Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1397868136\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | no (minimal twist has level 805) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22234 | −0.864327 | −0.432163 | − | 0.901795i | \(-0.642250\pi\) | ||||
−0.432163 | + | 0.901795i | \(0.642250\pi\) | |||||||
\(3\) | 1.28664 | 0.742839 | 0.371420 | − | 0.928465i | \(-0.378871\pi\) | ||||
0.371420 | + | 0.928465i | \(0.378871\pi\) | |||||||
\(4\) | −0.505878 | −0.252939 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.57271 | −0.642056 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 3.06304 | 1.08295 | ||||||||
\(9\) | −1.34457 | −0.448190 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.83173 | −0.552287 | −0.276143 | − | 0.961116i | \(-0.589056\pi\) | ||||
−0.276143 | + | 0.961116i | \(0.589056\pi\) | |||||||
\(12\) | −0.650880 | −0.187893 | ||||||||
\(13\) | 3.24693 | 0.900536 | 0.450268 | − | 0.892893i | \(-0.351328\pi\) | ||||
0.450268 | + | 0.892893i | \(0.351328\pi\) | |||||||
\(14\) | −1.22234 | −0.326685 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.73233 | −0.683083 | ||||||||
\(17\) | 5.53254 | 1.34184 | 0.670919 | − | 0.741531i | \(-0.265900\pi\) | ||||
0.670919 | + | 0.741531i | \(0.265900\pi\) | |||||||
\(18\) | 1.64352 | 0.387382 | ||||||||
\(19\) | −2.06793 | −0.474415 | −0.237207 | − | 0.971459i | \(-0.576232\pi\) | ||||
−0.237207 | + | 0.971459i | \(0.576232\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.28664 | 0.280767 | ||||||||
\(22\) | 2.23900 | 0.477356 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 3.94102 | 0.804457 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.96886 | −0.778358 | ||||||||
\(27\) | −5.58988 | −1.07577 | ||||||||
\(28\) | −0.505878 | −0.0956019 | ||||||||
\(29\) | 2.29813 | 0.426752 | 0.213376 | − | 0.976970i | \(-0.431554\pi\) | ||||
0.213376 | + | 0.976970i | \(0.431554\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.49162 | −0.447509 | −0.223754 | − | 0.974646i | \(-0.571831\pi\) | ||||
−0.223754 | + | 0.974646i | \(0.571831\pi\) | |||||||
\(32\) | −2.78624 | −0.492542 | ||||||||
\(33\) | −2.35677 | −0.410260 | ||||||||
\(34\) | −6.76266 | −1.15979 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.680188 | 0.113365 | ||||||||
\(37\) | 7.37033 | 1.21167 | 0.605837 | − | 0.795589i | \(-0.292838\pi\) | ||||
0.605837 | + | 0.795589i | \(0.292838\pi\) | |||||||
\(38\) | 2.52772 | 0.410050 | ||||||||
\(39\) | 4.17762 | 0.668954 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.4498 | 1.78816 | 0.894078 | − | 0.447912i | \(-0.147832\pi\) | ||||
0.894078 | + | 0.447912i | \(0.147832\pi\) | |||||||
\(42\) | −1.57271 | −0.242674 | ||||||||
\(43\) | −3.84395 | −0.586197 | −0.293099 | − | 0.956082i | \(-0.594686\pi\) | ||||
−0.293099 | + | 0.956082i | \(0.594686\pi\) | |||||||
\(44\) | 0.926631 | 0.139695 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.22234 | −0.180225 | ||||||||
\(47\) | −5.75277 | −0.839128 | −0.419564 | − | 0.907726i | \(-0.637817\pi\) | ||||
−0.419564 | + | 0.907726i | \(0.637817\pi\) | |||||||
\(48\) | −3.51552 | −0.507421 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.11836 | 0.996770 | ||||||||
\(52\) | −1.64255 | −0.227781 | ||||||||
\(53\) | −2.68696 | −0.369083 | −0.184541 | − | 0.982825i | \(-0.559080\pi\) | ||||
−0.184541 | + | 0.982825i | \(0.559080\pi\) | |||||||
\(54\) | 6.83275 | 0.929819 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.06304 | 0.409316 | ||||||||
\(57\) | −2.66067 | −0.352414 | ||||||||
\(58\) | −2.80910 | −0.368853 | ||||||||
\(59\) | 5.19513 | 0.676348 | 0.338174 | − | 0.941084i | \(-0.390191\pi\) | ||||
0.338174 | + | 0.941084i | \(0.390191\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.4038 | −1.46011 | −0.730055 | − | 0.683388i | \(-0.760506\pi\) | ||||
−0.730055 | + | 0.683388i | \(0.760506\pi\) | |||||||
\(62\) | 3.04562 | 0.386794 | ||||||||
\(63\) | −1.34457 | −0.169400 | ||||||||
\(64\) | 8.87040 | 1.10880 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.88078 | 0.354599 | ||||||||
\(67\) | 13.4901 | 1.64808 | 0.824039 | − | 0.566533i | \(-0.191716\pi\) | ||||
0.824039 | + | 0.566533i | \(0.191716\pi\) | |||||||
\(68\) | −2.79879 | −0.339403 | ||||||||
\(69\) | 1.28664 | 0.154893 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.68945 | −0.556535 | −0.278268 | − | 0.960504i | \(-0.589760\pi\) | ||||
−0.278268 | + | 0.960504i | \(0.589760\pi\) | |||||||
\(72\) | −4.11847 | −0.485366 | ||||||||
\(73\) | −13.7534 | −1.60972 | −0.804858 | − | 0.593467i | \(-0.797759\pi\) | ||||
−0.804858 | + | 0.593467i | \(0.797759\pi\) | |||||||
\(74\) | −9.00907 | −1.04728 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.04612 | 0.119998 | ||||||||
\(77\) | −1.83173 | −0.208745 | ||||||||
\(78\) | −5.10648 | −0.578195 | ||||||||
\(79\) | 5.30377 | 0.596721 | 0.298360 | − | 0.954453i | \(-0.403560\pi\) | ||||
0.298360 | + | 0.954453i | \(0.403560\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.15843 | −0.350936 | ||||||||
\(82\) | −13.9956 | −1.54555 | ||||||||
\(83\) | 11.7821 | 1.29326 | 0.646629 | − | 0.762805i | \(-0.276178\pi\) | ||||
0.646629 | + | 0.762805i | \(0.276178\pi\) | |||||||
\(84\) | −0.650880 | −0.0710169 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.69863 | 0.506666 | ||||||||
\(87\) | 2.95686 | 0.317008 | ||||||||
\(88\) | −5.61066 | −0.598098 | ||||||||
\(89\) | −12.4495 | −1.31965 | −0.659823 | − | 0.751421i | \(-0.729369\pi\) | ||||
−0.659823 | + | 0.751421i | \(0.729369\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.24693 | 0.340371 | ||||||||
\(92\) | −0.505878 | −0.0527414 | ||||||||
\(93\) | −3.20581 | −0.332427 | ||||||||
\(94\) | 7.03186 | 0.725281 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.58487 | −0.365879 | ||||||||
\(97\) | 9.36711 | 0.951086 | 0.475543 | − | 0.879693i | \(-0.342252\pi\) | ||||
0.475543 | + | 0.879693i | \(0.342252\pi\) | |||||||
\(98\) | −1.22234 | −0.123475 | ||||||||
\(99\) | 2.46288 | 0.247529 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.8806 | 1.67968 | 0.839839 | − | 0.542835i | \(-0.182649\pi\) | ||||
0.839839 | + | 0.542835i | \(0.182649\pi\) | |||||||
\(102\) | −8.70108 | −0.861535 | ||||||||
\(103\) | 11.6971 | 1.15255 | 0.576273 | − | 0.817257i | \(-0.304506\pi\) | ||||
0.576273 | + | 0.817257i | \(0.304506\pi\) | |||||||
\(104\) | 9.94548 | 0.975235 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.28439 | 0.319008 | ||||||||
\(107\) | 0.260335 | 0.0251675 | 0.0125838 | − | 0.999921i | \(-0.495994\pi\) | ||||
0.0125838 | + | 0.999921i | \(0.495994\pi\) | |||||||
\(108\) | 2.82779 | 0.272105 | ||||||||
\(109\) | 12.3958 | 1.18730 | 0.593652 | − | 0.804722i | \(-0.297686\pi\) | ||||
0.593652 | + | 0.804722i | \(0.297686\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.48293 | 0.900079 | ||||||||
\(112\) | −2.73233 | −0.258181 | ||||||||
\(113\) | −13.2257 | −1.24417 | −0.622084 | − | 0.782950i | \(-0.713714\pi\) | ||||
−0.622084 | + | 0.782950i | \(0.713714\pi\) | |||||||
\(114\) | 3.25225 | 0.304601 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.16257 | −0.107942 | ||||||||
\(117\) | −4.36572 | −0.403611 | ||||||||
\(118\) | −6.35023 | −0.584586 | ||||||||
\(119\) | 5.53254 | 0.507167 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.64477 | −0.694979 | ||||||||
\(122\) | 13.9394 | 1.26201 | ||||||||
\(123\) | 14.7317 | 1.32831 | ||||||||
\(124\) | 1.26046 | 0.113192 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.64352 | 0.146417 | ||||||||
\(127\) | 7.36812 | 0.653815 | 0.326908 | − | 0.945056i | \(-0.393993\pi\) | ||||
0.326908 | + | 0.945056i | \(0.393993\pi\) | |||||||
\(128\) | −5.27020 | −0.465824 | ||||||||
\(129\) | −4.94577 | −0.435450 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.9771 | 1.74541 | 0.872704 | − | 0.488250i | \(-0.162365\pi\) | ||||
0.872704 | + | 0.488250i | \(0.162365\pi\) | |||||||
\(132\) | 1.19224 | 0.103771 | ||||||||
\(133\) | −2.06793 | −0.179312 | ||||||||
\(134\) | −16.4895 | −1.42448 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16.9464 | 1.45314 | ||||||||
\(137\) | −14.3412 | −1.22525 | −0.612626 | − | 0.790373i | \(-0.709887\pi\) | ||||
−0.612626 | + | 0.790373i | \(0.709887\pi\) | |||||||
\(138\) | −1.57271 | −0.133878 | ||||||||
\(139\) | −5.88452 | −0.499119 | −0.249559 | − | 0.968359i | \(-0.580286\pi\) | ||||
−0.249559 | + | 0.968359i | \(0.580286\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.40172 | −0.623337 | ||||||||
\(142\) | 5.73212 | 0.481029 | ||||||||
\(143\) | −5.94749 | −0.497354 | ||||||||
\(144\) | 3.67381 | 0.306151 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 16.8114 | 1.39132 | ||||||||
\(147\) | 1.28664 | 0.106120 | ||||||||
\(148\) | −3.72849 | −0.306480 | ||||||||
\(149\) | −19.3463 | −1.58491 | −0.792455 | − | 0.609931i | \(-0.791197\pi\) | ||||
−0.792455 | + | 0.609931i | \(0.791197\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.4932 | 1.01668 | 0.508339 | − | 0.861157i | \(-0.330260\pi\) | ||||
0.508339 | + | 0.861157i | \(0.330260\pi\) | |||||||
\(152\) | −6.33415 | −0.513767 | ||||||||
\(153\) | −7.43888 | −0.601398 | ||||||||
\(154\) | 2.23900 | 0.180424 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.11336 | −0.169204 | ||||||||
\(157\) | −5.89291 | −0.470305 | −0.235153 | − | 0.971958i | \(-0.575559\pi\) | ||||
−0.235153 | + | 0.971958i | \(0.575559\pi\) | |||||||
\(158\) | −6.48302 | −0.515762 | ||||||||
\(159\) | −3.45714 | −0.274169 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 3.86068 | 0.303324 | ||||||||
\(163\) | 15.8132 | 1.23858 | 0.619292 | − | 0.785161i | \(-0.287420\pi\) | ||||
0.619292 | + | 0.785161i | \(0.287420\pi\) | |||||||
\(164\) | −5.79219 | −0.452294 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.4018 | −1.11780 | ||||||||
\(167\) | 11.3761 | 0.880312 | 0.440156 | − | 0.897921i | \(-0.354923\pi\) | ||||
0.440156 | + | 0.897921i | \(0.354923\pi\) | |||||||
\(168\) | 3.94102 | 0.304056 | ||||||||
\(169\) | −2.45745 | −0.189035 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.78047 | 0.212628 | ||||||||
\(172\) | 1.94457 | 0.148272 | ||||||||
\(173\) | −2.91057 | −0.221287 | −0.110643 | − | 0.993860i | \(-0.535291\pi\) | ||||
−0.110643 | + | 0.993860i | \(0.535291\pi\) | |||||||
\(174\) | −3.61429 | −0.273999 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.00489 | 0.377258 | ||||||||
\(177\) | 6.68424 | 0.502418 | ||||||||
\(178\) | 15.2176 | 1.14061 | ||||||||
\(179\) | 10.6611 | 0.796851 | 0.398426 | − | 0.917201i | \(-0.369557\pi\) | ||||
0.398426 | + | 0.917201i | \(0.369557\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.1456 | 1.57174 | 0.785869 | − | 0.618393i | \(-0.212216\pi\) | ||||
0.785869 | + | 0.618393i | \(0.212216\pi\) | |||||||
\(182\) | −3.96886 | −0.294192 | ||||||||
\(183\) | −14.6726 | −1.08463 | ||||||||
\(184\) | 3.06304 | 0.225810 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.91860 | 0.287326 | ||||||||
\(187\) | −10.1341 | −0.741079 | ||||||||
\(188\) | 2.91020 | 0.212248 | ||||||||
\(189\) | −5.58988 | −0.406604 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.0107 | −0.796704 | −0.398352 | − | 0.917233i | \(-0.630418\pi\) | ||||
−0.398352 | + | 0.917233i | \(0.630418\pi\) | |||||||
\(192\) | 11.4130 | 0.823660 | ||||||||
\(193\) | −7.87083 | −0.566555 | −0.283277 | − | 0.959038i | \(-0.591422\pi\) | ||||
−0.283277 | + | 0.959038i | \(0.591422\pi\) | |||||||
\(194\) | −11.4498 | −0.822049 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.505878 | −0.0361341 | ||||||||
\(197\) | 6.62074 | 0.471708 | 0.235854 | − | 0.971788i | \(-0.424211\pi\) | ||||
0.235854 | + | 0.971788i | \(0.424211\pi\) | |||||||
\(198\) | −3.01049 | −0.213946 | ||||||||
\(199\) | 22.2199 | 1.57513 | 0.787564 | − | 0.616233i | \(-0.211342\pi\) | ||||
0.787564 | + | 0.616233i | \(0.211342\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.3568 | 1.22426 | ||||||||
\(202\) | −20.6338 | −1.45179 | ||||||||
\(203\) | 2.29813 | 0.161297 | ||||||||
\(204\) | −3.60102 | −0.252122 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −14.2978 | −0.996177 | ||||||||
\(207\) | −1.34457 | −0.0934540 | ||||||||
\(208\) | −8.87169 | −0.615141 | ||||||||
\(209\) | 3.78788 | 0.262013 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.3521 | 1.12572 | 0.562862 | − | 0.826551i | \(-0.309700\pi\) | ||||
0.562862 | + | 0.826551i | \(0.309700\pi\) | |||||||
\(212\) | 1.35927 | 0.0933553 | ||||||||
\(213\) | −6.03361 | −0.413416 | ||||||||
\(214\) | −0.318218 | −0.0217530 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −17.1220 | −1.16501 | ||||||||
\(217\) | −2.49162 | −0.169142 | ||||||||
\(218\) | −15.1519 | −1.02622 | ||||||||
\(219\) | −17.6956 | −1.19576 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.9638 | 1.20837 | ||||||||
\(222\) | −11.5914 | −0.777963 | ||||||||
\(223\) | −20.0149 | −1.34030 | −0.670150 | − | 0.742226i | \(-0.733770\pi\) | ||||
−0.670150 | + | 0.742226i | \(0.733770\pi\) | |||||||
\(224\) | −2.78624 | −0.186163 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.1663 | 1.07537 | ||||||||
\(227\) | 11.6552 | 0.773584 | 0.386792 | − | 0.922167i | \(-0.373583\pi\) | ||||
0.386792 | + | 0.922167i | \(0.373583\pi\) | |||||||
\(228\) | 1.34597 | 0.0891392 | ||||||||
\(229\) | −5.91727 | −0.391024 | −0.195512 | − | 0.980701i | \(-0.562637\pi\) | ||||
−0.195512 | + | 0.980701i | \(0.562637\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.35677 | −0.155064 | ||||||||
\(232\) | 7.03927 | 0.462151 | ||||||||
\(233\) | 19.8087 | 1.29771 | 0.648854 | − | 0.760913i | \(-0.275249\pi\) | ||||
0.648854 | + | 0.760913i | \(0.275249\pi\) | |||||||
\(234\) | 5.33641 | 0.348852 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.62810 | −0.171075 | ||||||||
\(237\) | 6.82402 | 0.443268 | ||||||||
\(238\) | −6.76266 | −0.438358 | ||||||||
\(239\) | 11.0911 | 0.717424 | 0.358712 | − | 0.933448i | \(-0.383216\pi\) | ||||
0.358712 | + | 0.933448i | \(0.383216\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.1624 | 1.10553 | 0.552764 | − | 0.833338i | \(-0.313573\pi\) | ||||
0.552764 | + | 0.833338i | \(0.313573\pi\) | |||||||
\(242\) | 9.34453 | 0.600689 | ||||||||
\(243\) | 12.7059 | 0.815083 | ||||||||
\(244\) | 5.76894 | 0.369319 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −18.0072 | −1.14810 | ||||||||
\(247\) | −6.71441 | −0.427228 | ||||||||
\(248\) | −7.63195 | −0.484629 | ||||||||
\(249\) | 15.1593 | 0.960682 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.4425 | 0.785364 | 0.392682 | − | 0.919674i | \(-0.371547\pi\) | ||||
0.392682 | + | 0.919674i | \(0.371547\pi\) | |||||||
\(252\) | 0.680188 | 0.0428478 | ||||||||
\(253\) | −1.83173 | −0.115160 | ||||||||
\(254\) | −9.00637 | −0.565110 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.2988 | −0.706176 | ||||||||
\(257\) | −5.76924 | −0.359876 | −0.179938 | − | 0.983678i | \(-0.557590\pi\) | ||||
−0.179938 | + | 0.983678i | \(0.557590\pi\) | |||||||
\(258\) | 6.04542 | 0.376371 | ||||||||
\(259\) | 7.37033 | 0.457970 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.09000 | −0.191266 | ||||||||
\(262\) | −24.4189 | −1.50860 | ||||||||
\(263\) | −9.57794 | −0.590601 | −0.295301 | − | 0.955404i | \(-0.595420\pi\) | ||||
−0.295301 | + | 0.955404i | \(0.595420\pi\) | |||||||
\(264\) | −7.21888 | −0.444291 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.52772 | 0.154984 | ||||||||
\(267\) | −16.0180 | −0.980285 | ||||||||
\(268\) | −6.82434 | −0.416863 | ||||||||
\(269\) | −6.93406 | −0.422777 | −0.211388 | − | 0.977402i | \(-0.567799\pi\) | ||||
−0.211388 | + | 0.977402i | \(0.567799\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.6107 | 0.826789 | 0.413395 | − | 0.910552i | \(-0.364343\pi\) | ||||
0.413395 | + | 0.910552i | \(0.364343\pi\) | |||||||
\(272\) | −15.1167 | −0.916586 | ||||||||
\(273\) | 4.17762 | 0.252841 | ||||||||
\(274\) | 17.5299 | 1.05902 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.650880 | −0.0391784 | ||||||||
\(277\) | 4.68173 | 0.281298 | 0.140649 | − | 0.990060i | \(-0.455081\pi\) | ||||
0.140649 | + | 0.990060i | \(0.455081\pi\) | |||||||
\(278\) | 7.19291 | 0.431402 | ||||||||
\(279\) | 3.35016 | 0.200569 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.3490 | −1.09461 | −0.547306 | − | 0.836933i | \(-0.684347\pi\) | ||||
−0.547306 | + | 0.836933i | \(0.684347\pi\) | |||||||
\(282\) | 9.04744 | 0.538767 | ||||||||
\(283\) | −0.485253 | −0.0288453 | −0.0144227 | − | 0.999896i | \(-0.504591\pi\) | ||||
−0.0144227 | + | 0.999896i | \(0.504591\pi\) | |||||||
\(284\) | 2.37229 | 0.140769 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.26988 | 0.429877 | ||||||||
\(287\) | 11.4498 | 0.675859 | ||||||||
\(288\) | 3.74629 | 0.220752 | ||||||||
\(289\) | 13.6090 | 0.800528 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0521 | 0.706504 | ||||||||
\(292\) | 6.95755 | 0.407160 | ||||||||
\(293\) | 27.8795 | 1.62874 | 0.814369 | − | 0.580347i | \(-0.197083\pi\) | ||||
0.814369 | + | 0.580347i | \(0.197083\pi\) | |||||||
\(294\) | −1.57271 | −0.0917223 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 22.5756 | 1.31218 | ||||||||
\(297\) | 10.2391 | 0.594135 | ||||||||
\(298\) | 23.6478 | 1.36988 | ||||||||
\(299\) | 3.24693 | 0.187775 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.84395 | −0.221562 | ||||||||
\(302\) | −15.2709 | −0.878743 | ||||||||
\(303\) | 21.7191 | 1.24773 | ||||||||
\(304\) | 5.65026 | 0.324065 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.09286 | 0.519804 | ||||||||
\(307\) | −11.9358 | −0.681209 | −0.340605 | − | 0.940207i | \(-0.610632\pi\) | ||||
−0.340605 | + | 0.940207i | \(0.610632\pi\) | |||||||
\(308\) | 0.926631 | 0.0527997 | ||||||||
\(309\) | 15.0499 | 0.856157 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.2818 | −0.753142 | −0.376571 | − | 0.926388i | \(-0.622897\pi\) | ||||
−0.376571 | + | 0.926388i | \(0.622897\pi\) | |||||||
\(312\) | 12.7962 | 0.724443 | ||||||||
\(313\) | 32.8495 | 1.85676 | 0.928382 | − | 0.371628i | \(-0.121200\pi\) | ||||
0.928382 | + | 0.371628i | \(0.121200\pi\) | |||||||
\(314\) | 7.20316 | 0.406498 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.68306 | −0.150934 | ||||||||
\(317\) | 3.92301 | 0.220338 | 0.110169 | − | 0.993913i | \(-0.464861\pi\) | ||||
0.110169 | + | 0.993913i | \(0.464861\pi\) | |||||||
\(318\) | 4.22581 | 0.236972 | ||||||||
\(319\) | −4.20955 | −0.235690 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.334956 | 0.0186954 | ||||||||
\(322\) | −1.22234 | −0.0681185 | ||||||||
\(323\) | −11.4409 | −0.636588 | ||||||||
\(324\) | 1.59778 | 0.0887655 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −19.3291 | −1.07054 | ||||||||
\(327\) | 15.9489 | 0.881976 | ||||||||
\(328\) | 35.0712 | 1.93648 | ||||||||
\(329\) | −5.75277 | −0.317161 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.3199 | −1.61157 | −0.805783 | − | 0.592211i | \(-0.798255\pi\) | ||||
−0.805783 | + | 0.592211i | \(0.798255\pi\) | |||||||
\(332\) | −5.96032 | −0.327115 | ||||||||
\(333\) | −9.90991 | −0.543060 | ||||||||
\(334\) | −13.9055 | −0.760877 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.51552 | −0.191787 | ||||||||
\(337\) | 25.7628 | 1.40339 | 0.701695 | − | 0.712477i | \(-0.252427\pi\) | ||||
0.701695 | + | 0.712477i | \(0.252427\pi\) | |||||||
\(338\) | 3.00385 | 0.163388 | ||||||||
\(339\) | −17.0166 | −0.924217 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.56398 | 0.247153 | ||||||||
\(342\) | −3.39869 | −0.183780 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −11.7742 | −0.634822 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.55772 | 0.191264 | ||||||||
\(347\) | 5.39327 | 0.289526 | 0.144763 | − | 0.989466i | \(-0.453758\pi\) | ||||
0.144763 | + | 0.989466i | \(0.453758\pi\) | |||||||
\(348\) | −1.49581 | −0.0801837 | ||||||||
\(349\) | 10.7377 | 0.574773 | 0.287387 | − | 0.957815i | \(-0.407214\pi\) | ||||
0.287387 | + | 0.957815i | \(0.407214\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.1499 | −0.968772 | ||||||||
\(352\) | 5.10363 | 0.272024 | ||||||||
\(353\) | −12.4467 | −0.662470 | −0.331235 | − | 0.943548i | \(-0.607465\pi\) | ||||
−0.331235 | + | 0.943548i | \(0.607465\pi\) | |||||||
\(354\) | −8.17043 | −0.434253 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.29794 | 0.333790 | ||||||||
\(357\) | 7.11836 | 0.376744 | ||||||||
\(358\) | −13.0316 | −0.688740 | ||||||||
\(359\) | 28.0071 | 1.47816 | 0.739080 | − | 0.673618i | \(-0.235261\pi\) | ||||
0.739080 | + | 0.673618i | \(0.235261\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.7237 | −0.774931 | ||||||||
\(362\) | −25.8471 | −1.35850 | ||||||||
\(363\) | −9.83604 | −0.516258 | ||||||||
\(364\) | −1.64255 | −0.0860930 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 17.9349 | 0.937473 | ||||||||
\(367\) | 14.2872 | 0.745788 | 0.372894 | − | 0.927874i | \(-0.378366\pi\) | ||||
0.372894 | + | 0.927874i | \(0.378366\pi\) | |||||||
\(368\) | −2.73233 | −0.142433 | ||||||||
\(369\) | −15.3950 | −0.801433 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.68696 | −0.139500 | ||||||||
\(372\) | 1.62175 | 0.0840838 | ||||||||
\(373\) | −14.3470 | −0.742862 | −0.371431 | − | 0.928461i | \(-0.621133\pi\) | ||||
−0.371431 | + | 0.928461i | \(0.621133\pi\) | |||||||
\(374\) | 12.3874 | 0.640535 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.6210 | −0.908733 | ||||||||
\(377\) | 7.46187 | 0.384306 | ||||||||
\(378\) | 6.83275 | 0.351439 | ||||||||
\(379\) | 16.1205 | 0.828057 | 0.414028 | − | 0.910264i | \(-0.364121\pi\) | ||||
0.414028 | + | 0.910264i | \(0.364121\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.48009 | 0.485680 | ||||||||
\(382\) | 13.4588 | 0.688613 | ||||||||
\(383\) | −33.2713 | −1.70008 | −0.850041 | − | 0.526716i | \(-0.823423\pi\) | ||||
−0.850041 | + | 0.526716i | \(0.823423\pi\) | |||||||
\(384\) | −6.78082 | −0.346032 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.62085 | 0.489689 | ||||||||
\(387\) | 5.16846 | 0.262727 | ||||||||
\(388\) | −4.73861 | −0.240567 | ||||||||
\(389\) | −22.6075 | −1.14625 | −0.573123 | − | 0.819469i | \(-0.694268\pi\) | ||||
−0.573123 | + | 0.819469i | \(0.694268\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.53254 | 0.279792 | ||||||||
\(392\) | 3.06304 | 0.154707 | ||||||||
\(393\) | 25.7032 | 1.29656 | ||||||||
\(394\) | −8.09281 | −0.407710 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.24592 | −0.0626098 | ||||||||
\(397\) | −21.9272 | −1.10050 | −0.550248 | − | 0.835001i | \(-0.685467\pi\) | ||||
−0.550248 | + | 0.835001i | \(0.685467\pi\) | |||||||
\(398\) | −27.1603 | −1.36143 | ||||||||
\(399\) | −2.66067 | −0.133200 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.61845 | −0.180697 | −0.0903483 | − | 0.995910i | \(-0.528798\pi\) | ||||
−0.0903483 | + | 0.995910i | \(0.528798\pi\) | |||||||
\(402\) | −21.2160 | −1.05816 | ||||||||
\(403\) | −8.09013 | −0.402998 | ||||||||
\(404\) | −8.53950 | −0.424856 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.80910 | −0.139414 | ||||||||
\(407\) | −13.5004 | −0.669192 | ||||||||
\(408\) | 21.8038 | 1.07945 | ||||||||
\(409\) | 27.0595 | 1.33801 | 0.669003 | − | 0.743259i | \(-0.266721\pi\) | ||||
0.669003 | + | 0.743259i | \(0.266721\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.4519 | −0.910166 | ||||||||
\(412\) | −5.91729 | −0.291524 | ||||||||
\(413\) | 5.19513 | 0.255636 | ||||||||
\(414\) | 1.64352 | 0.0807748 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9.04672 | −0.443552 | ||||||||
\(417\) | −7.57124 | −0.370765 | ||||||||
\(418\) | −4.63009 | −0.226465 | ||||||||
\(419\) | 16.2266 | 0.792724 | 0.396362 | − | 0.918094i | \(-0.370273\pi\) | ||||
0.396362 | + | 0.918094i | \(0.370273\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.0320 | −1.36619 | −0.683097 | − | 0.730328i | \(-0.739367\pi\) | ||||
−0.683097 | + | 0.730328i | \(0.739367\pi\) | |||||||
\(422\) | −19.9879 | −0.972994 | ||||||||
\(423\) | 7.73500 | 0.376088 | ||||||||
\(424\) | −8.23028 | −0.399698 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.37515 | 0.357327 | ||||||||
\(427\) | −11.4038 | −0.551870 | ||||||||
\(428\) | −0.131698 | −0.00636584 | ||||||||
\(429\) | −7.65226 | −0.369454 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.31498 | 0.448687 | 0.224343 | − | 0.974510i | \(-0.427976\pi\) | ||||
0.224343 | + | 0.974510i | \(0.427976\pi\) | |||||||
\(432\) | 15.2734 | 0.734842 | ||||||||
\(433\) | 3.91036 | 0.187920 | 0.0939600 | − | 0.995576i | \(-0.470047\pi\) | ||||
0.0939600 | + | 0.995576i | \(0.470047\pi\) | |||||||
\(434\) | 3.04562 | 0.146194 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.27077 | −0.300315 | ||||||||
\(437\) | −2.06793 | −0.0989223 | ||||||||
\(438\) | 21.6302 | 1.03353 | ||||||||
\(439\) | 24.9948 | 1.19294 | 0.596469 | − | 0.802636i | \(-0.296570\pi\) | ||||
0.596469 | + | 0.802636i | \(0.296570\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.34457 | −0.0640271 | ||||||||
\(442\) | −21.9579 | −1.04443 | ||||||||
\(443\) | 22.6965 | 1.07834 | 0.539171 | − | 0.842196i | \(-0.318738\pi\) | ||||
0.539171 | + | 0.842196i | \(0.318738\pi\) | |||||||
\(444\) | −4.79720 | −0.227665 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 24.4651 | 1.15846 | ||||||||
\(447\) | −24.8916 | −1.17733 | ||||||||
\(448\) | 8.87040 | 0.419087 | ||||||||
\(449\) | 11.1526 | 0.526323 | 0.263161 | − | 0.964752i | \(-0.415235\pi\) | ||||
0.263161 | + | 0.964752i | \(0.415235\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.9729 | −0.987575 | ||||||||
\(452\) | 6.69058 | 0.314699 | ||||||||
\(453\) | 16.0741 | 0.755229 | ||||||||
\(454\) | −14.2467 | −0.668629 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.14974 | −0.381646 | ||||||||
\(457\) | 22.3240 | 1.04427 | 0.522136 | − | 0.852862i | \(-0.325135\pi\) | ||||
0.522136 | + | 0.852862i | \(0.325135\pi\) | |||||||
\(458\) | 7.23294 | 0.337973 | ||||||||
\(459\) | −30.9262 | −1.44351 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.79562 | 0.0836303 | 0.0418151 | − | 0.999125i | \(-0.486686\pi\) | ||||
0.0418151 | + | 0.999125i | \(0.486686\pi\) | |||||||
\(462\) | 2.88078 | 0.134026 | ||||||||
\(463\) | 16.5492 | 0.769106 | 0.384553 | − | 0.923103i | \(-0.374356\pi\) | ||||
0.384553 | + | 0.923103i | \(0.374356\pi\) | |||||||
\(464\) | −6.27926 | −0.291507 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.2130 | −1.12164 | ||||||||
\(467\) | −13.8185 | −0.639446 | −0.319723 | − | 0.947511i | \(-0.603590\pi\) | ||||
−0.319723 | + | 0.947511i | \(0.603590\pi\) | |||||||
\(468\) | 2.20852 | 0.102089 | ||||||||
\(469\) | 13.4901 | 0.622915 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.58203 | −0.349361 | ||||||||
\(472\) | 15.9129 | 0.732450 | ||||||||
\(473\) | 7.04107 | 0.323749 | ||||||||
\(474\) | −8.34129 | −0.383128 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.79879 | −0.128282 | ||||||||
\(477\) | 3.61281 | 0.165419 | ||||||||
\(478\) | −13.5571 | −0.620089 | ||||||||
\(479\) | 37.2072 | 1.70004 | 0.850020 | − | 0.526750i | \(-0.176590\pi\) | ||||
0.850020 | + | 0.526750i | \(0.176590\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.9309 | 1.09116 | ||||||||
\(482\) | −20.9784 | −0.955538 | ||||||||
\(483\) | 1.28664 | 0.0585439 | ||||||||
\(484\) | 3.86732 | 0.175787 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −15.5309 | −0.704498 | ||||||||
\(487\) | 8.57640 | 0.388634 | 0.194317 | − | 0.980939i | \(-0.437751\pi\) | ||||
0.194317 | + | 0.980939i | \(0.437751\pi\) | |||||||
\(488\) | −34.9304 | −1.58123 | ||||||||
\(489\) | 20.3458 | 0.920069 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.32697 | −0.150144 | −0.0750720 | − | 0.997178i | \(-0.523919\pi\) | ||||
−0.0750720 | + | 0.997178i | \(0.523919\pi\) | |||||||
\(492\) | −7.45244 | −0.335982 | ||||||||
\(493\) | 12.7145 | 0.572632 | ||||||||
\(494\) | 8.20731 | 0.369264 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.80794 | 0.305686 | ||||||||
\(497\) | −4.68945 | −0.210351 | ||||||||
\(498\) | −18.5299 | −0.830344 | ||||||||
\(499\) | 26.9826 | 1.20791 | 0.603954 | − | 0.797019i | \(-0.293591\pi\) | ||||
0.603954 | + | 0.797019i | \(0.293591\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.6369 | 0.653930 | ||||||||
\(502\) | −15.2090 | −0.678811 | ||||||||
\(503\) | −1.73343 | −0.0772897 | −0.0386449 | − | 0.999253i | \(-0.512304\pi\) | ||||
−0.0386449 | + | 0.999253i | \(0.512304\pi\) | |||||||
\(504\) | −4.11847 | −0.183451 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.23900 | 0.0995357 | ||||||||
\(507\) | −3.16184 | −0.140422 | ||||||||
\(508\) | −3.72737 | −0.165375 | ||||||||
\(509\) | −14.2686 | −0.632444 | −0.316222 | − | 0.948685i | \(-0.602414\pi\) | ||||
−0.316222 | + | 0.948685i | \(0.602414\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.7534 | −0.608416 | ||||||||
\(512\) | 24.3514 | 1.07619 | ||||||||
\(513\) | 11.5595 | 0.510362 | ||||||||
\(514\) | 7.05200 | 0.311050 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.50195 | 0.110142 | ||||||||
\(517\) | 10.5375 | 0.463439 | ||||||||
\(518\) | −9.00907 | −0.395836 | ||||||||
\(519\) | −3.74484 | −0.164380 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.9174 | −0.478300 | −0.239150 | − | 0.970983i | \(-0.576869\pi\) | ||||
−0.239150 | + | 0.970983i | \(0.576869\pi\) | |||||||
\(522\) | 3.77703 | 0.165316 | ||||||||
\(523\) | −29.9714 | −1.31056 | −0.655278 | − | 0.755388i | \(-0.727449\pi\) | ||||
−0.655278 | + | 0.755388i | \(0.727449\pi\) | |||||||
\(524\) | −10.1060 | −0.441481 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.7075 | 0.510473 | ||||||||
\(527\) | −13.7850 | −0.600484 | ||||||||
\(528\) | 6.43947 | 0.280242 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.98521 | −0.303132 | ||||||||
\(532\) | 1.04612 | 0.0453550 | ||||||||
\(533\) | 37.1766 | 1.61030 | ||||||||
\(534\) | 19.5795 | 0.847287 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 41.3208 | 1.78478 | ||||||||
\(537\) | 13.7170 | 0.591933 | ||||||||
\(538\) | 8.47580 | 0.365418 | ||||||||
\(539\) | −1.83173 | −0.0788981 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.6528 | −0.715962 | −0.357981 | − | 0.933729i | \(-0.616535\pi\) | ||||
−0.357981 | + | 0.933729i | \(0.616535\pi\) | |||||||
\(542\) | −16.6369 | −0.714616 | ||||||||
\(543\) | 27.2066 | 1.16755 | ||||||||
\(544\) | −15.4150 | −0.660911 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.10648 | −0.218537 | ||||||||
\(547\) | 32.1095 | 1.37290 | 0.686451 | − | 0.727176i | \(-0.259168\pi\) | ||||
0.686451 | + | 0.727176i | \(0.259168\pi\) | |||||||
\(548\) | 7.25490 | 0.309914 | ||||||||
\(549\) | 15.3332 | 0.654407 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.75237 | −0.202458 | ||||||||
\(552\) | 3.94102 | 0.167741 | ||||||||
\(553\) | 5.30377 | 0.225539 | ||||||||
\(554\) | −5.72268 | −0.243134 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.97685 | 0.126247 | ||||||||
\(557\) | −12.5917 | −0.533529 | −0.266765 | − | 0.963762i | \(-0.585955\pi\) | ||||
−0.266765 | + | 0.963762i | \(0.585955\pi\) | |||||||
\(558\) | −4.09504 | −0.173357 | ||||||||
\(559\) | −12.4810 | −0.527892 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.0389 | −0.550503 | ||||||||
\(562\) | 22.4288 | 0.946102 | ||||||||
\(563\) | 26.3644 | 1.11113 | 0.555563 | − | 0.831474i | \(-0.312503\pi\) | ||||
0.555563 | + | 0.831474i | \(0.312503\pi\) | |||||||
\(564\) | 3.74437 | 0.157666 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.593146 | 0.0249318 | ||||||||
\(567\) | −3.15843 | −0.132642 | ||||||||
\(568\) | −14.3640 | −0.602699 | ||||||||
\(569\) | −25.7791 | −1.08071 | −0.540357 | − | 0.841436i | \(-0.681711\pi\) | ||||
−0.540357 | + | 0.841436i | \(0.681711\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.2960 | 1.72818 | 0.864092 | − | 0.503334i | \(-0.167893\pi\) | ||||
0.864092 | + | 0.503334i | \(0.167893\pi\) | |||||||
\(572\) | 3.00870 | 0.125800 | ||||||||
\(573\) | −14.1667 | −0.591823 | ||||||||
\(574\) | −13.9956 | −0.584163 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.9269 | −0.496953 | ||||||||
\(577\) | 10.2107 | 0.425076 | 0.212538 | − | 0.977153i | \(-0.431827\pi\) | ||||
0.212538 | + | 0.977153i | \(0.431827\pi\) | |||||||
\(578\) | −16.6348 | −0.691918 | ||||||||
\(579\) | −10.1269 | −0.420859 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.7821 | 0.488805 | ||||||||
\(582\) | −14.7317 | −0.610650 | ||||||||
\(583\) | 4.92178 | 0.203839 | ||||||||
\(584\) | −42.1273 | −1.74324 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −34.0783 | −1.40776 | ||||||||
\(587\) | −10.4814 | −0.432612 | −0.216306 | − | 0.976326i | \(-0.569401\pi\) | ||||
−0.216306 | + | 0.976326i | \(0.569401\pi\) | |||||||
\(588\) | −0.650880 | −0.0268419 | ||||||||
\(589\) | 5.15249 | 0.212305 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.51848 | 0.350403 | ||||||||
\(592\) | −20.1382 | −0.827674 | ||||||||
\(593\) | −8.27127 | −0.339660 | −0.169830 | − | 0.985473i | \(-0.554322\pi\) | ||||
−0.169830 | + | 0.985473i | \(0.554322\pi\) | |||||||
\(594\) | −12.5157 | −0.513527 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.78686 | 0.400885 | ||||||||
\(597\) | 28.5889 | 1.17007 | ||||||||
\(598\) | −3.96886 | −0.162299 | ||||||||
\(599\) | −21.5408 | −0.880132 | −0.440066 | − | 0.897965i | \(-0.645045\pi\) | ||||
−0.440066 | + | 0.897965i | \(0.645045\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.9173 | 1.13877 | 0.569385 | − | 0.822071i | \(-0.307181\pi\) | ||||
0.569385 | + | 0.822071i | \(0.307181\pi\) | |||||||
\(602\) | 4.69863 | 0.191502 | ||||||||
\(603\) | −18.1384 | −0.738652 | ||||||||
\(604\) | −6.32001 | −0.257157 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −26.5482 | −1.07845 | ||||||||
\(607\) | −12.0650 | −0.489705 | −0.244852 | − | 0.969560i | \(-0.578739\pi\) | ||||
−0.244852 | + | 0.969560i | \(0.578739\pi\) | |||||||
\(608\) | 5.76173 | 0.233669 | ||||||||
\(609\) | 2.95686 | 0.119818 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.6788 | −0.755665 | ||||||||
\(612\) | 3.76316 | 0.152117 | ||||||||
\(613\) | 18.2200 | 0.735900 | 0.367950 | − | 0.929846i | \(-0.380060\pi\) | ||||
0.367950 | + | 0.929846i | \(0.380060\pi\) | |||||||
\(614\) | 14.5896 | 0.588788 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.61066 | −0.226060 | ||||||||
\(617\) | −2.56162 | −0.103127 | −0.0515634 | − | 0.998670i | \(-0.516420\pi\) | ||||
−0.0515634 | + | 0.998670i | \(0.516420\pi\) | |||||||
\(618\) | −18.3961 | −0.740000 | ||||||||
\(619\) | −4.51140 | −0.181328 | −0.0906642 | − | 0.995882i | \(-0.528899\pi\) | ||||
−0.0906642 | + | 0.995882i | \(0.528899\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.58988 | −0.224314 | ||||||||
\(622\) | 16.2349 | 0.650961 | ||||||||
\(623\) | −12.4495 | −0.498779 | ||||||||
\(624\) | −11.4146 | −0.456951 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −40.1534 | −1.60485 | ||||||||
\(627\) | 4.87362 | 0.194634 | ||||||||
\(628\) | 2.98109 | 0.118959 | ||||||||
\(629\) | 40.7766 | 1.62587 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.72514 | −0.0686766 | −0.0343383 | − | 0.999410i | \(-0.510932\pi\) | ||||
−0.0343383 | + | 0.999410i | \(0.510932\pi\) | |||||||
\(632\) | 16.2457 | 0.646218 | ||||||||
\(633\) | 21.0392 | 0.836232 | ||||||||
\(634\) | −4.79526 | −0.190444 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.74889 | 0.0693480 | ||||||||
\(637\) | 3.24693 | 0.128648 | ||||||||
\(638\) | 5.14552 | 0.203713 | ||||||||
\(639\) | 6.30529 | 0.249433 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.13847 | −0.242455 | −0.121227 | − | 0.992625i | \(-0.538683\pi\) | ||||
−0.121227 | + | 0.992625i | \(0.538683\pi\) | |||||||
\(642\) | −0.409431 | −0.0161590 | ||||||||
\(643\) | 1.81209 | 0.0714620 | 0.0357310 | − | 0.999361i | \(-0.488624\pi\) | ||||
0.0357310 | + | 0.999361i | \(0.488624\pi\) | |||||||
\(644\) | −0.505878 | −0.0199344 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.9847 | 0.550220 | ||||||||
\(647\) | −3.41295 | −0.134177 | −0.0670885 | − | 0.997747i | \(-0.521371\pi\) | ||||
−0.0670885 | + | 0.997747i | \(0.521371\pi\) | |||||||
\(648\) | −9.67440 | −0.380046 | ||||||||
\(649\) | −9.51606 | −0.373538 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.20581 | −0.125646 | ||||||||
\(652\) | −7.99954 | −0.313286 | ||||||||
\(653\) | −2.90584 | −0.113714 | −0.0568572 | − | 0.998382i | \(-0.518108\pi\) | ||||
−0.0568572 | + | 0.998382i | \(0.518108\pi\) | |||||||
\(654\) | −19.4950 | −0.762315 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −31.2846 | −1.22146 | ||||||||
\(657\) | 18.4924 | 0.721458 | ||||||||
\(658\) | 7.03186 | 0.274130 | ||||||||
\(659\) | −31.6685 | −1.23363 | −0.616814 | − | 0.787109i | \(-0.711577\pi\) | ||||
−0.616814 | + | 0.787109i | \(0.711577\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.28949 | −0.0890508 | −0.0445254 | − | 0.999008i | \(-0.514178\pi\) | ||||
−0.0445254 | + | 0.999008i | \(0.514178\pi\) | |||||||
\(662\) | 35.8389 | 1.39292 | ||||||||
\(663\) | 23.1128 | 0.897627 | ||||||||
\(664\) | 36.0892 | 1.40053 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.1133 | 0.469381 | ||||||||
\(667\) | 2.29813 | 0.0889840 | ||||||||
\(668\) | −5.75493 | −0.222665 | ||||||||
\(669\) | −25.7519 | −0.995628 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.8887 | 0.806400 | ||||||||
\(672\) | −3.58487 | −0.138289 | ||||||||
\(673\) | −37.1348 | −1.43144 | −0.715721 | − | 0.698386i | \(-0.753902\pi\) | ||||
−0.715721 | + | 0.698386i | \(0.753902\pi\) | |||||||
\(674\) | −31.4910 | −1.21299 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.24317 | 0.0478142 | ||||||||
\(677\) | −20.5072 | −0.788154 | −0.394077 | − | 0.919077i | \(-0.628936\pi\) | ||||
−0.394077 | + | 0.919077i | \(0.628936\pi\) | |||||||
\(678\) | 20.8002 | 0.798826 | ||||||||
\(679\) | 9.36711 | 0.359477 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.9960 | 0.574648 | ||||||||
\(682\) | −5.57875 | −0.213621 | ||||||||
\(683\) | −36.7749 | −1.40715 | −0.703577 | − | 0.710619i | \(-0.748415\pi\) | ||||
−0.703577 | + | 0.710619i | \(0.748415\pi\) | |||||||
\(684\) | −1.40658 | −0.0537818 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.22234 | −0.0466693 | ||||||||
\(687\) | −7.61338 | −0.290468 | ||||||||
\(688\) | 10.5030 | 0.400421 | ||||||||
\(689\) | −8.72438 | −0.332372 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.44402 | −0.169059 | −0.0845293 | − | 0.996421i | \(-0.526939\pi\) | ||||
−0.0845293 | + | 0.996421i | \(0.526939\pi\) | |||||||
\(692\) | 1.47239 | 0.0559720 | ||||||||
\(693\) | 2.46288 | 0.0935573 | ||||||||
\(694\) | −6.59242 | −0.250245 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 9.05698 | 0.343304 | ||||||||
\(697\) | 63.3463 | 2.39941 | ||||||||
\(698\) | −13.1251 | −0.496792 | ||||||||
\(699\) | 25.4865 | 0.963989 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.33291 | 0.201421 | 0.100711 | − | 0.994916i | \(-0.467888\pi\) | ||||
0.100711 | + | 0.994916i | \(0.467888\pi\) | |||||||
\(702\) | 22.1854 | 0.837336 | ||||||||
\(703\) | −15.2413 | −0.574836 | ||||||||
\(704\) | −16.2482 | −0.612376 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.2141 | 0.572591 | ||||||||
\(707\) | 16.8806 | 0.634859 | ||||||||
\(708\) | −3.38141 | −0.127081 | ||||||||
\(709\) | −17.4747 | −0.656276 | −0.328138 | − | 0.944630i | \(-0.606421\pi\) | ||||
−0.328138 | + | 0.944630i | \(0.606421\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.13128 | −0.267444 | ||||||||
\(712\) | −38.1334 | −1.42911 | ||||||||
\(713\) | −2.49162 | −0.0933120 | ||||||||
\(714\) | −8.70108 | −0.325630 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.39324 | −0.201555 | ||||||||
\(717\) | 14.2702 | 0.532930 | ||||||||
\(718\) | −34.2343 | −1.27761 | ||||||||
\(719\) | 20.0248 | 0.746797 | 0.373399 | − | 0.927671i | \(-0.378192\pi\) | ||||
0.373399 | + | 0.927671i | \(0.378192\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.6971 | 0.435622 | ||||||||
\(722\) | 17.9974 | 0.669793 | ||||||||
\(723\) | 22.0818 | 0.821230 | ||||||||
\(724\) | −10.6971 | −0.397554 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 12.0230 | 0.446216 | ||||||||
\(727\) | −21.4754 | −0.796479 | −0.398240 | − | 0.917281i | \(-0.630379\pi\) | ||||
−0.398240 | + | 0.917281i | \(0.630379\pi\) | |||||||
\(728\) | 9.94548 | 0.368604 | ||||||||
\(729\) | 25.8231 | 0.956412 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.2668 | −0.786581 | ||||||||
\(732\) | 7.42253 | 0.274345 | ||||||||
\(733\) | 15.8543 | 0.585594 | 0.292797 | − | 0.956175i | \(-0.405414\pi\) | ||||
0.292797 | + | 0.956175i | \(0.405414\pi\) | |||||||
\(734\) | −17.4639 | −0.644605 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.78624 | −0.102702 | ||||||||
\(737\) | −24.7102 | −0.910212 | ||||||||
\(738\) | 18.8180 | 0.692700 | ||||||||
\(739\) | −8.79859 | −0.323661 | −0.161831 | − | 0.986819i | \(-0.551740\pi\) | ||||
−0.161831 | + | 0.986819i | \(0.551740\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.63900 | −0.317362 | ||||||||
\(742\) | 3.28439 | 0.120574 | ||||||||
\(743\) | 33.6377 | 1.23405 | 0.617024 | − | 0.786945i | \(-0.288338\pi\) | ||||
0.617024 | + | 0.786945i | \(0.288338\pi\) | |||||||
\(744\) | −9.81954 | −0.360002 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.5370 | 0.642076 | ||||||||
\(747\) | −15.8419 | −0.579624 | ||||||||
\(748\) | 5.12662 | 0.187448 | ||||||||
\(749\) | 0.260335 | 0.00951243 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.6386 | −0.570662 | −0.285331 | − | 0.958429i | \(-0.592104\pi\) | ||||
−0.285331 | + | 0.958429i | \(0.592104\pi\) | |||||||
\(752\) | 15.7185 | 0.573194 | ||||||||
\(753\) | 16.0090 | 0.583399 | ||||||||
\(754\) | −9.12096 | −0.332166 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.82779 | 0.102846 | ||||||||
\(757\) | −8.01891 | −0.291452 | −0.145726 | − | 0.989325i | \(-0.546552\pi\) | ||||
−0.145726 | + | 0.989325i | \(0.546552\pi\) | |||||||
\(758\) | −19.7048 | −0.715712 | ||||||||
\(759\) | −2.35677 | −0.0855452 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.9368 | −0.903960 | −0.451980 | − | 0.892028i | \(-0.649282\pi\) | ||||
−0.451980 | + | 0.892028i | \(0.649282\pi\) | |||||||
\(762\) | −11.5879 | −0.419786 | ||||||||
\(763\) | 12.3958 | 0.448758 | ||||||||
\(764\) | 5.57005 | 0.201517 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 40.6689 | 1.46943 | ||||||||
\(767\) | 16.8682 | 0.609076 | ||||||||
\(768\) | −14.5375 | −0.524575 | ||||||||
\(769\) | 49.2378 | 1.77556 | 0.887781 | − | 0.460266i | \(-0.152246\pi\) | ||||
0.887781 | + | 0.460266i | \(0.152246\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.42292 | −0.267330 | ||||||||
\(772\) | 3.98168 | 0.143304 | ||||||||
\(773\) | −11.9397 | −0.429439 | −0.214720 | − | 0.976676i | \(-0.568884\pi\) | ||||
−0.214720 | + | 0.976676i | \(0.568884\pi\) | |||||||
\(774\) | −6.31763 | −0.227082 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 28.6918 | 1.02998 | ||||||||
\(777\) | 9.48293 | 0.340198 | ||||||||
\(778\) | 27.6341 | 0.990732 | ||||||||
\(779\) | −23.6773 | −0.848327 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.58980 | 0.307367 | ||||||||
\(782\) | −6.76266 | −0.241832 | ||||||||
\(783\) | −12.8463 | −0.459088 | ||||||||
\(784\) | −2.73233 | −0.0975833 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −31.4182 | −1.12065 | ||||||||
\(787\) | 29.9433 | 1.06736 | 0.533681 | − | 0.845686i | \(-0.320808\pi\) | ||||
0.533681 | + | 0.845686i | \(0.320808\pi\) | |||||||
\(788\) | −3.34928 | −0.119313 | ||||||||
\(789\) | −12.3233 | −0.438722 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.2257 | −0.470251 | ||||||||
\(792\) | 7.54392 | 0.268061 | ||||||||
\(793\) | −37.0274 | −1.31488 | ||||||||
\(794\) | 26.8026 | 0.951188 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.2406 | −0.398411 | ||||||||
\(797\) | −26.6201 | −0.942933 | −0.471467 | − | 0.881884i | \(-0.656275\pi\) | ||||
−0.471467 | + | 0.881884i | \(0.656275\pi\) | |||||||
\(798\) | 3.25225 | 0.115128 | ||||||||
\(799\) | −31.8274 | −1.12597 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.7392 | 0.591452 | ||||||||
\(802\) | 4.42298 | 0.156181 | ||||||||
\(803\) | 25.1925 | 0.889025 | ||||||||
\(804\) | −8.78044 | −0.309662 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.88891 | 0.348322 | ||||||||
\(807\) | −8.92161 | −0.314055 | ||||||||
\(808\) | 51.7059 | 1.81901 | ||||||||
\(809\) | −51.3101 | −1.80397 | −0.901984 | − | 0.431770i | \(-0.857889\pi\) | ||||
−0.901984 | + | 0.431770i | \(0.857889\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.55071 | 0.265141 | 0.132571 | − | 0.991174i | \(-0.457677\pi\) | ||||
0.132571 | + | 0.991174i | \(0.457677\pi\) | |||||||
\(812\) | −1.16257 | −0.0407983 | ||||||||
\(813\) | 17.5120 | 0.614172 | ||||||||
\(814\) | 16.5022 | 0.578401 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −19.4497 | −0.680876 | ||||||||
\(817\) | 7.94901 | 0.278101 | ||||||||
\(818\) | −33.0760 | −1.15648 | ||||||||
\(819\) | −4.36572 | −0.152551 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.3218 | −1.05824 | −0.529119 | − | 0.848548i | \(-0.677478\pi\) | ||||
−0.529119 | + | 0.848548i | \(0.677478\pi\) | |||||||
\(822\) | 22.5546 | 0.786681 | ||||||||
\(823\) | 10.7919 | 0.376182 | 0.188091 | − | 0.982152i | \(-0.439770\pi\) | ||||
0.188091 | + | 0.982152i | \(0.439770\pi\) | |||||||
\(824\) | 35.8286 | 1.24815 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.35023 | −0.220953 | ||||||||
\(827\) | −49.8826 | −1.73459 | −0.867293 | − | 0.497797i | \(-0.834142\pi\) | ||||
−0.867293 | + | 0.497797i | \(0.834142\pi\) | |||||||
\(828\) | 0.680188 | 0.0236382 | ||||||||
\(829\) | −31.6939 | −1.10078 | −0.550388 | − | 0.834909i | \(-0.685520\pi\) | ||||
−0.550388 | + | 0.834909i | \(0.685520\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.02368 | 0.208959 | ||||||||
\(832\) | 28.8016 | 0.998515 | ||||||||
\(833\) | 5.53254 | 0.191691 | ||||||||
\(834\) | 9.25465 | 0.320462 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.91620 | −0.0662733 | ||||||||
\(837\) | 13.9279 | 0.481418 | ||||||||
\(838\) | −19.8345 | −0.685172 | ||||||||
\(839\) | 1.58217 | 0.0546224 | 0.0273112 | − | 0.999627i | \(-0.491305\pi\) | ||||
0.0273112 | + | 0.999627i | \(0.491305\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.7186 | −0.817883 | ||||||||
\(842\) | 34.2647 | 1.18084 | ||||||||
\(843\) | −23.6085 | −0.813121 | ||||||||
\(844\) | −8.27216 | −0.284739 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.45482 | −0.325063 | ||||||||
\(847\) | −7.64477 | −0.262677 | ||||||||
\(848\) | 7.34167 | 0.252114 | ||||||||
\(849\) | −0.624344 | −0.0214274 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.37033 | 0.252652 | ||||||||
\(852\) | 3.05227 | 0.104569 | ||||||||
\(853\) | −15.6024 | −0.534215 | −0.267107 | − | 0.963667i | \(-0.586068\pi\) | ||||
−0.267107 | + | 0.963667i | \(0.586068\pi\) | |||||||
\(854\) | 13.9394 | 0.476996 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.797416 | 0.0272551 | ||||||||
\(857\) | 39.0023 | 1.33229 | 0.666147 | − | 0.745821i | \(-0.267942\pi\) | ||||
0.666147 | + | 0.745821i | \(0.267942\pi\) | |||||||
\(858\) | 9.35368 | 0.319329 | ||||||||
\(859\) | 29.7529 | 1.01516 | 0.507578 | − | 0.861606i | \(-0.330541\pi\) | ||||
0.507578 | + | 0.861606i | \(0.330541\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.7317 | 0.502055 | ||||||||
\(862\) | −11.3861 | −0.387812 | ||||||||
\(863\) | −27.6730 | −0.941999 | −0.471000 | − | 0.882133i | \(-0.656107\pi\) | ||||
−0.471000 | + | 0.882133i | \(0.656107\pi\) | |||||||
\(864\) | 15.5747 | 0.529863 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.77980 | −0.162424 | ||||||||
\(867\) | 17.5098 | 0.594663 | ||||||||
\(868\) | 1.26046 | 0.0427827 | ||||||||
\(869\) | −9.71506 | −0.329561 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.8014 | 1.48415 | ||||||||
\(872\) | 37.9689 | 1.28579 | ||||||||
\(873\) | −12.5947 | −0.426267 | ||||||||
\(874\) | 2.52772 | 0.0855012 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.95184 | 0.302454 | ||||||||
\(877\) | −3.88233 | −0.131097 | −0.0655486 | − | 0.997849i | \(-0.520880\pi\) | ||||
−0.0655486 | + | 0.997849i | \(0.520880\pi\) | |||||||
\(878\) | −30.5523 | −1.03109 | ||||||||
\(879\) | 35.8708 | 1.20989 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.3839 | −1.69748 | −0.848739 | − | 0.528812i | \(-0.822638\pi\) | ||||
−0.848739 | + | 0.528812i | \(0.822638\pi\) | |||||||
\(882\) | 1.64352 | 0.0553403 | ||||||||
\(883\) | −0.536806 | −0.0180650 | −0.00903248 | − | 0.999959i | \(-0.502875\pi\) | ||||
−0.00903248 | + | 0.999959i | \(0.502875\pi\) | |||||||
\(884\) | −9.08747 | −0.305645 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.7429 | −0.932041 | ||||||||
\(887\) | −13.9844 | −0.469551 | −0.234776 | − | 0.972050i | \(-0.575436\pi\) | ||||
−0.234776 | + | 0.972050i | \(0.575436\pi\) | |||||||
\(888\) | 29.0466 | 0.974740 | ||||||||
\(889\) | 7.36812 | 0.247119 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.78538 | 0.193818 | ||||||||
\(892\) | 10.1251 | 0.339014 | ||||||||
\(893\) | 11.8963 | 0.398095 | ||||||||
\(894\) | 30.4261 | 1.01760 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5.27020 | −0.176065 | ||||||||
\(897\) | 4.17762 | 0.139487 | ||||||||
\(898\) | −13.6323 | −0.454915 | ||||||||
\(899\) | −5.72608 | −0.190975 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.8657 | −0.495249 | ||||||||
\(902\) | 25.6361 | 0.853587 | ||||||||
\(903\) | −4.94577 | −0.164585 | ||||||||
\(904\) | −40.5108 | −1.34737 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −19.6481 | −0.652765 | ||||||||
\(907\) | −30.0013 | −0.996176 | −0.498088 | − | 0.867126i | \(-0.665964\pi\) | ||||
−0.498088 | + | 0.867126i | \(0.665964\pi\) | |||||||
\(908\) | −5.89611 | −0.195669 | ||||||||
\(909\) | −22.6971 | −0.752814 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.0932 | −0.765111 | −0.382555 | − | 0.923933i | \(-0.624956\pi\) | ||||
−0.382555 | + | 0.923933i | \(0.624956\pi\) | |||||||
\(912\) | 7.26983 | 0.240728 | ||||||||
\(913\) | −21.5817 | −0.714249 | ||||||||
\(914\) | −27.2876 | −0.902593 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.99342 | 0.0989053 | ||||||||
\(917\) | 19.9771 | 0.659702 | ||||||||
\(918\) | 37.8024 | 1.24767 | ||||||||
\(919\) | −22.8223 | −0.752837 | −0.376419 | − | 0.926450i | \(-0.622845\pi\) | ||||
−0.376419 | + | 0.926450i | \(0.622845\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.3570 | −0.506029 | ||||||||
\(922\) | −2.19486 | −0.0722839 | ||||||||
\(923\) | −15.2263 | −0.501180 | ||||||||
\(924\) | 1.19224 | 0.0392217 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −20.2288 | −0.664759 | ||||||||
\(927\) | −15.7275 | −0.516559 | ||||||||
\(928\) | −6.40314 | −0.210193 | ||||||||
\(929\) | 24.1707 | 0.793015 | 0.396508 | − | 0.918031i | \(-0.370222\pi\) | ||||
0.396508 | + | 0.918031i | \(0.370222\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.06793 | −0.0677736 | ||||||||
\(932\) | −10.0208 | −0.328241 | ||||||||
\(933\) | −17.0888 | −0.559463 | ||||||||
\(934\) | 16.8910 | 0.552690 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −13.3724 | −0.437090 | ||||||||
\(937\) | −26.9840 | −0.881530 | −0.440765 | − | 0.897622i | \(-0.645293\pi\) | ||||
−0.440765 | + | 0.897622i | \(0.645293\pi\) | |||||||
\(938\) | −16.4895 | −0.538402 | ||||||||
\(939\) | 42.2653 | 1.37928 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.4776 | −0.634950 | −0.317475 | − | 0.948267i | \(-0.602835\pi\) | ||||
−0.317475 | + | 0.948267i | \(0.602835\pi\) | |||||||
\(942\) | 9.26784 | 0.301962 | ||||||||
\(943\) | 11.4498 | 0.372856 | ||||||||
\(944\) | −14.1948 | −0.462002 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.60661 | −0.279825 | ||||||||
\(947\) | −37.7344 | −1.22620 | −0.613102 | − | 0.790004i | \(-0.710079\pi\) | ||||
−0.613102 | + | 0.790004i | \(0.710079\pi\) | |||||||
\(948\) | −3.45212 | −0.112120 | ||||||||
\(949\) | −44.6564 | −1.44961 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.04748 | 0.163676 | ||||||||
\(952\) | 16.9464 | 0.549236 | ||||||||
\(953\) | −58.4372 | −1.89297 | −0.946483 | − | 0.322754i | \(-0.895391\pi\) | ||||
−0.946483 | + | 0.322754i | \(0.895391\pi\) | |||||||
\(954\) | −4.41609 | −0.142976 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.61074 | −0.181464 | ||||||||
\(957\) | −5.41616 | −0.175080 | ||||||||
\(958\) | −45.4800 | −1.46939 | ||||||||
\(959\) | −14.3412 | −0.463102 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.7918 | −0.799736 | ||||||||
\(962\) | −29.2518 | −0.943116 | ||||||||
\(963\) | −0.350038 | −0.0112798 | ||||||||
\(964\) | −8.68208 | −0.279631 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.57271 | −0.0506011 | ||||||||
\(967\) | −37.3817 | −1.20211 | −0.601057 | − | 0.799206i | \(-0.705253\pi\) | ||||
−0.601057 | + | 0.799206i | \(0.705253\pi\) | |||||||
\(968\) | −23.4163 | −0.752627 | ||||||||
\(969\) | −14.7202 | −0.472882 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.35376 | −0.0434442 | −0.0217221 | − | 0.999764i | \(-0.506915\pi\) | ||||
−0.0217221 | + | 0.999764i | \(0.506915\pi\) | |||||||
\(972\) | −6.42762 | −0.206166 | ||||||||
\(973\) | −5.88452 | −0.188649 | ||||||||
\(974\) | −10.4833 | −0.335907 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 31.1591 | 0.997377 | ||||||||
\(977\) | −7.23001 | −0.231308 | −0.115654 | − | 0.993290i | \(-0.536896\pi\) | ||||
−0.115654 | + | 0.993290i | \(0.536896\pi\) | |||||||
\(978\) | −24.8696 | −0.795241 | ||||||||
\(979\) | 22.8041 | 0.728823 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.6670 | −0.532137 | ||||||||
\(982\) | 4.06670 | 0.129774 | ||||||||
\(983\) | 17.0572 | 0.544040 | 0.272020 | − | 0.962292i | \(-0.412308\pi\) | ||||
0.272020 | + | 0.962292i | \(0.412308\pi\) | |||||||
\(984\) | 45.1238 | 1.43849 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −15.5415 | −0.494941 | ||||||||
\(987\) | −7.40172 | −0.235599 | ||||||||
\(988\) | 3.39667 | 0.108063 | ||||||||
\(989\) | −3.84395 | −0.122231 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.7805 | 0.628348 | 0.314174 | − | 0.949365i | \(-0.398272\pi\) | ||||
0.314174 | + | 0.949365i | \(0.398272\pi\) | |||||||
\(992\) | 6.94225 | 0.220417 | ||||||||
\(993\) | −37.7240 | −1.19713 | ||||||||
\(994\) | 5.73212 | 0.181812 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.66876 | −0.242994 | ||||||||
\(997\) | −17.1094 | −0.541861 | −0.270931 | − | 0.962599i | \(-0.587331\pi\) | ||||
−0.270931 | + | 0.962599i | \(0.587331\pi\) | |||||||
\(998\) | −32.9820 | −1.04403 | ||||||||
\(999\) | −41.1992 | −1.30349 |
(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 | 4025.2.a.be.1.7 | 21 | ||
5.2 | odd | 4 | 805.2.c.c.484.15 | ✓ | 42 | ||
5.3 | odd | 4 | 805.2.c.c.484.28 | yes | 42 | ||
5.4 | even | 2 | 4025.2.a.bd.1.15 | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
805.2.c.c.484.15 | ✓ | 42 | 5.2 | odd | 4 | ||
805.2.c.c.484.28 | yes | 42 | 5.3 | odd | 4 | ||
4025.2.a.bd.1.15 | 21 | 5.4 | even | 2 | |||
4025.2.a.be.1.7 | 21 | 1.1 | even | 1 | trivial |