Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,2,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2151.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(17.1758214748\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 21 x^{18} + 96 x^{17} + 164 x^{16} - 936 x^{15} - 540 x^{14} + 4804 x^{13} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.61701\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61701 | −1.14340 | −0.571698 | − | 0.820464i | \(-0.693715\pi\) | ||||
−0.571698 | + | 0.820464i | \(0.693715\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.614711 | 0.307356 | ||||||||
\(5\) | −1.46591 | −0.655573 | −0.327787 | − | 0.944752i | \(-0.606303\pi\) | ||||
−0.327787 | + | 0.944752i | \(0.606303\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.83563 | 1.44973 | 0.724865 | − | 0.688891i | \(-0.241902\pi\) | ||||
0.724865 | + | 0.688891i | \(0.241902\pi\) | |||||||
\(8\) | 2.24002 | 0.791967 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.37038 | 0.749580 | ||||||||
\(11\) | −2.90374 | −0.875511 | −0.437755 | − | 0.899094i | \(-0.644226\pi\) | ||||
−0.437755 | + | 0.899094i | \(0.644226\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.33112 | 0.646537 | 0.323268 | − | 0.946307i | \(-0.395218\pi\) | ||||
0.323268 | + | 0.946307i | \(0.395218\pi\) | |||||||
\(14\) | −6.20223 | −1.65762 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85155 | −1.21289 | ||||||||
\(17\) | −3.77139 | −0.914697 | −0.457348 | − | 0.889288i | \(-0.651201\pi\) | ||||
−0.457348 | + | 0.889288i | \(0.651201\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.21740 | −0.279291 | −0.139646 | − | 0.990202i | \(-0.544596\pi\) | ||||
−0.139646 | + | 0.990202i | \(0.544596\pi\) | |||||||
\(20\) | −0.901109 | −0.201494 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.69537 | 1.00106 | ||||||||
\(23\) | 1.47665 | 0.307904 | 0.153952 | − | 0.988078i | \(-0.450800\pi\) | ||||
0.153952 | + | 0.988078i | \(0.450800\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.85112 | −0.570224 | ||||||||
\(26\) | −3.76944 | −0.739248 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.35780 | 0.445583 | ||||||||
\(29\) | −1.02391 | −0.190136 | −0.0950678 | − | 0.995471i | \(-0.530307\pi\) | ||||
−0.0950678 | + | 0.995471i | \(0.530307\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.72030 | −0.308975 | −0.154487 | − | 0.987995i | \(-0.549373\pi\) | ||||
−0.154487 | + | 0.987995i | \(0.549373\pi\) | |||||||
\(32\) | 3.36495 | 0.594845 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.09837 | 1.04586 | ||||||||
\(35\) | −5.62267 | −0.950404 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.08984 | −0.179169 | −0.0895845 | − | 0.995979i | \(-0.528554\pi\) | ||||
−0.0895845 | + | 0.995979i | \(0.528554\pi\) | |||||||
\(38\) | 1.96855 | 0.319341 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.28366 | −0.519192 | ||||||||
\(41\) | 1.58037 | 0.246812 | 0.123406 | − | 0.992356i | \(-0.460618\pi\) | ||||
0.123406 | + | 0.992356i | \(0.460618\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.433251 | 0.0660702 | 0.0330351 | − | 0.999454i | \(-0.489483\pi\) | ||||
0.0330351 | + | 0.999454i | \(0.489483\pi\) | |||||||
\(44\) | −1.78496 | −0.269093 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.38776 | −0.352056 | ||||||||
\(47\) | −7.65919 | −1.11721 | −0.558604 | − | 0.829434i | \(-0.688663\pi\) | ||||
−0.558604 | + | 0.829434i | \(0.688663\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.71202 | 1.10172 | ||||||||
\(50\) | 4.61028 | 0.651992 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.43297 | 0.198717 | ||||||||
\(53\) | −1.07471 | −0.147623 | −0.0738117 | − | 0.997272i | \(-0.523516\pi\) | ||||
−0.0738117 | + | 0.997272i | \(0.523516\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.25661 | 0.573961 | ||||||||
\(56\) | 8.59188 | 1.14814 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.65567 | 0.217400 | ||||||||
\(59\) | 4.82708 | 0.628432 | 0.314216 | − | 0.949351i | \(-0.398258\pi\) | ||||
0.314216 | + | 0.949351i | \(0.398258\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.7610 | 1.37780 | 0.688902 | − | 0.724854i | \(-0.258093\pi\) | ||||
0.688902 | + | 0.724854i | \(0.258093\pi\) | |||||||
\(62\) | 2.78174 | 0.353281 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.26196 | 0.532745 | ||||||||
\(65\) | −3.41720 | −0.423852 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.11056 | −0.746523 | −0.373262 | − | 0.927726i | \(-0.621761\pi\) | ||||
−0.373262 | + | 0.927726i | \(0.621761\pi\) | |||||||
\(68\) | −2.31832 | −0.281137 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 9.09189 | 1.08669 | ||||||||
\(71\) | −10.9308 | −1.29725 | −0.648626 | − | 0.761108i | \(-0.724656\pi\) | ||||
−0.648626 | + | 0.761108i | \(0.724656\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.1327 | −1.42003 | −0.710015 | − | 0.704187i | \(-0.751312\pi\) | ||||
−0.710015 | + | 0.704187i | \(0.751312\pi\) | |||||||
\(74\) | 1.76228 | 0.204861 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.748351 | −0.0858418 | ||||||||
\(77\) | −11.1377 | −1.26925 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.7398 | 1.65835 | 0.829177 | − | 0.558986i | \(-0.188810\pi\) | ||||
0.829177 | + | 0.558986i | \(0.188810\pi\) | |||||||
\(80\) | 7.11192 | 0.795137 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.55547 | −0.282204 | ||||||||
\(83\) | 13.0905 | 1.43686 | 0.718432 | − | 0.695597i | \(-0.244860\pi\) | ||||
0.718432 | + | 0.695597i | \(0.244860\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.52851 | 0.599651 | ||||||||
\(86\) | −0.700570 | −0.0755444 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.50444 | −0.693376 | ||||||||
\(89\) | 6.08868 | 0.645398 | 0.322699 | − | 0.946502i | \(-0.395410\pi\) | ||||
0.322699 | + | 0.946502i | \(0.395410\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.94131 | 0.937304 | ||||||||
\(92\) | 0.907716 | 0.0946359 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.3850 | 1.27741 | ||||||||
\(95\) | 1.78460 | 0.183096 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.99478 | 0.811747 | 0.405873 | − | 0.913929i | \(-0.366967\pi\) | ||||
0.405873 | + | 0.913929i | \(0.366967\pi\) | |||||||
\(98\) | −12.4704 | −1.25970 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.75261 | −0.175261 | ||||||||
\(101\) | −12.4894 | −1.24274 | −0.621371 | − | 0.783516i | \(-0.713424\pi\) | ||||
−0.621371 | + | 0.783516i | \(0.713424\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.88824 | −0.678719 | −0.339359 | − | 0.940657i | \(-0.610210\pi\) | ||||
−0.339359 | + | 0.940657i | \(0.610210\pi\) | |||||||
\(104\) | 5.22176 | 0.512036 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.73782 | 0.168792 | ||||||||
\(107\) | −16.7073 | −1.61515 | −0.807577 | − | 0.589763i | \(-0.799221\pi\) | ||||
−0.807577 | + | 0.589763i | \(0.799221\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.9013 | −1.52307 | −0.761534 | − | 0.648125i | \(-0.775554\pi\) | ||||
−0.761534 | + | 0.648125i | \(0.775554\pi\) | |||||||
\(110\) | −6.88297 | −0.656265 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −18.6087 | −1.75836 | ||||||||
\(113\) | −9.87403 | −0.928870 | −0.464435 | − | 0.885607i | \(-0.653743\pi\) | ||||
−0.464435 | + | 0.885607i | \(0.653743\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.16464 | −0.201853 | ||||||||
\(116\) | −0.629410 | −0.0584393 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.80542 | −0.718548 | ||||||||
\(119\) | −14.4656 | −1.32606 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.56829 | −0.233481 | ||||||||
\(122\) | −17.4006 | −1.57538 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.05749 | −0.0949652 | ||||||||
\(125\) | 11.5090 | 1.02940 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.3172 | −0.915505 | −0.457753 | − | 0.889080i | \(-0.651345\pi\) | ||||
−0.457753 | + | 0.889080i | \(0.651345\pi\) | |||||||
\(128\) | −13.6215 | −1.20398 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.52564 | 0.484631 | ||||||||
\(131\) | 9.86768 | 0.862143 | 0.431072 | − | 0.902318i | \(-0.358136\pi\) | ||||
0.431072 | + | 0.902318i | \(0.358136\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.66950 | −0.404897 | ||||||||
\(134\) | 9.88081 | 0.853572 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.44800 | −0.724410 | ||||||||
\(137\) | −3.24609 | −0.277332 | −0.138666 | − | 0.990339i | \(-0.544282\pi\) | ||||
−0.138666 | + | 0.990339i | \(0.544282\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.2318 | −1.20713 | −0.603564 | − | 0.797315i | \(-0.706253\pi\) | ||||
−0.603564 | + | 0.797315i | \(0.706253\pi\) | |||||||
\(140\) | −3.45632 | −0.292112 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 17.6752 | 1.48327 | ||||||||
\(143\) | −6.76897 | −0.566050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.50096 | 0.124648 | ||||||||
\(146\) | 19.6187 | 1.62366 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.669938 | −0.0550686 | ||||||||
\(149\) | −3.90332 | −0.319772 | −0.159886 | − | 0.987135i | \(-0.551113\pi\) | ||||
−0.159886 | + | 0.987135i | \(0.551113\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.699764 | −0.0569460 | −0.0284730 | − | 0.999595i | \(-0.509064\pi\) | ||||
−0.0284730 | + | 0.999595i | \(0.509064\pi\) | |||||||
\(152\) | −2.72701 | −0.221190 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 18.0097 | 1.45126 | ||||||||
\(155\) | 2.52180 | 0.202556 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.91363 | 0.152725 | 0.0763623 | − | 0.997080i | \(-0.475669\pi\) | ||||
0.0763623 | + | 0.997080i | \(0.475669\pi\) | |||||||
\(158\) | −23.8343 | −1.89616 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.93270 | −0.389964 | ||||||||
\(161\) | 5.66389 | 0.446377 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.1905 | −1.34647 | −0.673233 | − | 0.739430i | \(-0.735095\pi\) | ||||
−0.673233 | + | 0.739430i | \(0.735095\pi\) | |||||||
\(164\) | 0.971471 | 0.0758592 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −21.1673 | −1.64290 | ||||||||
\(167\) | −14.8924 | −1.15241 | −0.576205 | − | 0.817305i | \(-0.695467\pi\) | ||||
−0.576205 | + | 0.817305i | \(0.695467\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.56588 | −0.581990 | ||||||||
\(170\) | −8.93963 | −0.685639 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.266324 | 0.0203070 | ||||||||
\(173\) | 11.7169 | 0.890823 | 0.445411 | − | 0.895326i | \(-0.353057\pi\) | ||||
0.445411 | + | 0.895326i | \(0.353057\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.9358 | −0.826671 | ||||||||
\(176\) | 14.0876 | 1.06190 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.84543 | −0.737946 | ||||||||
\(179\) | 3.36761 | 0.251707 | 0.125854 | − | 0.992049i | \(-0.459833\pi\) | ||||
0.125854 | + | 0.992049i | \(0.459833\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.66617 | −0.495493 | −0.247746 | − | 0.968825i | \(-0.579690\pi\) | ||||
−0.247746 | + | 0.968825i | \(0.579690\pi\) | |||||||
\(182\) | −14.4582 | −1.07171 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.30774 | 0.243850 | ||||||||
\(185\) | 1.59761 | 0.117458 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.9511 | 0.800827 | ||||||||
\(188\) | −4.70819 | −0.343380 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.88571 | −0.209351 | ||||||||
\(191\) | 15.7911 | 1.14260 | 0.571300 | − | 0.820741i | \(-0.306439\pi\) | ||||
0.571300 | + | 0.820741i | \(0.306439\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.45917 | 0.608904 | 0.304452 | − | 0.952528i | \(-0.401527\pi\) | ||||
0.304452 | + | 0.952528i | \(0.401527\pi\) | |||||||
\(194\) | −12.9276 | −0.928149 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.74066 | 0.338619 | ||||||||
\(197\) | 4.68346 | 0.333683 | 0.166842 | − | 0.985984i | \(-0.446643\pi\) | ||||
0.166842 | + | 0.985984i | \(0.446643\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.8363 | −1.83149 | −0.915743 | − | 0.401764i | \(-0.868397\pi\) | ||||
−0.915743 | + | 0.401764i | \(0.868397\pi\) | |||||||
\(200\) | −6.38657 | −0.451599 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20.1955 | 1.42095 | ||||||||
\(203\) | −3.92734 | −0.275645 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.31667 | −0.161804 | ||||||||
\(206\) | 11.1383 | 0.776044 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −11.3096 | −0.784177 | ||||||||
\(209\) | 3.53502 | 0.244523 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.07485 | 0.280524 | 0.140262 | − | 0.990114i | \(-0.455205\pi\) | ||||
0.140262 | + | 0.990114i | \(0.455205\pi\) | |||||||
\(212\) | −0.660639 | −0.0453729 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 27.0158 | 1.84676 | ||||||||
\(215\) | −0.635106 | −0.0433138 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.59843 | −0.447930 | ||||||||
\(218\) | 25.7125 | 1.74147 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.61659 | 0.176410 | ||||||||
\(221\) | −8.79157 | −0.591385 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.44657 | −0.163835 | −0.0819173 | − | 0.996639i | \(-0.526104\pi\) | ||||
−0.0819173 | + | 0.996639i | \(0.526104\pi\) | |||||||
\(224\) | 12.9067 | 0.862364 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.9664 | 1.06207 | ||||||||
\(227\) | −2.74547 | −0.182223 | −0.0911115 | − | 0.995841i | \(-0.529042\pi\) | ||||
−0.0911115 | + | 0.995841i | \(0.529042\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.7145 | 0.906277 | 0.453139 | − | 0.891440i | \(-0.350304\pi\) | ||||
0.453139 | + | 0.891440i | \(0.350304\pi\) | |||||||
\(230\) | 3.50023 | 0.230798 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.29358 | −0.150581 | ||||||||
\(233\) | 5.36762 | 0.351645 | 0.175822 | − | 0.984422i | \(-0.443742\pi\) | ||||
0.175822 | + | 0.984422i | \(0.443742\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.2277 | 0.732412 | ||||||||
\(236\) | 2.96726 | 0.193152 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 23.3910 | 1.51622 | ||||||||
\(239\) | −1.00000 | −0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.9180 | −0.832120 | −0.416060 | − | 0.909337i | \(-0.636589\pi\) | ||||
−0.416060 | + | 0.909337i | \(0.636589\pi\) | |||||||
\(242\) | 4.15295 | 0.266962 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.61491 | 0.423476 | ||||||||
\(245\) | −11.3051 | −0.722256 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.83791 | −0.180572 | ||||||||
\(248\) | −3.85351 | −0.244698 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −18.6101 | −1.17701 | ||||||||
\(251\) | −18.9396 | −1.19546 | −0.597729 | − | 0.801698i | \(-0.703930\pi\) | ||||
−0.597729 | + | 0.801698i | \(0.703930\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.28782 | −0.269573 | ||||||||
\(254\) | 16.6830 | 1.04679 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5022 | 0.843886 | ||||||||
\(257\) | 15.3234 | 0.955847 | 0.477923 | − | 0.878402i | \(-0.341390\pi\) | ||||
0.477923 | + | 0.878402i | \(0.341390\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.18023 | −0.259747 | ||||||||
\(260\) | −2.10059 | −0.130273 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.9561 | −0.985771 | ||||||||
\(263\) | −27.1435 | −1.67374 | −0.836870 | − | 0.547402i | \(-0.815617\pi\) | ||||
−0.836870 | + | 0.547402i | \(0.815617\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.57543 | 0.0967779 | ||||||||
\(266\) | 7.55062 | 0.462958 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.75623 | −0.229448 | ||||||||
\(269\) | −12.7939 | −0.780058 | −0.390029 | − | 0.920802i | \(-0.627535\pi\) | ||||
−0.390029 | + | 0.920802i | \(0.627535\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.4970 | −1.73107 | −0.865533 | − | 0.500851i | \(-0.833020\pi\) | ||||
−0.865533 | + | 0.500851i | \(0.833020\pi\) | |||||||
\(272\) | 18.2971 | 1.10943 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.24895 | 0.317101 | ||||||||
\(275\) | 8.27891 | 0.499237 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.41529 | −0.145120 | −0.0725602 | − | 0.997364i | \(-0.523117\pi\) | ||||
−0.0725602 | + | 0.997364i | \(0.523117\pi\) | |||||||
\(278\) | 23.0130 | 1.38023 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −12.5949 | −0.752689 | ||||||||
\(281\) | 8.27813 | 0.493832 | 0.246916 | − | 0.969037i | \(-0.420583\pi\) | ||||
0.246916 | + | 0.969037i | \(0.420583\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.142683 | −0.00848163 | −0.00424082 | − | 0.999991i | \(-0.501350\pi\) | ||||
−0.00424082 | + | 0.999991i | \(0.501350\pi\) | |||||||
\(284\) | −6.71930 | −0.398717 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.9455 | 0.647219 | ||||||||
\(287\) | 6.06171 | 0.357811 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.77660 | −0.163329 | ||||||||
\(290\) | −2.42706 | −0.142522 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.45813 | −0.436454 | ||||||||
\(293\) | −12.9861 | −0.758657 | −0.379328 | − | 0.925262i | \(-0.623845\pi\) | ||||
−0.379328 | + | 0.925262i | \(0.623845\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.07605 | −0.411983 | ||||||||
\(296\) | −2.44127 | −0.141896 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.31169 | 0.365627 | ||||||||
\(299\) | 3.44226 | 0.199071 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.66179 | 0.0957839 | ||||||||
\(302\) | 1.13152 | 0.0651119 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.90629 | 0.338749 | ||||||||
\(305\) | −15.7746 | −0.903252 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.69912 | 0.439412 | 0.219706 | − | 0.975566i | \(-0.429490\pi\) | ||||
0.219706 | + | 0.975566i | \(0.429490\pi\) | |||||||
\(308\) | −6.84644 | −0.390112 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.07776 | −0.231601 | ||||||||
\(311\) | 0.0557085 | 0.00315894 | 0.00157947 | − | 0.999999i | \(-0.499497\pi\) | ||||
0.00157947 | + | 0.999999i | \(0.499497\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.73407 | −0.154538 | −0.0772692 | − | 0.997010i | \(-0.524620\pi\) | ||||
−0.0772692 | + | 0.997010i | \(0.524620\pi\) | |||||||
\(314\) | −3.09436 | −0.174625 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.06070 | 0.509704 | ||||||||
\(317\) | −5.74313 | −0.322566 | −0.161283 | − | 0.986908i | \(-0.551563\pi\) | ||||
−0.161283 | + | 0.986908i | \(0.551563\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.97317 | 0.166466 | ||||||||
\(320\) | −6.24763 | −0.349253 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.15855 | −0.510386 | ||||||||
\(323\) | 4.59130 | 0.255467 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.64630 | −0.368671 | ||||||||
\(326\) | 27.7972 | 1.53954 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.54006 | 0.195467 | ||||||||
\(329\) | −29.3778 | −1.61965 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.3302 | −1.77703 | −0.888514 | − | 0.458849i | \(-0.848262\pi\) | ||||
−0.888514 | + | 0.458849i | \(0.848262\pi\) | |||||||
\(332\) | 8.04685 | 0.441628 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 24.0811 | 1.31766 | ||||||||
\(335\) | 8.95750 | 0.489401 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.91558 | −0.267769 | −0.133884 | − | 0.990997i | \(-0.542745\pi\) | ||||
−0.133884 | + | 0.990997i | \(0.542745\pi\) | |||||||
\(338\) | 12.2341 | 0.665446 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.39843 | 0.184306 | ||||||||
\(341\) | 4.99530 | 0.270511 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.73104 | 0.147462 | ||||||||
\(344\) | 0.970492 | 0.0523254 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.9464 | −1.01856 | ||||||||
\(347\) | 28.7741 | 1.54467 | 0.772337 | − | 0.635213i | \(-0.219088\pi\) | ||||
0.772337 | + | 0.635213i | \(0.219088\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.6879 | −0.679168 | −0.339584 | − | 0.940576i | \(-0.610286\pi\) | ||||
−0.339584 | + | 0.940576i | \(0.610286\pi\) | |||||||
\(350\) | 17.6833 | 0.945212 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9.77094 | −0.520793 | ||||||||
\(353\) | 6.88724 | 0.366571 | 0.183285 | − | 0.983060i | \(-0.441327\pi\) | ||||
0.183285 | + | 0.983060i | \(0.441327\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.0236 | 0.850443 | ||||||||
\(356\) | 3.74278 | 0.198367 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.44545 | −0.287801 | ||||||||
\(359\) | 4.46094 | 0.235439 | 0.117720 | − | 0.993047i | \(-0.462442\pi\) | ||||
0.117720 | + | 0.993047i | \(0.462442\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.5179 | −0.921996 | ||||||||
\(362\) | 10.7792 | 0.566545 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.49632 | 0.288085 | ||||||||
\(365\) | 17.7855 | 0.930934 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.13856 | 0.216031 | 0.108016 | − | 0.994149i | \(-0.465550\pi\) | ||||
0.108016 | + | 0.994149i | \(0.465550\pi\) | |||||||
\(368\) | −7.16406 | −0.373453 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.58334 | −0.134302 | ||||||||
\(371\) | −4.12220 | −0.214014 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.9172 | −0.824161 | −0.412080 | − | 0.911148i | \(-0.635198\pi\) | ||||
−0.412080 | + | 0.911148i | \(0.635198\pi\) | |||||||
\(374\) | −17.7081 | −0.915663 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.1568 | −0.884792 | ||||||||
\(377\) | −2.38686 | −0.122930 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.7486 | 1.83628 | 0.918142 | − | 0.396252i | \(-0.129689\pi\) | ||||
0.918142 | + | 0.396252i | \(0.129689\pi\) | |||||||
\(380\) | 1.09701 | 0.0562756 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −25.5342 | −1.30645 | ||||||||
\(383\) | 22.7410 | 1.16201 | 0.581005 | − | 0.813900i | \(-0.302660\pi\) | ||||
0.581005 | + | 0.813900i | \(0.302660\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.3268 | 0.832089 | ||||||||
\(386\) | −13.6785 | −0.696219 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.91448 | 0.249495 | ||||||||
\(389\) | 2.53628 | 0.128594 | 0.0642972 | − | 0.997931i | \(-0.479519\pi\) | ||||
0.0642972 | + | 0.997931i | \(0.479519\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.56904 | −0.281639 | ||||||||
\(392\) | 17.2751 | 0.872524 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.57319 | −0.381532 | ||||||||
\(395\) | −21.6071 | −1.08717 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.3410 | −0.669564 | −0.334782 | − | 0.942296i | \(-0.608663\pi\) | ||||
−0.334782 | + | 0.942296i | \(0.608663\pi\) | |||||||
\(398\) | 41.7775 | 2.09412 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.8324 | 0.691618 | ||||||||
\(401\) | 0.833758 | 0.0416359 | 0.0208179 | − | 0.999783i | \(-0.493373\pi\) | ||||
0.0208179 | + | 0.999783i | \(0.493373\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.01023 | −0.199764 | ||||||||
\(404\) | −7.67738 | −0.381964 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.35054 | 0.315172 | ||||||||
\(407\) | 3.16462 | 0.156864 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.4602 | 0.616118 | 0.308059 | − | 0.951367i | \(-0.400321\pi\) | ||||
0.308059 | + | 0.951367i | \(0.400321\pi\) | |||||||
\(410\) | 3.74608 | 0.185006 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.23428 | −0.208608 | ||||||||
\(413\) | 18.5149 | 0.911057 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.1894 | −0.941969 | ||||||||
\(416\) | 7.84411 | 0.384589 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.71615 | −0.279586 | ||||||||
\(419\) | 9.75869 | 0.476743 | 0.238372 | − | 0.971174i | \(-0.423386\pi\) | ||||
0.238372 | + | 0.971174i | \(0.423386\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.1165 | 0.785470 | 0.392735 | − | 0.919652i | \(-0.371529\pi\) | ||||
0.392735 | + | 0.919652i | \(0.371529\pi\) | |||||||
\(422\) | −6.58906 | −0.320750 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.40738 | −0.116913 | ||||||||
\(425\) | 10.7527 | 0.521582 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 41.2752 | 1.99744 | ||||||||
\(428\) | −10.2701 | −0.496426 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.02697 | 0.0495249 | ||||||||
\(431\) | 23.3638 | 1.12539 | 0.562697 | − | 0.826663i | \(-0.309764\pi\) | ||||
0.562697 | + | 0.826663i | \(0.309764\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.8084 | −0.807758 | −0.403879 | − | 0.914812i | \(-0.632338\pi\) | ||||
−0.403879 | + | 0.914812i | \(0.632338\pi\) | |||||||
\(434\) | 10.6697 | 0.512162 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.77471 | −0.468124 | ||||||||
\(437\) | −1.79768 | −0.0859948 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.57370 | 0.218291 | 0.109145 | − | 0.994026i | \(-0.465189\pi\) | ||||
0.109145 | + | 0.994026i | \(0.465189\pi\) | |||||||
\(440\) | 9.53490 | 0.454558 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.2160 | 0.676188 | ||||||||
\(443\) | 8.43805 | 0.400904 | 0.200452 | − | 0.979704i | \(-0.435759\pi\) | ||||
0.200452 | + | 0.979704i | \(0.435759\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.92543 | −0.423106 | ||||||||
\(446\) | 3.95612 | 0.187328 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.3473 | 0.772336 | ||||||||
\(449\) | −11.3585 | −0.536043 | −0.268021 | − | 0.963413i | \(-0.586370\pi\) | ||||
−0.268021 | + | 0.963413i | \(0.586370\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.58898 | −0.216087 | ||||||||
\(452\) | −6.06967 | −0.285493 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.43944 | 0.208353 | ||||||||
\(455\) | −13.1071 | −0.614471 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.8039 | 0.645720 | 0.322860 | − | 0.946447i | \(-0.395356\pi\) | ||||
0.322860 | + | 0.946447i | \(0.395356\pi\) | |||||||
\(458\) | −22.1764 | −1.03623 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.33063 | −0.0620408 | ||||||||
\(461\) | −12.8220 | −0.597179 | −0.298589 | − | 0.954382i | \(-0.596516\pi\) | ||||
−0.298589 | + | 0.954382i | \(0.596516\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.22053 | −0.242618 | −0.121309 | − | 0.992615i | \(-0.538709\pi\) | ||||
−0.121309 | + | 0.992615i | \(0.538709\pi\) | |||||||
\(464\) | 4.96756 | 0.230613 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.67948 | −0.402069 | ||||||||
\(467\) | 8.47835 | 0.392331 | 0.196166 | − | 0.980571i | \(-0.437151\pi\) | ||||
0.196166 | + | 0.980571i | \(0.437151\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.4378 | −1.08226 | ||||||||
\(470\) | −18.1552 | −0.837437 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.8128 | 0.497698 | ||||||||
\(473\) | −1.25805 | −0.0578451 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.47096 | 0.159259 | ||||||||
\(476\) | −8.89219 | −0.407573 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.61701 | 0.0739602 | ||||||||
\(479\) | −37.0880 | −1.69459 | −0.847297 | − | 0.531119i | \(-0.821772\pi\) | ||||
−0.847297 | + | 0.531119i | \(0.821772\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.54056 | −0.115839 | ||||||||
\(482\) | 20.8885 | 0.951443 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.57876 | −0.0717618 | ||||||||
\(485\) | −11.7196 | −0.532159 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.2956 | 1.55408 | 0.777041 | − | 0.629450i | \(-0.216720\pi\) | ||||
0.777041 | + | 0.629450i | \(0.216720\pi\) | |||||||
\(488\) | 24.1049 | 1.09118 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 18.2804 | 0.825825 | ||||||||
\(491\) | 1.07986 | 0.0487335 | 0.0243667 | − | 0.999703i | \(-0.492243\pi\) | ||||
0.0243667 | + | 0.999703i | \(0.492243\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.86157 | 0.173916 | ||||||||
\(494\) | 4.58893 | 0.206466 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.34613 | 0.374752 | ||||||||
\(497\) | −41.9266 | −1.88066 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.972126 | 0.0435183 | 0.0217592 | − | 0.999763i | \(-0.493073\pi\) | ||||
0.0217592 | + | 0.999763i | \(0.493073\pi\) | |||||||
\(500\) | 7.07471 | 0.316391 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 30.6255 | 1.36688 | ||||||||
\(503\) | −30.5203 | −1.36083 | −0.680417 | − | 0.732825i | \(-0.738201\pi\) | ||||
−0.680417 | + | 0.732825i | \(0.738201\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.3083 | 0.814708 | ||||||||
\(506\) | 6.93343 | 0.308229 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.34211 | −0.281386 | ||||||||
\(509\) | 20.2337 | 0.896845 | 0.448422 | − | 0.893822i | \(-0.351986\pi\) | ||||
0.448422 | + | 0.893822i | \(0.351986\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −46.5367 | −2.05866 | ||||||||
\(512\) | 5.40993 | 0.239087 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −24.7780 | −1.09291 | ||||||||
\(515\) | 10.0975 | 0.444950 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.2403 | 0.978127 | ||||||||
\(518\) | 6.75946 | 0.296993 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.65461 | −0.335677 | ||||||||
\(521\) | 17.2171 | 0.754296 | 0.377148 | − | 0.926153i | \(-0.376905\pi\) | ||||
0.377148 | + | 0.926153i | \(0.376905\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.23753 | −0.0978405 | −0.0489202 | − | 0.998803i | \(-0.515578\pi\) | ||||
−0.0489202 | + | 0.998803i | \(0.515578\pi\) | |||||||
\(524\) | 6.06577 | 0.264985 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 43.8912 | 1.91375 | ||||||||
\(527\) | 6.48793 | 0.282618 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.8195 | −0.905195 | ||||||||
\(530\) | −2.54748 | −0.110656 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.87039 | −0.124447 | ||||||||
\(533\) | 3.68403 | 0.159573 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.4913 | 1.05885 | ||||||||
\(536\) | −13.6878 | −0.591222 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20.6878 | 0.891916 | ||||||||
\(539\) | −22.3937 | −0.964565 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.02257 | −0.172944 | −0.0864719 | − | 0.996254i | \(-0.527559\pi\) | ||||
−0.0864719 | + | 0.996254i | \(0.527559\pi\) | |||||||
\(542\) | 46.0798 | 1.97930 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12.6905 | −0.544103 | ||||||||
\(545\) | 23.3098 | 0.998483 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.4728 | −0.704327 | −0.352163 | − | 0.935939i | \(-0.614554\pi\) | ||||
−0.352163 | + | 0.935939i | \(0.614554\pi\) | |||||||
\(548\) | −1.99541 | −0.0852397 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −13.3871 | −0.570826 | ||||||||
\(551\) | 1.24651 | 0.0531033 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 56.5362 | 2.40417 | ||||||||
\(554\) | 3.90553 | 0.165930 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.74846 | −0.371018 | ||||||||
\(557\) | −28.4924 | −1.20726 | −0.603631 | − | 0.797264i | \(-0.706280\pi\) | ||||
−0.603631 | + | 0.797264i | \(0.706280\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.00996 | 0.0427168 | ||||||||
\(560\) | 27.2787 | 1.15273 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.3858 | −0.564646 | ||||||||
\(563\) | 19.7584 | 0.832716 | 0.416358 | − | 0.909201i | \(-0.363306\pi\) | ||||
0.416358 | + | 0.909201i | \(0.363306\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.4744 | 0.608942 | ||||||||
\(566\) | 0.230720 | 0.00969787 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24.4853 | −1.02738 | ||||||||
\(569\) | 9.62616 | 0.403550 | 0.201775 | − | 0.979432i | \(-0.435329\pi\) | ||||
0.201775 | + | 0.979432i | \(0.435329\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.4099 | 0.728583 | 0.364292 | − | 0.931285i | \(-0.381311\pi\) | ||||
0.364292 | + | 0.931285i | \(0.381311\pi\) | |||||||
\(572\) | −4.16096 | −0.173979 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.80182 | −0.409120 | ||||||||
\(575\) | −4.21012 | −0.175574 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.3271 | 1.63721 | 0.818605 | − | 0.574357i | \(-0.194748\pi\) | ||||
0.818605 | + | 0.574357i | \(0.194748\pi\) | |||||||
\(578\) | 4.48978 | 0.186750 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.922656 | 0.0383112 | ||||||||
\(581\) | 50.2101 | 2.08306 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.12069 | 0.129246 | ||||||||
\(584\) | −27.1776 | −1.12462 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.9986 | 0.867445 | ||||||||
\(587\) | 26.7724 | 1.10502 | 0.552508 | − | 0.833507i | \(-0.313671\pi\) | ||||
0.552508 | + | 0.833507i | \(0.313671\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.09430 | 0.0862941 | ||||||||
\(590\) | 11.4420 | 0.471060 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.28743 | 0.217312 | ||||||||
\(593\) | −44.4733 | −1.82630 | −0.913150 | − | 0.407623i | \(-0.866358\pi\) | ||||
−0.913150 | + | 0.407623i | \(0.866358\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.2053 | 0.869332 | ||||||||
\(596\) | −2.39941 | −0.0982838 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.56616 | −0.227617 | ||||||||
\(599\) | 19.6240 | 0.801815 | 0.400908 | − | 0.916118i | \(-0.368695\pi\) | ||||
0.400908 | + | 0.916118i | \(0.368695\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.4787 | 0.631389 | 0.315695 | − | 0.948861i | \(-0.397763\pi\) | ||||
0.315695 | + | 0.948861i | \(0.397763\pi\) | |||||||
\(602\) | −2.68712 | −0.109519 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.430153 | −0.0175027 | ||||||||
\(605\) | 3.76488 | 0.153064 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.5122 | 0.832566 | 0.416283 | − | 0.909235i | \(-0.363333\pi\) | ||||
0.416283 | + | 0.909235i | \(0.363333\pi\) | |||||||
\(608\) | −4.09650 | −0.166135 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 25.5077 | 1.03277 | ||||||||
\(611\) | −17.8545 | −0.722316 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.1077 | 1.29682 | 0.648409 | − | 0.761292i | \(-0.275435\pi\) | ||||
0.648409 | + | 0.761292i | \(0.275435\pi\) | |||||||
\(614\) | −12.4495 | −0.502422 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −24.9486 | −1.00521 | ||||||||
\(617\) | 16.7973 | 0.676233 | 0.338117 | − | 0.941104i | \(-0.390210\pi\) | ||||
0.338117 | + | 0.941104i | \(0.390210\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.4017 | 0.860206 | 0.430103 | − | 0.902780i | \(-0.358477\pi\) | ||||
0.430103 | + | 0.902780i | \(0.358477\pi\) | |||||||
\(620\) | 1.55018 | 0.0622566 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.0900810 | −0.00361192 | ||||||||
\(623\) | 23.3539 | 0.935653 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.61552 | −0.104621 | ||||||||
\(626\) | 4.42100 | 0.176699 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.17633 | 0.0469407 | ||||||||
\(629\) | 4.11022 | 0.163885 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0747 | −0.639924 | −0.319962 | − | 0.947430i | \(-0.603670\pi\) | ||||
−0.319962 | + | 0.947430i | \(0.603670\pi\) | |||||||
\(632\) | 33.0174 | 1.31336 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.28668 | 0.368821 | ||||||||
\(635\) | 15.1241 | 0.600181 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.9777 | 0.712300 | ||||||||
\(638\) | −4.80764 | −0.190336 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 19.9679 | 0.789299 | ||||||||
\(641\) | −35.1303 | −1.38756 | −0.693782 | − | 0.720185i | \(-0.744057\pi\) | ||||
−0.693782 | + | 0.720185i | \(0.744057\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.14336 | −0.0450898 | −0.0225449 | − | 0.999746i | \(-0.507177\pi\) | ||||
−0.0225449 | + | 0.999746i | \(0.507177\pi\) | |||||||
\(644\) | 3.48166 | 0.137197 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.42417 | −0.292100 | ||||||||
\(647\) | −11.6354 | −0.457433 | −0.228716 | − | 0.973493i | \(-0.573453\pi\) | ||||
−0.228716 | + | 0.973493i | \(0.573453\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.0166 | −0.550199 | ||||||||
\(650\) | 10.7471 | 0.421537 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.5672 | −0.413844 | ||||||||
\(653\) | 2.96261 | 0.115936 | 0.0579680 | − | 0.998318i | \(-0.481538\pi\) | ||||
0.0579680 | + | 0.998318i | \(0.481538\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.4651 | −0.565198 | ||||||||
\(656\) | −7.66725 | −0.299356 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 47.5041 | 1.85190 | ||||||||
\(659\) | 35.0365 | 1.36483 | 0.682415 | − | 0.730965i | \(-0.260930\pi\) | ||||
0.682415 | + | 0.730965i | \(0.260930\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.3727 | −1.18136 | −0.590681 | − | 0.806905i | \(-0.701141\pi\) | ||||
−0.590681 | + | 0.806905i | \(0.701141\pi\) | |||||||
\(662\) | 52.2782 | 2.03185 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 29.3229 | 1.13795 | ||||||||
\(665\) | 6.84505 | 0.265440 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.51196 | −0.0585435 | ||||||||
\(668\) | −9.15453 | −0.354199 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14.4843 | −0.559579 | ||||||||
\(671\) | −31.2471 | −1.20628 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.848634 | 0.0327124 | 0.0163562 | − | 0.999866i | \(-0.494793\pi\) | ||||
0.0163562 | + | 0.999866i | \(0.494793\pi\) | |||||||
\(674\) | 7.94852 | 0.306166 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.65083 | −0.178878 | ||||||||
\(677\) | 1.77815 | 0.0683400 | 0.0341700 | − | 0.999416i | \(-0.489121\pi\) | ||||
0.0341700 | + | 0.999416i | \(0.489121\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 30.6650 | 1.17681 | ||||||||
\(680\) | 12.3840 | 0.474904 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.07744 | −0.309301 | ||||||||
\(683\) | 34.3363 | 1.31384 | 0.656922 | − | 0.753959i | \(-0.271858\pi\) | ||||
0.656922 | + | 0.753959i | \(0.271858\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.75847 | 0.181812 | ||||||||
\(686\) | −4.41611 | −0.168608 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.10194 | −0.0801357 | ||||||||
\(689\) | −2.50529 | −0.0954439 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.6872 | 1.16740 | 0.583698 | − | 0.811971i | \(-0.301605\pi\) | ||||
0.583698 | + | 0.811971i | \(0.301605\pi\) | |||||||
\(692\) | 7.20254 | 0.273799 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −46.5279 | −1.76618 | ||||||||
\(695\) | 20.8625 | 0.791361 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.96020 | −0.225759 | ||||||||
\(698\) | 20.5164 | 0.776558 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.72237 | −0.254082 | ||||||||
\(701\) | −1.99537 | −0.0753641 | −0.0376820 | − | 0.999290i | \(-0.511997\pi\) | ||||
−0.0376820 | + | 0.999290i | \(0.511997\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.32678 | 0.0500404 | ||||||||
\(704\) | −12.3756 | −0.466424 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.1367 | −0.419136 | ||||||||
\(707\) | −47.9047 | −1.80164 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.9090 | 1.27348 | 0.636739 | − | 0.771080i | \(-0.280283\pi\) | ||||
0.636739 | + | 0.771080i | \(0.280283\pi\) | |||||||
\(710\) | −25.9102 | −0.972394 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.6388 | 0.511134 | ||||||||
\(713\) | −2.54029 | −0.0951345 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.92267 | 0.371087 | ||||||||
\(716\) | 2.07011 | 0.0773636 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.21337 | −0.269201 | ||||||||
\(719\) | −24.1685 | −0.901331 | −0.450666 | − | 0.892693i | \(-0.648813\pi\) | ||||
−0.450666 | + | 0.892693i | \(0.648813\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.4207 | −0.983959 | ||||||||
\(722\) | 28.3266 | 1.05421 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.09777 | −0.152292 | ||||||||
\(725\) | 2.91929 | 0.108420 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −46.2043 | −1.71362 | −0.856811 | − | 0.515631i | \(-0.827558\pi\) | ||||
−0.856811 | + | 0.515631i | \(0.827558\pi\) | |||||||
\(728\) | 20.0287 | 0.742314 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −28.7592 | −1.06443 | ||||||||
\(731\) | −1.63396 | −0.0604342 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.13031 | −0.115621 | −0.0578104 | − | 0.998328i | \(-0.518412\pi\) | ||||
−0.0578104 | + | 0.998328i | \(0.518412\pi\) | |||||||
\(734\) | −6.69208 | −0.247009 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.96887 | 0.183155 | ||||||||
\(737\) | 17.7435 | 0.653589 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −46.7714 | −1.72052 | −0.860258 | − | 0.509859i | \(-0.829697\pi\) | ||||
−0.860258 | + | 0.509859i | \(0.829697\pi\) | |||||||
\(740\) | 0.982067 | 0.0361015 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.66563 | 0.244703 | ||||||||
\(743\) | −41.7626 | −1.53212 | −0.766061 | − | 0.642768i | \(-0.777786\pi\) | ||||
−0.766061 | + | 0.642768i | \(0.777786\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.72190 | 0.209634 | ||||||||
\(746\) | 25.7382 | 0.942342 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.73179 | 0.246139 | ||||||||
\(749\) | −64.0828 | −2.34154 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.01683 | 0.146576 | 0.0732881 | − | 0.997311i | \(-0.476651\pi\) | ||||
0.0732881 | + | 0.997311i | \(0.476651\pi\) | |||||||
\(752\) | 37.1590 | 1.35505 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.85957 | 0.140557 | ||||||||
\(755\) | 1.02579 | 0.0373323 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.0626 | 1.23803 | 0.619014 | − | 0.785380i | \(-0.287532\pi\) | ||||
0.619014 | + | 0.785380i | \(0.287532\pi\) | |||||||
\(758\) | −57.8058 | −2.09960 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.99754 | 0.145006 | ||||||||
\(761\) | −17.7142 | −0.642139 | −0.321070 | − | 0.947056i | \(-0.604042\pi\) | ||||
−0.321070 | + | 0.947056i | \(0.604042\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −60.9914 | −2.20804 | ||||||||
\(764\) | 9.70694 | 0.351185 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −36.7723 | −1.32864 | ||||||||
\(767\) | 11.2525 | 0.406305 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.4368 | 0.700907 | 0.350454 | − | 0.936580i | \(-0.386027\pi\) | ||||
0.350454 | + | 0.936580i | \(0.386027\pi\) | |||||||
\(770\) | −26.4005 | −0.951407 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.19994 | 0.187150 | ||||||||
\(773\) | −15.5259 | −0.558428 | −0.279214 | − | 0.960229i | \(-0.590074\pi\) | ||||
−0.279214 | + | 0.960229i | \(0.590074\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.90478 | 0.176185 | ||||||||
\(776\) | 17.9085 | 0.642877 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.10118 | −0.147034 | ||||||||
\(779\) | −1.92395 | −0.0689326 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.7403 | 1.13576 | ||||||||
\(782\) | 9.00518 | 0.322024 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −37.4153 | −1.33626 | ||||||||
\(785\) | −2.80521 | −0.100122 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.2433 | −0.899828 | −0.449914 | − | 0.893072i | \(-0.648545\pi\) | ||||
−0.449914 | + | 0.893072i | \(0.648545\pi\) | |||||||
\(788\) | 2.87898 | 0.102559 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 34.9389 | 1.24307 | ||||||||
\(791\) | −37.8731 | −1.34661 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.0852 | 0.890801 | ||||||||
\(794\) | 21.5724 | 0.765577 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.8819 | −0.562918 | ||||||||
\(797\) | −39.2256 | −1.38944 | −0.694721 | − | 0.719279i | \(-0.744472\pi\) | ||||
−0.694721 | + | 0.719279i | \(0.744472\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.8858 | 1.02191 | ||||||||
\(800\) | −9.59388 | −0.339195 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.34819 | −0.0476063 | ||||||||
\(803\) | 35.2303 | 1.24325 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.30273 | −0.292633 | ||||||||
\(806\) | 6.48456 | 0.228409 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −27.9765 | −0.984211 | ||||||||
\(809\) | −21.5713 | −0.758405 | −0.379203 | − | 0.925314i | \(-0.623802\pi\) | ||||
−0.379203 | + | 0.925314i | \(0.623802\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.52560 | 0.0886858 | 0.0443429 | − | 0.999016i | \(-0.485881\pi\) | ||||
0.0443429 | + | 0.999016i | \(0.485881\pi\) | |||||||
\(812\) | −2.41418 | −0.0847211 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.11721 | −0.179358 | ||||||||
\(815\) | 25.1997 | 0.882707 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.527441 | −0.0184528 | ||||||||
\(818\) | −20.1482 | −0.704467 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.42409 | −0.0497312 | ||||||||
\(821\) | −21.8608 | −0.762949 | −0.381474 | − | 0.924379i | \(-0.624584\pi\) | ||||
−0.381474 | + | 0.924379i | \(0.624584\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.6288 | 0.544785 | 0.272393 | − | 0.962186i | \(-0.412185\pi\) | ||||
0.272393 | + | 0.962186i | \(0.412185\pi\) | |||||||
\(824\) | −15.4298 | −0.537523 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −29.9387 | −1.04170 | ||||||||
\(827\) | −1.15424 | −0.0401368 | −0.0200684 | − | 0.999799i | \(-0.506388\pi\) | ||||
−0.0200684 | + | 0.999799i | \(0.506388\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.5972 | 0.784832 | 0.392416 | − | 0.919788i | \(-0.371639\pi\) | ||||
0.392416 | + | 0.919788i | \(0.371639\pi\) | |||||||
\(830\) | 31.0293 | 1.07704 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.93514 | 0.344439 | ||||||||
\(833\) | −29.0851 | −1.00774 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.8309 | 0.755489 | ||||||||
\(836\) | 2.17302 | 0.0751554 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.7799 | −0.545106 | ||||||||
\(839\) | 26.1778 | 0.903757 | 0.451878 | − | 0.892080i | \(-0.350754\pi\) | ||||
0.451878 | + | 0.892080i | \(0.350754\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9516 | −0.963848 | ||||||||
\(842\) | −26.0605 | −0.898103 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.50486 | 0.0862207 | ||||||||
\(845\) | 11.0909 | 0.381537 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.85102 | −0.338485 | ||||||||
\(848\) | 5.21403 | 0.179051 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −17.3872 | −0.596375 | ||||||||
\(851\) | −1.60932 | −0.0551668 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.2252 | 0.692497 | 0.346249 | − | 0.938143i | \(-0.387455\pi\) | ||||
0.346249 | + | 0.938143i | \(0.387455\pi\) | |||||||
\(854\) | −66.7422 | −2.28387 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −37.4247 | −1.27915 | ||||||||
\(857\) | −24.4336 | −0.834636 | −0.417318 | − | 0.908761i | \(-0.637030\pi\) | ||||
−0.417318 | + | 0.908761i | \(0.637030\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.4278 | 1.24290 | 0.621451 | − | 0.783453i | \(-0.286543\pi\) | ||||
0.621451 | + | 0.783453i | \(0.286543\pi\) | |||||||
\(860\) | −0.390406 | −0.0133128 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −37.7794 | −1.28677 | ||||||||
\(863\) | 18.5506 | 0.631471 | 0.315735 | − | 0.948847i | \(-0.397749\pi\) | ||||
0.315735 | + | 0.948847i | \(0.397749\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.1759 | −0.583999 | ||||||||
\(866\) | 27.1792 | 0.923588 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.05613 | −0.137674 | ||||||||
\(869\) | −42.8005 | −1.45191 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.2444 | −0.482655 | ||||||||
\(872\) | −35.6193 | −1.20622 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.90687 | 0.0983262 | ||||||||
\(875\) | 44.1442 | 1.49235 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.5945 | 1.33701 | 0.668505 | − | 0.743708i | \(-0.266934\pi\) | ||||
0.668505 | + | 0.743708i | \(0.266934\pi\) | |||||||
\(878\) | −7.39570 | −0.249593 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −20.6512 | −0.696151 | ||||||||
\(881\) | −32.1516 | −1.08321 | −0.541607 | − | 0.840632i | \(-0.682184\pi\) | ||||
−0.541607 | + | 0.840632i | \(0.682184\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.8275 | 0.700900 | 0.350450 | − | 0.936581i | \(-0.386029\pi\) | ||||
0.350450 | + | 0.936581i | \(0.386029\pi\) | |||||||
\(884\) | −5.40428 | −0.181766 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.6444 | −0.458392 | ||||||||
\(887\) | −34.9748 | −1.17434 | −0.587170 | − | 0.809464i | \(-0.699758\pi\) | ||||
−0.587170 | + | 0.809464i | \(0.699758\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −39.5730 | −1.32724 | ||||||||
\(890\) | 14.4325 | 0.483778 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.50394 | −0.0503555 | ||||||||
\(893\) | 9.32432 | 0.312027 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.93660 | −0.165012 | ||||||||
\(896\) | −52.2470 | −1.74545 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.3668 | 0.612909 | ||||||||
\(899\) | 1.76144 | 0.0587472 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.05317 | 0.135031 | ||||||||
\(902\) | 7.42042 | 0.247073 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22.1180 | −0.735635 | ||||||||
\(905\) | 9.77198 | 0.324832 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.3094 | −0.939999 | −0.470000 | − | 0.882667i | \(-0.655746\pi\) | ||||
−0.470000 | + | 0.882667i | \(0.655746\pi\) | |||||||
\(908\) | −1.68767 | −0.0560073 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 21.1943 | 0.702584 | ||||||||
\(911\) | 47.1094 | 1.56081 | 0.780403 | − | 0.625277i | \(-0.215014\pi\) | ||||
0.780403 | + | 0.625277i | \(0.215014\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −38.0113 | −1.25799 | ||||||||
\(914\) | −22.3210 | −0.738314 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.43044 | 0.278549 | ||||||||
\(917\) | 37.8487 | 1.24987 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.0107 | −0.561131 | −0.280565 | − | 0.959835i | \(-0.590522\pi\) | ||||
−0.280565 | + | 0.959835i | \(0.590522\pi\) | |||||||
\(920\) | −4.84883 | −0.159861 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.7332 | 0.682812 | ||||||||
\(923\) | −25.4811 | −0.838720 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.10727 | 0.102166 | ||||||||
\(926\) | 8.44163 | 0.277409 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.44541 | −0.113101 | ||||||||
\(929\) | 0.496932 | 0.0163038 | 0.00815190 | − | 0.999967i | \(-0.497405\pi\) | ||||
0.00815190 | + | 0.999967i | \(0.497405\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.38864 | −0.307700 | ||||||||
\(932\) | 3.29954 | 0.108080 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13.7095 | −0.448590 | ||||||||
\(935\) | −16.0533 | −0.525001 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.22697 | 0.268763 | 0.134382 | − | 0.990930i | \(-0.457095\pi\) | ||||
0.134382 | + | 0.990930i | \(0.457095\pi\) | |||||||
\(938\) | 37.8991 | 1.23745 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.90177 | 0.225111 | ||||||||
\(941\) | −50.1600 | −1.63517 | −0.817584 | − | 0.575809i | \(-0.804687\pi\) | ||||
−0.817584 | + | 0.575809i | \(0.804687\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.33366 | 0.0759944 | ||||||||
\(944\) | −23.4188 | −0.762218 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.03427 | 0.0661399 | ||||||||
\(947\) | −11.6253 | −0.377773 | −0.188886 | − | 0.981999i | \(-0.560488\pi\) | ||||
−0.188886 | + | 0.981999i | \(0.560488\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.2829 | −0.918101 | ||||||||
\(950\) | −5.61257 | −0.182096 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −32.4034 | −1.05020 | ||||||||
\(953\) | −27.5219 | −0.891522 | −0.445761 | − | 0.895152i | \(-0.647067\pi\) | ||||
−0.445761 | + | 0.895152i | \(0.647067\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.1482 | −0.749058 | ||||||||
\(956\) | −0.614711 | −0.0198812 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 59.9716 | 1.93759 | ||||||||
\(959\) | −12.4508 | −0.402057 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.0406 | −0.904534 | ||||||||
\(962\) | 4.10809 | 0.132450 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.94082 | −0.255757 | ||||||||
\(965\) | −12.4003 | −0.399181 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.9315 | −1.34843 | −0.674213 | − | 0.738537i | \(-0.735517\pi\) | ||||
−0.674213 | + | 0.738537i | \(0.735517\pi\) | |||||||
\(968\) | −5.75304 | −0.184910 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 18.9507 | 0.608469 | ||||||||
\(971\) | 44.8246 | 1.43849 | 0.719244 | − | 0.694757i | \(-0.244488\pi\) | ||||
0.719244 | + | 0.694757i | \(0.244488\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −54.5880 | −1.75001 | ||||||||
\(974\) | −55.4562 | −1.77693 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −52.2075 | −1.67112 | ||||||||
\(977\) | 36.6672 | 1.17309 | 0.586544 | − | 0.809917i | \(-0.300488\pi\) | ||||
0.586544 | + | 0.809917i | \(0.300488\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.6799 | −0.565053 | ||||||||
\(980\) | −6.94937 | −0.221989 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.74614 | −0.0557217 | ||||||||
\(983\) | 43.4827 | 1.38688 | 0.693441 | − | 0.720513i | \(-0.256094\pi\) | ||||
0.693441 | + | 0.720513i | \(0.256094\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.86552 | −0.218754 | ||||||||
\(986\) | −6.24419 | −0.198856 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.74450 | −0.0554998 | ||||||||
\(989\) | 0.639762 | 0.0203433 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.85590 | −0.154253 | −0.0771263 | − | 0.997021i | \(-0.524574\pi\) | ||||
−0.0771263 | + | 0.997021i | \(0.524574\pi\) | |||||||
\(992\) | −5.78872 | −0.183792 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 67.7956 | 2.15034 | ||||||||
\(995\) | 37.8736 | 1.20067 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.2069 | −0.323257 | −0.161628 | − | 0.986852i | \(-0.551675\pi\) | ||||
−0.161628 | + | 0.986852i | \(0.551675\pi\) | |||||||
\(998\) | −1.57193 | −0.0497587 | ||||||||
\(999\) | 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 | 2151.2.a.j.1.6 | ✓ | 20 | |
3.2 | odd | 2 | 2151.2.a.k.1.15 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.2.a.j.1.6 | ✓ | 20 | 1.1 | even | 1 | trivial | |
2151.2.a.k.1.15 | yes | 20 | 3.2 | odd | 2 |