\) | 105.122 | 4.87492 | ||||||||
\(466\) | −24.2903 | −1.12523 | ||||||||
\(467\) | −17.6281 | −0.815732 | −0.407866 | − | 0.913042i | \(-0.633727\pi\) | ||||
−0.407866 | + | 0.913042i | \(0.633727\pi\) | |||||||
\(468\) | −1.94890 | −0.0900878 | ||||||||
\(469\) | −12.0377 | −0.555849 | ||||||||
\(470\) | 61.1156 | 2.81905 | ||||||||
\(471\) | 46.5560 | 2.14519 | ||||||||
\(472\) | 13.5673 | 0.624487 | ||||||||
\(473\) | −1.97734 | −0.0909181 | ||||||||
\(474\) | 45.8084 | 2.10405 | ||||||||
\(475\) | 48.1583 | 2.20966 | ||||||||
\(476\) | −0.939485 | −0.0430612 | ||||||||
\(477\) | 46.7616 | 2.14107 | ||||||||
\(478\) | −1.90188 | −0.0869902 | ||||||||
\(479\) | −11.7457 | −0.536673 | −0.268336 | − | 0.963325i | \(-0.586474\pi\) | ||||
−0.268336 | + | 0.963325i | \(0.586474\pi\) | |||||||
\(480\) | 16.7704 | 0.765460 | ||||||||
\(481\) | 11.0538 | 0.504010 | ||||||||
\(482\) | 3.14887 | 0.143427 | ||||||||
\(483\) | 3.04067 | 0.138355 | ||||||||
\(484\) | −2.74594 | −0.124815 | ||||||||
\(485\) | 42.0241 | 1.90822 | ||||||||
\(486\) | 7.00860 | 0.317916 | ||||||||
\(487\) | 22.9380 | 1.03942 | 0.519710 | − | 0.854342i | \(-0.326040\pi\) | ||||
0.519710 | + | 0.854342i | \(0.326040\pi\) | |||||||
\(488\) | 8.54229 | 0.386691 | ||||||||
\(489\) | 12.0069 | 0.542970 | ||||||||
\(490\) | 5.74433 | 0.259502 | ||||||||
\(491\) | 11.5682 | 0.522067 | 0.261034 | − | 0.965330i | \(-0.415937\pi\) | ||||
0.261034 | + | 0.965330i | \(0.415937\pi\) | |||||||
\(492\) | 3.79386 | 0.171041 | ||||||||
\(493\) | −13.6571 | −0.615084 | ||||||||
\(494\) | 9.14567 | 0.411483 | ||||||||
\(495\) | 12.9455 | 0.581855 | ||||||||
\(496\) | −40.2055 | −1.80528 | ||||||||
\(497\) | −5.29796 | −0.237646 | ||||||||
\(498\) | 34.9332 | 1.56540 | ||||||||
\(499\) | 25.0063 | 1.11943 | 0.559717 | − | 0.828684i | \(-0.310910\pi\) | ||||
0.559717 | + | 0.828684i | \(0.310910\pi\) | |||||||
\(500\) | −4.53457 | −0.202792 | ||||||||
\(501\) | −5.70891 | −0.255055 | ||||||||
\(502\) | −17.3297 | −0.773462 | ||||||||
\(503\) | 16.1238 | 0.718925 | 0.359463 | − | 0.933160i | \(-0.382960\pi\) | ||||
0.359463 | + | 0.933160i | \(0.382960\pi\) | |||||||
\(504\) | 16.3577 | 0.728630 | ||||||||
\(505\) | −13.7613 | −0.612370 | ||||||||
\(506\) | −0.814198 | −0.0361955 | ||||||||
\(507\) | 35.0280 | 1.55565 | ||||||||
\(508\) | 2.26767 | 0.100612 | ||||||||
\(509\) | −1.46604 | −0.0649809 | −0.0324905 | − | 0.999472i | \(-0.510344\pi\) | ||||
−0.0324905 | + | 0.999472i | \(0.510344\pi\) | |||||||
\(510\) | 63.9800 | 2.83308 | ||||||||
\(511\) | 8.19070 | 0.362335 | ||||||||
\(512\) | 16.8806 | 0.746025 | ||||||||
\(513\) | −49.3878 | −2.18052 | ||||||||
\(514\) | −22.0136 | −0.970978 | ||||||||
\(515\) | −36.2789 | −1.59864 | ||||||||
\(516\) | −2.84505 | −0.125247 | ||||||||
\(517\) | −5.76669 | −0.253619 | ||||||||
\(518\) | 13.6481 | 0.599663 | ||||||||
\(519\) | −33.2181 | −1.45811 | ||||||||
\(520\) | 12.1849 | 0.534342 | ||||||||
\(521\) | −31.1921 | −1.36655 | −0.683276 | − | 0.730160i | \(-0.739446\pi\) | ||||
−0.683276 | + | 0.730160i | \(0.739446\pi\) | |||||||
\(522\) | −34.9798 | −1.53103 | ||||||||
\(523\) | −25.0064 | −1.09345 | −0.546727 | − | 0.837311i | \(-0.684126\pi\) | ||||
−0.546727 | + | 0.837311i | \(0.684126\pi\) | |||||||
\(524\) | −0.653850 | −0.0285636 | ||||||||
\(525\) | −29.2615 | −1.27708 | ||||||||
\(526\) | 34.1190 | 1.48766 | ||||||||
\(527\) | −33.1159 | −1.44255 | ||||||||
\(528\) | −7.32940 | −0.318971 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 43.0080 | 1.86815 | ||||||||
\(531\) | 32.3543 | 1.40406 | ||||||||
\(532\) | 1.28351 | 0.0556472 | ||||||||
\(533\) | 5.91852 | 0.256360 | ||||||||
\(534\) | −21.6824 | −0.938288 | ||||||||
\(535\) | −25.2500 | −1.09165 | ||||||||
\(536\) | −31.5272 | −1.36177 | ||||||||
\(537\) | −14.4205 | −0.622290 | ||||||||
\(538\) | −37.6824 | −1.62460 | ||||||||
\(539\) | −0.542019 | −0.0233464 | ||||||||
\(540\) | 9.67950 | 0.416539 | ||||||||
\(541\) | −29.8577 | −1.28368 | −0.641842 | − | 0.766837i | \(-0.721829\pi\) | ||||
−0.641842 | + | 0.766837i | \(0.721829\pi\) | |||||||
\(542\) | 42.0954 | 1.80815 | ||||||||
\(543\) | −8.60013 | −0.369067 | ||||||||
\(544\) | −5.28306 | −0.226510 | ||||||||
\(545\) | −4.23423 | −0.181375 | ||||||||
\(546\) | −5.55700 | −0.237818 | ||||||||
\(547\) | 29.1669 | 1.24708 | 0.623542 | − | 0.781789i | \(-0.285693\pi\) | ||||
0.623542 | + | 0.781789i | \(0.285693\pi\) | |||||||
\(548\) | 3.49493 | 0.149296 | ||||||||
\(549\) | 20.3710 | 0.869411 | ||||||||
\(550\) | 7.83532 | 0.334099 | ||||||||
\(551\) | 18.6581 | 0.794862 | ||||||||
\(552\) | 7.96365 | 0.338955 | ||||||||
\(553\) | 10.0291 | 0.426479 | ||||||||
\(554\) | 24.4390 | 1.03831 | ||||||||
\(555\) | −105.645 | −4.48439 | ||||||||
\(556\) | −4.62860 | −0.196297 | ||||||||
\(557\) | 40.2543 | 1.70563 | 0.852814 | − | 0.522214i | \(-0.174894\pi\) | ||||
0.852814 | + | 0.522214i | \(0.174894\pi\) | |||||||
\(558\) | −84.8196 | −3.59070 | ||||||||
\(559\) | −4.43835 | −0.187722 | ||||||||
\(560\) | 17.0062 | 0.718645 | ||||||||
\(561\) | −6.03697 | −0.254881 | ||||||||
\(562\) | 20.2332 | 0.853486 | ||||||||
\(563\) | −22.5130 | −0.948808 | −0.474404 | − | 0.880307i | \(-0.657336\pi\) | ||||
−0.474404 | + | 0.880307i | \(0.657336\pi\) | |||||||
\(564\) | −8.29729 | −0.349379 | ||||||||
\(565\) | −1.65673 | −0.0696994 | ||||||||
\(566\) | −27.1163 | −1.13978 | ||||||||
\(567\) | 11.2715 | 0.473357 | ||||||||
\(568\) | −13.8756 | −0.582207 | ||||||||
\(569\) | 6.81862 | 0.285852 | 0.142926 | − | 0.989733i | \(-0.454349\pi\) | ||||
0.142926 | + | 0.989733i | \(0.454349\pi\) | |||||||
\(570\) | −87.4085 | −3.66114 | ||||||||
\(571\) | −0.873495 | −0.0365546 | −0.0182773 | − | 0.999833i | \(-0.505818\pi\) | ||||
−0.0182773 | + | 0.999833i | \(0.505818\pi\) | |||||||
\(572\) | 0.169131 | 0.00707173 | ||||||||
\(573\) | 10.8503 | 0.453276 | ||||||||
\(574\) | 7.30758 | 0.305013 | ||||||||
\(575\) | −9.62336 | −0.401322 | ||||||||
\(576\) | 42.0198 | 1.75083 | ||||||||
\(577\) | −16.4150 | −0.683366 | −0.341683 | − | 0.939815i | \(-0.610997\pi\) | ||||
−0.341683 | + | 0.939815i | \(0.610997\pi\) | |||||||
\(578\) | 5.38150 | 0.223841 | ||||||||
\(579\) | −63.5981 | −2.64305 | ||||||||
\(580\) | −3.65679 | −0.151840 | ||||||||
\(581\) | 7.64810 | 0.317297 | ||||||||
\(582\) | −50.1950 | −2.08065 | ||||||||
\(583\) | −4.05812 | −0.168070 | ||||||||
\(584\) | 21.4518 | 0.887681 | ||||||||
\(585\) | 29.0575 | 1.20138 | ||||||||
\(586\) | −34.7781 | −1.43667 | ||||||||
\(587\) | −9.97331 | −0.411643 | −0.205821 | − | 0.978590i | \(-0.565987\pi\) | ||||
−0.205821 | + | 0.978590i | \(0.565987\pi\) | |||||||
\(588\) | −0.779873 | −0.0321614 | ||||||||
\(589\) | 45.2424 | 1.86418 | ||||||||
\(590\) | 29.7572 | 1.22508 | ||||||||
\(591\) | −16.8628 | −0.693644 | ||||||||
\(592\) | 40.4055 | 1.66066 | ||||||||
\(593\) | −20.5516 | −0.843951 | −0.421976 | − | 0.906607i | \(-0.638663\pi\) | ||||
−0.421976 | + | 0.906607i | \(0.638663\pi\) | |||||||
\(594\) | −8.03535 | −0.329694 | ||||||||
\(595\) | 14.0075 | 0.574250 | ||||||||
\(596\) | 3.54400 | 0.145168 | ||||||||
\(597\) | 23.5289 | 0.962975 | ||||||||
\(598\) | −1.82756 | −0.0747344 | ||||||||
\(599\) | 15.5468 | 0.635224 | 0.317612 | − | 0.948221i | \(-0.397119\pi\) | ||||
0.317612 | + | 0.948221i | \(0.397119\pi\) | |||||||
\(600\) | −76.6370 | −3.12869 | ||||||||
\(601\) | −29.3814 | −1.19849 | −0.599246 | − | 0.800565i | \(-0.704533\pi\) | ||||
−0.599246 | + | 0.800565i | \(0.704533\pi\) | |||||||
\(602\) | −5.48003 | −0.223349 | ||||||||
\(603\) | −75.1836 | −3.06171 | ||||||||
\(604\) | 4.13991 | 0.168450 | ||||||||
\(605\) | 40.9411 | 1.66449 | ||||||||
\(606\) | 16.4369 | 0.667705 | ||||||||
\(607\) | 31.1108 | 1.26275 | 0.631374 | − | 0.775478i | \(-0.282491\pi\) | ||||
0.631374 | + | 0.775478i | \(0.282491\pi\) | |||||||
\(608\) | 7.21764 | 0.292714 | ||||||||
\(609\) | −11.3368 | −0.459392 | ||||||||
\(610\) | 18.7358 | 0.758589 | ||||||||
\(611\) | −12.9440 | −0.523657 | ||||||||
\(612\) | −5.86772 | −0.237189 | ||||||||
\(613\) | −27.7365 | −1.12026 | −0.560132 | − | 0.828403i | \(-0.689250\pi\) | ||||
−0.560132 | + | 0.828403i | \(0.689250\pi\) | |||||||
\(614\) | 1.71699 | 0.0692920 | ||||||||
\(615\) | −56.5654 | −2.28094 | ||||||||
\(616\) | −1.41957 | −0.0571961 | ||||||||
\(617\) | −20.6041 | −0.829490 | −0.414745 | − | 0.909938i | \(-0.636129\pi\) | ||||
−0.414745 | + | 0.909938i | \(0.636129\pi\) | |||||||
\(618\) | 43.3327 | 1.74310 | ||||||||
\(619\) | −9.83894 | −0.395460 | −0.197730 | − | 0.980256i | \(-0.563357\pi\) | ||||
−0.197730 | + | 0.980256i | \(0.563357\pi\) | |||||||
\(620\) | −8.86704 | −0.356109 | ||||||||
\(621\) | 9.86904 | 0.396031 | ||||||||
\(622\) | 29.0211 | 1.16364 | ||||||||
\(623\) | −4.74703 | −0.190186 | ||||||||
\(624\) | −16.4516 | −0.658593 | ||||||||
\(625\) | 19.4923 | 0.779690 | ||||||||
\(626\) | 26.1586 | 1.04551 | ||||||||
\(627\) | 8.24762 | 0.329378 | ||||||||
\(628\) | −3.92700 | −0.156704 | ||||||||
\(629\) | 33.2807 | 1.32699 | ||||||||
\(630\) | 35.8772 | 1.42938 | ||||||||
\(631\) | 2.65314 | 0.105620 | 0.0528098 | − | 0.998605i | \(-0.483182\pi\) | ||||
0.0528098 | + | 0.998605i | \(0.483182\pi\) | |||||||
\(632\) | 26.2665 | 1.04483 | ||||||||
\(633\) | −28.7014 | −1.14078 | ||||||||
\(634\) | −2.14226 | −0.0850800 | ||||||||
\(635\) | −33.8103 | −1.34172 | ||||||||
\(636\) | −5.83894 | −0.231529 | ||||||||
\(637\) | −1.21662 | −0.0482043 | ||||||||
\(638\) | 3.03566 | 0.120183 | ||||||||
\(639\) | −33.0894 | −1.30899 | ||||||||
\(640\) | 49.6775 | 1.96368 | ||||||||
\(641\) | −46.9550 | −1.85461 | −0.927306 | − | 0.374304i | \(-0.877882\pi\) | ||||
−0.927306 | + | 0.374304i | \(0.877882\pi\) | |||||||
\(642\) | 30.1594 | 1.19030 | ||||||||
\(643\) | −8.01924 | −0.316248 | −0.158124 | − | 0.987419i | \(-0.550545\pi\) | ||||
−0.158124 | + | 0.987419i | \(0.550545\pi\) | |||||||
\(644\) | −0.256481 | −0.0101067 | ||||||||
\(645\) | 42.4189 | 1.67024 | ||||||||
\(646\) | 27.5357 | 1.08338 | ||||||||
\(647\) | 20.3950 | 0.801810 | 0.400905 | − | 0.916120i | \(-0.368696\pi\) | ||||
0.400905 | + | 0.916120i | \(0.368696\pi\) | |||||||
\(648\) | 29.5204 | 1.15967 | ||||||||
\(649\) | −2.80780 | −0.110216 | ||||||||
\(650\) | 17.5872 | 0.689828 | ||||||||
\(651\) | −27.4897 | −1.07741 | ||||||||
\(652\) | −1.01278 | −0.0396635 | ||||||||
\(653\) | −30.9134 | −1.20973 | −0.604867 | − | 0.796326i | \(-0.706774\pi\) | ||||
−0.604867 | + | 0.796326i | \(0.706774\pi\) | |||||||
\(654\) | 5.05750 | 0.197764 | ||||||||
\(655\) | 9.74871 | 0.380913 | ||||||||
\(656\) | 21.6343 | 0.844677 | ||||||||
\(657\) | 51.1565 | 1.99580 | ||||||||
\(658\) | −15.9819 | −0.623039 | ||||||||
\(659\) | 8.74476 | 0.340647 | 0.170324 | − | 0.985388i | \(-0.445519\pi\) | ||||
0.170324 | + | 0.985388i | \(0.445519\pi\) | |||||||
\(660\) | −1.61645 | −0.0629201 | ||||||||
\(661\) | 36.1030 | 1.40424 | 0.702121 | − | 0.712057i | \(-0.252236\pi\) | ||||
0.702121 | + | 0.712057i | \(0.252236\pi\) | |||||||
\(662\) | −5.88380 | −0.228680 | ||||||||
\(663\) | −13.5506 | −0.526264 | ||||||||
\(664\) | 20.0307 | 0.777342 | ||||||||
\(665\) | −19.1368 | −0.742092 | ||||||||
\(666\) | 85.2416 | 3.30305 | ||||||||
\(667\) | −3.72840 | −0.144364 | ||||||||
\(668\) | 0.481546 | 0.0186316 | ||||||||
\(669\) | −33.7545 | −1.30502 | ||||||||
\(670\) | −69.1485 | −2.67144 | ||||||||
\(671\) | −1.76785 | −0.0682472 | ||||||||
\(672\) | −4.38551 | −0.169175 | ||||||||
\(673\) | −37.5762 | −1.44845 | −0.724227 | − | 0.689561i | \(-0.757803\pi\) | ||||
−0.724227 | + | 0.689561i | \(0.757803\pi\) | |||||||
\(674\) | −11.6214 | −0.447639 | ||||||||
\(675\) | −94.9733 | −3.65552 | ||||||||
\(676\) | −2.95461 | −0.113639 | ||||||||
\(677\) | −21.5389 | −0.827807 | −0.413904 | − | 0.910321i | \(-0.635835\pi\) | ||||
−0.413904 | + | 0.910321i | \(0.635835\pi\) | |||||||
\(678\) | 1.97886 | 0.0759976 | ||||||||
\(679\) | −10.9894 | −0.421736 | ||||||||
\(680\) | 36.6861 | 1.40685 | ||||||||
\(681\) | −63.8015 | −2.44488 | ||||||||
\(682\) | 7.36090 | 0.281863 | ||||||||
\(683\) | 20.0545 | 0.767364 | 0.383682 | − | 0.923465i | \(-0.374656\pi\) | ||||
0.383682 | + | 0.923465i | \(0.374656\pi\) | |||||||
\(684\) | 8.01639 | 0.306514 | ||||||||
\(685\) | −52.1084 | −1.99096 | ||||||||
\(686\) | −1.50216 | −0.0573527 | ||||||||
\(687\) | −14.0949 | −0.537753 | ||||||||
\(688\) | −16.2238 | −0.618525 | ||||||||
\(689\) | −9.10888 | −0.347021 | ||||||||
\(690\) | 17.4666 | 0.664943 | ||||||||
\(691\) | 36.3245 | 1.38185 | 0.690925 | − | 0.722927i | \(-0.257204\pi\) | ||||
0.690925 | + | 0.722927i | \(0.257204\pi\) | |||||||
\(692\) | 2.80195 | 0.106514 | ||||||||
\(693\) | −3.38527 | −0.128596 | ||||||||
\(694\) | 48.1165 | 1.82648 | ||||||||
\(695\) | 69.0111 | 2.61774 | ||||||||
\(696\) | −29.6917 | −1.12546 | ||||||||
\(697\) | 17.8194 | 0.674959 | ||||||||
\(698\) | −43.6297 | −1.65141 | ||||||||
\(699\) | −49.1685 | −1.85972 | ||||||||
\(700\) | 2.46820 | 0.0932894 | ||||||||
\(701\) | 28.3217 | 1.06969 | 0.534847 | − | 0.844949i | \(-0.320369\pi\) | ||||
0.534847 | + | 0.844949i | \(0.320369\pi\) | |||||||
\(702\) | −18.0362 | −0.680734 | ||||||||
\(703\) | −45.4675 | −1.71484 | ||||||||
\(704\) | −3.64660 | −0.137437 | ||||||||
\(705\) | 123.710 | 4.65920 | ||||||||
\(706\) | −21.2424 | −0.799466 | ||||||||
\(707\) | 3.59862 | 0.135340 | ||||||||
\(708\) | −4.03995 | −0.151831 | ||||||||
\(709\) | 21.4326 | 0.804919 | 0.402460 | − | 0.915438i | \(-0.368155\pi\) | ||||
0.402460 | + | 0.915438i | \(0.368155\pi\) | |||||||
\(710\) | −30.4332 | −1.14214 | ||||||||
\(711\) | 62.6383 | 2.34912 | ||||||||
\(712\) | −12.4327 | −0.465934 | ||||||||
\(713\) | −9.04067 | −0.338576 | ||||||||
\(714\) | −16.7310 | −0.626140 | ||||||||
\(715\) | −2.52170 | −0.0943061 | ||||||||
\(716\) | 1.21637 | 0.0454578 | ||||||||
\(717\) | −3.84980 | −0.143773 | ||||||||
\(718\) | −10.9034 | −0.406912 | ||||||||
\(719\) | 46.7125 | 1.74208 | 0.871040 | − | 0.491212i | \(-0.163446\pi\) | ||||
0.871040 | + | 0.491212i | \(0.163446\pi\) | |||||||
\(720\) | 106.215 | 3.95842 | ||||||||
\(721\) | 9.48704 | 0.353316 | ||||||||
\(722\) | −9.07783 | −0.337842 | ||||||||
\(723\) | 6.37394 | 0.237050 | ||||||||
\(724\) | 0.725421 | 0.0269601 | ||||||||
\(725\) | 35.8797 | 1.33254 | ||||||||
\(726\) | −48.9014 | −1.81490 | ||||||||
\(727\) | 17.3705 | 0.644237 | 0.322119 | − | 0.946699i | \(-0.395605\pi\) | ||||
0.322119 | + | 0.946699i | \(0.395605\pi\) | |||||||
\(728\) | −3.18638 | −0.118095 | ||||||||
\(729\) | −19.6276 | −0.726947 | ||||||||
\(730\) | 47.0501 | 1.74140 | ||||||||
\(731\) | −13.3630 | −0.494247 | ||||||||
\(732\) | −2.54364 | −0.0940156 | ||||||||
\(733\) | 15.4702 | 0.571404 | 0.285702 | − | 0.958318i | \(-0.407773\pi\) | ||||
0.285702 | + | 0.958318i | \(0.407773\pi\) | |||||||
\(734\) | 23.6841 | 0.874195 | ||||||||
\(735\) | 11.6277 | 0.428893 | ||||||||
\(736\) | −1.44228 | −0.0531632 | ||||||||
\(737\) | 6.52465 | 0.240339 | ||||||||
\(738\) | 45.6408 | 1.68006 | ||||||||
\(739\) | −17.5944 | −0.647221 | −0.323611 | − | 0.946190i | \(-0.604897\pi\) | ||||
−0.323611 | + | 0.946190i | \(0.604897\pi\) | |||||||
\(740\) | 8.91116 | 0.327581 | ||||||||
\(741\) | 18.5127 | 0.680080 | ||||||||
\(742\) | −11.2467 | −0.412880 | ||||||||
\(743\) | −32.0161 | −1.17456 | −0.587278 | − | 0.809385i | \(-0.699801\pi\) | ||||
−0.587278 | + | 0.809385i | \(0.699801\pi\) | |||||||
\(744\) | −71.9967 | −2.63953 | ||||||||
\(745\) | −52.8399 | −1.93591 | ||||||||
\(746\) | −6.26111 | −0.229236 | ||||||||
\(747\) | 47.7676 | 1.74772 | ||||||||
\(748\) | 0.509219 | 0.0186189 | ||||||||
\(749\) | 6.60294 | 0.241266 | ||||||||
\(750\) | −80.7545 | −2.94874 | ||||||||
\(751\) | 38.1097 | 1.39064 | 0.695321 | − | 0.718700i | \(-0.255262\pi\) | ||||
0.695321 | + | 0.718700i | \(0.255262\pi\) | |||||||
\(752\) | −47.3148 | −1.72539 | ||||||||
\(753\) | −35.0788 | −1.27834 | ||||||||
\(754\) | 6.81386 | 0.248146 | ||||||||
\(755\) | −61.7248 | −2.24640 | ||||||||
\(756\) | −2.53122 | −0.0920594 | ||||||||
\(757\) | 19.5846 | 0.711814 | 0.355907 | − | 0.934521i | \(-0.384172\pi\) | ||||
0.355907 | + | 0.934521i | \(0.384172\pi\) | |||||||
\(758\) | −28.0261 | −1.01795 | ||||||||
\(759\) | −1.64810 | −0.0598223 | ||||||||
\(760\) | −50.1200 | −1.81804 | ||||||||
\(761\) | −1.99465 | −0.0723058 | −0.0361529 | − | 0.999346i | \(-0.511510\pi\) | ||||
−0.0361529 | + | 0.999346i | \(0.511510\pi\) | |||||||
\(762\) | 40.3841 | 1.46296 | ||||||||
\(763\) | 1.10726 | 0.0400856 | ||||||||
\(764\) | −0.915220 | −0.0331115 | ||||||||
\(765\) | 87.4860 | 3.16306 | ||||||||
\(766\) | 45.4897 | 1.64361 | ||||||||
\(767\) | −6.30242 | −0.227567 | ||||||||
\(768\) | −18.4223 | −0.664757 | ||||||||
\(769\) | 11.5731 | 0.417338 | 0.208669 | − | 0.977986i | \(-0.433087\pi\) | ||||
0.208669 | + | 0.977986i | \(0.433087\pi\) | |||||||
\(770\) | −3.11353 | −0.112204 | ||||||||
\(771\) | −44.5599 | −1.60479 | ||||||||
\(772\) | 5.36450 | 0.193073 | ||||||||
\(773\) | −47.3961 | −1.70472 | −0.852360 | − | 0.522955i | \(-0.824830\pi\) | ||||
−0.852360 | + | 0.522955i | \(0.824830\pi\) | |||||||
\(774\) | −34.2265 | −1.23025 | ||||||||
\(775\) | 87.0016 | 3.12519 | ||||||||
\(776\) | −28.7818 | −1.03321 | ||||||||
\(777\) | 27.6265 | 0.991095 | ||||||||
\(778\) | 21.1394 | 0.757886 | ||||||||
\(779\) | −24.3446 | −0.872236 | ||||||||
\(780\) | −3.62829 | −0.129914 | ||||||||
\(781\) | 2.87159 | 0.102754 | ||||||||
\(782\) | −5.50239 | −0.196765 | ||||||||
\(783\) | −36.7957 | −1.31497 | ||||||||
\(784\) | −4.44718 | −0.158828 | ||||||||
\(785\) | 58.5504 | 2.08975 | ||||||||
\(786\) | −11.6442 | −0.415334 | ||||||||
\(787\) | −30.1964 | −1.07639 | −0.538193 | − | 0.842822i | \(-0.680893\pi\) | ||||
−0.538193 | + | 0.842822i | \(0.680893\pi\) | |||||||
\(788\) | 1.42238 | 0.0506701 | ||||||||
\(789\) | 69.0638 | 2.45874 | ||||||||
\(790\) | 57.6102 | 2.04968 | ||||||||
\(791\) | 0.433241 | 0.0154043 | ||||||||
\(792\) | −8.86618 | −0.315046 | ||||||||
\(793\) | −3.96814 | −0.140913 | ||||||||
\(794\) | −45.4287 | −1.61220 | ||||||||
\(795\) | 87.0569 | 3.08759 | ||||||||
\(796\) | −1.98467 | −0.0703446 | ||||||||
\(797\) | −41.0916 | −1.45554 | −0.727770 | − | 0.685821i | \(-0.759443\pi\) | ||||
−0.727770 | + | 0.685821i | \(0.759443\pi\) | |||||||
\(798\) | 22.8576 | 0.809149 | ||||||||
\(799\) | −38.9716 | −1.37872 | ||||||||
\(800\) | 13.8796 | 0.490718 | ||||||||
\(801\) | −29.6484 | −1.04757 | ||||||||
\(802\) | 1.00439 | 0.0354662 | ||||||||
\(803\) | −4.43951 | −0.156667 | ||||||||
\(804\) | 9.38787 | 0.331085 | ||||||||
\(805\) | 3.82405 | 0.134780 | ||||||||
\(806\) | 16.5223 | 0.581975 | ||||||||
\(807\) | −76.2768 | −2.68507 | ||||||||
\(808\) | 9.42494 | 0.331568 | ||||||||
\(809\) | 17.9154 | 0.629870 | 0.314935 | − | 0.949113i | \(-0.398017\pi\) | ||||
0.314935 | + | 0.949113i | \(0.398017\pi\) | |||||||
\(810\) | 64.7470 | 2.27498 | ||||||||
\(811\) | 10.1577 | 0.356686 | 0.178343 | − | 0.983968i | \(-0.442926\pi\) | ||||
0.178343 | + | 0.983968i | \(0.442926\pi\) | |||||||
\(812\) | 0.956262 | 0.0335582 | ||||||||
\(813\) | 85.2095 | 2.98843 | ||||||||
\(814\) | −7.39753 | −0.259283 | ||||||||
\(815\) | 15.1003 | 0.528939 | ||||||||
\(816\) | −49.5324 | −1.73398 | ||||||||
\(817\) | 18.2563 | 0.638705 | ||||||||
\(818\) | 13.6036 | 0.475638 | ||||||||
\(819\) | −7.59862 | −0.265517 | ||||||||
\(820\) | 4.77129 | 0.166621 | ||||||||
\(821\) | −15.2289 | −0.531491 | −0.265745 | − | 0.964043i | \(-0.585618\pi\) | ||||
−0.265745 | + | 0.964043i | \(0.585618\pi\) | |||||||
\(822\) | 62.2400 | 2.17087 | ||||||||
\(823\) | −20.0090 | −0.697468 | −0.348734 | − | 0.937222i | \(-0.613388\pi\) | ||||
−0.348734 | + | 0.937222i | \(0.613388\pi\) | |||||||
\(824\) | 24.8470 | 0.865585 | ||||||||
\(825\) | 15.8603 | 0.552184 | ||||||||
\(826\) | −7.78158 | −0.270756 | ||||||||
\(827\) | 18.0259 | 0.626822 | 0.313411 | − | 0.949618i | \(-0.398528\pi\) | ||||
0.313411 | + | 0.949618i | \(0.398528\pi\) | |||||||
\(828\) | −1.60189 | −0.0556697 | ||||||||
\(829\) | 14.2616 | 0.495327 | 0.247664 | − | 0.968846i | \(-0.420337\pi\) | ||||
0.247664 | + | 0.968846i | \(0.420337\pi\) | |||||||
\(830\) | 43.9332 | 1.52494 | ||||||||
\(831\) | 49.4694 | 1.71607 | ||||||||
\(832\) | −8.18520 | −0.283771 | ||||||||
\(833\) | −3.66299 | −0.126915 | ||||||||
\(834\) | −82.4291 | −2.85429 | ||||||||
\(835\) | −7.17971 | −0.248464 | ||||||||
\(836\) | −0.695686 | −0.0240608 | ||||||||
\(837\) | −89.2227 | −3.08399 | ||||||||
\(838\) | 29.9818 | 1.03570 | ||||||||
\(839\) | 51.5877 | 1.78101 | 0.890503 | − | 0.454977i | \(-0.150353\pi\) | ||||
0.890503 | + | 0.454977i | \(0.150353\pi\) | |||||||
\(840\) | 30.4534 | 1.05074 | ||||||||
\(841\) | −15.0990 | −0.520656 | ||||||||
\(842\) | 10.3093 | 0.355280 | ||||||||
\(843\) | 40.9561 | 1.41060 | ||||||||
\(844\) | 2.42097 | 0.0833331 | ||||||||
\(845\) | 44.0524 | 1.51545 | ||||||||
\(846\) | −99.8178 | −3.43181 | ||||||||
\(847\) | −10.7062 | −0.367870 | ||||||||
\(848\) | −33.2962 | −1.14340 | ||||||||
\(849\) | −54.8889 | −1.88378 | ||||||||
\(850\) | 52.9515 | 1.81622 | ||||||||
\(851\) | 9.08566 | 0.311452 | ||||||||
\(852\) | 4.13174 | 0.141551 | ||||||||
\(853\) | 48.2610 | 1.65243 | 0.826213 | − | 0.563358i | \(-0.190491\pi\) | ||||
0.826213 | + | 0.563358i | \(0.190491\pi\) | |||||||
\(854\) | −4.89945 | −0.167656 | ||||||||
\(855\) | −119.522 | −4.08757 | ||||||||
\(856\) | 17.2934 | 0.591075 | ||||||||
\(857\) | −1.37665 | −0.0470256 | −0.0235128 | − | 0.999724i | \(-0.507485\pi\) | ||||
−0.0235128 | + | 0.999724i | \(0.507485\pi\) | |||||||
\(858\) | 3.01200 | 0.102828 | ||||||||
\(859\) | −36.3622 | −1.24066 | −0.620331 | − | 0.784340i | \(-0.713002\pi\) | ||||
−0.620331 | + | 0.784340i | \(0.713002\pi\) | |||||||
\(860\) | −3.57804 | −0.122010 | ||||||||
\(861\) | 14.7920 | 0.504110 | ||||||||
\(862\) | −6.79215 | −0.231342 | ||||||||
\(863\) | 44.8731 | 1.52750 | 0.763749 | − | 0.645514i | \(-0.223357\pi\) | ||||
0.763749 | + | 0.645514i | \(0.223357\pi\) | |||||||
\(864\) | −14.2339 | −0.484248 | ||||||||
\(865\) | −41.7762 | −1.42043 | ||||||||
\(866\) | −21.8068 | −0.741025 | ||||||||
\(867\) | 10.8932 | 0.369954 | ||||||||
\(868\) | 2.31876 | 0.0787037 | ||||||||
\(869\) | −5.43594 | −0.184402 | ||||||||
\(870\) | −65.1225 | −2.20786 | ||||||||
\(871\) | 14.6453 | 0.496237 | ||||||||
\(872\) | 2.89997 | 0.0982054 | ||||||||
\(873\) | −68.6364 | −2.32299 | ||||||||
\(874\) | 7.51728 | 0.254276 | ||||||||
\(875\) | −17.6800 | −0.597692 | ||||||||
\(876\) | −6.38770 | −0.215820 | ||||||||
\(877\) | 42.2559 | 1.42688 | 0.713441 | − | 0.700716i | \(-0.247136\pi\) | ||||
0.713441 | + | 0.700716i | \(0.247136\pi\) | |||||||
\(878\) | −38.3137 | −1.29303 | ||||||||
\(879\) | −70.3979 | −2.37446 | ||||||||
\(880\) | −9.21770 | −0.310729 | ||||||||
\(881\) | 51.1432 | 1.72306 | 0.861529 | − | 0.507708i | \(-0.169507\pi\) | ||||
0.861529 | + | 0.507708i | \(0.169507\pi\) | |||||||
\(882\) | −9.38200 | −0.315908 | ||||||||
\(883\) | 52.6889 | 1.77312 | 0.886562 | − | 0.462610i | \(-0.153087\pi\) | ||||
0.886562 | + | 0.462610i | \(0.153087\pi\) | |||||||
\(884\) | 1.14300 | 0.0384432 | ||||||||
\(885\) | 60.2345 | 2.02476 | ||||||||
\(886\) | −20.9451 | −0.703666 | ||||||||
\(887\) | −42.9102 | −1.44078 | −0.720391 | − | 0.693568i | \(-0.756038\pi\) | ||||
−0.720391 | + | 0.693568i | \(0.756038\pi\) | |||||||
\(888\) | 72.3550 | 2.42807 | ||||||||
\(889\) | 8.84149 | 0.296534 | ||||||||
\(890\) | −27.2685 | −0.914042 | ||||||||
\(891\) | −6.10934 | −0.204671 | ||||||||
\(892\) | 2.84719 | 0.0953311 | ||||||||
\(893\) | 53.2424 | 1.78169 | ||||||||
\(894\) | 63.1137 | 2.11084 | ||||||||
\(895\) | −18.1357 | −0.606209 | ||||||||
\(896\) | −12.9908 | −0.433993 | ||||||||
\(897\) | −3.69934 | −0.123517 | ||||||||
\(898\) | 33.8446 | 1.12941 | ||||||||
\(899\) | 33.7072 | 1.12420 | ||||||||
\(900\) | 15.4156 | 0.513854 | ||||||||
\(901\) | −27.4249 | −0.913657 | ||||||||
\(902\) | −3.96085 | −0.131882 | ||||||||
\(903\) | −11.0927 | −0.369141 | ||||||||
\(904\) | 1.13468 | 0.0377388 | ||||||||
\(905\) | −10.8158 | −0.359530 | ||||||||
\(906\) | 73.7261 | 2.44939 | ||||||||
\(907\) | −24.5213 | −0.814217 | −0.407108 | − | 0.913380i | \(-0.633463\pi\) | ||||
−0.407108 | + | 0.913380i | \(0.633463\pi\) | |||||||
\(908\) | 5.38166 | 0.178597 | ||||||||
\(909\) | 22.4758 | 0.745476 | ||||||||
\(910\) | −6.98867 | −0.231672 | ||||||||
\(911\) | −31.6347 | −1.04810 | −0.524052 | − | 0.851686i | \(-0.675580\pi\) | ||||
−0.524052 | + | 0.851686i | \(0.675580\pi\) | |||||||
\(912\) | 67.6704 | 2.24079 | ||||||||
\(913\) | −4.14541 | −0.137193 | ||||||||
\(914\) | 19.4663 | 0.643888 | ||||||||
\(915\) | 37.9249 | 1.25376 | ||||||||
\(916\) | 1.18890 | 0.0392824 | ||||||||
\(917\) | −2.54931 | −0.0841858 | ||||||||
\(918\) | −54.3033 | −1.79228 | ||||||||
\(919\) | −43.7293 | −1.44250 | −0.721249 | − | 0.692676i | \(-0.756431\pi\) | ||||
−0.721249 | + | 0.692676i | \(0.756431\pi\) | |||||||
\(920\) | 10.0154 | 0.330196 | ||||||||
\(921\) | 3.47553 | 0.114523 | ||||||||
\(922\) | −22.4294 | −0.738674 | ||||||||
\(923\) | 6.44561 | 0.212160 | ||||||||
\(924\) | 0.422706 | 0.0139060 | ||||||||
\(925\) | −87.4346 | −2.87483 | ||||||||
\(926\) | −26.2788 | −0.863576 | ||||||||
\(927\) | 59.2530 | 1.94612 | ||||||||
\(928\) | 5.37741 | 0.176522 | ||||||||
\(929\) | 3.63411 | 0.119231 | 0.0596157 | − | 0.998221i | \(-0.481012\pi\) | ||||
0.0596157 | + | 0.998221i | \(0.481012\pi\) | |||||||
\(930\) | −157.910 | −5.17807 | ||||||||
\(931\) | 5.00432 | 0.164010 | ||||||||
\(932\) | 4.14736 | 0.135851 | ||||||||
\(933\) | 58.7445 | 1.92321 | ||||||||
\(934\) | 26.4802 | 0.866460 | ||||||||
\(935\) | −7.59230 | −0.248295 | ||||||||
\(936\) | −19.9011 | −0.650488 | ||||||||
\(937\) | −10.3649 | −0.338606 | −0.169303 | − | 0.985564i | \(-0.554152\pi\) | ||||
−0.169303 | + | 0.985564i | \(0.554152\pi\) | |||||||
\(938\) | 18.0825 | 0.590415 | ||||||||
\(939\) | 52.9503 | 1.72797 | ||||||||
\(940\) | −10.4350 | −0.340351 | ||||||||
\(941\) | −29.8720 | −0.973800 | −0.486900 | − | 0.873458i | \(-0.661872\pi\) | ||||
−0.486900 | + | 0.873458i | \(0.661872\pi\) | |||||||
\(942\) | −69.9345 | −2.27859 | ||||||||
\(943\) | 4.86472 | 0.158417 | ||||||||
\(944\) | −23.0376 | −0.749809 | ||||||||
\(945\) | 37.7397 | 1.22767 | ||||||||
\(946\) | 2.97028 | 0.0965720 | ||||||||
\(947\) | 7.17017 | 0.232999 | 0.116500 | − | 0.993191i | \(-0.462833\pi\) | ||||
0.116500 | + | 0.993191i | \(0.462833\pi\) | |||||||
\(948\) | −7.82139 | −0.254027 | ||||||||
\(949\) | −9.96497 | −0.323477 | ||||||||
\(950\) | −72.3415 | −2.34707 | ||||||||
\(951\) | −4.33636 | −0.140616 | ||||||||
\(952\) | −9.59352 | −0.310928 | ||||||||
\(953\) | 16.0495 | 0.519894 | 0.259947 | − | 0.965623i | \(-0.416295\pi\) | ||||
0.259947 | + | 0.965623i | \(0.416295\pi\) | |||||||
\(954\) | −70.2434 | −2.27421 | ||||||||
\(955\) | 13.6457 | 0.441563 | ||||||||
\(956\) | 0.324730 | 0.0105025 | ||||||||
\(957\) | 6.14478 | 0.198632 | ||||||||
\(958\) | 17.6438 | 0.570046 | ||||||||
\(959\) | 13.6265 | 0.440022 | ||||||||
\(960\) | 78.2289 | 2.52483 | ||||||||
\(961\) | 50.7337 | 1.63657 | ||||||||
\(962\) | −16.6046 | −0.535352 | ||||||||
\(963\) | 41.2398 | 1.32893 | ||||||||
\(964\) | −0.537642 | −0.0173163 | ||||||||
\(965\) | −79.9832 | −2.57475 | ||||||||
\(966\) | −4.56757 | −0.146959 | ||||||||
\(967\) | 33.5360 | 1.07845 | 0.539223 | − | 0.842163i | \(-0.318718\pi\) | ||||
0.539223 | + | 0.842163i | \(0.318718\pi\) | |||||||
\(968\) | −28.0400 | −0.901241 | ||||||||
\(969\) | 55.7378 | 1.79056 | ||||||||
\(970\) | −63.1269 | −2.02688 | ||||||||
\(971\) | −17.5189 | −0.562208 | −0.281104 | − | 0.959677i | \(-0.590701\pi\) | ||||
−0.281104 | + | 0.959677i | \(0.590701\pi\) | |||||||
\(972\) | −1.19666 | −0.0383828 | ||||||||
\(973\) | −18.0466 | −0.578548 | ||||||||
\(974\) | −34.4565 | −1.10406 | ||||||||
\(975\) | 35.6001 | 1.14012 | ||||||||
\(976\) | −14.5050 | −0.464292 | ||||||||
\(977\) | 50.1902 | 1.60573 | 0.802863 | − | 0.596163i | \(-0.203309\pi\) | ||||
0.802863 | + | 0.596163i | \(0.203309\pi\) | |||||||
\(978\) | −18.0362 | −0.576735 | ||||||||
\(979\) | 2.57298 | 0.0822327 | ||||||||
\(980\) | −0.980794 | −0.0313303 | ||||||||
\(981\) | 6.91561 | 0.220798 | ||||||||
\(982\) | −17.3773 | −0.554533 | ||||||||
\(983\) | −22.7924 | −0.726966 | −0.363483 | − | 0.931601i | \(-0.618413\pi\) | ||||
−0.363483 | + | 0.931601i | \(0.618413\pi\) | |||||||
\(984\) | 38.7409 | 1.23502 | ||||||||
\(985\) | −21.2073 | −0.675719 | ||||||||
\(986\) | 20.5151 | 0.653334 | ||||||||
\(987\) | −32.3506 | −1.02973 | ||||||||
\(988\) | −1.56154 | −0.0496793 | ||||||||
\(989\) | −3.64810 | −0.116003 | ||||||||
\(990\) | −19.4461 | −0.618039 | ||||||||
\(991\) | −0.965443 | −0.0306683 | −0.0153342 | − | 0.999882i | \(-0.504881\pi\) | ||||
−0.0153342 | + | 0.999882i | \(0.504881\pi\) | |||||||
\(992\) | 13.0392 | 0.413995 | ||||||||
\(993\) | −11.9100 | −0.377952 | ||||||||
\(994\) | 7.95838 | 0.252424 | ||||||||
\(995\) | 29.5908 | 0.938091 | ||||||||
\(996\) | −5.96455 | −0.188994 | ||||||||
\(997\) | −4.22619 | −0.133845 | −0.0669224 | − | 0.997758i | \(-0.521318\pi\) | ||||
−0.0669224 | + | 0.997758i | \(0.521318\pi\) | |||||||
\(998\) | −37.5634 | −1.18905 | ||||||||
\(999\) | 89.6667 | 2.83693 |
(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 | 161.2.a.d.1.2 | ✓ | 5 | |
3.2 | odd | 2 | 1449.2.a.r.1.4 | 5 | |||
4.3 | odd | 2 | 2576.2.a.bd.1.5 | 5 | |||
5.4 | even | 2 | 4025.2.a.p.1.4 | 5 | |||
7.6 | odd | 2 | 1127.2.a.h.1.2 | 5 | |||
23.22 | odd | 2 | 3703.2.a.j.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
161.2.a.d.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
1127.2.a.h.1.2 | 5 | 7.6 | odd | 2 | |||
1449.2.a.r.1.4 | 5 | 3.2 | odd | 2 | |||
2576.2.a.bd.1.5 | 5 | 4.3 | odd | 2 | |||
3703.2.a.j.1.2 | 5 | 23.22 | odd | 2 | |||
4025.2.a.p.1.4 | 5 | 5.4 | even | 2 |