Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8024,2,Mod(1,8024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8024 = 2^{3} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8024.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: | \(64.0719625819\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 9 x^{17} - 2 x^{16} + 212 x^{15} - 289 x^{14} - 2094 x^{13} + 3933 x^{12} + 11326 x^{11} - 23166 x^{10} - 36429 x^{9} + 72042 x^{8} + 69272 x^{7} - 119982 x^{6} + \cdots + 1136 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.16635\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8024.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.16635 | −1.25074 | −0.625372 | − | 0.780327i | \(-0.715053\pi\) | ||||
−0.625372 | + | 0.780327i | \(0.715053\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.18635 | 1.42498 | 0.712490 | − | 0.701683i | \(-0.247568\pi\) | ||||
0.712490 | + | 0.701683i | \(0.247568\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.65768 | 0.626544 | 0.313272 | − | 0.949664i | \(-0.398575\pi\) | ||||
0.313272 | + | 0.949664i | \(0.398575\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.69308 | 0.564360 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.87664 | 0.565827 | 0.282914 | − | 0.959145i | \(-0.408699\pi\) | ||||
0.282914 | + | 0.959145i | \(0.408699\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.01378 | −0.281173 | −0.140587 | − | 0.990068i | \(-0.544899\pi\) | ||||
−0.140587 | + | 0.990068i | \(0.544899\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.90276 | −1.78228 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.11204 | −0.255120 | −0.127560 | − | 0.991831i | \(-0.540715\pi\) | ||||
−0.127560 | + | 0.991831i | \(0.540715\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.59111 | −0.783645 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.18438 | 0.246961 | 0.123481 | − | 0.992347i | \(-0.460594\pi\) | ||||
0.123481 | + | 0.992347i | \(0.460594\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.15283 | 1.03057 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.83125 | 0.544874 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.37401 | −1.36932 | −0.684659 | − | 0.728863i | \(-0.740049\pi\) | ||||
−0.684659 | + | 0.728863i | \(0.740049\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.6347 | 1.91005 | 0.955023 | − | 0.296533i | \(-0.0958305\pi\) | ||||
0.955023 | + | 0.296533i | \(0.0958305\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.06546 | −0.707705 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.28194 | 0.892811 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.75358 | 0.452686 | 0.226343 | − | 0.974048i | \(-0.427323\pi\) | ||||
0.226343 | + | 0.974048i | \(0.427323\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.19621 | 0.351675 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.46162 | −1.16531 | −0.582654 | − | 0.812720i | \(-0.697986\pi\) | ||||
−0.582654 | + | 0.812720i | \(0.697986\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.91216 | 0.596600 | 0.298300 | − | 0.954472i | \(-0.403580\pi\) | ||||
0.298300 | + | 0.954472i | \(0.403580\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.39475 | 0.804201 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.3554 | −1.51049 | −0.755245 | − | 0.655443i | \(-0.772482\pi\) | ||||
−0.755245 | + | 0.655443i | \(0.772482\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.25210 | −0.607443 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.16635 | −0.303350 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.85631 | 0.392345 | 0.196172 | − | 0.980569i | \(-0.437149\pi\) | ||||
0.196172 | + | 0.980569i | \(0.437149\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.97962 | 0.806292 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.40907 | 0.319090 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.465944 | 0.0596580 | 0.0298290 | − | 0.999555i | \(-0.490504\pi\) | ||||
0.0298290 | + | 0.999555i | \(0.490504\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.80658 | 0.353596 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.23027 | −0.400666 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.9041 | 1.57648 | 0.788241 | − | 0.615367i | \(-0.210992\pi\) | ||||
0.788241 | + | 0.615367i | \(0.210992\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.56579 | −0.308885 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.88814 | −0.342759 | −0.171379 | − | 0.985205i | \(-0.554822\pi\) | ||||
−0.171379 | + | 0.985205i | \(0.554822\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.4871 | 1.81263 | 0.906313 | − | 0.422606i | \(-0.138885\pi\) | ||||
0.906313 | + | 0.422606i | \(0.138885\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.1628 | −1.28897 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.11086 | 0.354515 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.3000 | 1.72139 | 0.860693 | − | 0.509125i | \(-0.170031\pi\) | ||||
0.860693 | + | 0.509125i | \(0.170031\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2127 | −1.24586 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.9680 | 1.53319 | 0.766595 | − | 0.642131i | \(-0.221949\pi\) | ||||
0.766595 | + | 0.642131i | \(0.221949\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.18635 | 0.345608 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.9747 | 1.71267 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.92874 | 0.840444 | 0.420222 | − | 0.907421i | \(-0.361952\pi\) | ||||
0.420222 | + | 0.907421i | \(0.361952\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.68053 | −0.176167 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −23.0385 | −2.38898 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.54336 | −0.363541 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.06172 | −0.818544 | −0.409272 | − | 0.912412i | \(-0.634217\pi\) | ||||
−0.409272 | + | 0.912412i | \(0.634217\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.17730 | 0.319330 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.969119 | 0.0964309 | 0.0482154 | − | 0.998837i | \(-0.484647\pi\) | ||||
0.0482154 | + | 0.998837i | \(0.484647\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.07840 | 0.894522 | 0.447261 | − | 0.894404i | \(-0.352400\pi\) | ||||
0.447261 | + | 0.894404i | \(0.352400\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.4425 | −1.11668 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.0608 | −1.26264 | −0.631319 | − | 0.775523i | \(-0.717486\pi\) | ||||
−0.631319 | + | 0.775523i | \(0.717486\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.47445 | 0.428575 | 0.214287 | − | 0.976771i | \(-0.431257\pi\) | ||||
0.214287 | + | 0.976771i | \(0.431257\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.96523 | −0.566195 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.268210 | −0.0252311 | −0.0126156 | − | 0.999920i | \(-0.504016\pi\) | ||||
−0.0126156 | + | 0.999920i | \(0.504016\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.77386 | 0.351914 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.71642 | −0.158683 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.65768 | 0.151959 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.47823 | −0.679839 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.1645 | 1.45750 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.486961 | 0.0435551 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.7994 | 1.22450 | 0.612250 | − | 0.790665i | \(-0.290265\pi\) | ||||
0.612250 | + | 0.790665i | \(0.290265\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.47513 | −0.746193 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.52266 | 0.744628 | 0.372314 | − | 0.928107i | \(-0.378564\pi\) | ||||
0.372314 | + | 0.928107i | \(0.378564\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.84341 | −0.159844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.02135 | 0.776434 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.0419670 | −0.00358548 | −0.00179274 | − | 0.999998i | \(-0.500571\pi\) | ||||
−0.00179274 | + | 0.999998i | \(0.500571\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.72151 | −0.230835 | −0.115418 | − | 0.993317i | \(-0.536821\pi\) | ||||
−0.115418 | + | 0.993317i | \(0.536821\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22.4334 | 1.88924 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.90250 | −0.159095 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −23.4962 | −1.95125 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.21155 | 0.759756 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.17409 | 0.0961853 | 0.0480926 | − | 0.998843i | \(-0.484686\pi\) | ||||
0.0480926 | + | 0.998843i | \(0.484686\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.63061 | 0.539591 | 0.269796 | − | 0.962918i | \(-0.413044\pi\) | ||||
0.269796 | + | 0.962918i | \(0.413044\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.69308 | 0.136877 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 33.8858 | 2.72177 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0668 | 0.883231 | 0.441615 | − | 0.897204i | \(-0.354406\pi\) | ||||
0.441615 | + | 0.897204i | \(0.354406\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.18778 | −0.490723 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.96333 | 0.154732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.3442 | −1.04520 | −0.522599 | − | 0.852579i | \(-0.675038\pi\) | ||||
−0.522599 | + | 0.852579i | \(0.675038\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.9540 | −1.00846 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.6402 | −1.59719 | −0.798594 | − | 0.601871i | \(-0.794422\pi\) | ||||
−0.798594 | + | 0.601871i | \(0.794422\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.9722 | −0.920942 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.88278 | −0.143980 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.23972 | 0.246312 | 0.123156 | − | 0.992387i | \(-0.460699\pi\) | ||||
0.123156 | + | 0.992387i | \(0.460699\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.54173 | 0.645694 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.16635 | 0.162833 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.54149 | 0.488934 | 0.244467 | − | 0.969658i | \(-0.421387\pi\) | ||||
0.244467 | + | 0.969658i | \(0.421387\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.11871 | −0.454800 | −0.227400 | − | 0.973801i | \(-0.573022\pi\) | ||||
−0.227400 | + | 0.973801i | \(0.573022\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.00940 | −0.0746169 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.77388 | 0.645069 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.87664 | 0.137233 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.69330 | 0.341387 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.1982 | 1.60620 | 0.803101 | − | 0.595842i | \(-0.203182\pi\) | ||||
0.803101 | + | 0.595842i | \(0.203182\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.9317 | 1.14679 | 0.573394 | − | 0.819280i | \(-0.305627\pi\) | ||||
0.573394 | + | 0.819280i | \(0.305627\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.99790 | 0.501130 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.5410 | −1.10725 | −0.553627 | − | 0.832765i | \(-0.686757\pi\) | ||||
−0.553627 | + | 0.832765i | \(0.686757\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.59991 | −0.255191 | −0.127596 | − | 0.991826i | \(-0.540726\pi\) | ||||
−0.127596 | + | 0.991826i | \(0.540726\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −27.9547 | −1.97178 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.2237 | −0.857938 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −23.7753 | −1.66054 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.00526 | 0.139375 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.08690 | −0.144354 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.31397 | −0.572357 | −0.286179 | − | 0.958176i | \(-0.592385\pi\) | ||||
−0.286179 | + | 0.958176i | \(0.592385\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.25672 | 0.428703 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.4655 | 0.850142 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.6289 | 1.19673 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −33.5505 | −2.26713 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.01378 | −0.0681945 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.3942 | −0.696049 | −0.348025 | − | 0.937485i | \(-0.613147\pi\) | ||||
−0.348025 | + | 0.937485i | \(0.613147\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.72415 | 0.581610 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.78914 | −0.384239 | −0.192119 | − | 0.981372i | \(-0.561536\pi\) | ||||
−0.192119 | + | 0.981372i | \(0.561536\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.4176 | 0.820577 | 0.410288 | − | 0.911956i | \(-0.365428\pi\) | ||||
0.410288 | + | 0.911956i | \(0.365428\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.73922 | −0.443408 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.27800 | 0.476798 | 0.238399 | − | 0.971167i | \(-0.423377\pi\) | ||||
0.238399 | + | 0.971167i | \(0.423377\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −32.9959 | −2.15242 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −33.1452 | −2.15301 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.8762 | −1.09163 | −0.545816 | − | 0.837905i | \(-0.683780\pi\) | ||||
−0.545816 | + | 0.837905i | \(0.683780\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.98035 | −0.642891 | −0.321445 | − | 0.946928i | \(-0.604169\pi\) | ||||
−0.321445 | + | 0.946928i | \(0.604169\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.7970 | 1.01338 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.5487 | −0.865594 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.12737 | 0.0717329 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −30.2597 | −1.91763 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.39332 | 0.466662 | 0.233331 | − | 0.972397i | \(-0.425037\pi\) | ||||
0.233331 | + | 0.972397i | \(0.425037\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.22266 | 0.139737 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.90276 | −0.432267 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.7605 | −1.54452 | −0.772260 | − | 0.635307i | \(-0.780874\pi\) | ||||
−0.772260 | + | 0.635307i | \(0.780874\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.56456 | 0.283628 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.4848 | −0.772789 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.12000 | 0.500701 | 0.250350 | − | 0.968155i | \(-0.419454\pi\) | ||||
0.250350 | + | 0.968155i | \(0.419454\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.10121 | 0.559083 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.1764 | −1.05118 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.7149 | 1.56787 | 0.783933 | − | 0.620845i | \(-0.213210\pi\) | ||||
0.783933 | + | 0.620845i | \(0.213210\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.9557 | −1.15147 | −0.575737 | − | 0.817635i | \(-0.695285\pi\) | ||||
−0.575737 | + | 0.817635i | \(0.695285\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.64061 | 0.220340 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.66999 | 0.583122 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.5029 | 0.751227 | 0.375613 | − | 0.926776i | \(-0.377432\pi\) | ||||
0.375613 | + | 0.926776i | \(0.377432\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18.0054 | 1.07795 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.7899 | 1.65781 | 0.828904 | − | 0.559391i | \(-0.188965\pi\) | ||||
0.828904 | + | 0.559391i | \(0.188965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.1837 | −1.31868 | −0.659342 | − | 0.751843i | \(-0.729165\pi\) | ||||
−0.659342 | + | 0.751843i | \(0.729165\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.67616 | 0.454696 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.3690 | −0.730117 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.4645 | 1.02379 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.8763 | 0.810660 | 0.405330 | − | 0.914170i | \(-0.367157\pi\) | ||||
0.405330 | + | 0.914170i | \(0.367157\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.18635 | −0.185516 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.31322 | 0.308305 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.20071 | −0.0694388 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.48511 | 0.373796 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.09945 | −0.120610 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.48466 | 0.0850114 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.1804 | 1.43712 | 0.718559 | − | 0.695466i | \(-0.244802\pi\) | ||||
0.718559 | + | 0.695466i | \(0.244802\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.6670 | −1.11882 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.2728 | 1.43309 | 0.716544 | − | 0.697542i | \(-0.245723\pi\) | ||||
0.716544 | + | 0.697542i | \(0.245723\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.6955 | −1.67849 | −0.839245 | − | 0.543753i | \(-0.817003\pi\) | ||||
−0.839245 | + | 0.543753i | \(0.817003\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.94276 | 0.503867 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.8039 | −0.943801 | −0.471901 | − | 0.881652i | \(-0.656432\pi\) | ||||
−0.471901 | + | 0.881652i | \(0.656432\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.8383 | −0.774798 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 28.2944 | 1.57924 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.11204 | −0.0618757 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.22385 | −0.289767 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.69323 | −0.536037 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.1659 | −0.946388 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.80132 | 0.428799 | 0.214400 | − | 0.976746i | \(-0.431221\pi\) | ||||
0.214400 | + | 0.976746i | \(0.431221\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.66204 | 0.255478 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 41.1169 | 2.24645 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.82641 | 0.317385 | 0.158692 | − | 0.987328i | \(-0.449272\pi\) | ||||
0.158692 | + | 0.987328i | \(0.449272\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.581038 | 0.0315577 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.9574 | 1.08076 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.6524 | −1.00713 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.17551 | −0.440155 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.6440 | 1.26928 | 0.634639 | − | 0.772809i | \(-0.281149\pi\) | ||||
0.634639 | + | 0.772809i | \(0.281149\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.6135 | −0.621659 | −0.310829 | − | 0.950466i | \(-0.600607\pi\) | ||||
−0.310829 | + | 0.950466i | \(0.600607\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.87027 | −0.153204 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.73008 | 0.411431 | 0.205715 | − | 0.978612i | \(-0.434048\pi\) | ||||
0.205715 | + | 0.978612i | \(0.434048\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.20262 | −0.488424 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.59111 | −0.190062 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.7309 | −1.56913 | −0.784567 | − | 0.620043i | \(-0.787115\pi\) | ||||
−0.784567 | + | 0.620043i | \(0.787115\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7634 | −0.934914 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.2005 | 0.850305 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 49.3473 | 2.58296 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.5954 | 0.866270 | 0.433135 | − | 0.901329i | \(-0.357407\pi\) | ||||
0.433135 | + | 0.901329i | \(0.357407\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.6331 | −0.657654 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.73485 | 0.245821 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.4901 | −0.646712 | −0.323356 | − | 0.946277i | \(-0.604811\pi\) | ||||
−0.323356 | + | 0.946277i | \(0.604811\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.05493 | −0.0544763 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.47565 | 0.385016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.41680 | 0.278242 | 0.139121 | − | 0.990275i | \(-0.455572\pi\) | ||||
0.139121 | + | 0.990275i | \(0.455572\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −29.8944 | −1.53153 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.6960 | −1.00642 | −0.503211 | − | 0.864164i | \(-0.667848\pi\) | ||||
−0.503211 | + | 0.864164i | \(0.667848\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.91229 | 0.505177 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.62361 | 0.336697 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.45402 | −0.479338 | −0.239669 | − | 0.970855i | \(-0.577039\pi\) | ||||
−0.239669 | + | 0.970855i | \(0.577039\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.18438 | 0.0598969 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.4631 | −0.931339 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 48.7512 | 2.45294 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.9285 | 1.80320 | 0.901600 | − | 0.432570i | \(-0.142393\pi\) | ||||
0.901600 | + | 0.432570i | \(0.142393\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.99347 | 0.199924 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.0663 | −0.802313 | −0.401156 | − | 0.916010i | \(-0.631392\pi\) | ||||
−0.401156 | + | 0.916010i | \(0.631392\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.7813 | −0.537053 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −35.7277 | −1.77532 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.16748 | 0.256142 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.1364 | 1.04513 | 0.522565 | − | 0.852599i | \(-0.324975\pi\) | ||||
0.522565 | + | 0.852599i | \(0.324975\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.0909153 | 0.00448452 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.65768 | −0.0815690 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 44.5070 | 2.18476 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.89574 | 0.288716 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.8210 | 1.55456 | 0.777278 | − | 0.629158i | \(-0.216600\pi\) | ||||
0.777278 | + | 0.629158i | \(0.216600\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.808973 | 0.0394269 | 0.0197135 | − | 0.999806i | \(-0.493725\pi\) | ||||
0.0197135 | + | 0.999806i | \(0.493725\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −17.5325 | −0.852460 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.15283 | 0.249949 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.772385 | 0.0373783 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.12149 | 0.198988 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.6050 | 1.37786 | 0.688928 | − | 0.724830i | \(-0.258082\pi\) | ||||
0.688928 | + | 0.724830i | \(0.258082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.4313 | 0.837696 | 0.418848 | − | 0.908056i | \(-0.362434\pi\) | ||||
0.418848 | + | 0.908056i | \(0.362434\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 50.9010 | 2.44052 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.31708 | −0.0630047 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.9819 | 1.71732 | 0.858661 | − | 0.512543i | \(-0.171297\pi\) | ||||
0.858661 | + | 0.512543i | \(0.171297\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.19915 | −0.342817 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.12059 | 0.243287 | 0.121643 | − | 0.992574i | \(-0.461184\pi\) | ||||
0.121643 | + | 0.992574i | \(0.461184\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.2637 | 1.19762 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.54349 | −0.120303 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.04482 | −0.426851 | −0.213426 | − | 0.976959i | \(-0.568462\pi\) | ||||
−0.213426 | + | 0.976959i | \(0.568462\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.0027 | −0.659363 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.3642 | −0.674891 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.35475 | −0.251035 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.05890 | 0.330202 | 0.165101 | − | 0.986277i | \(-0.447205\pi\) | ||||
0.165101 | + | 0.986277i | \(0.447205\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.83125 | 0.132151 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.8936 | 0.553939 | 0.276970 | − | 0.960879i | \(-0.410670\pi\) | ||||
0.276970 | + | 0.960879i | \(0.410670\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.55726 | 0.211794 | 0.105897 | − | 0.994377i | \(-0.466229\pi\) | ||||
0.105897 | + | 0.994377i | \(0.466229\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −73.4086 | −3.40424 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.00374 | −0.0464474 | −0.0232237 | − | 0.999730i | \(-0.507393\pi\) | ||||
−0.0232237 | + | 0.999730i | \(0.507393\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.3908 | 0.987735 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.9747 | −1.10470 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.34171 | 0.337572 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.73016 | −0.262918 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.83597 | 0.221424 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.8181 | −0.722749 | −0.361375 | − | 0.932421i | \(-0.617692\pi\) | ||||
−0.361375 | + | 0.932421i | \(0.617692\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.79154 | −0.127283 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.25326 | −0.193530 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −25.6875 | −1.16641 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.6728 | 1.75243 | 0.876215 | − | 0.481920i | \(-0.160060\pi\) | ||||
0.876215 | + | 0.481920i | \(0.160060\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 28.9082 | 1.30728 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.4063 | 1.91377 | 0.956885 | − | 0.290468i | \(-0.0938109\pi\) | ||||
0.956885 | + | 0.290468i | \(0.0938109\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.37401 | −0.332109 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.1240 | 0.455039 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.78760 | −0.214753 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.3674 | 1.26990 | 0.634950 | − | 0.772553i | \(-0.281020\pi\) | ||||
0.634950 | + | 0.772553i | \(0.281020\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 44.7140 | 1.99767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.7740 | −1.01544 | −0.507720 | − | 0.861522i | \(-0.669512\pi\) | ||||
−0.507720 | + | 0.861522i | \(0.669512\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.08795 | 0.137412 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.9361 | 1.15186 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.6639 | 1.00456 | 0.502280 | − | 0.864705i | \(-0.332495\pi\) | ||||
0.502280 | + | 0.864705i | \(0.332495\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.6726 | 1.13569 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.14847 | −0.139008 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.9270 | 1.27467 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.4333 | −0.854677 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.01838 | −0.308073 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.2146 | 0.797995 | 0.398998 | − | 0.916952i | \(-0.369358\pi\) | ||||
0.398998 | + | 0.916952i | \(0.369358\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.3071 | 1.89369 | 0.946843 | − | 0.321696i | \(-0.104253\pi\) | ||||
0.946843 | + | 0.321696i | \(0.104253\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.5044 | −0.807598 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.6347 | 0.463254 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.5972 | −0.939010 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.69308 | −0.0734734 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.56447 | 0.327653 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −41.6164 | −1.79923 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.1712 | −0.611531 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.97965 | −0.343708 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.2653 | −0.527328 | −0.263664 | − | 0.964615i | \(-0.584931\pi\) | ||||
−0.263664 | + | 0.964615i | \(0.584931\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.2553 | 0.568838 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.2572 | 0.610710 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.637254 | −0.0272470 | −0.0136235 | − | 0.999907i | \(-0.504337\pi\) | ||||
−0.0136235 | + | 0.999907i | \(0.504337\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.788880 | 0.0336686 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.20021 | 0.349341 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.3625 | 1.07852 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19.0073 | −0.806816 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.5516 | 0.701312 | 0.350656 | − | 0.936504i | \(-0.385959\pi\) | ||||
0.350656 | + | 0.936504i | \(0.385959\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.96609 | −0.167748 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.06546 | −0.171644 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.6047 | −0.868385 | −0.434193 | − | 0.900820i | \(-0.642966\pi\) | ||||
−0.434193 | + | 0.900820i | \(0.642966\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.854612 | −0.0359538 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.5871 | −0.780584 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.1979 | −0.511363 | −0.255682 | − | 0.966761i | \(-0.582300\pi\) | ||||
−0.255682 | + | 0.966761i | \(0.582300\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.85609 | 0.161372 | 0.0806862 | − | 0.996740i | \(-0.474289\pi\) | ||||
0.0806862 | + | 0.996740i | \(0.474289\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −48.0890 | −2.00895 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.10293 | 0.254510 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.8143 | 1.36608 | 0.683039 | − | 0.730382i | \(-0.260658\pi\) | ||||
0.683039 | + | 0.730382i | \(0.260658\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −34.5136 | −1.43434 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.1545 | 0.960610 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.36026 | 0.221999 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.46911 | −0.226120 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.7219 | −1.55695 | −0.778475 | − | 0.627676i | \(-0.784006\pi\) | ||||
−0.778475 | + | 0.627676i | \(0.784006\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.8262 | −0.487291 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 33.6674 | 1.38489 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.4049 | 1.12538 | 0.562692 | − | 0.826667i | \(-0.309766\pi\) | ||||
0.562692 | + | 0.826667i | \(0.309766\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.28194 | 0.216539 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.79868 | 0.319179 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.7537 | 1.62429 | 0.812146 | − | 0.583454i | \(-0.198299\pi\) | ||||
0.812146 | + | 0.583454i | \(0.198299\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.3539 | 1.31974 | 0.659872 | − | 0.751378i | \(-0.270610\pi\) | ||||
0.659872 | + | 0.751378i | \(0.270610\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.8476 | 0.889704 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23.8283 | −0.968757 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.0704 | −0.936398 | −0.468199 | − | 0.883623i | \(-0.655097\pi\) | ||||
−0.468199 | + | 0.883623i | \(0.655097\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 26.4809 | 1.07306 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.4981 | 0.424709 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.1921 | −1.30023 | −0.650113 | − | 0.759838i | \(-0.725278\pi\) | ||||
−0.650113 | + | 0.759838i | \(0.725278\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 51.5057 | 2.07691 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.1283 | 0.850594 | 0.425297 | − | 0.905054i | \(-0.360170\pi\) | ||||
0.425297 | + | 0.905054i | \(0.360170\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.58930 | 0.104073 | 0.0520365 | − | 0.998645i | \(-0.483429\pi\) | ||||
0.0520365 | + | 0.998645i | \(0.483429\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.35328 | 0.134563 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.1433 | 0.526575 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2125 | −0.968500 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.52096 | 0.180550 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.75358 | 0.109793 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.52022 | 0.259566 | 0.129783 | − | 0.991542i | \(-0.458572\pi\) | ||||
0.129783 | + | 0.991542i | \(0.458572\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.0110 | 0.715872 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 43.9697 | 1.74489 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.31071 | 0.170797 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.88985 | −0.193439 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.8628 | 1.10051 | 0.550257 | − | 0.834995i | \(-0.314530\pi\) | ||||
0.550257 | + | 0.834995i | \(0.314530\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.7812 | −0.858968 | −0.429484 | − | 0.903074i | \(-0.641305\pi\) | ||||
−0.429484 | + | 0.903074i | \(0.641305\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27.0047 | −1.06331 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.3676 | −1.07593 | −0.537966 | − | 0.842967i | \(-0.680807\pi\) | ||||
−0.537966 | + | 0.842967i | \(0.680807\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.87664 | −0.0736644 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −38.1904 | −1.49680 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.2041 | 0.712380 | 0.356190 | − | 0.934414i | \(-0.384076\pi\) | ||||
0.356190 | + | 0.934414i | \(0.384076\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.1562 | 1.06108 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 26.2209 | 1.02297 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.9510 | −1.01091 | −0.505454 | − | 0.862853i | \(-0.668675\pi\) | ||||
−0.505454 | + | 0.862853i | \(0.668675\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.9721 | −1.01020 | −0.505099 | − | 0.863061i | \(-0.668544\pi\) | ||||
−0.505099 | + | 0.863061i | \(0.668544\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.19621 | 0.0852938 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.87374 | −0.227774 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.73366 | −0.338169 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22.5176 | 0.870580 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.874408 | 0.0337561 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.9691 | 1.30941 | 0.654705 | − | 0.755884i | \(-0.272793\pi\) | ||||
0.654705 | + | 0.755884i | \(0.272793\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.5889 | 0.561528 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.6022 | −0.714940 | −0.357470 | − | 0.933925i | \(-0.616361\pi\) | ||||
−0.357470 | + | 0.933925i | \(0.616361\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.3637 | −0.512853 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.5413 | 0.480584 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.5792 | −1.24661 | −0.623305 | − | 0.781979i | \(-0.714210\pi\) | ||||
−0.623305 | + | 0.781979i | \(0.714210\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.133722 | −0.00510924 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.9009 | −1.02633 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.89568 | −0.110317 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.9518 | 0.911168 | 0.455584 | − | 0.890193i | \(-0.349430\pi\) | ||||
0.455584 | + | 0.890193i | \(0.349430\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.26694 | 0.200074 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.67168 | −0.328936 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.46162 | −0.282629 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.7667 | −0.596352 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.2196 | 1.33022 | 0.665112 | − | 0.746743i | \(-0.268384\pi\) | ||||
0.665112 | + | 0.746743i | \(0.268384\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.06210 | −0.115489 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 71.4808 | 2.69212 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.60649 | 0.0604182 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.3697 | −1.36589 | −0.682947 | − | 0.730468i | \(-0.739302\pi\) | ||||
−0.682947 | + | 0.730468i | \(0.739302\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.9042 | 0.971482 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.5955 | 0.471707 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.06205 | −0.226708 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 36.5598 | 1.36535 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.15496 | −0.266835 | −0.133417 | − | 0.991060i | \(-0.542595\pi\) | ||||
−0.133417 | + | 0.991060i | \(0.542595\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.0491 | 0.560457 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.6209 | 0.804092 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −37.9970 | −1.41117 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.7924 | −1.17911 | −0.589557 | − | 0.807726i | \(-0.700698\pi\) | ||||
−0.589557 | + | 0.807726i | \(0.700698\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.583601 | −0.0216149 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.91216 | 0.144697 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.25692 | −0.0464255 | −0.0232127 | − | 0.999731i | \(-0.507390\pi\) | ||||
−0.0232127 | + | 0.999731i | \(0.507390\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 29.3512 | 1.08264 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.2162 | 0.892017 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.2812 | 1.33462 | 0.667312 | − | 0.744778i | \(-0.267445\pi\) | ||||
0.667312 | + | 0.744778i | \(0.267445\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.44228 | −0.0897194 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −47.4654 | −1.74134 | −0.870669 | − | 0.491869i | \(-0.836314\pi\) | ||||
−0.870669 | + | 0.491869i | \(0.836314\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.74106 | 0.137062 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23.6490 | 0.865271 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −21.6507 | −0.791098 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.05538 | −0.0385114 | −0.0192557 | − | 0.999815i | \(-0.506130\pi\) | ||||
−0.0192557 | + | 0.999815i | \(0.506130\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.0165 | −0.583675 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.1274 | 0.768907 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.2820 | −0.882544 | −0.441272 | − | 0.897373i | \(-0.645473\pi\) | ||||
−0.441272 | + | 0.897373i | \(0.645473\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.81506 | −0.174776 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.2735 | −1.06116 | −0.530582 | − | 0.847633i | \(-0.678027\pi\) | ||||
−0.530582 | + | 0.847633i | \(0.678027\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.41720 | 0.268521 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.39475 | 0.195047 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.01378 | 0.0366056 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.3600 | −0.373592 | −0.186796 | − | 0.982399i | \(-0.559810\pi\) | ||||
−0.186796 | + | 0.982399i | \(0.559810\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 53.6400 | 1.93180 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.4009 | −0.877638 | −0.438819 | − | 0.898576i | \(-0.644603\pi\) | ||||
−0.438819 | + | 0.898576i | \(0.644603\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 54.7987 | 1.96843 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.88843 | −0.354746 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.29763 | 0.297293 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.41999 | −0.193942 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.8776 | −0.746106 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 35.2629 | 1.25859 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.0275 | −1.46247 | −0.731237 | − | 0.682124i | \(-0.761057\pi\) | ||||
−0.731237 | + | 0.682124i | \(0.761057\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −17.5908 | −0.626249 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.444607 | −0.0158084 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.472366 | −0.0167742 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.7164 | −0.699270 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.4387 | 1.21988 | 0.609941 | − | 0.792447i | \(-0.291193\pi\) | ||||
0.609941 | + | 0.792447i | \(0.291193\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.3554 | −0.366348 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.4240 | 0.474313 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29.0636 | 1.02563 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.25585 | 0.220490 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −55.7076 | −1.96100 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.9459 | 0.701261 | 0.350631 | − | 0.936514i | \(-0.385967\pi\) | ||||
0.350631 | + | 0.936514i | \(0.385967\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.3658 | 1.52278 | 0.761390 | − | 0.648294i | \(-0.224517\pi\) | ||||
0.761390 | + | 0.648294i | \(0.224517\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 41.0646 | 1.44020 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −42.5193 | −1.48939 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.35049 | −0.152204 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.84527 | −0.0994217 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.5480 | −1.13593 | −0.567966 | − | 0.823052i | \(-0.692270\pi\) | ||||
−0.567966 | + | 0.823052i | \(0.692270\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.5485 | 0.367696 | 0.183848 | − | 0.982955i | \(-0.441145\pi\) | ||||
0.183848 | + | 0.982955i | \(0.441145\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −20.9486 | −0.729336 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.14650 | 0.0746411 | 0.0373206 | − | 0.999303i | \(-0.488118\pi\) | ||||
0.0373206 | + | 0.999303i | \(0.488118\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.4056 | −0.812911 | −0.406455 | − | 0.913671i | \(-0.633235\pi\) | ||||
−0.406455 | + | 0.913671i | \(0.633235\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.0857 | −0.939592 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.25210 | −0.147327 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −65.7669 | −2.27596 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30.1094 | 1.04073 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.6831 | −1.30096 | −0.650482 | − | 0.759521i | \(-0.725433\pi\) | ||||
−0.650482 | + | 0.759521i | \(0.725433\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.3760 | 0.875035 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −60.2027 | −2.07349 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −38.1478 | −1.31232 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.3965 | −0.425949 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 48.0577 | 1.64934 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.26130 | 0.111796 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.6183 | 1.01411 | 0.507055 | − | 0.861914i | \(-0.330734\pi\) | ||||
0.507055 | + | 0.861914i | \(0.330734\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.99919 | −0.205168 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −54.3763 | −1.85746 | −0.928730 | − | 0.370757i | \(-0.879098\pi\) | ||||
−0.928730 | + | 0.370757i | \(0.879098\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.71947 | −0.126907 | −0.0634534 | − | 0.997985i | \(-0.520211\pi\) | ||||
−0.0634534 | + | 0.997985i | \(0.520211\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26.7955 | 0.913189 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.22578 | 0.143847 | 0.0719236 | − | 0.997410i | \(-0.477086\pi\) | ||||
0.0719236 | + | 0.997410i | \(0.477086\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.3229 | 0.350989 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.16635 | −0.0735732 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.7126 | 0.974007 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.0819 | −0.443264 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.6491 | −0.461954 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.807225 | 0.0272892 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.95400 | 0.0659820 | 0.0329910 | − | 0.999456i | \(-0.489497\pi\) | ||||
0.0329910 | + | 0.999456i | \(0.489497\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −30.0609 | −1.01393 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.4670 | 0.723241 | 0.361621 | − | 0.932325i | \(-0.382224\pi\) | ||||
0.361621 | + | 0.932325i | \(0.382224\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.8490 | 1.13911 | 0.569554 | − | 0.821954i | \(-0.307116\pi\) | ||||
0.569554 | + | 0.821954i | \(0.307116\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.90276 | 0.232034 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.6648 | −1.49970 | −0.749848 | − | 0.661610i | \(-0.769874\pi\) | ||||
−0.749848 | + | 0.661610i | \(0.769874\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.8750 | 0.767202 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.0422 | −0.704940 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.5156 | 0.385356 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.8435 | 0.696720 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.60116 | 0.0868502 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −78.4202 | −2.61546 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.85631 | 0.0951576 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.0490 | −0.467523 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.4964 | −0.648081 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.9524 | −0.596099 | −0.298049 | − | 0.954550i | \(-0.596336\pi\) | ||||
−0.298049 | + | 0.954550i | \(0.596336\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.64080 | 0.0544218 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.1198 | −1.06418 | −0.532089 | − | 0.846688i | \(-0.678593\pi\) | ||||
−0.532089 | + | 0.846688i | \(0.678593\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.2129 | 0.867521 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.21630 | −0.106327 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.1278 | 0.466542 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.11835 | −0.0698778 | −0.0349389 | − | 0.999389i | \(-0.511124\pi\) | ||||
−0.0349389 | + | 0.999389i | \(0.511124\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −54.5495 | −1.79747 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.92795 | 0.0963745 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.1887 | 0.466523 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.3705 | 0.504832 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.7331 | −1.13955 | −0.569777 | − | 0.821799i | \(-0.692971\pi\) | ||||
−0.569777 | + | 0.821799i | \(0.692971\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.72852 | 0.154971 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −54.7497 | −1.79243 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.97962 | 0.195555 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.39058 | 0.0454283 | 0.0227142 | − | 0.999742i | \(-0.492769\pi\) | ||||
0.0227142 | + | 0.999742i | \(0.492769\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 64.3309 | 2.09936 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.5529 | 1.06119 | 0.530597 | − | 0.847624i | \(-0.321968\pi\) | ||||
0.530597 | + | 0.847624i | \(0.321968\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.83742 | −0.287786 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.9545 | 0.486470 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.4737 | 1.54269 | 0.771343 | − | 0.636419i | \(-0.219585\pi\) | ||||
0.771343 | + | 0.636419i | \(0.219585\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.7006 | −0.509662 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 36.4032 | 1.18045 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.7290 | 0.671479 | 0.335740 | − | 0.941955i | \(-0.391014\pi\) | ||||
0.335740 | + | 0.941955i | \(0.391014\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 70.7311 | 2.28881 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29.9787 | 0.969074 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.0695678 | −0.00224646 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 82.0964 | 2.64827 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.1130 | −0.712583 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 50.7639 | 1.63415 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.4293 | −1.46091 | −0.730454 | − | 0.682962i | \(-0.760691\pi\) | ||||
−0.730454 | + | 0.682962i | \(0.760691\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.40907 | 0.0773906 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.3642 | 1.42371 | 0.711857 | − | 0.702324i | \(-0.247854\pi\) | ||||
0.711857 | + | 0.702324i | \(0.247854\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.51139 | −0.144628 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.3167 | 0.362425 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.1563 | 0.484892 | 0.242446 | − | 0.970165i | \(-0.422050\pi\) | ||||
0.242446 | + | 0.970165i | \(0.422050\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.8794 | 0.475546 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.57560 | 0.241870 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.1736 | 0.515859 | 0.257929 | − | 0.966164i | \(-0.416960\pi\) | ||||
0.257929 | + | 0.966164i | \(0.416960\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −49.5192 | −1.57781 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 37.1874 | 1.18369 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.63350 | 0.147337 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.8053 | 0.438539 | 0.219270 | − | 0.975664i | \(-0.429633\pi\) | ||||
0.219270 | + | 0.975664i | \(0.429633\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.9004 | −0.536318 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.4706 | −0.363642 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.2008 | −0.924798 | −0.462399 | − | 0.886672i | \(-0.653011\pi\) | ||||
−0.462399 | + | 0.886672i | \(0.653011\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.79608 | 0.246657 |
(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 | 8024.2.a.v.1.3 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8024.2.a.v.1.3 | ✓ | 18 | 1.1 | even | 1 | trivial |