Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} - 745 x^{5} - 802 x^{4} + 386 x^{3} + 74 x^{2} - 15 x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2013) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(1.61392\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61392 | 1.14122 | 0.570608 | − | 0.821222i | \(-0.306708\pi\) | ||||
0.570608 | + | 0.821222i | \(0.306708\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.604750 | 0.302375 | ||||||||
\(5\) | 3.65776 | 1.63580 | 0.817901 | − | 0.575359i | \(-0.195138\pi\) | ||||
0.817901 | + | 0.575359i | \(0.195138\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.985739 | 0.372574 | 0.186287 | − | 0.982495i | \(-0.440355\pi\) | ||||
0.186287 | + | 0.982495i | \(0.440355\pi\) | |||||||
\(8\) | −2.25183 | −0.796141 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.90335 | 1.86680 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.65320 | 0.735866 | 0.367933 | − | 0.929852i | \(-0.380066\pi\) | ||||
0.367933 | + | 0.929852i | \(0.380066\pi\) | |||||||
\(14\) | 1.59091 | 0.425188 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.84378 | −1.21094 | ||||||||
\(17\) | 6.25317 | 1.51662 | 0.758308 | − | 0.651896i | \(-0.226026\pi\) | ||||
0.758308 | + | 0.651896i | \(0.226026\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.35459 | 0.310763 | 0.155382 | − | 0.987855i | \(-0.450339\pi\) | ||||
0.155382 | + | 0.987855i | \(0.450339\pi\) | |||||||
\(20\) | 2.21203 | 0.494626 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.61392 | 0.344090 | ||||||||
\(23\) | −2.24451 | −0.468012 | −0.234006 | − | 0.972235i | \(-0.575184\pi\) | ||||
−0.234006 | + | 0.972235i | \(0.575184\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.37924 | 1.67585 | ||||||||
\(26\) | 4.28207 | 0.839782 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.596126 | 0.112657 | ||||||||
\(29\) | 4.46976 | 0.830014 | 0.415007 | − | 0.909818i | \(-0.363779\pi\) | ||||
0.415007 | + | 0.909818i | \(0.363779\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00805 | −0.719867 | −0.359934 | − | 0.932978i | \(-0.617201\pi\) | ||||
−0.359934 | + | 0.932978i | \(0.617201\pi\) | |||||||
\(32\) | −3.31383 | −0.585808 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.0921 | 1.73079 | ||||||||
\(35\) | 3.60560 | 0.609458 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.24458 | −0.204608 | −0.102304 | − | 0.994753i | \(-0.532621\pi\) | ||||
−0.102304 | + | 0.994753i | \(0.532621\pi\) | |||||||
\(38\) | 2.18620 | 0.354648 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.23665 | −1.30233 | ||||||||
\(41\) | −6.27870 | −0.980568 | −0.490284 | − | 0.871563i | \(-0.663107\pi\) | ||||
−0.490284 | + | 0.871563i | \(0.663107\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.305238 | 0.0465483 | 0.0232742 | − | 0.999729i | \(-0.492591\pi\) | ||||
0.0232742 | + | 0.999729i | \(0.492591\pi\) | |||||||
\(44\) | 0.604750 | 0.0911695 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.62247 | −0.534103 | ||||||||
\(47\) | 10.8096 | 1.57675 | 0.788374 | − | 0.615197i | \(-0.210923\pi\) | ||||
0.788374 | + | 0.615197i | \(0.210923\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.02832 | −0.861188 | ||||||||
\(50\) | 13.5235 | 1.91251 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.60452 | 0.222507 | ||||||||
\(53\) | 10.0242 | 1.37693 | 0.688466 | − | 0.725269i | \(-0.258285\pi\) | ||||
0.688466 | + | 0.725269i | \(0.258285\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.65776 | 0.493213 | ||||||||
\(56\) | −2.21971 | −0.296622 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.21386 | 0.947226 | ||||||||
\(59\) | −8.28564 | −1.07870 | −0.539350 | − | 0.842082i | \(-0.681330\pi\) | ||||
−0.539350 | + | 0.842082i | \(0.681330\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −6.46869 | −0.821524 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.33928 | 0.542410 | ||||||||
\(65\) | 9.70479 | 1.20373 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.5138 | −1.89531 | −0.947654 | − | 0.319298i | \(-0.896553\pi\) | ||||
−0.947654 | + | 0.319298i | \(0.896553\pi\) | |||||||
\(68\) | 3.78160 | 0.458587 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.81917 | 0.695524 | ||||||||
\(71\) | 8.28871 | 0.983689 | 0.491845 | − | 0.870683i | \(-0.336323\pi\) | ||||
0.491845 | + | 0.870683i | \(0.336323\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.53532 | 0.998984 | 0.499492 | − | 0.866319i | \(-0.333520\pi\) | ||||
0.499492 | + | 0.866319i | \(0.333520\pi\) | |||||||
\(74\) | −2.00866 | −0.233502 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.819186 | 0.0939670 | ||||||||
\(77\) | 0.985739 | 0.112335 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.4999 | −1.51886 | −0.759429 | − | 0.650590i | \(-0.774522\pi\) | ||||
−0.759429 | + | 0.650590i | \(0.774522\pi\) | |||||||
\(80\) | −17.7174 | −1.98087 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.1333 | −1.11904 | ||||||||
\(83\) | −4.84293 | −0.531581 | −0.265790 | − | 0.964031i | \(-0.585633\pi\) | ||||
−0.265790 | + | 0.964031i | \(0.585633\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.8726 | 2.48088 | ||||||||
\(86\) | 0.492631 | 0.0531217 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.25183 | −0.240046 | ||||||||
\(89\) | 15.4360 | 1.63621 | 0.818105 | − | 0.575069i | \(-0.195025\pi\) | ||||
0.818105 | + | 0.575069i | \(0.195025\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.61537 | 0.274165 | ||||||||
\(92\) | −1.35737 | −0.141515 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 17.4459 | 1.79941 | ||||||||
\(95\) | 4.95476 | 0.508347 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.8187 | 1.09847 | 0.549235 | − | 0.835668i | \(-0.314919\pi\) | ||||
0.549235 | + | 0.835668i | \(0.314919\pi\) | |||||||
\(98\) | −9.72925 | −0.982802 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.06735 | 0.506735 | ||||||||
\(101\) | −18.5401 | −1.84481 | −0.922406 | − | 0.386221i | \(-0.873780\pi\) | ||||
−0.922406 | + | 0.386221i | \(0.873780\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.3353 | 1.31396 | 0.656982 | − | 0.753907i | \(-0.271833\pi\) | ||||
0.656982 | + | 0.753907i | \(0.271833\pi\) | |||||||
\(104\) | −5.97455 | −0.585853 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 16.1783 | 1.57138 | ||||||||
\(107\) | −12.9262 | −1.24962 | −0.624811 | − | 0.780776i | \(-0.714824\pi\) | ||||
−0.624811 | + | 0.780776i | \(0.714824\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.1301 | 1.64077 | 0.820384 | − | 0.571813i | \(-0.193760\pi\) | ||||
0.820384 | + | 0.571813i | \(0.193760\pi\) | |||||||
\(110\) | 5.90335 | 0.562863 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.77470 | −0.451167 | ||||||||
\(113\) | −12.6163 | −1.18685 | −0.593423 | − | 0.804891i | \(-0.702224\pi\) | ||||
−0.593423 | + | 0.804891i | \(0.702224\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.20988 | −0.765576 | ||||||||
\(116\) | 2.70309 | 0.250976 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.3724 | −1.23103 | ||||||||
\(119\) | 6.16399 | 0.565052 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.61392 | 0.146118 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.42387 | −0.217670 | ||||||||
\(125\) | 12.3605 | 1.10555 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.7816 | 1.31166 | 0.655828 | − | 0.754910i | \(-0.272320\pi\) | ||||
0.655828 | + | 0.754910i | \(0.272320\pi\) | |||||||
\(128\) | 13.6309 | 1.20482 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 15.6628 | 1.37372 | ||||||||
\(131\) | −12.0226 | −1.05042 | −0.525210 | − | 0.850972i | \(-0.676013\pi\) | ||||
−0.525210 | + | 0.850972i | \(0.676013\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.33527 | 0.115782 | ||||||||
\(134\) | −25.0380 | −2.16296 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −14.0811 | −1.20744 | ||||||||
\(137\) | 12.6310 | 1.07914 | 0.539568 | − | 0.841942i | \(-0.318587\pi\) | ||||
0.539568 | + | 0.841942i | \(0.318587\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.6404 | −1.41142 | −0.705711 | − | 0.708500i | \(-0.749372\pi\) | ||||
−0.705711 | + | 0.708500i | \(0.749372\pi\) | |||||||
\(140\) | 2.18049 | 0.184285 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13.3774 | 1.12260 | ||||||||
\(143\) | 2.65320 | 0.221872 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.3493 | 1.35774 | ||||||||
\(146\) | 13.7754 | 1.14006 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.752659 | −0.0618682 | ||||||||
\(149\) | 3.29899 | 0.270264 | 0.135132 | − | 0.990828i | \(-0.456854\pi\) | ||||
0.135132 | + | 0.990828i | \(0.456854\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.8467 | 1.12683 | 0.563413 | − | 0.826176i | \(-0.309488\pi\) | ||||
0.563413 | + | 0.826176i | \(0.309488\pi\) | |||||||
\(152\) | −3.05029 | −0.247411 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.59091 | 0.128199 | ||||||||
\(155\) | −14.6605 | −1.17756 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.10610 | −0.407512 | −0.203756 | − | 0.979022i | \(-0.565315\pi\) | ||||
−0.203756 | + | 0.979022i | \(0.565315\pi\) | |||||||
\(158\) | −21.7878 | −1.73335 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −12.1212 | −0.958267 | ||||||||
\(161\) | −2.21250 | −0.174369 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.0106 | 1.09739 | 0.548696 | − | 0.836022i | \(-0.315124\pi\) | ||||
0.548696 | + | 0.836022i | \(0.315124\pi\) | |||||||
\(164\) | −3.79704 | −0.296499 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.81612 | −0.606648 | ||||||||
\(167\) | 19.1530 | 1.48210 | 0.741052 | − | 0.671448i | \(-0.234327\pi\) | ||||
0.741052 | + | 0.671448i | \(0.234327\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.96052 | −0.458502 | ||||||||
\(170\) | 36.9147 | 2.83123 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.184593 | 0.0140751 | ||||||||
\(173\) | 22.4432 | 1.70632 | 0.853161 | − | 0.521647i | \(-0.174682\pi\) | ||||
0.853161 | + | 0.521647i | \(0.174682\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.25975 | 0.624378 | ||||||||
\(176\) | −4.84378 | −0.365113 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 24.9125 | 1.86727 | ||||||||
\(179\) | −13.1373 | −0.981927 | −0.490964 | − | 0.871180i | \(-0.663355\pi\) | ||||
−0.490964 | + | 0.871180i | \(0.663355\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.41628 | 0.551247 | 0.275624 | − | 0.961266i | \(-0.411116\pi\) | ||||
0.275624 | + | 0.961266i | \(0.411116\pi\) | |||||||
\(182\) | 4.22100 | 0.312881 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.05425 | 0.372604 | ||||||||
\(185\) | −4.55238 | −0.334698 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.25317 | 0.457277 | ||||||||
\(188\) | 6.53713 | 0.476769 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.99660 | 0.580134 | ||||||||
\(191\) | 6.22085 | 0.450125 | 0.225063 | − | 0.974344i | \(-0.427741\pi\) | ||||
0.225063 | + | 0.974344i | \(0.427741\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.95576 | −0.140779 | −0.0703893 | − | 0.997520i | \(-0.522424\pi\) | ||||
−0.0703893 | + | 0.997520i | \(0.522424\pi\) | |||||||
\(194\) | 17.4605 | 1.25359 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.64563 | −0.260402 | ||||||||
\(197\) | −27.6283 | −1.96843 | −0.984217 | − | 0.176968i | \(-0.943371\pi\) | ||||
−0.984217 | + | 0.176968i | \(0.943371\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.84659 | −0.272678 | −0.136339 | − | 0.990662i | \(-0.543534\pi\) | ||||
−0.136339 | + | 0.990662i | \(0.543534\pi\) | |||||||
\(200\) | −18.8686 | −1.33421 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −29.9224 | −2.10533 | ||||||||
\(203\) | 4.40602 | 0.309242 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.9660 | −1.60402 | ||||||||
\(206\) | 21.5221 | 1.49952 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.8515 | −0.891093 | ||||||||
\(209\) | 1.35459 | 0.0936987 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.4958 | −0.791405 | −0.395703 | − | 0.918379i | \(-0.629499\pi\) | ||||
−0.395703 | + | 0.918379i | \(0.629499\pi\) | |||||||
\(212\) | 6.06214 | 0.416350 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −20.8619 | −1.42609 | ||||||||
\(215\) | 1.11649 | 0.0761439 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.95089 | −0.268204 | ||||||||
\(218\) | 27.6467 | 1.87247 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.21203 | 0.149135 | ||||||||
\(221\) | 16.5909 | 1.11603 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.82324 | 0.657813 | 0.328906 | − | 0.944363i | \(-0.393320\pi\) | ||||
0.328906 | + | 0.944363i | \(0.393320\pi\) | |||||||
\(224\) | −3.26658 | −0.218257 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.3618 | −1.35445 | ||||||||
\(227\) | −12.7593 | −0.846867 | −0.423433 | − | 0.905927i | \(-0.639175\pi\) | ||||
−0.423433 | + | 0.905927i | \(0.639175\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.6052 | 0.700808 | 0.350404 | − | 0.936599i | \(-0.386044\pi\) | ||||
0.350404 | + | 0.936599i | \(0.386044\pi\) | |||||||
\(230\) | −13.2501 | −0.873688 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.0651 | −0.660809 | ||||||||
\(233\) | −23.6060 | −1.54648 | −0.773239 | − | 0.634115i | \(-0.781365\pi\) | ||||
−0.773239 | + | 0.634115i | \(0.781365\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 39.5391 | 2.57925 | ||||||||
\(236\) | −5.01074 | −0.326172 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.94822 | 0.644847 | ||||||||
\(239\) | 7.79900 | 0.504476 | 0.252238 | − | 0.967665i | \(-0.418833\pi\) | ||||
0.252238 | + | 0.967665i | \(0.418833\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.4302 | −0.929531 | −0.464766 | − | 0.885434i | \(-0.653861\pi\) | ||||
−0.464766 | + | 0.885434i | \(0.653861\pi\) | |||||||
\(242\) | 1.61392 | 0.103747 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.604750 | 0.0387151 | ||||||||
\(245\) | −22.0502 | −1.40873 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.59399 | 0.228680 | ||||||||
\(248\) | 9.02544 | 0.573116 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 19.9489 | 1.26168 | ||||||||
\(251\) | −27.7902 | −1.75410 | −0.877050 | − | 0.480399i | \(-0.840492\pi\) | ||||
−0.877050 | + | 0.480399i | \(0.840492\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.24451 | −0.141111 | ||||||||
\(254\) | 23.8564 | 1.49688 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.3207 | 0.832545 | ||||||||
\(257\) | −1.48481 | −0.0926199 | −0.0463100 | − | 0.998927i | \(-0.514746\pi\) | ||||
−0.0463100 | + | 0.998927i | \(0.514746\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.22683 | −0.0762316 | ||||||||
\(260\) | 5.86897 | 0.363978 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −19.4036 | −1.19876 | ||||||||
\(263\) | 1.16715 | 0.0719693 | 0.0359847 | − | 0.999352i | \(-0.488543\pi\) | ||||
0.0359847 | + | 0.999352i | \(0.488543\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 36.6662 | 2.25239 | ||||||||
\(266\) | 2.15502 | 0.132133 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.38195 | −0.573094 | ||||||||
\(269\) | −26.7060 | −1.62829 | −0.814147 | − | 0.580659i | \(-0.802795\pi\) | ||||
−0.814147 | + | 0.580659i | \(0.802795\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.63024 | 0.159776 | 0.0798879 | − | 0.996804i | \(-0.474544\pi\) | ||||
0.0798879 | + | 0.996804i | \(0.474544\pi\) | |||||||
\(272\) | −30.2890 | −1.83654 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.3854 | 1.23153 | ||||||||
\(275\) | 8.37924 | 0.505287 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.34527 | −0.441335 | −0.220667 | − | 0.975349i | \(-0.570824\pi\) | ||||
−0.220667 | + | 0.975349i | \(0.570824\pi\) | |||||||
\(278\) | −26.8564 | −1.61074 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.11919 | −0.485215 | ||||||||
\(281\) | −6.09887 | −0.363828 | −0.181914 | − | 0.983314i | \(-0.558229\pi\) | ||||
−0.181914 | + | 0.983314i | \(0.558229\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.2465 | 1.32242 | 0.661209 | − | 0.750202i | \(-0.270044\pi\) | ||||
0.661209 | + | 0.750202i | \(0.270044\pi\) | |||||||
\(284\) | 5.01260 | 0.297443 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.28207 | 0.253204 | ||||||||
\(287\) | −6.18916 | −0.365335 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.1021 | 1.30013 | ||||||||
\(290\) | 26.3866 | 1.54947 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.16173 | 0.302068 | ||||||||
\(293\) | 7.69309 | 0.449435 | 0.224718 | − | 0.974424i | \(-0.427854\pi\) | ||||
0.224718 | + | 0.974424i | \(0.427854\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −30.3069 | −1.76454 | ||||||||
\(296\) | 2.80258 | 0.162897 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.32431 | 0.308429 | ||||||||
\(299\) | −5.95513 | −0.344394 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.300885 | 0.0173427 | ||||||||
\(302\) | 22.3475 | 1.28595 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.56131 | −0.376317 | ||||||||
\(305\) | 3.65776 | 0.209443 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.6159 | 0.605879 | 0.302939 | − | 0.953010i | \(-0.402032\pi\) | ||||
0.302939 | + | 0.953010i | \(0.402032\pi\) | |||||||
\(308\) | 0.596126 | 0.0339674 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −23.6609 | −1.34385 | ||||||||
\(311\) | 34.2582 | 1.94261 | 0.971303 | − | 0.237847i | \(-0.0764417\pi\) | ||||
0.971303 | + | 0.237847i | \(0.0764417\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.50686 | 0.367789 | 0.183895 | − | 0.982946i | \(-0.441129\pi\) | ||||
0.183895 | + | 0.982946i | \(0.441129\pi\) | |||||||
\(314\) | −8.24086 | −0.465059 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.16407 | −0.459265 | ||||||||
\(317\) | −8.11911 | −0.456015 | −0.228007 | − | 0.973659i | \(-0.573221\pi\) | ||||
−0.228007 | + | 0.973659i | \(0.573221\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.46976 | 0.250259 | ||||||||
\(320\) | 15.8721 | 0.887276 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.57081 | −0.198993 | ||||||||
\(323\) | 8.47045 | 0.471309 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.2318 | 1.23320 | ||||||||
\(326\) | 22.6120 | 1.25236 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 14.1385 | 0.780671 | ||||||||
\(329\) | 10.6555 | 0.587456 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.4323 | −1.72768 | −0.863839 | − | 0.503768i | \(-0.831947\pi\) | ||||
−0.863839 | + | 0.503768i | \(0.831947\pi\) | |||||||
\(332\) | −2.92876 | −0.160737 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 30.9115 | 1.69140 | ||||||||
\(335\) | −56.7457 | −3.10035 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.6087 | −1.01368 | −0.506841 | − | 0.862040i | \(-0.669187\pi\) | ||||
−0.506841 | + | 0.862040i | \(0.669187\pi\) | |||||||
\(338\) | −9.61982 | −0.523249 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 13.8322 | 0.750157 | ||||||||
\(341\) | −4.00805 | −0.217048 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.8425 | −0.693431 | ||||||||
\(344\) | −0.687343 | −0.0370591 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 36.2216 | 1.94728 | ||||||||
\(347\) | 4.39085 | 0.235713 | 0.117856 | − | 0.993031i | \(-0.462398\pi\) | ||||
0.117856 | + | 0.993031i | \(0.462398\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.5921 | 1.10227 | 0.551134 | − | 0.834417i | \(-0.314195\pi\) | ||||
0.551134 | + | 0.834417i | \(0.314195\pi\) | |||||||
\(350\) | 13.3306 | 0.712551 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.31383 | −0.176628 | ||||||||
\(353\) | 8.31752 | 0.442697 | 0.221348 | − | 0.975195i | \(-0.428954\pi\) | ||||
0.221348 | + | 0.975195i | \(0.428954\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.3182 | 1.60912 | ||||||||
\(356\) | 9.33490 | 0.494749 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.2026 | −1.12059 | ||||||||
\(359\) | −15.5845 | −0.822520 | −0.411260 | − | 0.911518i | \(-0.634911\pi\) | ||||
−0.411260 | + | 0.911518i | \(0.634911\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1651 | −0.903426 | ||||||||
\(362\) | 11.9693 | 0.629093 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.58164 | 0.0829006 | ||||||||
\(365\) | 31.2202 | 1.63414 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.5398 | 0.550175 | 0.275088 | − | 0.961419i | \(-0.411293\pi\) | ||||
0.275088 | + | 0.961419i | \(0.411293\pi\) | |||||||
\(368\) | 10.8719 | 0.566737 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.34719 | −0.381962 | ||||||||
\(371\) | 9.88126 | 0.513009 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.3765 | 1.00328 | 0.501638 | − | 0.865078i | \(-0.332731\pi\) | ||||
0.501638 | + | 0.865078i | \(0.332731\pi\) | |||||||
\(374\) | 10.0921 | 0.521852 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.3414 | −1.25531 | ||||||||
\(377\) | 11.8592 | 0.610779 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.66214 | −0.342211 | −0.171106 | − | 0.985253i | \(-0.554734\pi\) | ||||
−0.171106 | + | 0.985253i | \(0.554734\pi\) | |||||||
\(380\) | 2.99639 | 0.153711 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.0400 | 0.513690 | ||||||||
\(383\) | −18.7882 | −0.960031 | −0.480016 | − | 0.877260i | \(-0.659369\pi\) | ||||
−0.480016 | + | 0.877260i | \(0.659369\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.60560 | 0.183759 | ||||||||
\(386\) | −3.15645 | −0.160659 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.54259 | 0.332150 | ||||||||
\(389\) | 21.2173 | 1.07576 | 0.537880 | − | 0.843021i | \(-0.319225\pi\) | ||||
0.537880 | + | 0.843021i | \(0.319225\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.0353 | −0.709795 | ||||||||
\(392\) | 13.5747 | 0.685627 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −44.5899 | −2.24641 | ||||||||
\(395\) | −49.3795 | −2.48455 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.82400 | −0.0915440 | −0.0457720 | − | 0.998952i | \(-0.514575\pi\) | ||||
−0.0457720 | + | 0.998952i | \(0.514575\pi\) | |||||||
\(398\) | −6.20810 | −0.311184 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −40.5872 | −2.02936 | ||||||||
\(401\) | −18.6265 | −0.930164 | −0.465082 | − | 0.885268i | \(-0.653975\pi\) | ||||
−0.465082 | + | 0.885268i | \(0.653975\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.6342 | −0.529726 | ||||||||
\(404\) | −11.2121 | −0.557825 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.11098 | 0.352912 | ||||||||
\(407\) | −1.24458 | −0.0616915 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.3454 | −1.40159 | −0.700795 | − | 0.713362i | \(-0.747171\pi\) | ||||
−0.700795 | + | 0.713362i | \(0.747171\pi\) | |||||||
\(410\) | −37.0654 | −1.83053 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.06450 | 0.397310 | ||||||||
\(413\) | −8.16749 | −0.401896 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.7143 | −0.869561 | ||||||||
\(416\) | −8.79227 | −0.431076 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.18620 | 0.106930 | ||||||||
\(419\) | −14.0074 | −0.684307 | −0.342154 | − | 0.939644i | \(-0.611156\pi\) | ||||
−0.342154 | + | 0.939644i | \(0.611156\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.242484 | −0.0118180 | −0.00590898 | − | 0.999983i | \(-0.501881\pi\) | ||||
−0.00590898 | + | 0.999983i | \(0.501881\pi\) | |||||||
\(422\) | −18.5534 | −0.903165 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −22.5728 | −1.09623 | ||||||||
\(425\) | 52.3968 | 2.54162 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.985739 | 0.0477033 | ||||||||
\(428\) | −7.81712 | −0.377855 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.80193 | 0.0868967 | ||||||||
\(431\) | 20.9192 | 1.00764 | 0.503822 | − | 0.863807i | \(-0.331927\pi\) | ||||
0.503822 | + | 0.863807i | \(0.331927\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.5719 | 1.85364 | 0.926822 | − | 0.375500i | \(-0.122529\pi\) | ||||
0.926822 | + | 0.375500i | \(0.122529\pi\) | |||||||
\(434\) | −6.37644 | −0.306079 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.3594 | 0.496127 | ||||||||
\(437\) | −3.04038 | −0.145441 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.54989 | −0.360337 | −0.180168 | − | 0.983636i | \(-0.557664\pi\) | ||||
−0.180168 | + | 0.983636i | \(0.557664\pi\) | |||||||
\(440\) | −8.23665 | −0.392667 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 26.7765 | 1.27363 | ||||||||
\(443\) | 7.89709 | 0.375202 | 0.187601 | − | 0.982245i | \(-0.439929\pi\) | ||||
0.187601 | + | 0.982245i | \(0.439929\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 56.4611 | 2.67651 | ||||||||
\(446\) | 15.8540 | 0.750707 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.27740 | 0.202088 | ||||||||
\(449\) | −21.7371 | −1.02584 | −0.512919 | − | 0.858437i | \(-0.671436\pi\) | ||||
−0.512919 | + | 0.858437i | \(0.671436\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.27870 | −0.295652 | ||||||||
\(452\) | −7.62973 | −0.358872 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −20.5926 | −0.966458 | ||||||||
\(455\) | 9.56639 | 0.448479 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.7422 | −0.829943 | −0.414972 | − | 0.909834i | \(-0.636209\pi\) | ||||
−0.414972 | + | 0.909834i | \(0.636209\pi\) | |||||||
\(458\) | 17.1159 | 0.799774 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.96493 | −0.231491 | ||||||||
\(461\) | 5.74408 | 0.267529 | 0.133764 | − | 0.991013i | \(-0.457294\pi\) | ||||
0.133764 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.0072 | 0.511550 | 0.255775 | − | 0.966736i | \(-0.417669\pi\) | ||||
0.255775 | + | 0.966736i | \(0.417669\pi\) | |||||||
\(464\) | −21.6505 | −1.00510 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −38.0982 | −1.76487 | ||||||||
\(467\) | −20.3504 | −0.941704 | −0.470852 | − | 0.882212i | \(-0.656053\pi\) | ||||
−0.470852 | + | 0.882212i | \(0.656053\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.2925 | −0.706144 | ||||||||
\(470\) | 63.8131 | 2.94348 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 18.6578 | 0.858797 | ||||||||
\(473\) | 0.305238 | 0.0140349 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.3504 | 0.520792 | ||||||||
\(476\) | 3.72768 | 0.170858 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.5870 | 0.575716 | ||||||||
\(479\) | −18.4382 | −0.842463 | −0.421232 | − | 0.906953i | \(-0.638402\pi\) | ||||
−0.421232 | + | 0.906953i | \(0.638402\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.30212 | −0.150564 | ||||||||
\(482\) | −23.2892 | −1.06080 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.604750 | 0.0274886 | ||||||||
\(485\) | 39.5721 | 1.79688 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.57853 | 0.252787 | 0.126394 | − | 0.991980i | \(-0.459660\pi\) | ||||
0.126394 | + | 0.991980i | \(0.459660\pi\) | |||||||
\(488\) | −2.25183 | −0.101935 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −35.5873 | −1.60767 | ||||||||
\(491\) | −18.1802 | −0.820461 | −0.410231 | − | 0.911982i | \(-0.634552\pi\) | ||||
−0.410231 | + | 0.911982i | \(0.634552\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.9502 | 1.25881 | ||||||||
\(494\) | 5.80043 | 0.260973 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19.4141 | 0.871719 | ||||||||
\(497\) | 8.17051 | 0.366498 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.6130 | −0.475104 | −0.237552 | − | 0.971375i | \(-0.576345\pi\) | ||||
−0.237552 | + | 0.971375i | \(0.576345\pi\) | |||||||
\(500\) | 7.47500 | 0.334292 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −44.8512 | −2.00181 | ||||||||
\(503\) | −34.9625 | −1.55890 | −0.779449 | − | 0.626465i | \(-0.784501\pi\) | ||||
−0.779449 | + | 0.626465i | \(0.784501\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −67.8155 | −3.01775 | ||||||||
\(506\) | −3.62247 | −0.161038 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.93918 | 0.396612 | ||||||||
\(509\) | −10.0360 | −0.444838 | −0.222419 | − | 0.974951i | \(-0.571395\pi\) | ||||
−0.222419 | + | 0.974951i | \(0.571395\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.41360 | 0.372196 | ||||||||
\(512\) | −5.76323 | −0.254701 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.39637 | −0.105699 | ||||||||
\(515\) | 48.7773 | 2.14938 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.8096 | 0.475407 | ||||||||
\(518\) | −1.98001 | −0.0869967 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −21.8535 | −0.958340 | ||||||||
\(521\) | 34.0373 | 1.49120 | 0.745601 | − | 0.666393i | \(-0.232163\pi\) | ||||
0.745601 | + | 0.666393i | \(0.232163\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.293817 | −0.0128477 | −0.00642386 | − | 0.999979i | \(-0.502045\pi\) | ||||
−0.00642386 | + | 0.999979i | \(0.502045\pi\) | |||||||
\(524\) | −7.27067 | −0.317621 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.88369 | 0.0821326 | ||||||||
\(527\) | −25.0630 | −1.09176 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.9622 | −0.780964 | ||||||||
\(530\) | 59.1765 | 2.57046 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.807504 | 0.0350097 | ||||||||
\(533\) | −16.6587 | −0.721567 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −47.2810 | −2.04414 | ||||||||
\(536\) | 34.9343 | 1.50893 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −43.1014 | −1.85824 | ||||||||
\(539\) | −6.02832 | −0.259658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.6219 | −1.53151 | −0.765753 | − | 0.643134i | \(-0.777634\pi\) | ||||
−0.765753 | + | 0.643134i | \(0.777634\pi\) | |||||||
\(542\) | 4.24501 | 0.182339 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −20.7220 | −0.888447 | ||||||||
\(545\) | 62.6580 | 2.68397 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.3050 | 1.85159 | 0.925794 | − | 0.378029i | \(-0.123398\pi\) | ||||
0.925794 | + | 0.378029i | \(0.123398\pi\) | |||||||
\(548\) | 7.63858 | 0.326304 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 13.5235 | 0.576642 | ||||||||
\(551\) | 6.05468 | 0.257938 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.3074 | −0.565888 | ||||||||
\(554\) | −11.8547 | −0.503658 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.0633 | −0.426779 | ||||||||
\(557\) | −23.9291 | −1.01391 | −0.506954 | − | 0.861973i | \(-0.669229\pi\) | ||||
−0.506954 | + | 0.861973i | \(0.669229\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.809858 | 0.0342533 | ||||||||
\(560\) | −17.4647 | −0.738020 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.84310 | −0.415206 | ||||||||
\(563\) | −6.09496 | −0.256872 | −0.128436 | − | 0.991718i | \(-0.540996\pi\) | ||||
−0.128436 | + | 0.991718i | \(0.540996\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −46.1476 | −1.94144 | ||||||||
\(566\) | 35.9042 | 1.50917 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18.6648 | −0.783156 | ||||||||
\(569\) | 11.4324 | 0.479271 | 0.239635 | − | 0.970863i | \(-0.422972\pi\) | ||||
0.239635 | + | 0.970863i | \(0.422972\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.26007 | 0.178278 | 0.0891392 | − | 0.996019i | \(-0.471588\pi\) | ||||
0.0891392 | + | 0.996019i | \(0.471588\pi\) | |||||||
\(572\) | 1.60452 | 0.0670885 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.98884 | −0.416926 | ||||||||
\(575\) | −18.8073 | −0.784318 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.0517 | 1.29270 | 0.646351 | − | 0.763041i | \(-0.276294\pi\) | ||||
0.646351 | + | 0.763041i | \(0.276294\pi\) | |||||||
\(578\) | 35.6711 | 1.48372 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.88726 | 0.410546 | ||||||||
\(581\) | −4.77387 | −0.198053 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0242 | 0.415160 | ||||||||
\(584\) | −19.2201 | −0.795332 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.4161 | 0.512903 | ||||||||
\(587\) | −12.7689 | −0.527030 | −0.263515 | − | 0.964655i | \(-0.584882\pi\) | ||||
−0.263515 | + | 0.964655i | \(0.584882\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.42925 | −0.223708 | ||||||||
\(590\) | −48.9131 | −2.01372 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.02847 | 0.247768 | ||||||||
\(593\) | 20.4992 | 0.841800 | 0.420900 | − | 0.907107i | \(-0.361714\pi\) | ||||
0.420900 | + | 0.907107i | \(0.361714\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.5464 | 0.924314 | ||||||||
\(596\) | 1.99506 | 0.0817209 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.61113 | −0.393028 | ||||||||
\(599\) | −4.42860 | −0.180948 | −0.0904739 | − | 0.995899i | \(-0.528838\pi\) | ||||
−0.0904739 | + | 0.995899i | \(0.528838\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.08793 | 0.0443774 | 0.0221887 | − | 0.999754i | \(-0.492937\pi\) | ||||
0.0221887 | + | 0.999754i | \(0.492937\pi\) | |||||||
\(602\) | 0.485605 | 0.0197918 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.37377 | 0.340724 | ||||||||
\(605\) | 3.65776 | 0.148709 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.52522 | 0.0619067 | 0.0309534 | − | 0.999521i | \(-0.490146\pi\) | ||||
0.0309534 | + | 0.999521i | \(0.490146\pi\) | |||||||
\(608\) | −4.48887 | −0.182048 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.90335 | 0.239020 | ||||||||
\(611\) | 28.6801 | 1.16027 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.3564 | 0.943356 | 0.471678 | − | 0.881771i | \(-0.343648\pi\) | ||||
0.471678 | + | 0.881771i | \(0.343648\pi\) | |||||||
\(614\) | 17.1332 | 0.691439 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.21971 | −0.0894348 | ||||||||
\(617\) | −34.2890 | −1.38042 | −0.690211 | − | 0.723608i | \(-0.742482\pi\) | ||||
−0.690211 | + | 0.723608i | \(0.742482\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.90023 | −0.397924 | −0.198962 | − | 0.980007i | \(-0.563757\pi\) | ||||
−0.198962 | + | 0.980007i | \(0.563757\pi\) | |||||||
\(620\) | −8.86594 | −0.356065 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 55.2901 | 2.21693 | ||||||||
\(623\) | 15.2158 | 0.609610 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.31550 | 0.132620 | ||||||||
\(626\) | 10.5016 | 0.419727 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.08792 | −0.123221 | ||||||||
\(629\) | −7.78257 | −0.310311 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.6953 | −0.505390 | −0.252695 | − | 0.967546i | \(-0.581317\pi\) | ||||
−0.252695 | + | 0.967546i | \(0.581317\pi\) | |||||||
\(632\) | 30.3995 | 1.20923 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.1036 | −0.520412 | ||||||||
\(635\) | 54.0677 | 2.14561 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.9943 | −0.633719 | ||||||||
\(638\) | 7.21386 | 0.285599 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 49.8588 | 1.97084 | ||||||||
\(641\) | −14.9145 | −0.589087 | −0.294544 | − | 0.955638i | \(-0.595168\pi\) | ||||
−0.294544 | + | 0.955638i | \(0.595168\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.7823 | −0.819576 | −0.409788 | − | 0.912181i | \(-0.634397\pi\) | ||||
−0.409788 | + | 0.912181i | \(0.634397\pi\) | |||||||
\(644\) | −1.33801 | −0.0527250 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.6707 | 0.537865 | ||||||||
\(647\) | −2.22546 | −0.0874919 | −0.0437460 | − | 0.999043i | \(-0.513929\pi\) | ||||
−0.0437460 | + | 0.999043i | \(0.513929\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.28564 | −0.325240 | ||||||||
\(650\) | 35.8805 | 1.40735 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.47289 | 0.331824 | ||||||||
\(653\) | 11.3494 | 0.444135 | 0.222068 | − | 0.975031i | \(-0.428719\pi\) | ||||
0.222068 | + | 0.975031i | \(0.428719\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −43.9759 | −1.71828 | ||||||||
\(656\) | 30.4126 | 1.18741 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 17.1971 | 0.670414 | ||||||||
\(659\) | −1.23695 | −0.0481847 | −0.0240923 | − | 0.999710i | \(-0.507670\pi\) | ||||
−0.0240923 | + | 0.999710i | \(0.507670\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.0520 | 1.32447 | 0.662234 | − | 0.749297i | \(-0.269608\pi\) | ||||
0.662234 | + | 0.749297i | \(0.269608\pi\) | |||||||
\(662\) | −50.7294 | −1.97165 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.9054 | 0.423213 | ||||||||
\(665\) | 4.88410 | 0.189397 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.0324 | −0.388457 | ||||||||
\(668\) | 11.5828 | 0.448151 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −91.5833 | −3.53817 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.1078 | 0.659456 | 0.329728 | − | 0.944076i | \(-0.393043\pi\) | ||||
0.329728 | + | 0.944076i | \(0.393043\pi\) | |||||||
\(674\) | −30.0331 | −1.15683 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.60462 | −0.138639 | ||||||||
\(677\) | −18.9338 | −0.727687 | −0.363843 | − | 0.931460i | \(-0.618536\pi\) | ||||
−0.363843 | + | 0.931460i | \(0.618536\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.6644 | 0.409262 | ||||||||
\(680\) | −51.5052 | −1.97513 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.46869 | −0.247699 | ||||||||
\(683\) | −34.1390 | −1.30629 | −0.653146 | − | 0.757232i | \(-0.726551\pi\) | ||||
−0.653146 | + | 0.757232i | \(0.726551\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 46.2011 | 1.76525 | ||||||||
\(686\) | −20.7269 | −0.791355 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.47850 | −0.0563675 | ||||||||
\(689\) | 26.5963 | 1.01324 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.19429 | 0.159558 | 0.0797792 | − | 0.996813i | \(-0.474578\pi\) | ||||
0.0797792 | + | 0.996813i | \(0.474578\pi\) | |||||||
\(692\) | 13.5725 | 0.515949 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.08649 | 0.268999 | ||||||||
\(695\) | −60.8668 | −2.30881 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39.2618 | −1.48715 | ||||||||
\(698\) | 33.2340 | 1.25793 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.99508 | 0.188796 | ||||||||
\(701\) | 44.7848 | 1.69150 | 0.845749 | − | 0.533581i | \(-0.179154\pi\) | ||||
0.845749 | + | 0.533581i | \(0.179154\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.68589 | −0.0635845 | ||||||||
\(704\) | 4.33928 | 0.163543 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.4238 | 0.505213 | ||||||||
\(707\) | −18.2757 | −0.687330 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −45.6124 | −1.71301 | −0.856504 | − | 0.516140i | \(-0.827369\pi\) | ||||
−0.856504 | + | 0.516140i | \(0.827369\pi\) | |||||||
\(710\) | 48.9312 | 1.83636 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −34.7591 | −1.30265 | ||||||||
\(713\) | 8.99610 | 0.336907 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.70479 | 0.362939 | ||||||||
\(716\) | −7.94478 | −0.296910 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −25.1523 | −0.938674 | ||||||||
\(719\) | −27.9564 | −1.04260 | −0.521299 | − | 0.853374i | \(-0.674552\pi\) | ||||
−0.521299 | + | 0.853374i | \(0.674552\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.1451 | 0.489549 | ||||||||
\(722\) | −27.7032 | −1.03100 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.48499 | 0.166683 | ||||||||
\(725\) | 37.4532 | 1.39098 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.9140 | 1.29489 | 0.647445 | − | 0.762112i | \(-0.275837\pi\) | ||||
0.647445 | + | 0.762112i | \(0.275837\pi\) | |||||||
\(728\) | −5.88935 | −0.218274 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 50.3870 | 1.86491 | ||||||||
\(731\) | 1.90870 | 0.0705960 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.5891 | 1.01903 | 0.509514 | − | 0.860462i | \(-0.329825\pi\) | ||||
0.509514 | + | 0.860462i | \(0.329825\pi\) | |||||||
\(734\) | 17.0105 | 0.627869 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.43793 | 0.274166 | ||||||||
\(737\) | −15.5138 | −0.571457 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.9604 | −1.32282 | −0.661412 | − | 0.750023i | \(-0.730042\pi\) | ||||
−0.661412 | + | 0.750023i | \(0.730042\pi\) | |||||||
\(740\) | −2.75305 | −0.101204 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 15.9476 | 0.585455 | ||||||||
\(743\) | −47.0587 | −1.72642 | −0.863208 | − | 0.504849i | \(-0.831548\pi\) | ||||
−0.863208 | + | 0.504849i | \(0.831548\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.0669 | 0.442098 | ||||||||
\(746\) | 31.2722 | 1.14495 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.78160 | 0.138269 | ||||||||
\(749\) | −12.7419 | −0.465577 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.48808 | 0.127282 | 0.0636410 | − | 0.997973i | \(-0.479729\pi\) | ||||
0.0636410 | + | 0.997973i | \(0.479729\pi\) | |||||||
\(752\) | −52.3595 | −1.90935 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 19.1398 | 0.697031 | ||||||||
\(755\) | 50.6478 | 1.84326 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.7003 | −0.752364 | −0.376182 | − | 0.926546i | \(-0.622763\pi\) | ||||
−0.376182 | + | 0.926546i | \(0.622763\pi\) | |||||||
\(758\) | −10.7522 | −0.390537 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.1573 | −0.404716 | ||||||||
\(761\) | −19.3864 | −0.702756 | −0.351378 | − | 0.936234i | \(-0.614287\pi\) | ||||
−0.351378 | + | 0.936234i | \(0.614287\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.8858 | 0.611308 | ||||||||
\(764\) | 3.76206 | 0.136107 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30.3227 | −1.09560 | ||||||||
\(767\) | −21.9835 | −0.793778 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.9108 | 1.54740 | 0.773702 | − | 0.633549i | \(-0.218403\pi\) | ||||
0.773702 | + | 0.633549i | \(0.218403\pi\) | |||||||
\(770\) | 5.81917 | 0.209708 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.18275 | −0.0425679 | ||||||||
\(773\) | 8.56024 | 0.307890 | 0.153945 | − | 0.988079i | \(-0.450802\pi\) | ||||
0.153945 | + | 0.988079i | \(0.450802\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.5844 | −1.20639 | ||||||||
\(776\) | −24.3618 | −0.874537 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.2431 | 1.22768 | ||||||||
\(779\) | −8.50504 | −0.304725 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.28871 | 0.296594 | ||||||||
\(782\) | −22.6519 | −0.810030 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 29.1998 | 1.04285 | ||||||||
\(785\) | −18.6769 | −0.666608 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.09934 | 0.217418 | 0.108709 | − | 0.994074i | \(-0.465328\pi\) | ||||
0.108709 | + | 0.994074i | \(0.465328\pi\) | |||||||
\(788\) | −16.7082 | −0.595205 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −79.6947 | −2.83541 | ||||||||
\(791\) | −12.4364 | −0.442188 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.65320 | 0.0942180 | ||||||||
\(794\) | −2.94380 | −0.104471 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.32623 | −0.0824509 | ||||||||
\(797\) | −17.6881 | −0.626546 | −0.313273 | − | 0.949663i | \(-0.601425\pi\) | ||||
−0.313273 | + | 0.949663i | \(0.601425\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 67.5945 | 2.39132 | ||||||||
\(800\) | −27.7674 | −0.981726 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −30.0618 | −1.06152 | ||||||||
\(803\) | 8.53532 | 0.301205 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.09281 | −0.285234 | ||||||||
\(806\) | −17.1627 | −0.604532 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 41.7492 | 1.46873 | ||||||||
\(809\) | 3.78295 | 0.133001 | 0.0665007 | − | 0.997786i | \(-0.478817\pi\) | ||||
0.0665007 | + | 0.997786i | \(0.478817\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.6839 | 1.70952 | 0.854761 | − | 0.519021i | \(-0.173703\pi\) | ||||
0.854761 | + | 0.519021i | \(0.173703\pi\) | |||||||
\(812\) | 2.66454 | 0.0935071 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.00866 | −0.0704034 | ||||||||
\(815\) | 51.2474 | 1.79512 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.413471 | 0.0144655 | ||||||||
\(818\) | −45.7473 | −1.59952 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13.8887 | −0.485014 | ||||||||
\(821\) | 15.5709 | 0.543429 | 0.271714 | − | 0.962378i | \(-0.412409\pi\) | ||||
0.271714 | + | 0.962378i | \(0.412409\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.6529 | −0.824487 | −0.412244 | − | 0.911074i | \(-0.635255\pi\) | ||||
−0.412244 | + | 0.911074i | \(0.635255\pi\) | |||||||
\(824\) | −30.0287 | −1.04610 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.1817 | −0.458650 | ||||||||
\(827\) | 24.0287 | 0.835560 | 0.417780 | − | 0.908548i | \(-0.362808\pi\) | ||||
0.417780 | + | 0.908548i | \(0.362808\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.8171 | −1.41764 | −0.708818 | − | 0.705391i | \(-0.750771\pi\) | ||||
−0.708818 | + | 0.705391i | \(0.750771\pi\) | |||||||
\(830\) | −28.5895 | −0.992357 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.5130 | 0.399141 | ||||||||
\(833\) | −37.6961 | −1.30609 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 70.0572 | 2.42443 | ||||||||
\(836\) | 0.819186 | 0.0283321 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22.6069 | −0.780943 | ||||||||
\(839\) | −15.1758 | −0.523927 | −0.261963 | − | 0.965078i | \(-0.584370\pi\) | ||||
−0.261963 | + | 0.965078i | \(0.584370\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.02121 | −0.311076 | ||||||||
\(842\) | −0.391351 | −0.0134868 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.95210 | −0.239301 | ||||||||
\(845\) | −21.8022 | −0.750018 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.985739 | 0.0338704 | ||||||||
\(848\) | −48.5551 | −1.66739 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 84.5645 | 2.90054 | ||||||||
\(851\) | 2.79347 | 0.0957589 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.51030 | 0.0859511 | 0.0429756 | − | 0.999076i | \(-0.486316\pi\) | ||||
0.0429756 | + | 0.999076i | \(0.486316\pi\) | |||||||
\(854\) | 1.59091 | 0.0544398 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.1076 | 0.994876 | ||||||||
\(857\) | 30.5364 | 1.04310 | 0.521552 | − | 0.853219i | \(-0.325353\pi\) | ||||
0.521552 | + | 0.853219i | \(0.325353\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.4340 | 0.356003 | 0.178001 | − | 0.984030i | \(-0.443037\pi\) | ||||
0.178001 | + | 0.984030i | \(0.443037\pi\) | |||||||
\(860\) | 0.675196 | 0.0230240 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.7621 | 1.14994 | ||||||||
\(863\) | −7.19925 | −0.245065 | −0.122533 | − | 0.992464i | \(-0.539102\pi\) | ||||
−0.122533 | + | 0.992464i | \(0.539102\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 82.0918 | 2.79121 | ||||||||
\(866\) | 62.2520 | 2.11541 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.38930 | −0.0810982 | ||||||||
\(869\) | −13.4999 | −0.457953 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.1612 | −1.39469 | ||||||||
\(872\) | −38.5741 | −1.30628 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.90694 | −0.165980 | ||||||||
\(875\) | 12.1842 | 0.411901 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.2304 | −0.885738 | −0.442869 | − | 0.896586i | \(-0.646039\pi\) | ||||
−0.442869 | + | 0.896586i | \(0.646039\pi\) | |||||||
\(878\) | −12.1849 | −0.411222 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −17.7174 | −0.597253 | ||||||||
\(881\) | −16.5850 | −0.558764 | −0.279382 | − | 0.960180i | \(-0.590130\pi\) | ||||
−0.279382 | + | 0.960180i | \(0.590130\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.1642 | −0.981452 | −0.490726 | − | 0.871314i | \(-0.663268\pi\) | ||||
−0.490726 | + | 0.871314i | \(0.663268\pi\) | |||||||
\(884\) | 10.0334 | 0.337458 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.7453 | 0.428187 | ||||||||
\(887\) | 20.2621 | 0.680334 | 0.340167 | − | 0.940365i | \(-0.389516\pi\) | ||||
0.340167 | + | 0.940365i | \(0.389516\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.5708 | 0.488689 | ||||||||
\(890\) | 91.1240 | 3.05448 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.94060 | 0.198906 | ||||||||
\(893\) | 14.6426 | 0.489995 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −48.0531 | −1.60624 | ||||||||
\(896\) | 13.4365 | 0.448884 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −35.0820 | −1.17070 | ||||||||
\(899\) | −17.9150 | −0.597500 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 62.6831 | 2.08828 | ||||||||
\(902\) | −10.1333 | −0.337403 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 28.4098 | 0.944896 | ||||||||
\(905\) | 27.1270 | 0.901732 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.5315 | 1.14660 | 0.573300 | − | 0.819345i | \(-0.305663\pi\) | ||||
0.573300 | + | 0.819345i | \(0.305663\pi\) | |||||||
\(908\) | −7.71621 | −0.256071 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 15.4394 | 0.511812 | ||||||||
\(911\) | −5.96287 | −0.197559 | −0.0987794 | − | 0.995109i | \(-0.531494\pi\) | ||||
−0.0987794 | + | 0.995109i | \(0.531494\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.84293 | −0.160278 | ||||||||
\(914\) | −28.6345 | −0.947145 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.41347 | 0.211907 | ||||||||
\(917\) | −11.8512 | −0.391360 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.1321 | 1.02695 | 0.513476 | − | 0.858104i | \(-0.328358\pi\) | ||||
0.513476 | + | 0.858104i | \(0.328358\pi\) | |||||||
\(920\) | 18.4872 | 0.609506 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.27051 | 0.305308 | ||||||||
\(923\) | 21.9916 | 0.723863 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.4286 | −0.342891 | ||||||||
\(926\) | 17.7648 | 0.583789 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −14.8121 | −0.486229 | ||||||||
\(929\) | −16.4949 | −0.541181 | −0.270591 | − | 0.962695i | \(-0.587219\pi\) | ||||
−0.270591 | + | 0.962695i | \(0.587219\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.16587 | −0.267626 | ||||||||
\(932\) | −14.2757 | −0.467616 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −32.8440 | −1.07469 | ||||||||
\(935\) | 22.8726 | 0.748015 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.65979 | −0.0542229 | −0.0271114 | − | 0.999632i | \(-0.508631\pi\) | ||||
−0.0271114 | + | 0.999632i | \(0.508631\pi\) | |||||||
\(938\) | −24.6810 | −0.805863 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 23.9113 | 0.779900 | ||||||||
\(941\) | −16.4332 | −0.535707 | −0.267853 | − | 0.963460i | \(-0.586314\pi\) | ||||
−0.267853 | + | 0.963460i | \(0.586314\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.0926 | 0.458918 | ||||||||
\(944\) | 40.1338 | 1.30624 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.492631 | 0.0160168 | ||||||||
\(947\) | −7.61673 | −0.247510 | −0.123755 | − | 0.992313i | \(-0.539494\pi\) | ||||
−0.123755 | + | 0.992313i | \(0.539494\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.6459 | 0.735118 | ||||||||
\(950\) | 18.3187 | 0.594337 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −13.8803 | −0.449862 | ||||||||
\(953\) | 36.1956 | 1.17249 | 0.586246 | − | 0.810133i | \(-0.300605\pi\) | ||||
0.586246 | + | 0.810133i | \(0.300605\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.7544 | 0.736316 | ||||||||
\(956\) | 4.71645 | 0.152541 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −29.7579 | −0.961433 | ||||||||
\(959\) | 12.4508 | 0.402059 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.9355 | −0.481791 | ||||||||
\(962\) | −5.32937 | −0.171826 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.72666 | −0.281067 | ||||||||
\(965\) | −7.15371 | −0.230286 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.3745 | −0.397936 | −0.198968 | − | 0.980006i | \(-0.563759\pi\) | ||||
−0.198968 | + | 0.980006i | \(0.563759\pi\) | |||||||
\(968\) | −2.25183 | −0.0723765 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 63.8664 | 2.05063 | ||||||||
\(971\) | −46.6524 | −1.49715 | −0.748574 | − | 0.663052i | \(-0.769261\pi\) | ||||
−0.748574 | + | 0.663052i | \(0.769261\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.4031 | −0.525860 | ||||||||
\(974\) | 9.00332 | 0.288485 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.84378 | −0.155046 | ||||||||
\(977\) | −54.8844 | −1.75591 | −0.877953 | − | 0.478746i | \(-0.841091\pi\) | ||||
−0.877953 | + | 0.478746i | \(0.841091\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.4360 | 0.493336 | ||||||||
\(980\) | −13.3348 | −0.425966 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −29.3415 | −0.936324 | ||||||||
\(983\) | −37.6301 | −1.20021 | −0.600107 | − | 0.799920i | \(-0.704875\pi\) | ||||
−0.600107 | + | 0.799920i | \(0.704875\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −101.058 | −3.21997 | ||||||||
\(986\) | 45.1095 | 1.43658 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.17346 | 0.0691471 | ||||||||
\(989\) | −0.685109 | −0.0217852 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.0536 | −1.71707 | −0.858535 | − | 0.512755i | \(-0.828625\pi\) | ||||
−0.858535 | + | 0.512755i | \(0.828625\pi\) | |||||||
\(992\) | 13.2820 | 0.421704 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 13.1866 | 0.418253 | ||||||||
\(995\) | −14.0699 | −0.446047 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.87216 | 0.312655 | 0.156327 | − | 0.987705i | \(-0.450035\pi\) | ||||
0.156327 | + | 0.987705i | \(0.450035\pi\) | |||||||
\(998\) | −17.1286 | −0.542197 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6039.2.a.j.1.10 | 14 | ||
3.2 | odd | 2 | 2013.2.a.h.1.5 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.h.1.5 | ✓ | 14 | 3.2 | odd | 2 | ||
6039.2.a.j.1.10 | 14 | 1.1 | even | 1 | trivial |