Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 14 x^{14} + 68 x^{13} + 64 x^{12} - 456 x^{11} - 54 x^{10} + 1532 x^{9} - 400 x^{8} + \cdots - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.64639\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.64639 | −1.16417 | −0.582086 | − | 0.813127i | \(-0.697763\pi\) | ||||
−0.582086 | + | 0.813127i | \(0.697763\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.710595 | 0.355297 | ||||||||
\(5\) | 0.0457395 | 0.0204553 | 0.0102277 | − | 0.999948i | \(-0.496744\pi\) | ||||
0.0102277 | + | 0.999948i | \(0.496744\pi\) | |||||||
\(6\) | −1.64639 | −0.672135 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.12286 | 0.750545 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.0753050 | −0.0238135 | ||||||||
\(11\) | 0.153516 | 0.0462868 | 0.0231434 | − | 0.999732i | \(-0.492633\pi\) | ||||
0.0231434 | + | 0.999732i | \(0.492633\pi\) | |||||||
\(12\) | 0.710595 | 0.205131 | ||||||||
\(13\) | 3.46056 | 0.959786 | 0.479893 | − | 0.877327i | \(-0.340675\pi\) | ||||
0.479893 | + | 0.877327i | \(0.340675\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0457395 | 0.0118099 | ||||||||
\(16\) | −4.91624 | −1.22906 | ||||||||
\(17\) | −0.713284 | −0.172997 | −0.0864984 | − | 0.996252i | \(-0.527568\pi\) | ||||
−0.0864984 | + | 0.996252i | \(0.527568\pi\) | |||||||
\(18\) | −1.64639 | −0.388057 | ||||||||
\(19\) | −6.38590 | −1.46503 | −0.732513 | − | 0.680754i | \(-0.761652\pi\) | ||||
−0.732513 | + | 0.680754i | \(0.761652\pi\) | |||||||
\(20\) | 0.0325023 | 0.00726773 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.252747 | −0.0538858 | ||||||||
\(23\) | −1.26532 | −0.263838 | −0.131919 | − | 0.991261i | \(-0.542114\pi\) | ||||
−0.131919 | + | 0.991261i | \(0.542114\pi\) | |||||||
\(24\) | 2.12286 | 0.433327 | ||||||||
\(25\) | −4.99791 | −0.999582 | ||||||||
\(26\) | −5.69742 | −1.11736 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.30954 | 0.243175 | 0.121587 | − | 0.992581i | \(-0.461202\pi\) | ||||
0.121587 | + | 0.992581i | \(0.461202\pi\) | |||||||
\(30\) | −0.0753050 | −0.0137487 | ||||||||
\(31\) | 0.735747 | 0.132144 | 0.0660721 | − | 0.997815i | \(-0.478953\pi\) | ||||
0.0660721 | + | 0.997815i | \(0.478953\pi\) | |||||||
\(32\) | 3.84832 | 0.680294 | ||||||||
\(33\) | 0.153516 | 0.0267237 | ||||||||
\(34\) | 1.17434 | 0.201398 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.710595 | 0.118432 | ||||||||
\(37\) | 9.12498 | 1.50014 | 0.750069 | − | 0.661360i | \(-0.230020\pi\) | ||||
0.750069 | + | 0.661360i | \(0.230020\pi\) | |||||||
\(38\) | 10.5137 | 1.70554 | ||||||||
\(39\) | 3.46056 | 0.554133 | ||||||||
\(40\) | 0.0970987 | 0.0153526 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.39572 | 0.365344 | 0.182672 | − | 0.983174i | \(-0.441525\pi\) | ||||
0.182672 | + | 0.983174i | \(0.441525\pi\) | |||||||
\(44\) | 0.109088 | 0.0164456 | ||||||||
\(45\) | 0.0457395 | 0.00681844 | ||||||||
\(46\) | 2.08321 | 0.307152 | ||||||||
\(47\) | 9.00229 | 1.31312 | 0.656560 | − | 0.754274i | \(-0.272011\pi\) | ||||
0.656560 | + | 0.754274i | \(0.272011\pi\) | |||||||
\(48\) | −4.91624 | −0.709599 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 8.22850 | 1.16369 | ||||||||
\(51\) | −0.713284 | −0.0998798 | ||||||||
\(52\) | 2.45905 | 0.341009 | ||||||||
\(53\) | −14.1311 | −1.94106 | −0.970529 | − | 0.240985i | \(-0.922529\pi\) | ||||
−0.970529 | + | 0.240985i | \(0.922529\pi\) | |||||||
\(54\) | −1.64639 | −0.224045 | ||||||||
\(55\) | 0.00702175 | 0.000946812 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.38590 | −0.845833 | ||||||||
\(58\) | −2.15600 | −0.283097 | ||||||||
\(59\) | −11.3136 | −1.47291 | −0.736454 | − | 0.676488i | \(-0.763501\pi\) | ||||
−0.736454 | + | 0.676488i | \(0.763501\pi\) | |||||||
\(60\) | 0.0325023 | 0.00419602 | ||||||||
\(61\) | −14.2763 | −1.82789 | −0.913946 | − | 0.405836i | \(-0.866980\pi\) | ||||
−0.913946 | + | 0.405836i | \(0.866980\pi\) | |||||||
\(62\) | −1.21133 | −0.153839 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.49665 | 0.437081 | ||||||||
\(65\) | 0.158284 | 0.0196327 | ||||||||
\(66\) | −0.252747 | −0.0311110 | ||||||||
\(67\) | −13.3603 | −1.63222 | −0.816109 | − | 0.577898i | \(-0.803873\pi\) | ||||
−0.816109 | + | 0.577898i | \(0.803873\pi\) | |||||||
\(68\) | −0.506856 | −0.0614653 | ||||||||
\(69\) | −1.26532 | −0.152327 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.60480 | −0.783846 | −0.391923 | − | 0.919998i | \(-0.628190\pi\) | ||||
−0.391923 | + | 0.919998i | \(0.628190\pi\) | |||||||
\(72\) | 2.12286 | 0.250182 | ||||||||
\(73\) | 15.8710 | 1.85756 | 0.928778 | − | 0.370637i | \(-0.120861\pi\) | ||||
0.928778 | + | 0.370637i | \(0.120861\pi\) | |||||||
\(74\) | −15.0233 | −1.74642 | ||||||||
\(75\) | −4.99791 | −0.577109 | ||||||||
\(76\) | −4.53778 | −0.520520 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.69742 | −0.645106 | ||||||||
\(79\) | −6.18509 | −0.695877 | −0.347938 | − | 0.937517i | \(-0.613118\pi\) | ||||
−0.347938 | + | 0.937517i | \(0.613118\pi\) | |||||||
\(80\) | −0.224867 | −0.0251409 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.64639 | −0.181813 | ||||||||
\(83\) | −2.20561 | −0.242097 | −0.121048 | − | 0.992647i | \(-0.538626\pi\) | ||||
−0.121048 | + | 0.992647i | \(0.538626\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0326253 | −0.00353871 | ||||||||
\(86\) | −3.94428 | −0.425323 | ||||||||
\(87\) | 1.30954 | 0.140397 | ||||||||
\(88\) | 0.325893 | 0.0347403 | ||||||||
\(89\) | −14.3331 | −1.51930 | −0.759651 | − | 0.650332i | \(-0.774630\pi\) | ||||
−0.759651 | + | 0.650332i | \(0.774630\pi\) | |||||||
\(90\) | −0.0753050 | −0.00793784 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.899130 | −0.0937408 | ||||||||
\(93\) | 0.735747 | 0.0762935 | ||||||||
\(94\) | −14.8213 | −1.52870 | ||||||||
\(95\) | −0.292088 | −0.0299676 | ||||||||
\(96\) | 3.84832 | 0.392768 | ||||||||
\(97\) | −8.42652 | −0.855583 | −0.427792 | − | 0.903877i | \(-0.640708\pi\) | ||||
−0.427792 | + | 0.903877i | \(0.640708\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.153516 | 0.0154289 | ||||||||
\(100\) | −3.55149 | −0.355149 | ||||||||
\(101\) | −4.27869 | −0.425746 | −0.212873 | − | 0.977080i | \(-0.568282\pi\) | ||||
−0.212873 | + | 0.977080i | \(0.568282\pi\) | |||||||
\(102\) | 1.17434 | 0.116277 | ||||||||
\(103\) | 8.86287 | 0.873284 | 0.436642 | − | 0.899635i | \(-0.356168\pi\) | ||||
0.436642 | + | 0.899635i | \(0.356168\pi\) | |||||||
\(104\) | 7.34629 | 0.720363 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 23.2653 | 2.25973 | ||||||||
\(107\) | 2.93535 | 0.283771 | 0.141886 | − | 0.989883i | \(-0.454683\pi\) | ||||
0.141886 | + | 0.989883i | \(0.454683\pi\) | |||||||
\(108\) | 0.710595 | 0.0683770 | ||||||||
\(109\) | −8.56169 | −0.820061 | −0.410030 | − | 0.912072i | \(-0.634482\pi\) | ||||
−0.410030 | + | 0.912072i | \(0.634482\pi\) | |||||||
\(110\) | −0.0115605 | −0.00110225 | ||||||||
\(111\) | 9.12498 | 0.866105 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.56761 | 0.805973 | 0.402986 | − | 0.915206i | \(-0.367972\pi\) | ||||
0.402986 | + | 0.915206i | \(0.367972\pi\) | |||||||
\(114\) | 10.5137 | 0.984695 | ||||||||
\(115\) | −0.0578751 | −0.00539688 | ||||||||
\(116\) | 0.930549 | 0.0863993 | ||||||||
\(117\) | 3.46056 | 0.319929 | ||||||||
\(118\) | 18.6266 | 1.71472 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.0970987 | 0.00886385 | ||||||||
\(121\) | −10.9764 | −0.997858 | ||||||||
\(122\) | 23.5043 | 2.12798 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 0.522818 | 0.0469505 | ||||||||
\(125\) | −0.457299 | −0.0409021 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.852507 | −0.0756478 | −0.0378239 | − | 0.999284i | \(-0.512043\pi\) | ||||
−0.0378239 | + | 0.999284i | \(0.512043\pi\) | |||||||
\(128\) | −13.4535 | −1.18913 | ||||||||
\(129\) | 2.39572 | 0.210931 | ||||||||
\(130\) | −0.260597 | −0.0228559 | ||||||||
\(131\) | −10.6329 | −0.928999 | −0.464499 | − | 0.885573i | \(-0.653766\pi\) | ||||
−0.464499 | + | 0.885573i | \(0.653766\pi\) | |||||||
\(132\) | 0.109088 | 0.00949486 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 21.9962 | 1.90018 | ||||||||
\(135\) | 0.0457395 | 0.00393663 | ||||||||
\(136\) | −1.51420 | −0.129842 | ||||||||
\(137\) | 21.2240 | 1.81329 | 0.906645 | − | 0.421895i | \(-0.138635\pi\) | ||||
0.906645 | + | 0.421895i | \(0.138635\pi\) | |||||||
\(138\) | 2.08321 | 0.177334 | ||||||||
\(139\) | 12.0384 | 1.02108 | 0.510541 | − | 0.859854i | \(-0.329445\pi\) | ||||
0.510541 | + | 0.859854i | \(0.329445\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.00229 | 0.758130 | ||||||||
\(142\) | 10.8741 | 0.912531 | ||||||||
\(143\) | 0.531251 | 0.0444254 | ||||||||
\(144\) | −4.91624 | −0.409687 | ||||||||
\(145\) | 0.0598975 | 0.00497422 | ||||||||
\(146\) | −26.1298 | −2.16252 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.48416 | 0.532995 | ||||||||
\(149\) | −15.5561 | −1.27441 | −0.637203 | − | 0.770696i | \(-0.719909\pi\) | ||||
−0.637203 | + | 0.770696i | \(0.719909\pi\) | |||||||
\(150\) | 8.22850 | 0.671854 | ||||||||
\(151\) | 23.1467 | 1.88365 | 0.941826 | − | 0.336100i | \(-0.109108\pi\) | ||||
0.941826 | + | 0.336100i | \(0.109108\pi\) | |||||||
\(152\) | −13.5564 | −1.09957 | ||||||||
\(153\) | −0.713284 | −0.0576656 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0336527 | 0.00270305 | ||||||||
\(156\) | 2.45905 | 0.196882 | ||||||||
\(157\) | 13.5629 | 1.08244 | 0.541219 | − | 0.840882i | \(-0.317963\pi\) | ||||
0.541219 | + | 0.840882i | \(0.317963\pi\) | |||||||
\(158\) | 10.1831 | 0.810120 | ||||||||
\(159\) | −14.1311 | −1.12067 | ||||||||
\(160\) | 0.176020 | 0.0139156 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.64639 | −0.129352 | ||||||||
\(163\) | 18.8746 | 1.47837 | 0.739184 | − | 0.673503i | \(-0.235211\pi\) | ||||
0.739184 | + | 0.673503i | \(0.235211\pi\) | |||||||
\(164\) | 0.710595 | 0.0554881 | ||||||||
\(165\) | 0.00702175 | 0.000546642 0 | ||||||||
\(166\) | 3.63128 | 0.281842 | ||||||||
\(167\) | 1.10994 | 0.0858894 | 0.0429447 | − | 0.999077i | \(-0.486326\pi\) | ||||
0.0429447 | + | 0.999077i | \(0.486326\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.02454 | −0.0788109 | ||||||||
\(170\) | 0.0537139 | 0.00411967 | ||||||||
\(171\) | −6.38590 | −0.488342 | ||||||||
\(172\) | 1.70239 | 0.129806 | ||||||||
\(173\) | −21.6857 | −1.64874 | −0.824368 | − | 0.566054i | \(-0.808469\pi\) | ||||
−0.824368 | + | 0.566054i | \(0.808469\pi\) | |||||||
\(174\) | −2.15600 | −0.163446 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.754722 | −0.0568893 | ||||||||
\(177\) | −11.3136 | −0.850383 | ||||||||
\(178\) | 23.5978 | 1.76873 | ||||||||
\(179\) | −7.05942 | −0.527646 | −0.263823 | − | 0.964571i | \(-0.584983\pi\) | ||||
−0.263823 | + | 0.964571i | \(0.584983\pi\) | |||||||
\(180\) | 0.0325023 | 0.00242258 | ||||||||
\(181\) | 13.1070 | 0.974234 | 0.487117 | − | 0.873337i | \(-0.338049\pi\) | ||||
0.487117 | + | 0.873337i | \(0.338049\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.2763 | −1.05533 | ||||||||
\(184\) | −2.68610 | −0.198022 | ||||||||
\(185\) | 0.417372 | 0.0306858 | ||||||||
\(186\) | −1.21133 | −0.0888187 | ||||||||
\(187\) | −0.109501 | −0.00800747 | ||||||||
\(188\) | 6.39698 | 0.466548 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.480890 | 0.0348874 | ||||||||
\(191\) | 9.51467 | 0.688457 | 0.344229 | − | 0.938886i | \(-0.388140\pi\) | ||||
0.344229 | + | 0.938886i | \(0.388140\pi\) | |||||||
\(192\) | 3.49665 | 0.252349 | ||||||||
\(193\) | −10.1608 | −0.731389 | −0.365695 | − | 0.930735i | \(-0.619169\pi\) | ||||
−0.365695 | + | 0.930735i | \(0.619169\pi\) | |||||||
\(194\) | 13.8733 | 0.996047 | ||||||||
\(195\) | 0.158284 | 0.0113350 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.54126 | 0.537293 | 0.268646 | − | 0.963239i | \(-0.413424\pi\) | ||||
0.268646 | + | 0.963239i | \(0.413424\pi\) | |||||||
\(198\) | −0.252747 | −0.0179619 | ||||||||
\(199\) | 25.9232 | 1.83765 | 0.918823 | − | 0.394671i | \(-0.129141\pi\) | ||||
0.918823 | + | 0.394671i | \(0.129141\pi\) | |||||||
\(200\) | −10.6099 | −0.750231 | ||||||||
\(201\) | −13.3603 | −0.942361 | ||||||||
\(202\) | 7.04439 | 0.495641 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.506856 | −0.0354870 | ||||||||
\(205\) | 0.0457395 | 0.00319459 | ||||||||
\(206\) | −14.5917 | −1.01665 | ||||||||
\(207\) | −1.26532 | −0.0879458 | ||||||||
\(208\) | −17.0129 | −1.17964 | ||||||||
\(209\) | −0.980337 | −0.0678113 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.2724 | −0.982555 | −0.491277 | − | 0.871003i | \(-0.663470\pi\) | ||||
−0.491277 | + | 0.871003i | \(0.663470\pi\) | |||||||
\(212\) | −10.0415 | −0.689653 | ||||||||
\(213\) | −6.60480 | −0.452553 | ||||||||
\(214\) | −4.83273 | −0.330359 | ||||||||
\(215\) | 0.109579 | 0.00747322 | ||||||||
\(216\) | 2.12286 | 0.144442 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 14.0959 | 0.954692 | ||||||||
\(219\) | 15.8710 | 1.07246 | ||||||||
\(220\) | 0.00498962 | 0.000336400 0 | ||||||||
\(221\) | −2.46836 | −0.166040 | ||||||||
\(222\) | −15.0233 | −1.00830 | ||||||||
\(223\) | −15.5265 | −1.03973 | −0.519866 | − | 0.854248i | \(-0.674018\pi\) | ||||
−0.519866 | + | 0.854248i | \(0.674018\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.99791 | −0.333194 | ||||||||
\(226\) | −14.1056 | −0.938291 | ||||||||
\(227\) | −22.0233 | −1.46174 | −0.730870 | − | 0.682517i | \(-0.760886\pi\) | ||||
−0.730870 | + | 0.682517i | \(0.760886\pi\) | |||||||
\(228\) | −4.53778 | −0.300522 | ||||||||
\(229\) | −14.6238 | −0.966369 | −0.483184 | − | 0.875519i | \(-0.660520\pi\) | ||||
−0.483184 | + | 0.875519i | \(0.660520\pi\) | |||||||
\(230\) | 0.0952849 | 0.00628290 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.77996 | 0.182514 | ||||||||
\(233\) | 4.56710 | 0.299200 | 0.149600 | − | 0.988747i | \(-0.452201\pi\) | ||||
0.149600 | + | 0.988747i | \(0.452201\pi\) | |||||||
\(234\) | −5.69742 | −0.372452 | ||||||||
\(235\) | 0.411760 | 0.0268603 | ||||||||
\(236\) | −8.03940 | −0.523320 | ||||||||
\(237\) | −6.18509 | −0.401765 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.1362 | 0.979079 | 0.489540 | − | 0.871981i | \(-0.337165\pi\) | ||||
0.489540 | + | 0.871981i | \(0.337165\pi\) | |||||||
\(240\) | −0.224867 | −0.0145151 | ||||||||
\(241\) | −12.9806 | −0.836153 | −0.418077 | − | 0.908412i | \(-0.637296\pi\) | ||||
−0.418077 | + | 0.908412i | \(0.637296\pi\) | |||||||
\(242\) | 18.0715 | 1.16168 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −10.1447 | −0.649445 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.64639 | −0.104970 | ||||||||
\(247\) | −22.0988 | −1.40611 | ||||||||
\(248\) | 1.56189 | 0.0991801 | ||||||||
\(249\) | −2.20561 | −0.139775 | ||||||||
\(250\) | 0.752892 | 0.0476171 | ||||||||
\(251\) | −21.8010 | −1.37607 | −0.688033 | − | 0.725679i | \(-0.741526\pi\) | ||||
−0.688033 | + | 0.725679i | \(0.741526\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.194247 | −0.0122122 | ||||||||
\(254\) | 1.40356 | 0.0880671 | ||||||||
\(255\) | −0.0326253 | −0.00204307 | ||||||||
\(256\) | 15.1564 | 0.947274 | ||||||||
\(257\) | −8.80386 | −0.549170 | −0.274585 | − | 0.961563i | \(-0.588540\pi\) | ||||
−0.274585 | + | 0.961563i | \(0.588540\pi\) | |||||||
\(258\) | −3.94428 | −0.245560 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.112476 | 0.00697546 | ||||||||
\(261\) | 1.30954 | 0.0810582 | ||||||||
\(262\) | 17.5058 | 1.08151 | ||||||||
\(263\) | −24.6440 | −1.51962 | −0.759808 | − | 0.650147i | \(-0.774707\pi\) | ||||
−0.759808 | + | 0.650147i | \(0.774707\pi\) | |||||||
\(264\) | 0.325893 | 0.0200573 | ||||||||
\(265\) | −0.646350 | −0.0397050 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.3331 | −0.877169 | ||||||||
\(268\) | −9.49375 | −0.579923 | ||||||||
\(269\) | −13.5580 | −0.826648 | −0.413324 | − | 0.910584i | \(-0.635632\pi\) | ||||
−0.413324 | + | 0.910584i | \(0.635632\pi\) | |||||||
\(270\) | −0.0753050 | −0.00458292 | ||||||||
\(271\) | 19.5011 | 1.18461 | 0.592305 | − | 0.805714i | \(-0.298218\pi\) | ||||
0.592305 | + | 0.805714i | \(0.298218\pi\) | |||||||
\(272\) | 3.50668 | 0.212624 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −34.9430 | −2.11098 | ||||||||
\(275\) | −0.767259 | −0.0462674 | ||||||||
\(276\) | −0.899130 | −0.0541213 | ||||||||
\(277\) | 9.02931 | 0.542519 | 0.271259 | − | 0.962506i | \(-0.412560\pi\) | ||||
0.271259 | + | 0.962506i | \(0.412560\pi\) | |||||||
\(278\) | −19.8198 | −1.18871 | ||||||||
\(279\) | 0.735747 | 0.0440480 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.893294 | 0.0532895 | 0.0266447 | − | 0.999645i | \(-0.491518\pi\) | ||||
0.0266447 | + | 0.999645i | \(0.491518\pi\) | |||||||
\(282\) | −14.8213 | −0.882594 | ||||||||
\(283\) | 20.6014 | 1.22463 | 0.612313 | − | 0.790615i | \(-0.290239\pi\) | ||||
0.612313 | + | 0.790615i | \(0.290239\pi\) | |||||||
\(284\) | −4.69334 | −0.278498 | ||||||||
\(285\) | −0.292088 | −0.0173018 | ||||||||
\(286\) | −0.874645 | −0.0517189 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.84832 | 0.226765 | ||||||||
\(289\) | −16.4912 | −0.970072 | ||||||||
\(290\) | −0.0986146 | −0.00579085 | ||||||||
\(291\) | −8.42652 | −0.493971 | ||||||||
\(292\) | 11.2778 | 0.659985 | ||||||||
\(293\) | 17.0744 | 0.997495 | 0.498747 | − | 0.866747i | \(-0.333794\pi\) | ||||
0.498747 | + | 0.866747i | \(0.333794\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.517479 | −0.0301288 | ||||||||
\(296\) | 19.3711 | 1.12592 | ||||||||
\(297\) | 0.153516 | 0.00890790 | ||||||||
\(298\) | 25.6114 | 1.48363 | ||||||||
\(299\) | −4.37871 | −0.253228 | ||||||||
\(300\) | −3.55149 | −0.205045 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −38.1085 | −2.19290 | ||||||||
\(303\) | −4.27869 | −0.245804 | ||||||||
\(304\) | 31.3946 | 1.80061 | ||||||||
\(305\) | −0.652991 | −0.0373901 | ||||||||
\(306\) | 1.17434 | 0.0671327 | ||||||||
\(307\) | 6.13820 | 0.350325 | 0.175163 | − | 0.984539i | \(-0.443955\pi\) | ||||
0.175163 | + | 0.984539i | \(0.443955\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.86287 | 0.504191 | ||||||||
\(310\) | −0.0554055 | −0.00314682 | ||||||||
\(311\) | 15.6468 | 0.887247 | 0.443624 | − | 0.896213i | \(-0.353693\pi\) | ||||
0.443624 | + | 0.896213i | \(0.353693\pi\) | |||||||
\(312\) | 7.34629 | 0.415901 | ||||||||
\(313\) | 16.9514 | 0.958150 | 0.479075 | − | 0.877774i | \(-0.340972\pi\) | ||||
0.479075 | + | 0.877774i | \(0.340972\pi\) | |||||||
\(314\) | −22.3298 | −1.26015 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.39509 | −0.247243 | ||||||||
\(317\) | −8.16987 | −0.458866 | −0.229433 | − | 0.973324i | \(-0.573687\pi\) | ||||
−0.229433 | + | 0.973324i | \(0.573687\pi\) | |||||||
\(318\) | 23.2653 | 1.30465 | ||||||||
\(319\) | 0.201035 | 0.0112558 | ||||||||
\(320\) | 0.159935 | 0.00894065 | ||||||||
\(321\) | 2.93535 | 0.163836 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.55496 | 0.253445 | ||||||||
\(324\) | 0.710595 | 0.0394775 | ||||||||
\(325\) | −17.2955 | −0.959384 | ||||||||
\(326\) | −31.0748 | −1.72108 | ||||||||
\(327\) | −8.56169 | −0.473462 | ||||||||
\(328\) | 2.12286 | 0.117215 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.0115605 | −0.000636386 0 | ||||||||
\(331\) | 7.85298 | 0.431639 | 0.215820 | − | 0.976433i | \(-0.430758\pi\) | ||||
0.215820 | + | 0.976433i | \(0.430758\pi\) | |||||||
\(332\) | −1.56729 | −0.0860163 | ||||||||
\(333\) | 9.12498 | 0.500046 | ||||||||
\(334\) | −1.82738 | −0.0999900 | ||||||||
\(335\) | −0.611093 | −0.0333876 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.3559 | −0.564124 | −0.282062 | − | 0.959396i | \(-0.591018\pi\) | ||||
−0.282062 | + | 0.959396i | \(0.591018\pi\) | |||||||
\(338\) | 1.68679 | 0.0917495 | ||||||||
\(339\) | 8.56761 | 0.465328 | ||||||||
\(340\) | −0.0231834 | −0.00125729 | ||||||||
\(341\) | 0.112949 | 0.00611653 | ||||||||
\(342\) | 10.5137 | 0.568514 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.08578 | 0.274207 | ||||||||
\(345\) | −0.0578751 | −0.00311589 | ||||||||
\(346\) | 35.7032 | 1.91941 | ||||||||
\(347\) | −28.8340 | −1.54789 | −0.773944 | − | 0.633254i | \(-0.781719\pi\) | ||||
−0.773944 | + | 0.633254i | \(0.781719\pi\) | |||||||
\(348\) | 0.930549 | 0.0498827 | ||||||||
\(349\) | −2.39890 | −0.128410 | −0.0642051 | − | 0.997937i | \(-0.520451\pi\) | ||||
−0.0642051 | + | 0.997937i | \(0.520451\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.46056 | 0.184711 | ||||||||
\(352\) | 0.590779 | 0.0314886 | ||||||||
\(353\) | −0.720190 | −0.0383318 | −0.0191659 | − | 0.999816i | \(-0.506101\pi\) | ||||
−0.0191659 | + | 0.999816i | \(0.506101\pi\) | |||||||
\(354\) | 18.6266 | 0.989993 | ||||||||
\(355\) | −0.302100 | −0.0160338 | ||||||||
\(356\) | −10.1850 | −0.539804 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.6225 | 0.614271 | ||||||||
\(359\) | −18.3701 | −0.969535 | −0.484767 | − | 0.874643i | \(-0.661096\pi\) | ||||
−0.484767 | + | 0.874643i | \(0.661096\pi\) | |||||||
\(360\) | 0.0970987 | 0.00511755 | ||||||||
\(361\) | 21.7797 | 1.14630 | ||||||||
\(362\) | −21.5792 | −1.13418 | ||||||||
\(363\) | −10.9764 | −0.576113 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.725930 | 0.0379969 | ||||||||
\(366\) | 23.5043 | 1.22859 | ||||||||
\(367\) | −7.81632 | −0.408009 | −0.204004 | − | 0.978970i | \(-0.565396\pi\) | ||||
−0.204004 | + | 0.978970i | \(0.565396\pi\) | |||||||
\(368\) | 6.22062 | 0.324272 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | −0.687157 | −0.0357236 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.522818 | 0.0271069 | ||||||||
\(373\) | −24.2133 | −1.25372 | −0.626859 | − | 0.779133i | \(-0.715660\pi\) | ||||
−0.626859 | + | 0.779133i | \(0.715660\pi\) | |||||||
\(374\) | 0.180280 | 0.00932208 | ||||||||
\(375\) | −0.457299 | −0.0236148 | ||||||||
\(376\) | 19.1106 | 0.985555 | ||||||||
\(377\) | 4.53172 | 0.233396 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.6238 | −0.802538 | −0.401269 | − | 0.915960i | \(-0.631431\pi\) | ||||
−0.401269 | + | 0.915960i | \(0.631431\pi\) | |||||||
\(380\) | −0.207556 | −0.0106474 | ||||||||
\(381\) | −0.852507 | −0.0436753 | ||||||||
\(382\) | −15.6648 | −0.801483 | ||||||||
\(383\) | 32.9203 | 1.68215 | 0.841073 | − | 0.540921i | \(-0.181924\pi\) | ||||
0.841073 | + | 0.540921i | \(0.181924\pi\) | |||||||
\(384\) | −13.4535 | −0.686546 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.7286 | 0.851463 | ||||||||
\(387\) | 2.39572 | 0.121781 | ||||||||
\(388\) | −5.98784 | −0.303987 | ||||||||
\(389\) | −22.7504 | −1.15349 | −0.576745 | − | 0.816924i | \(-0.695678\pi\) | ||||
−0.576745 | + | 0.816924i | \(0.695678\pi\) | |||||||
\(390\) | −0.260597 | −0.0131959 | ||||||||
\(391\) | 0.902533 | 0.0456431 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.6329 | −0.536358 | ||||||||
\(394\) | −12.4158 | −0.625501 | ||||||||
\(395\) | −0.282903 | −0.0142344 | ||||||||
\(396\) | 0.109088 | 0.00548186 | ||||||||
\(397\) | −5.59969 | −0.281040 | −0.140520 | − | 0.990078i | \(-0.544877\pi\) | ||||
−0.140520 | + | 0.990078i | \(0.544877\pi\) | |||||||
\(398\) | −42.6796 | −2.13934 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 24.5709 | 1.22855 | ||||||||
\(401\) | −24.1918 | −1.20808 | −0.604041 | − | 0.796953i | \(-0.706444\pi\) | ||||
−0.604041 | + | 0.796953i | \(0.706444\pi\) | |||||||
\(402\) | 21.9962 | 1.09707 | ||||||||
\(403\) | 2.54610 | 0.126830 | ||||||||
\(404\) | −3.04042 | −0.151266 | ||||||||
\(405\) | 0.0457395 | 0.00227281 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.40083 | 0.0694366 | ||||||||
\(408\) | −1.51420 | −0.0749643 | ||||||||
\(409\) | −18.2159 | −0.900716 | −0.450358 | − | 0.892848i | \(-0.648704\pi\) | ||||
−0.450358 | + | 0.892848i | \(0.648704\pi\) | |||||||
\(410\) | −0.0753050 | −0.00371905 | ||||||||
\(411\) | 21.2240 | 1.04690 | ||||||||
\(412\) | 6.29791 | 0.310276 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.08321 | 0.102384 | ||||||||
\(415\) | −0.100883 | −0.00495217 | ||||||||
\(416\) | 13.3173 | 0.652937 | ||||||||
\(417\) | 12.0384 | 0.589521 | ||||||||
\(418\) | 1.61402 | 0.0789441 | ||||||||
\(419\) | −39.5625 | −1.93275 | −0.966377 | − | 0.257128i | \(-0.917224\pi\) | ||||
−0.966377 | + | 0.257128i | \(0.917224\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.8389 | −1.64921 | −0.824603 | − | 0.565712i | \(-0.808601\pi\) | ||||
−0.824603 | + | 0.565712i | \(0.808601\pi\) | |||||||
\(422\) | 23.4980 | 1.14386 | ||||||||
\(423\) | 9.00229 | 0.437706 | ||||||||
\(424\) | −29.9984 | −1.45685 | ||||||||
\(425\) | 3.56493 | 0.172925 | ||||||||
\(426\) | 10.8741 | 0.526850 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.08585 | 0.100823 | ||||||||
\(429\) | 0.531251 | 0.0256490 | ||||||||
\(430\) | −0.180410 | −0.00870012 | ||||||||
\(431\) | −16.8579 | −0.812016 | −0.406008 | − | 0.913869i | \(-0.633080\pi\) | ||||
−0.406008 | + | 0.913869i | \(0.633080\pi\) | |||||||
\(432\) | −4.91624 | −0.236533 | ||||||||
\(433\) | −2.77987 | −0.133592 | −0.0667961 | − | 0.997767i | \(-0.521278\pi\) | ||||
−0.0667961 | + | 0.997767i | \(0.521278\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.0598975 | 0.00287187 | ||||||||
\(436\) | −6.08389 | −0.291365 | ||||||||
\(437\) | 8.08020 | 0.386529 | ||||||||
\(438\) | −26.1298 | −1.24853 | ||||||||
\(439\) | −15.5531 | −0.742309 | −0.371154 | − | 0.928571i | \(-0.621038\pi\) | ||||
−0.371154 | + | 0.928571i | \(0.621038\pi\) | |||||||
\(440\) | 0.0149062 | 0.000710625 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.06388 | 0.193299 | ||||||||
\(443\) | −19.3228 | −0.918056 | −0.459028 | − | 0.888422i | \(-0.651802\pi\) | ||||
−0.459028 | + | 0.888422i | \(0.651802\pi\) | |||||||
\(444\) | 6.48416 | 0.307725 | ||||||||
\(445\) | −0.655587 | −0.0310778 | ||||||||
\(446\) | 25.5627 | 1.21043 | ||||||||
\(447\) | −15.5561 | −0.735779 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.7895 | −1.40585 | −0.702926 | − | 0.711263i | \(-0.748124\pi\) | ||||
−0.702926 | + | 0.711263i | \(0.748124\pi\) | |||||||
\(450\) | 8.22850 | 0.387895 | ||||||||
\(451\) | 0.153516 | 0.00722879 | ||||||||
\(452\) | 6.08810 | 0.286360 | ||||||||
\(453\) | 23.1467 | 1.08753 | ||||||||
\(454\) | 36.2590 | 1.70172 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.5564 | −0.634835 | ||||||||
\(457\) | −19.4583 | −0.910223 | −0.455111 | − | 0.890434i | \(-0.650401\pi\) | ||||
−0.455111 | + | 0.890434i | \(0.650401\pi\) | |||||||
\(458\) | 24.0765 | 1.12502 | ||||||||
\(459\) | −0.713284 | −0.0332933 | ||||||||
\(460\) | −0.0411258 | −0.00191750 | ||||||||
\(461\) | −8.86653 | −0.412955 | −0.206478 | − | 0.978451i | \(-0.566200\pi\) | ||||
−0.206478 | + | 0.978451i | \(0.566200\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.0442 | 1.07096 | 0.535478 | − | 0.844549i | \(-0.320131\pi\) | ||||
0.535478 | + | 0.844549i | \(0.320131\pi\) | |||||||
\(464\) | −6.43800 | −0.298877 | ||||||||
\(465\) | 0.0336527 | 0.00156061 | ||||||||
\(466\) | −7.51921 | −0.348321 | ||||||||
\(467\) | −6.62006 | −0.306340 | −0.153170 | − | 0.988200i | \(-0.548948\pi\) | ||||
−0.153170 | + | 0.988200i | \(0.548948\pi\) | |||||||
\(468\) | 2.45905 | 0.113670 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.677918 | −0.0312700 | ||||||||
\(471\) | 13.5629 | 0.624946 | ||||||||
\(472\) | −24.0172 | −1.10548 | ||||||||
\(473\) | 0.367781 | 0.0169106 | ||||||||
\(474\) | 10.1831 | 0.467723 | ||||||||
\(475\) | 31.9161 | 1.46441 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.1311 | −0.647019 | ||||||||
\(478\) | −24.9201 | −1.13982 | ||||||||
\(479\) | 16.9788 | 0.775782 | 0.387891 | − | 0.921705i | \(-0.373204\pi\) | ||||
0.387891 | + | 0.921705i | \(0.373204\pi\) | |||||||
\(480\) | 0.176020 | 0.00803420 | ||||||||
\(481\) | 31.5775 | 1.43981 | ||||||||
\(482\) | 21.3711 | 0.973426 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.79980 | −0.354536 | ||||||||
\(485\) | −0.385425 | −0.0175012 | ||||||||
\(486\) | −1.64639 | −0.0746817 | ||||||||
\(487\) | 18.3314 | 0.830677 | 0.415338 | − | 0.909667i | \(-0.363663\pi\) | ||||
0.415338 | + | 0.909667i | \(0.363663\pi\) | |||||||
\(488\) | −30.3066 | −1.37192 | ||||||||
\(489\) | 18.8746 | 0.853537 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.45168 | −0.291160 | −0.145580 | − | 0.989346i | \(-0.546505\pi\) | ||||
−0.145580 | + | 0.989346i | \(0.546505\pi\) | |||||||
\(492\) | 0.710595 | 0.0320361 | ||||||||
\(493\) | −0.934072 | −0.0420685 | ||||||||
\(494\) | 36.3831 | 1.63696 | ||||||||
\(495\) | 0.00702175 | 0.000315604 0 | ||||||||
\(496\) | −3.61711 | −0.162413 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.63128 | 0.162722 | ||||||||
\(499\) | 9.71812 | 0.435043 | 0.217521 | − | 0.976056i | \(-0.430203\pi\) | ||||
0.217521 | + | 0.976056i | \(0.430203\pi\) | |||||||
\(500\) | −0.324955 | −0.0145324 | ||||||||
\(501\) | 1.10994 | 0.0495882 | ||||||||
\(502\) | 35.8929 | 1.60198 | ||||||||
\(503\) | 19.3611 | 0.863269 | 0.431634 | − | 0.902049i | \(-0.357937\pi\) | ||||
0.431634 | + | 0.902049i | \(0.357937\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.195705 | −0.00870877 | ||||||||
\(506\) | 0.319806 | 0.0142171 | ||||||||
\(507\) | −1.02454 | −0.0455015 | ||||||||
\(508\) | −0.605787 | −0.0268775 | ||||||||
\(509\) | 4.52576 | 0.200601 | 0.100300 | − | 0.994957i | \(-0.468020\pi\) | ||||
0.100300 | + | 0.994957i | \(0.468020\pi\) | |||||||
\(510\) | 0.0537139 | 0.00237849 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.95371 | 0.0863426 | ||||||||
\(513\) | −6.38590 | −0.281944 | ||||||||
\(514\) | 14.4946 | 0.639328 | ||||||||
\(515\) | 0.405383 | 0.0178633 | ||||||||
\(516\) | 1.70239 | 0.0749433 | ||||||||
\(517\) | 1.38200 | 0.0607801 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.6857 | −0.951899 | ||||||||
\(520\) | 0.336015 | 0.0147353 | ||||||||
\(521\) | −6.12296 | −0.268252 | −0.134126 | − | 0.990964i | \(-0.542823\pi\) | ||||
−0.134126 | + | 0.990964i | \(0.542823\pi\) | |||||||
\(522\) | −2.15600 | −0.0943658 | ||||||||
\(523\) | 12.0382 | 0.526394 | 0.263197 | − | 0.964742i | \(-0.415223\pi\) | ||||
0.263197 | + | 0.964742i | \(0.415223\pi\) | |||||||
\(524\) | −7.55567 | −0.330071 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 40.5737 | 1.76910 | ||||||||
\(527\) | −0.524797 | −0.0228605 | ||||||||
\(528\) | −0.754722 | −0.0328451 | ||||||||
\(529\) | −21.3990 | −0.930390 | ||||||||
\(530\) | 1.06414 | 0.0462234 | ||||||||
\(531\) | −11.3136 | −0.490969 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.46056 | 0.149893 | ||||||||
\(534\) | 23.5978 | 1.02118 | ||||||||
\(535\) | 0.134262 | 0.00580464 | ||||||||
\(536\) | −28.3620 | −1.22505 | ||||||||
\(537\) | −7.05942 | −0.304636 | ||||||||
\(538\) | 22.3218 | 0.962361 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.0325023 | 0.00139867 | ||||||||
\(541\) | −43.0826 | −1.85226 | −0.926132 | − | 0.377199i | \(-0.876887\pi\) | ||||
−0.926132 | + | 0.377199i | \(0.876887\pi\) | |||||||
\(542\) | −32.1064 | −1.37909 | ||||||||
\(543\) | 13.1070 | 0.562474 | ||||||||
\(544\) | −2.74495 | −0.117689 | ||||||||
\(545\) | −0.391607 | −0.0167746 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.8040 | −0.889514 | −0.444757 | − | 0.895651i | \(-0.646710\pi\) | ||||
−0.444757 | + | 0.895651i | \(0.646710\pi\) | |||||||
\(548\) | 15.0817 | 0.644257 | ||||||||
\(549\) | −14.2763 | −0.609297 | ||||||||
\(550\) | 1.26321 | 0.0538633 | ||||||||
\(551\) | −8.36256 | −0.356257 | ||||||||
\(552\) | −2.68610 | −0.114328 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −14.8657 | −0.631585 | ||||||||
\(555\) | 0.417372 | 0.0177165 | ||||||||
\(556\) | 8.55440 | 0.362787 | ||||||||
\(557\) | −17.5841 | −0.745060 | −0.372530 | − | 0.928020i | \(-0.621510\pi\) | ||||
−0.372530 | + | 0.928020i | \(0.621510\pi\) | |||||||
\(558\) | −1.21133 | −0.0512795 | ||||||||
\(559\) | 8.29052 | 0.350652 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.109501 | −0.00462312 | ||||||||
\(562\) | −1.47071 | −0.0620381 | ||||||||
\(563\) | −17.7830 | −0.749463 | −0.374731 | − | 0.927133i | \(-0.622265\pi\) | ||||
−0.374731 | + | 0.927133i | \(0.622265\pi\) | |||||||
\(564\) | 6.39698 | 0.269362 | ||||||||
\(565\) | 0.391878 | 0.0164864 | ||||||||
\(566\) | −33.9179 | −1.42568 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.0211 | −0.588311 | ||||||||
\(569\) | −2.63154 | −0.110320 | −0.0551599 | − | 0.998478i | \(-0.517567\pi\) | ||||
−0.0551599 | + | 0.998478i | \(0.517567\pi\) | |||||||
\(570\) | 0.480890 | 0.0201423 | ||||||||
\(571\) | −5.24279 | −0.219404 | −0.109702 | − | 0.993965i | \(-0.534990\pi\) | ||||
−0.109702 | + | 0.993965i | \(0.534990\pi\) | |||||||
\(572\) | 0.377504 | 0.0157842 | ||||||||
\(573\) | 9.51467 | 0.397481 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.32395 | 0.263727 | ||||||||
\(576\) | 3.49665 | 0.145694 | ||||||||
\(577\) | 30.1299 | 1.25432 | 0.627162 | − | 0.778888i | \(-0.284216\pi\) | ||||
0.627162 | + | 0.778888i | \(0.284216\pi\) | |||||||
\(578\) | 27.1510 | 1.12933 | ||||||||
\(579\) | −10.1608 | −0.422268 | ||||||||
\(580\) | 0.0425629 | 0.00176733 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 13.8733 | 0.575068 | ||||||||
\(583\) | −2.16935 | −0.0898454 | ||||||||
\(584\) | 33.6919 | 1.39418 | ||||||||
\(585\) | 0.158284 | 0.00654425 | ||||||||
\(586\) | −28.1110 | −1.16126 | ||||||||
\(587\) | −27.5676 | −1.13784 | −0.568918 | − | 0.822394i | \(-0.692638\pi\) | ||||
−0.568918 | + | 0.822394i | \(0.692638\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.69841 | −0.193594 | ||||||||
\(590\) | 0.851972 | 0.0350751 | ||||||||
\(591\) | 7.54126 | 0.310206 | ||||||||
\(592\) | −44.8606 | −1.84376 | ||||||||
\(593\) | 18.6723 | 0.766780 | 0.383390 | − | 0.923586i | \(-0.374756\pi\) | ||||
0.383390 | + | 0.923586i | \(0.374756\pi\) | |||||||
\(594\) | −0.252747 | −0.0103703 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.0541 | −0.452793 | ||||||||
\(597\) | 25.9232 | 1.06096 | ||||||||
\(598\) | 7.20906 | 0.294801 | ||||||||
\(599\) | 16.7957 | 0.686253 | 0.343127 | − | 0.939289i | \(-0.388514\pi\) | ||||
0.343127 | + | 0.939289i | \(0.388514\pi\) | |||||||
\(600\) | −10.6099 | −0.433146 | ||||||||
\(601\) | −7.92057 | −0.323087 | −0.161543 | − | 0.986866i | \(-0.551647\pi\) | ||||
−0.161543 | + | 0.986866i | \(0.551647\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.3603 | −0.544073 | ||||||||
\(604\) | 16.4479 | 0.669257 | ||||||||
\(605\) | −0.502057 | −0.0204115 | ||||||||
\(606\) | 7.04439 | 0.286159 | ||||||||
\(607\) | 29.7076 | 1.20579 | 0.602897 | − | 0.797819i | \(-0.294013\pi\) | ||||
0.602897 | + | 0.797819i | \(0.294013\pi\) | |||||||
\(608\) | −24.5750 | −0.996648 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.07508 | 0.0435286 | ||||||||
\(611\) | 31.1529 | 1.26031 | ||||||||
\(612\) | −0.506856 | −0.0204884 | ||||||||
\(613\) | 21.3366 | 0.861776 | 0.430888 | − | 0.902406i | \(-0.358200\pi\) | ||||
0.430888 | + | 0.902406i | \(0.358200\pi\) | |||||||
\(614\) | −10.1059 | −0.407839 | ||||||||
\(615\) | 0.0457395 | 0.00184440 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.34012 | 0.214985 | 0.107493 | − | 0.994206i | \(-0.465718\pi\) | ||||
0.107493 | + | 0.994206i | \(0.465718\pi\) | |||||||
\(618\) | −14.5917 | −0.586965 | ||||||||
\(619\) | 8.18591 | 0.329019 | 0.164510 | − | 0.986375i | \(-0.447396\pi\) | ||||
0.164510 | + | 0.986375i | \(0.447396\pi\) | |||||||
\(620\) | 0.0239135 | 0.000960387 0 | ||||||||
\(621\) | −1.26532 | −0.0507756 | ||||||||
\(622\) | −25.7607 | −1.03291 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −17.0129 | −0.681063 | ||||||||
\(625\) | 24.9686 | 0.998745 | ||||||||
\(626\) | −27.9086 | −1.11545 | ||||||||
\(627\) | −0.980337 | −0.0391509 | ||||||||
\(628\) | 9.63774 | 0.384588 | ||||||||
\(629\) | −6.50871 | −0.259519 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.64661 | 0.145169 | 0.0725845 | − | 0.997362i | \(-0.476875\pi\) | ||||
0.0725845 | + | 0.997362i | \(0.476875\pi\) | |||||||
\(632\) | −13.1301 | −0.522287 | ||||||||
\(633\) | −14.2724 | −0.567278 | ||||||||
\(634\) | 13.4508 | 0.534199 | ||||||||
\(635\) | −0.0389933 | −0.00154740 | ||||||||
\(636\) | −10.0415 | −0.398171 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.330981 | −0.0131037 | ||||||||
\(639\) | −6.60480 | −0.261282 | ||||||||
\(640\) | −0.615356 | −0.0243241 | ||||||||
\(641\) | −33.2611 | −1.31373 | −0.656867 | − | 0.754007i | \(-0.728119\pi\) | ||||
−0.656867 | + | 0.754007i | \(0.728119\pi\) | |||||||
\(642\) | −4.83273 | −0.190733 | ||||||||
\(643\) | 31.6609 | 1.24858 | 0.624291 | − | 0.781192i | \(-0.285388\pi\) | ||||
0.624291 | + | 0.781192i | \(0.285388\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.109579 | 0.00431467 | ||||||||
\(646\) | −7.49923 | −0.295053 | ||||||||
\(647\) | −19.7459 | −0.776291 | −0.388146 | − | 0.921598i | \(-0.626884\pi\) | ||||
−0.388146 | + | 0.921598i | \(0.626884\pi\) | |||||||
\(648\) | 2.12286 | 0.0833939 | ||||||||
\(649\) | −1.73682 | −0.0681762 | ||||||||
\(650\) | 28.4752 | 1.11689 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.4122 | 0.525261 | ||||||||
\(653\) | 12.9661 | 0.507403 | 0.253702 | − | 0.967283i | \(-0.418352\pi\) | ||||
0.253702 | + | 0.967283i | \(0.418352\pi\) | |||||||
\(654\) | 14.0959 | 0.551192 | ||||||||
\(655\) | −0.486343 | −0.0190030 | ||||||||
\(656\) | −4.91624 | −0.191947 | ||||||||
\(657\) | 15.8710 | 0.619185 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.26699 | 0.166218 | 0.0831091 | − | 0.996540i | \(-0.473515\pi\) | ||||
0.0831091 | + | 0.996540i | \(0.473515\pi\) | |||||||
\(660\) | 0.00498962 | 0.000194221 0 | ||||||||
\(661\) | 6.81866 | 0.265215 | 0.132608 | − | 0.991169i | \(-0.457665\pi\) | ||||
0.132608 | + | 0.991169i | \(0.457665\pi\) | |||||||
\(662\) | −12.9291 | −0.502502 | ||||||||
\(663\) | −2.46836 | −0.0958632 | ||||||||
\(664\) | −4.68220 | −0.181704 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −15.0233 | −0.582140 | ||||||||
\(667\) | −1.65698 | −0.0641586 | ||||||||
\(668\) | 0.788714 | 0.0305163 | ||||||||
\(669\) | −15.5265 | −0.600289 | ||||||||
\(670\) | 1.00610 | 0.0388689 | ||||||||
\(671\) | −2.19164 | −0.0846073 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.9850 | −1.38712 | −0.693559 | − | 0.720400i | \(-0.743958\pi\) | ||||
−0.693559 | + | 0.720400i | \(0.743958\pi\) | |||||||
\(674\) | 17.0499 | 0.656738 | ||||||||
\(675\) | −4.99791 | −0.192370 | ||||||||
\(676\) | −0.728034 | −0.0280013 | ||||||||
\(677\) | 33.0463 | 1.27007 | 0.635036 | − | 0.772482i | \(-0.280985\pi\) | ||||
0.635036 | + | 0.772482i | \(0.280985\pi\) | |||||||
\(678\) | −14.1056 | −0.541723 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.0692590 | −0.00265596 | ||||||||
\(681\) | −22.0233 | −0.843936 | ||||||||
\(682\) | −0.185958 | −0.00712070 | ||||||||
\(683\) | 40.0689 | 1.53319 | 0.766596 | − | 0.642130i | \(-0.221949\pi\) | ||||
0.766596 | + | 0.642130i | \(0.221949\pi\) | |||||||
\(684\) | −4.53778 | −0.173507 | ||||||||
\(685\) | 0.970776 | 0.0370914 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.6238 | −0.557933 | ||||||||
\(688\) | −11.7779 | −0.449030 | ||||||||
\(689\) | −48.9015 | −1.86300 | ||||||||
\(690\) | 0.0952849 | 0.00362744 | ||||||||
\(691\) | −13.5466 | −0.515335 | −0.257668 | − | 0.966234i | \(-0.582954\pi\) | ||||
−0.257668 | + | 0.966234i | \(0.582954\pi\) | |||||||
\(692\) | −15.4098 | −0.585792 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 47.4719 | 1.80201 | ||||||||
\(695\) | 0.550629 | 0.0208866 | ||||||||
\(696\) | 2.77996 | 0.105374 | ||||||||
\(697\) | −0.713284 | −0.0270176 | ||||||||
\(698\) | 3.94952 | 0.149492 | ||||||||
\(699\) | 4.56710 | 0.172743 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.1232 | 0.533428 | 0.266714 | − | 0.963776i | \(-0.414062\pi\) | ||||
0.266714 | + | 0.963776i | \(0.414062\pi\) | |||||||
\(702\) | −5.69742 | −0.215035 | ||||||||
\(703\) | −58.2712 | −2.19774 | ||||||||
\(704\) | 0.536792 | 0.0202311 | ||||||||
\(705\) | 0.411760 | 0.0155078 | ||||||||
\(706\) | 1.18571 | 0.0446249 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −8.03940 | −0.302139 | ||||||||
\(709\) | 25.2039 | 0.946554 | 0.473277 | − | 0.880914i | \(-0.343071\pi\) | ||||
0.473277 | + | 0.880914i | \(0.343071\pi\) | |||||||
\(710\) | 0.497374 | 0.0186661 | ||||||||
\(711\) | −6.18509 | −0.231959 | ||||||||
\(712\) | −30.4271 | −1.14030 | ||||||||
\(713\) | −0.930956 | −0.0348646 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0242992 | 0.000908737 0 | ||||||||
\(716\) | −5.01639 | −0.187471 | ||||||||
\(717\) | 15.1362 | 0.565272 | ||||||||
\(718\) | 30.2443 | 1.12871 | ||||||||
\(719\) | 3.91519 | 0.146012 | 0.0730059 | − | 0.997332i | \(-0.476741\pi\) | ||||
0.0730059 | + | 0.997332i | \(0.476741\pi\) | |||||||
\(720\) | −0.224867 | −0.00838028 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −35.8578 | −1.33449 | ||||||||
\(723\) | −12.9806 | −0.482753 | ||||||||
\(724\) | 9.31375 | 0.346143 | ||||||||
\(725\) | −6.54494 | −0.243073 | ||||||||
\(726\) | 18.0715 | 0.670695 | ||||||||
\(727\) | 44.3489 | 1.64481 | 0.822406 | − | 0.568902i | \(-0.192632\pi\) | ||||
0.822406 | + | 0.568902i | \(0.192632\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.19516 | −0.0442350 | ||||||||
\(731\) | −1.70883 | −0.0632033 | ||||||||
\(732\) | −10.1447 | −0.374957 | ||||||||
\(733\) | 48.1470 | 1.77835 | 0.889175 | − | 0.457568i | \(-0.151279\pi\) | ||||
0.889175 | + | 0.457568i | \(0.151279\pi\) | |||||||
\(734\) | 12.8687 | 0.474993 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.86936 | −0.179487 | ||||||||
\(737\) | −2.05102 | −0.0755502 | ||||||||
\(738\) | −1.64639 | −0.0606044 | ||||||||
\(739\) | 34.4634 | 1.26776 | 0.633878 | − | 0.773433i | \(-0.281462\pi\) | ||||
0.633878 | + | 0.773433i | \(0.281462\pi\) | |||||||
\(740\) | 0.296583 | 0.0109026 | ||||||||
\(741\) | −22.0988 | −0.811818 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.7819 | −1.05591 | −0.527953 | − | 0.849273i | \(-0.677040\pi\) | ||||
−0.527953 | + | 0.849273i | \(0.677040\pi\) | |||||||
\(744\) | 1.56189 | 0.0572617 | ||||||||
\(745\) | −0.711529 | −0.0260684 | ||||||||
\(746\) | 39.8645 | 1.45954 | ||||||||
\(747\) | −2.20561 | −0.0806989 | ||||||||
\(748\) | −0.0778105 | −0.00284503 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.752892 | 0.0274917 | ||||||||
\(751\) | −45.4779 | −1.65951 | −0.829756 | − | 0.558127i | \(-0.811520\pi\) | ||||
−0.829756 | + | 0.558127i | \(0.811520\pi\) | |||||||
\(752\) | −44.2575 | −1.61390 | ||||||||
\(753\) | −21.8010 | −0.794472 | ||||||||
\(754\) | −7.46098 | −0.271713 | ||||||||
\(755\) | 1.05872 | 0.0385307 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.6583 | −1.18699 | −0.593493 | − | 0.804839i | \(-0.702252\pi\) | ||||
−0.593493 | + | 0.804839i | \(0.702252\pi\) | |||||||
\(758\) | 25.7228 | 0.934293 | ||||||||
\(759\) | −0.194247 | −0.00705071 | ||||||||
\(760\) | −0.620062 | −0.0224920 | ||||||||
\(761\) | 22.5014 | 0.815676 | 0.407838 | − | 0.913054i | \(-0.366283\pi\) | ||||
0.407838 | + | 0.913054i | \(0.366283\pi\) | |||||||
\(762\) | 1.40356 | 0.0508456 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.76108 | 0.244607 | ||||||||
\(765\) | −0.0326253 | −0.00117957 | ||||||||
\(766\) | −54.1995 | −1.95831 | ||||||||
\(767\) | −39.1514 | −1.41368 | ||||||||
\(768\) | 15.1564 | 0.546909 | ||||||||
\(769\) | 6.24290 | 0.225125 | 0.112562 | − | 0.993645i | \(-0.464094\pi\) | ||||
0.112562 | + | 0.993645i | \(0.464094\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.80386 | −0.317063 | ||||||||
\(772\) | −7.22020 | −0.259861 | ||||||||
\(773\) | −21.8999 | −0.787684 | −0.393842 | − | 0.919178i | \(-0.628854\pi\) | ||||
−0.393842 | + | 0.919178i | \(0.628854\pi\) | |||||||
\(774\) | −3.94428 | −0.141774 | ||||||||
\(775\) | −3.67720 | −0.132089 | ||||||||
\(776\) | −17.8883 | −0.642154 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 37.4560 | 1.34286 | ||||||||
\(779\) | −6.38590 | −0.228798 | ||||||||
\(780\) | 0.112476 | 0.00402728 | ||||||||
\(781\) | −1.01394 | −0.0362817 | ||||||||
\(782\) | −1.48592 | −0.0531364 | ||||||||
\(783\) | 1.30954 | 0.0467990 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.620361 | 0.0221416 | ||||||||
\(786\) | 17.5058 | 0.624413 | ||||||||
\(787\) | 37.6171 | 1.34090 | 0.670452 | − | 0.741953i | \(-0.266100\pi\) | ||||
0.670452 | + | 0.741953i | \(0.266100\pi\) | |||||||
\(788\) | 5.35878 | 0.190899 | ||||||||
\(789\) | −24.6440 | −0.877351 | ||||||||
\(790\) | 0.465768 | 0.0165713 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.325893 | 0.0115801 | ||||||||
\(793\) | −49.4039 | −1.75438 | ||||||||
\(794\) | 9.21926 | 0.327179 | ||||||||
\(795\) | −0.646350 | −0.0229237 | ||||||||
\(796\) | 18.4209 | 0.652911 | ||||||||
\(797\) | −20.5650 | −0.728449 | −0.364224 | − | 0.931311i | \(-0.618666\pi\) | ||||
−0.364224 | + | 0.931311i | \(0.618666\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.42119 | −0.227166 | ||||||||
\(800\) | −19.2336 | −0.680009 | ||||||||
\(801\) | −14.3331 | −0.506434 | ||||||||
\(802\) | 39.8292 | 1.40642 | ||||||||
\(803\) | 2.43645 | 0.0859803 | ||||||||
\(804\) | −9.49375 | −0.334819 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.19186 | −0.147652 | ||||||||
\(807\) | −13.5580 | −0.477265 | ||||||||
\(808\) | −9.08307 | −0.319541 | ||||||||
\(809\) | −43.8207 | −1.54065 | −0.770327 | − | 0.637649i | \(-0.779907\pi\) | ||||
−0.770327 | + | 0.637649i | \(0.779907\pi\) | |||||||
\(810\) | −0.0753050 | −0.00264595 | ||||||||
\(811\) | −28.5288 | −1.00178 | −0.500891 | − | 0.865511i | \(-0.666994\pi\) | ||||
−0.500891 | + | 0.865511i | \(0.666994\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.5011 | 0.683935 | ||||||||
\(814\) | −2.30631 | −0.0808362 | ||||||||
\(815\) | 0.863313 | 0.0302405 | ||||||||
\(816\) | 3.50668 | 0.122758 | ||||||||
\(817\) | −15.2988 | −0.535238 | ||||||||
\(818\) | 29.9904 | 1.04859 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0325023 | 0.00113503 | ||||||||
\(821\) | 36.1062 | 1.26012 | 0.630058 | − | 0.776548i | \(-0.283031\pi\) | ||||
0.630058 | + | 0.776548i | \(0.283031\pi\) | |||||||
\(822\) | −34.9430 | −1.21878 | ||||||||
\(823\) | 42.3799 | 1.47727 | 0.738635 | − | 0.674106i | \(-0.235471\pi\) | ||||
0.738635 | + | 0.674106i | \(0.235471\pi\) | |||||||
\(824\) | 18.8146 | 0.655439 | ||||||||
\(825\) | −0.767259 | −0.0267125 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −52.9489 | −1.84121 | −0.920606 | − | 0.390492i | \(-0.872305\pi\) | ||||
−0.920606 | + | 0.390492i | \(0.872305\pi\) | |||||||
\(828\) | −0.899130 | −0.0312469 | ||||||||
\(829\) | −9.16919 | −0.318459 | −0.159230 | − | 0.987242i | \(-0.550901\pi\) | ||||
−0.159230 | + | 0.987242i | \(0.550901\pi\) | |||||||
\(830\) | 0.166093 | 0.00576518 | ||||||||
\(831\) | 9.02931 | 0.313223 | ||||||||
\(832\) | 12.1004 | 0.419505 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −19.8198 | −0.686305 | ||||||||
\(835\) | 0.0507679 | 0.00175690 | ||||||||
\(836\) | −0.696622 | −0.0240932 | ||||||||
\(837\) | 0.735747 | 0.0254312 | ||||||||
\(838\) | 65.1352 | 2.25006 | ||||||||
\(839\) | −42.6983 | −1.47411 | −0.737055 | − | 0.675833i | \(-0.763784\pi\) | ||||
−0.737055 | + | 0.675833i | \(0.763784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2851 | −0.940866 | ||||||||
\(842\) | 55.7119 | 1.91996 | ||||||||
\(843\) | 0.893294 | 0.0307667 | ||||||||
\(844\) | −10.1419 | −0.349099 | ||||||||
\(845\) | −0.0468620 | −0.00161210 | ||||||||
\(846\) | −14.8213 | −0.509566 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 69.4720 | 2.38568 | ||||||||
\(849\) | 20.6014 | 0.707039 | ||||||||
\(850\) | −5.86926 | −0.201314 | ||||||||
\(851\) | −11.5460 | −0.395793 | ||||||||
\(852\) | −4.69334 | −0.160791 | ||||||||
\(853\) | 12.6282 | 0.432381 | 0.216190 | − | 0.976351i | \(-0.430637\pi\) | ||||
0.216190 | + | 0.976351i | \(0.430637\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.292088 | −0.00998919 | ||||||||
\(856\) | 6.23135 | 0.212983 | ||||||||
\(857\) | −55.6169 | −1.89984 | −0.949919 | − | 0.312497i | \(-0.898835\pi\) | ||||
−0.949919 | + | 0.312497i | \(0.898835\pi\) | |||||||
\(858\) | −0.874645 | −0.0298599 | ||||||||
\(859\) | −6.63053 | −0.226231 | −0.113115 | − | 0.993582i | \(-0.536083\pi\) | ||||
−0.113115 | + | 0.993582i | \(0.536083\pi\) | |||||||
\(860\) | 0.0778663 | 0.00265522 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.7546 | 0.945327 | ||||||||
\(863\) | −35.9010 | −1.22208 | −0.611042 | − | 0.791598i | \(-0.709250\pi\) | ||||
−0.611042 | + | 0.791598i | \(0.709250\pi\) | |||||||
\(864\) | 3.84832 | 0.130923 | ||||||||
\(865\) | −0.991895 | −0.0337255 | ||||||||
\(866\) | 4.57675 | 0.155524 | ||||||||
\(867\) | −16.4912 | −0.560071 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.949510 | −0.0322099 | ||||||||
\(870\) | −0.0986146 | −0.00334335 | ||||||||
\(871\) | −46.2340 | −1.56658 | ||||||||
\(872\) | −18.1753 | −0.615492 | ||||||||
\(873\) | −8.42652 | −0.285194 | ||||||||
\(874\) | −13.3032 | −0.449986 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.2778 | 0.381042 | ||||||||
\(877\) | −34.1017 | −1.15153 | −0.575766 | − | 0.817615i | \(-0.695296\pi\) | ||||
−0.575766 | + | 0.817615i | \(0.695296\pi\) | |||||||
\(878\) | 25.6064 | 0.864175 | ||||||||
\(879\) | 17.0744 | 0.575904 | ||||||||
\(880\) | −0.0345206 | −0.00116369 | ||||||||
\(881\) | −4.69337 | −0.158124 | −0.0790619 | − | 0.996870i | \(-0.525192\pi\) | ||||
−0.0790619 | + | 0.996870i | \(0.525192\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.6223 | 0.693995 | 0.346998 | − | 0.937866i | \(-0.387201\pi\) | ||||
0.346998 | + | 0.937866i | \(0.387201\pi\) | |||||||
\(884\) | −1.75401 | −0.0589936 | ||||||||
\(885\) | −0.517479 | −0.0173949 | ||||||||
\(886\) | 31.8129 | 1.06878 | ||||||||
\(887\) | −4.96347 | −0.166657 | −0.0833285 | − | 0.996522i | \(-0.526555\pi\) | ||||
−0.0833285 | + | 0.996522i | \(0.526555\pi\) | |||||||
\(888\) | 19.3711 | 0.650051 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.07935 | 0.0361799 | ||||||||
\(891\) | 0.153516 | 0.00514298 | ||||||||
\(892\) | −11.0331 | −0.369414 | ||||||||
\(893\) | −57.4877 | −1.92375 | ||||||||
\(894\) | 25.6114 | 0.856573 | ||||||||
\(895\) | −0.322894 | −0.0107932 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.37871 | −0.146201 | ||||||||
\(898\) | 49.0451 | 1.63665 | ||||||||
\(899\) | 0.963488 | 0.0321341 | ||||||||
\(900\) | −3.55149 | −0.118383 | ||||||||
\(901\) | 10.0795 | 0.335797 | ||||||||
\(902\) | −0.252747 | −0.00841555 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.1878 | 0.604919 | ||||||||
\(905\) | 0.599507 | 0.0199283 | ||||||||
\(906\) | −38.1085 | −1.26607 | ||||||||
\(907\) | −46.7190 | −1.55128 | −0.775640 | − | 0.631176i | \(-0.782573\pi\) | ||||
−0.775640 | + | 0.631176i | \(0.782573\pi\) | |||||||
\(908\) | −15.6497 | −0.519353 | ||||||||
\(909\) | −4.27869 | −0.141915 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.07687 | −0.234467 | −0.117234 | − | 0.993104i | \(-0.537403\pi\) | ||||
−0.117234 | + | 0.993104i | \(0.537403\pi\) | |||||||
\(912\) | 31.3946 | 1.03958 | ||||||||
\(913\) | −0.338596 | −0.0112059 | ||||||||
\(914\) | 32.0360 | 1.05966 | ||||||||
\(915\) | −0.652991 | −0.0215872 | ||||||||
\(916\) | −10.3916 | −0.343348 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.17434 | 0.0387591 | ||||||||
\(919\) | 12.9722 | 0.427914 | 0.213957 | − | 0.976843i | \(-0.431365\pi\) | ||||
0.213957 | + | 0.976843i | \(0.431365\pi\) | |||||||
\(920\) | −0.122861 | −0.00405060 | ||||||||
\(921\) | 6.13820 | 0.202261 | ||||||||
\(922\) | 14.5977 | 0.480751 | ||||||||
\(923\) | −22.8563 | −0.752324 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −45.6058 | −1.49951 | ||||||||
\(926\) | −37.9398 | −1.24678 | ||||||||
\(927\) | 8.86287 | 0.291095 | ||||||||
\(928\) | 5.03952 | 0.165430 | ||||||||
\(929\) | 17.1271 | 0.561921 | 0.280961 | − | 0.959719i | \(-0.409347\pi\) | ||||
0.280961 | + | 0.959719i | \(0.409347\pi\) | |||||||
\(930\) | −0.0554055 | −0.00181682 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.24536 | 0.106305 | ||||||||
\(933\) | 15.6468 | 0.512253 | ||||||||
\(934\) | 10.8992 | 0.356633 | ||||||||
\(935\) | −0.00500850 | −0.000163796 0 | ||||||||
\(936\) | 7.34629 | 0.240121 | ||||||||
\(937\) | 51.2625 | 1.67467 | 0.837337 | − | 0.546687i | \(-0.184111\pi\) | ||||
0.837337 | + | 0.546687i | \(0.184111\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.9514 | 0.553188 | ||||||||
\(940\) | 0.292595 | 0.00954339 | ||||||||
\(941\) | 35.2503 | 1.14913 | 0.574564 | − | 0.818460i | \(-0.305172\pi\) | ||||
0.574564 | + | 0.818460i | \(0.305172\pi\) | |||||||
\(942\) | −22.3298 | −0.727545 | ||||||||
\(943\) | −1.26532 | −0.0412045 | ||||||||
\(944\) | 55.6205 | 1.81029 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.605510 | −0.0196868 | ||||||||
\(947\) | −36.1653 | −1.17521 | −0.587607 | − | 0.809146i | \(-0.699930\pi\) | ||||
−0.587607 | + | 0.809146i | \(0.699930\pi\) | |||||||
\(948\) | −4.39509 | −0.142746 | ||||||||
\(949\) | 54.9224 | 1.78286 | ||||||||
\(950\) | −52.5463 | −1.70483 | ||||||||
\(951\) | −8.16987 | −0.264926 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.7601 | −0.640093 | −0.320046 | − | 0.947402i | \(-0.603699\pi\) | ||||
−0.320046 | + | 0.947402i | \(0.603699\pi\) | |||||||
\(954\) | 23.2653 | 0.753242 | ||||||||
\(955\) | 0.435196 | 0.0140826 | ||||||||
\(956\) | 10.7557 | 0.347864 | ||||||||
\(957\) | 0.201035 | 0.00649853 | ||||||||
\(958\) | −27.9537 | −0.903144 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.159935 | 0.00516188 | ||||||||
\(961\) | −30.4587 | −0.982538 | ||||||||
\(962\) | −51.9889 | −1.67619 | ||||||||
\(963\) | 2.93535 | 0.0945905 | ||||||||
\(964\) | −9.22394 | −0.297083 | ||||||||
\(965\) | −0.464749 | −0.0149608 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.4406 | −0.528695 | −0.264347 | − | 0.964428i | \(-0.585157\pi\) | ||||
−0.264347 | + | 0.964428i | \(0.585157\pi\) | |||||||
\(968\) | −23.3014 | −0.748937 | ||||||||
\(969\) | 4.55496 | 0.146326 | ||||||||
\(970\) | 0.634559 | 0.0203745 | ||||||||
\(971\) | 41.5017 | 1.33185 | 0.665926 | − | 0.746018i | \(-0.268037\pi\) | ||||
0.665926 | + | 0.746018i | \(0.268037\pi\) | |||||||
\(972\) | 0.710595 | 0.0227923 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −30.1807 | −0.967051 | ||||||||
\(975\) | −17.2955 | −0.553901 | ||||||||
\(976\) | 70.1857 | 2.24659 | ||||||||
\(977\) | −10.0675 | −0.322089 | −0.161044 | − | 0.986947i | \(-0.551486\pi\) | ||||
−0.161044 | + | 0.986947i | \(0.551486\pi\) | |||||||
\(978\) | −31.0748 | −0.993664 | ||||||||
\(979\) | −2.20035 | −0.0703236 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.56169 | −0.273354 | ||||||||
\(982\) | 10.6220 | 0.338961 | ||||||||
\(983\) | 49.9216 | 1.59225 | 0.796126 | − | 0.605132i | \(-0.206879\pi\) | ||||
0.796126 | + | 0.605132i | \(0.206879\pi\) | |||||||
\(984\) | 2.12286 | 0.0676744 | ||||||||
\(985\) | 0.344934 | 0.0109905 | ||||||||
\(986\) | 1.53784 | 0.0489750 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15.7033 | −0.499587 | ||||||||
\(989\) | −3.03135 | −0.0963913 | ||||||||
\(990\) | −0.0115605 | −0.000367417 0 | ||||||||
\(991\) | −27.4632 | −0.872397 | −0.436199 | − | 0.899850i | \(-0.643675\pi\) | ||||
−0.436199 | + | 0.899850i | \(0.643675\pi\) | |||||||
\(992\) | 2.83140 | 0.0898969 | ||||||||
\(993\) | 7.85298 | 0.249207 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.18571 | 0.0375896 | ||||||||
\(996\) | −1.56729 | −0.0496615 | ||||||||
\(997\) | 15.3608 | 0.486482 | 0.243241 | − | 0.969966i | \(-0.421789\pi\) | ||||
0.243241 | + | 0.969966i | \(0.421789\pi\) | |||||||
\(998\) | −15.9998 | −0.506465 | ||||||||
\(999\) | 9.12498 | 0.288702 |
(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 | 6027.2.a.bm.1.4 | yes | 16 | |
7.6 | odd | 2 | 6027.2.a.bl.1.4 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bl.1.4 | ✓ | 16 | 7.6 | odd | 2 | ||
6027.2.a.bm.1.4 | yes | 16 | 1.1 | even | 1 | trivial |