Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(1,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, 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("847.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.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: | \(6.76332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.7674048.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.70320\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70320 | −1.91145 | −0.955724 | − | 0.294264i | \(-0.904925\pi\) | ||||
−0.955724 | + | 0.294264i | \(0.904925\pi\) | |||||||
\(3\) | −2.80719 | −1.62073 | −0.810366 | − | 0.585924i | \(-0.800732\pi\) | ||||
−0.810366 | + | 0.585924i | \(0.800732\pi\) | |||||||
\(4\) | 5.30727 | 2.65363 | ||||||||
\(5\) | −0.445072 | −0.199042 | −0.0995212 | − | 0.995035i | \(-0.531731\pi\) | ||||
−0.0995212 | + | 0.995035i | \(0.531731\pi\) | |||||||
\(6\) | 7.58839 | 3.09795 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −8.94020 | −3.16084 | ||||||||
\(9\) | 4.88032 | 1.62677 | ||||||||
\(10\) | 1.20312 | 0.380459 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −14.8985 | −4.30083 | ||||||||
\(13\) | −0.450933 | −0.125066 | −0.0625332 | − | 0.998043i | \(-0.519918\pi\) | ||||
−0.0625332 | + | 0.998043i | \(0.519918\pi\) | |||||||
\(14\) | 2.70320 | 0.722460 | ||||||||
\(15\) | 1.24940 | 0.322594 | ||||||||
\(16\) | 13.5526 | 3.38814 | ||||||||
\(17\) | −4.83117 | −1.17173 | −0.585866 | − | 0.810408i | \(-0.699245\pi\) | ||||
−0.585866 | + | 0.810408i | \(0.699245\pi\) | |||||||
\(18\) | −13.1925 | −3.10949 | ||||||||
\(19\) | 1.08644 | 0.249246 | 0.124623 | − | 0.992204i | \(-0.460228\pi\) | ||||
0.124623 | + | 0.992204i | \(0.460228\pi\) | |||||||
\(20\) | −2.36212 | −0.528186 | ||||||||
\(21\) | 2.80719 | 0.612579 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.57222 | 0.953373 | 0.476687 | − | 0.879073i | \(-0.341838\pi\) | ||||
0.476687 | + | 0.879073i | \(0.341838\pi\) | |||||||
\(24\) | 25.0968 | 5.12287 | ||||||||
\(25\) | −4.80191 | −0.960382 | ||||||||
\(26\) | 1.21896 | 0.239058 | ||||||||
\(27\) | −5.27841 | −1.01583 | ||||||||
\(28\) | −5.30727 | −1.00298 | ||||||||
\(29\) | 1.98431 | 0.368478 | 0.184239 | − | 0.982881i | \(-0.441018\pi\) | ||||
0.184239 | + | 0.982881i | \(0.441018\pi\) | |||||||
\(30\) | −3.37738 | −0.616623 | ||||||||
\(31\) | 8.25861 | 1.48329 | 0.741645 | − | 0.670793i | \(-0.234046\pi\) | ||||
0.741645 | + | 0.670793i | \(0.234046\pi\) | |||||||
\(32\) | −18.7549 | −3.31542 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.0596 | 2.23970 | ||||||||
\(35\) | 0.445072 | 0.0752309 | ||||||||
\(36\) | 25.9012 | 4.31686 | ||||||||
\(37\) | 7.31725 | 1.20295 | 0.601474 | − | 0.798892i | \(-0.294580\pi\) | ||||
0.601474 | + | 0.798892i | \(0.294580\pi\) | |||||||
\(38\) | −2.93685 | −0.476421 | ||||||||
\(39\) | 1.26586 | 0.202699 | ||||||||
\(40\) | 3.97903 | 0.629140 | ||||||||
\(41\) | −1.77073 | −0.276542 | −0.138271 | − | 0.990394i | \(-0.544154\pi\) | ||||
−0.138271 | + | 0.990394i | \(0.544154\pi\) | |||||||
\(42\) | −7.58839 | −1.17091 | ||||||||
\(43\) | 11.4084 | 1.73977 | 0.869884 | − | 0.493257i | \(-0.164194\pi\) | ||||
0.869884 | + | 0.493257i | \(0.164194\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.17209 | −0.323797 | ||||||||
\(46\) | −12.3596 | −1.82232 | ||||||||
\(47\) | 1.02259 | 0.149159 | 0.0745797 | − | 0.997215i | \(-0.476238\pi\) | ||||
0.0745797 | + | 0.997215i | \(0.476238\pi\) | |||||||
\(48\) | −38.0446 | −5.49127 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 12.9805 | 1.83572 | ||||||||
\(51\) | 13.5620 | 1.89906 | ||||||||
\(52\) | −2.39322 | −0.331880 | ||||||||
\(53\) | −3.57222 | −0.490682 | −0.245341 | − | 0.969437i | \(-0.578900\pi\) | ||||
−0.245341 | + | 0.969437i | \(0.578900\pi\) | |||||||
\(54\) | 14.2686 | 1.94171 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.94020 | 1.19468 | ||||||||
\(57\) | −3.04984 | −0.403961 | ||||||||
\(58\) | −5.36399 | −0.704326 | ||||||||
\(59\) | −14.3996 | −1.87467 | −0.937333 | − | 0.348435i | \(-0.886713\pi\) | ||||
−0.937333 | + | 0.348435i | \(0.886713\pi\) | |||||||
\(60\) | 6.63092 | 0.856048 | ||||||||
\(61\) | −4.92965 | −0.631177 | −0.315588 | − | 0.948896i | \(-0.602202\pi\) | ||||
−0.315588 | + | 0.948896i | \(0.602202\pi\) | |||||||
\(62\) | −22.3246 | −2.83523 | ||||||||
\(63\) | −4.88032 | −0.614862 | ||||||||
\(64\) | 23.5929 | 2.94911 | ||||||||
\(65\) | 0.200698 | 0.0248935 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.18858 | −0.756055 | −0.378028 | − | 0.925794i | \(-0.623398\pi\) | ||||
−0.378028 | + | 0.925794i | \(0.623398\pi\) | |||||||
\(68\) | −25.6403 | −3.10935 | ||||||||
\(69\) | −12.8351 | −1.54516 | ||||||||
\(70\) | −1.20312 | −0.143800 | ||||||||
\(71\) | −5.92165 | −0.702771 | −0.351385 | − | 0.936231i | \(-0.614289\pi\) | ||||
−0.351385 | + | 0.936231i | \(0.614289\pi\) | |||||||
\(72\) | −43.6310 | −5.14196 | ||||||||
\(73\) | 1.65776 | 0.194027 | 0.0970133 | − | 0.995283i | \(-0.469071\pi\) | ||||
0.0970133 | + | 0.995283i | \(0.469071\pi\) | |||||||
\(74\) | −19.7800 | −2.29937 | ||||||||
\(75\) | 13.4799 | 1.55652 | ||||||||
\(76\) | 5.76602 | 0.661407 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.42186 | −0.387449 | ||||||||
\(79\) | 3.60833 | 0.405969 | 0.202984 | − | 0.979182i | \(-0.434936\pi\) | ||||
0.202984 | + | 0.979182i | \(0.434936\pi\) | |||||||
\(80\) | −6.03187 | −0.674384 | ||||||||
\(81\) | 0.176558 | 0.0196175 | ||||||||
\(82\) | 4.78663 | 0.528595 | ||||||||
\(83\) | 10.8048 | 1.18598 | 0.592992 | − | 0.805208i | \(-0.297947\pi\) | ||||
0.592992 | + | 0.805208i | \(0.297947\pi\) | |||||||
\(84\) | 14.8985 | 1.62556 | ||||||||
\(85\) | 2.15022 | 0.233224 | ||||||||
\(86\) | −30.8392 | −3.32548 | ||||||||
\(87\) | −5.57035 | −0.597204 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.21170 | −0.552439 | −0.276220 | − | 0.961095i | \(-0.589082\pi\) | ||||
−0.276220 | + | 0.961095i | \(0.589082\pi\) | |||||||
\(90\) | 5.87160 | 0.618921 | ||||||||
\(91\) | 0.450933 | 0.0472706 | ||||||||
\(92\) | 24.2660 | 2.52990 | ||||||||
\(93\) | −23.1835 | −2.40402 | ||||||||
\(94\) | −2.76425 | −0.285110 | ||||||||
\(95\) | −0.483543 | −0.0496105 | ||||||||
\(96\) | 52.6484 | 5.37341 | ||||||||
\(97\) | −5.30985 | −0.539133 | −0.269567 | − | 0.962982i | \(-0.586880\pi\) | ||||
−0.269567 | + | 0.962982i | \(0.586880\pi\) | |||||||
\(98\) | −2.70320 | −0.273064 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −25.4850 | −2.54850 | ||||||||
\(101\) | −15.5604 | −1.54832 | −0.774158 | − | 0.632992i | \(-0.781826\pi\) | ||||
−0.774158 | + | 0.632992i | \(0.781826\pi\) | |||||||
\(102\) | −36.6608 | −3.62996 | ||||||||
\(103\) | −14.1713 | −1.39634 | −0.698172 | − | 0.715930i | \(-0.746003\pi\) | ||||
−0.698172 | + | 0.715930i | \(0.746003\pi\) | |||||||
\(104\) | 4.03143 | 0.395314 | ||||||||
\(105\) | −1.24940 | −0.121929 | ||||||||
\(106\) | 9.65640 | 0.937913 | ||||||||
\(107\) | 11.7551 | 1.13641 | 0.568205 | − | 0.822887i | \(-0.307638\pi\) | ||||
0.568205 | + | 0.822887i | \(0.307638\pi\) | |||||||
\(108\) | −28.0140 | −2.69565 | ||||||||
\(109\) | −15.7800 | −1.51145 | −0.755723 | − | 0.654891i | \(-0.772714\pi\) | ||||
−0.755723 | + | 0.654891i | \(0.772714\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.5409 | −1.94966 | ||||||||
\(112\) | −13.5526 | −1.28060 | ||||||||
\(113\) | −5.92347 | −0.557233 | −0.278617 | − | 0.960402i | \(-0.589876\pi\) | ||||
−0.278617 | + | 0.960402i | \(0.589876\pi\) | |||||||
\(114\) | 8.24431 | 0.772150 | ||||||||
\(115\) | −2.03497 | −0.189762 | ||||||||
\(116\) | 10.5313 | 0.977805 | ||||||||
\(117\) | −2.20070 | −0.203455 | ||||||||
\(118\) | 38.9249 | 3.58333 | ||||||||
\(119\) | 4.83117 | 0.442873 | ||||||||
\(120\) | −11.1699 | −1.01967 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 13.3258 | 1.20646 | ||||||||
\(123\) | 4.97078 | 0.448200 | ||||||||
\(124\) | 43.8306 | 3.93611 | ||||||||
\(125\) | 4.36256 | 0.390199 | ||||||||
\(126\) | 13.1925 | 1.17528 | ||||||||
\(127\) | −10.1337 | −0.899222 | −0.449611 | − | 0.893224i | \(-0.648437\pi\) | ||||
−0.449611 | + | 0.893224i | \(0.648437\pi\) | |||||||
\(128\) | −26.2666 | −2.32166 | ||||||||
\(129\) | −32.0256 | −2.81970 | ||||||||
\(130\) | −0.542526 | −0.0475826 | ||||||||
\(131\) | 6.83340 | 0.597037 | 0.298519 | − | 0.954404i | \(-0.403508\pi\) | ||||
0.298519 | + | 0.954404i | \(0.403508\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.08644 | −0.0942061 | ||||||||
\(134\) | 16.7289 | 1.44516 | ||||||||
\(135\) | 2.34928 | 0.202193 | ||||||||
\(136\) | 43.1916 | 3.70365 | ||||||||
\(137\) | 14.4673 | 1.23602 | 0.618012 | − | 0.786169i | \(-0.287938\pi\) | ||||
0.618012 | + | 0.786169i | \(0.287938\pi\) | |||||||
\(138\) | 34.6958 | 2.95350 | ||||||||
\(139\) | 14.6957 | 1.24647 | 0.623235 | − | 0.782035i | \(-0.285818\pi\) | ||||
0.623235 | + | 0.782035i | \(0.285818\pi\) | |||||||
\(140\) | 2.36212 | 0.199635 | ||||||||
\(141\) | −2.87059 | −0.241747 | ||||||||
\(142\) | 16.0074 | 1.34331 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 66.1409 | 5.51174 | ||||||||
\(145\) | −0.883163 | −0.0733427 | ||||||||
\(146\) | −4.48126 | −0.370872 | ||||||||
\(147\) | −2.80719 | −0.231533 | ||||||||
\(148\) | 38.8346 | 3.19219 | ||||||||
\(149\) | −1.00140 | −0.0820377 | −0.0410189 | − | 0.999158i | \(-0.513060\pi\) | ||||
−0.0410189 | + | 0.999158i | \(0.513060\pi\) | |||||||
\(150\) | −36.4388 | −2.97521 | ||||||||
\(151\) | −1.37539 | −0.111927 | −0.0559636 | − | 0.998433i | \(-0.517823\pi\) | ||||
−0.0559636 | + | 0.998433i | \(0.517823\pi\) | |||||||
\(152\) | −9.71297 | −0.787826 | ||||||||
\(153\) | −23.5777 | −1.90614 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.67568 | −0.295237 | ||||||||
\(156\) | 6.71824 | 0.537889 | ||||||||
\(157\) | 5.37668 | 0.429106 | 0.214553 | − | 0.976712i | \(-0.431171\pi\) | ||||
0.214553 | + | 0.976712i | \(0.431171\pi\) | |||||||
\(158\) | −9.75403 | −0.775989 | ||||||||
\(159\) | 10.0279 | 0.795264 | ||||||||
\(160\) | 8.34726 | 0.659909 | ||||||||
\(161\) | −4.57222 | −0.360341 | ||||||||
\(162\) | −0.477270 | −0.0374979 | ||||||||
\(163\) | −9.42513 | −0.738233 | −0.369116 | − | 0.929383i | \(-0.620340\pi\) | ||||
−0.369116 | + | 0.929383i | \(0.620340\pi\) | |||||||
\(164\) | −9.39775 | −0.733841 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −29.2076 | −2.26695 | ||||||||
\(167\) | −20.0118 | −1.54856 | −0.774281 | − | 0.632842i | \(-0.781888\pi\) | ||||
−0.774281 | + | 0.632842i | \(0.781888\pi\) | |||||||
\(168\) | −25.0968 | −1.93626 | ||||||||
\(169\) | −12.7967 | −0.984358 | ||||||||
\(170\) | −5.81247 | −0.445796 | ||||||||
\(171\) | 5.30216 | 0.405466 | ||||||||
\(172\) | 60.5476 | 4.61671 | ||||||||
\(173\) | −10.8465 | −0.824647 | −0.412324 | − | 0.911037i | \(-0.635283\pi\) | ||||
−0.412324 | + | 0.911037i | \(0.635283\pi\) | |||||||
\(174\) | 15.0577 | 1.14152 | ||||||||
\(175\) | 4.80191 | 0.362990 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 40.4224 | 3.03833 | ||||||||
\(178\) | 14.0883 | 1.05596 | ||||||||
\(179\) | 16.8484 | 1.25931 | 0.629654 | − | 0.776876i | \(-0.283197\pi\) | ||||
0.629654 | + | 0.776876i | \(0.283197\pi\) | |||||||
\(180\) | −11.5279 | −0.859238 | ||||||||
\(181\) | −20.3041 | −1.50919 | −0.754597 | − | 0.656188i | \(-0.772168\pi\) | ||||
−0.754597 | + | 0.656188i | \(0.772168\pi\) | |||||||
\(182\) | −1.21896 | −0.0903554 | ||||||||
\(183\) | 13.8385 | 1.02297 | ||||||||
\(184\) | −40.8765 | −3.01346 | ||||||||
\(185\) | −3.25671 | −0.239438 | ||||||||
\(186\) | 62.6695 | 4.59515 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.42714 | 0.395815 | ||||||||
\(189\) | 5.27841 | 0.383948 | ||||||||
\(190\) | 1.30711 | 0.0948279 | ||||||||
\(191\) | 2.54435 | 0.184103 | 0.0920513 | − | 0.995754i | \(-0.470658\pi\) | ||||
0.0920513 | + | 0.995754i | \(0.470658\pi\) | |||||||
\(192\) | −66.2298 | −4.77972 | ||||||||
\(193\) | −17.5086 | −1.26030 | −0.630148 | − | 0.776475i | \(-0.717006\pi\) | ||||
−0.630148 | + | 0.776475i | \(0.717006\pi\) | |||||||
\(194\) | 14.3536 | 1.03053 | ||||||||
\(195\) | −0.563397 | −0.0403457 | ||||||||
\(196\) | 5.30727 | 0.379091 | ||||||||
\(197\) | 2.16558 | 0.154291 | 0.0771457 | − | 0.997020i | \(-0.475419\pi\) | ||||
0.0771457 | + | 0.997020i | \(0.475419\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.5756 | −1.03324 | −0.516620 | − | 0.856215i | \(-0.672810\pi\) | ||||
−0.516620 | + | 0.856215i | \(0.672810\pi\) | |||||||
\(200\) | 42.9300 | 3.03561 | ||||||||
\(201\) | 17.3725 | 1.22536 | ||||||||
\(202\) | 42.0628 | 2.95953 | ||||||||
\(203\) | −1.98431 | −0.139272 | ||||||||
\(204\) | 71.9773 | 5.03942 | ||||||||
\(205\) | 0.788103 | 0.0550435 | ||||||||
\(206\) | 38.3079 | 2.66904 | ||||||||
\(207\) | 22.3139 | 1.55092 | ||||||||
\(208\) | −6.11130 | −0.423743 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.37738 | 0.233061 | ||||||||
\(211\) | 3.63034 | 0.249923 | 0.124961 | − | 0.992162i | \(-0.460119\pi\) | ||||
0.124961 | + | 0.992162i | \(0.460119\pi\) | |||||||
\(212\) | −18.9587 | −1.30209 | ||||||||
\(213\) | 16.6232 | 1.13900 | ||||||||
\(214\) | −31.7764 | −2.17219 | ||||||||
\(215\) | −5.07757 | −0.346287 | ||||||||
\(216\) | 47.1901 | 3.21088 | ||||||||
\(217\) | −8.25861 | −0.560631 | ||||||||
\(218\) | 42.6563 | 2.88905 | ||||||||
\(219\) | −4.65366 | −0.314465 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.17854 | 0.146544 | ||||||||
\(222\) | 55.5261 | 3.72667 | ||||||||
\(223\) | −4.84062 | −0.324152 | −0.162076 | − | 0.986778i | \(-0.551819\pi\) | ||||
−0.162076 | + | 0.986778i | \(0.551819\pi\) | |||||||
\(224\) | 18.7549 | 1.25311 | ||||||||
\(225\) | −23.4349 | −1.56232 | ||||||||
\(226\) | 16.0123 | 1.06512 | ||||||||
\(227\) | −22.7306 | −1.50868 | −0.754342 | − | 0.656482i | \(-0.772044\pi\) | ||||
−0.754342 | + | 0.656482i | \(0.772044\pi\) | |||||||
\(228\) | −16.1863 | −1.07196 | ||||||||
\(229\) | −22.6732 | −1.49828 | −0.749142 | − | 0.662409i | \(-0.769534\pi\) | ||||
−0.749142 | + | 0.662409i | \(0.769534\pi\) | |||||||
\(230\) | 5.50092 | 0.362720 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −17.7402 | −1.16470 | ||||||||
\(233\) | 0.587282 | 0.0384741 | 0.0192371 | − | 0.999815i | \(-0.493876\pi\) | ||||
0.0192371 | + | 0.999815i | \(0.493876\pi\) | |||||||
\(234\) | 5.94892 | 0.388893 | ||||||||
\(235\) | −0.455124 | −0.0296890 | ||||||||
\(236\) | −76.4225 | −4.97468 | ||||||||
\(237\) | −10.1293 | −0.657967 | ||||||||
\(238\) | −13.0596 | −0.846529 | ||||||||
\(239\) | 14.9721 | 0.968465 | 0.484233 | − | 0.874939i | \(-0.339099\pi\) | ||||
0.484233 | + | 0.874939i | \(0.339099\pi\) | |||||||
\(240\) | 16.9326 | 1.09300 | ||||||||
\(241\) | 18.2746 | 1.17717 | 0.588586 | − | 0.808435i | \(-0.299685\pi\) | ||||
0.588586 | + | 0.808435i | \(0.299685\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3396 | 0.984037 | ||||||||
\(244\) | −26.1630 | −1.67491 | ||||||||
\(245\) | −0.445072 | −0.0284346 | ||||||||
\(246\) | −13.4370 | −0.856711 | ||||||||
\(247\) | −0.489911 | −0.0311723 | ||||||||
\(248\) | −73.8336 | −4.68844 | ||||||||
\(249\) | −30.3312 | −1.92216 | ||||||||
\(250\) | −11.7929 | −0.745845 | ||||||||
\(251\) | 10.5649 | 0.666850 | 0.333425 | − | 0.942777i | \(-0.391796\pi\) | ||||
0.333425 | + | 0.942777i | \(0.391796\pi\) | |||||||
\(252\) | −25.9012 | −1.63162 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 27.3934 | 1.71882 | ||||||||
\(255\) | −6.03608 | −0.377994 | ||||||||
\(256\) | 23.8178 | 1.48861 | ||||||||
\(257\) | −19.4680 | −1.21438 | −0.607189 | − | 0.794557i | \(-0.707703\pi\) | ||||
−0.607189 | + | 0.794557i | \(0.707703\pi\) | |||||||
\(258\) | 86.5715 | 5.38971 | ||||||||
\(259\) | −7.31725 | −0.454672 | ||||||||
\(260\) | 1.06516 | 0.0660583 | ||||||||
\(261\) | 9.68408 | 0.599430 | ||||||||
\(262\) | −18.4720 | −1.14121 | ||||||||
\(263\) | −21.1885 | −1.30654 | −0.653269 | − | 0.757126i | \(-0.726603\pi\) | ||||
−0.653269 | + | 0.757126i | \(0.726603\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.58989 | 0.0976665 | ||||||||
\(266\) | 2.93685 | 0.180070 | ||||||||
\(267\) | 14.6302 | 0.895356 | ||||||||
\(268\) | −32.8444 | −2.00629 | ||||||||
\(269\) | 23.1564 | 1.41187 | 0.705935 | − | 0.708276i | \(-0.250527\pi\) | ||||
0.705935 | + | 0.708276i | \(0.250527\pi\) | |||||||
\(270\) | −6.35055 | −0.386482 | ||||||||
\(271\) | −26.8232 | −1.62939 | −0.814696 | − | 0.579888i | \(-0.803096\pi\) | ||||
−0.814696 | + | 0.579888i | \(0.803096\pi\) | |||||||
\(272\) | −65.4748 | −3.96999 | ||||||||
\(273\) | −1.26586 | −0.0766131 | ||||||||
\(274\) | −39.1079 | −2.36260 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −68.1193 | −4.10030 | ||||||||
\(277\) | 14.0508 | 0.844230 | 0.422115 | − | 0.906542i | \(-0.361288\pi\) | ||||
0.422115 | + | 0.906542i | \(0.361288\pi\) | |||||||
\(278\) | −39.7253 | −2.38256 | ||||||||
\(279\) | 40.3046 | 2.41298 | ||||||||
\(280\) | −3.97903 | −0.237793 | ||||||||
\(281\) | 1.74538 | 0.104120 | 0.0520602 | − | 0.998644i | \(-0.483421\pi\) | ||||
0.0520602 | + | 0.998644i | \(0.483421\pi\) | |||||||
\(282\) | 7.75977 | 0.462088 | ||||||||
\(283\) | 4.66531 | 0.277324 | 0.138662 | − | 0.990340i | \(-0.455720\pi\) | ||||
0.138662 | + | 0.990340i | \(0.455720\pi\) | |||||||
\(284\) | −31.4278 | −1.86490 | ||||||||
\(285\) | 1.35740 | 0.0804053 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.77073 | 0.104523 | ||||||||
\(288\) | −91.5297 | −5.39344 | ||||||||
\(289\) | 6.34024 | 0.372955 | ||||||||
\(290\) | 2.38736 | 0.140191 | ||||||||
\(291\) | 14.9057 | 0.873790 | ||||||||
\(292\) | 8.79820 | 0.514876 | ||||||||
\(293\) | −14.5092 | −0.847637 | −0.423819 | − | 0.905747i | \(-0.639311\pi\) | ||||
−0.423819 | + | 0.905747i | \(0.639311\pi\) | |||||||
\(294\) | 7.58839 | 0.442564 | ||||||||
\(295\) | 6.40886 | 0.373138 | ||||||||
\(296\) | −65.4177 | −3.80232 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.70698 | 0.156811 | ||||||||
\(299\) | −2.06176 | −0.119235 | ||||||||
\(300\) | 71.5413 | 4.13044 | ||||||||
\(301\) | −11.4084 | −0.657570 | ||||||||
\(302\) | 3.71794 | 0.213943 | ||||||||
\(303\) | 43.6810 | 2.50941 | ||||||||
\(304\) | 14.7240 | 0.844480 | ||||||||
\(305\) | 2.19405 | 0.125631 | ||||||||
\(306\) | 63.7351 | 3.64349 | ||||||||
\(307\) | −2.35679 | −0.134509 | −0.0672547 | − | 0.997736i | \(-0.521424\pi\) | ||||
−0.0672547 | + | 0.997736i | \(0.521424\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 39.7816 | 2.26310 | ||||||||
\(310\) | 9.93608 | 0.564331 | ||||||||
\(311\) | −20.0050 | −1.13438 | −0.567190 | − | 0.823587i | \(-0.691969\pi\) | ||||
−0.567190 | + | 0.823587i | \(0.691969\pi\) | |||||||
\(312\) | −11.3170 | −0.640699 | ||||||||
\(313\) | 18.7530 | 1.05998 | 0.529992 | − | 0.848003i | \(-0.322195\pi\) | ||||
0.529992 | + | 0.848003i | \(0.322195\pi\) | |||||||
\(314\) | −14.5342 | −0.820214 | ||||||||
\(315\) | 2.17209 | 0.122384 | ||||||||
\(316\) | 19.1504 | 1.07729 | ||||||||
\(317\) | 4.20203 | 0.236009 | 0.118005 | − | 0.993013i | \(-0.462350\pi\) | ||||
0.118005 | + | 0.993013i | \(0.462350\pi\) | |||||||
\(318\) | −27.1074 | −1.52011 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −10.5005 | −0.586999 | ||||||||
\(321\) | −32.9989 | −1.84182 | ||||||||
\(322\) | 12.3596 | 0.688774 | ||||||||
\(323\) | −5.24877 | −0.292049 | ||||||||
\(324\) | 0.937039 | 0.0520577 | ||||||||
\(325\) | 2.16534 | 0.120112 | ||||||||
\(326\) | 25.4780 | 1.41109 | ||||||||
\(327\) | 44.2974 | 2.44965 | ||||||||
\(328\) | 15.8307 | 0.874103 | ||||||||
\(329\) | −1.02259 | −0.0563770 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.0682694 | −0.00375242 | −0.00187621 | − | 0.999998i | \(-0.500597\pi\) | ||||
−0.00187621 | + | 0.999998i | \(0.500597\pi\) | |||||||
\(332\) | 57.3441 | 3.14717 | ||||||||
\(333\) | 35.7105 | 1.95692 | ||||||||
\(334\) | 54.0959 | 2.96000 | ||||||||
\(335\) | 2.75436 | 0.150487 | ||||||||
\(336\) | 38.0446 | 2.07551 | ||||||||
\(337\) | −21.7461 | −1.18459 | −0.592294 | − | 0.805722i | \(-0.701777\pi\) | ||||
−0.592294 | + | 0.805722i | \(0.701777\pi\) | |||||||
\(338\) | 34.5919 | 1.88155 | ||||||||
\(339\) | 16.6283 | 0.903126 | ||||||||
\(340\) | 11.4118 | 0.618892 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −14.3328 | −0.775028 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −101.994 | −5.49912 | ||||||||
\(345\) | 5.71254 | 0.307553 | ||||||||
\(346\) | 29.3203 | 1.57627 | ||||||||
\(347\) | −23.9351 | −1.28490 | −0.642452 | − | 0.766326i | \(-0.722083\pi\) | ||||
−0.642452 | + | 0.766326i | \(0.722083\pi\) | |||||||
\(348\) | −29.5633 | −1.58476 | ||||||||
\(349\) | 26.4151 | 1.41397 | 0.706983 | − | 0.707231i | \(-0.250056\pi\) | ||||
0.706983 | + | 0.707231i | \(0.250056\pi\) | |||||||
\(350\) | −12.9805 | −0.693837 | ||||||||
\(351\) | 2.38021 | 0.127046 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.44182 | −0.236414 | −0.118207 | − | 0.992989i | \(-0.537715\pi\) | ||||
−0.118207 | + | 0.992989i | \(0.537715\pi\) | |||||||
\(354\) | −109.270 | −5.80761 | ||||||||
\(355\) | 2.63556 | 0.139881 | ||||||||
\(356\) | −27.6599 | −1.46597 | ||||||||
\(357\) | −13.5620 | −0.717779 | ||||||||
\(358\) | −45.5445 | −2.40710 | ||||||||
\(359\) | 14.5325 | 0.766997 | 0.383499 | − | 0.923541i | \(-0.374719\pi\) | ||||
0.383499 | + | 0.923541i | \(0.374719\pi\) | |||||||
\(360\) | 19.4190 | 1.02347 | ||||||||
\(361\) | −17.8197 | −0.937876 | ||||||||
\(362\) | 54.8860 | 2.88475 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.39322 | 0.125439 | ||||||||
\(365\) | −0.737825 | −0.0386195 | ||||||||
\(366\) | −37.4081 | −1.95535 | ||||||||
\(367\) | 4.98158 | 0.260037 | 0.130018 | − | 0.991512i | \(-0.458496\pi\) | ||||
0.130018 | + | 0.991512i | \(0.458496\pi\) | |||||||
\(368\) | 61.9653 | 3.23016 | ||||||||
\(369\) | −8.64173 | −0.449871 | ||||||||
\(370\) | 8.80351 | 0.457673 | ||||||||
\(371\) | 3.57222 | 0.185460 | ||||||||
\(372\) | −123.041 | −6.37938 | ||||||||
\(373\) | 13.6638 | 0.707485 | 0.353743 | − | 0.935343i | \(-0.384909\pi\) | ||||
0.353743 | + | 0.935343i | \(0.384909\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.2465 | −0.632408 | ||||||||
\(376\) | −9.14211 | −0.471469 | ||||||||
\(377\) | −0.894793 | −0.0460842 | ||||||||
\(378\) | −14.2686 | −0.733897 | ||||||||
\(379\) | −8.36232 | −0.429544 | −0.214772 | − | 0.976664i | \(-0.568901\pi\) | ||||
−0.214772 | + | 0.976664i | \(0.568901\pi\) | |||||||
\(380\) | −2.56629 | −0.131648 | ||||||||
\(381\) | 28.4473 | 1.45740 | ||||||||
\(382\) | −6.87787 | −0.351902 | ||||||||
\(383\) | −1.98679 | −0.101520 | −0.0507601 | − | 0.998711i | \(-0.516164\pi\) | ||||
−0.0507601 | + | 0.998711i | \(0.516164\pi\) | |||||||
\(384\) | 73.7352 | 3.76278 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 47.3292 | 2.40899 | ||||||||
\(387\) | 55.6767 | 2.83021 | ||||||||
\(388\) | −28.1808 | −1.43066 | ||||||||
\(389\) | 14.8325 | 0.752039 | 0.376019 | − | 0.926612i | \(-0.377293\pi\) | ||||
0.376019 | + | 0.926612i | \(0.377293\pi\) | |||||||
\(390\) | 1.52297 | 0.0771187 | ||||||||
\(391\) | −22.0892 | −1.11710 | ||||||||
\(392\) | −8.94020 | −0.451548 | ||||||||
\(393\) | −19.1827 | −0.967637 | ||||||||
\(394\) | −5.85400 | −0.294920 | ||||||||
\(395\) | −1.60597 | −0.0808050 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.4630 | 0.575314 | 0.287657 | − | 0.957734i | \(-0.407124\pi\) | ||||
0.287657 | + | 0.957734i | \(0.407124\pi\) | |||||||
\(398\) | 39.4008 | 1.97498 | ||||||||
\(399\) | 3.04984 | 0.152683 | ||||||||
\(400\) | −65.0782 | −3.25391 | ||||||||
\(401\) | 4.31030 | 0.215246 | 0.107623 | − | 0.994192i | \(-0.465676\pi\) | ||||
0.107623 | + | 0.994192i | \(0.465676\pi\) | |||||||
\(402\) | −46.9613 | −2.34222 | ||||||||
\(403\) | −3.72408 | −0.185510 | ||||||||
\(404\) | −82.5831 | −4.10867 | ||||||||
\(405\) | −0.0785809 | −0.00390472 | ||||||||
\(406\) | 5.36399 | 0.266210 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −121.247 | −6.00263 | ||||||||
\(409\) | 9.31202 | 0.460450 | 0.230225 | − | 0.973137i | \(-0.426054\pi\) | ||||
0.230225 | + | 0.973137i | \(0.426054\pi\) | |||||||
\(410\) | −2.13040 | −0.105213 | ||||||||
\(411\) | −40.6124 | −2.00326 | ||||||||
\(412\) | −75.2111 | −3.70538 | ||||||||
\(413\) | 14.3996 | 0.708557 | ||||||||
\(414\) | −60.3188 | −2.96451 | ||||||||
\(415\) | −4.80893 | −0.236061 | ||||||||
\(416\) | 8.45719 | 0.414648 | ||||||||
\(417\) | −41.2535 | −2.02019 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.3424 | −1.28691 | −0.643454 | − | 0.765485i | \(-0.722499\pi\) | ||||
−0.643454 | + | 0.765485i | \(0.722499\pi\) | |||||||
\(420\) | −6.63092 | −0.323556 | ||||||||
\(421\) | 14.1792 | 0.691053 | 0.345526 | − | 0.938409i | \(-0.387700\pi\) | ||||
0.345526 | + | 0.938409i | \(0.387700\pi\) | |||||||
\(422\) | −9.81352 | −0.477715 | ||||||||
\(423\) | 4.99054 | 0.242648 | ||||||||
\(424\) | 31.9363 | 1.55097 | ||||||||
\(425\) | 23.1989 | 1.12531 | ||||||||
\(426\) | −44.9358 | −2.17715 | ||||||||
\(427\) | 4.92965 | 0.238562 | ||||||||
\(428\) | 62.3876 | 3.01562 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.7257 | 0.661911 | ||||||||
\(431\) | −7.59531 | −0.365853 | −0.182927 | − | 0.983127i | \(-0.558557\pi\) | ||||
−0.182927 | + | 0.983127i | \(0.558557\pi\) | |||||||
\(432\) | −71.5361 | −3.44178 | ||||||||
\(433\) | 22.4008 | 1.07652 | 0.538258 | − | 0.842780i | \(-0.319083\pi\) | ||||
0.538258 | + | 0.842780i | \(0.319083\pi\) | |||||||
\(434\) | 22.3246 | 1.07162 | ||||||||
\(435\) | 2.47921 | 0.118869 | ||||||||
\(436\) | −83.7485 | −4.01083 | ||||||||
\(437\) | 4.96743 | 0.237624 | ||||||||
\(438\) | 12.5798 | 0.601084 | ||||||||
\(439\) | −15.4051 | −0.735244 | −0.367622 | − | 0.929975i | \(-0.619828\pi\) | ||||
−0.367622 | + | 0.929975i | \(0.619828\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.88032 | 0.232396 | ||||||||
\(442\) | −5.88901 | −0.280112 | ||||||||
\(443\) | 21.2099 | 1.00771 | 0.503857 | − | 0.863787i | \(-0.331914\pi\) | ||||
0.503857 | + | 0.863787i | \(0.331914\pi\) | |||||||
\(444\) | −109.016 | −5.17368 | ||||||||
\(445\) | 2.31958 | 0.109959 | ||||||||
\(446\) | 13.0851 | 0.619599 | ||||||||
\(447\) | 2.81112 | 0.132961 | ||||||||
\(448\) | −23.5929 | −1.11466 | ||||||||
\(449\) | −11.6316 | −0.548931 | −0.274466 | − | 0.961597i | \(-0.588501\pi\) | ||||
−0.274466 | + | 0.961597i | \(0.588501\pi\) | |||||||
\(450\) | 63.3490 | 2.98630 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −31.4375 | −1.47869 | ||||||||
\(453\) | 3.86097 | 0.181404 | ||||||||
\(454\) | 61.4453 | 2.88377 | ||||||||
\(455\) | −0.200698 | −0.00940886 | ||||||||
\(456\) | 27.2661 | 1.27685 | ||||||||
\(457\) | −31.5976 | −1.47807 | −0.739037 | − | 0.673665i | \(-0.764719\pi\) | ||||
−0.739037 | + | 0.673665i | \(0.764719\pi\) | |||||||
\(458\) | 61.2900 | 2.86389 | ||||||||
\(459\) | 25.5009 | 1.19028 | ||||||||
\(460\) | −10.8001 | −0.503558 | ||||||||
\(461\) | 8.86324 | 0.412802 | 0.206401 | − | 0.978467i | \(-0.433825\pi\) | ||||
0.206401 | + | 0.978467i | \(0.433825\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.6132 | −1.19035 | −0.595173 | − | 0.803597i | \(-0.702917\pi\) | ||||
−0.595173 | + | 0.803597i | \(0.702917\pi\) | |||||||
\(464\) | 26.8925 | 1.24846 | ||||||||
\(465\) | 10.3183 | 0.478501 | ||||||||
\(466\) | −1.58754 | −0.0735413 | ||||||||
\(467\) | 20.5402 | 0.950486 | 0.475243 | − | 0.879855i | \(-0.342360\pi\) | ||||
0.475243 | + | 0.879855i | \(0.342360\pi\) | |||||||
\(468\) | −11.6797 | −0.539894 | ||||||||
\(469\) | 6.18858 | 0.285762 | ||||||||
\(470\) | 1.23029 | 0.0567491 | ||||||||
\(471\) | −15.0934 | −0.695466 | ||||||||
\(472\) | 128.735 | 5.92551 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 27.3814 | 1.25767 | ||||||||
\(475\) | −5.21698 | −0.239371 | ||||||||
\(476\) | 25.6403 | 1.17522 | ||||||||
\(477\) | −17.4336 | −0.798228 | ||||||||
\(478\) | −40.4726 | −1.85117 | ||||||||
\(479\) | 27.5487 | 1.25873 | 0.629367 | − | 0.777108i | \(-0.283314\pi\) | ||||
0.629367 | + | 0.777108i | \(0.283314\pi\) | |||||||
\(480\) | −23.4324 | −1.06954 | ||||||||
\(481\) | −3.29959 | −0.150448 | ||||||||
\(482\) | −49.3999 | −2.25010 | ||||||||
\(483\) | 12.8351 | 0.584017 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.36327 | 0.107310 | ||||||||
\(486\) | −41.4660 | −1.88093 | ||||||||
\(487\) | −12.1013 | −0.548364 | −0.274182 | − | 0.961678i | \(-0.588407\pi\) | ||||
−0.274182 | + | 0.961678i | \(0.588407\pi\) | |||||||
\(488\) | 44.0720 | 1.99505 | ||||||||
\(489\) | 26.4581 | 1.19648 | ||||||||
\(490\) | 1.20312 | 0.0543513 | ||||||||
\(491\) | 39.3867 | 1.77750 | 0.888749 | − | 0.458394i | \(-0.151575\pi\) | ||||
0.888749 | + | 0.458394i | \(0.151575\pi\) | |||||||
\(492\) | 26.3813 | 1.18936 | ||||||||
\(493\) | −9.58656 | −0.431757 | ||||||||
\(494\) | 1.32432 | 0.0595842 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 111.925 | 5.02560 | ||||||||
\(497\) | 5.92165 | 0.265622 | ||||||||
\(498\) | 81.9912 | 3.67411 | ||||||||
\(499\) | −34.7832 | −1.55711 | −0.778555 | − | 0.627576i | \(-0.784047\pi\) | ||||
−0.778555 | + | 0.627576i | \(0.784047\pi\) | |||||||
\(500\) | 23.1533 | 1.03545 | ||||||||
\(501\) | 56.1770 | 2.50981 | ||||||||
\(502\) | −28.5590 | −1.27465 | ||||||||
\(503\) | −3.23224 | −0.144119 | −0.0720593 | − | 0.997400i | \(-0.522957\pi\) | ||||
−0.0720593 | + | 0.997400i | \(0.522957\pi\) | |||||||
\(504\) | 43.6310 | 1.94348 | ||||||||
\(505\) | 6.92550 | 0.308181 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 35.9227 | 1.59538 | ||||||||
\(508\) | −53.7824 | −2.38621 | ||||||||
\(509\) | −13.2217 | −0.586042 | −0.293021 | − | 0.956106i | \(-0.594661\pi\) | ||||
−0.293021 | + | 0.956106i | \(0.594661\pi\) | |||||||
\(510\) | 16.3167 | 0.722516 | ||||||||
\(511\) | −1.65776 | −0.0733351 | ||||||||
\(512\) | −11.8512 | −0.523752 | ||||||||
\(513\) | −5.73467 | −0.253192 | ||||||||
\(514\) | 52.6257 | 2.32122 | ||||||||
\(515\) | 6.30727 | 0.277931 | ||||||||
\(516\) | −169.969 | −7.48245 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 19.7800 | 0.869082 | ||||||||
\(519\) | 30.4483 | 1.33653 | ||||||||
\(520\) | −1.79428 | −0.0786843 | ||||||||
\(521\) | 7.30239 | 0.319924 | 0.159962 | − | 0.987123i | \(-0.448863\pi\) | ||||
0.159962 | + | 0.987123i | \(0.448863\pi\) | |||||||
\(522\) | −26.1780 | −1.14578 | ||||||||
\(523\) | −8.38007 | −0.366435 | −0.183217 | − | 0.983072i | \(-0.558651\pi\) | ||||
−0.183217 | + | 0.983072i | \(0.558651\pi\) | |||||||
\(524\) | 36.2667 | 1.58432 | ||||||||
\(525\) | −13.4799 | −0.588310 | ||||||||
\(526\) | 57.2767 | 2.49738 | ||||||||
\(527\) | −39.8988 | −1.73802 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.09483 | −0.0910794 | ||||||||
\(530\) | −4.29780 | −0.186684 | ||||||||
\(531\) | −70.2746 | −3.04966 | ||||||||
\(532\) | −5.76602 | −0.249989 | ||||||||
\(533\) | 0.798481 | 0.0345861 | ||||||||
\(534\) | −39.5484 | −1.71143 | ||||||||
\(535\) | −5.23188 | −0.226194 | ||||||||
\(536\) | 55.3271 | 2.38977 | ||||||||
\(537\) | −47.2967 | −2.04100 | ||||||||
\(538\) | −62.5963 | −2.69872 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 12.4682 | 0.536548 | ||||||||
\(541\) | 3.79768 | 0.163275 | 0.0816375 | − | 0.996662i | \(-0.473985\pi\) | ||||
0.0816375 | + | 0.996662i | \(0.473985\pi\) | |||||||
\(542\) | 72.5083 | 3.11450 | ||||||||
\(543\) | 56.9976 | 2.44600 | ||||||||
\(544\) | 90.6080 | 3.88478 | ||||||||
\(545\) | 7.02323 | 0.300842 | ||||||||
\(546\) | 3.42186 | 0.146442 | ||||||||
\(547\) | −9.08985 | −0.388654 | −0.194327 | − | 0.980937i | \(-0.562252\pi\) | ||||
−0.194327 | + | 0.980937i | \(0.562252\pi\) | |||||||
\(548\) | 76.7818 | 3.27996 | ||||||||
\(549\) | −24.0583 | −1.02678 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.15583 | 0.0918416 | ||||||||
\(552\) | 114.748 | 4.88401 | ||||||||
\(553\) | −3.60833 | −0.153442 | ||||||||
\(554\) | −37.9820 | −1.61370 | ||||||||
\(555\) | 9.14219 | 0.388065 | ||||||||
\(556\) | 77.9939 | 3.30768 | ||||||||
\(557\) | −18.2372 | −0.772736 | −0.386368 | − | 0.922345i | \(-0.626270\pi\) | ||||
−0.386368 | + | 0.922345i | \(0.626270\pi\) | |||||||
\(558\) | −108.951 | −4.61228 | ||||||||
\(559\) | −5.14444 | −0.217586 | ||||||||
\(560\) | 6.03187 | 0.254893 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.71809 | −0.199021 | ||||||||
\(563\) | 15.5744 | 0.656384 | 0.328192 | − | 0.944611i | \(-0.393561\pi\) | ||||
0.328192 | + | 0.944611i | \(0.393561\pi\) | |||||||
\(564\) | −15.2350 | −0.641509 | ||||||||
\(565\) | 2.63637 | 0.110913 | ||||||||
\(566\) | −12.6112 | −0.530090 | ||||||||
\(567\) | −0.176558 | −0.00741473 | ||||||||
\(568\) | 52.9407 | 2.22134 | ||||||||
\(569\) | −24.4254 | −1.02397 | −0.511984 | − | 0.858995i | \(-0.671089\pi\) | ||||
−0.511984 | + | 0.858995i | \(0.671089\pi\) | |||||||
\(570\) | −3.66931 | −0.153691 | ||||||||
\(571\) | 14.9541 | 0.625808 | 0.312904 | − | 0.949785i | \(-0.398698\pi\) | ||||
0.312904 | + | 0.949785i | \(0.398698\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.14247 | −0.298381 | ||||||||
\(574\) | −4.78663 | −0.199790 | ||||||||
\(575\) | −21.9554 | −0.915603 | ||||||||
\(576\) | 115.141 | 4.79754 | ||||||||
\(577\) | −21.4682 | −0.893734 | −0.446867 | − | 0.894600i | \(-0.647460\pi\) | ||||
−0.446867 | + | 0.894600i | \(0.647460\pi\) | |||||||
\(578\) | −17.1389 | −0.712885 | ||||||||
\(579\) | 49.1500 | 2.04260 | ||||||||
\(580\) | −4.68718 | −0.194625 | ||||||||
\(581\) | −10.8048 | −0.448260 | ||||||||
\(582\) | −40.2932 | −1.67021 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −14.8207 | −0.613286 | ||||||||
\(585\) | 0.979470 | 0.0404961 | ||||||||
\(586\) | 39.2212 | 1.62021 | ||||||||
\(587\) | −20.6760 | −0.853391 | −0.426695 | − | 0.904395i | \(-0.640322\pi\) | ||||
−0.426695 | + | 0.904395i | \(0.640322\pi\) | |||||||
\(588\) | −14.8985 | −0.614404 | ||||||||
\(589\) | 8.97246 | 0.369704 | ||||||||
\(590\) | −17.3244 | −0.713234 | ||||||||
\(591\) | −6.07921 | −0.250065 | ||||||||
\(592\) | 99.1675 | 4.07576 | ||||||||
\(593\) | −3.30237 | −0.135612 | −0.0678060 | − | 0.997699i | \(-0.521600\pi\) | ||||
−0.0678060 | + | 0.997699i | \(0.521600\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.15022 | −0.0881505 | ||||||||
\(596\) | −5.31469 | −0.217698 | ||||||||
\(597\) | 40.9166 | 1.67461 | ||||||||
\(598\) | 5.57335 | 0.227911 | ||||||||
\(599\) | 38.9212 | 1.59028 | 0.795140 | − | 0.606426i | \(-0.207398\pi\) | ||||
0.795140 | + | 0.606426i | \(0.207398\pi\) | |||||||
\(600\) | −120.513 | −4.91991 | ||||||||
\(601\) | −44.3783 | −1.81023 | −0.905115 | − | 0.425168i | \(-0.860215\pi\) | ||||
−0.905115 | + | 0.425168i | \(0.860215\pi\) | |||||||
\(602\) | 30.8392 | 1.25691 | ||||||||
\(603\) | −30.2022 | −1.22993 | ||||||||
\(604\) | −7.29954 | −0.297014 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −118.078 | −4.79660 | ||||||||
\(607\) | 18.9059 | 0.767365 | 0.383683 | − | 0.923465i | \(-0.374656\pi\) | ||||
0.383683 | + | 0.923465i | \(0.374656\pi\) | |||||||
\(608\) | −20.3760 | −0.826355 | ||||||||
\(609\) | 5.57035 | 0.225722 | ||||||||
\(610\) | −5.93095 | −0.240137 | ||||||||
\(611\) | −0.461118 | −0.0186548 | ||||||||
\(612\) | −125.133 | −5.05820 | ||||||||
\(613\) | 9.68116 | 0.391018 | 0.195509 | − | 0.980702i | \(-0.437364\pi\) | ||||
0.195509 | + | 0.980702i | \(0.437364\pi\) | |||||||
\(614\) | 6.37088 | 0.257108 | ||||||||
\(615\) | −2.21236 | −0.0892108 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.2775 | −1.05789 | −0.528947 | − | 0.848655i | \(-0.677413\pi\) | ||||
−0.528947 | + | 0.848655i | \(0.677413\pi\) | |||||||
\(618\) | −107.538 | −4.32580 | ||||||||
\(619\) | −24.7954 | −0.996610 | −0.498305 | − | 0.867002i | \(-0.666044\pi\) | ||||
−0.498305 | + | 0.867002i | \(0.666044\pi\) | |||||||
\(620\) | −19.5078 | −0.783452 | ||||||||
\(621\) | −24.1341 | −0.968466 | ||||||||
\(622\) | 54.0774 | 2.16831 | ||||||||
\(623\) | 5.21170 | 0.208802 | ||||||||
\(624\) | 17.1556 | 0.686773 | ||||||||
\(625\) | 22.0679 | 0.882716 | ||||||||
\(626\) | −50.6931 | −2.02611 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 28.5355 | 1.13869 | ||||||||
\(629\) | −35.3509 | −1.40953 | ||||||||
\(630\) | −5.87160 | −0.233930 | ||||||||
\(631\) | −11.8107 | −0.470178 | −0.235089 | − | 0.971974i | \(-0.575538\pi\) | ||||
−0.235089 | + | 0.971974i | \(0.575538\pi\) | |||||||
\(632\) | −32.2592 | −1.28320 | ||||||||
\(633\) | −10.1911 | −0.405058 | ||||||||
\(634\) | −11.3589 | −0.451120 | ||||||||
\(635\) | 4.51024 | 0.178983 | ||||||||
\(636\) | 53.2207 | 2.11034 | ||||||||
\(637\) | −0.450933 | −0.0178666 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −28.8995 | −1.14325 | ||||||||
\(640\) | 11.6905 | 0.462108 | ||||||||
\(641\) | −22.5182 | −0.889416 | −0.444708 | − | 0.895676i | \(-0.646693\pi\) | ||||
−0.444708 | + | 0.895676i | \(0.646693\pi\) | |||||||
\(642\) | 89.2024 | 3.52054 | ||||||||
\(643\) | 13.8901 | 0.547774 | 0.273887 | − | 0.961762i | \(-0.411691\pi\) | ||||
0.273887 | + | 0.961762i | \(0.411691\pi\) | |||||||
\(644\) | −24.2660 | −0.956214 | ||||||||
\(645\) | 14.2537 | 0.561239 | ||||||||
\(646\) | 14.1885 | 0.558237 | ||||||||
\(647\) | 50.8116 | 1.99761 | 0.998805 | − | 0.0488792i | \(-0.0155649\pi\) | ||||
0.998805 | + | 0.0488792i | \(0.0155649\pi\) | |||||||
\(648\) | −1.57846 | −0.0620078 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −5.85334 | −0.229587 | ||||||||
\(651\) | 23.1835 | 0.908632 | ||||||||
\(652\) | −50.0217 | −1.95900 | ||||||||
\(653\) | −4.81411 | −0.188391 | −0.0941953 | − | 0.995554i | \(-0.530028\pi\) | ||||
−0.0941953 | + | 0.995554i | \(0.530028\pi\) | |||||||
\(654\) | −119.744 | −4.68238 | ||||||||
\(655\) | −3.04136 | −0.118836 | ||||||||
\(656\) | −23.9979 | −0.936962 | ||||||||
\(657\) | 8.09042 | 0.315637 | ||||||||
\(658\) | 2.76425 | 0.107762 | ||||||||
\(659\) | 28.0409 | 1.09232 | 0.546159 | − | 0.837681i | \(-0.316089\pi\) | ||||
0.546159 | + | 0.837681i | \(0.316089\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.7390 | −1.62346 | −0.811730 | − | 0.584033i | \(-0.801474\pi\) | ||||
−0.811730 | + | 0.584033i | \(0.801474\pi\) | |||||||
\(662\) | 0.184545 | 0.00717256 | ||||||||
\(663\) | −6.11557 | −0.237509 | ||||||||
\(664\) | −96.5973 | −3.74870 | ||||||||
\(665\) | 0.483543 | 0.0187510 | ||||||||
\(666\) | −96.5325 | −3.74056 | ||||||||
\(667\) | 9.07271 | 0.351297 | ||||||||
\(668\) | −106.208 | −4.10932 | ||||||||
\(669\) | 13.5885 | 0.525363 | ||||||||
\(670\) | −7.44559 | −0.287648 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −52.6484 | −2.03096 | ||||||||
\(673\) | 28.7747 | 1.10918 | 0.554592 | − | 0.832123i | \(-0.312874\pi\) | ||||
0.554592 | + | 0.832123i | \(0.312874\pi\) | |||||||
\(674\) | 58.7841 | 2.26428 | ||||||||
\(675\) | 25.3465 | 0.975586 | ||||||||
\(676\) | −67.9153 | −2.61213 | ||||||||
\(677\) | 12.2862 | 0.472195 | 0.236098 | − | 0.971729i | \(-0.424131\pi\) | ||||
0.236098 | + | 0.971729i | \(0.424131\pi\) | |||||||
\(678\) | −44.9496 | −1.72628 | ||||||||
\(679\) | 5.30985 | 0.203773 | ||||||||
\(680\) | −19.2234 | −0.737184 | ||||||||
\(681\) | 63.8092 | 2.44517 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.5940 | 1.17065 | 0.585323 | − | 0.810800i | \(-0.300968\pi\) | ||||
0.585323 | + | 0.810800i | \(0.300968\pi\) | |||||||
\(684\) | 28.1400 | 1.07596 | ||||||||
\(685\) | −6.43899 | −0.246021 | ||||||||
\(686\) | 2.70320 | 0.103209 | ||||||||
\(687\) | 63.6479 | 2.42832 | ||||||||
\(688\) | 154.613 | 5.89458 | ||||||||
\(689\) | 1.61083 | 0.0613678 | ||||||||
\(690\) | −15.4421 | −0.587871 | ||||||||
\(691\) | −17.1121 | −0.650976 | −0.325488 | − | 0.945546i | \(-0.605529\pi\) | ||||
−0.325488 | + | 0.945546i | \(0.605529\pi\) | |||||||
\(692\) | −57.5655 | −2.18831 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 64.7013 | 2.45603 | ||||||||
\(695\) | −6.54063 | −0.248100 | ||||||||
\(696\) | 49.8000 | 1.88766 | ||||||||
\(697\) | 8.55471 | 0.324033 | ||||||||
\(698\) | −71.4051 | −2.70272 | ||||||||
\(699\) | −1.64861 | −0.0623563 | ||||||||
\(700\) | 25.4850 | 0.963244 | ||||||||
\(701\) | −13.5936 | −0.513423 | −0.256712 | − | 0.966488i | \(-0.582639\pi\) | ||||
−0.256712 | + | 0.966488i | \(0.582639\pi\) | |||||||
\(702\) | −6.43418 | −0.242842 | ||||||||
\(703\) | 7.94974 | 0.299830 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.27762 | 0.0481180 | ||||||||
\(706\) | 12.0071 | 0.451893 | ||||||||
\(707\) | 15.5604 | 0.585208 | ||||||||
\(708\) | 214.532 | 8.06262 | ||||||||
\(709\) | 29.5995 | 1.11163 | 0.555816 | − | 0.831305i | \(-0.312406\pi\) | ||||
0.555816 | + | 0.831305i | \(0.312406\pi\) | |||||||
\(710\) | −7.12444 | −0.267376 | ||||||||
\(711\) | 17.6098 | 0.660419 | ||||||||
\(712\) | 46.5936 | 1.74617 | ||||||||
\(713\) | 37.7601 | 1.41413 | ||||||||
\(714\) | 36.6608 | 1.37200 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 89.4190 | 3.34174 | ||||||||
\(717\) | −42.0296 | −1.56962 | ||||||||
\(718\) | −39.2842 | −1.46608 | ||||||||
\(719\) | 45.5407 | 1.69838 | 0.849190 | − | 0.528087i | \(-0.177091\pi\) | ||||
0.849190 | + | 0.528087i | \(0.177091\pi\) | |||||||
\(720\) | −29.4375 | −1.09707 | ||||||||
\(721\) | 14.1713 | 0.527768 | ||||||||
\(722\) | 48.1700 | 1.79270 | ||||||||
\(723\) | −51.3004 | −1.90788 | ||||||||
\(724\) | −107.759 | −4.00485 | ||||||||
\(725\) | −9.52850 | −0.353880 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.8796 | −1.62740 | −0.813702 | − | 0.581283i | \(-0.802551\pi\) | ||||
−0.813702 | + | 0.581283i | \(0.802551\pi\) | |||||||
\(728\) | −4.03143 | −0.149415 | ||||||||
\(729\) | −43.5909 | −1.61448 | ||||||||
\(730\) | 1.99448 | 0.0738192 | ||||||||
\(731\) | −55.1161 | −2.03854 | ||||||||
\(732\) | 73.4445 | 2.71459 | ||||||||
\(733\) | −14.0878 | −0.520345 | −0.260172 | − | 0.965562i | \(-0.583779\pi\) | ||||
−0.260172 | + | 0.965562i | \(0.583779\pi\) | |||||||
\(734\) | −13.4662 | −0.497046 | ||||||||
\(735\) | 1.24940 | 0.0460849 | ||||||||
\(736\) | −85.7513 | −3.16083 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 23.3603 | 0.859904 | ||||||||
\(739\) | 39.4975 | 1.45294 | 0.726470 | − | 0.687199i | \(-0.241160\pi\) | ||||
0.726470 | + | 0.687199i | \(0.241160\pi\) | |||||||
\(740\) | −17.2842 | −0.635380 | ||||||||
\(741\) | 1.37527 | 0.0505219 | ||||||||
\(742\) | −9.65640 | −0.354498 | ||||||||
\(743\) | −18.6162 | −0.682962 | −0.341481 | − | 0.939889i | \(-0.610928\pi\) | ||||
−0.341481 | + | 0.939889i | \(0.610928\pi\) | |||||||
\(744\) | 207.265 | 7.59870 | ||||||||
\(745\) | 0.445694 | 0.0163290 | ||||||||
\(746\) | −36.9360 | −1.35232 | ||||||||
\(747\) | 52.7310 | 1.92933 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.7551 | −0.429523 | ||||||||
\(750\) | 33.1048 | 1.20882 | ||||||||
\(751\) | −15.8060 | −0.576768 | −0.288384 | − | 0.957515i | \(-0.593118\pi\) | ||||
−0.288384 | + | 0.957515i | \(0.593118\pi\) | |||||||
\(752\) | 13.8587 | 0.505373 | ||||||||
\(753\) | −29.6576 | −1.08078 | ||||||||
\(754\) | 2.41880 | 0.0880875 | ||||||||
\(755\) | 0.612146 | 0.0222783 | ||||||||
\(756\) | 28.0140 | 1.01886 | ||||||||
\(757\) | −3.61112 | −0.131248 | −0.0656241 | − | 0.997844i | \(-0.520904\pi\) | ||||
−0.0656241 | + | 0.997844i | \(0.520904\pi\) | |||||||
\(758\) | 22.6050 | 0.821051 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.32297 | 0.156811 | ||||||||
\(761\) | −39.5819 | −1.43484 | −0.717422 | − | 0.696639i | \(-0.754678\pi\) | ||||
−0.717422 | + | 0.696639i | \(0.754678\pi\) | |||||||
\(762\) | −76.8986 | −2.78574 | ||||||||
\(763\) | 15.7800 | 0.571273 | ||||||||
\(764\) | 13.5035 | 0.488541 | ||||||||
\(765\) | 10.4938 | 0.379403 | ||||||||
\(766\) | 5.37068 | 0.194051 | ||||||||
\(767\) | 6.49325 | 0.234458 | ||||||||
\(768\) | −66.8612 | −2.41265 | ||||||||
\(769\) | 10.5472 | 0.380341 | 0.190171 | − | 0.981751i | \(-0.439096\pi\) | ||||
0.190171 | + | 0.981751i | \(0.439096\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 54.6503 | 1.96818 | ||||||||
\(772\) | −92.9228 | −3.34437 | ||||||||
\(773\) | 41.5632 | 1.49492 | 0.747462 | − | 0.664305i | \(-0.231272\pi\) | ||||
0.747462 | + | 0.664305i | \(0.231272\pi\) | |||||||
\(774\) | −150.505 | −5.40979 | ||||||||
\(775\) | −39.6571 | −1.42452 | ||||||||
\(776\) | 47.4711 | 1.70411 | ||||||||
\(777\) | 20.5409 | 0.736901 | ||||||||
\(778\) | −40.0952 | −1.43748 | ||||||||
\(779\) | −1.92379 | −0.0689269 | ||||||||
\(780\) | −2.99010 | −0.107063 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 59.7114 | 2.13527 | ||||||||
\(783\) | −10.4740 | −0.374311 | ||||||||
\(784\) | 13.5526 | 0.484020 | ||||||||
\(785\) | −2.39301 | −0.0854103 | ||||||||
\(786\) | 51.8545 | 1.84959 | ||||||||
\(787\) | −11.5474 | −0.411620 | −0.205810 | − | 0.978592i | \(-0.565983\pi\) | ||||
−0.205810 | + | 0.978592i | \(0.565983\pi\) | |||||||
\(788\) | 11.4933 | 0.409433 | ||||||||
\(789\) | 59.4801 | 2.11755 | ||||||||
\(790\) | 4.34125 | 0.154455 | ||||||||
\(791\) | 5.92347 | 0.210614 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.22294 | 0.0789390 | ||||||||
\(794\) | −30.9869 | −1.09968 | ||||||||
\(795\) | −4.46314 | −0.158291 | ||||||||
\(796\) | −77.3569 | −2.74184 | ||||||||
\(797\) | 42.3155 | 1.49889 | 0.749447 | − | 0.662065i | \(-0.230320\pi\) | ||||
0.749447 | + | 0.662065i | \(0.230320\pi\) | |||||||
\(798\) | −8.24431 | −0.291845 | ||||||||
\(799\) | −4.94029 | −0.174775 | ||||||||
\(800\) | 90.0591 | 3.18407 | ||||||||
\(801\) | −25.4348 | −0.898693 | ||||||||
\(802\) | −11.6516 | −0.411431 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 92.2006 | 3.25167 | ||||||||
\(805\) | 2.03497 | 0.0717232 | ||||||||
\(806\) | 10.0669 | 0.354592 | ||||||||
\(807\) | −65.0044 | −2.28826 | ||||||||
\(808\) | 139.113 | 4.89397 | ||||||||
\(809\) | 17.9814 | 0.632194 | 0.316097 | − | 0.948727i | \(-0.397628\pi\) | ||||
0.316097 | + | 0.948727i | \(0.397628\pi\) | |||||||
\(810\) | 0.212420 | 0.00746367 | ||||||||
\(811\) | −31.1200 | −1.09277 | −0.546386 | − | 0.837533i | \(-0.683997\pi\) | ||||
−0.546386 | + | 0.837533i | \(0.683997\pi\) | |||||||
\(812\) | −10.5313 | −0.369576 | ||||||||
\(813\) | 75.2978 | 2.64081 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.19486 | 0.146940 | ||||||||
\(816\) | 183.800 | 6.43430 | ||||||||
\(817\) | 12.3945 | 0.433630 | ||||||||
\(818\) | −25.1722 | −0.880126 | ||||||||
\(819\) | 2.20070 | 0.0768986 | ||||||||
\(820\) | 4.18268 | 0.146065 | ||||||||
\(821\) | −48.8675 | −1.70549 | −0.852744 | − | 0.522329i | \(-0.825063\pi\) | ||||
−0.852744 | + | 0.522329i | \(0.825063\pi\) | |||||||
\(822\) | 109.783 | 3.82914 | ||||||||
\(823\) | 29.5821 | 1.03117 | 0.515584 | − | 0.856839i | \(-0.327575\pi\) | ||||
0.515584 | + | 0.856839i | \(0.327575\pi\) | |||||||
\(824\) | 126.695 | 4.41361 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −38.9249 | −1.35437 | ||||||||
\(827\) | −25.3924 | −0.882981 | −0.441490 | − | 0.897266i | \(-0.645550\pi\) | ||||
−0.441490 | + | 0.897266i | \(0.645550\pi\) | |||||||
\(828\) | 118.426 | 4.11558 | ||||||||
\(829\) | 7.09580 | 0.246447 | 0.123224 | − | 0.992379i | \(-0.460677\pi\) | ||||
0.123224 | + | 0.992379i | \(0.460677\pi\) | |||||||
\(830\) | 12.9995 | 0.451219 | ||||||||
\(831\) | −39.4432 | −1.36827 | ||||||||
\(832\) | −10.6388 | −0.368835 | ||||||||
\(833\) | −4.83117 | −0.167390 | ||||||||
\(834\) | 111.516 | 3.86150 | ||||||||
\(835\) | 8.90671 | 0.308230 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −43.5923 | −1.50677 | ||||||||
\(838\) | 71.2086 | 2.45986 | ||||||||
\(839\) | −23.7285 | −0.819197 | −0.409599 | − | 0.912266i | \(-0.634331\pi\) | ||||
−0.409599 | + | 0.912266i | \(0.634331\pi\) | |||||||
\(840\) | 11.1699 | 0.385398 | ||||||||
\(841\) | −25.0625 | −0.864224 | ||||||||
\(842\) | −38.3292 | −1.32091 | ||||||||
\(843\) | −4.89960 | −0.168751 | ||||||||
\(844\) | 19.2672 | 0.663204 | ||||||||
\(845\) | 5.69544 | 0.195929 | ||||||||
\(846\) | −13.4904 | −0.463810 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −48.4127 | −1.66250 | ||||||||
\(849\) | −13.0964 | −0.449467 | ||||||||
\(850\) | −62.7111 | −2.15097 | ||||||||
\(851\) | 33.4561 | 1.14686 | ||||||||
\(852\) | 88.2238 | 3.02250 | ||||||||
\(853\) | 38.6542 | 1.32350 | 0.661748 | − | 0.749726i | \(-0.269815\pi\) | ||||
0.661748 | + | 0.749726i | \(0.269815\pi\) | |||||||
\(854\) | −13.3258 | −0.456000 | ||||||||
\(855\) | −2.35985 | −0.0807050 | ||||||||
\(856\) | −105.093 | −3.59201 | ||||||||
\(857\) | −34.0838 | −1.16428 | −0.582139 | − | 0.813089i | \(-0.697784\pi\) | ||||
−0.582139 | + | 0.813089i | \(0.697784\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.7283 | 1.93555 | 0.967773 | − | 0.251825i | \(-0.0810308\pi\) | ||||
0.967773 | + | 0.251825i | \(0.0810308\pi\) | |||||||
\(860\) | −26.9480 | −0.918920 | ||||||||
\(861\) | −4.97078 | −0.169404 | ||||||||
\(862\) | 20.5316 | 0.699310 | ||||||||
\(863\) | 24.3930 | 0.830346 | 0.415173 | − | 0.909742i | \(-0.363721\pi\) | ||||
0.415173 | + | 0.909742i | \(0.363721\pi\) | |||||||
\(864\) | 98.9959 | 3.36791 | ||||||||
\(865\) | 4.82750 | 0.164140 | ||||||||
\(866\) | −60.5539 | −2.05770 | ||||||||
\(867\) | −17.7983 | −0.604461 | ||||||||
\(868\) | −43.8306 | −1.48771 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −6.70178 | −0.227212 | ||||||||
\(871\) | 2.79064 | 0.0945571 | ||||||||
\(872\) | 141.076 | 4.77744 | ||||||||
\(873\) | −25.9137 | −0.877047 | ||||||||
\(874\) | −13.4279 | −0.454207 | ||||||||
\(875\) | −4.36256 | −0.147481 | ||||||||
\(876\) | −24.6982 | −0.834475 | ||||||||
\(877\) | −30.4950 | −1.02974 | −0.514871 | − | 0.857267i | \(-0.672160\pi\) | ||||
−0.514871 | + | 0.857267i | \(0.672160\pi\) | |||||||
\(878\) | 41.6429 | 1.40538 | ||||||||
\(879\) | 40.7301 | 1.37379 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.10056 | 0.0707697 | 0.0353848 | − | 0.999374i | \(-0.488734\pi\) | ||||
0.0353848 | + | 0.999374i | \(0.488734\pi\) | |||||||
\(882\) | −13.1925 | −0.444213 | ||||||||
\(883\) | 45.1955 | 1.52095 | 0.760475 | − | 0.649367i | \(-0.224966\pi\) | ||||
0.760475 | + | 0.649367i | \(0.224966\pi\) | |||||||
\(884\) | 11.5621 | 0.388875 | ||||||||
\(885\) | −17.9909 | −0.604757 | ||||||||
\(886\) | −57.3346 | −1.92619 | ||||||||
\(887\) | −5.18758 | −0.174182 | −0.0870910 | − | 0.996200i | \(-0.527757\pi\) | ||||
−0.0870910 | + | 0.996200i | \(0.527757\pi\) | |||||||
\(888\) | 183.640 | 6.16255 | ||||||||
\(889\) | 10.1337 | 0.339874 | ||||||||
\(890\) | −6.27029 | −0.210181 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −25.6905 | −0.860181 | ||||||||
\(893\) | 1.11098 | 0.0371774 | ||||||||
\(894\) | −7.59900 | −0.254148 | ||||||||
\(895\) | −7.49875 | −0.250656 | ||||||||
\(896\) | 26.2666 | 0.877504 | ||||||||
\(897\) | 5.78777 | 0.193248 | ||||||||
\(898\) | 31.4426 | 1.04925 | ||||||||
\(899\) | 16.3877 | 0.546559 | ||||||||
\(900\) | −124.375 | −4.14584 | ||||||||
\(901\) | 17.2580 | 0.574947 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 32.0256 | 1.06575 | ||||||||
\(904\) | 52.9570 | 1.76132 | ||||||||
\(905\) | 9.03681 | 0.300394 | ||||||||
\(906\) | −10.4370 | −0.346745 | ||||||||
\(907\) | −38.6473 | −1.28326 | −0.641631 | − | 0.767013i | \(-0.721742\pi\) | ||||
−0.641631 | + | 0.767013i | \(0.721742\pi\) | |||||||
\(908\) | −120.637 | −4.00350 | ||||||||
\(909\) | −75.9396 | −2.51876 | ||||||||
\(910\) | 0.542526 | 0.0179846 | ||||||||
\(911\) | −18.3990 | −0.609585 | −0.304793 | − | 0.952419i | \(-0.598587\pi\) | ||||
−0.304793 | + | 0.952419i | \(0.598587\pi\) | |||||||
\(912\) | −41.3331 | −1.36868 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 85.4145 | 2.82526 | ||||||||
\(915\) | −6.15912 | −0.203614 | ||||||||
\(916\) | −120.333 | −3.97590 | ||||||||
\(917\) | −6.83340 | −0.225659 | ||||||||
\(918\) | −68.9340 | −2.27516 | ||||||||
\(919\) | −17.6533 | −0.582330 | −0.291165 | − | 0.956673i | \(-0.594043\pi\) | ||||
−0.291165 | + | 0.956673i | \(0.594043\pi\) | |||||||
\(920\) | 18.1930 | 0.599806 | ||||||||
\(921\) | 6.61597 | 0.218004 | ||||||||
\(922\) | −23.9591 | −0.789050 | ||||||||
\(923\) | 2.67027 | 0.0878930 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.1368 | −1.15529 | ||||||||
\(926\) | 69.2375 | 2.27529 | ||||||||
\(927\) | −69.1606 | −2.27153 | ||||||||
\(928\) | −37.2155 | −1.22166 | ||||||||
\(929\) | −13.4484 | −0.441226 | −0.220613 | − | 0.975361i | \(-0.570806\pi\) | ||||
−0.220613 | + | 0.975361i | \(0.570806\pi\) | |||||||
\(930\) | −27.8925 | −0.914630 | ||||||||
\(931\) | 1.08644 | 0.0356066 | ||||||||
\(932\) | 3.11687 | 0.102096 | ||||||||
\(933\) | 56.1579 | 1.83853 | ||||||||
\(934\) | −55.5241 | −1.81680 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 19.6747 | 0.643087 | ||||||||
\(937\) | 8.59580 | 0.280813 | 0.140406 | − | 0.990094i | \(-0.455159\pi\) | ||||
0.140406 | + | 0.990094i | \(0.455159\pi\) | |||||||
\(938\) | −16.7289 | −0.546219 | ||||||||
\(939\) | −52.6434 | −1.71795 | ||||||||
\(940\) | −2.41547 | −0.0787839 | ||||||||
\(941\) | 33.6975 | 1.09851 | 0.549254 | − | 0.835655i | \(-0.314912\pi\) | ||||
0.549254 | + | 0.835655i | \(0.314912\pi\) | |||||||
\(942\) | 40.8004 | 1.32935 | ||||||||
\(943\) | −8.09617 | −0.263647 | ||||||||
\(944\) | −195.151 | −6.35163 | ||||||||
\(945\) | −2.34928 | −0.0764220 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.3289 | −0.498121 | −0.249061 | − | 0.968488i | \(-0.580122\pi\) | ||||
−0.249061 | + | 0.968488i | \(0.580122\pi\) | |||||||
\(948\) | −53.7588 | −1.74600 | ||||||||
\(949\) | −0.747541 | −0.0242662 | ||||||||
\(950\) | 14.1025 | 0.457546 | ||||||||
\(951\) | −11.7959 | −0.382508 | ||||||||
\(952\) | −43.1916 | −1.39985 | ||||||||
\(953\) | −44.9376 | −1.45567 | −0.727835 | − | 0.685752i | \(-0.759473\pi\) | ||||
−0.727835 | + | 0.685752i | \(0.759473\pi\) | |||||||
\(954\) | 47.1263 | 1.52577 | ||||||||
\(955\) | −1.13242 | −0.0366442 | ||||||||
\(956\) | 79.4610 | 2.56995 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −74.4697 | −2.40601 | ||||||||
\(959\) | −14.4673 | −0.467173 | ||||||||
\(960\) | 29.4770 | 0.951368 | ||||||||
\(961\) | 37.2046 | 1.20015 | ||||||||
\(962\) | 8.91944 | 0.287574 | ||||||||
\(963\) | 57.3687 | 1.84868 | ||||||||
\(964\) | 96.9883 | 3.12378 | ||||||||
\(965\) | 7.79259 | 0.250852 | ||||||||
\(966\) | −34.6958 | −1.11632 | ||||||||
\(967\) | −33.9453 | −1.09161 | −0.545804 | − | 0.837913i | \(-0.683776\pi\) | ||||
−0.545804 | + | 0.837913i | \(0.683776\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.7343 | 0.473334 | ||||||||
\(970\) | −6.38837 | −0.205118 | ||||||||
\(971\) | −55.4600 | −1.77980 | −0.889899 | − | 0.456158i | \(-0.849225\pi\) | ||||
−0.889899 | + | 0.456158i | \(0.849225\pi\) | |||||||
\(972\) | 81.4114 | 2.61127 | ||||||||
\(973\) | −14.6957 | −0.471121 | ||||||||
\(974\) | 32.7123 | 1.04817 | ||||||||
\(975\) | −6.07852 | −0.194669 | ||||||||
\(976\) | −66.8094 | −2.13852 | ||||||||
\(977\) | −37.9269 | −1.21339 | −0.606694 | − | 0.794936i | \(-0.707505\pi\) | ||||
−0.606694 | + | 0.794936i | \(0.707505\pi\) | |||||||
\(978\) | −71.5215 | −2.28701 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2.36212 | −0.0754551 | ||||||||
\(981\) | −77.0113 | −2.45878 | ||||||||
\(982\) | −106.470 | −3.39760 | ||||||||
\(983\) | 31.5337 | 1.00577 | 0.502884 | − | 0.864354i | \(-0.332272\pi\) | ||||
0.502884 | + | 0.864354i | \(0.332272\pi\) | |||||||
\(984\) | −44.4397 | −1.41669 | ||||||||
\(985\) | −0.963841 | −0.0307105 | ||||||||
\(986\) | 25.9144 | 0.825281 | ||||||||
\(987\) | 2.87059 | 0.0913719 | ||||||||
\(988\) | −2.60009 | −0.0827198 | ||||||||
\(989\) | 52.1618 | 1.65865 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.8173 | 1.26484 | 0.632419 | − | 0.774627i | \(-0.282062\pi\) | ||||
0.632419 | + | 0.774627i | \(0.282062\pi\) | |||||||
\(992\) | −154.889 | −4.91773 | ||||||||
\(993\) | 0.191645 | 0.00608167 | ||||||||
\(994\) | −16.0074 | −0.507723 | ||||||||
\(995\) | 6.48721 | 0.205659 | ||||||||
\(996\) | −160.976 | −5.10072 | ||||||||
\(997\) | 18.7190 | 0.592836 | 0.296418 | − | 0.955058i | \(-0.404208\pi\) | ||||
0.296418 | + | 0.955058i | \(0.404208\pi\) | |||||||
\(998\) | 94.0258 | 2.97634 | ||||||||
\(999\) | −38.6235 | −1.22199 |
(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 | 847.2.a.m.1.1 | ✓ | 6 | |
3.2 | odd | 2 | 7623.2.a.cs.1.6 | 6 | |||
7.6 | odd | 2 | 5929.2.a.bj.1.1 | 6 | |||
11.2 | odd | 10 | 847.2.f.y.323.1 | 24 | |||
11.3 | even | 5 | 847.2.f.z.372.1 | 24 | |||
11.4 | even | 5 | 847.2.f.z.148.1 | 24 | |||
11.5 | even | 5 | 847.2.f.z.729.6 | 24 | |||
11.6 | odd | 10 | 847.2.f.y.729.1 | 24 | |||
11.7 | odd | 10 | 847.2.f.y.148.6 | 24 | |||
11.8 | odd | 10 | 847.2.f.y.372.6 | 24 | |||
11.9 | even | 5 | 847.2.f.z.323.6 | 24 | |||
11.10 | odd | 2 | 847.2.a.n.1.6 | yes | 6 | ||
33.32 | even | 2 | 7623.2.a.cp.1.1 | 6 | |||
77.76 | even | 2 | 5929.2.a.bm.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.m.1.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
847.2.a.n.1.6 | yes | 6 | 11.10 | odd | 2 | ||
847.2.f.y.148.6 | 24 | 11.7 | odd | 10 | |||
847.2.f.y.323.1 | 24 | 11.2 | odd | 10 | |||
847.2.f.y.372.6 | 24 | 11.8 | odd | 10 | |||
847.2.f.y.729.1 | 24 | 11.6 | odd | 10 | |||
847.2.f.z.148.1 | 24 | 11.4 | even | 5 | |||
847.2.f.z.323.6 | 24 | 11.9 | even | 5 | |||
847.2.f.z.372.1 | 24 | 11.3 | even | 5 | |||
847.2.f.z.729.6 | 24 | 11.5 | even | 5 | |||
5929.2.a.bj.1.1 | 6 | 7.6 | odd | 2 | |||
5929.2.a.bm.1.6 | 6 | 77.76 | even | 2 | |||
7623.2.a.cp.1.1 | 6 | 33.32 | even | 2 | |||
7623.2.a.cs.1.6 | 6 | 3.2 | odd | 2 |