Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, 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("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 10 x^{10} + 52 x^{9} + 18 x^{8} - 220 x^{7} + 61 x^{6} + 330 x^{5} - 145 x^{4} - 148 x^{3} + 71 x^{2} + 10 x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.298064\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.298064 | −0.210763 | −0.105382 | − | 0.994432i | \(-0.533606\pi\) | ||||
−0.105382 | + | 0.994432i | \(0.533606\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.91116 | −0.955579 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.298064 | −0.121684 | ||||||||
\(7\) | 2.32107 | 0.877281 | 0.438640 | − | 0.898663i | \(-0.355460\pi\) | ||||
0.438640 | + | 0.898663i | \(0.355460\pi\) | |||||||
\(8\) | 1.16578 | 0.412164 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.91116 | −0.551704 | ||||||||
\(13\) | −4.59081 | −1.27326 | −0.636631 | − | 0.771169i | \(-0.719672\pi\) | ||||
−0.636631 | + | 0.771169i | \(0.719672\pi\) | |||||||
\(14\) | −0.691827 | −0.184899 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.47484 | 0.868710 | ||||||||
\(17\) | 5.14046 | 1.24675 | 0.623373 | − | 0.781925i | \(-0.285762\pi\) | ||||
0.623373 | + | 0.781925i | \(0.285762\pi\) | |||||||
\(18\) | −0.298064 | −0.0702544 | ||||||||
\(19\) | 5.69187 | 1.30580 | 0.652902 | − | 0.757442i | \(-0.273551\pi\) | ||||
0.652902 | + | 0.757442i | \(0.273551\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.32107 | 0.506498 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.02600 | −1.25651 | −0.628254 | − | 0.778008i | \(-0.716230\pi\) | ||||
−0.628254 | + | 0.778008i | \(0.716230\pi\) | |||||||
\(24\) | 1.16578 | 0.237963 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.36836 | 0.268357 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.43592 | −0.838311 | ||||||||
\(29\) | −6.09737 | −1.13225 | −0.566127 | − | 0.824318i | \(-0.691559\pi\) | ||||
−0.566127 | + | 0.824318i | \(0.691559\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.43171 | −1.51438 | −0.757190 | − | 0.653195i | \(-0.773428\pi\) | ||||
−0.757190 | + | 0.653195i | \(0.773428\pi\) | |||||||
\(32\) | −3.36728 | −0.595256 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.53219 | −0.262768 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.91116 | −0.318526 | ||||||||
\(37\) | 3.17279 | 0.521604 | 0.260802 | − | 0.965392i | \(-0.416013\pi\) | ||||
0.260802 | + | 0.965392i | \(0.416013\pi\) | |||||||
\(38\) | −1.69654 | −0.275215 | ||||||||
\(39\) | −4.59081 | −0.735118 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.468592 | 0.0731817 | 0.0365909 | − | 0.999330i | \(-0.488350\pi\) | ||||
0.0365909 | + | 0.999330i | \(0.488350\pi\) | |||||||
\(42\) | −0.691827 | −0.106751 | ||||||||
\(43\) | −8.08805 | −1.23342 | −0.616708 | − | 0.787192i | \(-0.711534\pi\) | ||||
−0.616708 | + | 0.787192i | \(0.711534\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.79614 | 0.264826 | ||||||||
\(47\) | −9.18736 | −1.34011 | −0.670057 | − | 0.742309i | \(-0.733730\pi\) | ||||
−0.670057 | + | 0.742309i | \(0.733730\pi\) | |||||||
\(48\) | 3.47484 | 0.501550 | ||||||||
\(49\) | −1.61265 | −0.230378 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.14046 | 0.719809 | ||||||||
\(52\) | 8.77376 | 1.21670 | ||||||||
\(53\) | 4.25892 | 0.585007 | 0.292504 | − | 0.956264i | \(-0.405512\pi\) | ||||
0.292504 | + | 0.956264i | \(0.405512\pi\) | |||||||
\(54\) | −0.298064 | −0.0405614 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.70584 | 0.361584 | ||||||||
\(57\) | 5.69187 | 0.753906 | ||||||||
\(58\) | 1.81741 | 0.238637 | ||||||||
\(59\) | 6.65971 | 0.867021 | 0.433510 | − | 0.901149i | \(-0.357275\pi\) | ||||
0.433510 | + | 0.901149i | \(0.357275\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.82041 | −0.233079 | −0.116540 | − | 0.993186i | \(-0.537180\pi\) | ||||
−0.116540 | + | 0.993186i | \(0.537180\pi\) | |||||||
\(62\) | 2.51319 | 0.319175 | ||||||||
\(63\) | 2.32107 | 0.292427 | ||||||||
\(64\) | −5.94601 | −0.743252 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.86541 | 1.08308 | 0.541541 | − | 0.840674i | \(-0.317841\pi\) | ||||
0.541541 | + | 0.840674i | \(0.317841\pi\) | |||||||
\(68\) | −9.82424 | −1.19136 | ||||||||
\(69\) | −6.02600 | −0.725445 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.44868 | −0.290604 | −0.145302 | − | 0.989387i | \(-0.546415\pi\) | ||||
−0.145302 | + | 0.989387i | \(0.546415\pi\) | |||||||
\(72\) | 1.16578 | 0.137388 | ||||||||
\(73\) | −9.08299 | −1.06308 | −0.531542 | − | 0.847032i | \(-0.678387\pi\) | ||||
−0.531542 | + | 0.847032i | \(0.678387\pi\) | |||||||
\(74\) | −0.945695 | −0.109935 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.8781 | −1.24780 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.36836 | 0.154936 | ||||||||
\(79\) | −12.9262 | −1.45431 | −0.727154 | − | 0.686474i | \(-0.759157\pi\) | ||||
−0.727154 | + | 0.686474i | \(0.759157\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.139670 | −0.0154240 | ||||||||
\(83\) | 8.34751 | 0.916259 | 0.458129 | − | 0.888886i | \(-0.348520\pi\) | ||||
0.458129 | + | 0.888886i | \(0.348520\pi\) | |||||||
\(84\) | −4.43592 | −0.483999 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.41076 | 0.259959 | ||||||||
\(87\) | −6.09737 | −0.653707 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.73882 | −0.396314 | −0.198157 | − | 0.980170i | \(-0.563496\pi\) | ||||
−0.198157 | + | 0.980170i | \(0.563496\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.6556 | −1.11701 | ||||||||
\(92\) | 11.5166 | 1.20069 | ||||||||
\(93\) | −8.43171 | −0.874327 | ||||||||
\(94\) | 2.73842 | 0.282447 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.36728 | −0.343671 | ||||||||
\(97\) | −5.58998 | −0.567576 | −0.283788 | − | 0.958887i | \(-0.591591\pi\) | ||||
−0.283788 | + | 0.958887i | \(0.591591\pi\) | |||||||
\(98\) | 0.480673 | 0.0485553 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.61415 | −0.160614 | −0.0803069 | − | 0.996770i | \(-0.525590\pi\) | ||||
−0.0803069 | + | 0.996770i | \(0.525590\pi\) | |||||||
\(102\) | −1.53219 | −0.151709 | ||||||||
\(103\) | 8.51841 | 0.839344 | 0.419672 | − | 0.907676i | \(-0.362145\pi\) | ||||
0.419672 | + | 0.907676i | \(0.362145\pi\) | |||||||
\(104\) | −5.35186 | −0.524793 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.26943 | −0.123298 | ||||||||
\(107\) | −6.11405 | −0.591067 | −0.295534 | − | 0.955332i | \(-0.595497\pi\) | ||||
−0.295534 | + | 0.955332i | \(0.595497\pi\) | |||||||
\(108\) | −1.91116 | −0.183901 | ||||||||
\(109\) | 5.73259 | 0.549082 | 0.274541 | − | 0.961575i | \(-0.411474\pi\) | ||||
0.274541 | + | 0.961575i | \(0.411474\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.17279 | 0.301148 | ||||||||
\(112\) | 8.06533 | 0.762102 | ||||||||
\(113\) | −8.24031 | −0.775183 | −0.387592 | − | 0.921831i | \(-0.626693\pi\) | ||||
−0.387592 | + | 0.921831i | \(0.626693\pi\) | |||||||
\(114\) | −1.69654 | −0.158896 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 11.6530 | 1.08196 | ||||||||
\(117\) | −4.59081 | −0.424420 | ||||||||
\(118\) | −1.98502 | −0.182736 | ||||||||
\(119\) | 11.9314 | 1.09375 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0.542598 | 0.0491245 | ||||||||
\(123\) | 0.468592 | 0.0422515 | ||||||||
\(124\) | 16.1143 | 1.44711 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.691827 | −0.0616328 | ||||||||
\(127\) | 12.0783 | 1.07177 | 0.535887 | − | 0.844290i | \(-0.319977\pi\) | ||||
0.535887 | + | 0.844290i | \(0.319977\pi\) | |||||||
\(128\) | 8.50685 | 0.751906 | ||||||||
\(129\) | −8.08805 | −0.712113 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.28131 | 0.286689 | 0.143345 | − | 0.989673i | \(-0.454214\pi\) | ||||
0.143345 | + | 0.989673i | \(0.454214\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.2112 | 1.14556 | ||||||||
\(134\) | −2.64246 | −0.228274 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.99263 | 0.513864 | ||||||||
\(137\) | 4.01740 | 0.343230 | 0.171615 | − | 0.985164i | \(-0.445102\pi\) | ||||
0.171615 | + | 0.985164i | \(0.445102\pi\) | |||||||
\(138\) | 1.79614 | 0.152897 | ||||||||
\(139\) | −1.77948 | −0.150934 | −0.0754670 | − | 0.997148i | \(-0.524045\pi\) | ||||
−0.0754670 | + | 0.997148i | \(0.524045\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.18736 | −0.773715 | ||||||||
\(142\) | 0.729862 | 0.0612487 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.47484 | 0.289570 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.70732 | 0.224059 | ||||||||
\(147\) | −1.61265 | −0.133009 | ||||||||
\(148\) | −6.06370 | −0.498433 | ||||||||
\(149\) | −2.20781 | −0.180871 | −0.0904354 | − | 0.995902i | \(-0.528826\pi\) | ||||
−0.0904354 | + | 0.995902i | \(0.528826\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.8536 | −1.04601 | −0.523007 | − | 0.852329i | \(-0.675190\pi\) | ||||
−0.523007 | + | 0.852329i | \(0.675190\pi\) | |||||||
\(152\) | 6.63544 | 0.538205 | ||||||||
\(153\) | 5.14046 | 0.415582 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 8.77376 | 0.702463 | ||||||||
\(157\) | −0.839648 | −0.0670112 | −0.0335056 | − | 0.999439i | \(-0.510667\pi\) | ||||
−0.0335056 | + | 0.999439i | \(0.510667\pi\) | |||||||
\(158\) | 3.85283 | 0.306515 | ||||||||
\(159\) | 4.25892 | 0.337754 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.9868 | −1.10231 | ||||||||
\(162\) | −0.298064 | −0.0234181 | ||||||||
\(163\) | 11.0879 | 0.868469 | 0.434234 | − | 0.900800i | \(-0.357019\pi\) | ||||
0.434234 | + | 0.900800i | \(0.357019\pi\) | |||||||
\(164\) | −0.895553 | −0.0699309 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.48810 | −0.193114 | ||||||||
\(167\) | −4.46477 | −0.345494 | −0.172747 | − | 0.984966i | \(-0.555264\pi\) | ||||
−0.172747 | + | 0.984966i | \(0.555264\pi\) | |||||||
\(168\) | 2.70584 | 0.208760 | ||||||||
\(169\) | 8.07553 | 0.621195 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.69187 | 0.435268 | ||||||||
\(172\) | 15.4575 | 1.17863 | ||||||||
\(173\) | −18.0670 | −1.37361 | −0.686803 | − | 0.726843i | \(-0.740987\pi\) | ||||
−0.686803 | + | 0.726843i | \(0.740987\pi\) | |||||||
\(174\) | 1.81741 | 0.137777 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.65971 | 0.500575 | ||||||||
\(178\) | 1.11441 | 0.0835285 | ||||||||
\(179\) | −11.9744 | −0.895010 | −0.447505 | − | 0.894281i | \(-0.647687\pi\) | ||||
−0.447505 | + | 0.894281i | \(0.647687\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.8185 | 1.17578 | 0.587890 | − | 0.808941i | \(-0.299959\pi\) | ||||
0.587890 | + | 0.808941i | \(0.299959\pi\) | |||||||
\(182\) | 3.17605 | 0.235424 | ||||||||
\(183\) | −1.82041 | −0.134568 | ||||||||
\(184\) | −7.02497 | −0.517888 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.51319 | 0.184276 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 17.5585 | 1.28059 | ||||||||
\(189\) | 2.32107 | 0.168833 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.00747 | 0.651757 | 0.325879 | − | 0.945412i | \(-0.394340\pi\) | ||||
0.325879 | + | 0.945412i | \(0.394340\pi\) | |||||||
\(192\) | −5.94601 | −0.429117 | ||||||||
\(193\) | 3.83930 | 0.276359 | 0.138179 | − | 0.990407i | \(-0.455875\pi\) | ||||
0.138179 | + | 0.990407i | \(0.455875\pi\) | |||||||
\(194\) | 1.66617 | 0.119624 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.08203 | 0.220145 | ||||||||
\(197\) | 8.33739 | 0.594015 | 0.297007 | − | 0.954875i | \(-0.404011\pi\) | ||||
0.297007 | + | 0.954875i | \(0.404011\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.22397 | 0.157653 | 0.0788266 | − | 0.996888i | \(-0.474883\pi\) | ||||
0.0788266 | + | 0.996888i | \(0.474883\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.86541 | 0.625318 | ||||||||
\(202\) | 0.481120 | 0.0338515 | ||||||||
\(203\) | −14.1524 | −0.993305 | ||||||||
\(204\) | −9.82424 | −0.687834 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.53903 | −0.176903 | ||||||||
\(207\) | −6.02600 | −0.418836 | ||||||||
\(208\) | −15.9523 | −1.10609 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.02265 | 0.345774 | 0.172887 | − | 0.984942i | \(-0.444690\pi\) | ||||
0.172887 | + | 0.984942i | \(0.444690\pi\) | |||||||
\(212\) | −8.13946 | −0.559020 | ||||||||
\(213\) | −2.44868 | −0.167780 | ||||||||
\(214\) | 1.82238 | 0.124575 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.16578 | 0.0793210 | ||||||||
\(217\) | −19.5706 | −1.32854 | ||||||||
\(218\) | −1.70868 | −0.115726 | ||||||||
\(219\) | −9.08299 | −0.613772 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.5989 | −1.58743 | ||||||||
\(222\) | −0.945695 | −0.0634709 | ||||||||
\(223\) | −28.3725 | −1.89996 | −0.949980 | − | 0.312310i | \(-0.898897\pi\) | ||||
−0.949980 | + | 0.312310i | \(0.898897\pi\) | |||||||
\(224\) | −7.81568 | −0.522207 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.45614 | 0.163380 | ||||||||
\(227\) | −6.58235 | −0.436886 | −0.218443 | − | 0.975850i | \(-0.570098\pi\) | ||||
−0.218443 | + | 0.975850i | \(0.570098\pi\) | |||||||
\(228\) | −10.8781 | −0.720417 | ||||||||
\(229\) | −16.5282 | −1.09221 | −0.546107 | − | 0.837715i | \(-0.683891\pi\) | ||||
−0.546107 | + | 0.837715i | \(0.683891\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.10817 | −0.466674 | ||||||||
\(233\) | −23.3654 | −1.53072 | −0.765360 | − | 0.643602i | \(-0.777439\pi\) | ||||
−0.765360 | + | 0.643602i | \(0.777439\pi\) | |||||||
\(234\) | 1.36836 | 0.0894522 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −12.7278 | −0.828507 | ||||||||
\(237\) | −12.9262 | −0.839645 | ||||||||
\(238\) | −3.55631 | −0.230521 | ||||||||
\(239\) | 17.7858 | 1.15047 | 0.575233 | − | 0.817990i | \(-0.304911\pi\) | ||||
0.575233 | + | 0.817990i | \(0.304911\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.95713 | −0.448148 | −0.224074 | − | 0.974572i | \(-0.571936\pi\) | ||||
−0.224074 | + | 0.974572i | \(0.571936\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.47909 | 0.222726 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.139670 | −0.00890506 | ||||||||
\(247\) | −26.1303 | −1.66263 | ||||||||
\(248\) | −9.82948 | −0.624173 | ||||||||
\(249\) | 8.34751 | 0.529002 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.636701 | −0.0401882 | −0.0200941 | − | 0.999798i | \(-0.506397\pi\) | ||||
−0.0200941 | + | 0.999798i | \(0.506397\pi\) | |||||||
\(252\) | −4.43592 | −0.279437 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −3.60010 | −0.225891 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.35644 | 0.584777 | ||||||||
\(257\) | 0.482055 | 0.0300698 | 0.0150349 | − | 0.999887i | \(-0.495214\pi\) | ||||
0.0150349 | + | 0.999887i | \(0.495214\pi\) | |||||||
\(258\) | 2.41076 | 0.150087 | ||||||||
\(259\) | 7.36426 | 0.457593 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.09737 | −0.377418 | ||||||||
\(262\) | −0.978041 | −0.0604236 | ||||||||
\(263\) | −18.2072 | −1.12270 | −0.561351 | − | 0.827578i | \(-0.689718\pi\) | ||||
−0.561351 | + | 0.827578i | \(0.689718\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.93779 | −0.241441 | ||||||||
\(267\) | −3.73882 | −0.228812 | ||||||||
\(268\) | −16.9432 | −1.03497 | ||||||||
\(269\) | 26.0546 | 1.58858 | 0.794289 | − | 0.607540i | \(-0.207844\pi\) | ||||
0.794289 | + | 0.607540i | \(0.207844\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.294394 | 0.0178832 | 0.00894158 | − | 0.999960i | \(-0.497154\pi\) | ||||
0.00894158 | + | 0.999960i | \(0.497154\pi\) | |||||||
\(272\) | 17.8623 | 1.08306 | ||||||||
\(273\) | −10.6556 | −0.644905 | ||||||||
\(274\) | −1.19744 | −0.0723402 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 11.5166 | 0.693220 | ||||||||
\(277\) | −30.2893 | −1.81991 | −0.909953 | − | 0.414712i | \(-0.863882\pi\) | ||||
−0.909953 | + | 0.414712i | \(0.863882\pi\) | |||||||
\(278\) | 0.530401 | 0.0318113 | ||||||||
\(279\) | −8.43171 | −0.504793 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.7185 | −1.77286 | −0.886428 | − | 0.462866i | \(-0.846821\pi\) | ||||
−0.886428 | + | 0.462866i | \(0.846821\pi\) | |||||||
\(282\) | 2.73842 | 0.163071 | ||||||||
\(283\) | −1.58988 | −0.0945084 | −0.0472542 | − | 0.998883i | \(-0.515047\pi\) | ||||
−0.0472542 | + | 0.998883i | \(0.515047\pi\) | |||||||
\(284\) | 4.67980 | 0.277695 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.08763 | 0.0642009 | ||||||||
\(288\) | −3.36728 | −0.198419 | ||||||||
\(289\) | 9.42438 | 0.554375 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.58998 | −0.327690 | ||||||||
\(292\) | 17.3590 | 1.01586 | ||||||||
\(293\) | 0.421054 | 0.0245982 | 0.0122991 | − | 0.999924i | \(-0.496085\pi\) | ||||
0.0122991 | + | 0.999924i | \(0.496085\pi\) | |||||||
\(294\) | 0.480673 | 0.0280334 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.69876 | 0.214986 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.658069 | 0.0381209 | ||||||||
\(299\) | 27.6642 | 1.59986 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.7729 | −1.08205 | ||||||||
\(302\) | 3.83121 | 0.220461 | ||||||||
\(303\) | −1.61415 | −0.0927304 | ||||||||
\(304\) | 19.7783 | 1.13436 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.53219 | −0.0875894 | ||||||||
\(307\) | −9.29536 | −0.530514 | −0.265257 | − | 0.964178i | \(-0.585457\pi\) | ||||
−0.265257 | + | 0.964178i | \(0.585457\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.51841 | 0.484595 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0947 | 0.685825 | 0.342912 | − | 0.939367i | \(-0.388587\pi\) | ||||
0.342912 | + | 0.939367i | \(0.388587\pi\) | |||||||
\(312\) | −5.35186 | −0.302989 | ||||||||
\(313\) | −6.97604 | −0.394309 | −0.197155 | − | 0.980372i | \(-0.563170\pi\) | ||||
−0.197155 | + | 0.980372i | \(0.563170\pi\) | |||||||
\(314\) | 0.250269 | 0.0141235 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.7040 | 1.38971 | ||||||||
\(317\) | 7.23947 | 0.406609 | 0.203304 | − | 0.979116i | \(-0.434832\pi\) | ||||
0.203304 | + | 0.979116i | \(0.434832\pi\) | |||||||
\(318\) | −1.26943 | −0.0711861 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.11405 | −0.341253 | ||||||||
\(322\) | 4.16895 | 0.232327 | ||||||||
\(323\) | 29.2588 | 1.62801 | ||||||||
\(324\) | −1.91116 | −0.106175 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.30490 | −0.183041 | ||||||||
\(327\) | 5.73259 | 0.317013 | ||||||||
\(328\) | 0.546273 | 0.0301629 | ||||||||
\(329\) | −21.3245 | −1.17566 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.6629 | 1.52049 | 0.760244 | − | 0.649637i | \(-0.225079\pi\) | ||||
0.760244 | + | 0.649637i | \(0.225079\pi\) | |||||||
\(332\) | −15.9534 | −0.875557 | ||||||||
\(333\) | 3.17279 | 0.173868 | ||||||||
\(334\) | 1.33079 | 0.0728175 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 8.06533 | 0.440000 | ||||||||
\(337\) | −22.0178 | −1.19939 | −0.599694 | − | 0.800229i | \(-0.704711\pi\) | ||||
−0.599694 | + | 0.800229i | \(0.704711\pi\) | |||||||
\(338\) | −2.40703 | −0.130925 | ||||||||
\(339\) | −8.24031 | −0.447552 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.69654 | −0.0917385 | ||||||||
\(343\) | −19.9905 | −1.07939 | ||||||||
\(344\) | −9.42886 | −0.508370 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.38512 | 0.289506 | ||||||||
\(347\) | −26.7672 | −1.43694 | −0.718469 | − | 0.695559i | \(-0.755157\pi\) | ||||
−0.718469 | + | 0.695559i | \(0.755157\pi\) | |||||||
\(348\) | 11.6530 | 0.624669 | ||||||||
\(349\) | −21.6412 | −1.15843 | −0.579215 | − | 0.815175i | \(-0.696641\pi\) | ||||
−0.579215 | + | 0.815175i | \(0.696641\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.59081 | −0.245039 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.5144 | 1.67734 | 0.838672 | − | 0.544636i | \(-0.183332\pi\) | ||||
0.838672 | + | 0.544636i | \(0.183332\pi\) | |||||||
\(354\) | −1.98502 | −0.105503 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.14548 | 0.378710 | ||||||||
\(357\) | 11.9314 | 0.631475 | ||||||||
\(358\) | 3.56915 | 0.188635 | ||||||||
\(359\) | −4.46095 | −0.235440 | −0.117720 | − | 0.993047i | \(-0.537559\pi\) | ||||
−0.117720 | + | 0.993047i | \(0.537559\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.3973 | 0.705124 | ||||||||
\(362\) | −4.71493 | −0.247811 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 20.3645 | 1.06739 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.542598 | 0.0283621 | ||||||||
\(367\) | −1.03300 | −0.0539222 | −0.0269611 | − | 0.999636i | \(-0.508583\pi\) | ||||
−0.0269611 | + | 0.999636i | \(0.508583\pi\) | |||||||
\(368\) | −20.9394 | −1.09154 | ||||||||
\(369\) | 0.468592 | 0.0243939 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.88523 | 0.513215 | ||||||||
\(372\) | 16.1143 | 0.835489 | ||||||||
\(373\) | −32.6921 | −1.69273 | −0.846367 | − | 0.532600i | \(-0.821215\pi\) | ||||
−0.846367 | + | 0.532600i | \(0.821215\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.7104 | −0.552347 | ||||||||
\(377\) | 27.9919 | 1.44166 | ||||||||
\(378\) | −0.691827 | −0.0355837 | ||||||||
\(379\) | −4.28279 | −0.219992 | −0.109996 | − | 0.993932i | \(-0.535084\pi\) | ||||
−0.109996 | + | 0.993932i | \(0.535084\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.0783 | 0.618789 | ||||||||
\(382\) | −2.68480 | −0.137366 | ||||||||
\(383\) | −26.9383 | −1.37648 | −0.688241 | − | 0.725482i | \(-0.741617\pi\) | ||||
−0.688241 | + | 0.725482i | \(0.741617\pi\) | |||||||
\(384\) | 8.50685 | 0.434113 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.14436 | −0.0582462 | ||||||||
\(387\) | −8.08805 | −0.411139 | ||||||||
\(388\) | 10.6833 | 0.542364 | ||||||||
\(389\) | 36.7033 | 1.86093 | 0.930465 | − | 0.366382i | \(-0.119403\pi\) | ||||
0.930465 | + | 0.366382i | \(0.119403\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.9765 | −1.56655 | ||||||||
\(392\) | −1.87999 | −0.0949537 | ||||||||
\(393\) | 3.28131 | 0.165520 | ||||||||
\(394\) | −2.48508 | −0.125196 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.52289 | −0.377563 | −0.188782 | − | 0.982019i | \(-0.560454\pi\) | ||||
−0.188782 | + | 0.982019i | \(0.560454\pi\) | |||||||
\(398\) | −0.662887 | −0.0332275 | ||||||||
\(399\) | 13.2112 | 0.661387 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.3995 | 0.769013 | 0.384506 | − | 0.923122i | \(-0.374372\pi\) | ||||
0.384506 | + | 0.923122i | \(0.374372\pi\) | |||||||
\(402\) | −2.64246 | −0.131794 | ||||||||
\(403\) | 38.7084 | 1.92820 | ||||||||
\(404\) | 3.08489 | 0.153479 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.21833 | 0.209352 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 5.99263 | 0.296679 | ||||||||
\(409\) | 16.2884 | 0.805411 | 0.402706 | − | 0.915330i | \(-0.368070\pi\) | ||||
0.402706 | + | 0.915330i | \(0.368070\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.01740 | 0.198164 | ||||||||
\(412\) | −16.2800 | −0.802059 | ||||||||
\(413\) | 15.4576 | 0.760620 | ||||||||
\(414\) | 1.79614 | 0.0882752 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 15.4585 | 0.757917 | ||||||||
\(417\) | −1.77948 | −0.0871417 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.3868 | −0.556281 | −0.278140 | − | 0.960540i | \(-0.589718\pi\) | ||||
−0.278140 | + | 0.960540i | \(0.589718\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0773 | −0.539876 | −0.269938 | − | 0.962878i | \(-0.587003\pi\) | ||||
−0.269938 | + | 0.962878i | \(0.587003\pi\) | |||||||
\(422\) | −1.49707 | −0.0728764 | ||||||||
\(423\) | −9.18736 | −0.446705 | ||||||||
\(424\) | 4.96494 | 0.241119 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.729862 | 0.0353620 | ||||||||
\(427\) | −4.22529 | −0.204476 | ||||||||
\(428\) | 11.6849 | 0.564811 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.4478 | −1.46662 | −0.733311 | − | 0.679894i | \(-0.762026\pi\) | ||||
−0.733311 | + | 0.679894i | \(0.762026\pi\) | |||||||
\(432\) | 3.47484 | 0.167183 | ||||||||
\(433\) | 15.1047 | 0.725885 | 0.362943 | − | 0.931812i | \(-0.381772\pi\) | ||||
0.362943 | + | 0.931812i | \(0.381772\pi\) | |||||||
\(434\) | 5.83328 | 0.280006 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.9559 | −0.524691 | ||||||||
\(437\) | −34.2992 | −1.64075 | ||||||||
\(438\) | 2.70732 | 0.129361 | ||||||||
\(439\) | 23.6799 | 1.13018 | 0.565090 | − | 0.825030i | \(-0.308842\pi\) | ||||
0.565090 | + | 0.825030i | \(0.308842\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.61265 | −0.0767928 | ||||||||
\(442\) | 7.03399 | 0.334573 | ||||||||
\(443\) | 30.7817 | 1.46248 | 0.731242 | − | 0.682119i | \(-0.238941\pi\) | ||||
0.731242 | + | 0.682119i | \(0.238941\pi\) | |||||||
\(444\) | −6.06370 | −0.287771 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.45681 | 0.400442 | ||||||||
\(447\) | −2.20781 | −0.104426 | ||||||||
\(448\) | −13.8011 | −0.652040 | ||||||||
\(449\) | −4.60851 | −0.217489 | −0.108744 | − | 0.994070i | \(-0.534683\pi\) | ||||
−0.108744 | + | 0.994070i | \(0.534683\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 15.7485 | 0.740749 | ||||||||
\(453\) | −12.8536 | −0.603916 | ||||||||
\(454\) | 1.96196 | 0.0920795 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.63544 | 0.310733 | ||||||||
\(457\) | −29.2281 | −1.36723 | −0.683616 | − | 0.729842i | \(-0.739594\pi\) | ||||
−0.683616 | + | 0.729842i | \(0.739594\pi\) | |||||||
\(458\) | 4.92647 | 0.230199 | ||||||||
\(459\) | 5.14046 | 0.239936 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.76367 | 0.268441 | 0.134220 | − | 0.990951i | \(-0.457147\pi\) | ||||
0.134220 | + | 0.990951i | \(0.457147\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.9028 | 1.01791 | 0.508954 | − | 0.860794i | \(-0.330032\pi\) | ||||
0.508954 | + | 0.860794i | \(0.330032\pi\) | |||||||
\(464\) | −21.1874 | −0.983600 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.96440 | 0.322620 | ||||||||
\(467\) | −14.6356 | −0.677253 | −0.338627 | − | 0.940921i | \(-0.609962\pi\) | ||||
−0.338627 | + | 0.940921i | \(0.609962\pi\) | |||||||
\(468\) | 8.77376 | 0.405567 | ||||||||
\(469\) | 20.5772 | 0.950167 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.839648 | −0.0386889 | ||||||||
\(472\) | 7.76373 | 0.357355 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.85283 | 0.176966 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −22.8027 | −1.04516 | ||||||||
\(477\) | 4.25892 | 0.195002 | ||||||||
\(478\) | −5.30130 | −0.242476 | ||||||||
\(479\) | 28.8633 | 1.31880 | 0.659398 | − | 0.751794i | \(-0.270811\pi\) | ||||
0.659398 | + | 0.751794i | \(0.270811\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.5657 | −0.664138 | ||||||||
\(482\) | 2.07367 | 0.0944531 | ||||||||
\(483\) | −13.9868 | −0.636419 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.298064 | −0.0135205 | ||||||||
\(487\) | 22.1587 | 1.00411 | 0.502054 | − | 0.864836i | \(-0.332578\pi\) | ||||
0.502054 | + | 0.864836i | \(0.332578\pi\) | |||||||
\(488\) | −2.12219 | −0.0960669 | ||||||||
\(489\) | 11.0879 | 0.501411 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.1229 | −0.727616 | −0.363808 | − | 0.931474i | \(-0.618524\pi\) | ||||
−0.363808 | + | 0.931474i | \(0.618524\pi\) | |||||||
\(492\) | −0.895553 | −0.0403746 | ||||||||
\(493\) | −31.3433 | −1.41163 | ||||||||
\(494\) | 7.78850 | 0.350421 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −29.2988 | −1.31556 | ||||||||
\(497\) | −5.68354 | −0.254942 | ||||||||
\(498\) | −2.48810 | −0.111494 | ||||||||
\(499\) | −30.8626 | −1.38160 | −0.690799 | − | 0.723047i | \(-0.742741\pi\) | ||||
−0.690799 | + | 0.723047i | \(0.742741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.46477 | −0.199471 | ||||||||
\(502\) | 0.189778 | 0.00847020 | ||||||||
\(503\) | −8.43173 | −0.375952 | −0.187976 | − | 0.982174i | \(-0.560193\pi\) | ||||
−0.187976 | + | 0.982174i | \(0.560193\pi\) | |||||||
\(504\) | 2.70584 | 0.120528 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.07553 | 0.358647 | ||||||||
\(508\) | −23.0835 | −1.02416 | ||||||||
\(509\) | −29.4916 | −1.30719 | −0.653596 | − | 0.756843i | \(-0.726741\pi\) | ||||
−0.653596 | + | 0.756843i | \(0.726741\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.0822 | −0.932623 | ||||||||
\(512\) | −19.8025 | −0.875156 | ||||||||
\(513\) | 5.69187 | 0.251302 | ||||||||
\(514\) | −0.143683 | −0.00633761 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 15.4575 | 0.680480 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.19502 | −0.0964437 | ||||||||
\(519\) | −18.0670 | −0.793052 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.61116 | −0.421072 | −0.210536 | − | 0.977586i | \(-0.567521\pi\) | ||||
−0.210536 | + | 0.977586i | \(0.567521\pi\) | |||||||
\(522\) | 1.81741 | 0.0795458 | ||||||||
\(523\) | −4.14721 | −0.181345 | −0.0906725 | − | 0.995881i | \(-0.528902\pi\) | ||||
−0.0906725 | + | 0.995881i | \(0.528902\pi\) | |||||||
\(524\) | −6.27110 | −0.273954 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.42690 | 0.236624 | ||||||||
\(527\) | −43.3429 | −1.88805 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.3127 | 0.578813 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.65971 | 0.289007 | ||||||||
\(532\) | −25.2487 | −1.09467 | ||||||||
\(533\) | −2.15122 | −0.0931795 | ||||||||
\(534\) | 1.11441 | 0.0482252 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 10.3351 | 0.446408 | ||||||||
\(537\) | −11.9744 | −0.516734 | ||||||||
\(538\) | −7.76595 | −0.334814 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.2524 | 1.34364 | 0.671822 | − | 0.740713i | \(-0.265512\pi\) | ||||
0.671822 | + | 0.740713i | \(0.265512\pi\) | |||||||
\(542\) | −0.0877483 | −0.00376911 | ||||||||
\(543\) | 15.8185 | 0.678836 | ||||||||
\(544\) | −17.3094 | −0.742133 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.17605 | 0.135922 | ||||||||
\(547\) | −9.02639 | −0.385940 | −0.192970 | − | 0.981205i | \(-0.561812\pi\) | ||||
−0.192970 | + | 0.981205i | \(0.561812\pi\) | |||||||
\(548\) | −7.67788 | −0.327983 | ||||||||
\(549\) | −1.82041 | −0.0776931 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.7054 | −1.47850 | ||||||||
\(552\) | −7.02497 | −0.299003 | ||||||||
\(553\) | −30.0025 | −1.27584 | ||||||||
\(554\) | 9.02815 | 0.383569 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.40088 | 0.144229 | ||||||||
\(557\) | −7.20535 | −0.305301 | −0.152650 | − | 0.988280i | \(-0.548781\pi\) | ||||
−0.152650 | + | 0.988280i | \(0.548781\pi\) | |||||||
\(558\) | 2.51319 | 0.106392 | ||||||||
\(559\) | 37.1307 | 1.57046 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.85802 | 0.373653 | ||||||||
\(563\) | 26.4111 | 1.11310 | 0.556548 | − | 0.830815i | \(-0.312125\pi\) | ||||
0.556548 | + | 0.830815i | \(0.312125\pi\) | |||||||
\(564\) | 17.5585 | 0.739346 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.473885 | 0.0199189 | ||||||||
\(567\) | 2.32107 | 0.0974756 | ||||||||
\(568\) | −2.85461 | −0.119777 | ||||||||
\(569\) | 43.3048 | 1.81543 | 0.907715 | − | 0.419587i | \(-0.137825\pi\) | ||||
0.907715 | + | 0.419587i | \(0.137825\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.82495 | −0.0763718 | −0.0381859 | − | 0.999271i | \(-0.512158\pi\) | ||||
−0.0381859 | + | 0.999271i | \(0.512158\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.00747 | 0.376292 | ||||||||
\(574\) | −0.324184 | −0.0135312 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5.94601 | −0.247751 | ||||||||
\(577\) | 26.0123 | 1.08291 | 0.541454 | − | 0.840731i | \(-0.317874\pi\) | ||||
0.541454 | + | 0.840731i | \(0.317874\pi\) | |||||||
\(578\) | −2.80907 | −0.116842 | ||||||||
\(579\) | 3.83930 | 0.159556 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.3751 | 0.803816 | ||||||||
\(582\) | 1.66617 | 0.0690651 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −10.5887 | −0.438165 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.125501 | −0.00518440 | ||||||||
\(587\) | 4.00349 | 0.165242 | 0.0826209 | − | 0.996581i | \(-0.473671\pi\) | ||||
0.0826209 | + | 0.996581i | \(0.473671\pi\) | |||||||
\(588\) | 3.08203 | 0.127101 | ||||||||
\(589\) | −47.9921 | −1.97748 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.33739 | 0.342954 | ||||||||
\(592\) | 11.0249 | 0.453122 | ||||||||
\(593\) | −32.2116 | −1.32277 | −0.661386 | − | 0.750045i | \(-0.730032\pi\) | ||||
−0.661386 | + | 0.750045i | \(0.730032\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.21947 | 0.172836 | ||||||||
\(597\) | 2.22397 | 0.0910212 | ||||||||
\(598\) | −8.24572 | −0.337192 | ||||||||
\(599\) | −13.5168 | −0.552281 | −0.276140 | − | 0.961117i | \(-0.589055\pi\) | ||||
−0.276140 | + | 0.961117i | \(0.589055\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.4926 | 1.12145 | 0.560724 | − | 0.828003i | \(-0.310523\pi\) | ||||
0.560724 | + | 0.828003i | \(0.310523\pi\) | |||||||
\(602\) | 5.59553 | 0.228057 | ||||||||
\(603\) | 8.86541 | 0.361027 | ||||||||
\(604\) | 24.5653 | 0.999548 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.481120 | 0.0195442 | ||||||||
\(607\) | −37.6114 | −1.52660 | −0.763300 | − | 0.646044i | \(-0.776422\pi\) | ||||
−0.763300 | + | 0.646044i | \(0.776422\pi\) | |||||||
\(608\) | −19.1661 | −0.777288 | ||||||||
\(609\) | −14.1524 | −0.573485 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 42.1774 | 1.70632 | ||||||||
\(612\) | −9.82424 | −0.397121 | ||||||||
\(613\) | −29.0831 | −1.17466 | −0.587328 | − | 0.809349i | \(-0.699820\pi\) | ||||
−0.587328 | + | 0.809349i | \(0.699820\pi\) | |||||||
\(614\) | 2.77062 | 0.111813 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.61911 | 0.387251 | 0.193625 | − | 0.981076i | \(-0.437975\pi\) | ||||
0.193625 | + | 0.981076i | \(0.437975\pi\) | |||||||
\(618\) | −2.53903 | −0.102135 | ||||||||
\(619\) | −23.4074 | −0.940824 | −0.470412 | − | 0.882447i | \(-0.655895\pi\) | ||||
−0.470412 | + | 0.882447i | \(0.655895\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.02600 | −0.241815 | ||||||||
\(622\) | −3.60498 | −0.144547 | ||||||||
\(623\) | −8.67806 | −0.347679 | ||||||||
\(624\) | −15.9523 | −0.638604 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.07931 | 0.0831059 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.60470 | 0.0640345 | ||||||||
\(629\) | 16.3096 | 0.650307 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.6565 | −0.901942 | −0.450971 | − | 0.892539i | \(-0.648922\pi\) | ||||
−0.450971 | + | 0.892539i | \(0.648922\pi\) | |||||||
\(632\) | −15.0690 | −0.599414 | ||||||||
\(633\) | 5.02265 | 0.199633 | ||||||||
\(634\) | −2.15783 | −0.0856982 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.13946 | −0.322751 | ||||||||
\(637\) | 7.40336 | 0.293332 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.44868 | −0.0968681 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.9966 | 0.908313 | 0.454156 | − | 0.890922i | \(-0.349941\pi\) | ||||
0.454156 | + | 0.890922i | \(0.349941\pi\) | |||||||
\(642\) | 1.82238 | 0.0719235 | ||||||||
\(643\) | −11.6129 | −0.457970 | −0.228985 | − | 0.973430i | \(-0.573541\pi\) | ||||
−0.228985 | + | 0.973430i | \(0.573541\pi\) | |||||||
\(644\) | 26.7309 | 1.05334 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.72101 | −0.343124 | ||||||||
\(647\) | −36.1713 | −1.42204 | −0.711020 | − | 0.703172i | \(-0.751766\pi\) | ||||
−0.711020 | + | 0.703172i | \(0.751766\pi\) | |||||||
\(648\) | 1.16578 | 0.0457960 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.5706 | −0.767030 | ||||||||
\(652\) | −21.1907 | −0.829890 | ||||||||
\(653\) | −8.65293 | −0.338615 | −0.169308 | − | 0.985563i | \(-0.554153\pi\) | ||||
−0.169308 | + | 0.985563i | \(0.554153\pi\) | |||||||
\(654\) | −1.70868 | −0.0668146 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.62828 | 0.0635737 | ||||||||
\(657\) | −9.08299 | −0.354361 | ||||||||
\(658\) | 6.35607 | 0.247785 | ||||||||
\(659\) | −17.4599 | −0.680143 | −0.340071 | − | 0.940400i | \(-0.610451\pi\) | ||||
−0.340071 | + | 0.940400i | \(0.610451\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.2393 | 0.631636 | 0.315818 | − | 0.948820i | \(-0.397721\pi\) | ||||
0.315818 | + | 0.948820i | \(0.397721\pi\) | |||||||
\(662\) | −8.24531 | −0.320463 | ||||||||
\(663\) | −23.5989 | −0.916505 | ||||||||
\(664\) | 9.73133 | 0.377649 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.945695 | −0.0366449 | ||||||||
\(667\) | 36.7428 | 1.42269 | ||||||||
\(668\) | 8.53288 | 0.330147 | ||||||||
\(669\) | −28.3725 | −1.09694 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −7.81568 | −0.301496 | ||||||||
\(673\) | −26.4394 | −1.01916 | −0.509582 | − | 0.860422i | \(-0.670200\pi\) | ||||
−0.509582 | + | 0.860422i | \(0.670200\pi\) | |||||||
\(674\) | 6.56273 | 0.252787 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.4336 | −0.593600 | ||||||||
\(677\) | 31.3550 | 1.20507 | 0.602534 | − | 0.798093i | \(-0.294158\pi\) | ||||
0.602534 | + | 0.798093i | \(0.294158\pi\) | |||||||
\(678\) | 2.45614 | 0.0943276 | ||||||||
\(679\) | −12.9747 | −0.497924 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.58235 | −0.252236 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.85934 | 0.147674 | 0.0738368 | − | 0.997270i | \(-0.476476\pi\) | ||||
0.0738368 | + | 0.997270i | \(0.476476\pi\) | |||||||
\(684\) | −10.8781 | −0.415933 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 5.95846 | 0.227495 | ||||||||
\(687\) | −16.5282 | −0.630590 | ||||||||
\(688\) | −28.1047 | −1.07148 | ||||||||
\(689\) | −19.5519 | −0.744867 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.0718 | −0.839651 | −0.419825 | − | 0.907605i | \(-0.637909\pi\) | ||||
−0.419825 | + | 0.907605i | \(0.637909\pi\) | |||||||
\(692\) | 34.5288 | 1.31259 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.97835 | 0.302854 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.10817 | −0.269435 | ||||||||
\(697\) | 2.40878 | 0.0912390 | ||||||||
\(698\) | 6.45048 | 0.244154 | ||||||||
\(699\) | −23.3654 | −0.883762 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.4034 | 1.29940 | 0.649699 | − | 0.760192i | \(-0.274895\pi\) | ||||
0.649699 | + | 0.760192i | \(0.274895\pi\) | |||||||
\(702\) | 1.36836 | 0.0516453 | ||||||||
\(703\) | 18.0591 | 0.681112 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.39333 | −0.353523 | ||||||||
\(707\) | −3.74655 | −0.140903 | ||||||||
\(708\) | −12.7278 | −0.478338 | ||||||||
\(709\) | −25.1938 | −0.946172 | −0.473086 | − | 0.881016i | \(-0.656860\pi\) | ||||
−0.473086 | + | 0.881016i | \(0.656860\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.9262 | −0.484769 | ||||||||
\(712\) | −4.35863 | −0.163347 | ||||||||
\(713\) | 50.8095 | 1.90283 | ||||||||
\(714\) | −3.55631 | −0.133092 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 22.8850 | 0.855253 | ||||||||
\(717\) | 17.7858 | 0.664222 | ||||||||
\(718\) | 1.32965 | 0.0496221 | ||||||||
\(719\) | −17.4770 | −0.651784 | −0.325892 | − | 0.945407i | \(-0.605665\pi\) | ||||
−0.325892 | + | 0.945407i | \(0.605665\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.7718 | 0.736340 | ||||||||
\(722\) | −3.99327 | −0.148614 | ||||||||
\(723\) | −6.95713 | −0.258738 | ||||||||
\(724\) | −30.2316 | −1.12355 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.60045 | −0.133533 | −0.0667666 | − | 0.997769i | \(-0.521268\pi\) | ||||
−0.0667666 | + | 0.997769i | \(0.521268\pi\) | |||||||
\(728\) | −12.4220 | −0.460391 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −41.5763 | −1.53776 | ||||||||
\(732\) | 3.47909 | 0.128591 | ||||||||
\(733\) | −21.8840 | −0.808305 | −0.404153 | − | 0.914692i | \(-0.632434\pi\) | ||||
−0.404153 | + | 0.914692i | \(0.632434\pi\) | |||||||
\(734\) | 0.307901 | 0.0113648 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.2912 | 0.747944 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.139670 | −0.00514134 | ||||||||
\(739\) | −5.74815 | −0.211449 | −0.105724 | − | 0.994395i | \(-0.533716\pi\) | ||||
−0.105724 | + | 0.994395i | \(0.533716\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −26.1303 | −0.959920 | ||||||||
\(742\) | −2.94643 | −0.108167 | ||||||||
\(743\) | −18.0014 | −0.660406 | −0.330203 | − | 0.943910i | \(-0.607117\pi\) | ||||
−0.330203 | + | 0.943910i | \(0.607117\pi\) | |||||||
\(744\) | −9.82948 | −0.360366 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.74435 | 0.356766 | ||||||||
\(747\) | 8.34751 | 0.305420 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.1911 | −0.518532 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.0167 | −0.693928 | −0.346964 | − | 0.937878i | \(-0.612787\pi\) | ||||
−0.346964 | + | 0.937878i | \(0.612787\pi\) | |||||||
\(752\) | −31.9246 | −1.16417 | ||||||||
\(753\) | −0.636701 | −0.0232027 | ||||||||
\(754\) | −8.34338 | −0.303848 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.43592 | −0.161333 | ||||||||
\(757\) | −2.39560 | −0.0870694 | −0.0435347 | − | 0.999052i | \(-0.513862\pi\) | ||||
−0.0435347 | + | 0.999052i | \(0.513862\pi\) | |||||||
\(758\) | 1.27655 | 0.0463663 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.4089 | 1.64607 | 0.823035 | − | 0.567991i | \(-0.192279\pi\) | ||||
0.823035 | + | 0.567991i | \(0.192279\pi\) | |||||||
\(762\) | −3.60010 | −0.130418 | ||||||||
\(763\) | 13.3057 | 0.481699 | ||||||||
\(764\) | −17.2147 | −0.622806 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.02934 | 0.290112 | ||||||||
\(767\) | −30.5735 | −1.10394 | ||||||||
\(768\) | 9.35644 | 0.337621 | ||||||||
\(769\) | −49.1931 | −1.77395 | −0.886975 | − | 0.461818i | \(-0.847197\pi\) | ||||
−0.886975 | + | 0.461818i | \(0.847197\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.482055 | 0.0173608 | ||||||||
\(772\) | −7.33750 | −0.264082 | ||||||||
\(773\) | −21.2288 | −0.763549 | −0.381774 | − | 0.924256i | \(-0.624687\pi\) | ||||
−0.381774 | + | 0.924256i | \(0.624687\pi\) | |||||||
\(774\) | 2.41076 | 0.0866529 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.51666 | −0.233935 | ||||||||
\(777\) | 7.36426 | 0.264191 | ||||||||
\(778\) | −10.9399 | −0.392216 | ||||||||
\(779\) | 2.66716 | 0.0955610 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 9.23297 | 0.330170 | ||||||||
\(783\) | −6.09737 | −0.217902 | ||||||||
\(784\) | −5.60370 | −0.200132 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.978041 | −0.0348856 | ||||||||
\(787\) | −8.25347 | −0.294204 | −0.147102 | − | 0.989121i | \(-0.546995\pi\) | ||||
−0.147102 | + | 0.989121i | \(0.546995\pi\) | |||||||
\(788\) | −15.9341 | −0.567628 | ||||||||
\(789\) | −18.2072 | −0.648192 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.1263 | −0.680053 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.35714 | 0.296771 | ||||||||
\(794\) | 2.24231 | 0.0795764 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.25036 | −0.150650 | ||||||||
\(797\) | −6.29828 | −0.223096 | −0.111548 | − | 0.993759i | \(-0.535581\pi\) | ||||
−0.111548 | + | 0.993759i | \(0.535581\pi\) | |||||||
\(798\) | −3.93779 | −0.139396 | ||||||||
\(799\) | −47.2273 | −1.67078 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.73882 | −0.132105 | ||||||||
\(802\) | −4.59003 | −0.162080 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −16.9432 | −0.597540 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11.5376 | −0.406394 | ||||||||
\(807\) | 26.0546 | 0.917166 | ||||||||
\(808\) | −1.88174 | −0.0661992 | ||||||||
\(809\) | 54.5843 | 1.91908 | 0.959540 | − | 0.281571i | \(-0.0908556\pi\) | ||||
0.959540 | + | 0.281571i | \(0.0908556\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.0167 | −0.386850 | −0.193425 | − | 0.981115i | \(-0.561960\pi\) | ||||
−0.193425 | + | 0.981115i | \(0.561960\pi\) | |||||||
\(812\) | 27.0475 | 0.949181 | ||||||||
\(813\) | 0.294394 | 0.0103248 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 17.8623 | 0.625305 | ||||||||
\(817\) | −46.0361 | −1.61060 | ||||||||
\(818\) | −4.85500 | −0.169751 | ||||||||
\(819\) | −10.6556 | −0.372336 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.7127 | 1.45578 | 0.727892 | − | 0.685692i | \(-0.240500\pi\) | ||||
0.727892 | + | 0.685692i | \(0.240500\pi\) | |||||||
\(822\) | −1.19744 | −0.0417656 | ||||||||
\(823\) | −3.00669 | −0.104806 | −0.0524032 | − | 0.998626i | \(-0.516688\pi\) | ||||
−0.0524032 | + | 0.998626i | \(0.516688\pi\) | |||||||
\(824\) | 9.93056 | 0.345947 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.60737 | −0.160311 | ||||||||
\(827\) | 44.8126 | 1.55829 | 0.779143 | − | 0.626846i | \(-0.215655\pi\) | ||||
0.779143 | + | 0.626846i | \(0.215655\pi\) | |||||||
\(828\) | 11.5166 | 0.400231 | ||||||||
\(829\) | −38.6918 | −1.34382 | −0.671911 | − | 0.740631i | \(-0.734526\pi\) | ||||
−0.671911 | + | 0.740631i | \(0.734526\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.2893 | −1.05072 | ||||||||
\(832\) | 27.2970 | 0.946354 | ||||||||
\(833\) | −8.28977 | −0.287223 | ||||||||
\(834\) | 0.530401 | 0.0183663 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.43171 | −0.291442 | ||||||||
\(838\) | 3.39399 | 0.117244 | ||||||||
\(839\) | −21.2861 | −0.734879 | −0.367440 | − | 0.930047i | \(-0.619766\pi\) | ||||
−0.367440 | + | 0.930047i | \(0.619766\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.17796 | 0.281999 | ||||||||
\(842\) | 3.30176 | 0.113786 | ||||||||
\(843\) | −29.7185 | −1.02356 | ||||||||
\(844\) | −9.59908 | −0.330414 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.73842 | 0.0941490 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 14.7990 | 0.508201 | ||||||||
\(849\) | −1.58988 | −0.0545644 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.1192 | −0.655399 | ||||||||
\(852\) | 4.67980 | 0.160327 | ||||||||
\(853\) | 23.9145 | 0.818815 | 0.409408 | − | 0.912352i | \(-0.365735\pi\) | ||||
0.409408 | + | 0.912352i | \(0.365735\pi\) | |||||||
\(854\) | 1.25941 | 0.0430960 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.12761 | −0.243617 | ||||||||
\(857\) | −23.7057 | −0.809773 | −0.404886 | − | 0.914367i | \(-0.632689\pi\) | ||||
−0.404886 | + | 0.914367i | \(0.632689\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.2131 | −0.996739 | −0.498369 | − | 0.866965i | \(-0.666068\pi\) | ||||
−0.498369 | + | 0.866965i | \(0.666068\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.08763 | 0.0370664 | ||||||||
\(862\) | 9.07541 | 0.309110 | ||||||||
\(863\) | −37.2828 | −1.26912 | −0.634560 | − | 0.772874i | \(-0.718819\pi\) | ||||
−0.634560 | + | 0.772874i | \(0.718819\pi\) | |||||||
\(864\) | −3.36728 | −0.114557 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.50217 | −0.152990 | ||||||||
\(867\) | 9.42438 | 0.320069 | ||||||||
\(868\) | 37.4024 | 1.26952 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −40.6994 | −1.37905 | ||||||||
\(872\) | 6.68291 | 0.226312 | ||||||||
\(873\) | −5.58998 | −0.189192 | ||||||||
\(874\) | 10.2234 | 0.345810 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 17.3590 | 0.586507 | ||||||||
\(877\) | 26.7080 | 0.901865 | 0.450932 | − | 0.892558i | \(-0.351092\pi\) | ||||
0.450932 | + | 0.892558i | \(0.351092\pi\) | |||||||
\(878\) | −7.05813 | −0.238200 | ||||||||
\(879\) | 0.421054 | 0.0142018 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.3146 | 1.72883 | 0.864417 | − | 0.502775i | \(-0.167688\pi\) | ||||
0.864417 | + | 0.502775i | \(0.167688\pi\) | |||||||
\(882\) | 0.480673 | 0.0161851 | ||||||||
\(883\) | 54.9200 | 1.84820 | 0.924102 | − | 0.382145i | \(-0.124815\pi\) | ||||
0.924102 | + | 0.382145i | \(0.124815\pi\) | |||||||
\(884\) | 45.1012 | 1.51692 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.17493 | −0.308238 | ||||||||
\(887\) | 5.07251 | 0.170318 | 0.0851592 | − | 0.996367i | \(-0.472860\pi\) | ||||
0.0851592 | + | 0.996367i | \(0.472860\pi\) | |||||||
\(888\) | 3.69876 | 0.124122 | ||||||||
\(889\) | 28.0345 | 0.940247 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 54.2242 | 1.81556 | ||||||||
\(893\) | −52.2932 | −1.74993 | ||||||||
\(894\) | 0.658069 | 0.0220091 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 19.7450 | 0.659633 | ||||||||
\(897\) | 27.6642 | 0.923682 | ||||||||
\(898\) | 1.37363 | 0.0458387 | ||||||||
\(899\) | 51.4113 | 1.71466 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.8928 | 0.729355 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.7729 | −0.624723 | ||||||||
\(904\) | −9.60636 | −0.319503 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.83121 | 0.127283 | ||||||||
\(907\) | 23.8325 | 0.791346 | 0.395673 | − | 0.918392i | \(-0.370511\pi\) | ||||
0.395673 | + | 0.918392i | \(0.370511\pi\) | |||||||
\(908\) | 12.5799 | 0.417479 | ||||||||
\(909\) | −1.61415 | −0.0535379 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.9409 | 0.528147 | 0.264074 | − | 0.964503i | \(-0.414934\pi\) | ||||
0.264074 | + | 0.964503i | \(0.414934\pi\) | |||||||
\(912\) | 19.7783 | 0.654926 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 8.71185 | 0.288162 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 31.5880 | 1.04370 | ||||||||
\(917\) | 7.61614 | 0.251507 | ||||||||
\(918\) | −1.53219 | −0.0505698 | ||||||||
\(919\) | −34.9656 | −1.15341 | −0.576705 | − | 0.816952i | \(-0.695662\pi\) | ||||
−0.576705 | + | 0.816952i | \(0.695662\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.29536 | −0.306293 | ||||||||
\(922\) | −1.71794 | −0.0565775 | ||||||||
\(923\) | 11.2414 | 0.370015 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.52843 | −0.214538 | ||||||||
\(927\) | 8.51841 | 0.279781 | ||||||||
\(928\) | 20.5315 | 0.673981 | ||||||||
\(929\) | −34.3129 | −1.12577 | −0.562885 | − | 0.826535i | \(-0.690308\pi\) | ||||
−0.562885 | + | 0.826535i | \(0.690308\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.17898 | −0.300829 | ||||||||
\(932\) | 44.6550 | 1.46272 | ||||||||
\(933\) | 12.0947 | 0.395961 | ||||||||
\(934\) | 4.36234 | 0.142740 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.35186 | −0.174931 | ||||||||
\(937\) | 28.9980 | 0.947322 | 0.473661 | − | 0.880707i | \(-0.342932\pi\) | ||||
0.473661 | + | 0.880707i | \(0.342932\pi\) | |||||||
\(938\) | −6.13333 | −0.200260 | ||||||||
\(939\) | −6.97604 | −0.227655 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.7926 | 0.547424 | 0.273712 | − | 0.961812i | \(-0.411749\pi\) | ||||
0.273712 | + | 0.961812i | \(0.411749\pi\) | |||||||
\(942\) | 0.250269 | 0.00815421 | ||||||||
\(943\) | −2.82373 | −0.0919534 | ||||||||
\(944\) | 23.1414 | 0.753189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.4385 | −0.566677 | −0.283338 | − | 0.959020i | \(-0.591442\pi\) | ||||
−0.283338 | + | 0.959020i | \(0.591442\pi\) | |||||||
\(948\) | 24.7040 | 0.802347 | ||||||||
\(949\) | 41.6983 | 1.35358 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.23947 | 0.234756 | ||||||||
\(952\) | 13.9093 | 0.450803 | ||||||||
\(953\) | −1.47790 | −0.0478739 | −0.0239369 | − | 0.999713i | \(-0.507620\pi\) | ||||
−0.0239369 | + | 0.999713i | \(0.507620\pi\) | |||||||
\(954\) | −1.26943 | −0.0410993 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −33.9914 | −1.09936 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.60310 | −0.277954 | ||||||||
\(959\) | 9.32465 | 0.301109 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.0937 | 1.29334 | ||||||||
\(962\) | 4.34151 | 0.139976 | ||||||||
\(963\) | −6.11405 | −0.197022 | ||||||||
\(964\) | 13.2962 | 0.428241 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.16895 | 0.134134 | ||||||||
\(967\) | −26.6515 | −0.857054 | −0.428527 | − | 0.903529i | \(-0.640967\pi\) | ||||
−0.428527 | + | 0.903529i | \(0.640967\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 29.2588 | 0.939929 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.7025 | −1.24202 | −0.621011 | − | 0.783802i | \(-0.713278\pi\) | ||||
−0.621011 | + | 0.783802i | \(0.713278\pi\) | |||||||
\(972\) | −1.91116 | −0.0613004 | ||||||||
\(973\) | −4.13030 | −0.132411 | ||||||||
\(974\) | −6.60473 | −0.211629 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.32562 | −0.202478 | ||||||||
\(977\) | −49.7415 | −1.59137 | −0.795686 | − | 0.605709i | \(-0.792890\pi\) | ||||
−0.795686 | + | 0.605709i | \(0.792890\pi\) | |||||||
\(978\) | −3.30490 | −0.105679 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.73259 | 0.183027 | ||||||||
\(982\) | 4.80566 | 0.153355 | ||||||||
\(983\) | −24.5431 | −0.782802 | −0.391401 | − | 0.920220i | \(-0.628009\pi\) | ||||
−0.391401 | + | 0.920220i | \(0.628009\pi\) | |||||||
\(984\) | 0.546273 | 0.0174145 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.34233 | 0.297520 | ||||||||
\(987\) | −21.3245 | −0.678766 | ||||||||
\(988\) | 49.9391 | 1.58877 | ||||||||
\(989\) | 48.7386 | 1.54980 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.4673 | 1.03136 | 0.515679 | − | 0.856782i | \(-0.327540\pi\) | ||||
0.515679 | + | 0.856782i | \(0.327540\pi\) | |||||||
\(992\) | 28.3919 | 0.901444 | ||||||||
\(993\) | 27.6629 | 0.877855 | ||||||||
\(994\) | 1.69406 | 0.0537323 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −15.9534 | −0.505503 | ||||||||
\(997\) | −39.6946 | −1.25714 | −0.628571 | − | 0.777752i | \(-0.716360\pi\) | ||||
−0.628571 | + | 0.777752i | \(0.716360\pi\) | |||||||
\(998\) | 9.19902 | 0.291190 | ||||||||
\(999\) | 3.17279 | 0.100383 |
(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 | 9075.2.a.dy.1.7 | 12 | ||
5.2 | odd | 4 | 1815.2.c.j.364.11 | 24 | |||
5.3 | odd | 4 | 1815.2.c.j.364.14 | 24 | |||
5.4 | even | 2 | 9075.2.a.dz.1.6 | 12 | |||
11.3 | even | 5 | 825.2.n.p.526.4 | 24 | |||
11.4 | even | 5 | 825.2.n.p.676.4 | 24 | |||
11.10 | odd | 2 | 9075.2.a.ea.1.6 | 12 | |||
55.3 | odd | 20 | 165.2.s.a.64.7 | yes | 48 | ||
55.4 | even | 10 | 825.2.n.o.676.3 | 24 | |||
55.14 | even | 10 | 825.2.n.o.526.3 | 24 | |||
55.32 | even | 4 | 1815.2.c.k.364.14 | 24 | |||
55.37 | odd | 20 | 165.2.s.a.49.7 | yes | 48 | ||
55.43 | even | 4 | 1815.2.c.k.364.11 | 24 | |||
55.47 | odd | 20 | 165.2.s.a.64.6 | yes | 48 | ||
55.48 | odd | 20 | 165.2.s.a.49.6 | ✓ | 48 | ||
55.54 | odd | 2 | 9075.2.a.dx.1.7 | 12 | |||
165.47 | even | 20 | 495.2.ba.c.64.7 | 48 | |||
165.92 | even | 20 | 495.2.ba.c.379.6 | 48 | |||
165.113 | even | 20 | 495.2.ba.c.64.6 | 48 | |||
165.158 | even | 20 | 495.2.ba.c.379.7 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.s.a.49.6 | ✓ | 48 | 55.48 | odd | 20 | ||
165.2.s.a.49.7 | yes | 48 | 55.37 | odd | 20 | ||
165.2.s.a.64.6 | yes | 48 | 55.47 | odd | 20 | ||
165.2.s.a.64.7 | yes | 48 | 55.3 | odd | 20 | ||
495.2.ba.c.64.6 | 48 | 165.113 | even | 20 | |||
495.2.ba.c.64.7 | 48 | 165.47 | even | 20 | |||
495.2.ba.c.379.6 | 48 | 165.92 | even | 20 | |||
495.2.ba.c.379.7 | 48 | 165.158 | even | 20 | |||
825.2.n.o.526.3 | 24 | 55.14 | even | 10 | |||
825.2.n.o.676.3 | 24 | 55.4 | even | 10 | |||
825.2.n.p.526.4 | 24 | 11.3 | even | 5 | |||
825.2.n.p.676.4 | 24 | 11.4 | even | 5 | |||
1815.2.c.j.364.11 | 24 | 5.2 | odd | 4 | |||
1815.2.c.j.364.14 | 24 | 5.3 | odd | 4 | |||
1815.2.c.k.364.11 | 24 | 55.43 | even | 4 | |||
1815.2.c.k.364.14 | 24 | 55.32 | even | 4 | |||
9075.2.a.dx.1.7 | 12 | 55.54 | odd | 2 | |||
9075.2.a.dy.1.7 | 12 | 1.1 | even | 1 | trivial | ||
9075.2.a.dz.1.6 | 12 | 5.4 | even | 2 | |||
9075.2.a.ea.1.6 | 12 | 11.10 | odd | 2 |