Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6525,2,Mod(1,6525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6525, 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("6525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6525 = 3^{2} \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6525.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: | \(52.1023873189\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{12} - 20x^{10} + 148x^{8} - 502x^{6} + 792x^{4} - 496x^{2} + 45 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 1305) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.27263\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6525.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.27263 | 0.899884 | 0.449942 | − | 0.893058i | \(-0.351445\pi\) | ||||
0.449942 | + | 0.893058i | \(0.351445\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.380419 | −0.190209 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.255813 | 0.0966884 | 0.0483442 | − | 0.998831i | \(-0.484606\pi\) | ||||
0.0483442 | + | 0.998831i | \(0.484606\pi\) | |||||||
\(8\) | −3.02939 | −1.07105 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.63446 | −1.39734 | −0.698672 | − | 0.715442i | \(-0.746225\pi\) | ||||
−0.698672 | + | 0.715442i | \(0.746225\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.02700 | 1.39424 | 0.697120 | − | 0.716955i | \(-0.254465\pi\) | ||||
0.697120 | + | 0.716955i | \(0.254465\pi\) | |||||||
\(14\) | 0.325555 | 0.0870083 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.09444 | −0.773611 | ||||||||
\(17\) | −0.336444 | −0.0815995 | −0.0407998 | − | 0.999167i | \(-0.512991\pi\) | ||||
−0.0407998 | + | 0.999167i | \(0.512991\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.91437 | −0.668602 | −0.334301 | − | 0.942466i | \(-0.608500\pi\) | ||||
−0.334301 | + | 0.942466i | \(0.608500\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.89795 | −1.25745 | ||||||||
\(23\) | 8.65656 | 1.80502 | 0.902509 | − | 0.430671i | \(-0.141723\pi\) | ||||
0.902509 | + | 0.430671i | \(0.141723\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.39750 | 1.25465 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.0973162 | −0.0183910 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.26943 | −0.587207 | −0.293603 | − | 0.955927i | \(-0.594854\pi\) | ||||
−0.293603 | + | 0.955927i | \(0.594854\pi\) | |||||||
\(32\) | 2.12070 | 0.374890 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.428167 | −0.0734301 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.86954 | −0.636148 | −0.318074 | − | 0.948066i | \(-0.603036\pi\) | ||||
−0.318074 | + | 0.948066i | \(0.603036\pi\) | |||||||
\(38\) | −3.70891 | −0.601664 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.71649 | −0.892765 | −0.446383 | − | 0.894842i | \(-0.647288\pi\) | ||||
−0.446383 | + | 0.894842i | \(0.647288\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.98619 | 1.06538 | 0.532692 | − | 0.846309i | \(-0.321180\pi\) | ||||
0.532692 | + | 0.846309i | \(0.321180\pi\) | |||||||
\(44\) | 1.76304 | 0.265788 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.0166 | 1.62431 | ||||||||
\(47\) | −0.336444 | −0.0490753 | −0.0245377 | − | 0.999699i | \(-0.507811\pi\) | ||||
−0.0245377 | + | 0.999699i | \(0.507811\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.93456 | −0.990651 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.91237 | −0.265197 | ||||||||
\(53\) | 6.01484 | 0.826202 | 0.413101 | − | 0.910685i | \(-0.364446\pi\) | ||||
0.413101 | + | 0.910685i | \(0.364446\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.774958 | −0.103558 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.27263 | −0.167104 | ||||||||
\(59\) | 13.2799 | 1.72890 | 0.864451 | − | 0.502718i | \(-0.167666\pi\) | ||||
0.864451 | + | 0.502718i | \(0.167666\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.77792 | −0.995861 | −0.497930 | − | 0.867217i | \(-0.665906\pi\) | ||||
−0.497930 | + | 0.867217i | \(0.665906\pi\) | |||||||
\(62\) | −4.16077 | −0.528418 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.88775 | 1.11097 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.2605 | −1.37569 | −0.687847 | − | 0.725856i | \(-0.741444\pi\) | ||||
−0.687847 | + | 0.725856i | \(0.741444\pi\) | |||||||
\(68\) | 0.127989 | 0.0155210 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.9668 | 1.65756 | 0.828778 | − | 0.559578i | \(-0.189037\pi\) | ||||
0.828778 | + | 0.559578i | \(0.189037\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.46426 | 0.990667 | 0.495333 | − | 0.868703i | \(-0.335046\pi\) | ||||
0.495333 | + | 0.868703i | \(0.335046\pi\) | |||||||
\(74\) | −4.92448 | −0.572459 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.10868 | 0.127174 | ||||||||
\(77\) | −1.18556 | −0.135107 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.3102 | −1.72253 | −0.861267 | − | 0.508153i | \(-0.830328\pi\) | ||||
−0.861267 | + | 0.508153i | \(0.830328\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.27496 | −0.803385 | ||||||||
\(83\) | 7.60521 | 0.834781 | 0.417390 | − | 0.908727i | \(-0.362945\pi\) | ||||
0.417390 | + | 0.908727i | \(0.362945\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.89082 | 0.958722 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 14.0396 | 1.49662 | ||||||||
\(89\) | 13.0383 | 1.38206 | 0.691029 | − | 0.722827i | \(-0.257157\pi\) | ||||
0.691029 | + | 0.722827i | \(0.257157\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.28597 | 0.134807 | ||||||||
\(92\) | −3.29312 | −0.343331 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.428167 | −0.0441621 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.5445 | 1.17216 | 0.586081 | − | 0.810253i | \(-0.300670\pi\) | ||||
0.586081 | + | 0.810253i | \(0.300670\pi\) | |||||||
\(98\) | −8.82511 | −0.891471 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.19832 | 0.815763 | 0.407882 | − | 0.913035i | \(-0.366268\pi\) | ||||
0.407882 | + | 0.913035i | \(0.366268\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.73014 | −0.170476 | −0.0852380 | − | 0.996361i | \(-0.527165\pi\) | ||||
−0.0852380 | + | 0.996361i | \(0.527165\pi\) | |||||||
\(104\) | −15.2287 | −1.49330 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.65465 | 0.743486 | ||||||||
\(107\) | 5.38921 | 0.520995 | 0.260497 | − | 0.965475i | \(-0.416113\pi\) | ||||
0.260497 | + | 0.965475i | \(0.416113\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.2391 | 1.36386 | 0.681929 | − | 0.731418i | \(-0.261141\pi\) | ||||
0.681929 | + | 0.731418i | \(0.261141\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.791600 | −0.0747992 | ||||||||
\(113\) | −9.89466 | −0.930811 | −0.465406 | − | 0.885098i | \(-0.654091\pi\) | ||||
−0.465406 | + | 0.885098i | \(0.654091\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.380419 | 0.0353210 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 16.9004 | 1.55581 | ||||||||
\(119\) | −0.0860668 | −0.00788973 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4783 | 0.952569 | ||||||||
\(122\) | −9.89840 | −0.896159 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.24375 | 0.111692 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.2226 | 1.08458 | 0.542291 | − | 0.840191i | \(-0.317557\pi\) | ||||
0.542291 | + | 0.840191i | \(0.317557\pi\) | |||||||
\(128\) | 7.06940 | 0.624852 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0464 | 1.05250 | 0.526250 | − | 0.850330i | \(-0.323598\pi\) | ||||
0.526250 | + | 0.850330i | \(0.323598\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.745535 | −0.0646461 | ||||||||
\(134\) | −14.3305 | −1.23796 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.01922 | 0.0873972 | ||||||||
\(137\) | −5.47512 | −0.467771 | −0.233886 | − | 0.972264i | \(-0.575144\pi\) | ||||
−0.233886 | + | 0.972264i | \(0.575144\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.71403 | 0.230201 | 0.115100 | − | 0.993354i | \(-0.463281\pi\) | ||||
0.115100 | + | 0.993354i | \(0.463281\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 17.7745 | 1.49161 | ||||||||
\(143\) | −23.2975 | −1.94823 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.7719 | 0.891485 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.47204 | 0.121001 | ||||||||
\(149\) | 3.70395 | 0.303439 | 0.151720 | − | 0.988424i | \(-0.451519\pi\) | ||||
0.151720 | + | 0.988424i | \(0.451519\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.3481 | 1.24901 | 0.624505 | − | 0.781021i | \(-0.285301\pi\) | ||||
0.624505 | + | 0.781021i | \(0.285301\pi\) | |||||||
\(152\) | 8.82875 | 0.716107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.50877 | −0.121580 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.8231 | 1.74168 | 0.870838 | − | 0.491571i | \(-0.163577\pi\) | ||||
0.870838 | + | 0.491571i | \(0.163577\pi\) | |||||||
\(158\) | −19.4842 | −1.55008 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.21447 | 0.174524 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.08019 | −0.241259 | −0.120630 | − | 0.992698i | \(-0.538491\pi\) | ||||
−0.120630 | + | 0.992698i | \(0.538491\pi\) | |||||||
\(164\) | 2.17466 | 0.169812 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.67861 | 0.751206 | ||||||||
\(167\) | 8.55017 | 0.661632 | 0.330816 | − | 0.943695i | \(-0.392676\pi\) | ||||
0.330816 | + | 0.943695i | \(0.392676\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.2707 | 0.943903 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.65768 | −0.202646 | ||||||||
\(173\) | 5.76340 | 0.438183 | 0.219092 | − | 0.975704i | \(-0.429691\pi\) | ||||
0.219092 | + | 0.975704i | \(0.429691\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 14.3411 | 1.08100 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 16.5929 | 1.24369 | ||||||||
\(179\) | −14.1430 | −1.05710 | −0.528548 | − | 0.848903i | \(-0.677264\pi\) | ||||
−0.528548 | + | 0.848903i | \(0.677264\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0322 | −1.11734 | −0.558668 | − | 0.829391i | \(-0.688688\pi\) | ||||
−0.558668 | + | 0.829391i | \(0.688688\pi\) | |||||||
\(182\) | 1.63657 | 0.121310 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −26.2241 | −1.93326 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.55924 | 0.114023 | ||||||||
\(188\) | 0.127989 | 0.00933459 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.2634 | 0.887346 | 0.443673 | − | 0.896189i | \(-0.353675\pi\) | ||||
0.443673 | + | 0.896189i | \(0.353675\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.34203 | 0.600472 | 0.300236 | − | 0.953865i | \(-0.402935\pi\) | ||||
0.300236 | + | 0.953865i | \(0.402935\pi\) | |||||||
\(194\) | 14.6918 | 1.05481 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.63804 | 0.188431 | ||||||||
\(197\) | 6.69263 | 0.476830 | 0.238415 | − | 0.971163i | \(-0.423372\pi\) | ||||
0.238415 | + | 0.971163i | \(0.423372\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.5583 | 0.890235 | 0.445117 | − | 0.895472i | \(-0.353162\pi\) | ||||
0.445117 | + | 0.895472i | \(0.353162\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.4334 | 0.734092 | ||||||||
\(203\) | −0.255813 | −0.0179546 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.20183 | −0.153409 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −15.5558 | −1.07860 | ||||||||
\(209\) | 13.5065 | 0.934267 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.6479 | −0.939563 | −0.469782 | − | 0.882783i | \(-0.655667\pi\) | ||||
−0.469782 | + | 0.882783i | \(0.655667\pi\) | |||||||
\(212\) | −2.28816 | −0.157151 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.85846 | 0.468835 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.836364 | −0.0567761 | ||||||||
\(218\) | 18.1211 | 1.22731 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.69130 | −0.113769 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.4721 | 0.902158 | 0.451079 | − | 0.892484i | \(-0.351039\pi\) | ||||
0.451079 | + | 0.892484i | \(0.351039\pi\) | |||||||
\(224\) | 0.542503 | 0.0362475 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.5922 | −0.837622 | ||||||||
\(227\) | −1.54298 | −0.102411 | −0.0512057 | − | 0.998688i | \(-0.516306\pi\) | ||||
−0.0512057 | + | 0.998688i | \(0.516306\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.89526 | 0.521734 | 0.260867 | − | 0.965375i | \(-0.415992\pi\) | ||||
0.260867 | + | 0.965375i | \(0.415992\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.02939 | 0.198889 | ||||||||
\(233\) | 28.4782 | 1.86567 | 0.932836 | − | 0.360301i | \(-0.117326\pi\) | ||||
0.932836 | + | 0.360301i | \(0.117326\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.05194 | −0.328853 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.109531 | −0.00709984 | ||||||||
\(239\) | −8.88508 | −0.574728 | −0.287364 | − | 0.957821i | \(-0.592779\pi\) | ||||
−0.287364 | + | 0.957821i | \(0.592779\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29.8901 | −1.92539 | −0.962695 | − | 0.270589i | \(-0.912782\pi\) | ||||
−0.962695 | + | 0.270589i | \(0.912782\pi\) | |||||||
\(242\) | 13.3349 | 0.857202 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.95887 | 0.189422 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.6505 | −0.932192 | ||||||||
\(248\) | 9.90437 | 0.628928 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.9551 | 1.00708 | 0.503539 | − | 0.863973i | \(-0.332031\pi\) | ||||
0.503539 | + | 0.863973i | \(0.332031\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −40.1185 | −2.52223 | ||||||||
\(254\) | 15.5548 | 0.975998 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.77878 | −0.548674 | ||||||||
\(257\) | −17.1593 | −1.07037 | −0.535185 | − | 0.844735i | \(-0.679758\pi\) | ||||
−0.535185 | + | 0.844735i | \(0.679758\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.989880 | −0.0615081 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.3306 | 0.947128 | ||||||||
\(263\) | 1.72781 | 0.106542 | 0.0532708 | − | 0.998580i | \(-0.483035\pi\) | ||||
0.0532708 | + | 0.998580i | \(0.483035\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.948789 | −0.0581740 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.28372 | 0.261670 | ||||||||
\(269\) | 4.97931 | 0.303594 | 0.151797 | − | 0.988412i | \(-0.451494\pi\) | ||||
0.151797 | + | 0.988412i | \(0.451494\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.0881 | 0.795047 | 0.397524 | − | 0.917592i | \(-0.369870\pi\) | ||||
0.397524 | + | 0.917592i | \(0.369870\pi\) | |||||||
\(272\) | 1.04111 | 0.0631263 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.96779 | −0.420939 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.8147 | 1.25063 | 0.625316 | − | 0.780371i | \(-0.284970\pi\) | ||||
0.625316 | + | 0.780371i | \(0.284970\pi\) | |||||||
\(278\) | 3.45394 | 0.207154 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.93338 | −0.234646 | −0.117323 | − | 0.993094i | \(-0.537431\pi\) | ||||
−0.117323 | + | 0.993094i | \(0.537431\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.47745 | −0.325600 | −0.162800 | − | 0.986659i | \(-0.552053\pi\) | ||||
−0.162800 | + | 0.986659i | \(0.552053\pi\) | |||||||
\(284\) | −5.31324 | −0.315282 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −29.6490 | −1.75318 | ||||||||
\(287\) | −1.46235 | −0.0863201 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8868 | −0.993342 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.21996 | −0.188434 | ||||||||
\(293\) | −11.9974 | −0.700893 | −0.350446 | − | 0.936583i | \(-0.613970\pi\) | ||||
−0.350446 | + | 0.936583i | \(0.613970\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 11.7223 | 0.681347 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.71375 | 0.273060 | ||||||||
\(299\) | 43.5166 | 2.51663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.78716 | 0.103010 | ||||||||
\(302\) | 19.5324 | 1.12396 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.01836 | 0.517238 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.4807 | −1.51133 | −0.755666 | − | 0.654957i | \(-0.772687\pi\) | ||||
−0.755666 | + | 0.654957i | \(0.772687\pi\) | |||||||
\(308\) | 0.451009 | 0.0256986 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.71530 | 0.0972660 | 0.0486330 | − | 0.998817i | \(-0.484514\pi\) | ||||
0.0486330 | + | 0.998817i | \(0.484514\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.3782 | −1.88665 | −0.943325 | − | 0.331871i | \(-0.892320\pi\) | ||||
−0.943325 | + | 0.331871i | \(0.892320\pi\) | |||||||
\(314\) | 27.7727 | 1.56731 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.82429 | 0.327642 | ||||||||
\(317\) | −17.9712 | −1.00936 | −0.504682 | − | 0.863305i | \(-0.668390\pi\) | ||||
−0.504682 | + | 0.863305i | \(0.668390\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.63446 | 0.259480 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.81819 | 0.157052 | ||||||||
\(323\) | 0.980521 | 0.0545577 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.91994 | −0.217105 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 17.3175 | 0.956196 | ||||||||
\(329\) | −0.0860668 | −0.00474501 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.49393 | 0.356939 | 0.178469 | − | 0.983945i | \(-0.442885\pi\) | ||||
0.178469 | + | 0.983945i | \(0.442885\pi\) | |||||||
\(332\) | −2.89317 | −0.158783 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.8812 | 0.595392 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.36156 | 0.346536 | 0.173268 | − | 0.984875i | \(-0.444567\pi\) | ||||
0.173268 | + | 0.984875i | \(0.444567\pi\) | |||||||
\(338\) | 15.6161 | 0.849403 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.1521 | 0.820530 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.56465 | −0.192473 | ||||||||
\(344\) | −21.1639 | −1.14108 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.33466 | 0.394314 | ||||||||
\(347\) | 21.6036 | 1.15974 | 0.579871 | − | 0.814708i | \(-0.303103\pi\) | ||||
0.579871 | + | 0.814708i | \(0.303103\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.12603 | −0.220861 | −0.110431 | − | 0.993884i | \(-0.535223\pi\) | ||||
−0.110431 | + | 0.993884i | \(0.535223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9.82830 | −0.523850 | ||||||||
\(353\) | 7.07724 | 0.376684 | 0.188342 | − | 0.982104i | \(-0.439689\pi\) | ||||
0.188342 | + | 0.982104i | \(0.439689\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.96002 | −0.262881 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −17.9988 | −0.951264 | ||||||||
\(359\) | 14.4359 | 0.761900 | 0.380950 | − | 0.924596i | \(-0.375597\pi\) | ||||
0.380950 | + | 0.924596i | \(0.375597\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.5064 | −0.552971 | ||||||||
\(362\) | −19.1304 | −1.00547 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.489209 | −0.0256415 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.4145 | 0.804630 | 0.402315 | − | 0.915501i | \(-0.368206\pi\) | ||||
0.402315 | + | 0.915501i | \(0.368206\pi\) | |||||||
\(368\) | −26.7873 | −1.39638 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.53868 | 0.0798841 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.8574 | 1.54596 | 0.772979 | − | 0.634432i | \(-0.218766\pi\) | ||||
0.772979 | + | 0.634432i | \(0.218766\pi\) | |||||||
\(374\) | 1.98433 | 0.102607 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.01922 | 0.0525621 | ||||||||
\(377\) | −5.02700 | −0.258904 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 37.3451 | 1.91829 | 0.959144 | − | 0.282920i | \(-0.0913030\pi\) | ||||
0.959144 | + | 0.282920i | \(0.0913030\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.6067 | 0.798508 | ||||||||
\(383\) | −25.8159 | −1.31913 | −0.659566 | − | 0.751647i | \(-0.729260\pi\) | ||||
−0.659566 | + | 0.751647i | \(0.729260\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.6163 | 0.540355 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.39173 | −0.222956 | ||||||||
\(389\) | −20.6935 | −1.04920 | −0.524600 | − | 0.851349i | \(-0.675785\pi\) | ||||
−0.524600 | + | 0.851349i | \(0.675785\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.91245 | −0.147289 | ||||||||
\(392\) | 21.0075 | 1.06104 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.51723 | 0.429092 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.38045 | 0.119471 | 0.0597357 | − | 0.998214i | \(-0.480974\pi\) | ||||
0.0597357 | + | 0.998214i | \(0.480974\pi\) | |||||||
\(398\) | 15.9820 | 0.801108 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.0936 | 1.60268 | 0.801339 | − | 0.598211i | \(-0.204121\pi\) | ||||
0.801339 | + | 0.598211i | \(0.204121\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.4354 | −0.818707 | ||||||||
\(404\) | −3.11879 | −0.155166 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.325555 | −0.0161570 | ||||||||
\(407\) | 17.9332 | 0.888918 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.5011 | −1.55763 | −0.778815 | − | 0.627253i | \(-0.784179\pi\) | ||||
−0.778815 | + | 0.627253i | \(0.784179\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.658179 | 0.0324261 | ||||||||
\(413\) | 3.39719 | 0.167165 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10.6608 | 0.522686 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 17.1888 | 0.840732 | ||||||||
\(419\) | 3.15481 | 0.154123 | 0.0770613 | − | 0.997026i | \(-0.475446\pi\) | ||||
0.0770613 | + | 0.997026i | \(0.475446\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.9631 | −0.583048 | −0.291524 | − | 0.956564i | \(-0.594162\pi\) | ||||
−0.291524 | + | 0.956564i | \(0.594162\pi\) | |||||||
\(422\) | −17.3687 | −0.845497 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18.2213 | −0.884904 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.98970 | −0.0962882 | ||||||||
\(428\) | −2.05016 | −0.0990981 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.2658 | 1.50602 | 0.753011 | − | 0.658008i | \(-0.228601\pi\) | ||||
0.753011 | + | 0.658008i | \(0.228601\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.6459 | −1.47275 | −0.736373 | − | 0.676575i | \(-0.763463\pi\) | ||||
−0.736373 | + | 0.676575i | \(0.763463\pi\) | |||||||
\(434\) | −1.06438 | −0.0510919 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.41682 | −0.259419 | ||||||||
\(437\) | −25.2284 | −1.20684 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.717425 | 0.0342408 | 0.0171204 | − | 0.999853i | \(-0.494550\pi\) | ||||
0.0171204 | + | 0.999853i | \(0.494550\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.15240 | −0.102379 | ||||||||
\(443\) | −27.0649 | −1.28589 | −0.642947 | − | 0.765911i | \(-0.722288\pi\) | ||||
−0.642947 | + | 0.765911i | \(0.722288\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 17.1450 | 0.811838 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.27361 | 0.107418 | ||||||||
\(449\) | 30.3663 | 1.43307 | 0.716536 | − | 0.697550i | \(-0.245727\pi\) | ||||
0.716536 | + | 0.697550i | \(0.245727\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.4929 | 1.24750 | ||||||||
\(452\) | 3.76411 | 0.177049 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.96364 | −0.0921584 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.43167 | −0.113749 | −0.0568743 | − | 0.998381i | \(-0.518113\pi\) | ||||
−0.0568743 | + | 0.998381i | \(0.518113\pi\) | |||||||
\(458\) | 10.0477 | 0.469500 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.28439 | −0.385842 | −0.192921 | − | 0.981214i | \(-0.561796\pi\) | ||||
−0.192921 | + | 0.981214i | \(0.561796\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.05654 | −0.327945 | −0.163973 | − | 0.986465i | \(-0.552431\pi\) | ||||
−0.163973 | + | 0.986465i | \(0.552431\pi\) | |||||||
\(464\) | 3.09444 | 0.143656 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 36.2422 | 1.67889 | ||||||||
\(467\) | −6.07165 | −0.280963 | −0.140481 | − | 0.990083i | \(-0.544865\pi\) | ||||
−0.140481 | + | 0.990083i | \(0.544865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.88060 | −0.133014 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −40.2301 | −1.85174 | ||||||||
\(473\) | −32.3773 | −1.48871 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.0327414 | 0.00150070 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.3074 | −0.517188 | ||||||||
\(479\) | 29.7675 | 1.36011 | 0.680055 | − | 0.733161i | \(-0.261956\pi\) | ||||
0.680055 | + | 0.733161i | \(0.261956\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.4522 | −0.886943 | ||||||||
\(482\) | −38.0390 | −1.73263 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.98613 | −0.181188 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41.9050 | −1.89890 | −0.949448 | − | 0.313923i | \(-0.898357\pi\) | ||||
−0.949448 | + | 0.313923i | \(0.898357\pi\) | |||||||
\(488\) | 23.5623 | 1.06662 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.22435 | 0.326030 | 0.163015 | − | 0.986624i | \(-0.447878\pi\) | ||||
0.163015 | + | 0.986624i | \(0.447878\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.336444 | 0.0151527 | ||||||||
\(494\) | −18.6447 | −0.838864 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.1171 | 0.454270 | ||||||||
\(497\) | 3.57290 | 0.160266 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.5607 | −0.696593 | −0.348296 | − | 0.937384i | \(-0.613240\pi\) | ||||
−0.348296 | + | 0.937384i | \(0.613240\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.3049 | 0.906253 | ||||||||
\(503\) | 38.5096 | 1.71706 | 0.858529 | − | 0.512765i | \(-0.171379\pi\) | ||||
0.858529 | + | 0.512765i | \(0.171379\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −51.0560 | −2.26971 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.64971 | −0.206298 | ||||||||
\(509\) | −31.6646 | −1.40351 | −0.701754 | − | 0.712419i | \(-0.747600\pi\) | ||||
−0.701754 | + | 0.712419i | \(0.747600\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.16527 | 0.0957860 | ||||||||
\(512\) | −25.3109 | −1.11860 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −21.8375 | −0.963209 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.55924 | 0.0685751 | ||||||||
\(518\) | −1.25975 | −0.0553502 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.2023 | −0.885079 | −0.442539 | − | 0.896749i | \(-0.645922\pi\) | ||||
−0.442539 | + | 0.896749i | \(0.645922\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.1052 | 0.529325 | 0.264663 | − | 0.964341i | \(-0.414739\pi\) | ||||
0.264663 | + | 0.964341i | \(0.414739\pi\) | |||||||
\(524\) | −4.58268 | −0.200195 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.19886 | 0.0958751 | ||||||||
\(527\) | 1.09998 | 0.0479158 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 51.9361 | 2.25809 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.283615 | 0.0122963 | ||||||||
\(533\) | −28.7368 | −1.24473 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 34.1125 | 1.47344 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.33681 | 0.273199 | ||||||||
\(539\) | 32.1380 | 1.38428 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.4279 | −0.620304 | −0.310152 | − | 0.950687i | \(-0.600380\pi\) | ||||
−0.310152 | + | 0.950687i | \(0.600380\pi\) | |||||||
\(542\) | 16.6563 | 0.715450 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.713495 | −0.0305909 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.9178 | −1.79228 | −0.896139 | − | 0.443774i | \(-0.853639\pi\) | ||||
−0.896139 | + | 0.443774i | \(0.853639\pi\) | |||||||
\(548\) | 2.08284 | 0.0889744 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.91437 | 0.124156 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.91656 | −0.166549 | ||||||||
\(554\) | 26.4893 | 1.12542 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.03247 | −0.0437863 | ||||||||
\(557\) | 3.60324 | 0.152674 | 0.0763372 | − | 0.997082i | \(-0.475677\pi\) | ||||
0.0763372 | + | 0.997082i | \(0.475677\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.1196 | 1.48540 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.00573 | −0.211154 | ||||||||
\(563\) | 15.5829 | 0.656741 | 0.328370 | − | 0.944549i | \(-0.393501\pi\) | ||||
0.328370 | + | 0.944549i | \(0.393501\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.97075 | −0.293003 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −42.3109 | −1.77532 | ||||||||
\(569\) | −36.9718 | −1.54994 | −0.774970 | − | 0.631998i | \(-0.782235\pi\) | ||||
−0.774970 | + | 0.631998i | \(0.782235\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.9692 | 1.25417 | 0.627086 | − | 0.778950i | \(-0.284248\pi\) | ||||
0.627086 | + | 0.778950i | \(0.284248\pi\) | |||||||
\(572\) | 8.86279 | 0.370572 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.86103 | −0.0776780 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.12327 | −0.296546 | −0.148273 | − | 0.988946i | \(-0.547371\pi\) | ||||
−0.148273 | + | 0.988946i | \(0.547371\pi\) | |||||||
\(578\) | −21.4906 | −0.893892 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.94552 | 0.0807136 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.8756 | −1.15449 | ||||||||
\(584\) | −25.6415 | −1.06105 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.2682 | −0.630722 | ||||||||
\(587\) | −7.87237 | −0.324928 | −0.162464 | − | 0.986715i | \(-0.551944\pi\) | ||||
−0.162464 | + | 0.986715i | \(0.551944\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.52833 | 0.392608 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.9741 | 0.492131 | ||||||||
\(593\) | −17.9188 | −0.735836 | −0.367918 | − | 0.929858i | \(-0.619929\pi\) | ||||
−0.367918 | + | 0.929858i | \(0.619929\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.40905 | −0.0577170 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 55.3804 | 2.26467 | ||||||||
\(599\) | −20.1934 | −0.825078 | −0.412539 | − | 0.910940i | \(-0.635358\pi\) | ||||
−0.412539 | + | 0.910940i | \(0.635358\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.2527 | 0.948496 | 0.474248 | − | 0.880391i | \(-0.342720\pi\) | ||||
0.474248 | + | 0.880391i | \(0.342720\pi\) | |||||||
\(602\) | 2.27439 | 0.0926973 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.83870 | −0.237573 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.6177 | −0.715082 | −0.357541 | − | 0.933897i | \(-0.616385\pi\) | ||||
−0.357541 | + | 0.933897i | \(0.616385\pi\) | |||||||
\(608\) | −6.18050 | −0.250652 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.69130 | −0.0684228 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.4161 | 0.541873 | 0.270937 | − | 0.962597i | \(-0.412667\pi\) | ||||
0.270937 | + | 0.962597i | \(0.412667\pi\) | |||||||
\(614\) | −33.7001 | −1.36002 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.59151 | 0.144706 | ||||||||
\(617\) | 7.99166 | 0.321732 | 0.160866 | − | 0.986976i | \(-0.448571\pi\) | ||||
0.160866 | + | 0.986976i | \(0.448571\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.0770 | −0.605996 | −0.302998 | − | 0.952991i | \(-0.597988\pi\) | ||||
−0.302998 | + | 0.952991i | \(0.597988\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.18294 | 0.0875281 | ||||||||
\(623\) | 3.33538 | 0.133629 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −42.4781 | −1.69776 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.30193 | −0.331283 | ||||||||
\(629\) | 1.30188 | 0.0519094 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.5154 | 0.418611 | 0.209306 | − | 0.977850i | \(-0.432880\pi\) | ||||
0.209306 | + | 0.977850i | \(0.432880\pi\) | |||||||
\(632\) | 46.3805 | 1.84492 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −22.8707 | −0.908311 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34.8600 | −1.38121 | ||||||||
\(638\) | 5.89795 | 0.233502 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.2479 | 1.07623 | 0.538113 | − | 0.842873i | \(-0.319137\pi\) | ||||
0.538113 | + | 0.842873i | \(0.319137\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.3023 | 1.43162 | 0.715812 | − | 0.698293i | \(-0.246057\pi\) | ||||
0.715812 | + | 0.698293i | \(0.246057\pi\) | |||||||
\(644\) | −0.842424 | −0.0331962 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.24784 | 0.0490955 | ||||||||
\(647\) | 8.77892 | 0.345135 | 0.172567 | − | 0.984998i | \(-0.444794\pi\) | ||||
0.172567 | + | 0.984998i | \(0.444794\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −61.5454 | −2.41587 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.17176 | 0.0458898 | ||||||||
\(653\) | 44.1466 | 1.72759 | 0.863794 | − | 0.503845i | \(-0.168082\pi\) | ||||
0.863794 | + | 0.503845i | \(0.168082\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 17.6894 | 0.690653 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.109531 | −0.00426996 | ||||||||
\(659\) | −22.7653 | −0.886810 | −0.443405 | − | 0.896321i | \(-0.646230\pi\) | ||||
−0.443405 | + | 0.896321i | \(0.646230\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.3474 | 1.14148 | 0.570740 | − | 0.821131i | \(-0.306656\pi\) | ||||
0.570740 | + | 0.821131i | \(0.306656\pi\) | |||||||
\(662\) | 8.26435 | 0.321203 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −23.0391 | −0.894092 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.65656 | −0.335183 | ||||||||
\(668\) | −3.25264 | −0.125849 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.0465 | 1.39156 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.2267 | −1.62772 | −0.813860 | − | 0.581060i | \(-0.802638\pi\) | ||||
−0.813860 | + | 0.581060i | \(0.802638\pi\) | |||||||
\(674\) | 8.09590 | 0.311842 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.66802 | −0.179539 | ||||||||
\(677\) | −19.9803 | −0.767907 | −0.383953 | − | 0.923353i | \(-0.625438\pi\) | ||||
−0.383953 | + | 0.923353i | \(0.625438\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.95323 | 0.113334 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 19.2829 | 0.738381 | ||||||||
\(683\) | 23.0491 | 0.881950 | 0.440975 | − | 0.897519i | \(-0.354633\pi\) | ||||
0.440975 | + | 0.897519i | \(0.354633\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.53647 | −0.173203 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −21.6184 | −0.824193 | ||||||||
\(689\) | 30.2366 | 1.15192 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.01208 | 0.152627 | 0.0763134 | − | 0.997084i | \(-0.475685\pi\) | ||||
0.0763134 | + | 0.997084i | \(0.475685\pi\) | |||||||
\(692\) | −2.19250 | −0.0833465 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.4933 | 1.04363 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.92328 | 0.0728493 | ||||||||
\(698\) | −5.25090 | −0.198750 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.49887 | −0.169920 | −0.0849599 | − | 0.996384i | \(-0.527076\pi\) | ||||
−0.0849599 | + | 0.996384i | \(0.527076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.2773 | 0.425330 | ||||||||
\(704\) | −41.1900 | −1.55240 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.00670 | 0.338971 | ||||||||
\(707\) | 2.09724 | 0.0788748 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.7777 | 1.38121 | 0.690607 | − | 0.723230i | \(-0.257343\pi\) | ||||
0.690607 | + | 0.723230i | \(0.257343\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −39.4981 | −1.48025 | ||||||||
\(713\) | −28.3020 | −1.05992 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.38026 | 0.201070 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.3716 | 0.685621 | ||||||||
\(719\) | 25.4279 | 0.948300 | 0.474150 | − | 0.880444i | \(-0.342755\pi\) | ||||
0.474150 | + | 0.880444i | \(0.342755\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.442594 | −0.0164831 | ||||||||
\(722\) | −13.3708 | −0.497609 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.71854 | 0.212528 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.6265 | 0.431205 | 0.215602 | − | 0.976481i | \(-0.430829\pi\) | ||||
0.215602 | + | 0.976481i | \(0.430829\pi\) | |||||||
\(728\) | −3.89571 | −0.144385 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.35046 | −0.0869349 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.6926 | 0.948978 | 0.474489 | − | 0.880261i | \(-0.342633\pi\) | ||||
0.474489 | + | 0.880261i | \(0.342633\pi\) | |||||||
\(734\) | 19.6169 | 0.724073 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.3580 | 0.676683 | ||||||||
\(737\) | 52.1866 | 1.92232 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.3612 | −1.22721 | −0.613606 | − | 0.789612i | \(-0.710282\pi\) | ||||
−0.613606 | + | 0.789612i | \(0.710282\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.95816 | 0.0718864 | ||||||||
\(743\) | 25.6430 | 0.940750 | 0.470375 | − | 0.882467i | \(-0.344119\pi\) | ||||
0.470375 | + | 0.882467i | \(0.344119\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 37.9973 | 1.39118 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.593162 | −0.0216882 | ||||||||
\(749\) | 1.37863 | 0.0503741 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.6411 | 1.70196 | 0.850979 | − | 0.525200i | \(-0.176009\pi\) | ||||
0.850979 | + | 0.525200i | \(0.176009\pi\) | |||||||
\(752\) | 1.04111 | 0.0379652 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.39750 | −0.232983 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.69262 | 0.0978650 | 0.0489325 | − | 0.998802i | \(-0.484418\pi\) | ||||
0.0489325 | + | 0.998802i | \(0.484418\pi\) | |||||||
\(758\) | 47.5264 | 1.72624 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.471501 | 0.0170919 | 0.00854595 | − | 0.999963i | \(-0.497280\pi\) | ||||
0.00854595 | + | 0.999963i | \(0.497280\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.64255 | 0.131869 | ||||||||
\(764\) | −4.66521 | −0.168781 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.8540 | −1.18706 | ||||||||
\(767\) | 66.7583 | 2.41050 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.04380 | 0.326128 | 0.163064 | − | 0.986616i | \(-0.447862\pi\) | ||||
0.163064 | + | 0.986616i | \(0.447862\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.17346 | −0.114215 | ||||||||
\(773\) | −9.91726 | −0.356699 | −0.178350 | − | 0.983967i | \(-0.557076\pi\) | ||||
−0.178350 | + | 0.983967i | \(0.557076\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −34.9726 | −1.25544 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.3351 | −0.944159 | ||||||||
\(779\) | 16.6600 | 0.596905 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −64.7287 | −2.31617 | ||||||||
\(782\) | −3.70646 | −0.132543 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 21.4586 | 0.766379 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.53609 | 0.304279 | 0.152139 | − | 0.988359i | \(-0.451384\pi\) | ||||
0.152139 | + | 0.988359i | \(0.451384\pi\) | |||||||
\(788\) | −2.54600 | −0.0906976 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.53119 | −0.0899986 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.0996 | −1.38847 | ||||||||
\(794\) | 3.02943 | 0.107510 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.77741 | −0.169331 | ||||||||
\(797\) | −12.5563 | −0.444768 | −0.222384 | − | 0.974959i | \(-0.571384\pi\) | ||||
−0.222384 | + | 0.974959i | \(0.571384\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.113194 | 0.00400453 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 40.8432 | 1.44222 | ||||||||
\(803\) | −39.2273 | −1.38430 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.9162 | −0.736741 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −24.8359 | −0.873723 | ||||||||
\(809\) | −16.4082 | −0.576883 | −0.288441 | − | 0.957498i | \(-0.593137\pi\) | ||||
−0.288441 | + | 0.957498i | \(0.593137\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.4688 | 1.03479 | 0.517394 | − | 0.855747i | \(-0.326902\pi\) | ||||
0.517394 | + | 0.855747i | \(0.326902\pi\) | |||||||
\(812\) | 0.0973162 | 0.00341513 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22.8223 | 0.799923 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.3603 | −0.712318 | ||||||||
\(818\) | −40.0892 | −1.40169 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.5209 | 0.995385 | 0.497693 | − | 0.867353i | \(-0.334181\pi\) | ||||
0.497693 | + | 0.867353i | \(0.334181\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.7546 | 0.584028 | 0.292014 | − | 0.956414i | \(-0.405675\pi\) | ||||
0.292014 | + | 0.956414i | \(0.405675\pi\) | |||||||
\(824\) | 5.24127 | 0.182588 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.32336 | 0.150429 | ||||||||
\(827\) | 3.38369 | 0.117662 | 0.0588312 | − | 0.998268i | \(-0.481263\pi\) | ||||
0.0588312 | + | 0.998268i | \(0.481263\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.4434 | −0.501639 | −0.250819 | − | 0.968034i | \(-0.580700\pi\) | ||||
−0.250819 | + | 0.968034i | \(0.580700\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 44.6787 | 1.54896 | ||||||||
\(833\) | 2.33309 | 0.0808367 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.13814 | −0.177706 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.01490 | 0.138692 | ||||||||
\(839\) | −27.6642 | −0.955075 | −0.477538 | − | 0.878611i | \(-0.658471\pi\) | ||||
−0.477538 | + | 0.878611i | \(0.658471\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −15.2246 | −0.524675 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.19193 | 0.178714 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.68048 | 0.0921024 | ||||||||
\(848\) | −18.6126 | −0.639159 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33.4969 | −1.14826 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.26068 | 0.145883 | 0.0729415 | − | 0.997336i | \(-0.476761\pi\) | ||||
0.0729415 | + | 0.997336i | \(0.476761\pi\) | |||||||
\(854\) | −2.53214 | −0.0866481 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.3260 | −0.558011 | ||||||||
\(857\) | −28.7104 | −0.980729 | −0.490364 | − | 0.871518i | \(-0.663136\pi\) | ||||
−0.490364 | + | 0.871518i | \(0.663136\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.3734 | −1.34340 | −0.671701 | − | 0.740822i | \(-0.734436\pi\) | ||||
−0.671701 | + | 0.740822i | \(0.734436\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 39.7898 | 1.35525 | ||||||||
\(863\) | −22.1235 | −0.753094 | −0.376547 | − | 0.926398i | \(-0.622889\pi\) | ||||
−0.376547 | + | 0.926398i | \(0.622889\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −39.0008 | −1.32530 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.318168 | 0.0107993 | ||||||||
\(869\) | 70.9546 | 2.40697 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −56.6068 | −1.91805 | ||||||||
\(872\) | −43.1357 | −1.46076 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −32.1064 | −1.08602 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.3439 | −1.09217 | −0.546087 | − | 0.837728i | \(-0.683883\pi\) | ||||
−0.546087 | + | 0.837728i | \(0.683883\pi\) | |||||||
\(878\) | 0.913015 | 0.0308128 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.6109 | −1.83989 | −0.919944 | − | 0.392051i | \(-0.871766\pi\) | ||||
−0.919944 | + | 0.392051i | \(0.871766\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.5511 | 1.60022 | 0.800111 | − | 0.599852i | \(-0.204774\pi\) | ||||
0.800111 | + | 0.599852i | \(0.204774\pi\) | |||||||
\(884\) | 0.643403 | 0.0216400 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −34.4436 | −1.15715 | ||||||||
\(887\) | −10.4630 | −0.351312 | −0.175656 | − | 0.984452i | \(-0.556205\pi\) | ||||
−0.175656 | + | 0.984452i | \(0.556205\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.12671 | 0.104866 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.12504 | −0.171599 | ||||||||
\(893\) | 0.980521 | 0.0328119 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.80845 | 0.0604160 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 38.6449 | 1.28960 | ||||||||
\(899\) | 3.26943 | 0.109042 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.02365 | −0.0674177 | ||||||||
\(902\) | 33.7156 | 1.12261 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 29.9747 | 0.996945 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.7211 | 0.355989 | 0.177994 | − | 0.984032i | \(-0.443039\pi\) | ||||
0.177994 | + | 0.984032i | \(0.443039\pi\) | |||||||
\(908\) | 0.586980 | 0.0194796 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.57634 | −0.118489 | −0.0592447 | − | 0.998243i | \(-0.518869\pi\) | ||||
−0.0592447 | + | 0.998243i | \(0.518869\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.2461 | −1.16648 | ||||||||
\(914\) | −3.09461 | −0.102361 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.00351 | −0.0992386 | ||||||||
\(917\) | 3.08163 | 0.101765 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.2776 | −0.734870 | −0.367435 | − | 0.930049i | \(-0.619764\pi\) | ||||
−0.367435 | + | 0.930049i | \(0.619764\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.5429 | −0.347213 | ||||||||
\(923\) | 70.2112 | 2.31103 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.98035 | −0.295113 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.12070 | −0.0696153 | ||||||||
\(929\) | −21.1779 | −0.694826 | −0.347413 | − | 0.937712i | \(-0.612940\pi\) | ||||
−0.347413 | + | 0.937712i | \(0.612940\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.2099 | 0.662352 | ||||||||
\(932\) | −10.8337 | −0.354868 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.72695 | −0.252834 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.4462 | −1.12531 | −0.562654 | − | 0.826693i | \(-0.690220\pi\) | ||||
−0.562654 | + | 0.826693i | \(0.690220\pi\) | |||||||
\(938\) | −3.66593 | −0.119697 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.296167 | 0.00965477 | 0.00482738 | − | 0.999988i | \(-0.498463\pi\) | ||||
0.00482738 | + | 0.999988i | \(0.498463\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −49.4851 | −1.61146 | ||||||||
\(944\) | −41.0940 | −1.33750 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −41.2042 | −1.33966 | ||||||||
\(947\) | −46.9467 | −1.52556 | −0.762782 | − | 0.646656i | \(-0.776167\pi\) | ||||
−0.762782 | + | 0.646656i | \(0.776167\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.5498 | 1.38123 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.260730 | 0.00845029 | ||||||||
\(953\) | 1.91375 | 0.0619926 | 0.0309963 | − | 0.999519i | \(-0.490132\pi\) | ||||
0.0309963 | + | 0.999519i | \(0.490132\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.38005 | 0.109319 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 37.8829 | 1.22394 | ||||||||
\(959\) | −1.40061 | −0.0452280 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.3108 | −0.655188 | ||||||||
\(962\) | −24.7554 | −0.798145 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.3707 | 0.366227 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.01326 | 0.129058 | 0.0645288 | − | 0.997916i | \(-0.479446\pi\) | ||||
0.0645288 | + | 0.997916i | \(0.479446\pi\) | |||||||
\(968\) | −31.7427 | −1.02025 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.54751 | −0.145937 | −0.0729683 | − | 0.997334i | \(-0.523247\pi\) | ||||
−0.0729683 | + | 0.997334i | \(0.523247\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.694284 | 0.0222577 | ||||||||
\(974\) | −53.3295 | −1.70879 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.0683 | 0.770409 | ||||||||
\(977\) | 44.2333 | 1.41515 | 0.707574 | − | 0.706639i | \(-0.249789\pi\) | ||||
0.707574 | + | 0.706639i | \(0.249789\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −60.4256 | −1.93121 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.19391 | 0.293389 | ||||||||
\(983\) | 34.2083 | 1.09107 | 0.545537 | − | 0.838087i | \(-0.316326\pi\) | ||||
0.545537 | + | 0.838087i | \(0.316326\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.428167 | 0.0136356 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.57334 | 0.177312 | ||||||||
\(989\) | 60.4764 | 1.92304 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.76770 | −0.0561528 | −0.0280764 | − | 0.999606i | \(-0.508938\pi\) | ||||
−0.0280764 | + | 0.999606i | \(0.508938\pi\) | |||||||
\(992\) | −6.93347 | −0.220138 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.54697 | 0.144221 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.7398 | 0.751848 | 0.375924 | − | 0.926650i | \(-0.377325\pi\) | ||||
0.375924 | + | 0.926650i | \(0.377325\pi\) | |||||||
\(998\) | −19.8030 | −0.626853 | ||||||||
\(999\) | 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 | 6525.2.a.cf.1.8 | 12 | ||
3.2 | odd | 2 | 6525.2.a.ce.1.5 | 12 | |||
5.2 | odd | 4 | 1305.2.c.l.784.8 | yes | 12 | ||
5.3 | odd | 4 | 1305.2.c.l.784.5 | yes | 12 | ||
5.4 | even | 2 | inner | 6525.2.a.cf.1.5 | 12 | ||
15.2 | even | 4 | 1305.2.c.k.784.5 | ✓ | 12 | ||
15.8 | even | 4 | 1305.2.c.k.784.8 | yes | 12 | ||
15.14 | odd | 2 | 6525.2.a.ce.1.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1305.2.c.k.784.5 | ✓ | 12 | 15.2 | even | 4 | ||
1305.2.c.k.784.8 | yes | 12 | 15.8 | even | 4 | ||
1305.2.c.l.784.5 | yes | 12 | 5.3 | odd | 4 | ||
1305.2.c.l.784.8 | yes | 12 | 5.2 | odd | 4 | ||
6525.2.a.ce.1.5 | 12 | 3.2 | odd | 2 | |||
6525.2.a.ce.1.8 | 12 | 15.14 | odd | 2 | |||
6525.2.a.cf.1.5 | 12 | 5.4 | even | 2 | inner | ||
6525.2.a.cf.1.8 | 12 | 1.1 | even | 1 | trivial |