Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 16x^{6} + 69x^{4} - 10x^{3} - 70x^{2} + 10x + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.00431\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 2.00431 | 1.15719 | 0.578593 | − | 0.815616i | \(-0.303602\pi\) | ||||
0.578593 | + | 0.815616i | \(0.303602\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.00431 | −0.818254 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.01724 | 0.339080 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.00431 | 0.578593 | ||||||||
\(13\) | 4.02930 | 1.11753 | 0.558764 | − | 0.829327i | \(-0.311276\pi\) | ||||
0.558764 | + | 0.829327i | \(0.311276\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −2.00431 | −0.517509 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.300566 | −0.0728979 | −0.0364490 | − | 0.999336i | \(-0.511605\pi\) | ||||
−0.0364490 | + | 0.999336i | \(0.511605\pi\) | |||||||
\(18\) | −1.01724 | −0.239766 | ||||||||
\(19\) | −7.73531 | −1.77460 | −0.887301 | − | 0.461191i | \(-0.847422\pi\) | ||||
−0.887301 | + | 0.461191i | \(0.847422\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 2.00431 | 0.437375 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.48607 | −1.35244 | −0.676219 | − | 0.736700i | \(-0.736383\pi\) | ||||
−0.676219 | + | 0.736700i | \(0.736383\pi\) | |||||||
\(24\) | −2.00431 | −0.409127 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.02930 | −0.790211 | ||||||||
\(27\) | −3.97405 | −0.764807 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −1.81673 | −0.337358 | −0.168679 | − | 0.985671i | \(-0.553950\pi\) | ||||
−0.168679 | + | 0.985671i | \(0.553950\pi\) | |||||||
\(30\) | 2.00431 | 0.365934 | ||||||||
\(31\) | 7.53480 | 1.35329 | 0.676645 | − | 0.736310i | \(-0.263433\pi\) | ||||
0.676645 | + | 0.736310i | \(0.263433\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.300566 | 0.0515466 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 1.01724 | 0.169540 | ||||||||
\(37\) | 9.11210 | 1.49802 | 0.749010 | − | 0.662559i | \(-0.230530\pi\) | ||||
0.749010 | + | 0.662559i | \(0.230530\pi\) | |||||||
\(38\) | 7.73531 | 1.25483 | ||||||||
\(39\) | 8.07596 | 1.29319 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −9.68330 | −1.51228 | −0.756139 | − | 0.654411i | \(-0.772917\pi\) | ||||
−0.756139 | + | 0.654411i | \(0.772917\pi\) | |||||||
\(42\) | −2.00431 | −0.309271 | ||||||||
\(43\) | −3.42569 | −0.522412 | −0.261206 | − | 0.965283i | \(-0.584120\pi\) | ||||
−0.261206 | + | 0.965283i | \(0.584120\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.01724 | −0.151641 | ||||||||
\(46\) | 6.48607 | 0.956319 | ||||||||
\(47\) | −6.21202 | −0.906116 | −0.453058 | − | 0.891481i | \(-0.649667\pi\) | ||||
−0.453058 | + | 0.891481i | \(0.649667\pi\) | |||||||
\(48\) | 2.00431 | 0.289297 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −0.602426 | −0.0843565 | ||||||||
\(52\) | 4.02930 | 0.558764 | ||||||||
\(53\) | 6.39502 | 0.878423 | 0.439212 | − | 0.898384i | \(-0.355258\pi\) | ||||
0.439212 | + | 0.898384i | \(0.355258\pi\) | |||||||
\(54\) | 3.97405 | 0.540800 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −15.5039 | −2.05355 | ||||||||
\(58\) | 1.81673 | 0.238548 | ||||||||
\(59\) | 5.51945 | 0.718571 | 0.359286 | − | 0.933228i | \(-0.383020\pi\) | ||||
0.359286 | + | 0.933228i | \(0.383020\pi\) | |||||||
\(60\) | −2.00431 | −0.258755 | ||||||||
\(61\) | 3.62844 | 0.464574 | 0.232287 | − | 0.972647i | \(-0.425379\pi\) | ||||
0.232287 | + | 0.972647i | \(0.425379\pi\) | |||||||
\(62\) | −7.53480 | −0.956920 | ||||||||
\(63\) | 1.01724 | 0.128160 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.02930 | −0.499774 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.505448 | 0.0617503 | 0.0308751 | − | 0.999523i | \(-0.490171\pi\) | ||||
0.0308751 | + | 0.999523i | \(0.490171\pi\) | |||||||
\(68\) | −0.300566 | −0.0364490 | ||||||||
\(69\) | −13.0001 | −1.56502 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 8.37915 | 0.994422 | 0.497211 | − | 0.867630i | \(-0.334357\pi\) | ||||
0.497211 | + | 0.867630i | \(0.334357\pi\) | |||||||
\(72\) | −1.01724 | −0.119883 | ||||||||
\(73\) | −1.40274 | −0.164178 | −0.0820892 | − | 0.996625i | \(-0.526159\pi\) | ||||
−0.0820892 | + | 0.996625i | \(0.526159\pi\) | |||||||
\(74\) | −9.11210 | −1.05926 | ||||||||
\(75\) | 2.00431 | 0.231437 | ||||||||
\(76\) | −7.73531 | −0.887301 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −8.07596 | −0.914422 | ||||||||
\(79\) | −6.20005 | −0.697560 | −0.348780 | − | 0.937205i | \(-0.613404\pi\) | ||||
−0.348780 | + | 0.937205i | \(0.613404\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −11.0169 | −1.22410 | ||||||||
\(82\) | 9.68330 | 1.06934 | ||||||||
\(83\) | −14.5768 | −1.60001 | −0.800006 | − | 0.599992i | \(-0.795170\pi\) | ||||
−0.800006 | + | 0.599992i | \(0.795170\pi\) | |||||||
\(84\) | 2.00431 | 0.218688 | ||||||||
\(85\) | 0.300566 | 0.0326009 | ||||||||
\(86\) | 3.42569 | 0.369401 | ||||||||
\(87\) | −3.64127 | −0.390386 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.92815 | 0.204384 | 0.102192 | − | 0.994765i | \(-0.467414\pi\) | ||||
0.102192 | + | 0.994765i | \(0.467414\pi\) | |||||||
\(90\) | 1.01724 | 0.107227 | ||||||||
\(91\) | 4.02930 | 0.422386 | ||||||||
\(92\) | −6.48607 | −0.676219 | ||||||||
\(93\) | 15.1020 | 1.56601 | ||||||||
\(94\) | 6.21202 | 0.640721 | ||||||||
\(95\) | 7.73531 | 0.793626 | ||||||||
\(96\) | −2.00431 | −0.204564 | ||||||||
\(97\) | −16.4944 | −1.67475 | −0.837374 | − | 0.546630i | \(-0.815910\pi\) | ||||
−0.837374 | + | 0.546630i | \(0.815910\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −9.44404 | −0.939717 | −0.469859 | − | 0.882742i | \(-0.655695\pi\) | ||||
−0.469859 | + | 0.882742i | \(0.655695\pi\) | |||||||
\(102\) | 0.602426 | 0.0596491 | ||||||||
\(103\) | −3.51983 | −0.346820 | −0.173410 | − | 0.984850i | \(-0.555479\pi\) | ||||
−0.173410 | + | 0.984850i | \(0.555479\pi\) | |||||||
\(104\) | −4.02930 | −0.395106 | ||||||||
\(105\) | −2.00431 | −0.195600 | ||||||||
\(106\) | −6.39502 | −0.621139 | ||||||||
\(107\) | −10.4251 | −1.00783 | −0.503917 | − | 0.863752i | \(-0.668108\pi\) | ||||
−0.503917 | + | 0.863752i | \(0.668108\pi\) | |||||||
\(108\) | −3.97405 | −0.382404 | ||||||||
\(109\) | −12.1571 | −1.16444 | −0.582221 | − | 0.813030i | \(-0.697816\pi\) | ||||
−0.582221 | + | 0.813030i | \(0.697816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.2634 | 1.73349 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −6.67216 | −0.627664 | −0.313832 | − | 0.949478i | \(-0.601613\pi\) | ||||
−0.313832 | + | 0.949478i | \(0.601613\pi\) | |||||||
\(114\) | 15.5039 | 1.45208 | ||||||||
\(115\) | 6.48607 | 0.604829 | ||||||||
\(116\) | −1.81673 | −0.168679 | ||||||||
\(117\) | 4.09877 | 0.378932 | ||||||||
\(118\) | −5.51945 | −0.508106 | ||||||||
\(119\) | −0.300566 | −0.0275528 | ||||||||
\(120\) | 2.00431 | 0.182967 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −3.62844 | −0.328503 | ||||||||
\(123\) | −19.4083 | −1.74999 | ||||||||
\(124\) | 7.53480 | 0.676645 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.01724 | −0.0906231 | ||||||||
\(127\) | 12.8919 | 1.14397 | 0.571984 | − | 0.820265i | \(-0.306174\pi\) | ||||
0.571984 | + | 0.820265i | \(0.306174\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −6.86612 | −0.604528 | ||||||||
\(130\) | 4.02930 | 0.353393 | ||||||||
\(131\) | −20.3862 | −1.78115 | −0.890577 | − | 0.454833i | \(-0.849699\pi\) | ||||
−0.890577 | + | 0.454833i | \(0.849699\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.73531 | −0.670737 | ||||||||
\(134\) | −0.505448 | −0.0436640 | ||||||||
\(135\) | 3.97405 | 0.342032 | ||||||||
\(136\) | 0.300566 | 0.0257733 | ||||||||
\(137\) | −17.6954 | −1.51182 | −0.755911 | − | 0.654674i | \(-0.772806\pi\) | ||||
−0.755911 | + | 0.654674i | \(0.772806\pi\) | |||||||
\(138\) | 13.0001 | 1.10664 | ||||||||
\(139\) | −13.4774 | −1.14314 | −0.571570 | − | 0.820553i | \(-0.693665\pi\) | ||||
−0.571570 | + | 0.820553i | \(0.693665\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −12.4508 | −1.04855 | ||||||||
\(142\) | −8.37915 | −0.703163 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.01724 | 0.0847701 | ||||||||
\(145\) | 1.81673 | 0.150871 | ||||||||
\(146\) | 1.40274 | 0.116092 | ||||||||
\(147\) | 2.00431 | 0.165312 | ||||||||
\(148\) | 9.11210 | 0.749010 | ||||||||
\(149\) | 1.72417 | 0.141249 | 0.0706246 | − | 0.997503i | \(-0.477501\pi\) | ||||
0.0706246 | + | 0.997503i | \(0.477501\pi\) | |||||||
\(150\) | −2.00431 | −0.163651 | ||||||||
\(151\) | 9.14895 | 0.744531 | 0.372266 | − | 0.928126i | \(-0.378581\pi\) | ||||
0.372266 | + | 0.928126i | \(0.378581\pi\) | |||||||
\(152\) | 7.73531 | 0.627417 | ||||||||
\(153\) | −0.305748 | −0.0247183 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.53480 | −0.605209 | ||||||||
\(156\) | 8.07596 | 0.646594 | ||||||||
\(157\) | −0.876025 | −0.0699144 | −0.0349572 | − | 0.999389i | \(-0.511129\pi\) | ||||
−0.0349572 | + | 0.999389i | \(0.511129\pi\) | |||||||
\(158\) | 6.20005 | 0.493250 | ||||||||
\(159\) | 12.8176 | 1.01650 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −6.48607 | −0.511174 | ||||||||
\(162\) | 11.0169 | 0.865573 | ||||||||
\(163\) | −6.49269 | −0.508547 | −0.254274 | − | 0.967132i | \(-0.581836\pi\) | ||||
−0.254274 | + | 0.967132i | \(0.581836\pi\) | |||||||
\(164\) | −9.68330 | −0.756139 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.5768 | 1.13138 | ||||||||
\(167\) | 20.0322 | 1.55014 | 0.775070 | − | 0.631875i | \(-0.217714\pi\) | ||||
0.775070 | + | 0.631875i | \(0.217714\pi\) | |||||||
\(168\) | −2.00431 | −0.154636 | ||||||||
\(169\) | 3.23529 | 0.248868 | ||||||||
\(170\) | −0.300566 | −0.0230524 | ||||||||
\(171\) | −7.86868 | −0.601733 | ||||||||
\(172\) | −3.42569 | −0.261206 | ||||||||
\(173\) | −1.52088 | −0.115630 | −0.0578151 | − | 0.998327i | \(-0.518413\pi\) | ||||
−0.0578151 | + | 0.998327i | \(0.518413\pi\) | |||||||
\(174\) | 3.64127 | 0.276044 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.0627 | 0.831521 | ||||||||
\(178\) | −1.92815 | −0.144521 | ||||||||
\(179\) | 24.1512 | 1.80515 | 0.902573 | − | 0.430537i | \(-0.141676\pi\) | ||||
0.902573 | + | 0.430537i | \(0.141676\pi\) | |||||||
\(180\) | −1.01724 | −0.0758207 | ||||||||
\(181\) | 16.6623 | 1.23850 | 0.619249 | − | 0.785195i | \(-0.287437\pi\) | ||||
0.619249 | + | 0.785195i | \(0.287437\pi\) | |||||||
\(182\) | −4.02930 | −0.298672 | ||||||||
\(183\) | 7.27250 | 0.537598 | ||||||||
\(184\) | 6.48607 | 0.478159 | ||||||||
\(185\) | −9.11210 | −0.669935 | ||||||||
\(186\) | −15.1020 | −1.10733 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.21202 | −0.453058 | ||||||||
\(189\) | −3.97405 | −0.289070 | ||||||||
\(190\) | −7.73531 | −0.561178 | ||||||||
\(191\) | −2.97548 | −0.215298 | −0.107649 | − | 0.994189i | \(-0.534332\pi\) | ||||
−0.107649 | + | 0.994189i | \(0.534332\pi\) | |||||||
\(192\) | 2.00431 | 0.144648 | ||||||||
\(193\) | 11.5006 | 0.827831 | 0.413916 | − | 0.910315i | \(-0.364161\pi\) | ||||
0.413916 | + | 0.910315i | \(0.364161\pi\) | |||||||
\(194\) | 16.4944 | 1.18423 | ||||||||
\(195\) | −8.07596 | −0.578331 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −16.0597 | −1.14420 | −0.572101 | − | 0.820183i | \(-0.693872\pi\) | ||||
−0.572101 | + | 0.820183i | \(0.693872\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.0899 | 0.786140 | 0.393070 | − | 0.919509i | \(-0.371413\pi\) | ||||
0.393070 | + | 0.919509i | \(0.371413\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 1.01307 | 0.0714566 | ||||||||
\(202\) | 9.44404 | 0.664480 | ||||||||
\(203\) | −1.81673 | −0.127509 | ||||||||
\(204\) | −0.602426 | −0.0421783 | ||||||||
\(205\) | 9.68330 | 0.676311 | ||||||||
\(206\) | 3.51983 | 0.245238 | ||||||||
\(207\) | −6.59790 | −0.458586 | ||||||||
\(208\) | 4.02930 | 0.279382 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.00431 | 0.138310 | ||||||||
\(211\) | 25.5146 | 1.75650 | 0.878250 | − | 0.478203i | \(-0.158712\pi\) | ||||
0.878250 | + | 0.478203i | \(0.158712\pi\) | |||||||
\(212\) | 6.39502 | 0.439212 | ||||||||
\(213\) | 16.7944 | 1.15073 | ||||||||
\(214\) | 10.4251 | 0.712646 | ||||||||
\(215\) | 3.42569 | 0.233630 | ||||||||
\(216\) | 3.97405 | 0.270400 | ||||||||
\(217\) | 7.53480 | 0.511495 | ||||||||
\(218\) | 12.1571 | 0.823385 | ||||||||
\(219\) | −2.81152 | −0.189985 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.21107 | −0.0814655 | ||||||||
\(222\) | −18.2634 | −1.22576 | ||||||||
\(223\) | −23.1843 | −1.55254 | −0.776268 | − | 0.630403i | \(-0.782890\pi\) | ||||
−0.776268 | + | 0.630403i | \(0.782890\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 1.01724 | 0.0678161 | ||||||||
\(226\) | 6.67216 | 0.443826 | ||||||||
\(227\) | 4.97362 | 0.330111 | 0.165055 | − | 0.986284i | \(-0.447220\pi\) | ||||
0.165055 | + | 0.986284i | \(0.447220\pi\) | |||||||
\(228\) | −15.5039 | −1.02677 | ||||||||
\(229\) | −25.6627 | −1.69584 | −0.847921 | − | 0.530123i | \(-0.822146\pi\) | ||||
−0.847921 | + | 0.530123i | \(0.822146\pi\) | |||||||
\(230\) | −6.48607 | −0.427679 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.81673 | 0.119274 | ||||||||
\(233\) | −3.81437 | −0.249888 | −0.124944 | − | 0.992164i | \(-0.539875\pi\) | ||||
−0.124944 | + | 0.992164i | \(0.539875\pi\) | |||||||
\(234\) | −4.09877 | −0.267945 | ||||||||
\(235\) | 6.21202 | 0.405227 | ||||||||
\(236\) | 5.51945 | 0.359286 | ||||||||
\(237\) | −12.4268 | −0.807207 | ||||||||
\(238\) | 0.300566 | 0.0194828 | ||||||||
\(239\) | −6.58100 | −0.425689 | −0.212845 | − | 0.977086i | \(-0.568273\pi\) | ||||
−0.212845 | + | 0.977086i | \(0.568273\pi\) | |||||||
\(240\) | −2.00431 | −0.129377 | ||||||||
\(241\) | −23.9679 | −1.54391 | −0.771955 | − | 0.635677i | \(-0.780721\pi\) | ||||
−0.771955 | + | 0.635677i | \(0.780721\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.1592 | −0.651710 | ||||||||
\(244\) | 3.62844 | 0.232287 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 19.4083 | 1.23743 | ||||||||
\(247\) | −31.1679 | −1.98317 | ||||||||
\(248\) | −7.53480 | −0.478460 | ||||||||
\(249\) | −29.2164 | −1.85151 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 5.08595 | 0.321022 | 0.160511 | − | 0.987034i | \(-0.448686\pi\) | ||||
0.160511 | + | 0.987034i | \(0.448686\pi\) | |||||||
\(252\) | 1.01724 | 0.0640802 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −12.8919 | −0.808908 | ||||||||
\(255\) | 0.602426 | 0.0377254 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.0968 | 0.692198 | 0.346099 | − | 0.938198i | \(-0.387506\pi\) | ||||
0.346099 | + | 0.938198i | \(0.387506\pi\) | |||||||
\(258\) | 6.86612 | 0.427466 | ||||||||
\(259\) | 9.11210 | 0.566198 | ||||||||
\(260\) | −4.02930 | −0.249887 | ||||||||
\(261\) | −1.84805 | −0.114391 | ||||||||
\(262\) | 20.3862 | 1.25947 | ||||||||
\(263\) | 2.64779 | 0.163270 | 0.0816348 | − | 0.996662i | \(-0.473986\pi\) | ||||
0.0816348 | + | 0.996662i | \(0.473986\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.39502 | −0.392843 | ||||||||
\(266\) | 7.73531 | 0.474282 | ||||||||
\(267\) | 3.86460 | 0.236510 | ||||||||
\(268\) | 0.505448 | 0.0308751 | ||||||||
\(269\) | −3.42199 | −0.208642 | −0.104321 | − | 0.994544i | \(-0.533267\pi\) | ||||
−0.104321 | + | 0.994544i | \(0.533267\pi\) | |||||||
\(270\) | −3.97405 | −0.241853 | ||||||||
\(271\) | 21.1788 | 1.28652 | 0.643259 | − | 0.765649i | \(-0.277582\pi\) | ||||
0.643259 | + | 0.765649i | \(0.277582\pi\) | |||||||
\(272\) | −0.300566 | −0.0182245 | ||||||||
\(273\) | 8.07596 | 0.488779 | ||||||||
\(274\) | 17.6954 | 1.06902 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −13.0001 | −0.782512 | ||||||||
\(277\) | −27.3915 | −1.64580 | −0.822899 | − | 0.568188i | \(-0.807645\pi\) | ||||
−0.822899 | + | 0.568188i | \(0.807645\pi\) | |||||||
\(278\) | 13.4774 | 0.808322 | ||||||||
\(279\) | 7.66470 | 0.458874 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | −11.2620 | −0.671832 | −0.335916 | − | 0.941892i | \(-0.609046\pi\) | ||||
−0.335916 | + | 0.941892i | \(0.609046\pi\) | |||||||
\(282\) | 12.4508 | 0.741433 | ||||||||
\(283\) | 20.2928 | 1.20628 | 0.603142 | − | 0.797634i | \(-0.293915\pi\) | ||||
0.603142 | + | 0.797634i | \(0.293915\pi\) | |||||||
\(284\) | 8.37915 | 0.497211 | ||||||||
\(285\) | 15.5039 | 0.918373 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.68330 | −0.571587 | ||||||||
\(288\) | −1.01724 | −0.0599415 | ||||||||
\(289\) | −16.9097 | −0.994686 | ||||||||
\(290\) | −1.81673 | −0.106682 | ||||||||
\(291\) | −33.0597 | −1.93800 | ||||||||
\(292\) | −1.40274 | −0.0820892 | ||||||||
\(293\) | 11.9548 | 0.698405 | 0.349202 | − | 0.937047i | \(-0.386453\pi\) | ||||
0.349202 | + | 0.937047i | \(0.386453\pi\) | |||||||
\(294\) | −2.00431 | −0.116893 | ||||||||
\(295\) | −5.51945 | −0.321355 | ||||||||
\(296\) | −9.11210 | −0.529630 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.72417 | −0.0998783 | ||||||||
\(299\) | −26.1343 | −1.51139 | ||||||||
\(300\) | 2.00431 | 0.115719 | ||||||||
\(301\) | −3.42569 | −0.197453 | ||||||||
\(302\) | −9.14895 | −0.526463 | ||||||||
\(303\) | −18.9287 | −1.08743 | ||||||||
\(304\) | −7.73531 | −0.443651 | ||||||||
\(305\) | −3.62844 | −0.207764 | ||||||||
\(306\) | 0.305748 | 0.0174785 | ||||||||
\(307\) | 19.6625 | 1.12220 | 0.561100 | − | 0.827748i | \(-0.310378\pi\) | ||||
0.561100 | + | 0.827748i | \(0.310378\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.05482 | −0.401335 | ||||||||
\(310\) | 7.53480 | 0.427948 | ||||||||
\(311\) | −10.8025 | −0.612552 | −0.306276 | − | 0.951943i | \(-0.599083\pi\) | ||||
−0.306276 | + | 0.951943i | \(0.599083\pi\) | |||||||
\(312\) | −8.07596 | −0.457211 | ||||||||
\(313\) | −14.7449 | −0.833431 | −0.416715 | − | 0.909037i | \(-0.636819\pi\) | ||||
−0.416715 | + | 0.909037i | \(0.636819\pi\) | |||||||
\(314\) | 0.876025 | 0.0494370 | ||||||||
\(315\) | −1.01724 | −0.0573151 | ||||||||
\(316\) | −6.20005 | −0.348780 | ||||||||
\(317\) | 17.4668 | 0.981035 | 0.490518 | − | 0.871431i | \(-0.336808\pi\) | ||||
0.490518 | + | 0.871431i | \(0.336808\pi\) | |||||||
\(318\) | −12.8176 | −0.718774 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −20.8951 | −1.16625 | ||||||||
\(322\) | 6.48607 | 0.361455 | ||||||||
\(323\) | 2.32497 | 0.129365 | ||||||||
\(324\) | −11.0169 | −0.612052 | ||||||||
\(325\) | 4.02930 | 0.223506 | ||||||||
\(326\) | 6.49269 | 0.359597 | ||||||||
\(327\) | −24.3666 | −1.34748 | ||||||||
\(328\) | 9.68330 | 0.534671 | ||||||||
\(329\) | −6.21202 | −0.342480 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.3375 | 1.22778 | 0.613890 | − | 0.789391i | \(-0.289604\pi\) | ||||
0.613890 | + | 0.789391i | \(0.289604\pi\) | |||||||
\(332\) | −14.5768 | −0.800006 | ||||||||
\(333\) | 9.26920 | 0.507949 | ||||||||
\(334\) | −20.0322 | −1.09611 | ||||||||
\(335\) | −0.505448 | −0.0276156 | ||||||||
\(336\) | 2.00431 | 0.109344 | ||||||||
\(337\) | −14.2386 | −0.775624 | −0.387812 | − | 0.921739i | \(-0.626769\pi\) | ||||
−0.387812 | + | 0.921739i | \(0.626769\pi\) | |||||||
\(338\) | −3.23529 | −0.175976 | ||||||||
\(339\) | −13.3731 | −0.726325 | ||||||||
\(340\) | 0.300566 | 0.0163005 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 7.86868 | 0.425489 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 3.42569 | 0.184701 | ||||||||
\(345\) | 13.0001 | 0.699900 | ||||||||
\(346\) | 1.52088 | 0.0817629 | ||||||||
\(347\) | −20.6300 | −1.10748 | −0.553739 | − | 0.832690i | \(-0.686800\pi\) | ||||
−0.553739 | + | 0.832690i | \(0.686800\pi\) | |||||||
\(348\) | −3.64127 | −0.195193 | ||||||||
\(349\) | 16.0047 | 0.856711 | 0.428355 | − | 0.903610i | \(-0.359093\pi\) | ||||
0.428355 | + | 0.903610i | \(0.359093\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −16.0127 | −0.854693 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.46881 | −0.0781767 | −0.0390883 | − | 0.999236i | \(-0.512445\pi\) | ||||
−0.0390883 | + | 0.999236i | \(0.512445\pi\) | |||||||
\(354\) | −11.0627 | −0.587974 | ||||||||
\(355\) | −8.37915 | −0.444719 | ||||||||
\(356\) | 1.92815 | 0.102192 | ||||||||
\(357\) | −0.602426 | −0.0318838 | ||||||||
\(358\) | −24.1512 | −1.27643 | ||||||||
\(359\) | 8.43193 | 0.445020 | 0.222510 | − | 0.974930i | \(-0.428575\pi\) | ||||
0.222510 | + | 0.974930i | \(0.428575\pi\) | |||||||
\(360\) | 1.01724 | 0.0536133 | ||||||||
\(361\) | 40.8350 | 2.14921 | ||||||||
\(362\) | −16.6623 | −0.875750 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.02930 | 0.211193 | ||||||||
\(365\) | 1.40274 | 0.0734228 | ||||||||
\(366\) | −7.27250 | −0.380139 | ||||||||
\(367\) | 27.2590 | 1.42291 | 0.711454 | − | 0.702732i | \(-0.248037\pi\) | ||||
0.711454 | + | 0.702732i | \(0.248037\pi\) | |||||||
\(368\) | −6.48607 | −0.338110 | ||||||||
\(369\) | −9.85025 | −0.512784 | ||||||||
\(370\) | 9.11210 | 0.473715 | ||||||||
\(371\) | 6.39502 | 0.332013 | ||||||||
\(372\) | 15.1020 | 0.783004 | ||||||||
\(373\) | −14.7417 | −0.763299 | −0.381649 | − | 0.924307i | \(-0.624644\pi\) | ||||
−0.381649 | + | 0.924307i | \(0.624644\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.00431 | −0.103502 | ||||||||
\(376\) | 6.21202 | 0.320360 | ||||||||
\(377\) | −7.32014 | −0.377006 | ||||||||
\(378\) | 3.97405 | 0.204403 | ||||||||
\(379\) | −26.2074 | −1.34618 | −0.673091 | − | 0.739560i | \(-0.735034\pi\) | ||||
−0.673091 | + | 0.739560i | \(0.735034\pi\) | |||||||
\(380\) | 7.73531 | 0.396813 | ||||||||
\(381\) | 25.8392 | 1.32378 | ||||||||
\(382\) | 2.97548 | 0.152239 | ||||||||
\(383\) | −18.0535 | −0.922492 | −0.461246 | − | 0.887272i | \(-0.652597\pi\) | ||||
−0.461246 | + | 0.887272i | \(0.652597\pi\) | |||||||
\(384\) | −2.00431 | −0.102282 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.5006 | −0.585365 | ||||||||
\(387\) | −3.48475 | −0.177140 | ||||||||
\(388\) | −16.4944 | −0.837374 | ||||||||
\(389\) | −21.4054 | −1.08530 | −0.542648 | − | 0.839960i | \(-0.682578\pi\) | ||||
−0.542648 | + | 0.839960i | \(0.682578\pi\) | |||||||
\(390\) | 8.07596 | 0.408942 | ||||||||
\(391\) | 1.94949 | 0.0985900 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −40.8602 | −2.06113 | ||||||||
\(394\) | 16.0597 | 0.809074 | ||||||||
\(395\) | 6.20005 | 0.311959 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.87615 | 0.244727 | 0.122364 | − | 0.992485i | \(-0.460953\pi\) | ||||
0.122364 | + | 0.992485i | \(0.460953\pi\) | |||||||
\(398\) | −11.0899 | −0.555885 | ||||||||
\(399\) | −15.5039 | −0.776167 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 15.6680 | 0.782423 | 0.391212 | − | 0.920301i | \(-0.372056\pi\) | ||||
0.391212 | + | 0.920301i | \(0.372056\pi\) | |||||||
\(402\) | −1.01307 | −0.0505274 | ||||||||
\(403\) | 30.3600 | 1.51234 | ||||||||
\(404\) | −9.44404 | −0.469859 | ||||||||
\(405\) | 11.0169 | 0.547436 | ||||||||
\(406\) | 1.81673 | 0.0901626 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.602426 | 0.0298245 | ||||||||
\(409\) | −37.1821 | −1.83854 | −0.919268 | − | 0.393633i | \(-0.871218\pi\) | ||||
−0.919268 | + | 0.393633i | \(0.871218\pi\) | |||||||
\(410\) | −9.68330 | −0.478224 | ||||||||
\(411\) | −35.4670 | −1.74946 | ||||||||
\(412\) | −3.51983 | −0.173410 | ||||||||
\(413\) | 5.51945 | 0.271594 | ||||||||
\(414\) | 6.59790 | 0.324269 | ||||||||
\(415\) | 14.5768 | 0.715547 | ||||||||
\(416\) | −4.02930 | −0.197553 | ||||||||
\(417\) | −27.0129 | −1.32283 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.2599 | −1.33173 | −0.665865 | − | 0.746072i | \(-0.731938\pi\) | ||||
−0.665865 | + | 0.746072i | \(0.731938\pi\) | |||||||
\(420\) | −2.00431 | −0.0978001 | ||||||||
\(421\) | −13.1997 | −0.643315 | −0.321658 | − | 0.946856i | \(-0.604240\pi\) | ||||
−0.321658 | + | 0.946856i | \(0.604240\pi\) | |||||||
\(422\) | −25.5146 | −1.24203 | ||||||||
\(423\) | −6.31912 | −0.307246 | ||||||||
\(424\) | −6.39502 | −0.310570 | ||||||||
\(425\) | −0.300566 | −0.0145796 | ||||||||
\(426\) | −16.7944 | −0.813690 | ||||||||
\(427\) | 3.62844 | 0.175592 | ||||||||
\(428\) | −10.4251 | −0.503917 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.42569 | −0.165201 | ||||||||
\(431\) | 17.4534 | 0.840699 | 0.420350 | − | 0.907362i | \(-0.361907\pi\) | ||||
0.420350 | + | 0.907362i | \(0.361907\pi\) | |||||||
\(432\) | −3.97405 | −0.191202 | ||||||||
\(433\) | −28.2800 | −1.35905 | −0.679525 | − | 0.733652i | \(-0.737814\pi\) | ||||
−0.679525 | + | 0.733652i | \(0.737814\pi\) | |||||||
\(434\) | −7.53480 | −0.361682 | ||||||||
\(435\) | 3.64127 | 0.174586 | ||||||||
\(436\) | −12.1571 | −0.582221 | ||||||||
\(437\) | 50.1718 | 2.40004 | ||||||||
\(438\) | 2.81152 | 0.134340 | ||||||||
\(439\) | −35.7484 | −1.70618 | −0.853090 | − | 0.521764i | \(-0.825274\pi\) | ||||
−0.853090 | + | 0.521764i | \(0.825274\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.01724 | 0.0484401 | ||||||||
\(442\) | 1.21107 | 0.0576048 | ||||||||
\(443\) | 14.9441 | 0.710016 | 0.355008 | − | 0.934863i | \(-0.384478\pi\) | ||||
0.355008 | + | 0.934863i | \(0.384478\pi\) | |||||||
\(444\) | 18.2634 | 0.866744 | ||||||||
\(445\) | −1.92815 | −0.0914031 | ||||||||
\(446\) | 23.1843 | 1.09781 | ||||||||
\(447\) | 3.45576 | 0.163452 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 13.9847 | 0.659981 | 0.329990 | − | 0.943984i | \(-0.392954\pi\) | ||||
0.329990 | + | 0.943984i | \(0.392954\pi\) | |||||||
\(450\) | −1.01724 | −0.0479532 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6.67216 | −0.313832 | ||||||||
\(453\) | 18.3373 | 0.861562 | ||||||||
\(454\) | −4.97362 | −0.233423 | ||||||||
\(455\) | −4.02930 | −0.188897 | ||||||||
\(456\) | 15.5039 | 0.726038 | ||||||||
\(457\) | −10.2714 | −0.480477 | −0.240238 | − | 0.970714i | \(-0.577226\pi\) | ||||
−0.240238 | + | 0.970714i | \(0.577226\pi\) | |||||||
\(458\) | 25.6627 | 1.19914 | ||||||||
\(459\) | 1.19447 | 0.0557529 | ||||||||
\(460\) | 6.48607 | 0.302415 | ||||||||
\(461\) | 17.4058 | 0.810671 | 0.405335 | − | 0.914168i | \(-0.367155\pi\) | ||||
0.405335 | + | 0.914168i | \(0.367155\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.3943 | −1.41254 | −0.706271 | − | 0.707942i | \(-0.749624\pi\) | ||||
−0.706271 | + | 0.707942i | \(0.749624\pi\) | |||||||
\(464\) | −1.81673 | −0.0843394 | ||||||||
\(465\) | −15.1020 | −0.700340 | ||||||||
\(466\) | 3.81437 | 0.176697 | ||||||||
\(467\) | 23.8052 | 1.10158 | 0.550788 | − | 0.834646i | \(-0.314327\pi\) | ||||
0.550788 | + | 0.834646i | \(0.314327\pi\) | |||||||
\(468\) | 4.09877 | 0.189466 | ||||||||
\(469\) | 0.505448 | 0.0233394 | ||||||||
\(470\) | −6.21202 | −0.286539 | ||||||||
\(471\) | −1.75582 | −0.0809040 | ||||||||
\(472\) | −5.51945 | −0.254053 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 12.4268 | 0.570782 | ||||||||
\(475\) | −7.73531 | −0.354920 | ||||||||
\(476\) | −0.300566 | −0.0137764 | ||||||||
\(477\) | 6.50528 | 0.297856 | ||||||||
\(478\) | 6.58100 | 0.301008 | ||||||||
\(479\) | −7.79996 | −0.356389 | −0.178195 | − | 0.983995i | \(-0.557026\pi\) | ||||
−0.178195 | + | 0.983995i | \(0.557026\pi\) | |||||||
\(480\) | 2.00431 | 0.0914836 | ||||||||
\(481\) | 36.7154 | 1.67408 | ||||||||
\(482\) | 23.9679 | 1.09171 | ||||||||
\(483\) | −13.0001 | −0.591523 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.4944 | 0.748970 | ||||||||
\(486\) | 10.1592 | 0.460829 | ||||||||
\(487\) | −19.3109 | −0.875060 | −0.437530 | − | 0.899204i | \(-0.644147\pi\) | ||||
−0.437530 | + | 0.899204i | \(0.644147\pi\) | |||||||
\(488\) | −3.62844 | −0.164252 | ||||||||
\(489\) | −13.0133 | −0.588484 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −16.5180 | −0.745449 | −0.372724 | − | 0.927942i | \(-0.621576\pi\) | ||||
−0.372724 | + | 0.927942i | \(0.621576\pi\) | |||||||
\(492\) | −19.4083 | −0.874994 | ||||||||
\(493\) | 0.546046 | 0.0245927 | ||||||||
\(494\) | 31.1679 | 1.40231 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.53480 | 0.338322 | ||||||||
\(497\) | 8.37915 | 0.375856 | ||||||||
\(498\) | 29.2164 | 1.30922 | ||||||||
\(499\) | 11.8692 | 0.531341 | 0.265670 | − | 0.964064i | \(-0.414407\pi\) | ||||
0.265670 | + | 0.964064i | \(0.414407\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 40.1507 | 1.79380 | ||||||||
\(502\) | −5.08595 | −0.226997 | ||||||||
\(503\) | 6.76151 | 0.301481 | 0.150741 | − | 0.988573i | \(-0.451834\pi\) | ||||
0.150741 | + | 0.988573i | \(0.451834\pi\) | |||||||
\(504\) | −1.01724 | −0.0453115 | ||||||||
\(505\) | 9.44404 | 0.420254 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.48451 | 0.287987 | ||||||||
\(508\) | 12.8919 | 0.571984 | ||||||||
\(509\) | −37.3337 | −1.65479 | −0.827393 | − | 0.561624i | \(-0.810177\pi\) | ||||
−0.827393 | + | 0.561624i | \(0.810177\pi\) | |||||||
\(510\) | −0.602426 | −0.0266759 | ||||||||
\(511\) | −1.40274 | −0.0620536 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 30.7405 | 1.35723 | ||||||||
\(514\) | −11.0968 | −0.489458 | ||||||||
\(515\) | 3.51983 | 0.155102 | ||||||||
\(516\) | −6.86612 | −0.302264 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −9.11210 | −0.400363 | ||||||||
\(519\) | −3.04831 | −0.133806 | ||||||||
\(520\) | 4.02930 | 0.176697 | ||||||||
\(521\) | −13.6299 | −0.597137 | −0.298569 | − | 0.954388i | \(-0.596509\pi\) | ||||
−0.298569 | + | 0.954388i | \(0.596509\pi\) | |||||||
\(522\) | 1.84805 | 0.0808869 | ||||||||
\(523\) | 7.03010 | 0.307405 | 0.153702 | − | 0.988117i | \(-0.450880\pi\) | ||||
0.153702 | + | 0.988117i | \(0.450880\pi\) | |||||||
\(524\) | −20.3862 | −0.890577 | ||||||||
\(525\) | 2.00431 | 0.0874751 | ||||||||
\(526\) | −2.64779 | −0.115449 | ||||||||
\(527\) | −2.26470 | −0.0986520 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0691 | 0.829091 | ||||||||
\(530\) | 6.39502 | 0.277782 | ||||||||
\(531\) | 5.61461 | 0.243653 | ||||||||
\(532\) | −7.73531 | −0.335368 | ||||||||
\(533\) | −39.0170 | −1.69001 | ||||||||
\(534\) | −3.86460 | −0.167238 | ||||||||
\(535\) | 10.4251 | 0.450717 | ||||||||
\(536\) | −0.505448 | −0.0218320 | ||||||||
\(537\) | 48.4064 | 2.08889 | ||||||||
\(538\) | 3.42199 | 0.147532 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.97405 | 0.171016 | ||||||||
\(541\) | −15.3397 | −0.659507 | −0.329753 | − | 0.944067i | \(-0.606966\pi\) | ||||
−0.329753 | + | 0.944067i | \(0.606966\pi\) | |||||||
\(542\) | −21.1788 | −0.909706 | ||||||||
\(543\) | 33.3963 | 1.43317 | ||||||||
\(544\) | 0.300566 | 0.0128867 | ||||||||
\(545\) | 12.1571 | 0.520755 | ||||||||
\(546\) | −8.07596 | −0.345619 | ||||||||
\(547\) | −17.6527 | −0.754775 | −0.377388 | − | 0.926055i | \(-0.623178\pi\) | ||||
−0.377388 | + | 0.926055i | \(0.623178\pi\) | |||||||
\(548\) | −17.6954 | −0.755911 | ||||||||
\(549\) | 3.69100 | 0.157528 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.0529 | 0.598675 | ||||||||
\(552\) | 13.0001 | 0.553320 | ||||||||
\(553\) | −6.20005 | −0.263653 | ||||||||
\(554\) | 27.3915 | 1.16375 | ||||||||
\(555\) | −18.2634 | −0.775239 | ||||||||
\(556\) | −13.4774 | −0.571570 | ||||||||
\(557\) | −27.5742 | −1.16836 | −0.584178 | − | 0.811626i | \(-0.698583\pi\) | ||||
−0.584178 | + | 0.811626i | \(0.698583\pi\) | |||||||
\(558\) | −7.66470 | −0.324473 | ||||||||
\(559\) | −13.8031 | −0.583810 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.2620 | 0.475057 | ||||||||
\(563\) | 14.3283 | 0.603866 | 0.301933 | − | 0.953329i | \(-0.402368\pi\) | ||||
0.301933 | + | 0.953329i | \(0.402368\pi\) | |||||||
\(564\) | −12.4508 | −0.524273 | ||||||||
\(565\) | 6.67216 | 0.280700 | ||||||||
\(566\) | −20.2928 | −0.852971 | ||||||||
\(567\) | −11.0169 | −0.462668 | ||||||||
\(568\) | −8.37915 | −0.351581 | ||||||||
\(569\) | 29.2285 | 1.22532 | 0.612662 | − | 0.790345i | \(-0.290099\pi\) | ||||
0.612662 | + | 0.790345i | \(0.290099\pi\) | |||||||
\(570\) | −15.5039 | −0.649388 | ||||||||
\(571\) | 42.5911 | 1.78238 | 0.891190 | − | 0.453630i | \(-0.149871\pi\) | ||||
0.891190 | + | 0.453630i | \(0.149871\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.96378 | −0.249140 | ||||||||
\(574\) | 9.68330 | 0.404173 | ||||||||
\(575\) | −6.48607 | −0.270488 | ||||||||
\(576\) | 1.01724 | 0.0423851 | ||||||||
\(577\) | 25.4138 | 1.05799 | 0.528994 | − | 0.848625i | \(-0.322569\pi\) | ||||
0.528994 | + | 0.848625i | \(0.322569\pi\) | |||||||
\(578\) | 16.9097 | 0.703349 | ||||||||
\(579\) | 23.0507 | 0.957955 | ||||||||
\(580\) | 1.81673 | 0.0754354 | ||||||||
\(581\) | −14.5768 | −0.604748 | ||||||||
\(582\) | 33.0597 | 1.37037 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.40274 | 0.0580458 | ||||||||
\(585\) | −4.09877 | −0.169463 | ||||||||
\(586\) | −11.9548 | −0.493847 | ||||||||
\(587\) | 48.0000 | 1.98117 | 0.990586 | − | 0.136892i | \(-0.0437115\pi\) | ||||
0.990586 | + | 0.136892i | \(0.0437115\pi\) | |||||||
\(588\) | 2.00431 | 0.0826562 | ||||||||
\(589\) | −58.2840 | −2.40155 | ||||||||
\(590\) | 5.51945 | 0.227232 | ||||||||
\(591\) | −32.1884 | −1.32406 | ||||||||
\(592\) | 9.11210 | 0.374505 | ||||||||
\(593\) | −3.34128 | −0.137210 | −0.0686050 | − | 0.997644i | \(-0.521855\pi\) | ||||
−0.0686050 | + | 0.997644i | \(0.521855\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.300566 | 0.0123220 | ||||||||
\(596\) | 1.72417 | 0.0706246 | ||||||||
\(597\) | 22.2275 | 0.909711 | ||||||||
\(598\) | 26.1343 | 1.06871 | ||||||||
\(599\) | −43.1060 | −1.76126 | −0.880632 | − | 0.473800i | \(-0.842882\pi\) | ||||
−0.880632 | + | 0.473800i | \(0.842882\pi\) | |||||||
\(600\) | −2.00431 | −0.0818254 | ||||||||
\(601\) | 17.8432 | 0.727840 | 0.363920 | − | 0.931430i | \(-0.381438\pi\) | ||||
0.363920 | + | 0.931430i | \(0.381438\pi\) | |||||||
\(602\) | 3.42569 | 0.139621 | ||||||||
\(603\) | 0.514162 | 0.0209383 | ||||||||
\(604\) | 9.14895 | 0.372266 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 18.9287 | 0.768928 | ||||||||
\(607\) | 11.3238 | 0.459619 | 0.229809 | − | 0.973236i | \(-0.426190\pi\) | ||||
0.229809 | + | 0.973236i | \(0.426190\pi\) | |||||||
\(608\) | 7.73531 | 0.313708 | ||||||||
\(609\) | −3.64127 | −0.147552 | ||||||||
\(610\) | 3.62844 | 0.146911 | ||||||||
\(611\) | −25.0301 | −1.01261 | ||||||||
\(612\) | −0.305748 | −0.0123591 | ||||||||
\(613\) | 36.2483 | 1.46405 | 0.732027 | − | 0.681275i | \(-0.238574\pi\) | ||||
0.732027 | + | 0.681275i | \(0.238574\pi\) | |||||||
\(614\) | −19.6625 | −0.793516 | ||||||||
\(615\) | 19.4083 | 0.782618 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.1661 | 1.61702 | 0.808512 | − | 0.588479i | \(-0.200273\pi\) | ||||
0.808512 | + | 0.588479i | \(0.200273\pi\) | |||||||
\(618\) | 7.05482 | 0.283787 | ||||||||
\(619\) | 8.86070 | 0.356141 | 0.178071 | − | 0.984018i | \(-0.443014\pi\) | ||||
0.178071 | + | 0.984018i | \(0.443014\pi\) | |||||||
\(620\) | −7.53480 | −0.302605 | ||||||||
\(621\) | 25.7760 | 1.03436 | ||||||||
\(622\) | 10.8025 | 0.433139 | ||||||||
\(623\) | 1.92815 | 0.0772497 | ||||||||
\(624\) | 8.07596 | 0.323297 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 14.7449 | 0.589325 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.876025 | −0.0349572 | ||||||||
\(629\) | −2.73879 | −0.109203 | ||||||||
\(630\) | 1.01724 | 0.0405279 | ||||||||
\(631\) | −2.39090 | −0.0951802 | −0.0475901 | − | 0.998867i | \(-0.515154\pi\) | ||||
−0.0475901 | + | 0.998867i | \(0.515154\pi\) | |||||||
\(632\) | 6.20005 | 0.246625 | ||||||||
\(633\) | 51.1391 | 2.03260 | ||||||||
\(634\) | −17.4668 | −0.693697 | ||||||||
\(635\) | −12.8919 | −0.511598 | ||||||||
\(636\) | 12.8176 | 0.508250 | ||||||||
\(637\) | 4.02930 | 0.159647 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.52362 | 0.337189 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −7.27551 | −0.287365 | −0.143683 | − | 0.989624i | \(-0.545894\pi\) | ||||
−0.143683 | + | 0.989624i | \(0.545894\pi\) | |||||||
\(642\) | 20.8951 | 0.824664 | ||||||||
\(643\) | −9.04508 | −0.356703 | −0.178352 | − | 0.983967i | \(-0.557076\pi\) | ||||
−0.178352 | + | 0.983967i | \(0.557076\pi\) | |||||||
\(644\) | −6.48607 | −0.255587 | ||||||||
\(645\) | 6.86612 | 0.270353 | ||||||||
\(646\) | −2.32497 | −0.0914747 | ||||||||
\(647\) | −31.0318 | −1.21999 | −0.609993 | − | 0.792407i | \(-0.708828\pi\) | ||||
−0.609993 | + | 0.792407i | \(0.708828\pi\) | |||||||
\(648\) | 11.0169 | 0.432786 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.02930 | −0.158042 | ||||||||
\(651\) | 15.1020 | 0.591895 | ||||||||
\(652\) | −6.49269 | −0.254274 | ||||||||
\(653\) | 42.3720 | 1.65814 | 0.829072 | − | 0.559142i | \(-0.188870\pi\) | ||||
0.829072 | + | 0.559142i | \(0.188870\pi\) | |||||||
\(654\) | 24.3666 | 0.952810 | ||||||||
\(655\) | 20.3862 | 0.796556 | ||||||||
\(656\) | −9.68330 | −0.378069 | ||||||||
\(657\) | −1.42693 | −0.0556697 | ||||||||
\(658\) | 6.21202 | 0.242170 | ||||||||
\(659\) | −25.5490 | −0.995247 | −0.497624 | − | 0.867393i | \(-0.665794\pi\) | ||||
−0.497624 | + | 0.867393i | \(0.665794\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.55717 | 0.0605669 | 0.0302834 | − | 0.999541i | \(-0.490359\pi\) | ||||
0.0302834 | + | 0.999541i | \(0.490359\pi\) | |||||||
\(662\) | −22.3375 | −0.868172 | ||||||||
\(663\) | −2.42736 | −0.0942707 | ||||||||
\(664\) | 14.5768 | 0.565690 | ||||||||
\(665\) | 7.73531 | 0.299962 | ||||||||
\(666\) | −9.26920 | −0.359174 | ||||||||
\(667\) | 11.7834 | 0.456255 | ||||||||
\(668\) | 20.0322 | 0.775070 | ||||||||
\(669\) | −46.4684 | −1.79657 | ||||||||
\(670\) | 0.505448 | 0.0195271 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.00431 | −0.0773178 | ||||||||
\(673\) | −25.0244 | −0.964620 | −0.482310 | − | 0.876001i | \(-0.660202\pi\) | ||||
−0.482310 | + | 0.876001i | \(0.660202\pi\) | |||||||
\(674\) | 14.2386 | 0.548449 | ||||||||
\(675\) | −3.97405 | −0.152961 | ||||||||
\(676\) | 3.23529 | 0.124434 | ||||||||
\(677\) | −23.4532 | −0.901380 | −0.450690 | − | 0.892681i | \(-0.648822\pi\) | ||||
−0.450690 | + | 0.892681i | \(0.648822\pi\) | |||||||
\(678\) | 13.3731 | 0.513589 | ||||||||
\(679\) | −16.4944 | −0.632995 | ||||||||
\(680\) | −0.300566 | −0.0115262 | ||||||||
\(681\) | 9.96865 | 0.381999 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.6815 | −1.40358 | −0.701790 | − | 0.712384i | \(-0.747616\pi\) | ||||
−0.701790 | + | 0.712384i | \(0.747616\pi\) | |||||||
\(684\) | −7.86868 | −0.300866 | ||||||||
\(685\) | 17.6954 | 0.676107 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −51.4360 | −1.96240 | ||||||||
\(688\) | −3.42569 | −0.130603 | ||||||||
\(689\) | 25.7675 | 0.981662 | ||||||||
\(690\) | −13.0001 | −0.494904 | ||||||||
\(691\) | 27.6172 | 1.05061 | 0.525303 | − | 0.850915i | \(-0.323952\pi\) | ||||
0.525303 | + | 0.850915i | \(0.323952\pi\) | |||||||
\(692\) | −1.52088 | −0.0578151 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.6300 | 0.783106 | ||||||||
\(695\) | 13.4774 | 0.511228 | ||||||||
\(696\) | 3.64127 | 0.138022 | ||||||||
\(697\) | 2.91047 | 0.110242 | ||||||||
\(698\) | −16.0047 | −0.605786 | ||||||||
\(699\) | −7.64517 | −0.289167 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −29.9881 | −1.13263 | −0.566317 | − | 0.824188i | \(-0.691632\pi\) | ||||
−0.566317 | + | 0.824188i | \(0.691632\pi\) | |||||||
\(702\) | 16.0127 | 0.604359 | ||||||||
\(703\) | −70.4849 | −2.65839 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.4508 | 0.468924 | ||||||||
\(706\) | 1.46881 | 0.0552793 | ||||||||
\(707\) | −9.44404 | −0.355180 | ||||||||
\(708\) | 11.0627 | 0.415760 | ||||||||
\(709\) | −5.18512 | −0.194731 | −0.0973656 | − | 0.995249i | \(-0.531042\pi\) | ||||
−0.0973656 | + | 0.995249i | \(0.531042\pi\) | |||||||
\(710\) | 8.37915 | 0.314464 | ||||||||
\(711\) | −6.30695 | −0.236529 | ||||||||
\(712\) | −1.92815 | −0.0722605 | ||||||||
\(713\) | −48.8712 | −1.83024 | ||||||||
\(714\) | 0.602426 | 0.0225452 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.1512 | 0.902573 | ||||||||
\(717\) | −13.1903 | −0.492602 | ||||||||
\(718\) | −8.43193 | −0.314677 | ||||||||
\(719\) | −16.7828 | −0.625892 | −0.312946 | − | 0.949771i | \(-0.601316\pi\) | ||||
−0.312946 | + | 0.949771i | \(0.601316\pi\) | |||||||
\(720\) | −1.01724 | −0.0379103 | ||||||||
\(721\) | −3.51983 | −0.131085 | ||||||||
\(722\) | −40.8350 | −1.51972 | ||||||||
\(723\) | −48.0390 | −1.78659 | ||||||||
\(724\) | 16.6623 | 0.619249 | ||||||||
\(725\) | −1.81673 | −0.0674715 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.72794 | 0.360789 | 0.180395 | − | 0.983594i | \(-0.442263\pi\) | ||||
0.180395 | + | 0.983594i | \(0.442263\pi\) | |||||||
\(728\) | −4.02930 | −0.149336 | ||||||||
\(729\) | 12.6888 | 0.469954 | ||||||||
\(730\) | −1.40274 | −0.0519178 | ||||||||
\(731\) | 1.02964 | 0.0380828 | ||||||||
\(732\) | 7.27250 | 0.268799 | ||||||||
\(733\) | −10.5873 | −0.391050 | −0.195525 | − | 0.980699i | \(-0.562641\pi\) | ||||
−0.195525 | + | 0.980699i | \(0.562641\pi\) | |||||||
\(734\) | −27.2590 | −1.00615 | ||||||||
\(735\) | −2.00431 | −0.0739299 | ||||||||
\(736\) | 6.48607 | 0.239080 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 9.85025 | 0.362593 | ||||||||
\(739\) | 11.6909 | 0.430058 | 0.215029 | − | 0.976608i | \(-0.431015\pi\) | ||||
0.215029 | + | 0.976608i | \(0.431015\pi\) | |||||||
\(740\) | −9.11210 | −0.334967 | ||||||||
\(741\) | −62.4700 | −2.29489 | ||||||||
\(742\) | −6.39502 | −0.234768 | ||||||||
\(743\) | −2.32433 | −0.0852713 | −0.0426356 | − | 0.999091i | \(-0.513575\pi\) | ||||
−0.0426356 | + | 0.999091i | \(0.513575\pi\) | |||||||
\(744\) | −15.1020 | −0.553667 | ||||||||
\(745\) | −1.72417 | −0.0631686 | ||||||||
\(746\) | 14.7417 | 0.539734 | ||||||||
\(747\) | −14.8281 | −0.542533 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.4251 | −0.380925 | ||||||||
\(750\) | 2.00431 | 0.0731869 | ||||||||
\(751\) | −13.6597 | −0.498450 | −0.249225 | − | 0.968446i | \(-0.580176\pi\) | ||||
−0.249225 | + | 0.968446i | \(0.580176\pi\) | |||||||
\(752\) | −6.21202 | −0.226529 | ||||||||
\(753\) | 10.1938 | 0.371483 | ||||||||
\(754\) | 7.32014 | 0.266584 | ||||||||
\(755\) | −9.14895 | −0.332965 | ||||||||
\(756\) | −3.97405 | −0.144535 | ||||||||
\(757\) | 20.4404 | 0.742919 | 0.371460 | − | 0.928449i | \(-0.378857\pi\) | ||||
0.371460 | + | 0.928449i | \(0.378857\pi\) | |||||||
\(758\) | 26.2074 | 0.951894 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.73531 | −0.280589 | ||||||||
\(761\) | −5.54838 | −0.201129 | −0.100564 | − | 0.994931i | \(-0.532065\pi\) | ||||
−0.100564 | + | 0.994931i | \(0.532065\pi\) | |||||||
\(762\) | −25.8392 | −0.936057 | ||||||||
\(763\) | −12.1571 | −0.440118 | ||||||||
\(764\) | −2.97548 | −0.107649 | ||||||||
\(765\) | 0.305748 | 0.0110543 | ||||||||
\(766\) | 18.0535 | 0.652300 | ||||||||
\(767\) | 22.2395 | 0.803023 | ||||||||
\(768\) | 2.00431 | 0.0723242 | ||||||||
\(769\) | −8.18880 | −0.295296 | −0.147648 | − | 0.989040i | \(-0.547170\pi\) | ||||
−0.147648 | + | 0.989040i | \(0.547170\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.2413 | 0.801002 | ||||||||
\(772\) | 11.5006 | 0.413916 | ||||||||
\(773\) | 10.5045 | 0.377819 | 0.188909 | − | 0.981995i | \(-0.439505\pi\) | ||||
0.188909 | + | 0.981995i | \(0.439505\pi\) | |||||||
\(774\) | 3.48475 | 0.125257 | ||||||||
\(775\) | 7.53480 | 0.270658 | ||||||||
\(776\) | 16.4944 | 0.592113 | ||||||||
\(777\) | 18.2634 | 0.655197 | ||||||||
\(778\) | 21.4054 | 0.767420 | ||||||||
\(779\) | 74.9033 | 2.68369 | ||||||||
\(780\) | −8.07596 | −0.289166 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.94949 | −0.0697137 | ||||||||
\(783\) | 7.21977 | 0.258013 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 0.876025 | 0.0312667 | ||||||||
\(786\) | 40.8602 | 1.45744 | ||||||||
\(787\) | −11.8432 | −0.422166 | −0.211083 | − | 0.977468i | \(-0.567699\pi\) | ||||
−0.211083 | + | 0.977468i | \(0.567699\pi\) | |||||||
\(788\) | −16.0597 | −0.572101 | ||||||||
\(789\) | 5.30697 | 0.188933 | ||||||||
\(790\) | −6.20005 | −0.220588 | ||||||||
\(791\) | −6.67216 | −0.237235 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.6201 | 0.519174 | ||||||||
\(794\) | −4.87615 | −0.173048 | ||||||||
\(795\) | −12.8176 | −0.454592 | ||||||||
\(796\) | 11.0899 | 0.393070 | ||||||||
\(797\) | −22.3237 | −0.790747 | −0.395374 | − | 0.918520i | \(-0.629385\pi\) | ||||
−0.395374 | + | 0.918520i | \(0.629385\pi\) | |||||||
\(798\) | 15.5039 | 0.548833 | ||||||||
\(799\) | 1.86712 | 0.0660540 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 1.96139 | 0.0693025 | ||||||||
\(802\) | −15.6680 | −0.553257 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1.01307 | 0.0357283 | ||||||||
\(805\) | 6.48607 | 0.228604 | ||||||||
\(806\) | −30.3600 | −1.06938 | ||||||||
\(807\) | −6.85871 | −0.241438 | ||||||||
\(808\) | 9.44404 | 0.332240 | ||||||||
\(809\) | 32.0996 | 1.12856 | 0.564282 | − | 0.825582i | \(-0.309153\pi\) | ||||
0.564282 | + | 0.825582i | \(0.309153\pi\) | |||||||
\(810\) | −11.0169 | −0.387096 | ||||||||
\(811\) | −42.4498 | −1.49061 | −0.745306 | − | 0.666722i | \(-0.767697\pi\) | ||||
−0.745306 | + | 0.666722i | \(0.767697\pi\) | |||||||
\(812\) | −1.81673 | −0.0637546 | ||||||||
\(813\) | 42.4487 | 1.48874 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.49269 | 0.227429 | ||||||||
\(816\) | −0.602426 | −0.0210891 | ||||||||
\(817\) | 26.4987 | 0.927074 | ||||||||
\(818\) | 37.1821 | 1.30004 | ||||||||
\(819\) | 4.09877 | 0.143223 | ||||||||
\(820\) | 9.68330 | 0.338156 | ||||||||
\(821\) | 17.7352 | 0.618962 | 0.309481 | − | 0.950906i | \(-0.399845\pi\) | ||||
0.309481 | + | 0.950906i | \(0.399845\pi\) | |||||||
\(822\) | 35.4670 | 1.23706 | ||||||||
\(823\) | 37.9393 | 1.32248 | 0.661241 | − | 0.750173i | \(-0.270030\pi\) | ||||
0.661241 | + | 0.750173i | \(0.270030\pi\) | |||||||
\(824\) | 3.51983 | 0.122619 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.51945 | −0.192046 | ||||||||
\(827\) | −40.9256 | −1.42312 | −0.711561 | − | 0.702624i | \(-0.752012\pi\) | ||||
−0.711561 | + | 0.702624i | \(0.752012\pi\) | |||||||
\(828\) | −6.59790 | −0.229293 | ||||||||
\(829\) | 2.81991 | 0.0979395 | 0.0489698 | − | 0.998800i | \(-0.484406\pi\) | ||||
0.0489698 | + | 0.998800i | \(0.484406\pi\) | |||||||
\(830\) | −14.5768 | −0.505968 | ||||||||
\(831\) | −54.9010 | −1.90449 | ||||||||
\(832\) | 4.02930 | 0.139691 | ||||||||
\(833\) | −0.300566 | −0.0104140 | ||||||||
\(834\) | 27.0129 | 0.935379 | ||||||||
\(835\) | −20.0322 | −0.693244 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −29.9437 | −1.03501 | ||||||||
\(838\) | 27.2599 | 0.941676 | ||||||||
\(839\) | −55.3938 | −1.91241 | −0.956204 | − | 0.292701i | \(-0.905446\pi\) | ||||
−0.956204 | + | 0.292701i | \(0.905446\pi\) | |||||||
\(840\) | 2.00431 | 0.0691551 | ||||||||
\(841\) | −25.6995 | −0.886190 | ||||||||
\(842\) | 13.1997 | 0.454892 | ||||||||
\(843\) | −22.5724 | −0.777435 | ||||||||
\(844\) | 25.5146 | 0.878250 | ||||||||
\(845\) | −3.23529 | −0.111297 | ||||||||
\(846\) | 6.31912 | 0.217256 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.39502 | 0.219606 | ||||||||
\(849\) | 40.6730 | 1.39589 | ||||||||
\(850\) | 0.300566 | 0.0103093 | ||||||||
\(851\) | −59.1017 | −2.02598 | ||||||||
\(852\) | 16.7944 | 0.575366 | ||||||||
\(853\) | 49.6786 | 1.70096 | 0.850481 | − | 0.526006i | \(-0.176311\pi\) | ||||
0.850481 | + | 0.526006i | \(0.176311\pi\) | |||||||
\(854\) | −3.62844 | −0.124163 | ||||||||
\(855\) | 7.86868 | 0.269103 | ||||||||
\(856\) | 10.4251 | 0.356323 | ||||||||
\(857\) | 20.7002 | 0.707104 | 0.353552 | − | 0.935415i | \(-0.384974\pi\) | ||||
0.353552 | + | 0.935415i | \(0.384974\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.2630 | −0.520766 | −0.260383 | − | 0.965505i | \(-0.583849\pi\) | ||||
−0.260383 | + | 0.965505i | \(0.583849\pi\) | |||||||
\(860\) | 3.42569 | 0.116815 | ||||||||
\(861\) | −19.4083 | −0.661433 | ||||||||
\(862\) | −17.4534 | −0.594464 | ||||||||
\(863\) | 8.86338 | 0.301713 | 0.150857 | − | 0.988556i | \(-0.451797\pi\) | ||||
0.150857 | + | 0.988556i | \(0.451797\pi\) | |||||||
\(864\) | 3.97405 | 0.135200 | ||||||||
\(865\) | 1.52088 | 0.0517114 | ||||||||
\(866\) | 28.2800 | 0.960994 | ||||||||
\(867\) | −33.8921 | −1.15104 | ||||||||
\(868\) | 7.53480 | 0.255748 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −3.64127 | −0.123451 | ||||||||
\(871\) | 2.03660 | 0.0690076 | ||||||||
\(872\) | 12.1571 | 0.411693 | ||||||||
\(873\) | −16.7787 | −0.567874 | ||||||||
\(874\) | −50.1718 | −1.69709 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −2.81152 | −0.0949925 | ||||||||
\(877\) | −16.7377 | −0.565192 | −0.282596 | − | 0.959239i | \(-0.591196\pi\) | ||||
−0.282596 | + | 0.959239i | \(0.591196\pi\) | |||||||
\(878\) | 35.7484 | 1.20645 | ||||||||
\(879\) | 23.9610 | 0.808185 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.10239 | −0.138213 | −0.0691065 | − | 0.997609i | \(-0.522015\pi\) | ||||
−0.0691065 | + | 0.997609i | \(0.522015\pi\) | |||||||
\(882\) | −1.01724 | −0.0342523 | ||||||||
\(883\) | 40.7341 | 1.37081 | 0.685406 | − | 0.728161i | \(-0.259625\pi\) | ||||
0.685406 | + | 0.728161i | \(0.259625\pi\) | |||||||
\(884\) | −1.21107 | −0.0407327 | ||||||||
\(885\) | −11.0627 | −0.371867 | ||||||||
\(886\) | −14.9441 | −0.502057 | ||||||||
\(887\) | 17.7893 | 0.597305 | 0.298652 | − | 0.954362i | \(-0.403463\pi\) | ||||
0.298652 | + | 0.954362i | \(0.403463\pi\) | |||||||
\(888\) | −18.2634 | −0.612881 | ||||||||
\(889\) | 12.8919 | 0.432379 | ||||||||
\(890\) | 1.92815 | 0.0646318 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −23.1843 | −0.776268 | ||||||||
\(893\) | 48.0519 | 1.60800 | ||||||||
\(894\) | −3.45576 | −0.115578 | ||||||||
\(895\) | −24.1512 | −0.807286 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −52.3812 | −1.74896 | ||||||||
\(898\) | −13.9847 | −0.466677 | ||||||||
\(899\) | −13.6887 | −0.456542 | ||||||||
\(900\) | 1.01724 | 0.0339080 | ||||||||
\(901\) | −1.92212 | −0.0640352 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.86612 | −0.228490 | ||||||||
\(904\) | 6.67216 | 0.221913 | ||||||||
\(905\) | −16.6623 | −0.553873 | ||||||||
\(906\) | −18.3373 | −0.609216 | ||||||||
\(907\) | −3.77888 | −0.125476 | −0.0627379 | − | 0.998030i | \(-0.519983\pi\) | ||||
−0.0627379 | + | 0.998030i | \(0.519983\pi\) | |||||||
\(908\) | 4.97362 | 0.165055 | ||||||||
\(909\) | −9.60687 | −0.318640 | ||||||||
\(910\) | 4.02930 | 0.133570 | ||||||||
\(911\) | 36.8482 | 1.22084 | 0.610418 | − | 0.792080i | \(-0.291002\pi\) | ||||
0.610418 | + | 0.792080i | \(0.291002\pi\) | |||||||
\(912\) | −15.5039 | −0.513386 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 10.2714 | 0.339748 | ||||||||
\(915\) | −7.27250 | −0.240421 | ||||||||
\(916\) | −25.6627 | −0.847921 | ||||||||
\(917\) | −20.3862 | −0.673213 | ||||||||
\(918\) | −1.19447 | −0.0394232 | ||||||||
\(919\) | 56.7946 | 1.87348 | 0.936740 | − | 0.350025i | \(-0.113827\pi\) | ||||
0.936740 | + | 0.350025i | \(0.113827\pi\) | |||||||
\(920\) | −6.48607 | −0.213839 | ||||||||
\(921\) | 39.4098 | 1.29860 | ||||||||
\(922\) | −17.4058 | −0.573231 | ||||||||
\(923\) | 33.7621 | 1.11129 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.11210 | 0.299604 | ||||||||
\(926\) | 30.3943 | 0.998818 | ||||||||
\(927\) | −3.58052 | −0.117600 | ||||||||
\(928\) | 1.81673 | 0.0596369 | ||||||||
\(929\) | −18.0311 | −0.591580 | −0.295790 | − | 0.955253i | \(-0.595583\pi\) | ||||
−0.295790 | + | 0.955253i | \(0.595583\pi\) | |||||||
\(930\) | 15.1020 | 0.495215 | ||||||||
\(931\) | −7.73531 | −0.253515 | ||||||||
\(932\) | −3.81437 | −0.124944 | ||||||||
\(933\) | −21.6514 | −0.708836 | ||||||||
\(934\) | −23.8052 | −0.778931 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.09877 | −0.133973 | ||||||||
\(937\) | 20.7850 | 0.679016 | 0.339508 | − | 0.940603i | \(-0.389739\pi\) | ||||
0.339508 | + | 0.940603i | \(0.389739\pi\) | |||||||
\(938\) | −0.505448 | −0.0165035 | ||||||||
\(939\) | −29.5533 | −0.964435 | ||||||||
\(940\) | 6.21202 | 0.202614 | ||||||||
\(941\) | −4.11596 | −0.134176 | −0.0670882 | − | 0.997747i | \(-0.521371\pi\) | ||||
−0.0670882 | + | 0.997747i | \(0.521371\pi\) | |||||||
\(942\) | 1.75582 | 0.0572078 | ||||||||
\(943\) | 62.8066 | 2.04526 | ||||||||
\(944\) | 5.51945 | 0.179643 | ||||||||
\(945\) | 3.97405 | 0.129276 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.0569 | −1.00921 | −0.504607 | − | 0.863349i | \(-0.668363\pi\) | ||||
−0.504607 | + | 0.863349i | \(0.668363\pi\) | |||||||
\(948\) | −12.4268 | −0.403604 | ||||||||
\(949\) | −5.65207 | −0.183474 | ||||||||
\(950\) | 7.73531 | 0.250967 | ||||||||
\(951\) | 35.0089 | 1.13524 | ||||||||
\(952\) | 0.300566 | 0.00974140 | ||||||||
\(953\) | −17.8888 | −0.579474 | −0.289737 | − | 0.957106i | \(-0.593568\pi\) | ||||
−0.289737 | + | 0.957106i | \(0.593568\pi\) | |||||||
\(954\) | −6.50528 | −0.210616 | ||||||||
\(955\) | 2.97548 | 0.0962843 | ||||||||
\(956\) | −6.58100 | −0.212845 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.79996 | 0.252005 | ||||||||
\(959\) | −17.6954 | −0.571415 | ||||||||
\(960\) | −2.00431 | −0.0646887 | ||||||||
\(961\) | 25.7731 | 0.831392 | ||||||||
\(962\) | −36.7154 | −1.18375 | ||||||||
\(963\) | −10.6049 | −0.341737 | ||||||||
\(964\) | −23.9679 | −0.771955 | ||||||||
\(965\) | −11.5006 | −0.370217 | ||||||||
\(966\) | 13.0001 | 0.418270 | ||||||||
\(967\) | 59.5313 | 1.91440 | 0.957199 | − | 0.289431i | \(-0.0934662\pi\) | ||||
0.957199 | + | 0.289431i | \(0.0934662\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.65995 | 0.149699 | ||||||||
\(970\) | −16.4944 | −0.529602 | ||||||||
\(971\) | −43.1529 | −1.38484 | −0.692421 | − | 0.721494i | \(-0.743456\pi\) | ||||
−0.692421 | + | 0.721494i | \(0.743456\pi\) | |||||||
\(972\) | −10.1592 | −0.325855 | ||||||||
\(973\) | −13.4774 | −0.432066 | ||||||||
\(974\) | 19.3109 | 0.618761 | ||||||||
\(975\) | 8.07596 | 0.258638 | ||||||||
\(976\) | 3.62844 | 0.116143 | ||||||||
\(977\) | −46.0411 | −1.47299 | −0.736493 | − | 0.676445i | \(-0.763520\pi\) | ||||
−0.736493 | + | 0.676445i | \(0.763520\pi\) | |||||||
\(978\) | 13.0133 | 0.416121 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −12.3667 | −0.394840 | ||||||||
\(982\) | 16.5180 | 0.527112 | ||||||||
\(983\) | 45.1941 | 1.44147 | 0.720734 | − | 0.693212i | \(-0.243805\pi\) | ||||
0.720734 | + | 0.693212i | \(0.243805\pi\) | |||||||
\(984\) | 19.4083 | 0.618714 | ||||||||
\(985\) | 16.0597 | 0.511703 | ||||||||
\(986\) | −0.546046 | −0.0173896 | ||||||||
\(987\) | −12.4508 | −0.396313 | ||||||||
\(988\) | −31.1679 | −0.991584 | ||||||||
\(989\) | 22.2192 | 0.706531 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.5442 | −1.03380 | −0.516900 | − | 0.856046i | \(-0.672914\pi\) | ||||
−0.516900 | + | 0.856046i | \(0.672914\pi\) | |||||||
\(992\) | −7.53480 | −0.239230 | ||||||||
\(993\) | 44.7712 | 1.42077 | ||||||||
\(994\) | −8.37915 | −0.265770 | ||||||||
\(995\) | −11.0899 | −0.351573 | ||||||||
\(996\) | −29.2164 | −0.925756 | ||||||||
\(997\) | 44.8088 | 1.41911 | 0.709555 | − | 0.704650i | \(-0.248896\pi\) | ||||
0.709555 | + | 0.704650i | \(0.248896\pi\) | |||||||
\(998\) | −11.8692 | −0.375715 | ||||||||
\(999\) | −36.2120 | −1.14570 |
(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 | 8470.2.a.dg.1.7 | 8 | ||
11.2 | odd | 10 | 770.2.n.k.631.4 | yes | 16 | ||
11.6 | odd | 10 | 770.2.n.k.421.4 | ✓ | 16 | ||
11.10 | odd | 2 | 8470.2.a.dh.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.k.421.4 | ✓ | 16 | 11.6 | odd | 10 | ||
770.2.n.k.631.4 | yes | 16 | 11.2 | odd | 10 | ||
8470.2.a.dg.1.7 | 8 | 1.1 | even | 1 | trivial | ||
8470.2.a.dh.1.7 | 8 | 11.10 | odd | 2 |