Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8042,2,Mod(1,8042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8042 = 2 \cdot 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8042.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: | \(64.2156933055\) |
Analytic rank: | \(0\) |
Dimension: | \(86\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8042.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.17138 | −1.25365 | −0.626823 | − | 0.779162i | \(-0.715645\pi\) | ||||
−0.626823 | + | 0.779162i | \(0.715645\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.37288 | 1.50840 | 0.754198 | − | 0.656647i | \(-0.228026\pi\) | ||||
0.754198 | + | 0.656647i | \(0.228026\pi\) | |||||||
\(6\) | 2.17138 | 0.886461 | ||||||||
\(7\) | 0.0526160 | 0.0198870 | 0.00994349 | − | 0.999951i | \(-0.496835\pi\) | ||||
0.00994349 | + | 0.999951i | \(0.496835\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.71488 | 0.571627 | ||||||||
\(10\) | −3.37288 | −1.06660 | ||||||||
\(11\) | −3.41347 | −1.02920 | −0.514601 | − | 0.857430i | \(-0.672060\pi\) | ||||
−0.514601 | + | 0.857430i | \(0.672060\pi\) | |||||||
\(12\) | −2.17138 | −0.626823 | ||||||||
\(13\) | 0.293411 | 0.0813777 | 0.0406888 | − | 0.999172i | \(-0.487045\pi\) | ||||
0.0406888 | + | 0.999172i | \(0.487045\pi\) | |||||||
\(14\) | −0.0526160 | −0.0140622 | ||||||||
\(15\) | −7.32379 | −1.89099 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.08333 | −0.262745 | −0.131372 | − | 0.991333i | \(-0.541938\pi\) | ||||
−0.131372 | + | 0.991333i | \(0.541938\pi\) | |||||||
\(18\) | −1.71488 | −0.404202 | ||||||||
\(19\) | 4.94043 | 1.13341 | 0.566706 | − | 0.823920i | \(-0.308218\pi\) | ||||
0.566706 | + | 0.823920i | \(0.308218\pi\) | |||||||
\(20\) | 3.37288 | 0.754198 | ||||||||
\(21\) | −0.114249 | −0.0249312 | ||||||||
\(22\) | 3.41347 | 0.727755 | ||||||||
\(23\) | 4.89351 | 1.02037 | 0.510184 | − | 0.860065i | \(-0.329577\pi\) | ||||
0.510184 | + | 0.860065i | \(0.329577\pi\) | |||||||
\(24\) | 2.17138 | 0.443231 | ||||||||
\(25\) | 6.37629 | 1.27526 | ||||||||
\(26\) | −0.293411 | −0.0575427 | ||||||||
\(27\) | 2.79048 | 0.537027 | ||||||||
\(28\) | 0.0526160 | 0.00994349 | ||||||||
\(29\) | −1.82864 | −0.339570 | −0.169785 | − | 0.985481i | \(-0.554307\pi\) | ||||
−0.169785 | + | 0.985481i | \(0.554307\pi\) | |||||||
\(30\) | 7.32379 | 1.33713 | ||||||||
\(31\) | 8.89349 | 1.59732 | 0.798659 | − | 0.601784i | \(-0.205543\pi\) | ||||
0.798659 | + | 0.601784i | \(0.205543\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 7.41194 | 1.29025 | ||||||||
\(34\) | 1.08333 | 0.185789 | ||||||||
\(35\) | 0.177467 | 0.0299975 | ||||||||
\(36\) | 1.71488 | 0.285814 | ||||||||
\(37\) | 3.24810 | 0.533984 | 0.266992 | − | 0.963699i | \(-0.413970\pi\) | ||||
0.266992 | + | 0.963699i | \(0.413970\pi\) | |||||||
\(38\) | −4.94043 | −0.801443 | ||||||||
\(39\) | −0.637107 | −0.102019 | ||||||||
\(40\) | −3.37288 | −0.533298 | ||||||||
\(41\) | −5.40286 | −0.843785 | −0.421892 | − | 0.906646i | \(-0.638634\pi\) | ||||
−0.421892 | + | 0.906646i | \(0.638634\pi\) | |||||||
\(42\) | 0.114249 | 0.0176290 | ||||||||
\(43\) | 0.278980 | 0.0425441 | 0.0212720 | − | 0.999774i | \(-0.493228\pi\) | ||||
0.0212720 | + | 0.999774i | \(0.493228\pi\) | |||||||
\(44\) | −3.41347 | −0.514601 | ||||||||
\(45\) | 5.78409 | 0.862241 | ||||||||
\(46\) | −4.89351 | −0.721509 | ||||||||
\(47\) | −4.56043 | −0.665207 | −0.332604 | − | 0.943067i | \(-0.607927\pi\) | ||||
−0.332604 | + | 0.943067i | \(0.607927\pi\) | |||||||
\(48\) | −2.17138 | −0.313411 | ||||||||
\(49\) | −6.99723 | −0.999605 | ||||||||
\(50\) | −6.37629 | −0.901744 | ||||||||
\(51\) | 2.35231 | 0.329389 | ||||||||
\(52\) | 0.293411 | 0.0406888 | ||||||||
\(53\) | −6.10135 | −0.838086 | −0.419043 | − | 0.907967i | \(-0.637634\pi\) | ||||
−0.419043 | + | 0.907967i | \(0.637634\pi\) | |||||||
\(54\) | −2.79048 | −0.379736 | ||||||||
\(55\) | −11.5132 | −1.55244 | ||||||||
\(56\) | −0.0526160 | −0.00703111 | ||||||||
\(57\) | −10.7275 | −1.42090 | ||||||||
\(58\) | 1.82864 | 0.240113 | ||||||||
\(59\) | 6.43470 | 0.837727 | 0.418864 | − | 0.908049i | \(-0.362429\pi\) | ||||
0.418864 | + | 0.908049i | \(0.362429\pi\) | |||||||
\(60\) | −7.32379 | −0.945497 | ||||||||
\(61\) | −1.07070 | −0.137089 | −0.0685445 | − | 0.997648i | \(-0.521836\pi\) | ||||
−0.0685445 | + | 0.997648i | \(0.521836\pi\) | |||||||
\(62\) | −8.89349 | −1.12947 | ||||||||
\(63\) | 0.0902303 | 0.0113679 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.989640 | 0.122750 | ||||||||
\(66\) | −7.41194 | −0.912347 | ||||||||
\(67\) | −1.46666 | −0.179181 | −0.0895905 | − | 0.995979i | \(-0.528556\pi\) | ||||
−0.0895905 | + | 0.995979i | \(0.528556\pi\) | |||||||
\(68\) | −1.08333 | −0.131372 | ||||||||
\(69\) | −10.6257 | −1.27918 | ||||||||
\(70\) | −0.177467 | −0.0212114 | ||||||||
\(71\) | −0.917589 | −0.108898 | −0.0544489 | − | 0.998517i | \(-0.517340\pi\) | ||||
−0.0544489 | + | 0.998517i | \(0.517340\pi\) | |||||||
\(72\) | −1.71488 | −0.202101 | ||||||||
\(73\) | 9.92543 | 1.16168 | 0.580842 | − | 0.814017i | \(-0.302724\pi\) | ||||
0.580842 | + | 0.814017i | \(0.302724\pi\) | |||||||
\(74\) | −3.24810 | −0.377584 | ||||||||
\(75\) | −13.8453 | −1.59872 | ||||||||
\(76\) | 4.94043 | 0.566706 | ||||||||
\(77\) | −0.179603 | −0.0204677 | ||||||||
\(78\) | 0.637107 | 0.0721382 | ||||||||
\(79\) | 7.70598 | 0.866990 | 0.433495 | − | 0.901156i | \(-0.357280\pi\) | ||||
0.433495 | + | 0.901156i | \(0.357280\pi\) | |||||||
\(80\) | 3.37288 | 0.377099 | ||||||||
\(81\) | −11.2038 | −1.24487 | ||||||||
\(82\) | 5.40286 | 0.596646 | ||||||||
\(83\) | 6.94011 | 0.761776 | 0.380888 | − | 0.924621i | \(-0.375618\pi\) | ||||
0.380888 | + | 0.924621i | \(0.375618\pi\) | |||||||
\(84\) | −0.114249 | −0.0124656 | ||||||||
\(85\) | −3.65392 | −0.396323 | ||||||||
\(86\) | −0.278980 | −0.0300832 | ||||||||
\(87\) | 3.97067 | 0.425701 | ||||||||
\(88\) | 3.41347 | 0.363878 | ||||||||
\(89\) | −5.52579 | −0.585732 | −0.292866 | − | 0.956153i | \(-0.594609\pi\) | ||||
−0.292866 | + | 0.956153i | \(0.594609\pi\) | |||||||
\(90\) | −5.78409 | −0.609696 | ||||||||
\(91\) | 0.0154381 | 0.00161836 | ||||||||
\(92\) | 4.89351 | 0.510184 | ||||||||
\(93\) | −19.3111 | −2.00247 | ||||||||
\(94\) | 4.56043 | 0.470372 | ||||||||
\(95\) | 16.6634 | 1.70963 | ||||||||
\(96\) | 2.17138 | 0.221615 | ||||||||
\(97\) | 9.29685 | 0.943952 | 0.471976 | − | 0.881611i | \(-0.343541\pi\) | ||||
0.471976 | + | 0.881611i | \(0.343541\pi\) | |||||||
\(98\) | 6.99723 | 0.706827 | ||||||||
\(99\) | −5.85371 | −0.588320 | ||||||||
\(100\) | 6.37629 | 0.637629 | ||||||||
\(101\) | −5.28666 | −0.526042 | −0.263021 | − | 0.964790i | \(-0.584719\pi\) | ||||
−0.263021 | + | 0.964790i | \(0.584719\pi\) | |||||||
\(102\) | −2.35231 | −0.232913 | ||||||||
\(103\) | 2.54577 | 0.250842 | 0.125421 | − | 0.992104i | \(-0.459972\pi\) | ||||
0.125421 | + | 0.992104i | \(0.459972\pi\) | |||||||
\(104\) | −0.293411 | −0.0287713 | ||||||||
\(105\) | −0.385349 | −0.0376062 | ||||||||
\(106\) | 6.10135 | 0.592616 | ||||||||
\(107\) | −10.2676 | −0.992607 | −0.496304 | − | 0.868149i | \(-0.665310\pi\) | ||||
−0.496304 | + | 0.868149i | \(0.665310\pi\) | |||||||
\(108\) | 2.79048 | 0.268514 | ||||||||
\(109\) | 19.4556 | 1.86351 | 0.931756 | − | 0.363084i | \(-0.118276\pi\) | ||||
0.931756 | + | 0.363084i | \(0.118276\pi\) | |||||||
\(110\) | 11.5132 | 1.09774 | ||||||||
\(111\) | −7.05284 | −0.669426 | ||||||||
\(112\) | 0.0526160 | 0.00497175 | ||||||||
\(113\) | −10.1419 | −0.954073 | −0.477037 | − | 0.878883i | \(-0.658289\pi\) | ||||
−0.477037 | + | 0.878883i | \(0.658289\pi\) | |||||||
\(114\) | 10.7275 | 1.00473 | ||||||||
\(115\) | 16.5052 | 1.53912 | ||||||||
\(116\) | −1.82864 | −0.169785 | ||||||||
\(117\) | 0.503166 | 0.0465177 | ||||||||
\(118\) | −6.43470 | −0.592363 | ||||||||
\(119\) | −0.0570003 | −0.00522521 | ||||||||
\(120\) | 7.32379 | 0.668567 | ||||||||
\(121\) | 0.651811 | 0.0592556 | ||||||||
\(122\) | 1.07070 | 0.0969366 | ||||||||
\(123\) | 11.7317 | 1.05781 | ||||||||
\(124\) | 8.89349 | 0.798659 | ||||||||
\(125\) | 4.64206 | 0.415198 | ||||||||
\(126\) | −0.0902303 | −0.00803835 | ||||||||
\(127\) | −8.09666 | −0.718462 | −0.359231 | − | 0.933249i | \(-0.616961\pi\) | ||||
−0.359231 | + | 0.933249i | \(0.616961\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.605771 | −0.0533352 | ||||||||
\(130\) | −0.989640 | −0.0867972 | ||||||||
\(131\) | −14.9833 | −1.30910 | −0.654550 | − | 0.756018i | \(-0.727142\pi\) | ||||
−0.654550 | + | 0.756018i | \(0.727142\pi\) | |||||||
\(132\) | 7.41194 | 0.645127 | ||||||||
\(133\) | 0.259946 | 0.0225401 | ||||||||
\(134\) | 1.46666 | 0.126700 | ||||||||
\(135\) | 9.41193 | 0.810050 | ||||||||
\(136\) | 1.08333 | 0.0928944 | ||||||||
\(137\) | 20.2771 | 1.73239 | 0.866195 | − | 0.499707i | \(-0.166559\pi\) | ||||
0.866195 | + | 0.499707i | \(0.166559\pi\) | |||||||
\(138\) | 10.6257 | 0.904516 | ||||||||
\(139\) | 18.8107 | 1.59551 | 0.797753 | − | 0.602985i | \(-0.206022\pi\) | ||||
0.797753 | + | 0.602985i | \(0.206022\pi\) | |||||||
\(140\) | 0.177467 | 0.0149987 | ||||||||
\(141\) | 9.90242 | 0.833934 | ||||||||
\(142\) | 0.917589 | 0.0770024 | ||||||||
\(143\) | −1.00155 | −0.0837540 | ||||||||
\(144\) | 1.71488 | 0.142907 | ||||||||
\(145\) | −6.16778 | −0.512207 | ||||||||
\(146\) | −9.92543 | −0.821434 | ||||||||
\(147\) | 15.1936 | 1.25315 | ||||||||
\(148\) | 3.24810 | 0.266992 | ||||||||
\(149\) | 10.8116 | 0.885720 | 0.442860 | − | 0.896591i | \(-0.353964\pi\) | ||||
0.442860 | + | 0.896591i | \(0.353964\pi\) | |||||||
\(150\) | 13.8453 | 1.13047 | ||||||||
\(151\) | −1.73171 | −0.140925 | −0.0704623 | − | 0.997514i | \(-0.522447\pi\) | ||||
−0.0704623 | + | 0.997514i | \(0.522447\pi\) | |||||||
\(152\) | −4.94043 | −0.400721 | ||||||||
\(153\) | −1.85778 | −0.150192 | ||||||||
\(154\) | 0.179603 | 0.0144729 | ||||||||
\(155\) | 29.9966 | 2.40939 | ||||||||
\(156\) | −0.637107 | −0.0510094 | ||||||||
\(157\) | 6.56378 | 0.523847 | 0.261923 | − | 0.965089i | \(-0.415643\pi\) | ||||
0.261923 | + | 0.965089i | \(0.415643\pi\) | |||||||
\(158\) | −7.70598 | −0.613055 | ||||||||
\(159\) | 13.2483 | 1.05066 | ||||||||
\(160\) | −3.37288 | −0.266649 | ||||||||
\(161\) | 0.257477 | 0.0202920 | ||||||||
\(162\) | 11.2038 | 0.880256 | ||||||||
\(163\) | −4.01375 | −0.314381 | −0.157191 | − | 0.987568i | \(-0.550244\pi\) | ||||
−0.157191 | + | 0.987568i | \(0.550244\pi\) | |||||||
\(164\) | −5.40286 | −0.421892 | ||||||||
\(165\) | 24.9996 | 1.94621 | ||||||||
\(166\) | −6.94011 | −0.538657 | ||||||||
\(167\) | 16.5924 | 1.28396 | 0.641980 | − | 0.766722i | \(-0.278113\pi\) | ||||
0.641980 | + | 0.766722i | \(0.278113\pi\) | |||||||
\(168\) | 0.114249 | 0.00881452 | ||||||||
\(169\) | −12.9139 | −0.993378 | ||||||||
\(170\) | 3.65392 | 0.280243 | ||||||||
\(171\) | 8.47225 | 0.647889 | ||||||||
\(172\) | 0.278980 | 0.0212720 | ||||||||
\(173\) | −9.23659 | −0.702245 | −0.351122 | − | 0.936330i | \(-0.614200\pi\) | ||||
−0.351122 | + | 0.936330i | \(0.614200\pi\) | |||||||
\(174\) | −3.97067 | −0.301016 | ||||||||
\(175\) | 0.335495 | 0.0253610 | ||||||||
\(176\) | −3.41347 | −0.257300 | ||||||||
\(177\) | −13.9722 | −1.05021 | ||||||||
\(178\) | 5.52579 | 0.414175 | ||||||||
\(179\) | −4.66307 | −0.348534 | −0.174267 | − | 0.984698i | \(-0.555756\pi\) | ||||
−0.174267 | + | 0.984698i | \(0.555756\pi\) | |||||||
\(180\) | 5.78409 | 0.431120 | ||||||||
\(181\) | −5.89517 | −0.438184 | −0.219092 | − | 0.975704i | \(-0.570310\pi\) | ||||
−0.219092 | + | 0.975704i | \(0.570310\pi\) | |||||||
\(182\) | −0.0154381 | −0.00114435 | ||||||||
\(183\) | 2.32489 | 0.171861 | ||||||||
\(184\) | −4.89351 | −0.360754 | ||||||||
\(185\) | 10.9554 | 0.805459 | ||||||||
\(186\) | 19.3111 | 1.41596 | ||||||||
\(187\) | 3.69790 | 0.270418 | ||||||||
\(188\) | −4.56043 | −0.332604 | ||||||||
\(189\) | 0.146824 | 0.0106799 | ||||||||
\(190\) | −16.6634 | −1.20889 | ||||||||
\(191\) | 22.8960 | 1.65670 | 0.828348 | − | 0.560214i | \(-0.189281\pi\) | ||||
0.828348 | + | 0.560214i | \(0.189281\pi\) | |||||||
\(192\) | −2.17138 | −0.156706 | ||||||||
\(193\) | −13.8039 | −0.993626 | −0.496813 | − | 0.867858i | \(-0.665496\pi\) | ||||
−0.496813 | + | 0.867858i | \(0.665496\pi\) | |||||||
\(194\) | −9.29685 | −0.667475 | ||||||||
\(195\) | −2.14888 | −0.153885 | ||||||||
\(196\) | −6.99723 | −0.499802 | ||||||||
\(197\) | −6.71073 | −0.478120 | −0.239060 | − | 0.971005i | \(-0.576839\pi\) | ||||
−0.239060 | + | 0.971005i | \(0.576839\pi\) | |||||||
\(198\) | 5.85371 | 0.416005 | ||||||||
\(199\) | −20.9027 | −1.48175 | −0.740876 | − | 0.671642i | \(-0.765589\pi\) | ||||
−0.740876 | + | 0.671642i | \(0.765589\pi\) | |||||||
\(200\) | −6.37629 | −0.450872 | ||||||||
\(201\) | 3.18467 | 0.224630 | ||||||||
\(202\) | 5.28666 | 0.371968 | ||||||||
\(203\) | −0.0962159 | −0.00675303 | ||||||||
\(204\) | 2.35231 | 0.164695 | ||||||||
\(205\) | −18.2232 | −1.27276 | ||||||||
\(206\) | −2.54577 | −0.177372 | ||||||||
\(207\) | 8.39179 | 0.583270 | ||||||||
\(208\) | 0.293411 | 0.0203444 | ||||||||
\(209\) | −16.8640 | −1.16651 | ||||||||
\(210\) | 0.385349 | 0.0265916 | ||||||||
\(211\) | −12.4346 | −0.856035 | −0.428018 | − | 0.903770i | \(-0.640788\pi\) | ||||
−0.428018 | + | 0.903770i | \(0.640788\pi\) | |||||||
\(212\) | −6.10135 | −0.419043 | ||||||||
\(213\) | 1.99243 | 0.136519 | ||||||||
\(214\) | 10.2676 | 0.701879 | ||||||||
\(215\) | 0.940965 | 0.0641733 | ||||||||
\(216\) | −2.79048 | −0.189868 | ||||||||
\(217\) | 0.467940 | 0.0317658 | ||||||||
\(218\) | −19.4556 | −1.31770 | ||||||||
\(219\) | −21.5519 | −1.45634 | ||||||||
\(220\) | −11.5132 | −0.776222 | ||||||||
\(221\) | −0.317860 | −0.0213816 | ||||||||
\(222\) | 7.05284 | 0.473356 | ||||||||
\(223\) | 3.58277 | 0.239920 | 0.119960 | − | 0.992779i | \(-0.461723\pi\) | ||||
0.119960 | + | 0.992779i | \(0.461723\pi\) | |||||||
\(224\) | −0.0526160 | −0.00351556 | ||||||||
\(225\) | 10.9346 | 0.728973 | ||||||||
\(226\) | 10.1419 | 0.674632 | ||||||||
\(227\) | 3.29537 | 0.218721 | 0.109361 | − | 0.994002i | \(-0.465120\pi\) | ||||
0.109361 | + | 0.994002i | \(0.465120\pi\) | |||||||
\(228\) | −10.7275 | −0.710448 | ||||||||
\(229\) | 4.79651 | 0.316962 | 0.158481 | − | 0.987362i | \(-0.449340\pi\) | ||||
0.158481 | + | 0.987362i | \(0.449340\pi\) | |||||||
\(230\) | −16.5052 | −1.08832 | ||||||||
\(231\) | 0.389987 | 0.0256593 | ||||||||
\(232\) | 1.82864 | 0.120056 | ||||||||
\(233\) | −5.26170 | −0.344705 | −0.172353 | − | 0.985035i | \(-0.555137\pi\) | ||||
−0.172353 | + | 0.985035i | \(0.555137\pi\) | |||||||
\(234\) | −0.503166 | −0.0328930 | ||||||||
\(235\) | −15.3818 | −1.00340 | ||||||||
\(236\) | 6.43470 | 0.418864 | ||||||||
\(237\) | −16.7326 | −1.08690 | ||||||||
\(238\) | 0.0570003 | 0.00369478 | ||||||||
\(239\) | 15.1773 | 0.981736 | 0.490868 | − | 0.871234i | \(-0.336680\pi\) | ||||
0.490868 | + | 0.871234i | \(0.336680\pi\) | |||||||
\(240\) | −7.32379 | −0.472748 | ||||||||
\(241\) | 10.6380 | 0.685252 | 0.342626 | − | 0.939472i | \(-0.388684\pi\) | ||||
0.342626 | + | 0.939472i | \(0.388684\pi\) | |||||||
\(242\) | −0.651811 | −0.0419000 | ||||||||
\(243\) | 15.9563 | 1.02360 | ||||||||
\(244\) | −1.07070 | −0.0685445 | ||||||||
\(245\) | −23.6008 | −1.50780 | ||||||||
\(246\) | −11.7317 | −0.747983 | ||||||||
\(247\) | 1.44958 | 0.0922344 | ||||||||
\(248\) | −8.89349 | −0.564737 | ||||||||
\(249\) | −15.0696 | −0.954998 | ||||||||
\(250\) | −4.64206 | −0.293589 | ||||||||
\(251\) | 5.44235 | 0.343518 | 0.171759 | − | 0.985139i | \(-0.445055\pi\) | ||||
0.171759 | + | 0.985139i | \(0.445055\pi\) | |||||||
\(252\) | 0.0902303 | 0.00568397 | ||||||||
\(253\) | −16.7039 | −1.05016 | ||||||||
\(254\) | 8.09666 | 0.508029 | ||||||||
\(255\) | 7.93405 | 0.496849 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.5266 | 1.52993 | 0.764963 | − | 0.644074i | \(-0.222757\pi\) | ||||
0.764963 | + | 0.644074i | \(0.222757\pi\) | |||||||
\(258\) | 0.605771 | 0.0377137 | ||||||||
\(259\) | 0.170902 | 0.0106193 | ||||||||
\(260\) | 0.989640 | 0.0613749 | ||||||||
\(261\) | −3.13591 | −0.194108 | ||||||||
\(262\) | 14.9833 | 0.925674 | ||||||||
\(263\) | 8.42086 | 0.519253 | 0.259626 | − | 0.965709i | \(-0.416401\pi\) | ||||
0.259626 | + | 0.965709i | \(0.416401\pi\) | |||||||
\(264\) | −7.41194 | −0.456174 | ||||||||
\(265\) | −20.5791 | −1.26416 | ||||||||
\(266\) | −0.259946 | −0.0159383 | ||||||||
\(267\) | 11.9986 | 0.734301 | ||||||||
\(268\) | −1.46666 | −0.0895905 | ||||||||
\(269\) | −8.95887 | −0.546232 | −0.273116 | − | 0.961981i | \(-0.588054\pi\) | ||||
−0.273116 | + | 0.961981i | \(0.588054\pi\) | |||||||
\(270\) | −9.41193 | −0.572792 | ||||||||
\(271\) | −2.18160 | −0.132523 | −0.0662614 | − | 0.997802i | \(-0.521107\pi\) | ||||
−0.0662614 | + | 0.997802i | \(0.521107\pi\) | |||||||
\(272\) | −1.08333 | −0.0656862 | ||||||||
\(273\) | −0.0335220 | −0.00202885 | ||||||||
\(274\) | −20.2771 | −1.22498 | ||||||||
\(275\) | −21.7653 | −1.31250 | ||||||||
\(276\) | −10.6257 | −0.639590 | ||||||||
\(277\) | −1.57566 | −0.0946724 | −0.0473362 | − | 0.998879i | \(-0.515073\pi\) | ||||
−0.0473362 | + | 0.998879i | \(0.515073\pi\) | |||||||
\(278\) | −18.8107 | −1.12819 | ||||||||
\(279\) | 15.2513 | 0.913071 | ||||||||
\(280\) | −0.177467 | −0.0106057 | ||||||||
\(281\) | 4.90892 | 0.292841 | 0.146421 | − | 0.989222i | \(-0.453225\pi\) | ||||
0.146421 | + | 0.989222i | \(0.453225\pi\) | |||||||
\(282\) | −9.90242 | −0.589680 | ||||||||
\(283\) | 20.2031 | 1.20095 | 0.600475 | − | 0.799644i | \(-0.294978\pi\) | ||||
0.600475 | + | 0.799644i | \(0.294978\pi\) | |||||||
\(284\) | −0.917589 | −0.0544489 | ||||||||
\(285\) | −36.1826 | −2.14327 | ||||||||
\(286\) | 1.00155 | 0.0592230 | ||||||||
\(287\) | −0.284277 | −0.0167803 | ||||||||
\(288\) | −1.71488 | −0.101050 | ||||||||
\(289\) | −15.8264 | −0.930965 | ||||||||
\(290\) | 6.16778 | 0.362185 | ||||||||
\(291\) | −20.1870 | −1.18338 | ||||||||
\(292\) | 9.92543 | 0.580842 | ||||||||
\(293\) | −30.9205 | −1.80640 | −0.903198 | − | 0.429224i | \(-0.858787\pi\) | ||||
−0.903198 | + | 0.429224i | \(0.858787\pi\) | |||||||
\(294\) | −15.1936 | −0.886111 | ||||||||
\(295\) | 21.7035 | 1.26362 | ||||||||
\(296\) | −3.24810 | −0.188792 | ||||||||
\(297\) | −9.52522 | −0.552709 | ||||||||
\(298\) | −10.8116 | −0.626299 | ||||||||
\(299\) | 1.43581 | 0.0830351 | ||||||||
\(300\) | −13.8453 | −0.799361 | ||||||||
\(301\) | 0.0146788 | 0.000846073 0 | ||||||||
\(302\) | 1.73171 | 0.0996488 | ||||||||
\(303\) | 11.4793 | 0.659470 | ||||||||
\(304\) | 4.94043 | 0.283353 | ||||||||
\(305\) | −3.61134 | −0.206785 | ||||||||
\(306\) | 1.85778 | 0.106202 | ||||||||
\(307\) | 23.4009 | 1.33556 | 0.667779 | − | 0.744360i | \(-0.267245\pi\) | ||||
0.667779 | + | 0.744360i | \(0.267245\pi\) | |||||||
\(308\) | −0.179603 | −0.0102339 | ||||||||
\(309\) | −5.52782 | −0.314467 | ||||||||
\(310\) | −29.9966 | −1.70369 | ||||||||
\(311\) | 23.3127 | 1.32194 | 0.660972 | − | 0.750411i | \(-0.270144\pi\) | ||||
0.660972 | + | 0.750411i | \(0.270144\pi\) | |||||||
\(312\) | 0.637107 | 0.0360691 | ||||||||
\(313\) | 19.4779 | 1.10096 | 0.550478 | − | 0.834849i | \(-0.314445\pi\) | ||||
0.550478 | + | 0.834849i | \(0.314445\pi\) | |||||||
\(314\) | −6.56378 | −0.370415 | ||||||||
\(315\) | 0.304336 | 0.0171474 | ||||||||
\(316\) | 7.70598 | 0.433495 | ||||||||
\(317\) | −14.2608 | −0.800969 | −0.400484 | − | 0.916304i | \(-0.631158\pi\) | ||||
−0.400484 | + | 0.916304i | \(0.631158\pi\) | |||||||
\(318\) | −13.2483 | −0.742930 | ||||||||
\(319\) | 6.24203 | 0.349486 | ||||||||
\(320\) | 3.37288 | 0.188549 | ||||||||
\(321\) | 22.2949 | 1.24438 | ||||||||
\(322\) | −0.257477 | −0.0143486 | ||||||||
\(323\) | −5.35209 | −0.297798 | ||||||||
\(324\) | −11.2038 | −0.622435 | ||||||||
\(325\) | 1.87088 | 0.103778 | ||||||||
\(326\) | 4.01375 | 0.222301 | ||||||||
\(327\) | −42.2456 | −2.33618 | ||||||||
\(328\) | 5.40286 | 0.298323 | ||||||||
\(329\) | −0.239952 | −0.0132290 | ||||||||
\(330\) | −24.9996 | −1.37618 | ||||||||
\(331\) | −15.5598 | −0.855245 | −0.427622 | − | 0.903957i | \(-0.640649\pi\) | ||||
−0.427622 | + | 0.903957i | \(0.640649\pi\) | |||||||
\(332\) | 6.94011 | 0.380888 | ||||||||
\(333\) | 5.57010 | 0.305240 | ||||||||
\(334\) | −16.5924 | −0.907896 | ||||||||
\(335\) | −4.94686 | −0.270276 | ||||||||
\(336\) | −0.114249 | −0.00623281 | ||||||||
\(337\) | 30.5380 | 1.66351 | 0.831756 | − | 0.555141i | \(-0.187336\pi\) | ||||
0.831756 | + | 0.555141i | \(0.187336\pi\) | |||||||
\(338\) | 12.9139 | 0.702424 | ||||||||
\(339\) | 22.0220 | 1.19607 | ||||||||
\(340\) | −3.65392 | −0.198162 | ||||||||
\(341\) | −30.3577 | −1.64396 | ||||||||
\(342\) | −8.47225 | −0.458127 | ||||||||
\(343\) | −0.736479 | −0.0397661 | ||||||||
\(344\) | −0.278980 | −0.0150416 | ||||||||
\(345\) | −35.8390 | −1.92951 | ||||||||
\(346\) | 9.23659 | 0.496562 | ||||||||
\(347\) | 22.7161 | 1.21946 | 0.609732 | − | 0.792607i | \(-0.291277\pi\) | ||||
0.609732 | + | 0.792607i | \(0.291277\pi\) | |||||||
\(348\) | 3.97067 | 0.212850 | ||||||||
\(349\) | 2.98906 | 0.160001 | 0.0800005 | − | 0.996795i | \(-0.474508\pi\) | ||||
0.0800005 | + | 0.996795i | \(0.474508\pi\) | |||||||
\(350\) | −0.335495 | −0.0179330 | ||||||||
\(351\) | 0.818757 | 0.0437020 | ||||||||
\(352\) | 3.41347 | 0.181939 | ||||||||
\(353\) | 18.2499 | 0.971342 | 0.485671 | − | 0.874142i | \(-0.338575\pi\) | ||||
0.485671 | + | 0.874142i | \(0.338575\pi\) | |||||||
\(354\) | 13.9722 | 0.742613 | ||||||||
\(355\) | −3.09491 | −0.164261 | ||||||||
\(356\) | −5.52579 | −0.292866 | ||||||||
\(357\) | 0.123769 | 0.00655056 | ||||||||
\(358\) | 4.66307 | 0.246451 | ||||||||
\(359\) | −27.0261 | −1.42638 | −0.713191 | − | 0.700970i | \(-0.752751\pi\) | ||||
−0.713191 | + | 0.700970i | \(0.752751\pi\) | |||||||
\(360\) | −5.78409 | −0.304848 | ||||||||
\(361\) | 5.40781 | 0.284622 | ||||||||
\(362\) | 5.89517 | 0.309843 | ||||||||
\(363\) | −1.41533 | −0.0742855 | ||||||||
\(364\) | 0.0154381 | 0.000809178 0 | ||||||||
\(365\) | 33.4772 | 1.75228 | ||||||||
\(366\) | −2.32489 | −0.121524 | ||||||||
\(367\) | −13.0432 | −0.680851 | −0.340425 | − | 0.940272i | \(-0.610571\pi\) | ||||
−0.340425 | + | 0.940272i | \(0.610571\pi\) | |||||||
\(368\) | 4.89351 | 0.255092 | ||||||||
\(369\) | −9.26527 | −0.482331 | ||||||||
\(370\) | −10.9554 | −0.569545 | ||||||||
\(371\) | −0.321029 | −0.0166670 | ||||||||
\(372\) | −19.3111 | −1.00124 | ||||||||
\(373\) | 19.5704 | 1.01332 | 0.506659 | − | 0.862147i | \(-0.330880\pi\) | ||||
0.506659 | + | 0.862147i | \(0.330880\pi\) | |||||||
\(374\) | −3.69790 | −0.191214 | ||||||||
\(375\) | −10.0797 | −0.520511 | ||||||||
\(376\) | 4.56043 | 0.235186 | ||||||||
\(377\) | −0.536544 | −0.0276334 | ||||||||
\(378\) | −0.146824 | −0.00755180 | ||||||||
\(379\) | 17.7294 | 0.910700 | 0.455350 | − | 0.890313i | \(-0.349514\pi\) | ||||
0.455350 | + | 0.890313i | \(0.349514\pi\) | |||||||
\(380\) | 16.6634 | 0.854817 | ||||||||
\(381\) | 17.5809 | 0.900697 | ||||||||
\(382\) | −22.8960 | −1.17146 | ||||||||
\(383\) | −35.3338 | −1.80548 | −0.902738 | − | 0.430192i | \(-0.858446\pi\) | ||||
−0.902738 | + | 0.430192i | \(0.858446\pi\) | |||||||
\(384\) | 2.17138 | 0.110808 | ||||||||
\(385\) | −0.605780 | −0.0308734 | ||||||||
\(386\) | 13.8039 | 0.702599 | ||||||||
\(387\) | 0.478418 | 0.0243194 | ||||||||
\(388\) | 9.29685 | 0.471976 | ||||||||
\(389\) | −13.8339 | −0.701404 | −0.350702 | − | 0.936487i | \(-0.614057\pi\) | ||||
−0.350702 | + | 0.936487i | \(0.614057\pi\) | |||||||
\(390\) | 2.14888 | 0.108813 | ||||||||
\(391\) | −5.30126 | −0.268096 | ||||||||
\(392\) | 6.99723 | 0.353414 | ||||||||
\(393\) | 32.5345 | 1.64115 | ||||||||
\(394\) | 6.71073 | 0.338082 | ||||||||
\(395\) | 25.9913 | 1.30776 | ||||||||
\(396\) | −5.85371 | −0.294160 | ||||||||
\(397\) | −5.42374 | −0.272210 | −0.136105 | − | 0.990694i | \(-0.543458\pi\) | ||||
−0.136105 | + | 0.990694i | \(0.543458\pi\) | |||||||
\(398\) | 20.9027 | 1.04776 | ||||||||
\(399\) | −0.564440 | −0.0282574 | ||||||||
\(400\) | 6.37629 | 0.318815 | ||||||||
\(401\) | −21.3314 | −1.06524 | −0.532621 | − | 0.846354i | \(-0.678793\pi\) | ||||
−0.532621 | + | 0.846354i | \(0.678793\pi\) | |||||||
\(402\) | −3.18467 | −0.158837 | ||||||||
\(403\) | 2.60945 | 0.129986 | ||||||||
\(404\) | −5.28666 | −0.263021 | ||||||||
\(405\) | −37.7891 | −1.87776 | ||||||||
\(406\) | 0.0962159 | 0.00477512 | ||||||||
\(407\) | −11.0873 | −0.549577 | ||||||||
\(408\) | −2.35231 | −0.116457 | ||||||||
\(409\) | −1.57475 | −0.0778665 | −0.0389333 | − | 0.999242i | \(-0.512396\pi\) | ||||
−0.0389333 | + | 0.999242i | \(0.512396\pi\) | |||||||
\(410\) | 18.2232 | 0.899978 | ||||||||
\(411\) | −44.0292 | −2.17180 | ||||||||
\(412\) | 2.54577 | 0.125421 | ||||||||
\(413\) | 0.338569 | 0.0166599 | ||||||||
\(414\) | −8.39179 | −0.412434 | ||||||||
\(415\) | 23.4081 | 1.14906 | ||||||||
\(416\) | −0.293411 | −0.0143857 | ||||||||
\(417\) | −40.8452 | −2.00020 | ||||||||
\(418\) | 16.8640 | 0.824846 | ||||||||
\(419\) | 12.1007 | 0.591158 | 0.295579 | − | 0.955318i | \(-0.404487\pi\) | ||||
0.295579 | + | 0.955318i | \(0.404487\pi\) | |||||||
\(420\) | −0.385349 | −0.0188031 | ||||||||
\(421\) | 18.2144 | 0.887717 | 0.443859 | − | 0.896097i | \(-0.353609\pi\) | ||||
0.443859 | + | 0.896097i | \(0.353609\pi\) | |||||||
\(422\) | 12.4346 | 0.605308 | ||||||||
\(423\) | −7.82060 | −0.380251 | ||||||||
\(424\) | 6.10135 | 0.296308 | ||||||||
\(425\) | −6.90760 | −0.335068 | ||||||||
\(426\) | −1.99243 | −0.0965337 | ||||||||
\(427\) | −0.0563360 | −0.00272629 | ||||||||
\(428\) | −10.2676 | −0.496304 | ||||||||
\(429\) | 2.17475 | 0.104998 | ||||||||
\(430\) | −0.940965 | −0.0453774 | ||||||||
\(431\) | 31.0681 | 1.49650 | 0.748248 | − | 0.663419i | \(-0.230895\pi\) | ||||
0.748248 | + | 0.663419i | \(0.230895\pi\) | |||||||
\(432\) | 2.79048 | 0.134257 | ||||||||
\(433\) | 13.2693 | 0.637684 | 0.318842 | − | 0.947808i | \(-0.396706\pi\) | ||||
0.318842 | + | 0.947808i | \(0.396706\pi\) | |||||||
\(434\) | −0.467940 | −0.0224618 | ||||||||
\(435\) | 13.3926 | 0.642126 | ||||||||
\(436\) | 19.4556 | 0.931756 | ||||||||
\(437\) | 24.1760 | 1.15650 | ||||||||
\(438\) | 21.5519 | 1.02979 | ||||||||
\(439\) | 22.5930 | 1.07831 | 0.539153 | − | 0.842208i | \(-0.318744\pi\) | ||||
0.539153 | + | 0.842208i | \(0.318744\pi\) | |||||||
\(440\) | 11.5132 | 0.548872 | ||||||||
\(441\) | −11.9994 | −0.571401 | ||||||||
\(442\) | 0.317860 | 0.0151191 | ||||||||
\(443\) | 10.0573 | 0.477838 | 0.238919 | − | 0.971039i | \(-0.423207\pi\) | ||||
0.238919 | + | 0.971039i | \(0.423207\pi\) | |||||||
\(444\) | −7.05284 | −0.334713 | ||||||||
\(445\) | −18.6378 | −0.883516 | ||||||||
\(446\) | −3.58277 | −0.169649 | ||||||||
\(447\) | −23.4761 | −1.11038 | ||||||||
\(448\) | 0.0526160 | 0.00248587 | ||||||||
\(449\) | −21.1930 | −1.00016 | −0.500080 | − | 0.865979i | \(-0.666696\pi\) | ||||
−0.500080 | + | 0.865979i | \(0.666696\pi\) | |||||||
\(450\) | −10.9346 | −0.515461 | ||||||||
\(451\) | 18.4425 | 0.868425 | ||||||||
\(452\) | −10.1419 | −0.477037 | ||||||||
\(453\) | 3.76020 | 0.176670 | ||||||||
\(454\) | −3.29537 | −0.154659 | ||||||||
\(455\) | 0.0520709 | 0.00244112 | ||||||||
\(456\) | 10.7275 | 0.502363 | ||||||||
\(457\) | −17.9721 | −0.840700 | −0.420350 | − | 0.907362i | \(-0.638093\pi\) | ||||
−0.420350 | + | 0.907362i | \(0.638093\pi\) | |||||||
\(458\) | −4.79651 | −0.224126 | ||||||||
\(459\) | −3.02299 | −0.141101 | ||||||||
\(460\) | 16.5052 | 0.769559 | ||||||||
\(461\) | 24.1633 | 1.12540 | 0.562698 | − | 0.826663i | \(-0.309763\pi\) | ||||
0.562698 | + | 0.826663i | \(0.309763\pi\) | |||||||
\(462\) | −0.389987 | −0.0181438 | ||||||||
\(463\) | 28.9577 | 1.34578 | 0.672890 | − | 0.739742i | \(-0.265053\pi\) | ||||
0.672890 | + | 0.739742i | \(0.265053\pi\) | |||||||
\(464\) | −1.82864 | −0.0848926 | ||||||||
\(465\) | −65.1340 | −3.02052 | ||||||||
\(466\) | 5.26170 | 0.243743 | ||||||||
\(467\) | 33.3211 | 1.54192 | 0.770958 | − | 0.636885i | \(-0.219778\pi\) | ||||
0.770958 | + | 0.636885i | \(0.219778\pi\) | |||||||
\(468\) | 0.503166 | 0.0232589 | ||||||||
\(469\) | −0.0771698 | −0.00356337 | ||||||||
\(470\) | 15.3818 | 0.709508 | ||||||||
\(471\) | −14.2524 | −0.656718 | ||||||||
\(472\) | −6.43470 | −0.296181 | ||||||||
\(473\) | −0.952291 | −0.0437864 | ||||||||
\(474\) | 16.7326 | 0.768554 | ||||||||
\(475\) | 31.5016 | 1.44539 | ||||||||
\(476\) | −0.0570003 | −0.00261260 | ||||||||
\(477\) | −10.4631 | −0.479073 | ||||||||
\(478\) | −15.1773 | −0.694192 | ||||||||
\(479\) | −1.90854 | −0.0872034 | −0.0436017 | − | 0.999049i | \(-0.513883\pi\) | ||||
−0.0436017 | + | 0.999049i | \(0.513883\pi\) | |||||||
\(480\) | 7.32379 | 0.334284 | ||||||||
\(481\) | 0.953028 | 0.0434544 | ||||||||
\(482\) | −10.6380 | −0.484546 | ||||||||
\(483\) | −0.559080 | −0.0254390 | ||||||||
\(484\) | 0.651811 | 0.0296278 | ||||||||
\(485\) | 31.3571 | 1.42385 | ||||||||
\(486\) | −15.9563 | −0.723793 | ||||||||
\(487\) | 7.65935 | 0.347078 | 0.173539 | − | 0.984827i | \(-0.444480\pi\) | ||||
0.173539 | + | 0.984827i | \(0.444480\pi\) | |||||||
\(488\) | 1.07070 | 0.0484683 | ||||||||
\(489\) | 8.71537 | 0.394123 | ||||||||
\(490\) | 23.6008 | 1.06618 | ||||||||
\(491\) | 0.234956 | 0.0106034 | 0.00530172 | − | 0.999986i | \(-0.498312\pi\) | ||||
0.00530172 | + | 0.999986i | \(0.498312\pi\) | |||||||
\(492\) | 11.7317 | 0.528904 | ||||||||
\(493\) | 1.98101 | 0.0892204 | ||||||||
\(494\) | −1.44958 | −0.0652196 | ||||||||
\(495\) | −19.7438 | −0.887419 | ||||||||
\(496\) | 8.89349 | 0.399329 | ||||||||
\(497\) | −0.0482799 | −0.00216565 | ||||||||
\(498\) | 15.0696 | 0.675285 | ||||||||
\(499\) | −7.08820 | −0.317312 | −0.158656 | − | 0.987334i | \(-0.550716\pi\) | ||||
−0.158656 | + | 0.987334i | \(0.550716\pi\) | |||||||
\(500\) | 4.64206 | 0.207599 | ||||||||
\(501\) | −36.0284 | −1.60963 | ||||||||
\(502\) | −5.44235 | −0.242904 | ||||||||
\(503\) | −0.149938 | −0.00668542 | −0.00334271 | − | 0.999994i | \(-0.501064\pi\) | ||||
−0.00334271 | + | 0.999994i | \(0.501064\pi\) | |||||||
\(504\) | −0.0902303 | −0.00401918 | ||||||||
\(505\) | −17.8312 | −0.793480 | ||||||||
\(506\) | 16.7039 | 0.742578 | ||||||||
\(507\) | 28.0410 | 1.24534 | ||||||||
\(508\) | −8.09666 | −0.359231 | ||||||||
\(509\) | 29.7847 | 1.32018 | 0.660091 | − | 0.751185i | \(-0.270518\pi\) | ||||
0.660091 | + | 0.751185i | \(0.270518\pi\) | |||||||
\(510\) | −7.93405 | −0.351325 | ||||||||
\(511\) | 0.522237 | 0.0231024 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 13.7861 | 0.608673 | ||||||||
\(514\) | −24.5266 | −1.08182 | ||||||||
\(515\) | 8.58656 | 0.378369 | ||||||||
\(516\) | −0.605771 | −0.0266676 | ||||||||
\(517\) | 15.5669 | 0.684632 | ||||||||
\(518\) | −0.170902 | −0.00750900 | ||||||||
\(519\) | 20.0561 | 0.880366 | ||||||||
\(520\) | −0.989640 | −0.0433986 | ||||||||
\(521\) | −2.44679 | −0.107196 | −0.0535979 | − | 0.998563i | \(-0.517069\pi\) | ||||
−0.0535979 | + | 0.998563i | \(0.517069\pi\) | |||||||
\(522\) | 3.13591 | 0.137255 | ||||||||
\(523\) | 20.1564 | 0.881378 | 0.440689 | − | 0.897660i | \(-0.354734\pi\) | ||||
0.440689 | + | 0.897660i | \(0.354734\pi\) | |||||||
\(524\) | −14.9833 | −0.654550 | ||||||||
\(525\) | −0.728487 | −0.0317938 | ||||||||
\(526\) | −8.42086 | −0.367167 | ||||||||
\(527\) | −9.63454 | −0.419687 | ||||||||
\(528\) | 7.41194 | 0.322563 | ||||||||
\(529\) | 0.946438 | 0.0411495 | ||||||||
\(530\) | 20.5791 | 0.893899 | ||||||||
\(531\) | 11.0348 | 0.478868 | ||||||||
\(532\) | 0.259946 | 0.0112701 | ||||||||
\(533\) | −1.58526 | −0.0686652 | ||||||||
\(534\) | −11.9986 | −0.519229 | ||||||||
\(535\) | −34.6314 | −1.49724 | ||||||||
\(536\) | 1.46666 | 0.0633501 | ||||||||
\(537\) | 10.1253 | 0.436938 | ||||||||
\(538\) | 8.95887 | 0.386244 | ||||||||
\(539\) | 23.8849 | 1.02879 | ||||||||
\(540\) | 9.41193 | 0.405025 | ||||||||
\(541\) | 5.29232 | 0.227534 | 0.113767 | − | 0.993507i | \(-0.463708\pi\) | ||||
0.113767 | + | 0.993507i | \(0.463708\pi\) | |||||||
\(542\) | 2.18160 | 0.0937078 | ||||||||
\(543\) | 12.8006 | 0.549328 | ||||||||
\(544\) | 1.08333 | 0.0464472 | ||||||||
\(545\) | 65.6215 | 2.81092 | ||||||||
\(546\) | 0.0335220 | 0.00143461 | ||||||||
\(547\) | −7.44203 | −0.318198 | −0.159099 | − | 0.987263i | \(-0.550859\pi\) | ||||
−0.159099 | + | 0.987263i | \(0.550859\pi\) | |||||||
\(548\) | 20.2771 | 0.866195 | ||||||||
\(549\) | −1.83612 | −0.0783639 | ||||||||
\(550\) | 21.7653 | 0.928076 | ||||||||
\(551\) | −9.03427 | −0.384873 | ||||||||
\(552\) | 10.6257 | 0.452258 | ||||||||
\(553\) | 0.405458 | 0.0172418 | ||||||||
\(554\) | 1.57566 | 0.0669435 | ||||||||
\(555\) | −23.7884 | −1.00976 | ||||||||
\(556\) | 18.8107 | 0.797753 | ||||||||
\(557\) | −8.07540 | −0.342166 | −0.171083 | − | 0.985257i | \(-0.554727\pi\) | ||||
−0.171083 | + | 0.985257i | \(0.554727\pi\) | |||||||
\(558\) | −15.2513 | −0.645638 | ||||||||
\(559\) | 0.0818559 | 0.00346214 | ||||||||
\(560\) | 0.177467 | 0.00749936 | ||||||||
\(561\) | −8.02955 | −0.339008 | ||||||||
\(562\) | −4.90892 | −0.207070 | ||||||||
\(563\) | 42.8489 | 1.80587 | 0.902933 | − | 0.429782i | \(-0.141409\pi\) | ||||
0.902933 | + | 0.429782i | \(0.141409\pi\) | |||||||
\(564\) | 9.90242 | 0.416967 | ||||||||
\(565\) | −34.2075 | −1.43912 | ||||||||
\(566\) | −20.2031 | −0.849199 | ||||||||
\(567\) | −0.589501 | −0.0247567 | ||||||||
\(568\) | 0.917589 | 0.0385012 | ||||||||
\(569\) | −17.8550 | −0.748521 | −0.374261 | − | 0.927324i | \(-0.622103\pi\) | ||||
−0.374261 | + | 0.927324i | \(0.622103\pi\) | |||||||
\(570\) | 36.1826 | 1.51552 | ||||||||
\(571\) | −23.9931 | −1.00408 | −0.502039 | − | 0.864845i | \(-0.667417\pi\) | ||||
−0.502039 | + | 0.864845i | \(0.667417\pi\) | |||||||
\(572\) | −1.00155 | −0.0418770 | ||||||||
\(573\) | −49.7159 | −2.07691 | ||||||||
\(574\) | 0.284277 | 0.0118655 | ||||||||
\(575\) | 31.2024 | 1.30123 | ||||||||
\(576\) | 1.71488 | 0.0714534 | ||||||||
\(577\) | −20.7860 | −0.865331 | −0.432666 | − | 0.901554i | \(-0.642427\pi\) | ||||
−0.432666 | + | 0.901554i | \(0.642427\pi\) | |||||||
\(578\) | 15.8264 | 0.658292 | ||||||||
\(579\) | 29.9735 | 1.24565 | ||||||||
\(580\) | −6.16778 | −0.256103 | ||||||||
\(581\) | 0.365161 | 0.0151494 | ||||||||
\(582\) | 20.1870 | 0.836777 | ||||||||
\(583\) | 20.8268 | 0.862559 | ||||||||
\(584\) | −9.92543 | −0.410717 | ||||||||
\(585\) | 1.69712 | 0.0701671 | ||||||||
\(586\) | 30.9205 | 1.27732 | ||||||||
\(587\) | 26.8652 | 1.10884 | 0.554422 | − | 0.832236i | \(-0.312939\pi\) | ||||
0.554422 | + | 0.832236i | \(0.312939\pi\) | |||||||
\(588\) | 15.1936 | 0.626575 | ||||||||
\(589\) | 43.9376 | 1.81042 | ||||||||
\(590\) | −21.7035 | −0.893517 | ||||||||
\(591\) | 14.5715 | 0.599393 | ||||||||
\(592\) | 3.24810 | 0.133496 | ||||||||
\(593\) | −13.2738 | −0.545088 | −0.272544 | − | 0.962143i | \(-0.587865\pi\) | ||||
−0.272544 | + | 0.962143i | \(0.587865\pi\) | |||||||
\(594\) | 9.52522 | 0.390825 | ||||||||
\(595\) | −0.192255 | −0.00788168 | ||||||||
\(596\) | 10.8116 | 0.442860 | ||||||||
\(597\) | 45.3876 | 1.85759 | ||||||||
\(598\) | −1.43581 | −0.0587147 | ||||||||
\(599\) | 5.62060 | 0.229651 | 0.114826 | − | 0.993386i | \(-0.463369\pi\) | ||||
0.114826 | + | 0.993386i | \(0.463369\pi\) | |||||||
\(600\) | 13.8453 | 0.565233 | ||||||||
\(601\) | 2.97529 | 0.121365 | 0.0606823 | − | 0.998157i | \(-0.480672\pi\) | ||||
0.0606823 | + | 0.998157i | \(0.480672\pi\) | |||||||
\(602\) | −0.0146788 | −0.000598264 0 | ||||||||
\(603\) | −2.51515 | −0.102425 | ||||||||
\(604\) | −1.73171 | −0.0704623 | ||||||||
\(605\) | 2.19848 | 0.0893809 | ||||||||
\(606\) | −11.4793 | −0.466316 | ||||||||
\(607\) | 16.1148 | 0.654078 | 0.327039 | − | 0.945011i | \(-0.393949\pi\) | ||||
0.327039 | + | 0.945011i | \(0.393949\pi\) | |||||||
\(608\) | −4.94043 | −0.200361 | ||||||||
\(609\) | 0.208921 | 0.00846591 | ||||||||
\(610\) | 3.61134 | 0.146219 | ||||||||
\(611\) | −1.33808 | −0.0541330 | ||||||||
\(612\) | −1.85778 | −0.0750961 | ||||||||
\(613\) | −11.3163 | −0.457059 | −0.228530 | − | 0.973537i | \(-0.573392\pi\) | ||||
−0.228530 | + | 0.973537i | \(0.573392\pi\) | |||||||
\(614\) | −23.4009 | −0.944382 | ||||||||
\(615\) | 39.5694 | 1.59559 | ||||||||
\(616\) | 0.179603 | 0.00723643 | ||||||||
\(617\) | 10.1319 | 0.407894 | 0.203947 | − | 0.978982i | \(-0.434623\pi\) | ||||
0.203947 | + | 0.978982i | \(0.434623\pi\) | |||||||
\(618\) | 5.52782 | 0.222362 | ||||||||
\(619\) | −21.7799 | −0.875408 | −0.437704 | − | 0.899119i | \(-0.644208\pi\) | ||||
−0.437704 | + | 0.899119i | \(0.644208\pi\) | |||||||
\(620\) | 29.9966 | 1.20469 | ||||||||
\(621\) | 13.6552 | 0.547965 | ||||||||
\(622\) | −23.3127 | −0.934756 | ||||||||
\(623\) | −0.290745 | −0.0116485 | ||||||||
\(624\) | −0.637107 | −0.0255047 | ||||||||
\(625\) | −16.2244 | −0.648975 | ||||||||
\(626\) | −19.4779 | −0.778494 | ||||||||
\(627\) | 36.6182 | 1.46239 | ||||||||
\(628\) | 6.56378 | 0.261923 | ||||||||
\(629\) | −3.51875 | −0.140302 | ||||||||
\(630\) | −0.304336 | −0.0121250 | ||||||||
\(631\) | 8.62936 | 0.343529 | 0.171765 | − | 0.985138i | \(-0.445053\pi\) | ||||
0.171765 | + | 0.985138i | \(0.445053\pi\) | |||||||
\(632\) | −7.70598 | −0.306527 | ||||||||
\(633\) | 27.0003 | 1.07316 | ||||||||
\(634\) | 14.2608 | 0.566370 | ||||||||
\(635\) | −27.3090 | −1.08373 | ||||||||
\(636\) | 13.2483 | 0.525331 | ||||||||
\(637\) | −2.05307 | −0.0813455 | ||||||||
\(638\) | −6.24203 | −0.247124 | ||||||||
\(639\) | −1.57356 | −0.0622490 | ||||||||
\(640\) | −3.37288 | −0.133325 | ||||||||
\(641\) | −47.1639 | −1.86286 | −0.931431 | − | 0.363919i | \(-0.881439\pi\) | ||||
−0.931431 | + | 0.363919i | \(0.881439\pi\) | |||||||
\(642\) | −22.2949 | −0.879908 | ||||||||
\(643\) | −6.38361 | −0.251745 | −0.125872 | − | 0.992046i | \(-0.540173\pi\) | ||||
−0.125872 | + | 0.992046i | \(0.540173\pi\) | |||||||
\(644\) | 0.257477 | 0.0101460 | ||||||||
\(645\) | −2.04319 | −0.0804506 | ||||||||
\(646\) | 5.35209 | 0.210575 | ||||||||
\(647\) | −0.534438 | −0.0210109 | −0.0105055 | − | 0.999945i | \(-0.503344\pi\) | ||||
−0.0105055 | + | 0.999945i | \(0.503344\pi\) | |||||||
\(648\) | 11.2038 | 0.440128 | ||||||||
\(649\) | −21.9647 | −0.862190 | ||||||||
\(650\) | −1.87088 | −0.0733818 | ||||||||
\(651\) | −1.01607 | −0.0398231 | ||||||||
\(652\) | −4.01375 | −0.157191 | ||||||||
\(653\) | 27.1867 | 1.06390 | 0.531949 | − | 0.846776i | \(-0.321460\pi\) | ||||
0.531949 | + | 0.846776i | \(0.321460\pi\) | |||||||
\(654\) | 42.2456 | 1.65193 | ||||||||
\(655\) | −50.5370 | −1.97464 | ||||||||
\(656\) | −5.40286 | −0.210946 | ||||||||
\(657\) | 17.0209 | 0.664050 | ||||||||
\(658\) | 0.239952 | 0.00935429 | ||||||||
\(659\) | 18.3397 | 0.714414 | 0.357207 | − | 0.934025i | \(-0.383729\pi\) | ||||
0.357207 | + | 0.934025i | \(0.383729\pi\) | |||||||
\(660\) | 24.9996 | 0.973107 | ||||||||
\(661\) | −14.5315 | −0.565208 | −0.282604 | − | 0.959237i | \(-0.591198\pi\) | ||||
−0.282604 | + | 0.959237i | \(0.591198\pi\) | |||||||
\(662\) | 15.5598 | 0.604749 | ||||||||
\(663\) | 0.690194 | 0.0268049 | ||||||||
\(664\) | −6.94011 | −0.269329 | ||||||||
\(665\) | 0.876764 | 0.0339995 | ||||||||
\(666\) | −5.57010 | −0.215837 | ||||||||
\(667\) | −8.94848 | −0.346487 | ||||||||
\(668\) | 16.5924 | 0.641980 | ||||||||
\(669\) | −7.77955 | −0.300775 | ||||||||
\(670\) | 4.94686 | 0.191114 | ||||||||
\(671\) | 3.65481 | 0.141092 | ||||||||
\(672\) | 0.114249 | 0.00440726 | ||||||||
\(673\) | −4.44013 | −0.171154 | −0.0855771 | − | 0.996332i | \(-0.527273\pi\) | ||||
−0.0855771 | + | 0.996332i | \(0.527273\pi\) | |||||||
\(674\) | −30.5380 | −1.17628 | ||||||||
\(675\) | 17.7929 | 0.684848 | ||||||||
\(676\) | −12.9139 | −0.496689 | ||||||||
\(677\) | 10.9973 | 0.422659 | 0.211329 | − | 0.977415i | \(-0.432221\pi\) | ||||
0.211329 | + | 0.977415i | \(0.432221\pi\) | |||||||
\(678\) | −22.0220 | −0.845749 | ||||||||
\(679\) | 0.489163 | 0.0187724 | ||||||||
\(680\) | 3.65392 | 0.140121 | ||||||||
\(681\) | −7.15549 | −0.274199 | ||||||||
\(682\) | 30.3577 | 1.16246 | ||||||||
\(683\) | 17.4871 | 0.669124 | 0.334562 | − | 0.942374i | \(-0.391412\pi\) | ||||
0.334562 | + | 0.942374i | \(0.391412\pi\) | |||||||
\(684\) | 8.47225 | 0.323945 | ||||||||
\(685\) | 68.3921 | 2.61313 | ||||||||
\(686\) | 0.736479 | 0.0281189 | ||||||||
\(687\) | −10.4150 | −0.397359 | ||||||||
\(688\) | 0.278980 | 0.0106360 | ||||||||
\(689\) | −1.79021 | −0.0682014 | ||||||||
\(690\) | 35.8390 | 1.36437 | ||||||||
\(691\) | −9.77547 | −0.371877 | −0.185938 | − | 0.982561i | \(-0.559532\pi\) | ||||
−0.185938 | + | 0.982561i | \(0.559532\pi\) | |||||||
\(692\) | −9.23659 | −0.351122 | ||||||||
\(693\) | −0.307999 | −0.0116999 | ||||||||
\(694\) | −22.7161 | −0.862292 | ||||||||
\(695\) | 63.4463 | 2.40665 | ||||||||
\(696\) | −3.97067 | −0.150508 | ||||||||
\(697\) | 5.85305 | 0.221700 | ||||||||
\(698\) | −2.98906 | −0.113138 | ||||||||
\(699\) | 11.4251 | 0.432138 | ||||||||
\(700\) | 0.335495 | 0.0126805 | ||||||||
\(701\) | 11.8508 | 0.447597 | 0.223799 | − | 0.974635i | \(-0.428154\pi\) | ||||
0.223799 | + | 0.974635i | \(0.428154\pi\) | |||||||
\(702\) | −0.818757 | −0.0309020 | ||||||||
\(703\) | 16.0470 | 0.605223 | ||||||||
\(704\) | −3.41347 | −0.128650 | ||||||||
\(705\) | 33.3996 | 1.25790 | ||||||||
\(706\) | −18.2499 | −0.686843 | ||||||||
\(707\) | −0.278163 | −0.0104614 | ||||||||
\(708\) | −13.9722 | −0.525106 | ||||||||
\(709\) | 3.49044 | 0.131086 | 0.0655431 | − | 0.997850i | \(-0.479122\pi\) | ||||
0.0655431 | + | 0.997850i | \(0.479122\pi\) | |||||||
\(710\) | 3.09491 | 0.116150 | ||||||||
\(711\) | 13.2148 | 0.495596 | ||||||||
\(712\) | 5.52579 | 0.207088 | ||||||||
\(713\) | 43.5204 | 1.62985 | ||||||||
\(714\) | −0.123769 | −0.00463194 | ||||||||
\(715\) | −3.37811 | −0.126334 | ||||||||
\(716\) | −4.66307 | −0.174267 | ||||||||
\(717\) | −32.9556 | −1.23075 | ||||||||
\(718\) | 27.0261 | 1.00860 | ||||||||
\(719\) | 32.1353 | 1.19844 | 0.599222 | − | 0.800583i | \(-0.295477\pi\) | ||||
0.599222 | + | 0.800583i | \(0.295477\pi\) | |||||||
\(720\) | 5.78409 | 0.215560 | ||||||||
\(721\) | 0.133948 | 0.00498849 | ||||||||
\(722\) | −5.40781 | −0.201258 | ||||||||
\(723\) | −23.0991 | −0.859063 | ||||||||
\(724\) | −5.89517 | −0.219092 | ||||||||
\(725\) | −11.6600 | −0.433040 | ||||||||
\(726\) | 1.41533 | 0.0525278 | ||||||||
\(727\) | 18.5752 | 0.688918 | 0.344459 | − | 0.938801i | \(-0.388062\pi\) | ||||
0.344459 | + | 0.938801i | \(0.388062\pi\) | |||||||
\(728\) | −0.0154381 | −0.000572176 0 | ||||||||
\(729\) | −1.03571 | −0.0383596 | ||||||||
\(730\) | −33.4772 | −1.23905 | ||||||||
\(731\) | −0.302226 | −0.0111782 | ||||||||
\(732\) | 2.32489 | 0.0859306 | ||||||||
\(733\) | −29.9659 | −1.10681 | −0.553407 | − | 0.832911i | \(-0.686673\pi\) | ||||
−0.553407 | + | 0.832911i | \(0.686673\pi\) | |||||||
\(734\) | 13.0432 | 0.481434 | ||||||||
\(735\) | 51.2462 | 1.89025 | ||||||||
\(736\) | −4.89351 | −0.180377 | ||||||||
\(737\) | 5.00641 | 0.184413 | ||||||||
\(738\) | 9.26527 | 0.341059 | ||||||||
\(739\) | −16.7066 | −0.614563 | −0.307281 | − | 0.951619i | \(-0.599419\pi\) | ||||
−0.307281 | + | 0.951619i | \(0.599419\pi\) | |||||||
\(740\) | 10.9554 | 0.402729 | ||||||||
\(741\) | −3.14758 | −0.115629 | ||||||||
\(742\) | 0.321029 | 0.0117853 | ||||||||
\(743\) | 0.334126 | 0.0122579 | 0.00612894 | − | 0.999981i | \(-0.498049\pi\) | ||||
0.00612894 | + | 0.999981i | \(0.498049\pi\) | |||||||
\(744\) | 19.3111 | 0.707980 | ||||||||
\(745\) | 36.4662 | 1.33602 | ||||||||
\(746\) | −19.5704 | −0.716524 | ||||||||
\(747\) | 11.9015 | 0.435452 | ||||||||
\(748\) | 3.69790 | 0.135209 | ||||||||
\(749\) | −0.540241 | −0.0197400 | ||||||||
\(750\) | 10.0797 | 0.368057 | ||||||||
\(751\) | −15.6295 | −0.570329 | −0.285165 | − | 0.958479i | \(-0.592048\pi\) | ||||
−0.285165 | + | 0.958479i | \(0.592048\pi\) | |||||||
\(752\) | −4.56043 | −0.166302 | ||||||||
\(753\) | −11.8174 | −0.430650 | ||||||||
\(754\) | 0.536544 | 0.0195398 | ||||||||
\(755\) | −5.84085 | −0.212570 | ||||||||
\(756\) | 0.146824 | 0.00533993 | ||||||||
\(757\) | 28.6649 | 1.04184 | 0.520922 | − | 0.853604i | \(-0.325588\pi\) | ||||
0.520922 | + | 0.853604i | \(0.325588\pi\) | |||||||
\(758\) | −17.7294 | −0.643962 | ||||||||
\(759\) | 36.2704 | 1.31653 | ||||||||
\(760\) | −16.6634 | −0.604447 | ||||||||
\(761\) | 2.00984 | 0.0728568 | 0.0364284 | − | 0.999336i | \(-0.488402\pi\) | ||||
0.0364284 | + | 0.999336i | \(0.488402\pi\) | |||||||
\(762\) | −17.5809 | −0.636889 | ||||||||
\(763\) | 1.02368 | 0.0370597 | ||||||||
\(764\) | 22.8960 | 0.828348 | ||||||||
\(765\) | −6.26605 | −0.226549 | ||||||||
\(766\) | 35.3338 | 1.27666 | ||||||||
\(767\) | 1.88802 | 0.0681723 | ||||||||
\(768\) | −2.17138 | −0.0783529 | ||||||||
\(769\) | −18.7370 | −0.675674 | −0.337837 | − | 0.941205i | \(-0.609695\pi\) | ||||
−0.337837 | + | 0.941205i | \(0.609695\pi\) | |||||||
\(770\) | 0.605780 | 0.0218308 | ||||||||
\(771\) | −53.2565 | −1.91799 | ||||||||
\(772\) | −13.8039 | −0.496813 | ||||||||
\(773\) | 52.7636 | 1.89777 | 0.948887 | − | 0.315617i | \(-0.102211\pi\) | ||||
0.948887 | + | 0.315617i | \(0.102211\pi\) | |||||||
\(774\) | −0.478418 | −0.0171964 | ||||||||
\(775\) | 56.7075 | 2.03699 | ||||||||
\(776\) | −9.29685 | −0.333738 | ||||||||
\(777\) | −0.371093 | −0.0133129 | ||||||||
\(778\) | 13.8339 | 0.495968 | ||||||||
\(779\) | −26.6924 | −0.956356 | ||||||||
\(780\) | −2.14888 | −0.0769423 | ||||||||
\(781\) | 3.13217 | 0.112078 | ||||||||
\(782\) | 5.30126 | 0.189573 | ||||||||
\(783\) | −5.10278 | −0.182359 | ||||||||
\(784\) | −6.99723 | −0.249901 | ||||||||
\(785\) | 22.1388 | 0.790168 | ||||||||
\(786\) | −32.5345 | −1.16047 | ||||||||
\(787\) | 36.2565 | 1.29240 | 0.646202 | − | 0.763167i | \(-0.276356\pi\) | ||||
0.646202 | + | 0.763167i | \(0.276356\pi\) | |||||||
\(788\) | −6.71073 | −0.239060 | ||||||||
\(789\) | −18.2849 | −0.650959 | ||||||||
\(790\) | −25.9913 | −0.924729 | ||||||||
\(791\) | −0.533629 | −0.0189736 | ||||||||
\(792\) | 5.85371 | 0.208002 | ||||||||
\(793\) | −0.314156 | −0.0111560 | ||||||||
\(794\) | 5.42374 | 0.192481 | ||||||||
\(795\) | 44.6850 | 1.58481 | ||||||||
\(796\) | −20.9027 | −0.740876 | ||||||||
\(797\) | −44.3874 | −1.57228 | −0.786141 | − | 0.618047i | \(-0.787924\pi\) | ||||
−0.786141 | + | 0.618047i | \(0.787924\pi\) | |||||||
\(798\) | 0.564440 | 0.0199810 | ||||||||
\(799\) | 4.94043 | 0.174780 | ||||||||
\(800\) | −6.37629 | −0.225436 | ||||||||
\(801\) | −9.47608 | −0.334821 | ||||||||
\(802\) | 21.3314 | 0.753240 | ||||||||
\(803\) | −33.8802 | −1.19561 | ||||||||
\(804\) | 3.18467 | 0.112315 | ||||||||
\(805\) | 0.868438 | 0.0306084 | ||||||||
\(806\) | −2.60945 | −0.0919140 | ||||||||
\(807\) | 19.4531 | 0.684781 | ||||||||
\(808\) | 5.28666 | 0.185984 | ||||||||
\(809\) | −20.7123 | −0.728205 | −0.364103 | − | 0.931359i | \(-0.618624\pi\) | ||||
−0.364103 | + | 0.931359i | \(0.618624\pi\) | |||||||
\(810\) | 37.7891 | 1.32777 | ||||||||
\(811\) | 24.0203 | 0.843468 | 0.421734 | − | 0.906720i | \(-0.361422\pi\) | ||||
0.421734 | + | 0.906720i | \(0.361422\pi\) | |||||||
\(812\) | −0.0962159 | −0.00337652 | ||||||||
\(813\) | 4.73708 | 0.166137 | ||||||||
\(814\) | 11.0873 | 0.388610 | ||||||||
\(815\) | −13.5379 | −0.474211 | ||||||||
\(816\) | 2.35231 | 0.0823473 | ||||||||
\(817\) | 1.37828 | 0.0482199 | ||||||||
\(818\) | 1.57475 | 0.0550599 | ||||||||
\(819\) | 0.0264746 | 0.000925097 0 | ||||||||
\(820\) | −18.2232 | −0.636381 | ||||||||
\(821\) | −11.9459 | −0.416916 | −0.208458 | − | 0.978031i | \(-0.566844\pi\) | ||||
−0.208458 | + | 0.978031i | \(0.566844\pi\) | |||||||
\(822\) | 44.0292 | 1.53570 | ||||||||
\(823\) | −0.528155 | −0.0184103 | −0.00920516 | − | 0.999958i | \(-0.502930\pi\) | ||||
−0.00920516 | + | 0.999958i | \(0.502930\pi\) | |||||||
\(824\) | −2.54577 | −0.0886860 | ||||||||
\(825\) | 47.2607 | 1.64541 | ||||||||
\(826\) | −0.338569 | −0.0117803 | ||||||||
\(827\) | −32.2798 | −1.12248 | −0.561240 | − | 0.827653i | \(-0.689676\pi\) | ||||
−0.561240 | + | 0.827653i | \(0.689676\pi\) | |||||||
\(828\) | 8.39179 | 0.291635 | ||||||||
\(829\) | 22.0972 | 0.767469 | 0.383734 | − | 0.923443i | \(-0.374638\pi\) | ||||
0.383734 | + | 0.923443i | \(0.374638\pi\) | |||||||
\(830\) | −23.4081 | −0.812508 | ||||||||
\(831\) | 3.42136 | 0.118686 | ||||||||
\(832\) | 0.293411 | 0.0101722 | ||||||||
\(833\) | 7.58028 | 0.262641 | ||||||||
\(834\) | 40.8452 | 1.41435 | ||||||||
\(835\) | 55.9641 | 1.93672 | ||||||||
\(836\) | −16.8640 | −0.583254 | ||||||||
\(837\) | 24.8171 | 0.857803 | ||||||||
\(838\) | −12.1007 | −0.418012 | ||||||||
\(839\) | 16.9642 | 0.585670 | 0.292835 | − | 0.956163i | \(-0.405401\pi\) | ||||
0.292835 | + | 0.956163i | \(0.405401\pi\) | |||||||
\(840\) | 0.385349 | 0.0132958 | ||||||||
\(841\) | −25.6561 | −0.884692 | ||||||||
\(842\) | −18.2144 | −0.627711 | ||||||||
\(843\) | −10.6591 | −0.367119 | ||||||||
\(844\) | −12.4346 | −0.428018 | ||||||||
\(845\) | −43.5570 | −1.49841 | ||||||||
\(846\) | 7.82060 | 0.268878 | ||||||||
\(847\) | 0.0342957 | 0.00117842 | ||||||||
\(848\) | −6.10135 | −0.209521 | ||||||||
\(849\) | −43.8685 | −1.50556 | ||||||||
\(850\) | 6.90760 | 0.236929 | ||||||||
\(851\) | 15.8946 | 0.544860 | ||||||||
\(852\) | 1.99243 | 0.0682596 | ||||||||
\(853\) | −21.2802 | −0.728620 | −0.364310 | − | 0.931278i | \(-0.618695\pi\) | ||||
−0.364310 | + | 0.931278i | \(0.618695\pi\) | |||||||
\(854\) | 0.0563360 | 0.00192778 | ||||||||
\(855\) | 28.5758 | 0.977273 | ||||||||
\(856\) | 10.2676 | 0.350940 | ||||||||
\(857\) | 33.7329 | 1.15229 | 0.576147 | − | 0.817346i | \(-0.304555\pi\) | ||||
0.576147 | + | 0.817346i | \(0.304555\pi\) | |||||||
\(858\) | −2.17475 | −0.0742447 | ||||||||
\(859\) | 5.42159 | 0.184982 | 0.0924911 | − | 0.995714i | \(-0.470517\pi\) | ||||
0.0924911 | + | 0.995714i | \(0.470517\pi\) | |||||||
\(860\) | 0.940965 | 0.0320866 | ||||||||
\(861\) | 0.617273 | 0.0210366 | ||||||||
\(862\) | −31.0681 | −1.05818 | ||||||||
\(863\) | −13.6631 | −0.465097 | −0.232548 | − | 0.972585i | \(-0.574706\pi\) | ||||
−0.232548 | + | 0.972585i | \(0.574706\pi\) | |||||||
\(864\) | −2.79048 | −0.0949339 | ||||||||
\(865\) | −31.1539 | −1.05926 | ||||||||
\(866\) | −13.2693 | −0.450910 | ||||||||
\(867\) | 34.3651 | 1.16710 | ||||||||
\(868\) | 0.467940 | 0.0158829 | ||||||||
\(869\) | −26.3042 | −0.892308 | ||||||||
\(870\) | −13.3926 | −0.454051 | ||||||||
\(871\) | −0.430335 | −0.0145813 | ||||||||
\(872\) | −19.4556 | −0.658851 | ||||||||
\(873\) | 15.9430 | 0.539589 | ||||||||
\(874\) | −24.1760 | −0.817766 | ||||||||
\(875\) | 0.244247 | 0.00825704 | ||||||||
\(876\) | −21.5519 | −0.728170 | ||||||||
\(877\) | −17.9992 | −0.607788 | −0.303894 | − | 0.952706i | \(-0.598287\pi\) | ||||
−0.303894 | + | 0.952706i | \(0.598287\pi\) | |||||||
\(878\) | −22.5930 | −0.762478 | ||||||||
\(879\) | 67.1402 | 2.26458 | ||||||||
\(880\) | −11.5132 | −0.388111 | ||||||||
\(881\) | 14.3527 | 0.483554 | 0.241777 | − | 0.970332i | \(-0.422270\pi\) | ||||
0.241777 | + | 0.970332i | \(0.422270\pi\) | |||||||
\(882\) | 11.9994 | 0.404042 | ||||||||
\(883\) | −1.20679 | −0.0406117 | −0.0203058 | − | 0.999794i | \(-0.506464\pi\) | ||||
−0.0203058 | + | 0.999794i | \(0.506464\pi\) | |||||||
\(884\) | −0.317860 | −0.0106908 | ||||||||
\(885\) | −47.1264 | −1.58414 | ||||||||
\(886\) | −10.0573 | −0.337883 | ||||||||
\(887\) | 42.0093 | 1.41053 | 0.705267 | − | 0.708942i | \(-0.250827\pi\) | ||||
0.705267 | + | 0.708942i | \(0.250827\pi\) | |||||||
\(888\) | 7.05284 | 0.236678 | ||||||||
\(889\) | −0.426014 | −0.0142880 | ||||||||
\(890\) | 18.6378 | 0.624740 | ||||||||
\(891\) | 38.2440 | 1.28122 | ||||||||
\(892\) | 3.58277 | 0.119960 | ||||||||
\(893\) | −22.5305 | −0.753953 | ||||||||
\(894\) | 23.4761 | 0.785157 | ||||||||
\(895\) | −15.7279 | −0.525727 | ||||||||
\(896\) | −0.0526160 | −0.00175778 | ||||||||
\(897\) | −3.11769 | −0.104097 | ||||||||
\(898\) | 21.1930 | 0.707220 | ||||||||
\(899\) | −16.2630 | −0.542402 | ||||||||
\(900\) | 10.9346 | 0.364486 | ||||||||
\(901\) | 6.60975 | 0.220203 | ||||||||
\(902\) | −18.4425 | −0.614069 | ||||||||
\(903\) | −0.0318733 | −0.00106068 | ||||||||
\(904\) | 10.1419 | 0.337316 | ||||||||
\(905\) | −19.8837 | −0.660955 | ||||||||
\(906\) | −3.76020 | −0.124924 | ||||||||
\(907\) | 58.8286 | 1.95337 | 0.976685 | − | 0.214675i | \(-0.0688693\pi\) | ||||
0.976685 | + | 0.214675i | \(0.0688693\pi\) | |||||||
\(908\) | 3.29537 | 0.109361 | ||||||||
\(909\) | −9.06600 | −0.300700 | ||||||||
\(910\) | −0.0520709 | −0.00172613 | ||||||||
\(911\) | −9.36336 | −0.310222 | −0.155111 | − | 0.987897i | \(-0.549573\pi\) | ||||
−0.155111 | + | 0.987897i | \(0.549573\pi\) | |||||||
\(912\) | −10.7275 | −0.355224 | ||||||||
\(913\) | −23.6899 | −0.784021 | ||||||||
\(914\) | 17.9721 | 0.594464 | ||||||||
\(915\) | 7.84158 | 0.259235 | ||||||||
\(916\) | 4.79651 | 0.158481 | ||||||||
\(917\) | −0.788364 | −0.0260341 | ||||||||
\(918\) | 3.02299 | 0.0997736 | ||||||||
\(919\) | −28.0614 | −0.925659 | −0.462830 | − | 0.886447i | \(-0.653166\pi\) | ||||
−0.462830 | + | 0.886447i | \(0.653166\pi\) | |||||||
\(920\) | −16.5052 | −0.544160 | ||||||||
\(921\) | −50.8121 | −1.67432 | ||||||||
\(922\) | −24.1633 | −0.795775 | ||||||||
\(923\) | −0.269231 | −0.00886185 | ||||||||
\(924\) | 0.389987 | 0.0128296 | ||||||||
\(925\) | 20.7108 | 0.680967 | ||||||||
\(926\) | −28.9577 | −0.951611 | ||||||||
\(927\) | 4.36569 | 0.143388 | ||||||||
\(928\) | 1.82864 | 0.0600281 | ||||||||
\(929\) | 40.8244 | 1.33941 | 0.669703 | − | 0.742629i | \(-0.266421\pi\) | ||||
0.669703 | + | 0.742629i | \(0.266421\pi\) | |||||||
\(930\) | 65.1340 | 2.13583 | ||||||||
\(931\) | −34.5693 | −1.13296 | ||||||||
\(932\) | −5.26170 | −0.172353 | ||||||||
\(933\) | −50.6208 | −1.65725 | ||||||||
\(934\) | −33.3211 | −1.09030 | ||||||||
\(935\) | 12.4726 | 0.407897 | ||||||||
\(936\) | −0.503166 | −0.0164465 | ||||||||
\(937\) | 2.41784 | 0.0789873 | 0.0394936 | − | 0.999220i | \(-0.487426\pi\) | ||||
0.0394936 | + | 0.999220i | \(0.487426\pi\) | |||||||
\(938\) | 0.0771698 | 0.00251968 | ||||||||
\(939\) | −42.2939 | −1.38021 | ||||||||
\(940\) | −15.3818 | −0.501698 | ||||||||
\(941\) | −9.50988 | −0.310013 | −0.155007 | − | 0.987913i | \(-0.549540\pi\) | ||||
−0.155007 | + | 0.987913i | \(0.549540\pi\) | |||||||
\(942\) | 14.2524 | 0.464370 | ||||||||
\(943\) | −26.4389 | −0.860971 | ||||||||
\(944\) | 6.43470 | 0.209432 | ||||||||
\(945\) | 0.495218 | 0.0161095 | ||||||||
\(946\) | 0.952291 | 0.0309617 | ||||||||
\(947\) | −23.0342 | −0.748511 | −0.374255 | − | 0.927326i | \(-0.622102\pi\) | ||||
−0.374255 | + | 0.927326i | \(0.622102\pi\) | |||||||
\(948\) | −16.7326 | −0.543449 | ||||||||
\(949\) | 2.91223 | 0.0945351 | ||||||||
\(950\) | −31.5016 | −1.02205 | ||||||||
\(951\) | 30.9657 | 1.00413 | ||||||||
\(952\) | 0.0570003 | 0.00184739 | ||||||||
\(953\) | 43.4618 | 1.40786 | 0.703932 | − | 0.710267i | \(-0.251426\pi\) | ||||
0.703932 | + | 0.710267i | \(0.251426\pi\) | |||||||
\(954\) | 10.4631 | 0.338756 | ||||||||
\(955\) | 77.2254 | 2.49895 | ||||||||
\(956\) | 15.1773 | 0.490868 | ||||||||
\(957\) | −13.5538 | −0.438132 | ||||||||
\(958\) | 1.90854 | 0.0616621 | ||||||||
\(959\) | 1.06690 | 0.0344520 | ||||||||
\(960\) | −7.32379 | −0.236374 | ||||||||
\(961\) | 48.0941 | 1.55142 | ||||||||
\(962\) | −0.953028 | −0.0307269 | ||||||||
\(963\) | −17.6077 | −0.567402 | ||||||||
\(964\) | 10.6380 | 0.342626 | ||||||||
\(965\) | −46.5588 | −1.49878 | ||||||||
\(966\) | 0.559080 | 0.0179881 | ||||||||
\(967\) | 25.3324 | 0.814636 | 0.407318 | − | 0.913286i | \(-0.366464\pi\) | ||||
0.407318 | + | 0.913286i | \(0.366464\pi\) | |||||||
\(968\) | −0.651811 | −0.0209500 | ||||||||
\(969\) | 11.6214 | 0.373333 | ||||||||
\(970\) | −31.3571 | −1.00682 | ||||||||
\(971\) | −24.8363 | −0.797035 | −0.398517 | − | 0.917161i | \(-0.630475\pi\) | ||||
−0.398517 | + | 0.917161i | \(0.630475\pi\) | |||||||
\(972\) | 15.9563 | 0.511799 | ||||||||
\(973\) | 0.989746 | 0.0317298 | ||||||||
\(974\) | −7.65935 | −0.245421 | ||||||||
\(975\) | −4.06238 | −0.130100 | ||||||||
\(976\) | −1.07070 | −0.0342723 | ||||||||
\(977\) | −12.7607 | −0.408252 | −0.204126 | − | 0.978945i | \(-0.565435\pi\) | ||||
−0.204126 | + | 0.978945i | \(0.565435\pi\) | |||||||
\(978\) | −8.71537 | −0.278687 | ||||||||
\(979\) | 18.8621 | 0.602836 | ||||||||
\(980\) | −23.6008 | −0.753900 | ||||||||
\(981\) | 33.3641 | 1.06524 | ||||||||
\(982\) | −0.234956 | −0.00749776 | ||||||||
\(983\) | −5.46648 | −0.174353 | −0.0871767 | − | 0.996193i | \(-0.527784\pi\) | ||||
−0.0871767 | + | 0.996193i | \(0.527784\pi\) | |||||||
\(984\) | −11.7317 | −0.373991 | ||||||||
\(985\) | −22.6345 | −0.721194 | ||||||||
\(986\) | −1.98101 | −0.0630884 | ||||||||
\(987\) | 0.521026 | 0.0165844 | ||||||||
\(988\) | 1.44958 | 0.0461172 | ||||||||
\(989\) | 1.36519 | 0.0434106 | ||||||||
\(990\) | 19.7438 | 0.627500 | ||||||||
\(991\) | 25.6486 | 0.814756 | 0.407378 | − | 0.913260i | \(-0.366443\pi\) | ||||
0.407378 | + | 0.913260i | \(0.366443\pi\) | |||||||
\(992\) | −8.89349 | −0.282369 | ||||||||
\(993\) | 33.7862 | 1.07217 | ||||||||
\(994\) | 0.0482799 | 0.00153135 | ||||||||
\(995\) | −70.5021 | −2.23507 | ||||||||
\(996\) | −15.0696 | −0.477499 | ||||||||
\(997\) | 61.2966 | 1.94128 | 0.970641 | − | 0.240534i | \(-0.0773227\pi\) | ||||
0.970641 | + | 0.240534i | \(0.0773227\pi\) | |||||||
\(998\) | 7.08820 | 0.224373 | ||||||||
\(999\) | 9.06373 | 0.286764 |
(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 | 8042.2.a.c.1.15 | ✓ | 86 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8042.2.a.c.1.15 | ✓ | 86 | 1.1 | even | 1 | trivial |