Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.56709 | −1.81521 | −0.907604 | − | 0.419828i | \(-0.862090\pi\) | ||||
−0.907604 | + | 0.419828i | \(0.862090\pi\) | |||||||
\(3\) | −0.178555 | −0.103089 | −0.0515444 | − | 0.998671i | \(-0.516414\pi\) | ||||
−0.0515444 | + | 0.998671i | \(0.516414\pi\) | |||||||
\(4\) | 4.58996 | 2.29498 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.458367 | 0.187128 | ||||||||
\(7\) | 0.233097 | 0.0881023 | 0.0440511 | − | 0.999029i | \(-0.485974\pi\) | ||||
0.0440511 | + | 0.999029i | \(0.485974\pi\) | |||||||
\(8\) | −6.64865 | −2.35065 | ||||||||
\(9\) | −2.96812 | −0.989373 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.70454 | −0.815449 | −0.407724 | − | 0.913105i | \(-0.633678\pi\) | ||||
−0.407724 | + | 0.913105i | \(0.633678\pi\) | |||||||
\(12\) | −0.819560 | −0.236587 | ||||||||
\(13\) | 4.02919 | 1.11749 | 0.558747 | − | 0.829338i | \(-0.311282\pi\) | ||||
0.558747 | + | 0.829338i | \(0.311282\pi\) | |||||||
\(14\) | −0.598380 | −0.159924 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.88779 | 1.97195 | ||||||||
\(17\) | 2.29567 | 0.556782 | 0.278391 | − | 0.960468i | \(-0.410199\pi\) | ||||
0.278391 | + | 0.960468i | \(0.410199\pi\) | |||||||
\(18\) | 7.61943 | 1.79592 | ||||||||
\(19\) | −4.91592 | −1.12779 | −0.563895 | − | 0.825846i | \(-0.690698\pi\) | ||||
−0.563895 | + | 0.825846i | \(0.690698\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0416206 | −0.00908236 | ||||||||
\(22\) | 6.94279 | 1.48021 | ||||||||
\(23\) | 7.50314 | 1.56451 | 0.782256 | − | 0.622957i | \(-0.214069\pi\) | ||||
0.782256 | + | 0.622957i | \(0.214069\pi\) | |||||||
\(24\) | 1.18715 | 0.242326 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −10.3433 | −2.02849 | ||||||||
\(27\) | 1.06564 | 0.205082 | ||||||||
\(28\) | 1.06990 | 0.202193 | ||||||||
\(29\) | 4.49806 | 0.835269 | 0.417634 | − | 0.908615i | \(-0.362859\pi\) | ||||
0.417634 | + | 0.908615i | \(0.362859\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.05402 | 1.08733 | 0.543667 | − | 0.839301i | \(-0.317035\pi\) | ||||
0.543667 | + | 0.839301i | \(0.317035\pi\) | |||||||
\(32\) | −6.95136 | −1.22884 | ||||||||
\(33\) | 0.482909 | 0.0840636 | ||||||||
\(34\) | −5.89319 | −1.01067 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −13.6235 | −2.27059 | ||||||||
\(37\) | 5.80342 | 0.954076 | 0.477038 | − | 0.878883i | \(-0.341710\pi\) | ||||
0.477038 | + | 0.878883i | \(0.341710\pi\) | |||||||
\(38\) | 12.6196 | 2.04717 | ||||||||
\(39\) | −0.719432 | −0.115201 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.99623 | 1.40497 | 0.702487 | − | 0.711696i | \(-0.252073\pi\) | ||||
0.702487 | + | 0.711696i | \(0.252073\pi\) | |||||||
\(42\) | 0.106844 | 0.0164864 | ||||||||
\(43\) | −11.2724 | −1.71902 | −0.859509 | − | 0.511120i | \(-0.829231\pi\) | ||||
−0.859509 | + | 0.511120i | \(0.829231\pi\) | |||||||
\(44\) | −12.4137 | −1.87144 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −19.2612 | −2.83992 | ||||||||
\(47\) | 5.27836 | 0.769928 | 0.384964 | − | 0.922932i | \(-0.374214\pi\) | ||||
0.384964 | + | 0.922932i | \(0.374214\pi\) | |||||||
\(48\) | −1.40840 | −0.203286 | ||||||||
\(49\) | −6.94567 | −0.992238 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.409904 | −0.0573980 | ||||||||
\(52\) | 18.4938 | 2.56463 | ||||||||
\(53\) | 2.38830 | 0.328058 | 0.164029 | − | 0.986455i | \(-0.447551\pi\) | ||||
0.164029 | + | 0.986455i | \(0.447551\pi\) | |||||||
\(54\) | −2.73559 | −0.372267 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.54978 | −0.207098 | ||||||||
\(57\) | 0.877763 | 0.116263 | ||||||||
\(58\) | −11.5469 | −1.51619 | ||||||||
\(59\) | −9.48259 | −1.23453 | −0.617264 | − | 0.786756i | \(-0.711759\pi\) | ||||
−0.617264 | + | 0.786756i | \(0.711759\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.25056 | −1.05638 | −0.528188 | − | 0.849128i | \(-0.677128\pi\) | ||||
−0.528188 | + | 0.849128i | \(0.677128\pi\) | |||||||
\(62\) | −15.5412 | −1.97374 | ||||||||
\(63\) | −0.691859 | −0.0871660 | ||||||||
\(64\) | 2.06921 | 0.258651 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.23967 | −0.152593 | ||||||||
\(67\) | 6.20669 | 0.758268 | 0.379134 | − | 0.925342i | \(-0.376222\pi\) | ||||
0.379134 | + | 0.925342i | \(0.376222\pi\) | |||||||
\(68\) | 10.5370 | 1.27780 | ||||||||
\(69\) | −1.33972 | −0.161284 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.53076 | 0.300345 | 0.150173 | − | 0.988660i | \(-0.452017\pi\) | ||||
0.150173 | + | 0.988660i | \(0.452017\pi\) | |||||||
\(72\) | 19.7340 | 2.32567 | ||||||||
\(73\) | −14.9325 | −1.74771 | −0.873857 | − | 0.486184i | \(-0.838389\pi\) | ||||
−0.873857 | + | 0.486184i | \(0.838389\pi\) | |||||||
\(74\) | −14.8979 | −1.73185 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −22.5639 | −2.58825 | ||||||||
\(77\) | −0.630419 | −0.0718429 | ||||||||
\(78\) | 1.84685 | 0.209114 | ||||||||
\(79\) | −11.7640 | −1.32355 | −0.661775 | − | 0.749702i | \(-0.730197\pi\) | ||||
−0.661775 | + | 0.749702i | \(0.730197\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.71408 | 0.968231 | ||||||||
\(82\) | −23.0941 | −2.55032 | ||||||||
\(83\) | 10.5955 | 1.16300 | 0.581502 | − | 0.813545i | \(-0.302465\pi\) | ||||
0.581502 | + | 0.813545i | \(0.302465\pi\) | |||||||
\(84\) | −0.191037 | −0.0208438 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 28.9372 | 3.12037 | ||||||||
\(87\) | −0.803151 | −0.0861069 | ||||||||
\(88\) | 17.9815 | 1.91684 | ||||||||
\(89\) | 8.13410 | 0.862213 | 0.431107 | − | 0.902301i | \(-0.358123\pi\) | ||||
0.431107 | + | 0.902301i | \(0.358123\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.939190 | 0.0984538 | ||||||||
\(92\) | 34.4391 | 3.59052 | ||||||||
\(93\) | −1.08098 | −0.112092 | ||||||||
\(94\) | −13.5500 | −1.39758 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.24120 | 0.126680 | ||||||||
\(97\) | −14.0886 | −1.43048 | −0.715242 | − | 0.698877i | \(-0.753683\pi\) | ||||
−0.715242 | + | 0.698877i | \(0.753683\pi\) | |||||||
\(98\) | 17.8302 | 1.80112 | ||||||||
\(99\) | 8.02738 | 0.806783 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.76268 | −0.772416 | −0.386208 | − | 0.922412i | \(-0.626215\pi\) | ||||
−0.386208 | + | 0.922412i | \(0.626215\pi\) | |||||||
\(102\) | 1.05226 | 0.104189 | ||||||||
\(103\) | 8.88600 | 0.875563 | 0.437782 | − | 0.899081i | \(-0.355764\pi\) | ||||
0.437782 | + | 0.899081i | \(0.355764\pi\) | |||||||
\(104\) | −26.7887 | −2.62684 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.13099 | −0.595494 | ||||||||
\(107\) | −12.7644 | −1.23398 | −0.616989 | − | 0.786972i | \(-0.711648\pi\) | ||||
−0.616989 | + | 0.786972i | \(0.711648\pi\) | |||||||
\(108\) | 4.89123 | 0.470659 | ||||||||
\(109\) | −5.34986 | −0.512424 | −0.256212 | − | 0.966621i | \(-0.582474\pi\) | ||||
−0.256212 | + | 0.966621i | \(0.582474\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.03623 | −0.0983546 | ||||||||
\(112\) | 1.83862 | 0.173733 | ||||||||
\(113\) | −3.26328 | −0.306984 | −0.153492 | − | 0.988150i | \(-0.549052\pi\) | ||||
−0.153492 | + | 0.988150i | \(0.549052\pi\) | |||||||
\(114\) | −2.25330 | −0.211041 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 20.6459 | 1.91692 | ||||||||
\(117\) | −11.9591 | −1.10562 | ||||||||
\(118\) | 24.3427 | 2.24092 | ||||||||
\(119\) | 0.535113 | 0.0490537 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.68548 | −0.335044 | ||||||||
\(122\) | 21.1799 | 1.91754 | ||||||||
\(123\) | −1.60632 | −0.144837 | ||||||||
\(124\) | 27.7877 | 2.49541 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.77606 | 0.158224 | ||||||||
\(127\) | 1.32893 | 0.117923 | 0.0589617 | − | 0.998260i | \(-0.481221\pi\) | ||||
0.0589617 | + | 0.998260i | \(0.481221\pi\) | |||||||
\(128\) | 8.59089 | 0.759334 | ||||||||
\(129\) | 2.01274 | 0.177212 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.62895 | 0.491803 | 0.245902 | − | 0.969295i | \(-0.420916\pi\) | ||||
0.245902 | + | 0.969295i | \(0.420916\pi\) | |||||||
\(132\) | 2.21653 | 0.192924 | ||||||||
\(133\) | −1.14589 | −0.0993609 | ||||||||
\(134\) | −15.9331 | −1.37641 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.2631 | −1.30880 | ||||||||
\(137\) | −5.95727 | −0.508964 | −0.254482 | − | 0.967078i | \(-0.581905\pi\) | ||||
−0.254482 | + | 0.967078i | \(0.581905\pi\) | |||||||
\(138\) | 3.43919 | 0.292764 | ||||||||
\(139\) | 11.9718 | 1.01544 | 0.507718 | − | 0.861523i | \(-0.330489\pi\) | ||||
0.507718 | + | 0.861523i | \(0.330489\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.942479 | −0.0793710 | ||||||||
\(142\) | −6.49668 | −0.545189 | ||||||||
\(143\) | −10.8971 | −0.911260 | ||||||||
\(144\) | −23.4119 | −1.95099 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 38.3330 | 3.17246 | ||||||||
\(147\) | 1.24018 | 0.102289 | ||||||||
\(148\) | 26.6374 | 2.18958 | ||||||||
\(149\) | −6.34461 | −0.519770 | −0.259885 | − | 0.965640i | \(-0.583685\pi\) | ||||
−0.259885 | + | 0.965640i | \(0.583685\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.34920 | −0.109797 | −0.0548984 | − | 0.998492i | \(-0.517483\pi\) | ||||
−0.0548984 | + | 0.998492i | \(0.517483\pi\) | |||||||
\(152\) | 32.6843 | 2.65105 | ||||||||
\(153\) | −6.81382 | −0.550865 | ||||||||
\(154\) | 1.61834 | 0.130410 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.30216 | −0.264384 | ||||||||
\(157\) | −11.7955 | −0.941380 | −0.470690 | − | 0.882299i | \(-0.655995\pi\) | ||||
−0.470690 | + | 0.882299i | \(0.655995\pi\) | |||||||
\(158\) | 30.1992 | 2.40252 | ||||||||
\(159\) | −0.426443 | −0.0338192 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.74896 | 0.137837 | ||||||||
\(162\) | −22.3698 | −1.75754 | ||||||||
\(163\) | 0.738249 | 0.0578241 | 0.0289121 | − | 0.999582i | \(-0.490796\pi\) | ||||
0.0289121 | + | 0.999582i | \(0.490796\pi\) | |||||||
\(164\) | 41.2923 | 3.22439 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −27.1995 | −2.11109 | ||||||||
\(167\) | 22.9727 | 1.77768 | 0.888841 | − | 0.458217i | \(-0.151512\pi\) | ||||
0.888841 | + | 0.458217i | \(0.151512\pi\) | |||||||
\(168\) | 0.276721 | 0.0213495 | ||||||||
\(169\) | 3.23433 | 0.248795 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.5910 | 1.11580 | ||||||||
\(172\) | −51.7396 | −3.94511 | ||||||||
\(173\) | 9.38513 | 0.713538 | 0.356769 | − | 0.934193i | \(-0.383878\pi\) | ||||
0.356769 | + | 0.934193i | \(0.383878\pi\) | |||||||
\(174\) | 2.06176 | 0.156302 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −21.3328 | −1.60802 | ||||||||
\(177\) | 1.69316 | 0.127266 | ||||||||
\(178\) | −20.8810 | −1.56510 | ||||||||
\(179\) | 26.1678 | 1.95587 | 0.977937 | − | 0.208900i | \(-0.0669883\pi\) | ||||
0.977937 | + | 0.208900i | \(0.0669883\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.5772 | 1.60382 | 0.801909 | − | 0.597446i | \(-0.203818\pi\) | ||||
0.801909 | + | 0.597446i | \(0.203818\pi\) | |||||||
\(182\) | −2.41099 | −0.178714 | ||||||||
\(183\) | 1.47318 | 0.108901 | ||||||||
\(184\) | −49.8858 | −3.67763 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.77496 | 0.203470 | ||||||||
\(187\) | −6.20872 | −0.454027 | ||||||||
\(188\) | 24.2275 | 1.76697 | ||||||||
\(189\) | 0.248397 | 0.0180682 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.3838 | 1.04078 | 0.520388 | − | 0.853930i | \(-0.325787\pi\) | ||||
0.520388 | + | 0.853930i | \(0.325787\pi\) | |||||||
\(192\) | −0.369467 | −0.0266640 | ||||||||
\(193\) | 17.5667 | 1.26448 | 0.632239 | − | 0.774773i | \(-0.282136\pi\) | ||||
0.632239 | + | 0.774773i | \(0.282136\pi\) | |||||||
\(194\) | 36.1668 | 2.59662 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −31.8803 | −2.27716 | ||||||||
\(197\) | −14.9323 | −1.06388 | −0.531939 | − | 0.846782i | \(-0.678537\pi\) | ||||
−0.531939 | + | 0.846782i | \(0.678537\pi\) | |||||||
\(198\) | −20.6070 | −1.46448 | ||||||||
\(199\) | 20.4277 | 1.44808 | 0.724041 | − | 0.689757i | \(-0.242283\pi\) | ||||
0.724041 | + | 0.689757i | \(0.242283\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.10824 | −0.0781690 | ||||||||
\(202\) | 19.9275 | 1.40210 | ||||||||
\(203\) | 1.04848 | 0.0735891 | ||||||||
\(204\) | −1.88144 | −0.131727 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −22.8112 | −1.58933 | ||||||||
\(207\) | −22.2702 | −1.54789 | ||||||||
\(208\) | 31.7814 | 2.20364 | ||||||||
\(209\) | 13.2953 | 0.919655 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.8689 | 1.43667 | 0.718336 | − | 0.695697i | \(-0.244904\pi\) | ||||
0.718336 | + | 0.695697i | \(0.244904\pi\) | |||||||
\(212\) | 10.9622 | 0.752887 | ||||||||
\(213\) | −0.451879 | −0.0309623 | ||||||||
\(214\) | 32.7673 | 2.23993 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7.08506 | −0.482077 | ||||||||
\(217\) | 1.41117 | 0.0957966 | ||||||||
\(218\) | 13.7336 | 0.930155 | ||||||||
\(219\) | 2.66627 | 0.180170 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.24968 | 0.622201 | ||||||||
\(222\) | 2.66010 | 0.178534 | ||||||||
\(223\) | 18.1628 | 1.21627 | 0.608136 | − | 0.793833i | \(-0.291918\pi\) | ||||
0.608136 | + | 0.793833i | \(0.291918\pi\) | |||||||
\(224\) | −1.62034 | −0.108264 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.37714 | 0.557239 | ||||||||
\(227\) | −19.5161 | −1.29533 | −0.647664 | − | 0.761926i | \(-0.724254\pi\) | ||||
−0.647664 | + | 0.761926i | \(0.724254\pi\) | |||||||
\(228\) | 4.02890 | 0.266820 | ||||||||
\(229\) | −24.8125 | −1.63966 | −0.819828 | − | 0.572610i | \(-0.805931\pi\) | ||||
−0.819828 | + | 0.572610i | \(0.805931\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.112564 | 0.00740620 | ||||||||
\(232\) | −29.9060 | −1.96343 | ||||||||
\(233\) | 20.5870 | 1.34870 | 0.674349 | − | 0.738412i | \(-0.264424\pi\) | ||||
0.674349 | + | 0.738412i | \(0.264424\pi\) | |||||||
\(234\) | 30.7001 | 2.00693 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −43.5247 | −2.83321 | ||||||||
\(237\) | 2.10052 | 0.136443 | ||||||||
\(238\) | −1.37368 | −0.0890427 | ||||||||
\(239\) | −18.4486 | −1.19334 | −0.596670 | − | 0.802487i | \(-0.703510\pi\) | ||||
−0.596670 | + | 0.802487i | \(0.703510\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | 9.46096 | 0.608174 | ||||||||
\(243\) | −4.75286 | −0.304896 | ||||||||
\(244\) | −37.8697 | −2.42436 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.12357 | 0.262910 | ||||||||
\(247\) | −19.8072 | −1.26030 | ||||||||
\(248\) | −40.2511 | −2.55595 | ||||||||
\(249\) | −1.89187 | −0.119893 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.0239 | −1.26390 | −0.631948 | − | 0.775011i | \(-0.717744\pi\) | ||||
−0.631948 | + | 0.775011i | \(0.717744\pi\) | |||||||
\(252\) | −3.17560 | −0.200044 | ||||||||
\(253\) | −20.2925 | −1.27578 | ||||||||
\(254\) | −3.41148 | −0.214055 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −26.1920 | −1.63700 | ||||||||
\(257\) | 13.1798 | 0.822135 | 0.411067 | − | 0.911605i | \(-0.365156\pi\) | ||||
0.411067 | + | 0.911605i | \(0.365156\pi\) | |||||||
\(258\) | −5.16688 | −0.321676 | ||||||||
\(259\) | 1.35276 | 0.0840562 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.3508 | −0.826392 | ||||||||
\(262\) | −14.4500 | −0.892725 | ||||||||
\(263\) | 16.5297 | 1.01927 | 0.509633 | − | 0.860392i | \(-0.329781\pi\) | ||||
0.509633 | + | 0.860392i | \(0.329781\pi\) | |||||||
\(264\) | −3.21069 | −0.197605 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.94159 | 0.180361 | ||||||||
\(267\) | −1.45239 | −0.0888845 | ||||||||
\(268\) | 28.4885 | 1.74021 | ||||||||
\(269\) | −22.8468 | −1.39300 | −0.696498 | − | 0.717559i | \(-0.745259\pi\) | ||||
−0.696498 | + | 0.717559i | \(0.745259\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.40601 | 0.267646 | 0.133823 | − | 0.991005i | \(-0.457275\pi\) | ||||
0.133823 | + | 0.991005i | \(0.457275\pi\) | |||||||
\(272\) | 18.1078 | 1.09794 | ||||||||
\(273\) | −0.167697 | −0.0101495 | ||||||||
\(274\) | 15.2929 | 0.923875 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.14927 | −0.370143 | ||||||||
\(277\) | −19.2045 | −1.15388 | −0.576942 | − | 0.816785i | \(-0.695754\pi\) | ||||
−0.576942 | + | 0.816785i | \(0.695754\pi\) | |||||||
\(278\) | −30.7327 | −1.84323 | ||||||||
\(279\) | −17.9691 | −1.07578 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.4603 | 0.802974 | 0.401487 | − | 0.915865i | \(-0.368493\pi\) | ||||
0.401487 | + | 0.915865i | \(0.368493\pi\) | |||||||
\(282\) | 2.41943 | 0.144075 | ||||||||
\(283\) | 21.3025 | 1.26631 | 0.633153 | − | 0.774027i | \(-0.281761\pi\) | ||||
0.633153 | + | 0.774027i | \(0.281761\pi\) | |||||||
\(284\) | 11.6161 | 0.689286 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 27.9738 | 1.65413 | ||||||||
\(287\) | 2.09699 | 0.123781 | ||||||||
\(288\) | 20.6325 | 1.21578 | ||||||||
\(289\) | −11.7299 | −0.689994 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.51560 | 0.147467 | ||||||||
\(292\) | −68.5394 | −4.01096 | ||||||||
\(293\) | −13.5661 | −0.792538 | −0.396269 | − | 0.918135i | \(-0.629695\pi\) | ||||
−0.396269 | + | 0.918135i | \(0.629695\pi\) | |||||||
\(294\) | −3.18367 | −0.185675 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −38.5849 | −2.24270 | ||||||||
\(297\) | −2.88206 | −0.167234 | ||||||||
\(298\) | 16.2872 | 0.943491 | ||||||||
\(299\) | 30.2315 | 1.74834 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.62755 | −0.151449 | ||||||||
\(302\) | 3.46353 | 0.199304 | ||||||||
\(303\) | 1.38607 | 0.0796275 | ||||||||
\(304\) | −38.7758 | −2.22394 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 17.4917 | 0.999934 | ||||||||
\(307\) | 9.29421 | 0.530449 | 0.265224 | − | 0.964187i | \(-0.414554\pi\) | ||||
0.265224 | + | 0.964187i | \(0.414554\pi\) | |||||||
\(308\) | −2.89359 | −0.164878 | ||||||||
\(309\) | −1.58664 | −0.0902608 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.71432 | −0.267325 | −0.133662 | − | 0.991027i | \(-0.542674\pi\) | ||||
−0.133662 | + | 0.991027i | \(0.542674\pi\) | |||||||
\(312\) | 4.78325 | 0.270798 | ||||||||
\(313\) | −11.4092 | −0.644883 | −0.322442 | − | 0.946589i | \(-0.604504\pi\) | ||||
−0.322442 | + | 0.946589i | \(0.604504\pi\) | |||||||
\(314\) | 30.2800 | 1.70880 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −53.9961 | −3.03752 | ||||||||
\(317\) | 29.2232 | 1.64134 | 0.820670 | − | 0.571402i | \(-0.193600\pi\) | ||||
0.820670 | + | 0.571402i | \(0.193600\pi\) | |||||||
\(318\) | 1.09472 | 0.0613888 | ||||||||
\(319\) | −12.1652 | −0.681119 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.27914 | 0.127209 | ||||||||
\(322\) | −4.48973 | −0.250203 | ||||||||
\(323\) | −11.2853 | −0.627933 | ||||||||
\(324\) | 39.9972 | 2.22207 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.89515 | −0.104963 | ||||||||
\(327\) | 0.955245 | 0.0528252 | ||||||||
\(328\) | −59.8128 | −3.30261 | ||||||||
\(329\) | 1.23037 | 0.0678324 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.4423 | −0.903752 | −0.451876 | − | 0.892081i | \(-0.649245\pi\) | ||||
−0.451876 | + | 0.892081i | \(0.649245\pi\) | |||||||
\(332\) | 48.6327 | 2.66907 | ||||||||
\(333\) | −17.2252 | −0.943937 | ||||||||
\(334\) | −58.9730 | −3.22686 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.328295 | −0.0179099 | ||||||||
\(337\) | 25.8566 | 1.40850 | 0.704250 | − | 0.709952i | \(-0.251284\pi\) | ||||
0.704250 | + | 0.709952i | \(0.251284\pi\) | |||||||
\(338\) | −8.30283 | −0.451614 | ||||||||
\(339\) | 0.582676 | 0.0316466 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.3733 | −0.886665 | ||||||||
\(342\) | −37.4565 | −2.02542 | ||||||||
\(343\) | −3.25069 | −0.175521 | ||||||||
\(344\) | 74.9460 | 4.04082 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −24.0925 | −1.29522 | ||||||||
\(347\) | −12.0753 | −0.648235 | −0.324118 | − | 0.946017i | \(-0.605067\pi\) | ||||
−0.324118 | + | 0.946017i | \(0.605067\pi\) | |||||||
\(348\) | −3.68643 | −0.197613 | ||||||||
\(349\) | 5.32729 | 0.285163 | 0.142582 | − | 0.989783i | \(-0.454460\pi\) | ||||
0.142582 | + | 0.989783i | \(0.454460\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.29365 | 0.229178 | ||||||||
\(352\) | 18.8002 | 1.00206 | ||||||||
\(353\) | 23.9377 | 1.27407 | 0.637037 | − | 0.770833i | \(-0.280160\pi\) | ||||
0.637037 | + | 0.770833i | \(0.280160\pi\) | |||||||
\(354\) | −4.34651 | −0.231014 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 37.3352 | 1.97876 | ||||||||
\(357\) | −0.0955472 | −0.00505689 | ||||||||
\(358\) | −67.1752 | −3.55032 | ||||||||
\(359\) | −36.1319 | −1.90697 | −0.953483 | − | 0.301446i | \(-0.902531\pi\) | ||||
−0.953483 | + | 0.301446i | \(0.902531\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.16631 | 0.271911 | ||||||||
\(362\) | −55.3905 | −2.91126 | ||||||||
\(363\) | 0.658061 | 0.0345393 | ||||||||
\(364\) | 4.31084 | 0.225949 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.78178 | −0.197677 | ||||||||
\(367\) | 10.0823 | 0.526293 | 0.263146 | − | 0.964756i | \(-0.415240\pi\) | ||||
0.263146 | + | 0.964756i | \(0.415240\pi\) | |||||||
\(368\) | 59.1832 | 3.08514 | ||||||||
\(369\) | −26.7019 | −1.39004 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.556705 | 0.0289027 | ||||||||
\(372\) | −4.96164 | −0.257249 | ||||||||
\(373\) | 27.0997 | 1.40317 | 0.701583 | − | 0.712587i | \(-0.252477\pi\) | ||||
0.701583 | + | 0.712587i | \(0.252477\pi\) | |||||||
\(374\) | 15.9384 | 0.824153 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −35.0940 | −1.80984 | ||||||||
\(377\) | 18.1235 | 0.933408 | ||||||||
\(378\) | −0.637657 | −0.0327975 | ||||||||
\(379\) | 11.1061 | 0.570481 | 0.285241 | − | 0.958456i | \(-0.407926\pi\) | ||||
0.285241 | + | 0.958456i | \(0.407926\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.237287 | −0.0121566 | ||||||||
\(382\) | −36.9246 | −1.88923 | ||||||||
\(383\) | −5.90068 | −0.301511 | −0.150755 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150755 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(384\) | −1.53395 | −0.0782789 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −45.0953 | −2.29529 | ||||||||
\(387\) | 33.4577 | 1.70075 | ||||||||
\(388\) | −64.6662 | −3.28293 | ||||||||
\(389\) | 15.5666 | 0.789260 | 0.394630 | − | 0.918840i | \(-0.370873\pi\) | ||||
0.394630 | + | 0.918840i | \(0.370873\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.2247 | 0.871092 | ||||||||
\(392\) | 46.1793 | 2.33241 | ||||||||
\(393\) | −1.00508 | −0.0506994 | ||||||||
\(394\) | 38.3324 | 1.93116 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 36.8453 | 1.85155 | ||||||||
\(397\) | 3.12799 | 0.156989 | 0.0784947 | − | 0.996915i | \(-0.474989\pi\) | ||||
0.0784947 | + | 0.996915i | \(0.474989\pi\) | |||||||
\(398\) | −52.4398 | −2.62857 | ||||||||
\(399\) | 0.204604 | 0.0102430 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.8045 | −0.689366 | −0.344683 | − | 0.938719i | \(-0.612014\pi\) | ||||
−0.344683 | + | 0.938719i | \(0.612014\pi\) | |||||||
\(402\) | 2.84494 | 0.141893 | ||||||||
\(403\) | 24.3928 | 1.21509 | ||||||||
\(404\) | −35.6304 | −1.77268 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.69155 | −0.133579 | ||||||||
\(407\) | −15.6956 | −0.778000 | ||||||||
\(408\) | 2.72531 | 0.134923 | ||||||||
\(409\) | 39.2212 | 1.93936 | 0.969681 | − | 0.244372i | \(-0.0785819\pi\) | ||||
0.969681 | + | 0.244372i | \(0.0785819\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.06370 | 0.0524685 | ||||||||
\(412\) | 40.7863 | 2.00940 | ||||||||
\(413\) | −2.21036 | −0.108765 | ||||||||
\(414\) | 57.1696 | 2.80973 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −28.0083 | −1.37322 | ||||||||
\(417\) | −2.13763 | −0.104680 | ||||||||
\(418\) | −34.1302 | −1.66936 | ||||||||
\(419\) | 31.2132 | 1.52487 | 0.762433 | − | 0.647068i | \(-0.224005\pi\) | ||||
0.762433 | + | 0.647068i | \(0.224005\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.1438 | 1.37165 | 0.685823 | − | 0.727768i | \(-0.259442\pi\) | ||||
0.685823 | + | 0.727768i | \(0.259442\pi\) | |||||||
\(422\) | −53.5723 | −2.60786 | ||||||||
\(423\) | −15.6668 | −0.761746 | ||||||||
\(424\) | −15.8790 | −0.771152 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.16002 | 0.0562029 | ||||||||
\(427\) | −1.92318 | −0.0930691 | ||||||||
\(428\) | −58.5879 | −2.83195 | ||||||||
\(429\) | 1.94573 | 0.0939407 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.72745 | 0.275881 | 0.137941 | − | 0.990440i | \(-0.455952\pi\) | ||||
0.137941 | + | 0.990440i | \(0.455952\pi\) | |||||||
\(432\) | 8.40553 | 0.404411 | ||||||||
\(433\) | −26.5109 | −1.27403 | −0.637015 | − | 0.770851i | \(-0.719831\pi\) | ||||
−0.637015 | + | 0.770851i | \(0.719831\pi\) | |||||||
\(434\) | −3.62261 | −0.173891 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −24.5556 | −1.17600 | ||||||||
\(437\) | −36.8849 | −1.76444 | ||||||||
\(438\) | −6.84455 | −0.327045 | ||||||||
\(439\) | −4.16948 | −0.198998 | −0.0994991 | − | 0.995038i | \(-0.531724\pi\) | ||||
−0.0994991 | + | 0.995038i | \(0.531724\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.6156 | 0.981693 | ||||||||
\(442\) | −23.7448 | −1.12942 | ||||||||
\(443\) | 15.9514 | 0.757876 | 0.378938 | − | 0.925422i | \(-0.376289\pi\) | ||||
0.378938 | + | 0.925422i | \(0.376289\pi\) | |||||||
\(444\) | −4.75625 | −0.225722 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −46.6256 | −2.20778 | ||||||||
\(447\) | 1.13286 | 0.0535825 | ||||||||
\(448\) | 0.482325 | 0.0227877 | ||||||||
\(449\) | −11.6872 | −0.551555 | −0.275777 | − | 0.961222i | \(-0.588935\pi\) | ||||
−0.275777 | + | 0.961222i | \(0.588935\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.3306 | −1.14568 | ||||||||
\(452\) | −14.9783 | −0.704521 | ||||||||
\(453\) | 0.240907 | 0.0113188 | ||||||||
\(454\) | 50.0996 | 2.35129 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.83594 | −0.273293 | ||||||||
\(457\) | 17.7543 | 0.830512 | 0.415256 | − | 0.909705i | \(-0.363692\pi\) | ||||
0.415256 | + | 0.909705i | \(0.363692\pi\) | |||||||
\(458\) | 63.6959 | 2.97631 | ||||||||
\(459\) | 2.44635 | 0.114186 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.4673 | 0.860110 | 0.430055 | − | 0.902803i | \(-0.358494\pi\) | ||||
0.430055 | + | 0.902803i | \(0.358494\pi\) | |||||||
\(462\) | −0.288963 | −0.0134438 | ||||||||
\(463\) | 29.3713 | 1.36500 | 0.682501 | − | 0.730885i | \(-0.260892\pi\) | ||||
0.682501 | + | 0.730885i | \(0.260892\pi\) | |||||||
\(464\) | 35.4797 | 1.64711 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −52.8487 | −2.44817 | ||||||||
\(467\) | −25.3892 | −1.17487 | −0.587436 | − | 0.809271i | \(-0.699863\pi\) | ||||
−0.587436 | + | 0.809271i | \(0.699863\pi\) | |||||||
\(468\) | −54.8917 | −2.53737 | ||||||||
\(469\) | 1.44676 | 0.0668052 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.10614 | 0.0970458 | ||||||||
\(472\) | 63.0464 | 2.90195 | ||||||||
\(473\) | 30.4865 | 1.40177 | ||||||||
\(474\) | −5.39222 | −0.247673 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.45615 | 0.112577 | ||||||||
\(477\) | −7.08876 | −0.324572 | ||||||||
\(478\) | 47.3592 | 2.16616 | ||||||||
\(479\) | −0.814950 | −0.0372360 | −0.0186180 | − | 0.999827i | \(-0.505927\pi\) | ||||
−0.0186180 | + | 0.999827i | \(0.505927\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.3830 | 1.06617 | ||||||||
\(482\) | 2.56709 | 0.116928 | ||||||||
\(483\) | −0.312285 | −0.0142095 | ||||||||
\(484\) | −16.9162 | −0.768918 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 12.2010 | 0.553449 | ||||||||
\(487\) | 35.9667 | 1.62980 | 0.814902 | − | 0.579598i | \(-0.196790\pi\) | ||||
0.814902 | + | 0.579598i | \(0.196790\pi\) | |||||||
\(488\) | 54.8551 | 2.48317 | ||||||||
\(489\) | −0.131818 | −0.00596102 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.75932 | −0.305044 | −0.152522 | − | 0.988300i | \(-0.548739\pi\) | ||||
−0.152522 | + | 0.988300i | \(0.548739\pi\) | |||||||
\(492\) | −7.37295 | −0.332398 | ||||||||
\(493\) | 10.3261 | 0.465062 | ||||||||
\(494\) | 50.8468 | 2.28771 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 47.7528 | 2.14417 | ||||||||
\(497\) | 0.589911 | 0.0264611 | ||||||||
\(498\) | 4.85661 | 0.217630 | ||||||||
\(499\) | 23.2029 | 1.03870 | 0.519351 | − | 0.854561i | \(-0.326174\pi\) | ||||
0.519351 | + | 0.854561i | \(0.326174\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.10189 | −0.183259 | ||||||||
\(502\) | 51.4031 | 2.29423 | ||||||||
\(503\) | −12.1662 | −0.542466 | −0.271233 | − | 0.962514i | \(-0.587431\pi\) | ||||
−0.271233 | + | 0.962514i | \(0.587431\pi\) | |||||||
\(504\) | 4.59993 | 0.204897 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 52.0927 | 2.31580 | ||||||||
\(507\) | −0.577507 | −0.0256480 | ||||||||
\(508\) | 6.09973 | 0.270632 | ||||||||
\(509\) | −25.2595 | −1.11961 | −0.559803 | − | 0.828626i | \(-0.689123\pi\) | ||||
−0.559803 | + | 0.828626i | \(0.689123\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.48071 | −0.153977 | ||||||||
\(512\) | 50.0555 | 2.21216 | ||||||||
\(513\) | −5.23859 | −0.231290 | ||||||||
\(514\) | −33.8338 | −1.49234 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.23837 | 0.406697 | ||||||||
\(517\) | −14.2755 | −0.627837 | ||||||||
\(518\) | −3.47265 | −0.152580 | ||||||||
\(519\) | −1.67576 | −0.0735578 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.2216 | 0.623061 | 0.311531 | − | 0.950236i | \(-0.399158\pi\) | ||||
0.311531 | + | 0.950236i | \(0.399158\pi\) | |||||||
\(522\) | 34.2726 | 1.50007 | ||||||||
\(523\) | −5.16693 | −0.225934 | −0.112967 | − | 0.993599i | \(-0.536035\pi\) | ||||
−0.112967 | + | 0.993599i | \(0.536035\pi\) | |||||||
\(524\) | 25.8366 | 1.12868 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −42.4333 | −1.85018 | ||||||||
\(527\) | 13.8980 | 0.605408 | ||||||||
\(528\) | 3.80908 | 0.165769 | ||||||||
\(529\) | 33.2971 | 1.44770 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.1454 | 1.22141 | ||||||||
\(532\) | −5.25957 | −0.228031 | ||||||||
\(533\) | 36.2475 | 1.57005 | ||||||||
\(534\) | 3.72841 | 0.161344 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −41.2662 | −1.78243 | ||||||||
\(537\) | −4.67240 | −0.201629 | ||||||||
\(538\) | 58.6499 | 2.52858 | ||||||||
\(539\) | 18.7848 | 0.809119 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.312394 | 0.0134309 | 0.00671544 | − | 0.999977i | \(-0.497862\pi\) | ||||
0.00671544 | + | 0.999977i | \(0.497862\pi\) | |||||||
\(542\) | −11.3106 | −0.485833 | ||||||||
\(543\) | −3.85271 | −0.165336 | ||||||||
\(544\) | −15.9580 | −0.684195 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.430494 | 0.0184234 | ||||||||
\(547\) | −0.0177707 | −0.000759822 0 | −0.000379911 | − | 1.00000i | \(-0.500121\pi\) | ||||
−0.000379911 | 1.00000i | \(0.500121\pi\) | ||||||||
\(548\) | −27.3436 | −1.16806 | ||||||||
\(549\) | 24.4886 | 1.04515 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.1121 | −0.942008 | ||||||||
\(552\) | 8.90736 | 0.379122 | ||||||||
\(553\) | −2.74214 | −0.116608 | ||||||||
\(554\) | 49.2996 | 2.09454 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 54.9501 | 2.33040 | ||||||||
\(557\) | −8.43223 | −0.357285 | −0.178643 | − | 0.983914i | \(-0.557171\pi\) | ||||
−0.178643 | + | 0.983914i | \(0.557171\pi\) | |||||||
\(558\) | 46.1282 | 1.95276 | ||||||||
\(559\) | −45.4184 | −1.92099 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.10860 | 0.0468051 | ||||||||
\(562\) | −34.5538 | −1.45756 | ||||||||
\(563\) | 19.9555 | 0.841023 | 0.420511 | − | 0.907287i | \(-0.361851\pi\) | ||||
0.420511 | + | 0.907287i | \(0.361851\pi\) | |||||||
\(564\) | −4.32594 | −0.182155 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −54.6856 | −2.29861 | ||||||||
\(567\) | 2.03122 | 0.0853034 | ||||||||
\(568\) | −16.8261 | −0.706008 | ||||||||
\(569\) | −27.4439 | −1.15051 | −0.575254 | − | 0.817975i | \(-0.695097\pi\) | ||||
−0.575254 | + | 0.817975i | \(0.695097\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.2360 | −1.80937 | −0.904686 | − | 0.426080i | \(-0.859894\pi\) | ||||
−0.904686 | + | 0.426080i | \(0.859894\pi\) | |||||||
\(572\) | −50.0171 | −2.09132 | ||||||||
\(573\) | −2.56830 | −0.107292 | ||||||||
\(574\) | −5.38317 | −0.224689 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.14165 | −0.255902 | ||||||||
\(577\) | 25.9833 | 1.08170 | 0.540850 | − | 0.841119i | \(-0.318103\pi\) | ||||
0.540850 | + | 0.841119i | \(0.318103\pi\) | |||||||
\(578\) | 30.1117 | 1.25248 | ||||||||
\(579\) | −3.13662 | −0.130354 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.46977 | 0.102463 | ||||||||
\(582\) | −6.45776 | −0.267683 | ||||||||
\(583\) | −6.45925 | −0.267515 | ||||||||
\(584\) | 99.2808 | 4.10827 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 34.8253 | 1.43862 | ||||||||
\(587\) | 24.6564 | 1.01768 | 0.508840 | − | 0.860861i | \(-0.330075\pi\) | ||||
0.508840 | + | 0.860861i | \(0.330075\pi\) | |||||||
\(588\) | 5.69239 | 0.234750 | ||||||||
\(589\) | −29.7611 | −1.22629 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.66623 | 0.109674 | ||||||||
\(592\) | 45.7761 | 1.88139 | ||||||||
\(593\) | −8.55003 | −0.351108 | −0.175554 | − | 0.984470i | \(-0.556172\pi\) | ||||
−0.175554 | + | 0.984470i | \(0.556172\pi\) | |||||||
\(594\) | 7.39850 | 0.303564 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −29.1215 | −1.19286 | ||||||||
\(597\) | −3.64747 | −0.149281 | ||||||||
\(598\) | −77.6071 | −3.17359 | ||||||||
\(599\) | 39.3935 | 1.60957 | 0.804787 | − | 0.593564i | \(-0.202280\pi\) | ||||
0.804787 | + | 0.593564i | \(0.202280\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.7899 | 1.29674 | 0.648368 | − | 0.761327i | \(-0.275452\pi\) | ||||
0.648368 | + | 0.761327i | \(0.275452\pi\) | |||||||
\(602\) | 6.74516 | 0.274912 | ||||||||
\(603\) | −18.4222 | −0.750210 | ||||||||
\(604\) | −6.19279 | −0.251981 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.55816 | −0.144540 | ||||||||
\(607\) | 12.1431 | 0.492873 | 0.246437 | − | 0.969159i | \(-0.420740\pi\) | ||||
0.246437 | + | 0.969159i | \(0.420740\pi\) | |||||||
\(608\) | 34.1724 | 1.38587 | ||||||||
\(609\) | −0.187212 | −0.00758621 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.2675 | 0.860391 | ||||||||
\(612\) | −31.2751 | −1.26422 | ||||||||
\(613\) | −35.4694 | −1.43260 | −0.716298 | − | 0.697794i | \(-0.754165\pi\) | ||||
−0.716298 | + | 0.697794i | \(0.754165\pi\) | |||||||
\(614\) | −23.8591 | −0.962875 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.19144 | 0.168878 | ||||||||
\(617\) | 9.94466 | 0.400357 | 0.200178 | − | 0.979759i | \(-0.435848\pi\) | ||||
0.200178 | + | 0.979759i | \(0.435848\pi\) | |||||||
\(618\) | 4.07305 | 0.163842 | ||||||||
\(619\) | −6.24993 | −0.251206 | −0.125603 | − | 0.992081i | \(-0.540087\pi\) | ||||
−0.125603 | + | 0.992081i | \(0.540087\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.99563 | 0.320854 | ||||||||
\(622\) | 12.1021 | 0.485250 | ||||||||
\(623\) | 1.89603 | 0.0759629 | ||||||||
\(624\) | −5.67472 | −0.227171 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 29.2883 | 1.17060 | ||||||||
\(627\) | −2.37394 | −0.0948062 | ||||||||
\(628\) | −54.1407 | −2.16045 | ||||||||
\(629\) | 13.3227 | 0.531212 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.3762 | 0.731544 | 0.365772 | − | 0.930704i | \(-0.380805\pi\) | ||||
0.365772 | + | 0.930704i | \(0.380805\pi\) | |||||||
\(632\) | 78.2146 | 3.11121 | ||||||||
\(633\) | −3.72624 | −0.148105 | ||||||||
\(634\) | −75.0187 | −2.97937 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.95736 | −0.0776142 | ||||||||
\(637\) | −27.9854 | −1.10882 | ||||||||
\(638\) | 31.2291 | 1.23637 | ||||||||
\(639\) | −7.51158 | −0.297154 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.33886 | 0.131877 | 0.0659385 | − | 0.997824i | \(-0.478996\pi\) | ||||
0.0659385 | + | 0.997824i | \(0.478996\pi\) | |||||||
\(642\) | −5.85077 | −0.230911 | ||||||||
\(643\) | 13.7815 | 0.543490 | 0.271745 | − | 0.962369i | \(-0.412399\pi\) | ||||
0.271745 | + | 0.962369i | \(0.412399\pi\) | |||||||
\(644\) | 8.02764 | 0.316333 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 28.9705 | 1.13983 | ||||||||
\(647\) | −8.43659 | −0.331677 | −0.165838 | − | 0.986153i | \(-0.553033\pi\) | ||||
−0.165838 | + | 0.986153i | \(0.553033\pi\) | |||||||
\(648\) | −57.9369 | −2.27598 | ||||||||
\(649\) | 25.6460 | 1.00669 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.251972 | −0.00987556 | ||||||||
\(652\) | 3.38853 | 0.132705 | ||||||||
\(653\) | −5.61773 | −0.219839 | −0.109919 | − | 0.993941i | \(-0.535059\pi\) | ||||
−0.109919 | + | 0.993941i | \(0.535059\pi\) | |||||||
\(654\) | −2.45220 | −0.0958886 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 70.9603 | 2.77054 | ||||||||
\(657\) | 44.3213 | 1.72914 | ||||||||
\(658\) | −3.15847 | −0.123130 | ||||||||
\(659\) | 33.0347 | 1.28685 | 0.643426 | − | 0.765509i | \(-0.277513\pi\) | ||||
0.643426 | + | 0.765509i | \(0.277513\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.3730 | 0.636835 | 0.318418 | − | 0.947951i | \(-0.396849\pi\) | ||||
0.318418 | + | 0.947951i | \(0.396849\pi\) | |||||||
\(662\) | 42.2089 | 1.64050 | ||||||||
\(663\) | −1.65158 | −0.0641420 | ||||||||
\(664\) | −70.4456 | −2.73382 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 44.2187 | 1.71344 | ||||||||
\(667\) | 33.7496 | 1.30679 | ||||||||
\(668\) | 105.444 | 4.07974 | ||||||||
\(669\) | −3.24306 | −0.125384 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.3139 | 0.861420 | ||||||||
\(672\) | 0.289320 | 0.0111608 | ||||||||
\(673\) | −16.1568 | −0.622797 | −0.311399 | − | 0.950279i | \(-0.600797\pi\) | ||||
−0.311399 | + | 0.950279i | \(0.600797\pi\) | |||||||
\(674\) | −66.3763 | −2.55672 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.8455 | 0.570979 | ||||||||
\(677\) | 13.6410 | 0.524264 | 0.262132 | − | 0.965032i | \(-0.415574\pi\) | ||||
0.262132 | + | 0.965032i | \(0.415574\pi\) | |||||||
\(678\) | −1.49578 | −0.0574452 | ||||||||
\(679\) | −3.28401 | −0.126029 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.48470 | 0.133534 | ||||||||
\(682\) | 42.0318 | 1.60948 | ||||||||
\(683\) | 38.5051 | 1.47336 | 0.736679 | − | 0.676243i | \(-0.236393\pi\) | ||||
0.736679 | + | 0.676243i | \(0.236393\pi\) | |||||||
\(684\) | 66.9723 | 2.56075 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.34481 | 0.318606 | ||||||||
\(687\) | 4.43040 | 0.169030 | ||||||||
\(688\) | −88.9140 | −3.38981 | ||||||||
\(689\) | 9.62291 | 0.366604 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.7375 | 0.712808 | 0.356404 | − | 0.934332i | \(-0.384003\pi\) | ||||
0.356404 | + | 0.934332i | \(0.384003\pi\) | |||||||
\(692\) | 43.0773 | 1.63755 | ||||||||
\(693\) | 1.87116 | 0.0710794 | ||||||||
\(694\) | 30.9984 | 1.17668 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.33988 | 0.202407 | ||||||||
\(697\) | 20.6524 | 0.782264 | ||||||||
\(698\) | −13.6756 | −0.517631 | ||||||||
\(699\) | −3.67591 | −0.139036 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.9345 | 0.752915 | 0.376458 | − | 0.926434i | \(-0.377142\pi\) | ||||
0.376458 | + | 0.926434i | \(0.377142\pi\) | |||||||
\(702\) | −11.0222 | −0.416006 | ||||||||
\(703\) | −28.5292 | −1.07600 | ||||||||
\(704\) | −5.59624 | −0.210916 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −61.4502 | −2.31271 | ||||||||
\(707\) | −1.80946 | −0.0680516 | ||||||||
\(708\) | 7.77155 | 0.292073 | ||||||||
\(709\) | −45.9346 | −1.72511 | −0.862554 | − | 0.505965i | \(-0.831137\pi\) | ||||
−0.862554 | + | 0.505965i | \(0.831137\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 34.9169 | 1.30948 | ||||||||
\(712\) | −54.0808 | −2.02676 | ||||||||
\(713\) | 45.4242 | 1.70115 | ||||||||
\(714\) | 0.245278 | 0.00917931 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 120.109 | 4.48869 | ||||||||
\(717\) | 3.29409 | 0.123020 | ||||||||
\(718\) | 92.7538 | 3.46154 | ||||||||
\(719\) | 31.3581 | 1.16946 | 0.584730 | − | 0.811228i | \(-0.301200\pi\) | ||||
0.584730 | + | 0.811228i | \(0.301200\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.07130 | 0.0771391 | ||||||||
\(722\) | −13.2624 | −0.493575 | ||||||||
\(723\) | 0.178555 | 0.00664054 | ||||||||
\(724\) | 99.0382 | 3.68073 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.68930 | −0.0626959 | ||||||||
\(727\) | −4.85392 | −0.180022 | −0.0900110 | − | 0.995941i | \(-0.528690\pi\) | ||||
−0.0900110 | + | 0.995941i | \(0.528690\pi\) | |||||||
\(728\) | −6.24435 | −0.231431 | ||||||||
\(729\) | −25.2936 | −0.936800 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.8776 | −0.957118 | ||||||||
\(732\) | 6.76183 | 0.249924 | ||||||||
\(733\) | 9.39711 | 0.347090 | 0.173545 | − | 0.984826i | \(-0.444478\pi\) | ||||
0.173545 | + | 0.984826i | \(0.444478\pi\) | |||||||
\(734\) | −25.8822 | −0.955330 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −52.1571 | −1.92253 | ||||||||
\(737\) | −16.7862 | −0.618329 | ||||||||
\(738\) | 68.5461 | 2.52322 | ||||||||
\(739\) | −28.9878 | −1.06633 | −0.533167 | − | 0.846010i | \(-0.678998\pi\) | ||||
−0.533167 | + | 0.846010i | \(0.678998\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.53667 | 0.129923 | ||||||||
\(742\) | −1.42911 | −0.0524644 | ||||||||
\(743\) | 20.6365 | 0.757081 | 0.378541 | − | 0.925585i | \(-0.376426\pi\) | ||||
0.378541 | + | 0.925585i | \(0.376426\pi\) | |||||||
\(744\) | 7.18704 | 0.263490 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −69.5673 | −2.54704 | ||||||||
\(747\) | −31.4486 | −1.15064 | ||||||||
\(748\) | −28.4978 | −1.04198 | ||||||||
\(749\) | −2.97533 | −0.108716 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.6075 | 1.15337 | 0.576687 | − | 0.816965i | \(-0.304345\pi\) | ||||
0.576687 | + | 0.816965i | \(0.304345\pi\) | |||||||
\(752\) | 41.6346 | 1.51826 | ||||||||
\(753\) | 3.57537 | 0.130294 | ||||||||
\(754\) | −46.5247 | −1.69433 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.14013 | 0.0414661 | ||||||||
\(757\) | −22.2822 | −0.809860 | −0.404930 | − | 0.914348i | \(-0.632704\pi\) | ||||
−0.404930 | + | 0.914348i | \(0.632704\pi\) | |||||||
\(758\) | −28.5103 | −1.03554 | ||||||||
\(759\) | 3.62333 | 0.131519 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.6655 | 1.36537 | 0.682686 | − | 0.730712i | \(-0.260812\pi\) | ||||
0.682686 | + | 0.730712i | \(0.260812\pi\) | |||||||
\(762\) | 0.609138 | 0.0220667 | ||||||||
\(763\) | −1.24703 | −0.0451457 | ||||||||
\(764\) | 66.0211 | 2.38856 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.1476 | 0.547304 | ||||||||
\(767\) | −38.2071 | −1.37958 | ||||||||
\(768\) | 4.67672 | 0.168756 | ||||||||
\(769\) | 29.5848 | 1.06685 | 0.533427 | − | 0.845846i | \(-0.320904\pi\) | ||||
0.533427 | + | 0.845846i | \(0.320904\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.35332 | −0.0847529 | ||||||||
\(772\) | 80.6304 | 2.90195 | ||||||||
\(773\) | −13.5902 | −0.488804 | −0.244402 | − | 0.969674i | \(-0.578592\pi\) | ||||
−0.244402 | + | 0.969674i | \(0.578592\pi\) | |||||||
\(774\) | −85.8889 | −3.08721 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 93.6704 | 3.36257 | ||||||||
\(777\) | −0.241542 | −0.00866526 | ||||||||
\(778\) | −39.9610 | −1.43267 | ||||||||
\(779\) | −44.2248 | −1.58452 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.84452 | −0.244916 | ||||||||
\(782\) | −44.2175 | −1.58121 | ||||||||
\(783\) | 4.79330 | 0.171299 | ||||||||
\(784\) | −54.7859 | −1.95664 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.58012 | 0.0920300 | ||||||||
\(787\) | −12.9687 | −0.462284 | −0.231142 | − | 0.972920i | \(-0.574246\pi\) | ||||
−0.231142 | + | 0.972920i | \(0.574246\pi\) | |||||||
\(788\) | −68.5384 | −2.44158 | ||||||||
\(789\) | −2.95147 | −0.105075 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.760661 | −0.0270460 | ||||||||
\(792\) | −53.3713 | −1.89647 | ||||||||
\(793\) | −33.2430 | −1.18049 | ||||||||
\(794\) | −8.02984 | −0.284969 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 93.7622 | 3.32331 | ||||||||
\(797\) | −40.4854 | −1.43407 | −0.717033 | − | 0.697040i | \(-0.754500\pi\) | ||||
−0.717033 | + | 0.697040i | \(0.754500\pi\) | |||||||
\(798\) | −0.525236 | −0.0185932 | ||||||||
\(799\) | 12.1174 | 0.428682 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.1430 | −0.853050 | ||||||||
\(802\) | 35.4375 | 1.25134 | ||||||||
\(803\) | 40.3854 | 1.42517 | ||||||||
\(804\) | −5.08676 | −0.179396 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −62.6185 | −2.20564 | ||||||||
\(807\) | 4.07942 | 0.143602 | ||||||||
\(808\) | 51.6114 | 1.81568 | ||||||||
\(809\) | −51.2205 | −1.80082 | −0.900409 | − | 0.435045i | \(-0.856732\pi\) | ||||
−0.900409 | + | 0.435045i | \(0.856732\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.98579 | −0.280419 | −0.140210 | − | 0.990122i | \(-0.544778\pi\) | ||||
−0.140210 | + | 0.990122i | \(0.544778\pi\) | |||||||
\(812\) | 4.81249 | 0.168885 | ||||||||
\(813\) | −0.786715 | −0.0275913 | ||||||||
\(814\) | 40.2919 | 1.41223 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.23323 | −0.113186 | ||||||||
\(817\) | 55.4140 | 1.93869 | ||||||||
\(818\) | −100.684 | −3.52035 | ||||||||
\(819\) | −2.78763 | −0.0974075 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.48153 | 0.191307 | 0.0956534 | − | 0.995415i | \(-0.469506\pi\) | ||||
0.0956534 | + | 0.995415i | \(0.469506\pi\) | |||||||
\(822\) | −2.73062 | −0.0952412 | ||||||||
\(823\) | −1.02446 | −0.0357103 | −0.0178552 | − | 0.999841i | \(-0.505684\pi\) | ||||
−0.0178552 | + | 0.999841i | \(0.505684\pi\) | |||||||
\(824\) | −59.0799 | −2.05815 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.67419 | 0.197430 | ||||||||
\(827\) | 17.3217 | 0.602335 | 0.301167 | − | 0.953571i | \(-0.402624\pi\) | ||||
0.301167 | + | 0.953571i | \(0.402624\pi\) | |||||||
\(828\) | −102.219 | −3.55237 | ||||||||
\(829\) | −3.16805 | −0.110031 | −0.0550155 | − | 0.998486i | \(-0.517521\pi\) | ||||
−0.0550155 | + | 0.998486i | \(0.517521\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.42905 | 0.118953 | ||||||||
\(832\) | 8.33721 | 0.289041 | ||||||||
\(833\) | −15.9450 | −0.552460 | ||||||||
\(834\) | 5.48749 | 0.190016 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 61.0248 | 2.11059 | ||||||||
\(837\) | 6.45140 | 0.222993 | ||||||||
\(838\) | −80.1272 | −2.76795 | ||||||||
\(839\) | −11.1359 | −0.384455 | −0.192227 | − | 0.981350i | \(-0.561571\pi\) | ||||
−0.192227 | + | 0.981350i | \(0.561571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.76746 | −0.302326 | ||||||||
\(842\) | −72.2478 | −2.48982 | ||||||||
\(843\) | −2.40341 | −0.0827777 | ||||||||
\(844\) | 95.7872 | 3.29713 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 40.2181 | 1.38273 | ||||||||
\(847\) | −0.859073 | −0.0295181 | ||||||||
\(848\) | 18.8384 | 0.646914 | ||||||||
\(849\) | −3.80368 | −0.130542 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 43.5438 | 1.49266 | ||||||||
\(852\) | −2.07411 | −0.0710577 | ||||||||
\(853\) | −2.09383 | −0.0716912 | −0.0358456 | − | 0.999357i | \(-0.511412\pi\) | ||||
−0.0358456 | + | 0.999357i | \(0.511412\pi\) | |||||||
\(854\) | 4.93697 | 0.168940 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 84.8659 | 2.90066 | ||||||||
\(857\) | 25.1944 | 0.860623 | 0.430311 | − | 0.902680i | \(-0.358404\pi\) | ||||
0.430311 | + | 0.902680i | \(0.358404\pi\) | |||||||
\(858\) | −4.99486 | −0.170522 | ||||||||
\(859\) | 8.86442 | 0.302450 | 0.151225 | − | 0.988499i | \(-0.451678\pi\) | ||||
0.151225 | + | 0.988499i | \(0.451678\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.374428 | −0.0127605 | ||||||||
\(862\) | −14.7029 | −0.500782 | ||||||||
\(863\) | −22.5940 | −0.769109 | −0.384554 | − | 0.923102i | \(-0.625645\pi\) | ||||
−0.384554 | + | 0.923102i | \(0.625645\pi\) | |||||||
\(864\) | −7.40764 | −0.252013 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 68.0558 | 2.31263 | ||||||||
\(867\) | 2.09443 | 0.0711307 | ||||||||
\(868\) | 6.47722 | 0.219851 | ||||||||
\(869\) | 31.8161 | 1.07929 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.0079 | 0.847361 | ||||||||
\(872\) | 35.5694 | 1.20453 | ||||||||
\(873\) | 41.8167 | 1.41528 | ||||||||
\(874\) | 94.6868 | 3.20283 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.2381 | 0.413486 | ||||||||
\(877\) | 38.0079 | 1.28344 | 0.641719 | − | 0.766940i | \(-0.278222\pi\) | ||||
0.641719 | + | 0.766940i | \(0.278222\pi\) | |||||||
\(878\) | 10.7034 | 0.361223 | ||||||||
\(879\) | 2.42229 | 0.0817018 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.90728 | −0.232712 | −0.116356 | − | 0.993208i | \(-0.537121\pi\) | ||||
−0.116356 | + | 0.993208i | \(0.537121\pi\) | |||||||
\(882\) | −52.9220 | −1.78198 | ||||||||
\(883\) | 41.2023 | 1.38657 | 0.693283 | − | 0.720665i | \(-0.256163\pi\) | ||||
0.693283 | + | 0.720665i | \(0.256163\pi\) | |||||||
\(884\) | 42.4556 | 1.42794 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −40.9488 | −1.37570 | ||||||||
\(887\) | −5.64594 | −0.189572 | −0.0947861 | − | 0.995498i | \(-0.530217\pi\) | ||||
−0.0947861 | + | 0.995498i | \(0.530217\pi\) | |||||||
\(888\) | 6.88953 | 0.231198 | ||||||||
\(889\) | 0.309769 | 0.0103893 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.5675 | −0.789543 | ||||||||
\(892\) | 83.3665 | 2.79132 | ||||||||
\(893\) | −25.9480 | −0.868318 | ||||||||
\(894\) | −2.90816 | −0.0972634 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.00251 | 0.0668991 | ||||||||
\(897\) | −5.39800 | −0.180234 | ||||||||
\(898\) | 30.0022 | 1.00119 | ||||||||
\(899\) | 27.2313 | 0.908216 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.48275 | 0.182657 | ||||||||
\(902\) | 62.4589 | 2.07965 | ||||||||
\(903\) | 0.469162 | 0.0156127 | ||||||||
\(904\) | 21.6964 | 0.721613 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.618431 | −0.0205460 | ||||||||
\(907\) | −44.1151 | −1.46482 | −0.732408 | − | 0.680866i | \(-0.761604\pi\) | ||||
−0.732408 | + | 0.680866i | \(0.761604\pi\) | |||||||
\(908\) | −89.5780 | −2.97275 | ||||||||
\(909\) | 23.0406 | 0.764207 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.3556 | 0.508755 | 0.254377 | − | 0.967105i | \(-0.418129\pi\) | ||||
0.254377 | + | 0.967105i | \(0.418129\pi\) | |||||||
\(912\) | 6.92361 | 0.229264 | ||||||||
\(913\) | −28.6558 | −0.948369 | ||||||||
\(914\) | −45.5769 | −1.50755 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −113.888 | −3.76297 | ||||||||
\(917\) | 1.31209 | 0.0433290 | ||||||||
\(918\) | −6.28001 | −0.207271 | ||||||||
\(919\) | −6.50537 | −0.214592 | −0.107296 | − | 0.994227i | \(-0.534219\pi\) | ||||
−0.107296 | + | 0.994227i | \(0.534219\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.65953 | −0.0546833 | ||||||||
\(922\) | −47.4074 | −1.56128 | ||||||||
\(923\) | 10.1969 | 0.335635 | ||||||||
\(924\) | 0.516666 | 0.0169971 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −75.3989 | −2.47776 | ||||||||
\(927\) | −26.3747 | −0.866258 | ||||||||
\(928\) | −31.2676 | −1.02641 | ||||||||
\(929\) | 10.5985 | 0.347726 | 0.173863 | − | 0.984770i | \(-0.444375\pi\) | ||||
0.173863 | + | 0.984770i | \(0.444375\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.1444 | 1.11904 | ||||||||
\(932\) | 94.4934 | 3.09523 | ||||||||
\(933\) | 0.841766 | 0.0275582 | ||||||||
\(934\) | 65.1764 | 2.13264 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 79.5119 | 2.59893 | ||||||||
\(937\) | 7.20835 | 0.235487 | 0.117743 | − | 0.993044i | \(-0.462434\pi\) | ||||
0.117743 | + | 0.993044i | \(0.462434\pi\) | |||||||
\(938\) | −3.71396 | −0.121265 | ||||||||
\(939\) | 2.03716 | 0.0664803 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.2737 | 1.37808 | 0.689041 | − | 0.724722i | \(-0.258032\pi\) | ||||
0.689041 | + | 0.724722i | \(0.258032\pi\) | |||||||
\(942\) | −5.40665 | −0.176158 | ||||||||
\(943\) | 67.4999 | 2.19810 | ||||||||
\(944\) | −74.7966 | −2.43442 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −78.2616 | −2.54450 | ||||||||
\(947\) | 15.2553 | 0.495729 | 0.247865 | − | 0.968795i | \(-0.420271\pi\) | ||||
0.247865 | + | 0.968795i | \(0.420271\pi\) | |||||||
\(948\) | 9.64129 | 0.313134 | ||||||||
\(949\) | −60.1657 | −1.95306 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.21796 | −0.169204 | ||||||||
\(952\) | −3.55778 | −0.115308 | ||||||||
\(953\) | −2.48489 | −0.0804935 | −0.0402467 | − | 0.999190i | \(-0.512814\pi\) | ||||
−0.0402467 | + | 0.999190i | \(0.512814\pi\) | |||||||
\(954\) | 18.1975 | 0.589166 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −84.6782 | −2.73869 | ||||||||
\(957\) | 2.17215 | 0.0702157 | ||||||||
\(958\) | 2.09205 | 0.0675911 | ||||||||
\(959\) | −1.38862 | −0.0448409 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.65118 | 0.182296 | ||||||||
\(962\) | −60.0264 | −1.93533 | ||||||||
\(963\) | 37.8862 | 1.22086 | ||||||||
\(964\) | −4.58996 | −0.147833 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.801665 | 0.0257931 | ||||||||
\(967\) | −10.8209 | −0.347976 | −0.173988 | − | 0.984748i | \(-0.555665\pi\) | ||||
−0.173988 | + | 0.984748i | \(0.555665\pi\) | |||||||
\(968\) | 24.5035 | 0.787572 | ||||||||
\(969\) | 2.01505 | 0.0647329 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.3893 | −0.975239 | −0.487619 | − | 0.873056i | \(-0.662135\pi\) | ||||
−0.487619 | + | 0.873056i | \(0.662135\pi\) | |||||||
\(972\) | −21.8154 | −0.699730 | ||||||||
\(973\) | 2.79059 | 0.0894622 | ||||||||
\(974\) | −92.3297 | −2.95843 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −65.0787 | −2.08312 | ||||||||
\(977\) | 45.2298 | 1.44703 | 0.723515 | − | 0.690309i | \(-0.242525\pi\) | ||||
0.723515 | + | 0.690309i | \(0.242525\pi\) | |||||||
\(978\) | 0.338389 | 0.0108205 | ||||||||
\(979\) | −21.9990 | −0.703090 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.8790 | 0.506978 | ||||||||
\(982\) | 17.3518 | 0.553718 | ||||||||
\(983\) | 48.2460 | 1.53881 | 0.769405 | − | 0.638761i | \(-0.220553\pi\) | ||||
0.769405 | + | 0.638761i | \(0.220553\pi\) | |||||||
\(984\) | 10.6799 | 0.340462 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −26.5079 | −0.844185 | ||||||||
\(987\) | −0.219689 | −0.00699277 | ||||||||
\(988\) | −90.9140 | −2.89236 | ||||||||
\(989\) | −84.5781 | −2.68943 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.6368 | −0.782613 | −0.391306 | − | 0.920260i | \(-0.627977\pi\) | ||||
−0.391306 | + | 0.920260i | \(0.627977\pi\) | |||||||
\(992\) | −42.0837 | −1.33616 | ||||||||
\(993\) | 2.93586 | 0.0931667 | ||||||||
\(994\) | −1.51435 | −0.0480324 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.68362 | −0.275151 | ||||||||
\(997\) | 27.1574 | 0.860084 | 0.430042 | − | 0.902809i | \(-0.358499\pi\) | ||||
0.430042 | + | 0.902809i | \(0.358499\pi\) | |||||||
\(998\) | −59.5639 | −1.88546 | ||||||||
\(999\) | 6.18434 | 0.195664 |
(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 | 6025.2.a.o.1.1 | yes | 40 | |
5.4 | even | 2 | 6025.2.a.l.1.40 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.l.1.40 | ✓ | 40 | 5.4 | even | 2 | ||
6025.2.a.o.1.1 | yes | 40 | 1.1 | even | 1 | trivial |