Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4005,2,Mod(1,4005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4005, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4005 = 3^{2} \cdot 5 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4005.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: | \(31.9800860095\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 8x^{8} + 35x^{7} + 29x^{6} - 103x^{5} - 57x^{4} + 106x^{3} + 29x^{2} - 39x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1335) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.32759\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4005.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.32759 | −1.64585 | −0.822926 | − | 0.568149i | \(-0.807660\pi\) | ||||
−0.822926 | + | 0.568149i | \(0.807660\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.41766 | 1.70883 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.231668 | −0.0875624 | −0.0437812 | − | 0.999041i | \(-0.513940\pi\) | ||||
−0.0437812 | + | 0.999041i | \(0.513940\pi\) | |||||||
\(8\) | −3.29972 | −1.16663 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.32759 | 0.736047 | ||||||||
\(11\) | 3.13805 | 0.946157 | 0.473078 | − | 0.881020i | \(-0.343143\pi\) | ||||
0.473078 | + | 0.881020i | \(0.343143\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.17239 | 1.43456 | 0.717282 | − | 0.696783i | \(-0.245386\pi\) | ||||
0.717282 | + | 0.696783i | \(0.245386\pi\) | |||||||
\(14\) | 0.539228 | 0.144115 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.845067 | 0.211267 | ||||||||
\(17\) | 3.12793 | 0.758635 | 0.379318 | − | 0.925266i | \(-0.376159\pi\) | ||||
0.379318 | + | 0.925266i | \(0.376159\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.20035 | 1.88129 | 0.940645 | − | 0.339393i | \(-0.110222\pi\) | ||||
0.940645 | + | 0.339393i | \(0.110222\pi\) | |||||||
\(20\) | −3.41766 | −0.764211 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.30407 | −1.55723 | ||||||||
\(23\) | 2.60339 | 0.542844 | 0.271422 | − | 0.962460i | \(-0.412506\pi\) | ||||
0.271422 | + | 0.962460i | \(0.412506\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −12.0392 | −2.36108 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.791763 | −0.149629 | ||||||||
\(29\) | 1.75022 | 0.325008 | 0.162504 | − | 0.986708i | \(-0.448043\pi\) | ||||
0.162504 | + | 0.986708i | \(0.448043\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.4240 | 1.87220 | 0.936100 | − | 0.351734i | \(-0.114408\pi\) | ||||
0.936100 | + | 0.351734i | \(0.114408\pi\) | |||||||
\(32\) | 4.63247 | 0.818913 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.28054 | −1.24860 | ||||||||
\(35\) | 0.231668 | 0.0391591 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.0476589 | 0.00783508 | 0.00391754 | − | 0.999992i | \(-0.498753\pi\) | ||||
0.00391754 | + | 0.999992i | \(0.498753\pi\) | |||||||
\(38\) | −19.0870 | −3.09632 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.29972 | 0.521731 | ||||||||
\(41\) | 11.0892 | 1.73184 | 0.865919 | − | 0.500184i | \(-0.166734\pi\) | ||||
0.865919 | + | 0.500184i | \(0.166734\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.76699 | −0.879458 | −0.439729 | − | 0.898131i | \(-0.644925\pi\) | ||||
−0.439729 | + | 0.898131i | \(0.644925\pi\) | |||||||
\(44\) | 10.7248 | 1.61682 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.05961 | −0.893441 | ||||||||
\(47\) | 1.91824 | 0.279805 | 0.139902 | − | 0.990165i | \(-0.455321\pi\) | ||||
0.139902 | + | 0.990165i | \(0.455321\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.94633 | −0.992333 | ||||||||
\(50\) | −2.32759 | −0.329170 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 17.6775 | 2.45142 | ||||||||
\(53\) | 2.56217 | 0.351941 | 0.175971 | − | 0.984395i | \(-0.443694\pi\) | ||||
0.175971 | + | 0.984395i | \(0.443694\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.13805 | −0.423134 | ||||||||
\(56\) | 0.764441 | 0.102153 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.07379 | −0.534915 | ||||||||
\(59\) | 0.116362 | 0.0151490 | 0.00757452 | − | 0.999971i | \(-0.497589\pi\) | ||||
0.00757452 | + | 0.999971i | \(0.497589\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.140106 | −0.0179388 | −0.00896938 | − | 0.999960i | \(-0.502855\pi\) | ||||
−0.00896938 | + | 0.999960i | \(0.502855\pi\) | |||||||
\(62\) | −24.2627 | −3.08136 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.4726 | −1.55908 | ||||||||
\(65\) | −5.17239 | −0.641557 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.235930 | −0.0288235 | −0.0144117 | − | 0.999896i | \(-0.504588\pi\) | ||||
−0.0144117 | + | 0.999896i | \(0.504588\pi\) | |||||||
\(68\) | 10.6902 | 1.29638 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.539228 | −0.0644501 | ||||||||
\(71\) | 7.10782 | 0.843543 | 0.421771 | − | 0.906702i | \(-0.361409\pi\) | ||||
0.421771 | + | 0.906702i | \(0.361409\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.81061 | −1.03120 | −0.515602 | − | 0.856828i | \(-0.672432\pi\) | ||||
−0.515602 | + | 0.856828i | \(0.672432\pi\) | |||||||
\(74\) | −0.110930 | −0.0128954 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 28.0260 | 3.21480 | ||||||||
\(77\) | −0.726986 | −0.0828478 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.3149 | −1.16051 | −0.580256 | − | 0.814434i | \(-0.697047\pi\) | ||||
−0.580256 | + | 0.814434i | \(0.697047\pi\) | |||||||
\(80\) | −0.845067 | −0.0944814 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −25.8110 | −2.85035 | ||||||||
\(83\) | −8.88288 | −0.975023 | −0.487511 | − | 0.873117i | \(-0.662095\pi\) | ||||
−0.487511 | + | 0.873117i | \(0.662095\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.12793 | −0.339272 | ||||||||
\(86\) | 13.4232 | 1.44746 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.3547 | −1.10381 | ||||||||
\(89\) | −1.00000 | −0.106000 | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.19828 | −0.125614 | ||||||||
\(92\) | 8.89749 | 0.927627 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.46488 | −0.460517 | ||||||||
\(95\) | −8.20035 | −0.841338 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.8901 | 1.81647 | 0.908233 | − | 0.418464i | \(-0.137431\pi\) | ||||
0.908233 | + | 0.418464i | \(0.137431\pi\) | |||||||
\(98\) | 16.1682 | 1.63323 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.41766 | 0.341766 | ||||||||
\(101\) | −4.87170 | −0.484752 | −0.242376 | − | 0.970182i | \(-0.577927\pi\) | ||||
−0.242376 | + | 0.970182i | \(0.577927\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.5885 | −1.63451 | −0.817255 | − | 0.576276i | \(-0.804505\pi\) | ||||
−0.817255 | + | 0.576276i | \(0.804505\pi\) | |||||||
\(104\) | −17.0675 | −1.67360 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.96367 | −0.579243 | ||||||||
\(107\) | 14.3574 | 1.38798 | 0.693990 | − | 0.719985i | \(-0.255851\pi\) | ||||
0.693990 | + | 0.719985i | \(0.255851\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.7030 | 1.40829 | 0.704144 | − | 0.710057i | \(-0.251331\pi\) | ||||
0.704144 | + | 0.710057i | \(0.251331\pi\) | |||||||
\(110\) | 7.30407 | 0.696416 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.195775 | −0.0184990 | ||||||||
\(113\) | 1.84866 | 0.173907 | 0.0869535 | − | 0.996212i | \(-0.472287\pi\) | ||||
0.0869535 | + | 0.996212i | \(0.472287\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.60339 | −0.242767 | ||||||||
\(116\) | 5.98166 | 0.555383 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.270843 | −0.0249331 | ||||||||
\(119\) | −0.724643 | −0.0664279 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.15266 | −0.104788 | ||||||||
\(122\) | 0.326109 | 0.0295245 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 35.6255 | 3.19927 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.26036 | −0.289311 | −0.144655 | − | 0.989482i | \(-0.546207\pi\) | ||||
−0.144655 | + | 0.989482i | \(0.546207\pi\) | |||||||
\(128\) | 19.7661 | 1.74710 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.0392 | 1.05591 | ||||||||
\(131\) | −6.51671 | −0.569368 | −0.284684 | − | 0.958621i | \(-0.591889\pi\) | ||||
−0.284684 | + | 0.958621i | \(0.591889\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.89976 | −0.164730 | ||||||||
\(134\) | 0.549148 | 0.0474392 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.3213 | −0.885045 | ||||||||
\(137\) | −14.5049 | −1.23924 | −0.619619 | − | 0.784902i | \(-0.712713\pi\) | ||||
−0.619619 | + | 0.784902i | \(0.712713\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.18687 | −0.694401 | −0.347201 | − | 0.937791i | \(-0.612868\pi\) | ||||
−0.347201 | + | 0.937791i | \(0.612868\pi\) | |||||||
\(140\) | 0.791763 | 0.0669162 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.5441 | −1.38835 | ||||||||
\(143\) | 16.2312 | 1.35732 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.75022 | −0.145348 | ||||||||
\(146\) | 20.5074 | 1.69721 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.162882 | 0.0133888 | ||||||||
\(149\) | 2.00547 | 0.164295 | 0.0821474 | − | 0.996620i | \(-0.473822\pi\) | ||||
0.0821474 | + | 0.996620i | \(0.473822\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.5216 | 1.67002 | 0.835012 | − | 0.550232i | \(-0.185461\pi\) | ||||
0.835012 | + | 0.550232i | \(0.185461\pi\) | |||||||
\(152\) | −27.0589 | −2.19476 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.69212 | 0.136355 | ||||||||
\(155\) | −10.4240 | −0.837273 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.79244 | 0.382478 | 0.191239 | − | 0.981543i | \(-0.438749\pi\) | ||||
0.191239 | + | 0.981543i | \(0.438749\pi\) | |||||||
\(158\) | 24.0087 | 1.91003 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.63247 | −0.366229 | ||||||||
\(161\) | −0.603123 | −0.0475327 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.4650 | −0.819681 | −0.409841 | − | 0.912157i | \(-0.634416\pi\) | ||||
−0.409841 | + | 0.912157i | \(0.634416\pi\) | |||||||
\(164\) | 37.8990 | 2.95941 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 20.6757 | 1.60474 | ||||||||
\(167\) | −17.8728 | −1.38304 | −0.691519 | − | 0.722358i | \(-0.743058\pi\) | ||||
−0.691519 | + | 0.722358i | \(0.743058\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.7537 | 1.05797 | ||||||||
\(170\) | 7.28054 | 0.558392 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −19.7096 | −1.50284 | ||||||||
\(173\) | −17.7804 | −1.35182 | −0.675909 | − | 0.736985i | \(-0.736249\pi\) | ||||
−0.675909 | + | 0.736985i | \(0.736249\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.231668 | −0.0175125 | ||||||||
\(176\) | 2.65186 | 0.199891 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.32759 | 0.174460 | ||||||||
\(179\) | 17.8343 | 1.33300 | 0.666500 | − | 0.745505i | \(-0.267791\pi\) | ||||
0.666500 | + | 0.745505i | \(0.267791\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.3953 | 0.921332 | 0.460666 | − | 0.887574i | \(-0.347611\pi\) | ||||
0.460666 | + | 0.887574i | \(0.347611\pi\) | |||||||
\(182\) | 2.78910 | 0.206742 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.59045 | −0.633296 | ||||||||
\(185\) | −0.0476589 | −0.00350395 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.81560 | 0.717788 | ||||||||
\(188\) | 6.55590 | 0.478138 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 19.0870 | 1.38472 | ||||||||
\(191\) | 2.95826 | 0.214052 | 0.107026 | − | 0.994256i | \(-0.465867\pi\) | ||||
0.107026 | + | 0.994256i | \(0.465867\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.8981 | −1.21635 | −0.608177 | − | 0.793801i | \(-0.708099\pi\) | ||||
−0.608177 | + | 0.793801i | \(0.708099\pi\) | |||||||
\(194\) | −41.6408 | −2.98964 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −23.7402 | −1.69573 | ||||||||
\(197\) | −21.3318 | −1.51983 | −0.759915 | − | 0.650022i | \(-0.774760\pi\) | ||||
−0.759915 | + | 0.650022i | \(0.774760\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.6380 | −1.39210 | −0.696051 | − | 0.717993i | \(-0.745061\pi\) | ||||
−0.696051 | + | 0.717993i | \(0.745061\pi\) | |||||||
\(200\) | −3.29972 | −0.233325 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.3393 | 0.797831 | ||||||||
\(203\) | −0.405471 | −0.0284585 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.0892 | −0.774501 | ||||||||
\(206\) | 38.6111 | 2.69016 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.37102 | 0.303076 | ||||||||
\(209\) | 25.7331 | 1.77999 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.32091 | −0.159778 | −0.0798889 | − | 0.996804i | \(-0.525457\pi\) | ||||
−0.0798889 | + | 0.996804i | \(0.525457\pi\) | |||||||
\(212\) | 8.75662 | 0.601407 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −33.4180 | −2.28441 | ||||||||
\(215\) | 5.76699 | 0.393306 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.41490 | −0.163934 | ||||||||
\(218\) | −34.2224 | −2.31783 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.7248 | −0.723064 | ||||||||
\(221\) | 16.1789 | 1.08831 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.41824 | −0.429797 | −0.214899 | − | 0.976636i | \(-0.568942\pi\) | ||||
−0.214899 | + | 0.976636i | \(0.568942\pi\) | |||||||
\(224\) | −1.07320 | −0.0717060 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.30291 | −0.286225 | ||||||||
\(227\) | −9.48723 | −0.629690 | −0.314845 | − | 0.949143i | \(-0.601953\pi\) | ||||
−0.314845 | + | 0.949143i | \(0.601953\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.9079 | 1.97637 | 0.988185 | − | 0.153263i | \(-0.0489781\pi\) | ||||
0.988185 | + | 0.153263i | \(0.0489781\pi\) | |||||||
\(230\) | 6.05961 | 0.399559 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.77524 | −0.379163 | ||||||||
\(233\) | −18.6116 | −1.21929 | −0.609643 | − | 0.792676i | \(-0.708687\pi\) | ||||
−0.609643 | + | 0.792676i | \(0.708687\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.91824 | −0.125132 | ||||||||
\(236\) | 0.397686 | 0.0258871 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.68667 | 0.109331 | ||||||||
\(239\) | 7.65622 | 0.495240 | 0.247620 | − | 0.968857i | \(-0.420352\pi\) | ||||
0.247620 | + | 0.968857i | \(0.420352\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.09143 | 0.585631 | 0.292815 | − | 0.956169i | \(-0.405408\pi\) | ||||
0.292815 | + | 0.956169i | \(0.405408\pi\) | |||||||
\(242\) | 2.68292 | 0.172465 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.478835 | −0.0306543 | ||||||||
\(245\) | 6.94633 | 0.443785 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 42.4154 | 2.69883 | ||||||||
\(248\) | −34.3962 | −2.18416 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.32759 | 0.147209 | ||||||||
\(251\) | −23.8649 | −1.50634 | −0.753171 | − | 0.657825i | \(-0.771477\pi\) | ||||
−0.753171 | + | 0.657825i | \(0.771477\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.16955 | 0.513615 | ||||||||
\(254\) | 7.58878 | 0.476162 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −21.0622 | −1.31639 | ||||||||
\(257\) | 17.8544 | 1.11373 | 0.556863 | − | 0.830605i | \(-0.312005\pi\) | ||||
0.556863 | + | 0.830605i | \(0.312005\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.0110411 | −0.000686058 0 | ||||||||
\(260\) | −17.6775 | −1.09631 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.1682 | 0.937095 | ||||||||
\(263\) | 6.89818 | 0.425360 | 0.212680 | − | 0.977122i | \(-0.431781\pi\) | ||||
0.212680 | + | 0.977122i | \(0.431781\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.56217 | −0.157393 | ||||||||
\(266\) | 4.42186 | 0.271122 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.806329 | −0.0492544 | ||||||||
\(269\) | −11.5710 | −0.705495 | −0.352747 | − | 0.935719i | \(-0.614753\pi\) | ||||
−0.352747 | + | 0.935719i | \(0.614753\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.6367 | −1.67881 | −0.839406 | − | 0.543504i | \(-0.817097\pi\) | ||||
−0.839406 | + | 0.543504i | \(0.817097\pi\) | |||||||
\(272\) | 2.64331 | 0.160274 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 33.7614 | 2.03960 | ||||||||
\(275\) | 3.13805 | 0.189231 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.98870 | −0.479995 | −0.239997 | − | 0.970774i | \(-0.577147\pi\) | ||||
−0.239997 | + | 0.970774i | \(0.577147\pi\) | |||||||
\(278\) | 19.0556 | 1.14288 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.764441 | −0.0456841 | ||||||||
\(281\) | −16.6642 | −0.994104 | −0.497052 | − | 0.867721i | \(-0.665584\pi\) | ||||
−0.497052 | + | 0.867721i | \(0.665584\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.0186 | −0.595541 | −0.297771 | − | 0.954637i | \(-0.596243\pi\) | ||||
−0.297771 | + | 0.954637i | \(0.596243\pi\) | |||||||
\(284\) | 24.2921 | 1.44147 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −37.7795 | −2.23395 | ||||||||
\(287\) | −2.56901 | −0.151644 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.21603 | −0.424472 | ||||||||
\(290\) | 4.07379 | 0.239221 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −30.1116 | −1.76215 | ||||||||
\(293\) | 0.952327 | 0.0556356 | 0.0278178 | − | 0.999613i | \(-0.491144\pi\) | ||||
0.0278178 | + | 0.999613i | \(0.491144\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.116362 | −0.00677486 | ||||||||
\(296\) | −0.157261 | −0.00914061 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.66791 | −0.270405 | ||||||||
\(299\) | 13.4657 | 0.778744 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.33603 | 0.0770075 | ||||||||
\(302\) | −47.7658 | −2.74861 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.92984 | 0.397454 | ||||||||
\(305\) | 0.140106 | 0.00802245 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.68360 | 0.153161 | 0.0765806 | − | 0.997063i | \(-0.475600\pi\) | ||||
0.0765806 | + | 0.997063i | \(0.475600\pi\) | |||||||
\(308\) | −2.48459 | −0.141573 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 24.2627 | 1.37803 | ||||||||
\(311\) | 24.5758 | 1.39357 | 0.696783 | − | 0.717282i | \(-0.254614\pi\) | ||||
0.696783 | + | 0.717282i | \(0.254614\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.9809 | −0.677199 | −0.338599 | − | 0.940931i | \(-0.609953\pi\) | ||||
−0.338599 | + | 0.940931i | \(0.609953\pi\) | |||||||
\(314\) | −11.1548 | −0.629503 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −35.2526 | −1.98312 | ||||||||
\(317\) | −27.1918 | −1.52725 | −0.763623 | − | 0.645663i | \(-0.776581\pi\) | ||||
−0.763623 | + | 0.645663i | \(0.776581\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.49228 | 0.307509 | ||||||||
\(320\) | 12.4726 | 0.697240 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.40382 | 0.0782318 | ||||||||
\(323\) | 25.6501 | 1.42721 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.17239 | 0.286913 | ||||||||
\(326\) | 24.3582 | 1.34907 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −36.5912 | −2.02041 | ||||||||
\(329\) | −0.444396 | −0.0245004 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.1373 | 1.65650 | 0.828248 | − | 0.560361i | \(-0.189338\pi\) | ||||
0.828248 | + | 0.560361i | \(0.189338\pi\) | |||||||
\(332\) | −30.3586 | −1.66615 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 41.6005 | 2.27628 | ||||||||
\(335\) | 0.235930 | 0.0128903 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.13493 | 0.116297 | 0.0581486 | − | 0.998308i | \(-0.481480\pi\) | ||||
0.0581486 | + | 0.998308i | \(0.481480\pi\) | |||||||
\(338\) | −32.0128 | −1.74127 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.6902 | −0.579758 | ||||||||
\(341\) | 32.7109 | 1.77139 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.23092 | 0.174453 | ||||||||
\(344\) | 19.0295 | 1.02600 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 41.3854 | 2.22489 | ||||||||
\(347\) | 33.8723 | 1.81836 | 0.909180 | − | 0.416403i | \(-0.136710\pi\) | ||||
0.909180 | + | 0.416403i | \(0.136710\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.9187 | −0.959168 | −0.479584 | − | 0.877496i | \(-0.659212\pi\) | ||||
−0.479584 | + | 0.877496i | \(0.659212\pi\) | |||||||
\(350\) | 0.539228 | 0.0288230 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 14.5369 | 0.774820 | ||||||||
\(353\) | 17.0627 | 0.908158 | 0.454079 | − | 0.890961i | \(-0.349968\pi\) | ||||
0.454079 | + | 0.890961i | \(0.349968\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.10782 | −0.377244 | ||||||||
\(356\) | −3.41766 | −0.181135 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −41.5110 | −2.19392 | ||||||||
\(359\) | −35.0326 | −1.84895 | −0.924474 | − | 0.381245i | \(-0.875495\pi\) | ||||
−0.924474 | + | 0.381245i | \(0.875495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 48.2457 | 2.53925 | ||||||||
\(362\) | −28.8510 | −1.51638 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.09531 | −0.214653 | ||||||||
\(365\) | 8.81061 | 0.461168 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.12479 | 0.371911 | 0.185956 | − | 0.982558i | \(-0.440462\pi\) | ||||
0.185956 | + | 0.982558i | \(0.440462\pi\) | |||||||
\(368\) | 2.20004 | 0.114685 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.110930 | 0.00576699 | ||||||||
\(371\) | −0.593574 | −0.0308168 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.9155 | 1.23830 | 0.619148 | − | 0.785274i | \(-0.287478\pi\) | ||||
0.619148 | + | 0.785274i | \(0.287478\pi\) | |||||||
\(374\) | −22.8467 | −1.18137 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.32967 | −0.326428 | ||||||||
\(377\) | 9.05284 | 0.466245 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.25093 | 0.218355 | 0.109178 | − | 0.994022i | \(-0.465178\pi\) | ||||
0.109178 | + | 0.994022i | \(0.465178\pi\) | |||||||
\(380\) | −28.0260 | −1.43770 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.88560 | −0.352298 | ||||||||
\(383\) | 7.11909 | 0.363769 | 0.181884 | − | 0.983320i | \(-0.441780\pi\) | ||||
0.181884 | + | 0.983320i | \(0.441780\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.726986 | 0.0370506 | ||||||||
\(386\) | 39.3319 | 2.00194 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 61.1423 | 3.10403 | ||||||||
\(389\) | −22.6491 | −1.14835 | −0.574177 | − | 0.818731i | \(-0.694678\pi\) | ||||
−0.574177 | + | 0.818731i | \(0.694678\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.14323 | 0.411821 | ||||||||
\(392\) | 22.9209 | 1.15768 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 49.6517 | 2.50142 | ||||||||
\(395\) | 10.3149 | 0.518996 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.4196 | −1.12521 | −0.562605 | − | 0.826726i | \(-0.690201\pi\) | ||||
−0.562605 | + | 0.826726i | \(0.690201\pi\) | |||||||
\(398\) | 45.7092 | 2.29119 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.845067 | 0.0422534 | ||||||||
\(401\) | 28.6313 | 1.42978 | 0.714889 | − | 0.699238i | \(-0.246477\pi\) | ||||
0.714889 | + | 0.699238i | \(0.246477\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 53.9169 | 2.68579 | ||||||||
\(404\) | −16.6498 | −0.828359 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.943769 | 0.0468385 | ||||||||
\(407\) | 0.149556 | 0.00741321 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.5726 | 1.51172 | 0.755859 | − | 0.654734i | \(-0.227219\pi\) | ||||
0.755859 | + | 0.654734i | \(0.227219\pi\) | |||||||
\(410\) | 25.8110 | 1.27471 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −56.6937 | −2.79310 | ||||||||
\(413\) | −0.0269574 | −0.00132649 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.88288 | 0.436043 | ||||||||
\(416\) | 23.9610 | 1.17478 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −59.8960 | −2.92961 | ||||||||
\(419\) | −10.4624 | −0.511124 | −0.255562 | − | 0.966793i | \(-0.582260\pi\) | ||||
−0.255562 | + | 0.966793i | \(0.582260\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.28945 | −0.452740 | −0.226370 | − | 0.974041i | \(-0.572686\pi\) | ||||
−0.226370 | + | 0.974041i | \(0.572686\pi\) | |||||||
\(422\) | 5.40211 | 0.262970 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.45444 | −0.410584 | ||||||||
\(425\) | 3.12793 | 0.151727 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0324582 | 0.00157076 | ||||||||
\(428\) | 49.0686 | 2.37182 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.4232 | −0.647323 | ||||||||
\(431\) | 17.0955 | 0.823462 | 0.411731 | − | 0.911305i | \(-0.364924\pi\) | ||||
0.411731 | + | 0.911305i | \(0.364924\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.6947 | −0.994523 | −0.497261 | − | 0.867601i | \(-0.665661\pi\) | ||||
−0.497261 | + | 0.867601i | \(0.665661\pi\) | |||||||
\(434\) | 5.62090 | 0.269812 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 50.2497 | 2.40652 | ||||||||
\(437\) | 21.3487 | 1.02125 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.07115 | 0.0511230 | 0.0255615 | − | 0.999673i | \(-0.491863\pi\) | ||||
0.0255615 | + | 0.999673i | \(0.491863\pi\) | |||||||
\(440\) | 10.3547 | 0.493640 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −37.6578 | −1.79120 | ||||||||
\(443\) | 11.4820 | 0.545529 | 0.272764 | − | 0.962081i | \(-0.412062\pi\) | ||||
0.272764 | + | 0.962081i | \(0.412062\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.00000 | 0.0474045 | ||||||||
\(446\) | 14.9390 | 0.707383 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.88951 | 0.136517 | ||||||||
\(449\) | −13.8252 | −0.652451 | −0.326225 | − | 0.945292i | \(-0.605777\pi\) | ||||
−0.326225 | + | 0.945292i | \(0.605777\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.7983 | 1.63859 | ||||||||
\(452\) | 6.31808 | 0.297177 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.0824 | 1.03638 | ||||||||
\(455\) | 1.19828 | 0.0561762 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.7435 | 1.43812 | 0.719059 | − | 0.694949i | \(-0.244573\pi\) | ||||
0.719059 | + | 0.694949i | \(0.244573\pi\) | |||||||
\(458\) | −69.6133 | −3.25281 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.89749 | −0.414848 | ||||||||
\(461\) | 14.2580 | 0.664062 | 0.332031 | − | 0.943268i | \(-0.392266\pi\) | ||||
0.332031 | + | 0.943268i | \(0.392266\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.2904 | 1.77951 | 0.889753 | − | 0.456442i | \(-0.150876\pi\) | ||||
0.889753 | + | 0.456442i | \(0.150876\pi\) | |||||||
\(464\) | 1.47906 | 0.0686634 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 43.3201 | 2.00676 | ||||||||
\(467\) | −30.6489 | −1.41826 | −0.709132 | − | 0.705076i | \(-0.750913\pi\) | ||||
−0.709132 | + | 0.705076i | \(0.750913\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.0546576 | 0.00252385 | ||||||||
\(470\) | 4.46488 | 0.205949 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.383962 | −0.0176733 | ||||||||
\(473\) | −18.0971 | −0.832105 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.20035 | 0.376258 | ||||||||
\(476\) | −2.47658 | −0.113514 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.8205 | −0.815092 | ||||||||
\(479\) | −4.85526 | −0.221842 | −0.110921 | − | 0.993829i | \(-0.535380\pi\) | ||||
−0.110921 | + | 0.993829i | \(0.535380\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.246511 | 0.0112399 | ||||||||
\(482\) | −21.1611 | −0.963861 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.93941 | −0.179064 | ||||||||
\(485\) | −17.8901 | −0.812349 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.2097 | −1.50488 | −0.752438 | − | 0.658663i | \(-0.771122\pi\) | ||||
−0.752438 | + | 0.658663i | \(0.771122\pi\) | |||||||
\(488\) | 0.462311 | 0.0209278 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −16.1682 | −0.730404 | ||||||||
\(491\) | −17.7104 | −0.799260 | −0.399630 | − | 0.916677i | \(-0.630861\pi\) | ||||
−0.399630 | + | 0.916677i | \(0.630861\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.47458 | 0.246563 | ||||||||
\(494\) | −98.7256 | −4.44187 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.80895 | 0.395534 | ||||||||
\(497\) | −1.64666 | −0.0738626 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.20086 | 0.232823 | 0.116411 | − | 0.993201i | \(-0.462861\pi\) | ||||
0.116411 | + | 0.993201i | \(0.462861\pi\) | |||||||
\(500\) | −3.41766 | −0.152842 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 55.5477 | 2.47922 | ||||||||
\(503\) | 35.5133 | 1.58346 | 0.791729 | − | 0.610873i | \(-0.209181\pi\) | ||||
0.791729 | + | 0.610873i | \(0.209181\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.87170 | 0.216788 | ||||||||
\(506\) | −19.0153 | −0.845335 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.1428 | −0.494382 | ||||||||
\(509\) | −35.3342 | −1.56616 | −0.783081 | − | 0.621919i | \(-0.786353\pi\) | ||||
−0.783081 | + | 0.621919i | \(0.786353\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.04114 | 0.0902947 | ||||||||
\(512\) | 9.49172 | 0.419479 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −41.5576 | −1.83303 | ||||||||
\(515\) | 16.5885 | 0.730975 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.01954 | 0.264739 | ||||||||
\(518\) | 0.0256990 | 0.00112915 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 17.0675 | 0.748457 | ||||||||
\(521\) | 1.65866 | 0.0726674 | 0.0363337 | − | 0.999340i | \(-0.488432\pi\) | ||||
0.0363337 | + | 0.999340i | \(0.488432\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.5405 | 1.37917 | 0.689584 | − | 0.724205i | \(-0.257793\pi\) | ||||
0.689584 | + | 0.724205i | \(0.257793\pi\) | |||||||
\(524\) | −22.2719 | −0.972952 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.0561 | −0.700080 | ||||||||
\(527\) | 32.6055 | 1.42032 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.2224 | −0.705320 | ||||||||
\(530\) | 5.96367 | 0.259045 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.49273 | −0.281496 | ||||||||
\(533\) | 57.3576 | 2.48443 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.3574 | −0.620723 | ||||||||
\(536\) | 0.778504 | 0.0336263 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26.9324 | 1.16114 | ||||||||
\(539\) | −21.7979 | −0.938902 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.4402 | 1.22274 | 0.611369 | − | 0.791346i | \(-0.290619\pi\) | ||||
0.611369 | + | 0.791346i | \(0.290619\pi\) | |||||||
\(542\) | 64.3269 | 2.76308 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 14.4901 | 0.621257 | ||||||||
\(545\) | −14.7030 | −0.629806 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.21137 | −0.137308 | −0.0686541 | − | 0.997641i | \(-0.521870\pi\) | ||||
−0.0686541 | + | 0.997641i | \(0.521870\pi\) | |||||||
\(548\) | −49.5728 | −2.11765 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.30407 | −0.311447 | ||||||||
\(551\) | 14.3524 | 0.611434 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.38962 | 0.101617 | ||||||||
\(554\) | 18.5944 | 0.790000 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −27.9799 | −1.18661 | ||||||||
\(557\) | 7.74724 | 0.328261 | 0.164131 | − | 0.986439i | \(-0.447518\pi\) | ||||
0.164131 | + | 0.986439i | \(0.447518\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.8291 | −1.26164 | ||||||||
\(560\) | 0.195775 | 0.00827302 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 38.7874 | 1.63615 | ||||||||
\(563\) | −6.11227 | −0.257602 | −0.128801 | − | 0.991670i | \(-0.541113\pi\) | ||||
−0.128801 | + | 0.991670i | \(0.541113\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.84866 | −0.0777736 | ||||||||
\(566\) | 23.3190 | 0.980172 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −23.4538 | −0.984100 | ||||||||
\(569\) | −17.8784 | −0.749502 | −0.374751 | − | 0.927126i | \(-0.622272\pi\) | ||||
−0.374751 | + | 0.927126i | \(0.622272\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.88499 | −0.0788844 | −0.0394422 | − | 0.999222i | \(-0.512558\pi\) | ||||
−0.0394422 | + | 0.999222i | \(0.512558\pi\) | |||||||
\(572\) | 55.4727 | 2.31943 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.97959 | 0.249583 | ||||||||
\(575\) | 2.60339 | 0.108569 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.5466 | 0.855368 | 0.427684 | − | 0.903928i | \(-0.359330\pi\) | ||||
0.427684 | + | 0.903928i | \(0.359330\pi\) | |||||||
\(578\) | 16.7959 | 0.698619 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.98166 | −0.248375 | ||||||||
\(581\) | 2.05788 | 0.0853754 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.04021 | 0.332991 | ||||||||
\(584\) | 29.0725 | 1.20303 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.21662 | −0.0915679 | ||||||||
\(587\) | −14.3763 | −0.593372 | −0.296686 | − | 0.954975i | \(-0.595882\pi\) | ||||
−0.296686 | + | 0.954975i | \(0.595882\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 85.4802 | 3.52215 | ||||||||
\(590\) | 0.270843 | 0.0111504 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.0402750 | 0.00165529 | ||||||||
\(593\) | −4.67911 | −0.192148 | −0.0960741 | − | 0.995374i | \(-0.530629\pi\) | ||||
−0.0960741 | + | 0.995374i | \(0.530629\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.724643 | 0.0297075 | ||||||||
\(596\) | 6.85402 | 0.280752 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −31.3427 | −1.28170 | ||||||||
\(599\) | 38.8668 | 1.58806 | 0.794028 | − | 0.607881i | \(-0.207980\pi\) | ||||
0.794028 | + | 0.607881i | \(0.207980\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.2250 | 0.784202 | 0.392101 | − | 0.919922i | \(-0.371748\pi\) | ||||
0.392101 | + | 0.919922i | \(0.371748\pi\) | |||||||
\(602\) | −3.10972 | −0.126743 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 70.1358 | 2.85378 | ||||||||
\(605\) | 1.15266 | 0.0468624 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.77256 | −0.112535 | −0.0562673 | − | 0.998416i | \(-0.517920\pi\) | ||||
−0.0562673 | + | 0.998416i | \(0.517920\pi\) | |||||||
\(608\) | 37.9879 | 1.54061 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.326109 | −0.0132038 | ||||||||
\(611\) | 9.92191 | 0.401398 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.7952 | −1.04186 | −0.520930 | − | 0.853599i | \(-0.674415\pi\) | ||||
−0.520930 | + | 0.853599i | \(0.674415\pi\) | |||||||
\(614\) | −6.24631 | −0.252081 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.39885 | 0.0966524 | ||||||||
\(617\) | 6.65304 | 0.267841 | 0.133921 | − | 0.990992i | \(-0.457243\pi\) | ||||
0.133921 | + | 0.990992i | \(0.457243\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.4261 | −1.46409 | −0.732044 | − | 0.681258i | \(-0.761433\pi\) | ||||
−0.732044 | + | 0.681258i | \(0.761433\pi\) | |||||||
\(620\) | −35.6255 | −1.43076 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −57.2023 | −2.29360 | ||||||||
\(623\) | 0.231668 | 0.00928160 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 27.8865 | 1.11457 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.3789 | 0.653590 | ||||||||
\(629\) | 0.149074 | 0.00594397 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.4933 | −0.616780 | −0.308390 | − | 0.951260i | \(-0.599790\pi\) | ||||
−0.308390 | + | 0.951260i | \(0.599790\pi\) | |||||||
\(632\) | 34.0361 | 1.35388 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 63.2913 | 2.51362 | ||||||||
\(635\) | 3.26036 | 0.129384 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −35.9292 | −1.42356 | ||||||||
\(638\) | −12.7838 | −0.506114 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −19.7661 | −0.781325 | ||||||||
\(641\) | −21.3356 | −0.842704 | −0.421352 | − | 0.906897i | \(-0.638444\pi\) | ||||
−0.421352 | + | 0.906897i | \(0.638444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.08343 | 0.0821626 | 0.0410813 | − | 0.999156i | \(-0.486920\pi\) | ||||
0.0410813 | + | 0.999156i | \(0.486920\pi\) | |||||||
\(644\) | −2.06127 | −0.0812253 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −59.7029 | −2.34898 | ||||||||
\(647\) | −2.30024 | −0.0904318 | −0.0452159 | − | 0.998977i | \(-0.514398\pi\) | ||||
−0.0452159 | + | 0.998977i | \(0.514398\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.365149 | 0.0143334 | ||||||||
\(650\) | −12.0392 | −0.472216 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −35.7658 | −1.40070 | ||||||||
\(653\) | 23.5469 | 0.921463 | 0.460731 | − | 0.887540i | \(-0.347587\pi\) | ||||
0.460731 | + | 0.887540i | \(0.347587\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.51671 | 0.254629 | ||||||||
\(656\) | 9.37110 | 0.365880 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.03437 | 0.0403240 | ||||||||
\(659\) | −20.0639 | −0.781580 | −0.390790 | − | 0.920480i | \(-0.627798\pi\) | ||||
−0.390790 | + | 0.920480i | \(0.627798\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.43421 | 0.366948 | 0.183474 | − | 0.983025i | \(-0.441266\pi\) | ||||
0.183474 | + | 0.983025i | \(0.441266\pi\) | |||||||
\(662\) | −70.1472 | −2.72635 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 29.3110 | 1.13749 | ||||||||
\(665\) | 1.89976 | 0.0736696 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.55651 | 0.176429 | ||||||||
\(668\) | −61.0831 | −2.36338 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.549148 | −0.0212154 | ||||||||
\(671\) | −0.439660 | −0.0169729 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.9917 | −1.27173 | −0.635867 | − | 0.771798i | \(-0.719357\pi\) | ||||
−0.635867 | + | 0.771798i | \(0.719357\pi\) | |||||||
\(674\) | −4.96924 | −0.191408 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 47.0053 | 1.80790 | ||||||||
\(677\) | 15.0572 | 0.578695 | 0.289347 | − | 0.957224i | \(-0.406562\pi\) | ||||
0.289347 | + | 0.957224i | \(0.406562\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.14458 | −0.159054 | ||||||||
\(680\) | 10.3213 | 0.395804 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −76.1374 | −2.91545 | ||||||||
\(683\) | 42.2040 | 1.61489 | 0.807446 | − | 0.589942i | \(-0.200849\pi\) | ||||
0.807446 | + | 0.589942i | \(0.200849\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.5049 | 0.554204 | ||||||||
\(686\) | −7.52025 | −0.287125 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.87349 | −0.185800 | ||||||||
\(689\) | 13.2526 | 0.504882 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.3797 | 0.585073 | 0.292536 | − | 0.956254i | \(-0.405501\pi\) | ||||
0.292536 | + | 0.956254i | \(0.405501\pi\) | |||||||
\(692\) | −60.7672 | −2.31002 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −78.8407 | −2.99275 | ||||||||
\(695\) | 8.18687 | 0.310546 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.6862 | 1.31383 | ||||||||
\(698\) | 41.7074 | 1.57865 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.791763 | −0.0299258 | ||||||||
\(701\) | −18.5351 | −0.700063 | −0.350031 | − | 0.936738i | \(-0.613829\pi\) | ||||
−0.350031 | + | 0.936738i | \(0.613829\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.390820 | 0.0147400 | ||||||||
\(704\) | −39.1396 | −1.47513 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −39.7150 | −1.49469 | ||||||||
\(707\) | 1.12862 | 0.0424461 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.77286 | −0.216804 | −0.108402 | − | 0.994107i | \(-0.534573\pi\) | ||||
−0.108402 | + | 0.994107i | \(0.534573\pi\) | |||||||
\(710\) | 16.5441 | 0.620887 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.29972 | 0.123662 | ||||||||
\(713\) | 27.1376 | 1.01631 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.2312 | −0.607013 | ||||||||
\(716\) | 60.9516 | 2.27787 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 81.5413 | 3.04309 | ||||||||
\(719\) | 14.0660 | 0.524573 | 0.262287 | − | 0.964990i | \(-0.415523\pi\) | ||||
0.262287 | + | 0.964990i | \(0.415523\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.84302 | 0.143122 | ||||||||
\(722\) | −112.296 | −4.17923 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 42.3627 | 1.57440 | ||||||||
\(725\) | 1.75022 | 0.0650016 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.3160 | 0.716390 | 0.358195 | − | 0.933647i | \(-0.383392\pi\) | ||||
0.358195 | + | 0.933647i | \(0.383392\pi\) | |||||||
\(728\) | 3.95399 | 0.146545 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −20.5074 | −0.759015 | ||||||||
\(731\) | −18.0388 | −0.667188 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46.1230 | −1.70359 | −0.851795 | − | 0.523875i | \(-0.824486\pi\) | ||||
−0.851795 | + | 0.523875i | \(0.824486\pi\) | |||||||
\(734\) | −16.5836 | −0.612111 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.0601 | 0.444542 | ||||||||
\(737\) | −0.740360 | −0.0272715 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.81531 | −0.0667771 | −0.0333885 | − | 0.999442i | \(-0.510630\pi\) | ||||
−0.0333885 | + | 0.999442i | \(0.510630\pi\) | |||||||
\(740\) | −0.162882 | −0.00598766 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.38159 | 0.0507199 | ||||||||
\(743\) | −20.0513 | −0.735611 | −0.367805 | − | 0.929903i | \(-0.619891\pi\) | ||||
−0.367805 | + | 0.929903i | \(0.619891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.00547 | −0.0734749 | ||||||||
\(746\) | −55.6653 | −2.03805 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 33.5464 | 1.22658 | ||||||||
\(749\) | −3.32615 | −0.121535 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.4991 | 1.18591 | 0.592955 | − | 0.805235i | \(-0.297961\pi\) | ||||
0.592955 | + | 0.805235i | \(0.297961\pi\) | |||||||
\(752\) | 1.62104 | 0.0591134 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −21.0713 | −0.767370 | ||||||||
\(755\) | −20.5216 | −0.746857 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.19706 | −0.116199 | −0.0580995 | − | 0.998311i | \(-0.518504\pi\) | ||||
−0.0580995 | + | 0.998311i | \(0.518504\pi\) | |||||||
\(758\) | −9.89439 | −0.359381 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 27.0589 | 0.981528 | ||||||||
\(761\) | 1.78809 | 0.0648183 | 0.0324091 | − | 0.999475i | \(-0.489682\pi\) | ||||
0.0324091 | + | 0.999475i | \(0.489682\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.40621 | −0.123313 | ||||||||
\(764\) | 10.1103 | 0.365778 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.5703 | −0.598709 | ||||||||
\(767\) | 0.601870 | 0.0217323 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.4774 | 0.413884 | 0.206942 | − | 0.978353i | \(-0.433649\pi\) | ||||
0.206942 | + | 0.978353i | \(0.433649\pi\) | |||||||
\(770\) | −1.69212 | −0.0609799 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −57.7520 | −2.07854 | ||||||||
\(773\) | 33.9319 | 1.22045 | 0.610223 | − | 0.792230i | \(-0.291080\pi\) | ||||
0.610223 | + | 0.792230i | \(0.291080\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.4240 | 0.374440 | ||||||||
\(776\) | −59.0324 | −2.11914 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 52.7177 | 1.89002 | ||||||||
\(779\) | 90.9351 | 3.25809 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.3047 | 0.798123 | ||||||||
\(782\) | −18.9541 | −0.677796 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.87011 | −0.209647 | ||||||||
\(785\) | −4.79244 | −0.171049 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.6811 | −0.452034 | −0.226017 | − | 0.974123i | \(-0.572570\pi\) | ||||
−0.226017 | + | 0.974123i | \(0.572570\pi\) | |||||||
\(788\) | −72.9049 | −2.59713 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −24.0087 | −0.854191 | ||||||||
\(791\) | −0.428275 | −0.0152277 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.724684 | −0.0257343 | ||||||||
\(794\) | 52.1836 | 1.85193 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −67.1160 | −2.37886 | ||||||||
\(797\) | −49.4504 | −1.75162 | −0.875812 | − | 0.482653i | \(-0.839673\pi\) | ||||
−0.875812 | + | 0.482653i | \(0.839673\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.00014 | 0.212270 | ||||||||
\(800\) | 4.63247 | 0.163783 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −66.6418 | −2.35320 | ||||||||
\(803\) | −27.6481 | −0.975680 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.603123 | 0.0212573 | ||||||||
\(806\) | −125.496 | −4.42041 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.0752 | 0.565525 | ||||||||
\(809\) | −48.8608 | −1.71785 | −0.858926 | − | 0.512099i | \(-0.828868\pi\) | ||||
−0.858926 | + | 0.512099i | \(0.828868\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.1735 | 0.813731 | 0.406866 | − | 0.913488i | \(-0.366622\pi\) | ||||
0.406866 | + | 0.913488i | \(0.366622\pi\) | |||||||
\(812\) | −1.38576 | −0.0486307 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.348104 | −0.0122010 | ||||||||
\(815\) | 10.4650 | 0.366573 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −47.2913 | −1.65451 | ||||||||
\(818\) | −71.1604 | −2.48806 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −37.8990 | −1.32349 | ||||||||
\(821\) | −51.1545 | −1.78530 | −0.892652 | − | 0.450747i | \(-0.851158\pi\) | ||||
−0.892652 | + | 0.450747i | \(0.851158\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.0988 | −0.805175 | −0.402587 | − | 0.915382i | \(-0.631889\pi\) | ||||
−0.402587 | + | 0.915382i | \(0.631889\pi\) | |||||||
\(824\) | 54.7373 | 1.90686 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.0627457 | 0.00218320 | ||||||||
\(827\) | 9.60440 | 0.333978 | 0.166989 | − | 0.985959i | \(-0.446596\pi\) | ||||
0.166989 | + | 0.985959i | \(0.446596\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.6462 | −0.578148 | −0.289074 | − | 0.957307i | \(-0.593347\pi\) | ||||
−0.289074 | + | 0.957307i | \(0.593347\pi\) | |||||||
\(830\) | −20.6757 | −0.717663 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −64.5133 | −2.23660 | ||||||||
\(833\) | −21.7277 | −0.752819 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.8728 | 0.618514 | ||||||||
\(836\) | 87.9468 | 3.04171 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 24.3522 | 0.841234 | ||||||||
\(839\) | −51.5325 | −1.77910 | −0.889550 | − | 0.456839i | \(-0.848982\pi\) | ||||
−0.889550 | + | 0.456839i | \(0.848982\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.9367 | −0.894370 | ||||||||
\(842\) | 21.6220 | 0.745143 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.93206 | −0.273033 | ||||||||
\(845\) | −13.7537 | −0.473140 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.267035 | 0.00917545 | ||||||||
\(848\) | 2.16521 | 0.0743535 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.28054 | −0.249720 | ||||||||
\(851\) | 0.124075 | 0.00425322 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.83286 | −0.336671 | −0.168335 | − | 0.985730i | \(-0.553839\pi\) | ||||
−0.168335 | + | 0.985730i | \(0.553839\pi\) | |||||||
\(854\) | −0.0755492 | −0.00258524 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −47.3753 | −1.61925 | ||||||||
\(857\) | 17.5102 | 0.598138 | 0.299069 | − | 0.954232i | \(-0.403324\pi\) | ||||
0.299069 | + | 0.954232i | \(0.403324\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.18058 | −0.142640 | −0.0713198 | − | 0.997453i | \(-0.522721\pi\) | ||||
−0.0713198 | + | 0.997453i | \(0.522721\pi\) | |||||||
\(860\) | 19.7096 | 0.672092 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −39.7913 | −1.35530 | ||||||||
\(863\) | −40.8099 | −1.38918 | −0.694592 | − | 0.719404i | \(-0.744415\pi\) | ||||
−0.694592 | + | 0.719404i | \(0.744415\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.7804 | 0.604551 | ||||||||
\(866\) | 48.1687 | 1.63684 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.25331 | −0.280136 | ||||||||
\(869\) | −32.3685 | −1.09803 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.22032 | −0.0413491 | ||||||||
\(872\) | −48.5157 | −1.64295 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −49.6909 | −1.68082 | ||||||||
\(875\) | 0.231668 | 0.00783182 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.1475 | −1.55829 | −0.779145 | − | 0.626844i | \(-0.784346\pi\) | ||||
−0.779145 | + | 0.626844i | \(0.784346\pi\) | |||||||
\(878\) | −2.49318 | −0.0841408 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.65186 | −0.0893942 | ||||||||
\(881\) | −29.8832 | −1.00679 | −0.503396 | − | 0.864056i | \(-0.667916\pi\) | ||||
−0.503396 | + | 0.864056i | \(0.667916\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.2977 | 1.49073 | 0.745367 | − | 0.666654i | \(-0.232274\pi\) | ||||
0.745367 | + | 0.666654i | \(0.232274\pi\) | |||||||
\(884\) | 55.2940 | 1.85974 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.7255 | −0.897859 | ||||||||
\(887\) | 52.5198 | 1.76344 | 0.881721 | − | 0.471770i | \(-0.156385\pi\) | ||||
0.881721 | + | 0.471770i | \(0.156385\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.755323 | 0.0253327 | ||||||||
\(890\) | −2.32759 | −0.0780209 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −21.9354 | −0.734450 | ||||||||
\(893\) | 15.7303 | 0.526393 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.8343 | −0.596136 | ||||||||
\(896\) | −4.57919 | −0.152980 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 32.1793 | 1.07384 | ||||||||
\(899\) | 18.2443 | 0.608480 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.01430 | 0.266995 | ||||||||
\(902\) | −80.9961 | −2.69688 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.10005 | −0.202885 | ||||||||
\(905\) | −12.3953 | −0.412032 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.7670 | −0.457124 | −0.228562 | − | 0.973529i | \(-0.573402\pi\) | ||||
−0.228562 | + | 0.973529i | \(0.573402\pi\) | |||||||
\(908\) | −32.4241 | −1.07603 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.78910 | −0.0924578 | ||||||||
\(911\) | −24.4481 | −0.810001 | −0.405001 | − | 0.914316i | \(-0.632729\pi\) | ||||
−0.405001 | + | 0.914316i | \(0.632729\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.8749 | −0.922524 | ||||||||
\(914\) | −71.5580 | −2.36693 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 102.215 | 3.37728 | ||||||||
\(917\) | 1.50972 | 0.0498552 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.9181 | −0.953920 | −0.476960 | − | 0.878925i | \(-0.658261\pi\) | ||||
−0.476960 | + | 0.878925i | \(0.658261\pi\) | |||||||
\(920\) | 8.59045 | 0.283219 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −33.1868 | −1.09295 | ||||||||
\(923\) | 36.7644 | 1.21012 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.0476589 | 0.00156702 | ||||||||
\(926\) | −89.1243 | −2.92880 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.10786 | 0.266154 | ||||||||
\(929\) | −21.1894 | −0.695201 | −0.347601 | − | 0.937643i | \(-0.613003\pi\) | ||||
−0.347601 | + | 0.937643i | \(0.613003\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −56.9623 | −1.86686 | ||||||||
\(932\) | −63.6081 | −2.08355 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 71.3381 | 2.33425 | ||||||||
\(935\) | −9.81560 | −0.321005 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.8348 | 1.10534 | 0.552668 | − | 0.833401i | \(-0.313610\pi\) | ||||
0.552668 | + | 0.833401i | \(0.313610\pi\) | |||||||
\(938\) | −0.127220 | −0.00415389 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.55590 | −0.213830 | ||||||||
\(941\) | −28.9054 | −0.942288 | −0.471144 | − | 0.882056i | \(-0.656159\pi\) | ||||
−0.471144 | + | 0.882056i | \(0.656159\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.8694 | 0.940118 | ||||||||
\(944\) | 0.0983337 | 0.00320049 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 42.1225 | 1.36952 | ||||||||
\(947\) | 13.3591 | 0.434114 | 0.217057 | − | 0.976159i | \(-0.430354\pi\) | ||||
0.217057 | + | 0.976159i | \(0.430354\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45.5719 | −1.47933 | ||||||||
\(950\) | −19.0870 | −0.619265 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.39112 | 0.0774966 | ||||||||
\(953\) | 12.6493 | 0.409751 | 0.204875 | − | 0.978788i | \(-0.434321\pi\) | ||||
0.204875 | + | 0.978788i | \(0.434321\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.95826 | −0.0957270 | ||||||||
\(956\) | 26.1664 | 0.846280 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.3010 | 0.365120 | ||||||||
\(959\) | 3.36033 | 0.108511 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 77.6591 | 2.50513 | ||||||||
\(962\) | −0.573775 | −0.0184992 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 31.0714 | 1.00074 | ||||||||
\(965\) | 16.8981 | 0.543970 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.6366 | −0.406367 | −0.203183 | − | 0.979141i | \(-0.565129\pi\) | ||||
−0.203183 | + | 0.979141i | \(0.565129\pi\) | |||||||
\(968\) | 3.80346 | 0.122248 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 41.6408 | 1.33701 | ||||||||
\(971\) | −54.6786 | −1.75472 | −0.877360 | − | 0.479832i | \(-0.840697\pi\) | ||||
−0.877360 | + | 0.479832i | \(0.840697\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.89664 | 0.0608034 | ||||||||
\(974\) | 77.2985 | 2.47680 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.118399 | −0.00378986 | ||||||||
\(977\) | −26.1759 | −0.837442 | −0.418721 | − | 0.908115i | \(-0.637521\pi\) | ||||
−0.418721 | + | 0.908115i | \(0.637521\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.13805 | −0.100292 | ||||||||
\(980\) | 23.7402 | 0.758352 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 41.2225 | 1.31546 | ||||||||
\(983\) | 9.12819 | 0.291144 | 0.145572 | − | 0.989348i | \(-0.453498\pi\) | ||||
0.145572 | + | 0.989348i | \(0.453498\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.3318 | 0.679689 | ||||||||
\(986\) | −12.7426 | −0.405806 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 144.961 | 4.61184 | ||||||||
\(989\) | −15.0137 | −0.477408 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.6993 | −0.689301 | −0.344650 | − | 0.938731i | \(-0.612003\pi\) | ||||
−0.344650 | + | 0.938731i | \(0.612003\pi\) | |||||||
\(992\) | 48.2887 | 1.53317 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.83273 | 0.121567 | ||||||||
\(995\) | 19.6380 | 0.622567 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.02812 | 0.222583 | 0.111291 | − | 0.993788i | \(-0.464501\pi\) | ||||
0.111291 | + | 0.993788i | \(0.464501\pi\) | |||||||
\(998\) | −12.1055 | −0.383192 | ||||||||
\(999\) | 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 | 4005.2.a.r.1.3 | 10 | ||
3.2 | odd | 2 | 1335.2.a.k.1.8 | ✓ | 10 | ||
15.14 | odd | 2 | 6675.2.a.y.1.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1335.2.a.k.1.8 | ✓ | 10 | 3.2 | odd | 2 | ||
4005.2.a.r.1.3 | 10 | 1.1 | even | 1 | trivial | ||
6675.2.a.y.1.3 | 10 | 15.14 | odd | 2 |