Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(1,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("855.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.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: | \(6.82720937282\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 285) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 855.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41421 | −1.70711 | −0.853553 | − | 0.521005i | \(-0.825557\pi\) | ||||
−0.853553 | + | 0.521005i | \(0.825557\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41421 | −0.534522 | −0.267261 | − | 0.963624i | \(-0.586119\pi\) | ||||
−0.267261 | + | 0.963624i | \(0.586119\pi\) | |||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.41421 | −0.763441 | ||||||||
\(11\) | 2.24264 | 0.676182 | 0.338091 | − | 0.941113i | \(-0.390219\pi\) | ||||
0.338091 | + | 0.941113i | \(0.390219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.41421 | −0.946932 | −0.473466 | − | 0.880812i | \(-0.656997\pi\) | ||||
−0.473466 | + | 0.880812i | \(0.656997\pi\) | |||||||
\(14\) | 3.41421 | 0.912487 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | −1.17157 | −0.284148 | −0.142074 | − | 0.989856i | \(-0.545377\pi\) | ||||
−0.142074 | + | 0.989856i | \(0.545377\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 3.82843 | 0.856062 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.41421 | −1.15431 | ||||||||
\(23\) | −7.65685 | −1.59656 | −0.798282 | − | 0.602284i | \(-0.794258\pi\) | ||||
−0.798282 | + | 0.602284i | \(0.794258\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 8.24264 | 1.61651 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.41421 | −1.02319 | ||||||||
\(29\) | −1.41421 | −0.262613 | −0.131306 | − | 0.991342i | \(-0.541917\pi\) | ||||
−0.131306 | + | 0.991342i | \(0.541917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.17157 | −0.569631 | −0.284816 | − | 0.958582i | \(-0.591932\pi\) | ||||
−0.284816 | + | 0.958582i | \(0.591932\pi\) | |||||||
\(32\) | 1.58579 | 0.280330 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.82843 | 0.485071 | ||||||||
\(35\) | −1.41421 | −0.239046 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.41421 | −0.561293 | −0.280647 | − | 0.959811i | \(-0.590549\pi\) | ||||
−0.280647 | + | 0.959811i | \(0.590549\pi\) | |||||||
\(38\) | 2.41421 | 0.391637 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.41421 | −0.697948 | ||||||||
\(41\) | 0.242641 | 0.0378941 | 0.0189471 | − | 0.999820i | \(-0.493969\pi\) | ||||
0.0189471 | + | 0.999820i | \(0.493969\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.2426 | 1.86699 | 0.933493 | − | 0.358597i | \(-0.116745\pi\) | ||||
0.933493 | + | 0.358597i | \(0.116745\pi\) | |||||||
\(44\) | 8.58579 | 1.29436 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.4853 | 2.72551 | ||||||||
\(47\) | 7.65685 | 1.11687 | 0.558433 | − | 0.829549i | \(-0.311403\pi\) | ||||
0.558433 | + | 0.829549i | \(0.311403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | −2.41421 | −0.341421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −13.0711 | −1.81263 | ||||||||
\(53\) | −8.00000 | −1.09888 | −0.549442 | − | 0.835532i | \(-0.685160\pi\) | ||||
−0.549442 | + | 0.835532i | \(0.685160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.24264 | 0.302398 | ||||||||
\(56\) | 6.24264 | 0.834208 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.41421 | 0.448308 | ||||||||
\(59\) | −12.4853 | −1.62545 | −0.812723 | − | 0.582651i | \(-0.802016\pi\) | ||||
−0.812723 | + | 0.582651i | \(0.802016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.31371 | 0.936424 | 0.468212 | − | 0.883616i | \(-0.344898\pi\) | ||||
0.468212 | + | 0.883616i | \(0.344898\pi\) | |||||||
\(62\) | 7.65685 | 0.972421 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | −3.41421 | −0.423481 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.65685 | −1.17977 | −0.589886 | − | 0.807486i | \(-0.700827\pi\) | ||||
−0.589886 | + | 0.807486i | \(0.700827\pi\) | |||||||
\(68\) | −4.48528 | −0.543920 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.41421 | 0.408077 | ||||||||
\(71\) | 10.8284 | 1.28510 | 0.642549 | − | 0.766245i | \(-0.277877\pi\) | ||||
0.642549 | + | 0.766245i | \(0.277877\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.65685 | −0.896167 | −0.448084 | − | 0.893992i | \(-0.647893\pi\) | ||||
−0.448084 | + | 0.893992i | \(0.647893\pi\) | |||||||
\(74\) | 8.24264 | 0.958188 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.82843 | −0.439151 | ||||||||
\(77\) | −3.17157 | −0.361434 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.585786 | −0.0646893 | ||||||||
\(83\) | −12.8284 | −1.40810 | −0.704051 | − | 0.710149i | \(-0.748628\pi\) | ||||
−0.704051 | + | 0.710149i | \(0.748628\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.17157 | −0.127075 | ||||||||
\(86\) | −29.5563 | −3.18714 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.89949 | −1.05529 | ||||||||
\(89\) | −5.89949 | −0.625345 | −0.312673 | − | 0.949861i | \(-0.601224\pi\) | ||||
−0.312673 | + | 0.949861i | \(0.601224\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.82843 | 0.506157 | ||||||||
\(92\) | −29.3137 | −3.05617 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −18.4853 | −1.90661 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.75736 | −0.990710 | −0.495355 | − | 0.868691i | \(-0.664962\pi\) | ||||
−0.495355 | + | 0.868691i | \(0.664962\pi\) | |||||||
\(98\) | 12.0711 | 1.21936 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.82843 | 0.382843 | ||||||||
\(101\) | 3.17157 | 0.315583 | 0.157792 | − | 0.987472i | \(-0.449563\pi\) | ||||
0.157792 | + | 0.987472i | \(0.449563\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.31371 | −0.720641 | −0.360321 | − | 0.932829i | \(-0.617333\pi\) | ||||
−0.360321 | + | 0.932829i | \(0.617333\pi\) | |||||||
\(104\) | 15.0711 | 1.47784 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 19.3137 | 1.87591 | ||||||||
\(107\) | −19.3137 | −1.86713 | −0.933563 | − | 0.358412i | \(-0.883318\pi\) | ||||
−0.933563 | + | 0.358412i | \(0.883318\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.48528 | −0.621177 | −0.310589 | − | 0.950544i | \(-0.600526\pi\) | ||||
−0.310589 | + | 0.950544i | \(0.600526\pi\) | |||||||
\(110\) | −5.41421 | −0.516225 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.24264 | −0.400892 | ||||||||
\(113\) | −10.1421 | −0.954092 | −0.477046 | − | 0.878878i | \(-0.658292\pi\) | ||||
−0.477046 | + | 0.878878i | \(0.658292\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.65685 | −0.714005 | ||||||||
\(116\) | −5.41421 | −0.502697 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 30.1421 | 2.77481 | ||||||||
\(119\) | 1.65685 | 0.151884 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.97056 | −0.542778 | ||||||||
\(122\) | −17.6569 | −1.59858 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.1421 | −1.09040 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.3137 | 1.71381 | 0.856907 | − | 0.515471i | \(-0.172383\pi\) | ||||
0.856907 | + | 0.515471i | \(0.172383\pi\) | |||||||
\(128\) | 20.5563 | 1.81694 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.24264 | 0.722927 | ||||||||
\(131\) | 8.58579 | 0.750144 | 0.375072 | − | 0.926996i | \(-0.377618\pi\) | ||||
0.375072 | + | 0.926996i | \(0.377618\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.41421 | 0.122628 | ||||||||
\(134\) | 23.3137 | 2.01400 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.17157 | 0.443459 | ||||||||
\(137\) | −10.0000 | −0.854358 | −0.427179 | − | 0.904167i | \(-0.640493\pi\) | ||||
−0.427179 | + | 0.904167i | \(0.640493\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.1421 | −1.19952 | −0.599760 | − | 0.800180i | \(-0.704737\pi\) | ||||
−0.599760 | + | 0.800180i | \(0.704737\pi\) | |||||||
\(140\) | −5.41421 | −0.457585 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −26.1421 | −2.19380 | ||||||||
\(143\) | −7.65685 | −0.640298 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.41421 | −0.117444 | ||||||||
\(146\) | 18.4853 | 1.52985 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −13.0711 | −1.07444 | ||||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.48528 | −0.527765 | −0.263882 | − | 0.964555i | \(-0.585003\pi\) | ||||
−0.263882 | + | 0.964555i | \(0.585003\pi\) | |||||||
\(152\) | 4.41421 | 0.358040 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.65685 | 0.617007 | ||||||||
\(155\) | −3.17157 | −0.254747 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4853 | 0.836817 | 0.418408 | − | 0.908259i | \(-0.362588\pi\) | ||||
0.418408 | + | 0.908259i | \(0.362588\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.58579 | 0.125367 | ||||||||
\(161\) | 10.8284 | 0.853400 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.8995 | 1.71530 | 0.857650 | − | 0.514233i | \(-0.171923\pi\) | ||||
0.857650 | + | 0.514233i | \(0.171923\pi\) | |||||||
\(164\) | 0.928932 | 0.0725374 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 30.9706 | 2.40378 | ||||||||
\(167\) | 17.3137 | 1.33977 | 0.669887 | − | 0.742463i | \(-0.266342\pi\) | ||||
0.669887 | + | 0.742463i | \(0.266342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.34315 | −0.103319 | ||||||||
\(170\) | 2.82843 | 0.216930 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 46.8701 | 3.57381 | ||||||||
\(173\) | 19.7990 | 1.50529 | 0.752645 | − | 0.658427i | \(-0.228778\pi\) | ||||
0.752645 | + | 0.658427i | \(0.228778\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.41421 | −0.106904 | ||||||||
\(176\) | 6.72792 | 0.507136 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.2426 | 1.06753 | ||||||||
\(179\) | −16.4853 | −1.23217 | −0.616084 | − | 0.787681i | \(-0.711282\pi\) | ||||
−0.616084 | + | 0.787681i | \(0.711282\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.8284 | −1.54816 | −0.774082 | − | 0.633085i | \(-0.781788\pi\) | ||||
−0.774082 | + | 0.633085i | \(0.781788\pi\) | |||||||
\(182\) | −11.6569 | −0.864064 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 33.7990 | 2.49169 | ||||||||
\(185\) | −3.41421 | −0.251018 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.62742 | −0.192136 | ||||||||
\(188\) | 29.3137 | 2.13792 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.41421 | 0.175145 | ||||||||
\(191\) | −10.2426 | −0.741131 | −0.370566 | − | 0.928806i | \(-0.620836\pi\) | ||||
−0.370566 | + | 0.928806i | \(0.620836\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.07107 | 0.365023 | 0.182512 | − | 0.983204i | \(-0.441577\pi\) | ||||
0.182512 | + | 0.983204i | \(0.441577\pi\) | |||||||
\(194\) | 23.5563 | 1.69125 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −19.1421 | −1.36730 | ||||||||
\(197\) | −6.82843 | −0.486505 | −0.243253 | − | 0.969963i | \(-0.578214\pi\) | ||||
−0.243253 | + | 0.969963i | \(0.578214\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.1421 | 1.28606 | 0.643031 | − | 0.765840i | \(-0.277677\pi\) | ||||
0.643031 | + | 0.765840i | \(0.277677\pi\) | |||||||
\(200\) | −4.41421 | −0.312132 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.65685 | −0.538734 | ||||||||
\(203\) | 2.00000 | 0.140372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.242641 | 0.0169468 | ||||||||
\(206\) | 17.6569 | 1.23021 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10.2426 | −0.710199 | ||||||||
\(209\) | −2.24264 | −0.155127 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.31371 | 0.503496 | 0.251748 | − | 0.967793i | \(-0.418995\pi\) | ||||
0.251748 | + | 0.967793i | \(0.418995\pi\) | |||||||
\(212\) | −30.6274 | −2.10350 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 46.6274 | 3.18738 | ||||||||
\(215\) | 12.2426 | 0.834941 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.48528 | 0.304481 | ||||||||
\(218\) | 15.6569 | 1.06042 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.58579 | 0.578854 | ||||||||
\(221\) | 4.00000 | 0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.6274 | 1.24738 | 0.623692 | − | 0.781670i | \(-0.285632\pi\) | ||||
0.623692 | + | 0.781670i | \(0.285632\pi\) | |||||||
\(224\) | −2.24264 | −0.149843 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24.4853 | 1.62874 | ||||||||
\(227\) | −14.9706 | −0.993631 | −0.496816 | − | 0.867856i | \(-0.665497\pi\) | ||||
−0.496816 | + | 0.867856i | \(0.665497\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.6274 | −1.49526 | −0.747631 | − | 0.664114i | \(-0.768809\pi\) | ||||
−0.747631 | + | 0.664114i | \(0.768809\pi\) | |||||||
\(230\) | 18.4853 | 1.21888 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.24264 | 0.409849 | ||||||||
\(233\) | 0.343146 | 0.0224802 | 0.0112401 | − | 0.999937i | \(-0.496422\pi\) | ||||
0.0112401 | + | 0.999937i | \(0.496422\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.65685 | 0.499478 | ||||||||
\(236\) | −47.7990 | −3.11145 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.00000 | −0.259281 | ||||||||
\(239\) | 26.7279 | 1.72889 | 0.864443 | − | 0.502731i | \(-0.167671\pi\) | ||||
0.864443 | + | 0.502731i | \(0.167671\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.6569 | −1.26621 | −0.633105 | − | 0.774066i | \(-0.718220\pi\) | ||||
−0.633105 | + | 0.774066i | \(0.718220\pi\) | |||||||
\(242\) | 14.4142 | 0.926581 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 28.0000 | 1.79252 | ||||||||
\(245\) | −5.00000 | −0.319438 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.41421 | 0.217241 | ||||||||
\(248\) | 14.0000 | 0.889001 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.41421 | −0.152688 | ||||||||
\(251\) | 1.75736 | 0.110924 | 0.0554618 | − | 0.998461i | \(-0.482337\pi\) | ||||
0.0554618 | + | 0.998461i | \(0.482337\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.1716 | −1.07957 | ||||||||
\(254\) | −46.6274 | −2.92566 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 4.48528 | 0.279784 | 0.139892 | − | 0.990167i | \(-0.455324\pi\) | ||||
0.139892 | + | 0.990167i | \(0.455324\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.82843 | 0.300024 | ||||||||
\(260\) | −13.0711 | −0.810633 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.7279 | −1.28058 | ||||||||
\(263\) | 23.4558 | 1.44635 | 0.723175 | − | 0.690665i | \(-0.242682\pi\) | ||||
0.723175 | + | 0.690665i | \(0.242682\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.00000 | −0.491436 | ||||||||
\(266\) | −3.41421 | −0.209339 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −36.9706 | −2.25834 | ||||||||
\(269\) | 3.07107 | 0.187246 | 0.0936232 | − | 0.995608i | \(-0.470155\pi\) | ||||
0.0936232 | + | 0.995608i | \(0.470155\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.8284 | −0.657780 | −0.328890 | − | 0.944368i | \(-0.606675\pi\) | ||||
−0.328890 | + | 0.944368i | \(0.606675\pi\) | |||||||
\(272\) | −3.51472 | −0.213111 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 24.1421 | 1.45848 | ||||||||
\(275\) | 2.24264 | 0.135236 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.0000 | −1.32185 | −0.660926 | − | 0.750451i | \(-0.729836\pi\) | ||||
−0.660926 | + | 0.750451i | \(0.729836\pi\) | |||||||
\(278\) | 34.1421 | 2.04771 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.24264 | 0.373069 | ||||||||
\(281\) | 14.5858 | 0.870115 | 0.435058 | − | 0.900403i | \(-0.356728\pi\) | ||||
0.435058 | + | 0.900403i | \(0.356728\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.3848 | −0.617311 | −0.308655 | − | 0.951174i | \(-0.599879\pi\) | ||||
−0.308655 | + | 0.951174i | \(0.599879\pi\) | |||||||
\(284\) | 41.4558 | 2.45995 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.4853 | 1.09306 | ||||||||
\(287\) | −0.343146 | −0.0202553 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6274 | −0.919260 | ||||||||
\(290\) | 3.41421 | 0.200490 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −29.3137 | −1.71546 | ||||||||
\(293\) | 11.5147 | 0.672697 | 0.336349 | − | 0.941738i | \(-0.390808\pi\) | ||||
0.336349 | + | 0.941738i | \(0.390808\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.4853 | −0.726921 | ||||||||
\(296\) | 15.0711 | 0.875988 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.4853 | −0.839110 | ||||||||
\(299\) | 26.1421 | 1.51184 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.3137 | −0.997946 | ||||||||
\(302\) | 15.6569 | 0.900951 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.00000 | −0.172062 | ||||||||
\(305\) | 7.31371 | 0.418782 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.1716 | 1.20833 | 0.604163 | − | 0.796861i | \(-0.293508\pi\) | ||||
0.604163 | + | 0.796861i | \(0.293508\pi\) | |||||||
\(308\) | −12.1421 | −0.691862 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.65685 | 0.434880 | ||||||||
\(311\) | 6.24264 | 0.353988 | 0.176994 | − | 0.984212i | \(-0.443363\pi\) | ||||
0.176994 | + | 0.984212i | \(0.443363\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.79899 | 0.327778 | 0.163889 | − | 0.986479i | \(-0.447596\pi\) | ||||
0.163889 | + | 0.986479i | \(0.447596\pi\) | |||||||
\(314\) | −25.3137 | −1.42854 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.6274 | 1.49554 | 0.747772 | − | 0.663955i | \(-0.231123\pi\) | ||||
0.747772 | + | 0.663955i | \(0.231123\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.17157 | −0.177574 | ||||||||
\(320\) | −9.82843 | −0.549426 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −26.1421 | −1.45684 | ||||||||
\(323\) | 1.17157 | 0.0651881 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.41421 | −0.189386 | ||||||||
\(326\) | −52.8701 | −2.92820 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.07107 | −0.0591398 | ||||||||
\(329\) | −10.8284 | −0.596991 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.1421 | 1.54683 | 0.773416 | − | 0.633899i | \(-0.218547\pi\) | ||||
0.773416 | + | 0.633899i | \(0.218547\pi\) | |||||||
\(332\) | −49.1127 | −2.69541 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −41.7990 | −2.28714 | ||||||||
\(335\) | −9.65685 | −0.527610 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.5858 | −1.33927 | −0.669637 | − | 0.742689i | \(-0.733550\pi\) | ||||
−0.669637 | + | 0.742689i | \(0.733550\pi\) | |||||||
\(338\) | 3.24264 | 0.176376 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.48528 | −0.243249 | ||||||||
\(341\) | −7.11270 | −0.385174 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | −54.0416 | −2.91373 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −47.7990 | −2.56969 | ||||||||
\(347\) | 27.4558 | 1.47391 | 0.736953 | − | 0.675943i | \(-0.236264\pi\) | ||||
0.736953 | + | 0.675943i | \(0.236264\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.0000 | 0.963518 | 0.481759 | − | 0.876304i | \(-0.339998\pi\) | ||||
0.481759 | + | 0.876304i | \(0.339998\pi\) | |||||||
\(350\) | 3.41421 | 0.182497 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.55635 | 0.189554 | ||||||||
\(353\) | −3.65685 | −0.194635 | −0.0973174 | − | 0.995253i | \(-0.531026\pi\) | ||||
−0.0973174 | + | 0.995253i | \(0.531026\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.8284 | 0.574713 | ||||||||
\(356\) | −22.5858 | −1.19704 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 39.7990 | 2.10344 | ||||||||
\(359\) | −24.8701 | −1.31259 | −0.656296 | − | 0.754504i | \(-0.727878\pi\) | ||||
−0.656296 | + | 0.754504i | \(0.727878\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 50.2843 | 2.64288 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 18.4853 | 0.968892 | ||||||||
\(365\) | −7.65685 | −0.400778 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.3848 | −0.750879 | −0.375440 | − | 0.926847i | \(-0.622508\pi\) | ||||
−0.375440 | + | 0.926847i | \(0.622508\pi\) | |||||||
\(368\) | −22.9706 | −1.19742 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.24264 | 0.428514 | ||||||||
\(371\) | 11.3137 | 0.587378 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.585786 | 0.0303309 | 0.0151654 | − | 0.999885i | \(-0.495173\pi\) | ||||
0.0151654 | + | 0.999885i | \(0.495173\pi\) | |||||||
\(374\) | 6.34315 | 0.327996 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −33.7990 | −1.74305 | ||||||||
\(377\) | 4.82843 | 0.248677 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.17157 | 0.162913 | 0.0814564 | − | 0.996677i | \(-0.474043\pi\) | ||||
0.0814564 | + | 0.996677i | \(0.474043\pi\) | |||||||
\(380\) | −3.82843 | −0.196394 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 24.7279 | 1.26519 | ||||||||
\(383\) | −28.0000 | −1.43073 | −0.715367 | − | 0.698749i | \(-0.753740\pi\) | ||||
−0.715367 | + | 0.698749i | \(0.753740\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.17157 | −0.161638 | ||||||||
\(386\) | −12.2426 | −0.623134 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −37.3553 | −1.89643 | ||||||||
\(389\) | −30.9706 | −1.57027 | −0.785135 | − | 0.619325i | \(-0.787406\pi\) | ||||
−0.785135 | + | 0.619325i | \(0.787406\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.97056 | 0.453661 | ||||||||
\(392\) | 22.0711 | 1.11476 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16.4853 | 0.830516 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.6274 | 1.43677 | 0.718384 | − | 0.695646i | \(-0.244882\pi\) | ||||
0.718384 | + | 0.695646i | \(0.244882\pi\) | |||||||
\(398\) | −43.7990 | −2.19544 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | 7.75736 | 0.387384 | 0.193692 | − | 0.981062i | \(-0.437954\pi\) | ||||
0.193692 | + | 0.981062i | \(0.437954\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.8284 | 0.539402 | ||||||||
\(404\) | 12.1421 | 0.604094 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.82843 | −0.239631 | ||||||||
\(407\) | −7.65685 | −0.379536 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.8284 | −0.634325 | −0.317162 | − | 0.948371i | \(-0.602730\pi\) | ||||
−0.317162 | + | 0.948371i | \(0.602730\pi\) | |||||||
\(410\) | −0.585786 | −0.0289299 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −28.0000 | −1.37946 | ||||||||
\(413\) | 17.6569 | 0.868837 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.8284 | −0.629723 | ||||||||
\(416\) | −5.41421 | −0.265454 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.41421 | 0.264818 | ||||||||
\(419\) | −3.41421 | −0.166795 | −0.0833976 | − | 0.996516i | \(-0.526577\pi\) | ||||
−0.0833976 | + | 0.996516i | \(0.526577\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.31371 | 0.453922 | 0.226961 | − | 0.973904i | \(-0.427121\pi\) | ||||
0.226961 | + | 0.973904i | \(0.427121\pi\) | |||||||
\(422\) | −17.6569 | −0.859522 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 35.3137 | 1.71499 | ||||||||
\(425\) | −1.17157 | −0.0568296 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.3431 | −0.500540 | ||||||||
\(428\) | −73.9411 | −3.57408 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −29.5563 | −1.42533 | ||||||||
\(431\) | 31.1127 | 1.49865 | 0.749323 | − | 0.662205i | \(-0.230379\pi\) | ||||
0.749323 | + | 0.662205i | \(0.230379\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.9289 | −0.525211 | −0.262605 | − | 0.964903i | \(-0.584582\pi\) | ||||
−0.262605 | + | 0.964903i | \(0.584582\pi\) | |||||||
\(434\) | −10.8284 | −0.519781 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −24.8284 | −1.18907 | ||||||||
\(437\) | 7.65685 | 0.366277 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.6569 | −1.03363 | −0.516813 | − | 0.856099i | \(-0.672882\pi\) | ||||
−0.516813 | + | 0.856099i | \(0.672882\pi\) | |||||||
\(440\) | −9.89949 | −0.471940 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.65685 | −0.459330 | ||||||||
\(443\) | −18.0000 | −0.855206 | −0.427603 | − | 0.903967i | \(-0.640642\pi\) | ||||
−0.427603 | + | 0.903967i | \(0.640642\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.89949 | −0.279663 | ||||||||
\(446\) | −44.9706 | −2.12942 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 13.8995 | 0.656689 | ||||||||
\(449\) | 26.8701 | 1.26808 | 0.634038 | − | 0.773302i | \(-0.281396\pi\) | ||||
0.634038 | + | 0.773302i | \(0.281396\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.544156 | 0.0256233 | ||||||||
\(452\) | −38.8284 | −1.82634 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 36.1421 | 1.69623 | ||||||||
\(455\) | 4.82843 | 0.226360 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.8284 | 1.53565 | 0.767825 | − | 0.640660i | \(-0.221339\pi\) | ||||
0.767825 | + | 0.640660i | \(0.221339\pi\) | |||||||
\(458\) | 54.6274 | 2.55257 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −29.3137 | −1.36676 | ||||||||
\(461\) | −19.6569 | −0.915511 | −0.457755 | − | 0.889078i | \(-0.651346\pi\) | ||||
−0.457755 | + | 0.889078i | \(0.651346\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.2426 | 1.12665 | 0.563326 | − | 0.826235i | \(-0.309522\pi\) | ||||
0.563326 | + | 0.826235i | \(0.309522\pi\) | |||||||
\(464\) | −4.24264 | −0.196960 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.828427 | −0.0383761 | ||||||||
\(467\) | −35.6569 | −1.65000 | −0.825001 | − | 0.565131i | \(-0.808826\pi\) | ||||
−0.825001 | + | 0.565131i | \(0.808826\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.6569 | 0.630615 | ||||||||
\(470\) | −18.4853 | −0.852662 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 55.1127 | 2.53677 | ||||||||
\(473\) | 27.4558 | 1.26242 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 6.34315 | 0.290738 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −64.5269 | −2.95139 | ||||||||
\(479\) | −17.0711 | −0.779997 | −0.389998 | − | 0.920815i | \(-0.627524\pi\) | ||||
−0.389998 | + | 0.920815i | \(0.627524\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.6569 | 0.531507 | ||||||||
\(482\) | 47.4558 | 2.16155 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −22.8579 | −1.03899 | ||||||||
\(485\) | −9.75736 | −0.443059 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.4853 | 0.928277 | 0.464138 | − | 0.885763i | \(-0.346364\pi\) | ||||
0.464138 | + | 0.885763i | \(0.346364\pi\) | |||||||
\(488\) | −32.2843 | −1.46144 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 12.0711 | 0.545315 | ||||||||
\(491\) | 1.75736 | 0.0793085 | 0.0396543 | − | 0.999213i | \(-0.487374\pi\) | ||||
0.0396543 | + | 0.999213i | \(0.487374\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.65685 | 0.0746210 | ||||||||
\(494\) | −8.24264 | −0.370854 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.51472 | −0.427223 | ||||||||
\(497\) | −15.3137 | −0.686914 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.17157 | −0.231511 | −0.115756 | − | 0.993278i | \(-0.536929\pi\) | ||||
−0.115756 | + | 0.993278i | \(0.536929\pi\) | |||||||
\(500\) | 3.82843 | 0.171212 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.24264 | −0.189358 | ||||||||
\(503\) | −4.82843 | −0.215289 | −0.107644 | − | 0.994189i | \(-0.534331\pi\) | ||||
−0.107644 | + | 0.994189i | \(0.534331\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.17157 | 0.141133 | ||||||||
\(506\) | 41.4558 | 1.84294 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 73.9411 | 3.28061 | ||||||||
\(509\) | 0.727922 | 0.0322646 | 0.0161323 | − | 0.999870i | \(-0.494865\pi\) | ||||
0.0161323 | + | 0.999870i | \(0.494865\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.8284 | 0.479021 | ||||||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.8284 | −0.477621 | ||||||||
\(515\) | −7.31371 | −0.322281 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.1716 | 0.755205 | ||||||||
\(518\) | −11.6569 | −0.512173 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 15.0711 | 0.660910 | ||||||||
\(521\) | −7.75736 | −0.339856 | −0.169928 | − | 0.985456i | \(-0.554354\pi\) | ||||
−0.169928 | + | 0.985456i | \(0.554354\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.5147 | −0.678411 | −0.339206 | − | 0.940712i | \(-0.610158\pi\) | ||||
−0.339206 | + | 0.940712i | \(0.610158\pi\) | |||||||
\(524\) | 32.8701 | 1.43594 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −56.6274 | −2.46907 | ||||||||
\(527\) | 3.71573 | 0.161860 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.6274 | 1.54902 | ||||||||
\(530\) | 19.3137 | 0.838934 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.41421 | 0.234736 | ||||||||
\(533\) | −0.828427 | −0.0358832 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.3137 | −0.835004 | ||||||||
\(536\) | 42.6274 | 1.84122 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.41421 | −0.319649 | ||||||||
\(539\) | −11.2132 | −0.482987 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.0000 | 0.945854 | 0.472927 | − | 0.881102i | \(-0.343197\pi\) | ||||
0.472927 | + | 0.881102i | \(0.343197\pi\) | |||||||
\(542\) | 26.1421 | 1.12290 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.85786 | −0.0796553 | ||||||||
\(545\) | −6.48528 | −0.277799 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.4853 | 1.04692 | 0.523458 | − | 0.852052i | \(-0.324642\pi\) | ||||
0.523458 | + | 0.852052i | \(0.324642\pi\) | |||||||
\(548\) | −38.2843 | −1.63542 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.41421 | −0.230863 | ||||||||
\(551\) | 1.41421 | 0.0602475 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 53.1127 | 2.25654 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −54.1421 | −2.29614 | ||||||||
\(557\) | 25.3137 | 1.07258 | 0.536288 | − | 0.844035i | \(-0.319826\pi\) | ||||
0.536288 | + | 0.844035i | \(0.319826\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.7990 | −1.76791 | ||||||||
\(560\) | −4.24264 | −0.179284 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −35.2132 | −1.48538 | ||||||||
\(563\) | 30.2843 | 1.27633 | 0.638165 | − | 0.769900i | \(-0.279694\pi\) | ||||
0.638165 | + | 0.769900i | \(0.279694\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.1421 | −0.426683 | ||||||||
\(566\) | 25.0711 | 1.05382 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −47.7990 | −2.00560 | ||||||||
\(569\) | −31.0711 | −1.30257 | −0.651283 | − | 0.758835i | \(-0.725769\pi\) | ||||
−0.651283 | + | 0.758835i | \(0.725769\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.17157 | 0.383818 | 0.191909 | − | 0.981413i | \(-0.438532\pi\) | ||||
0.191909 | + | 0.981413i | \(0.438532\pi\) | |||||||
\(572\) | −29.3137 | −1.22567 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.828427 | 0.0345779 | ||||||||
\(575\) | −7.65685 | −0.319313 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.4558 | 0.809957 | 0.404979 | − | 0.914326i | \(-0.367279\pi\) | ||||
0.404979 | + | 0.914326i | \(0.367279\pi\) | |||||||
\(578\) | 37.7279 | 1.56927 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.41421 | −0.224813 | ||||||||
\(581\) | 18.1421 | 0.752663 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.9411 | −0.743045 | ||||||||
\(584\) | 33.7990 | 1.39861 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27.7990 | −1.14837 | ||||||||
\(587\) | 12.3431 | 0.509456 | 0.254728 | − | 0.967013i | \(-0.418014\pi\) | ||||
0.254728 | + | 0.967013i | \(0.418014\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.17157 | 0.130682 | ||||||||
\(590\) | 30.1421 | 1.24093 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.2426 | −0.420970 | ||||||||
\(593\) | −36.6274 | −1.50411 | −0.752054 | − | 0.659102i | \(-0.770937\pi\) | ||||
−0.752054 | + | 0.659102i | \(0.770937\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.65685 | 0.0679244 | ||||||||
\(596\) | 22.9706 | 0.940911 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −63.1127 | −2.58087 | ||||||||
\(599\) | 3.02944 | 0.123779 | 0.0618897 | − | 0.998083i | \(-0.480287\pi\) | ||||
0.0618897 | + | 0.998083i | \(0.480287\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.14214 | 0.332125 | 0.166062 | − | 0.986115i | \(-0.446895\pi\) | ||||
0.166062 | + | 0.986115i | \(0.446895\pi\) | |||||||
\(602\) | 41.7990 | 1.70360 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −24.8284 | −1.01025 | ||||||||
\(605\) | −5.97056 | −0.242738 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.4853 | 0.669117 | 0.334558 | − | 0.942375i | \(-0.391413\pi\) | ||||
0.334558 | + | 0.942375i | \(0.391413\pi\) | |||||||
\(608\) | −1.58579 | −0.0643121 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17.6569 | −0.714905 | ||||||||
\(611\) | −26.1421 | −1.05760 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.4853 | −0.423497 | −0.211748 | − | 0.977324i | \(-0.567916\pi\) | ||||
−0.211748 | + | 0.977324i | \(0.567916\pi\) | |||||||
\(614\) | −51.1127 | −2.06274 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.0000 | 0.564076 | ||||||||
\(617\) | −28.4853 | −1.14677 | −0.573387 | − | 0.819285i | \(-0.694371\pi\) | ||||
−0.573387 | + | 0.819285i | \(0.694371\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.4853 | −0.823373 | −0.411686 | − | 0.911326i | \(-0.635060\pi\) | ||||
−0.411686 | + | 0.911326i | \(0.635060\pi\) | |||||||
\(620\) | −12.1421 | −0.487640 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.0711 | −0.604295 | ||||||||
\(623\) | 8.34315 | 0.334261 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −14.0000 | −0.559553 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 40.1421 | 1.60185 | ||||||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −64.2843 | −2.55305 | ||||||||
\(635\) | 19.3137 | 0.766441 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.0711 | 0.676380 | ||||||||
\(638\) | 7.65685 | 0.303138 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 20.5563 | 0.812561 | ||||||||
\(641\) | 31.3553 | 1.23846 | 0.619231 | − | 0.785209i | \(-0.287445\pi\) | ||||
0.619231 | + | 0.785209i | \(0.287445\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.3848 | 1.67149 | 0.835746 | − | 0.549116i | \(-0.185035\pi\) | ||||
0.835746 | + | 0.549116i | \(0.185035\pi\) | |||||||
\(644\) | 41.4558 | 1.63359 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.82843 | −0.111283 | ||||||||
\(647\) | 36.1421 | 1.42089 | 0.710447 | − | 0.703751i | \(-0.248493\pi\) | ||||
0.710447 | + | 0.703751i | \(0.248493\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.0000 | −1.09910 | ||||||||
\(650\) | 8.24264 | 0.323303 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 83.8406 | 3.28345 | ||||||||
\(653\) | −42.8284 | −1.67601 | −0.838003 | − | 0.545666i | \(-0.816277\pi\) | ||||
−0.838003 | + | 0.545666i | \(0.816277\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.58579 | 0.335474 | ||||||||
\(656\) | 0.727922 | 0.0284206 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 26.1421 | 1.01913 | ||||||||
\(659\) | 18.6274 | 0.725621 | 0.362811 | − | 0.931863i | \(-0.381817\pi\) | ||||
0.362811 | + | 0.931863i | \(0.381817\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.45584 | 0.289999 | 0.144999 | − | 0.989432i | \(-0.453682\pi\) | ||||
0.144999 | + | 0.989432i | \(0.453682\pi\) | |||||||
\(662\) | −67.9411 | −2.64061 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 56.6274 | 2.19757 | ||||||||
\(665\) | 1.41421 | 0.0548408 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.8284 | 0.419278 | ||||||||
\(668\) | 66.2843 | 2.56462 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 23.3137 | 0.900687 | ||||||||
\(671\) | 16.4020 | 0.633193 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.1838 | −1.70316 | −0.851580 | − | 0.524225i | \(-0.824355\pi\) | ||||
−0.851580 | + | 0.524225i | \(0.824355\pi\) | |||||||
\(674\) | 59.3553 | 2.28628 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.14214 | −0.197774 | ||||||||
\(677\) | −16.9706 | −0.652232 | −0.326116 | − | 0.945330i | \(-0.605740\pi\) | ||||
−0.326116 | + | 0.945330i | \(0.605740\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.7990 | 0.529557 | ||||||||
\(680\) | 5.17157 | 0.198321 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 17.1716 | 0.657534 | ||||||||
\(683\) | −18.3431 | −0.701881 | −0.350940 | − | 0.936398i | \(-0.614138\pi\) | ||||
−0.350940 | + | 0.936398i | \(0.614138\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.0000 | −0.382080 | ||||||||
\(686\) | −40.9706 | −1.56426 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 36.7279 | 1.40024 | ||||||||
\(689\) | 27.3137 | 1.04057 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.8284 | 1.78144 | 0.890719 | − | 0.454555i | \(-0.150202\pi\) | ||||
0.890719 | + | 0.454555i | \(0.150202\pi\) | |||||||
\(692\) | 75.7990 | 2.88145 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −66.2843 | −2.51612 | ||||||||
\(695\) | −14.1421 | −0.536442 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.284271 | −0.0107675 | ||||||||
\(698\) | −43.4558 | −1.64483 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.41421 | −0.204638 | ||||||||
\(701\) | −6.68629 | −0.252538 | −0.126269 | − | 0.991996i | \(-0.540300\pi\) | ||||
−0.126269 | + | 0.991996i | \(0.540300\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.41421 | 0.128770 | ||||||||
\(704\) | −22.0416 | −0.830725 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.82843 | 0.332262 | ||||||||
\(707\) | −4.48528 | −0.168686 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.9706 | 1.08801 | 0.544006 | − | 0.839081i | \(-0.316907\pi\) | ||||
0.544006 | + | 0.839081i | \(0.316907\pi\) | |||||||
\(710\) | −26.1421 | −0.981097 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 26.0416 | 0.975951 | ||||||||
\(713\) | 24.2843 | 0.909453 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.65685 | −0.286350 | ||||||||
\(716\) | −63.1127 | −2.35863 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 60.0416 | 2.24073 | ||||||||
\(719\) | 1.07107 | 0.0399441 | 0.0199720 | − | 0.999801i | \(-0.493642\pi\) | ||||
0.0199720 | + | 0.999801i | \(0.493642\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.3431 | 0.385199 | ||||||||
\(722\) | −2.41421 | −0.0898477 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −79.7401 | −2.96352 | ||||||||
\(725\) | −1.41421 | −0.0525226 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.3553 | 1.75631 | 0.878156 | − | 0.478374i | \(-0.158774\pi\) | ||||
0.878156 | + | 0.478374i | \(0.158774\pi\) | |||||||
\(728\) | −21.3137 | −0.789939 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 18.4853 | 0.684171 | ||||||||
\(731\) | −14.3431 | −0.530500 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.0000 | −0.812589 | −0.406294 | − | 0.913742i | \(-0.633179\pi\) | ||||
−0.406294 | + | 0.913742i | \(0.633179\pi\) | |||||||
\(734\) | 34.7279 | 1.28183 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.1421 | −0.447565 | ||||||||
\(737\) | −21.6569 | −0.797740 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.3431 | 0.527621 | 0.263811 | − | 0.964575i | \(-0.415021\pi\) | ||||
0.263811 | + | 0.964575i | \(0.415021\pi\) | |||||||
\(740\) | −13.0711 | −0.480502 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −27.3137 | −1.00272 | ||||||||
\(743\) | 4.00000 | 0.146746 | 0.0733729 | − | 0.997305i | \(-0.476624\pi\) | ||||
0.0733729 | + | 0.997305i | \(0.476624\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | 0.219823 | ||||||||
\(746\) | −1.41421 | −0.0517780 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.0589 | −0.367789 | ||||||||
\(749\) | 27.3137 | 0.998021 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.1421 | −0.880959 | −0.440480 | − | 0.897763i | \(-0.645192\pi\) | ||||
−0.440480 | + | 0.897763i | \(0.645192\pi\) | |||||||
\(752\) | 22.9706 | 0.837650 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11.6569 | −0.424518 | ||||||||
\(755\) | −6.48528 | −0.236024 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.4264 | −1.17856 | −0.589279 | − | 0.807930i | \(-0.700588\pi\) | ||||
−0.589279 | + | 0.807930i | \(0.700588\pi\) | |||||||
\(758\) | −7.65685 | −0.278109 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.41421 | 0.160120 | ||||||||
\(761\) | −43.9411 | −1.59286 | −0.796432 | − | 0.604728i | \(-0.793282\pi\) | ||||
−0.796432 | + | 0.604728i | \(0.793282\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.17157 | 0.332033 | ||||||||
\(764\) | −39.2132 | −1.41868 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 67.5980 | 2.44241 | ||||||||
\(767\) | 42.6274 | 1.53919 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.9706 | 1.54956 | 0.774779 | − | 0.632232i | \(-0.217861\pi\) | ||||
0.774779 | + | 0.632232i | \(0.217861\pi\) | |||||||
\(770\) | 7.65685 | 0.275934 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 19.4142 | 0.698733 | ||||||||
\(773\) | 25.6569 | 0.922813 | 0.461406 | − | 0.887189i | \(-0.347345\pi\) | ||||
0.461406 | + | 0.887189i | \(0.347345\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.17157 | −0.113926 | ||||||||
\(776\) | 43.0711 | 1.54616 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 74.7696 | 2.68062 | ||||||||
\(779\) | −0.242641 | −0.00869350 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.2843 | 0.868960 | ||||||||
\(782\) | −21.6569 | −0.774448 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −15.0000 | −0.535714 | ||||||||
\(785\) | 10.4853 | 0.374236 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42.8284 | −1.52667 | −0.763334 | − | 0.646004i | \(-0.776439\pi\) | ||||
−0.763334 | + | 0.646004i | \(0.776439\pi\) | |||||||
\(788\) | −26.1421 | −0.931275 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.3431 | 0.509984 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.9706 | −0.886731 | ||||||||
\(794\) | −69.1127 | −2.45272 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 69.4558 | 2.46180 | ||||||||
\(797\) | 14.1421 | 0.500940 | 0.250470 | − | 0.968124i | \(-0.419415\pi\) | ||||
0.250470 | + | 0.968124i | \(0.419415\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.97056 | −0.317356 | ||||||||
\(800\) | 1.58579 | 0.0560660 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.7279 | −0.661306 | ||||||||
\(803\) | −17.1716 | −0.605972 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.8284 | 0.381652 | ||||||||
\(806\) | −26.1421 | −0.920817 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −14.0000 | −0.492518 | ||||||||
\(809\) | 2.00000 | 0.0703163 | 0.0351581 | − | 0.999382i | \(-0.488807\pi\) | ||||
0.0351581 | + | 0.999382i | \(0.488807\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.68629 | 0.305017 | 0.152508 | − | 0.988302i | \(-0.451265\pi\) | ||||
0.152508 | + | 0.988302i | \(0.451265\pi\) | |||||||
\(812\) | 7.65685 | 0.268703 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 18.4853 | 0.647909 | ||||||||
\(815\) | 21.8995 | 0.767106 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.2426 | −0.428316 | ||||||||
\(818\) | 30.9706 | 1.08286 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.928932 | 0.0324397 | ||||||||
\(821\) | −14.4853 | −0.505540 | −0.252770 | − | 0.967526i | \(-0.581342\pi\) | ||||
−0.252770 | + | 0.967526i | \(0.581342\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.0122 | −0.871870 | −0.435935 | − | 0.899978i | \(-0.643582\pi\) | ||||
−0.435935 | + | 0.899978i | \(0.643582\pi\) | |||||||
\(824\) | 32.2843 | 1.12468 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −42.6274 | −1.48320 | ||||||||
\(827\) | 2.68629 | 0.0934115 | 0.0467058 | − | 0.998909i | \(-0.485128\pi\) | ||||
0.0467058 | + | 0.998909i | \(0.485128\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.4853 | 1.61450 | 0.807250 | − | 0.590209i | \(-0.200955\pi\) | ||||
0.807250 | + | 0.590209i | \(0.200955\pi\) | |||||||
\(830\) | 30.9706 | 1.07500 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 33.5563 | 1.16336 | ||||||||
\(833\) | 5.85786 | 0.202963 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.3137 | 0.599166 | ||||||||
\(836\) | −8.58579 | −0.296946 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.24264 | 0.284737 | ||||||||
\(839\) | 9.85786 | 0.340331 | 0.170166 | − | 0.985415i | \(-0.445570\pi\) | ||||
0.170166 | + | 0.985415i | \(0.445570\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0000 | −0.931034 | ||||||||
\(842\) | −22.4853 | −0.774894 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 28.0000 | 0.963800 | ||||||||
\(845\) | −1.34315 | −0.0462056 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.44365 | 0.290127 | ||||||||
\(848\) | −24.0000 | −0.824163 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.82843 | 0.0970143 | ||||||||
\(851\) | 26.1421 | 0.896141 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.8284 | −0.576194 | −0.288097 | − | 0.957601i | \(-0.593023\pi\) | ||||
−0.288097 | + | 0.957601i | \(0.593023\pi\) | |||||||
\(854\) | 24.9706 | 0.854475 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 85.2548 | 2.91395 | ||||||||
\(857\) | −12.6863 | −0.433355 | −0.216678 | − | 0.976243i | \(-0.569522\pi\) | ||||
−0.216678 | + | 0.976243i | \(0.569522\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.9411 | −1.70397 | −0.851985 | − | 0.523567i | \(-0.824601\pi\) | ||||
−0.851985 | + | 0.523567i | \(0.824601\pi\) | |||||||
\(860\) | 46.8701 | 1.59826 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −75.1127 | −2.55835 | ||||||||
\(863\) | −8.68629 | −0.295685 | −0.147842 | − | 0.989011i | \(-0.547233\pi\) | ||||
−0.147842 | + | 0.989011i | \(0.547233\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.7990 | 0.673186 | ||||||||
\(866\) | 26.3848 | 0.896591 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 17.1716 | 0.582841 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.9706 | 1.11716 | ||||||||
\(872\) | 28.6274 | 0.969447 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −18.4853 | −0.625274 | ||||||||
\(875\) | −1.41421 | −0.0478091 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.9289 | −1.17947 | −0.589733 | − | 0.807598i | \(-0.700767\pi\) | ||||
−0.589733 | + | 0.807598i | \(0.700767\pi\) | |||||||
\(878\) | 52.2843 | 1.76451 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.72792 | 0.226798 | ||||||||
\(881\) | 5.79899 | 0.195373 | 0.0976865 | − | 0.995217i | \(-0.468856\pi\) | ||||
0.0976865 | + | 0.995217i | \(0.468856\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.0416 | −0.405233 | −0.202617 | − | 0.979258i | \(-0.564945\pi\) | ||||
−0.202617 | + | 0.979258i | \(0.564945\pi\) | |||||||
\(884\) | 15.3137 | 0.515056 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 43.4558 | 1.45993 | ||||||||
\(887\) | −25.9411 | −0.871018 | −0.435509 | − | 0.900184i | \(-0.643432\pi\) | ||||
−0.435509 | + | 0.900184i | \(0.643432\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.3137 | −0.916072 | ||||||||
\(890\) | 14.2426 | 0.477414 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 71.3137 | 2.38776 | ||||||||
\(893\) | −7.65685 | −0.256227 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.4853 | −0.551042 | ||||||||
\(896\) | −29.0711 | −0.971196 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −64.8701 | −2.16474 | ||||||||
\(899\) | 4.48528 | 0.149593 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.37258 | 0.312246 | ||||||||
\(902\) | −1.31371 | −0.0437417 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 44.7696 | 1.48901 | ||||||||
\(905\) | −20.8284 | −0.692360 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.1421 | −0.602400 | −0.301200 | − | 0.953561i | \(-0.597387\pi\) | ||||
−0.301200 | + | 0.953561i | \(0.597387\pi\) | |||||||
\(908\) | −57.3137 | −1.90202 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −11.6569 | −0.386421 | ||||||||
\(911\) | −8.68629 | −0.287790 | −0.143895 | − | 0.989593i | \(-0.545963\pi\) | ||||
−0.143895 | + | 0.989593i | \(0.545963\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.7696 | −0.952133 | ||||||||
\(914\) | −79.2548 | −2.62152 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −86.6274 | −2.86225 | ||||||||
\(917\) | −12.1421 | −0.400969 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.0000 | −0.395843 | −0.197922 | − | 0.980218i | \(-0.563419\pi\) | ||||
−0.197922 | + | 0.980218i | \(0.563419\pi\) | |||||||
\(920\) | 33.7990 | 1.11432 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 47.4558 | 1.56287 | ||||||||
\(923\) | −36.9706 | −1.21690 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.41421 | −0.112259 | ||||||||
\(926\) | −58.5269 | −1.92331 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.24264 | −0.0736183 | ||||||||
\(929\) | −33.1127 | −1.08639 | −0.543196 | − | 0.839606i | \(-0.682786\pi\) | ||||
−0.543196 | + | 0.839606i | \(0.682786\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.00000 | 0.163868 | ||||||||
\(932\) | 1.31371 | 0.0430320 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 86.0833 | 2.81673 | ||||||||
\(935\) | −2.62742 | −0.0859257 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.7990 | −0.973491 | −0.486745 | − | 0.873544i | \(-0.661816\pi\) | ||||
−0.486745 | + | 0.873544i | \(0.661816\pi\) | |||||||
\(938\) | −32.9706 | −1.07653 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 29.3137 | 0.956108 | ||||||||
\(941\) | −22.8701 | −0.745543 | −0.372771 | − | 0.927923i | \(-0.621592\pi\) | ||||
−0.372771 | + | 0.927923i | \(0.621592\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.85786 | −0.0605004 | ||||||||
\(944\) | −37.4558 | −1.21908 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −66.2843 | −2.15509 | ||||||||
\(947\) | 47.1716 | 1.53287 | 0.766435 | − | 0.642322i | \(-0.222029\pi\) | ||||
0.766435 | + | 0.642322i | \(0.222029\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.1421 | 0.848610 | ||||||||
\(950\) | 2.41421 | 0.0783274 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.31371 | −0.237039 | ||||||||
\(953\) | 53.4558 | 1.73160 | 0.865802 | − | 0.500386i | \(-0.166809\pi\) | ||||
0.865802 | + | 0.500386i | \(0.166809\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.2426 | −0.331444 | ||||||||
\(956\) | 102.326 | 3.30946 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 41.2132 | 1.33154 | ||||||||
\(959\) | 14.1421 | 0.456673 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.9411 | −0.675520 | ||||||||
\(962\) | −28.1421 | −0.907339 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −75.2548 | −2.42379 | ||||||||
\(965\) | 5.07107 | 0.163243 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.04163 | 0.258601 | 0.129301 | − | 0.991605i | \(-0.458727\pi\) | ||||
0.129301 | + | 0.991605i | \(0.458727\pi\) | |||||||
\(968\) | 26.3553 | 0.847093 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 23.5563 | 0.756349 | ||||||||
\(971\) | −22.3431 | −0.717026 | −0.358513 | − | 0.933525i | \(-0.616716\pi\) | ||||
−0.358513 | + | 0.933525i | \(0.616716\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.0000 | 0.641171 | ||||||||
\(974\) | −49.4558 | −1.58467 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 21.9411 | 0.702318 | ||||||||
\(977\) | −32.2843 | −1.03287 | −0.516433 | − | 0.856328i | \(-0.672740\pi\) | ||||
−0.516433 | + | 0.856328i | \(0.672740\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.2304 | −0.422847 | ||||||||
\(980\) | −19.1421 | −0.611473 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.24264 | −0.135388 | ||||||||
\(983\) | 24.6274 | 0.785493 | 0.392746 | − | 0.919647i | \(-0.371525\pi\) | ||||
0.392746 | + | 0.919647i | \(0.371525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.82843 | −0.217572 | ||||||||
\(986\) | −4.00000 | −0.127386 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.0711 | 0.415846 | ||||||||
\(989\) | −93.7401 | −2.98076 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.34315 | 0.0744325 | 0.0372162 | − | 0.999307i | \(-0.488151\pi\) | ||||
0.0372162 | + | 0.999307i | \(0.488151\pi\) | |||||||
\(992\) | −5.02944 | −0.159685 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 36.9706 | 1.17264 | ||||||||
\(995\) | 18.1421 | 0.575144 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.0833 | −1.20611 | −0.603054 | − | 0.797700i | \(-0.706050\pi\) | ||||
−0.603054 | + | 0.797700i | \(0.706050\pi\) | |||||||
\(998\) | 12.4853 | 0.395215 | ||||||||
\(999\) | 0 | 0 |
(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 | 855.2.a.d.1.1 | 2 | ||
3.2 | odd | 2 | 285.2.a.g.1.2 | ✓ | 2 | ||
5.4 | even | 2 | 4275.2.a.y.1.2 | 2 | |||
12.11 | even | 2 | 4560.2.a.bf.1.2 | 2 | |||
15.2 | even | 4 | 1425.2.c.l.799.4 | 4 | |||
15.8 | even | 4 | 1425.2.c.l.799.1 | 4 | |||
15.14 | odd | 2 | 1425.2.a.k.1.1 | 2 | |||
57.56 | even | 2 | 5415.2.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
285.2.a.g.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
855.2.a.d.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1425.2.a.k.1.1 | 2 | 15.14 | odd | 2 | |||
1425.2.c.l.799.1 | 4 | 15.8 | even | 4 | |||
1425.2.c.l.799.4 | 4 | 15.2 | even | 4 | |||
4275.2.a.y.1.2 | 2 | 5.4 | even | 2 | |||
4560.2.a.bf.1.2 | 2 | 12.11 | even | 2 | |||
5415.2.a.n.1.1 | 2 | 57.56 | even | 2 |