Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.57500224.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} - 7x^{4} + 12x^{3} + 11x^{2} - 18x + 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.12938\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.129383 | −0.0746994 | −0.0373497 | − | 0.999302i | \(-0.511892\pi\) | ||||
−0.0373497 | + | 0.999302i | \(0.511892\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.42012 | −0.635097 | −0.317548 | − | 0.948242i | \(-0.602860\pi\) | ||||
−0.317548 | + | 0.948242i | \(0.602860\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.10098 | −1.92799 | −0.963994 | − | 0.265924i | \(-0.914323\pi\) | ||||
−0.963994 | + | 0.265924i | \(0.914323\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98326 | −0.994420 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.03336 | −1.95070 | −0.975352 | − | 0.220657i | \(-0.929180\pi\) | ||||
−0.975352 | + | 0.220657i | \(0.929180\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.183739 | 0.0474413 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.23187 | −0.783843 | −0.391922 | − | 0.919999i | \(-0.628190\pi\) | ||||
−0.391922 | + | 0.919999i | \(0.628190\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.659980 | 0.144019 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.34958 | 1.32398 | 0.661990 | − | 0.749513i | \(-0.269712\pi\) | ||||
0.661990 | + | 0.749513i | \(0.269712\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.98326 | −0.596652 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.774133 | 0.148982 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.43101 | 0.451427 | 0.225714 | − | 0.974194i | \(-0.427529\pi\) | ||||
0.225714 | + | 0.974194i | \(0.427529\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.51543 | −1.52942 | −0.764708 | − | 0.644377i | \(-0.777117\pi\) | ||||
−0.764708 | + | 0.644377i | \(0.777117\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.129383 | 0.0225227 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.24400 | 1.22446 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.07874 | −1.49254 | −0.746268 | − | 0.665646i | \(-0.768156\pi\) | ||||
−0.746268 | + | 0.665646i | \(0.768156\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.909998 | 0.145716 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.74376 | −0.272329 | −0.136164 | − | 0.990686i | \(-0.543478\pi\) | ||||
−0.136164 | + | 0.990686i | \(0.543478\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.02847 | −0.309339 | −0.154669 | − | 0.987966i | \(-0.549431\pi\) | ||||
−0.154669 | + | 0.987966i | \(0.549431\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.23659 | 0.631553 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.67729 | 0.828118 | 0.414059 | − | 0.910250i | \(-0.364111\pi\) | ||||
0.414059 | + | 0.910250i | \(0.364111\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 19.0200 | 2.71714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.418149 | 0.0585526 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.28923 | −0.863892 | −0.431946 | − | 0.901900i | \(-0.642173\pi\) | ||||
−0.431946 | + | 0.901900i | \(0.642173\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.42012 | 0.191489 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.129383 | −0.0171372 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.86170 | 0.242372 | 0.121186 | − | 0.992630i | \(-0.461330\pi\) | ||||
0.121186 | + | 0.992630i | \(0.461330\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.98792 | 0.638638 | 0.319319 | − | 0.947647i | \(-0.396546\pi\) | ||||
0.319319 | + | 0.947647i | \(0.396546\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.2175 | 1.91723 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.98821 | 1.23889 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.01821 | −0.490903 | −0.245451 | − | 0.969409i | \(-0.578936\pi\) | ||||
−0.245451 | + | 0.969409i | \(0.578936\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.821529 | −0.0989005 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.62358 | −0.548718 | −0.274359 | − | 0.961627i | \(-0.588466\pi\) | ||||
−0.274359 | + | 0.961627i | \(0.588466\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.9755 | −1.63571 | −0.817854 | − | 0.575425i | \(-0.804837\pi\) | ||||
−0.817854 | + | 0.575425i | \(0.804837\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.385983 | 0.0445695 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.10098 | 0.581310 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.19839 | 0.809882 | 0.404941 | − | 0.914343i | \(-0.367292\pi\) | ||||
0.404941 | + | 0.914343i | \(0.367292\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.84962 | 0.983291 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.72806 | 1.06779 | 0.533897 | − | 0.845550i | \(-0.320727\pi\) | ||||
0.533897 | + | 0.845550i | \(0.320727\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.58964 | 0.497816 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.314532 | −0.0337213 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.1572 | 1.60666 | 0.803328 | − | 0.595537i | \(-0.203061\pi\) | ||||
0.803328 | + | 0.595537i | \(0.203061\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 35.8770 | 3.76093 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.10175 | 0.114246 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.42012 | −0.145701 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.23850 | −0.633424 | −0.316712 | − | 0.948522i | \(-0.602579\pi\) | ||||
−0.316712 | + | 0.948522i | \(0.602579\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.98326 | 0.299829 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.1093 | −1.10541 | −0.552706 | − | 0.833376i | \(-0.686405\pi\) | ||||
−0.552706 | + | 0.833376i | \(0.686405\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.0393809 | −0.00388031 | −0.00194016 | − | 0.999998i | \(-0.500618\pi\) | ||||
−0.00194016 | + | 0.999998i | \(0.500618\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.937251 | −0.0914663 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.9697 | 1.35050 | 0.675251 | − | 0.737588i | \(-0.264035\pi\) | ||||
0.675251 | + | 0.737588i | \(0.264035\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.4042 | −1.28389 | −0.641944 | − | 0.766752i | \(-0.721872\pi\) | ||||
−0.641944 | + | 0.766752i | \(0.721872\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.17464 | 0.111491 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.60293 | −0.338935 | −0.169468 | − | 0.985536i | \(-0.554205\pi\) | ||||
−0.169468 | + | 0.985536i | \(0.554205\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.01717 | −0.840855 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 20.9823 | 1.93982 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.4857 | 1.51124 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.225612 | 0.0203428 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3372 | 1.01403 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.8979 | −1.41071 | −0.705355 | − | 0.708854i | \(-0.749213\pi\) | ||||
−0.705355 | + | 0.708854i | \(0.749213\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.262450 | 0.0231074 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.1817 | 1.06432 | 0.532159 | − | 0.846645i | \(-0.321381\pi\) | ||||
0.532159 | + | 0.846645i | \(0.321381\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.10098 | −0.442311 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.09936 | −0.0946179 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.1220 | −1.20652 | −0.603261 | − | 0.797544i | \(-0.706132\pi\) | ||||
−0.603261 | + | 0.797544i | \(0.706132\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.86909 | −0.667447 | −0.333724 | − | 0.942671i | \(-0.608305\pi\) | ||||
−0.333724 | + | 0.942671i | \(0.608305\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.734546 | −0.0618599 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.03336 | 0.588159 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.45233 | −0.286700 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.46086 | −0.202968 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.6482 | −1.52772 | −0.763860 | − | 0.645382i | \(-0.776698\pi\) | ||||
−0.763860 | + | 0.645382i | \(0.776698\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.2749 | −1.81270 | −0.906352 | − | 0.422524i | \(-0.861144\pi\) | ||||
−0.906352 | + | 0.422524i | \(0.861144\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.64150 | 0.779469 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.0929 | 0.971328 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.14571 | 0.0914379 | 0.0457189 | − | 0.998954i | \(-0.485442\pi\) | ||||
0.0457189 | + | 0.998954i | \(0.485442\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.813720 | 0.0645322 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −32.3891 | −2.55262 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.17176 | 0.248432 | 0.124216 | − | 0.992255i | \(-0.460358\pi\) | ||||
0.124216 | + | 0.992255i | \(0.460358\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.183739 | −0.0143041 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.7261 | −1.06215 | −0.531077 | − | 0.847323i | \(-0.678213\pi\) | ||||
−0.531077 | + | 0.847323i | \(0.678213\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 36.4682 | 2.80524 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.98326 | −0.228136 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.4861 | −0.797243 | −0.398622 | − | 0.917116i | \(-0.630511\pi\) | ||||
−0.398622 | + | 0.917116i | \(0.630511\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.2175 | 1.15034 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.240872 | −0.0181051 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.9699 | 1.19365 | 0.596824 | − | 0.802372i | \(-0.296429\pi\) | ||||
0.596824 | + | 0.802372i | \(0.296429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.61072 | 0.342712 | 0.171356 | − | 0.985209i | \(-0.445185\pi\) | ||||
0.171356 | + | 0.985209i | \(0.445185\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.645353 | −0.0477059 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.8929 | 0.947905 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.23187 | 0.236338 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.94883 | −0.287235 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.4763 | 0.758039 | 0.379019 | − | 0.925389i | \(-0.376261\pi\) | ||||
0.379019 | + | 0.925389i | \(0.376261\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.5481 | 1.47908 | 0.739541 | − | 0.673112i | \(-0.235043\pi\) | ||||
0.739541 | + | 0.673112i | \(0.235043\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.29231 | −0.0925439 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.1568 | 1.22237 | 0.611184 | − | 0.791488i | \(-0.290693\pi\) | ||||
0.611184 | + | 0.791488i | \(0.290693\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.84693 | −0.698030 | −0.349015 | − | 0.937117i | \(-0.613484\pi\) | ||||
−0.349015 | + | 0.937117i | \(0.613484\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.519889 | 0.0366701 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.4005 | −0.870346 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.47634 | 0.172955 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.9425 | −1.31659 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.34597 | 0.230346 | 0.115173 | − | 0.993345i | \(-0.463258\pi\) | ||||
0.115173 | + | 0.993345i | \(0.463258\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.598213 | 0.0409889 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.88067 | 0.196460 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 43.4370 | 2.94870 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.80819 | 0.122186 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.7309 | 1.52905 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.61466 | −0.309021 | −0.154510 | − | 0.987991i | \(-0.549380\pi\) | ||||
−0.154510 | + | 0.987991i | \(0.549380\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.89984 | 0.593323 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.5399 | −1.69514 | −0.847570 | − | 0.530684i | \(-0.821935\pi\) | ||||
−0.847570 | + | 0.530684i | \(0.821935\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.1376 | −0.669913 | −0.334956 | − | 0.942234i | \(-0.608722\pi\) | ||||
−0.334956 | + | 0.942234i | \(0.608722\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.659980 | −0.0434235 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.5488 | −1.08415 | −0.542074 | − | 0.840331i | \(-0.682361\pi\) | ||||
−0.542074 | + | 0.840331i | \(0.682361\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.06244 | −0.525935 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.931350 | −0.0604977 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.2743 | −1.11738 | −0.558692 | − | 0.829375i | \(-0.688697\pi\) | ||||
−0.558692 | + | 0.829375i | \(0.688697\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.20538 | −0.528555 | −0.264277 | − | 0.964447i | \(-0.585133\pi\) | ||||
−0.264277 | + | 0.964447i | \(0.585133\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.46739 | −0.222433 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −27.0106 | −1.72564 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.03336 | −0.447522 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.25865 | −0.0797635 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.1629 | −0.893956 | −0.446978 | − | 0.894545i | \(-0.647500\pi\) | ||||
−0.446978 | + | 0.894545i | \(0.647500\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.34958 | −0.399195 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.593822 | −0.0371866 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.16251 | 0.259650 | 0.129825 | − | 0.991537i | \(-0.458558\pi\) | ||||
0.129825 | + | 0.991537i | \(0.458558\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 46.3104 | 2.87759 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.25234 | −0.448908 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.0445 | 1.29766 | 0.648829 | − | 0.760934i | \(-0.275259\pi\) | ||||
0.648829 | + | 0.760934i | \(0.275259\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.93146 | 0.548655 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.96108 | −0.120016 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.1828 | 0.986684 | 0.493342 | − | 0.869835i | \(-0.335775\pi\) | ||||
0.493342 | + | 0.869835i | \(0.335775\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.13639 | −0.494250 | −0.247125 | − | 0.968984i | \(-0.579486\pi\) | ||||
−0.247125 | + | 0.968984i | \(0.579486\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.64188 | −0.280939 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.98326 | 0.179897 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.8547 | 1.25304 | 0.626519 | − | 0.779406i | \(-0.284479\pi\) | ||||
0.626519 | + | 0.779406i | \(0.284479\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 25.4037 | 1.52088 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.5480 | −0.808207 | −0.404104 | − | 0.914713i | \(-0.632417\pi\) | ||||
−0.404104 | + | 0.914713i | \(0.632417\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.4618 | 0.681336 | 0.340668 | − | 0.940184i | \(-0.389347\pi\) | ||||
0.340668 | + | 0.940184i | \(0.389347\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.183739 | 0.0108838 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.89485 | 0.525047 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.55502 | −0.385590 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.807157 | 0.0473164 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.53367 | −0.381701 | −0.190850 | − | 0.981619i | \(-0.561125\pi\) | ||||
−0.190850 | + | 0.981619i | \(0.561125\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.64383 | −0.153930 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.774133 | −0.0449197 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −44.6589 | −2.58269 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.3472 | 0.596402 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.43735 | 0.0825736 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.08345 | −0.405597 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.6945 | −0.838659 | −0.419329 | − | 0.907834i | \(-0.637735\pi\) | ||||
−0.419329 | + | 0.907834i | \(0.637735\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.00509522 | 0.000289857 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.48959 | −0.197877 | −0.0989384 | − | 0.995094i | \(-0.531545\pi\) | ||||
−0.0989384 | + | 0.995094i | \(0.531545\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.6367 | −1.90126 | −0.950630 | − | 0.310327i | \(-0.899561\pi\) | ||||
−0.950630 | + | 0.310327i | \(0.899561\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −21.6107 | −1.21763 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.5336 | 1.09712 | 0.548559 | − | 0.836112i | \(-0.315177\pi\) | ||||
0.548559 | + | 0.836112i | \(0.315177\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.43101 | −0.136110 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.80744 | −0.100882 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.23187 | −0.179826 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.9823 | 1.16389 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.73427 | 0.0959056 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −28.9597 | −1.59660 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.76119 | 0.426594 | 0.213297 | − | 0.976987i | \(-0.431580\pi\) | ||||
0.213297 | + | 0.976987i | \(0.431580\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 27.0842 | 1.48421 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.70634 | 0.311771 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.11984 | −0.169949 | −0.0849743 | − | 0.996383i | \(-0.527081\pi\) | ||||
−0.0849743 | + | 0.996383i | \(0.527081\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.466158 | 0.0253182 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.51543 | 0.461136 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −61.3135 | −3.31062 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.16667 | 0.0628114 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.5881 | 0.675764 | 0.337882 | − | 0.941188i | \(-0.390290\pi\) | ||||
0.337882 | + | 0.941188i | \(0.390290\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.822765 | −0.0440416 | −0.0220208 | − | 0.999758i | \(-0.507010\pi\) | ||||
−0.0220208 | + | 0.999758i | \(0.507010\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.44475 | −0.290619 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.7990 | −1.26670 | −0.633348 | − | 0.773867i | \(-0.718320\pi\) | ||||
−0.633348 | + | 0.773867i | \(0.718320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.56604 | 0.348489 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.13297 | −0.112889 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.93003 | −0.524087 | −0.262043 | − | 0.965056i | \(-0.584396\pi\) | ||||
−0.262043 | + | 0.965056i | \(0.584396\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.129383 | −0.00679085 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.8469 | 1.03883 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.2495 | 0.743819 | 0.371909 | − | 0.928269i | \(-0.378703\pi\) | ||||
0.371909 | + | 0.928269i | \(0.378703\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.20207 | 0.270809 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 32.0812 | 1.66557 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.8427 | −0.820303 | −0.410152 | − | 0.912017i | \(-0.634524\pi\) | ||||
−0.410152 | + | 0.912017i | \(0.634524\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.46684 | −0.0757473 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.0982 | −0.880601 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.8261 | 0.658832 | 0.329416 | − | 0.944185i | \(-0.393148\pi\) | ||||
0.329416 | + | 0.944185i | \(0.393148\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.05692 | 0.105379 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.51579 | −0.0774530 | −0.0387265 | − | 0.999250i | \(-0.512330\pi\) | ||||
−0.0387265 | + | 0.999250i | \(0.512330\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.24400 | −0.369188 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.05146 | 0.307613 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.47555 | 0.0748132 | 0.0374066 | − | 0.999300i | \(-0.488090\pi\) | ||||
0.0374066 | + | 0.999300i | \(0.488090\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.5210 | −1.03779 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.57610 | −0.0795038 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.2226 | −0.514354 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.7378 | 0.789858 | 0.394929 | − | 0.918712i | \(-0.370769\pi\) | ||||
0.394929 | + | 0.918712i | \(0.370769\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.659980 | 0.0330403 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 39.1154 | 1.95333 | 0.976665 | − | 0.214766i | \(-0.0688990\pi\) | ||||
0.976665 | + | 0.214766i | \(0.0688990\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 59.8921 | 2.98344 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.5675 | −0.624485 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.07874 | 0.450017 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.9009 | 1.62684 | 0.813422 | − | 0.581674i | \(-0.197602\pi\) | ||||
0.813422 | + | 0.581674i | \(0.197602\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.82715 | 0.0901264 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.49647 | −0.467291 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.8150 | −0.678152 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.01813 | 0.0498579 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.5406 | 0.905768 | 0.452884 | − | 0.891570i | \(-0.350395\pi\) | ||||
0.452884 | + | 0.891570i | \(0.350395\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.49071 | 0.316338 | 0.158169 | − | 0.987412i | \(-0.449441\pi\) | ||||
0.158169 | + | 0.987412i | \(0.449441\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.9368 | −0.823497 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.64150 | 0.467682 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25.4433 | −1.23129 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.909998 | −0.0439351 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.5380 | 1.51913 | 0.759566 | − | 0.650431i | \(-0.225412\pi\) | ||||
0.759566 | + | 0.650431i | \(0.225412\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.533263 | 0.0256270 | 0.0128135 | − | 0.999918i | \(-0.495921\pi\) | ||||
0.0128135 | + | 0.999918i | \(0.495921\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.446673 | 0.0214163 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.34958 | 0.303742 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.2529 | −1.06207 | −0.531037 | − | 0.847349i | \(-0.678198\pi\) | ||||
−0.531037 | + | 0.847349i | \(0.678198\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −56.7415 | −2.70198 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.1549 | −1.00510 | −0.502550 | − | 0.864548i | \(-0.667605\pi\) | ||||
−0.502550 | + | 0.864548i | \(0.667605\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.5250 | −1.02038 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.41276 | 0.114120 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.9887 | −0.943326 | −0.471663 | − | 0.881779i | \(-0.656346\pi\) | ||||
−0.471663 | + | 0.881779i | \(0.656346\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.74376 | 0.0821102 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.88199 | 0.135408 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −50.9496 | −2.38856 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.0660 | −0.891869 | −0.445934 | − | 0.895066i | \(-0.647129\pi\) | ||||
−0.445934 | + | 0.895066i | \(0.647129\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.50190 | −0.116778 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.00040 | 0.326041 | 0.163021 | − | 0.986623i | \(-0.447876\pi\) | ||||
0.163021 | + | 0.986623i | \(0.447876\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.8340 | −1.01471 | −0.507356 | − | 0.861736i | \(-0.669377\pi\) | ||||
−0.507356 | + | 0.861736i | \(0.669377\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.56462 | −0.0725575 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.9124 | 1.56928 | 0.784640 | − | 0.619952i | \(-0.212848\pi\) | ||||
0.784640 | + | 0.619952i | \(0.212848\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.4968 | 0.946455 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.148236 | −0.00683035 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.02847 | 0.0932692 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.98326 | −0.136881 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.7624 | 0.859071 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.4815 | −1.02720 | −0.513602 | − | 0.858029i | \(-0.671689\pi\) | ||||
−0.513602 | + | 0.858029i | \(0.671689\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 63.8541 | 2.91149 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.19060 | 0.190679 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.85942 | 0.402286 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.01593 | −0.0913506 | −0.0456753 | − | 0.998956i | \(-0.514544\pi\) | ||||
−0.0456753 | + | 0.998956i | \(0.514544\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.410373 | −0.0185577 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.6022 | −0.613860 | −0.306930 | − | 0.951732i | \(-0.599302\pi\) | ||||
−0.306930 | + | 0.951732i | \(0.599302\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.85671 | −0.353848 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.23659 | −0.190420 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23.5848 | 1.05792 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.572450 | −0.0256264 | −0.0128132 | − | 0.999918i | \(-0.504079\pi\) | ||||
−0.0128132 | + | 0.999918i | \(0.504079\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.77592 | 0.0793423 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −43.9411 | −1.95924 | −0.979619 | − | 0.200865i | \(-0.935625\pi\) | ||||
−0.979619 | + | 0.200865i | \(0.935625\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.7765 | 0.702044 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.71836 | −0.209550 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.5696 | 0.601463 | 0.300731 | − | 0.953709i | \(-0.402769\pi\) | ||||
0.300731 | + | 0.953709i | \(0.402769\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 71.2887 | 3.15363 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.774133 | 0.0341788 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.0559255 | 0.00246437 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.67729 | −0.249687 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.35672 | 0.0595535 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.64074 | 0.159504 | 0.0797519 | − | 0.996815i | \(-0.474587\pi\) | ||||
0.0797519 | + | 0.996815i | \(0.474587\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.5655 | −0.593177 | −0.296588 | − | 0.955005i | \(-0.595849\pi\) | ||||
−0.296588 | + | 0.955005i | \(0.595849\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.96889 | −0.0859295 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 27.5208 | 1.19882 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.3172 | 0.752923 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.55393 | −0.241020 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.2645 | 0.531233 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.8387 | −0.857700 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.06624 | −0.0891647 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19.0200 | −0.819248 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.76498 | 0.419829 | 0.209915 | − | 0.977720i | \(-0.432681\pi\) | ||||
0.209915 | + | 0.977720i | \(0.432681\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.596549 | −0.0256004 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.0355 | 0.815393 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.0294 | 0.685367 | 0.342683 | − | 0.939451i | \(-0.388664\pi\) | ||||
0.342683 | + | 0.939451i | \(0.388664\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.8803 | −0.635075 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.43101 | 0.103565 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −36.7188 | −1.56144 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.66812 | −0.0708079 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 40.9882 | 1.73673 | 0.868363 | − | 0.495929i | \(-0.165173\pi\) | ||||
0.868363 | + | 0.495929i | \(0.165173\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.2670 | 0.603428 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.418149 | −0.0176543 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.8857 | −1.04881 | −0.524403 | − | 0.851470i | \(-0.675711\pi\) | ||||
−0.524403 | + | 0.851470i | \(0.675711\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.11659 | 0.215257 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −45.1417 | −1.89577 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.3845 | −1.27378 | −0.636892 | − | 0.770953i | \(-0.719780\pi\) | ||||
−0.636892 | + | 0.770953i | \(0.719780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 46.6318 | 1.95148 | 0.975741 | − | 0.218929i | \(-0.0702564\pi\) | ||||
0.975741 | + | 0.218929i | \(0.0702564\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.35546 | −0.0566250 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.9425 | −0.789955 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.07057 | −0.294352 | −0.147176 | − | 0.989110i | \(-0.547018\pi\) | ||||
−0.147176 | + | 0.989110i | \(0.547018\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.65857 | −0.110486 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −49.6226 | −2.05869 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.28923 | 0.260473 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −29.7974 | −1.23197 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.7052 | 1.10224 | 0.551120 | − | 0.834426i | \(-0.314201\pi\) | ||||
0.551120 | + | 0.834426i | \(0.314201\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.51543 | −0.350872 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.21979 | −0.0913102 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.1728 | 0.951593 | 0.475797 | − | 0.879555i | \(-0.342160\pi\) | ||||
0.475797 | + | 0.879555i | \(0.342160\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.4116 | −0.959784 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.27403 | 0.0521424 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.95574 | 0.406781 | 0.203390 | − | 0.979098i | \(-0.434804\pi\) | ||||
0.203390 | + | 0.979098i | \(0.434804\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.3446 | 0.421967 | 0.210983 | − | 0.977490i | \(-0.432333\pi\) | ||||
0.210983 | + | 0.977490i | \(0.432333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.9874 | 0.488164 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.42012 | −0.0577361 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.8505 | −0.927473 | −0.463736 | − | 0.885973i | \(-0.653492\pi\) | ||||
−0.463736 | + | 0.885973i | \(0.653492\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.60442 | 0.0650143 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −39.9304 | −1.61541 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.4830 | 1.15042 | 0.575208 | − | 0.818007i | \(-0.304921\pi\) | ||||
0.575208 | + | 0.818007i | \(0.304921\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.320397 | −0.0129196 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −45.0965 | −1.81552 | −0.907759 | − | 0.419493i | \(-0.862208\pi\) | ||||
−0.907759 | + | 0.419493i | \(0.862208\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.5698 | −0.465030 | −0.232515 | − | 0.972593i | \(-0.574696\pi\) | ||||
−0.232515 | + | 0.972593i | \(0.574696\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.91542 | 0.197249 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −77.3163 | −3.09761 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.18386 | −0.0473544 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.129383 | 0.00516706 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.3413 | 1.16991 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.8995 | 1.26990 | 0.634950 | − | 0.772554i | \(-0.281021\pi\) | ||||
0.634950 | + | 0.772554i | \(0.281021\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.432912 | −0.0172067 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.5769 | 0.895938 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −133.774 | −5.30033 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.7933 | 0.545656 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.7177 | −1.37127 | −0.685633 | − | 0.727947i | \(-0.740474\pi\) | ||||
−0.685633 | + | 0.727947i | \(0.740474\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −47.7147 | −1.88168 | −0.940842 | − | 0.338845i | \(-0.889964\pi\) | ||||
−0.940842 | + | 0.338845i | \(0.889964\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.372710 | −0.0146754 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.02131 | −0.118780 | −0.0593900 | − | 0.998235i | \(-0.518916\pi\) | ||||
−0.0593900 | + | 0.998235i | \(0.518916\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.86170 | −0.0730780 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.62001 | −0.220266 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.70288 | −0.223171 | −0.111585 | − | 0.993755i | \(-0.535593\pi\) | ||||
−0.111585 | + | 0.993755i | \(0.535593\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.2994 | −0.675945 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 41.6926 | 1.62658 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.3068 | 0.596269 | 0.298135 | − | 0.954524i | \(-0.403636\pi\) | ||||
0.298135 | + | 0.954524i | \(0.403636\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.4937 | −1.06938 | −0.534691 | − | 0.845048i | \(-0.679572\pi\) | ||||
−0.534691 | + | 0.845048i | \(0.679572\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.94099 | −0.114219 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.24400 | 0.280910 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.4359 | 0.597681 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.597059 | 0.0230836 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.98792 | −0.192557 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.3829 | −0.747156 | −0.373578 | − | 0.927599i | \(-0.621869\pi\) | ||||
−0.373578 | + | 0.927599i | \(0.621869\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.30944 | −0.0888903 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.9454 | −1.38150 | −0.690748 | − | 0.723096i | \(-0.742719\pi\) | ||||
−0.690748 | + | 0.723096i | \(0.742719\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.8225 | 1.22123 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.30443 | 0.126626 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.4639 | 0.706500 | 0.353250 | − | 0.935529i | \(-0.385076\pi\) | ||||
0.353250 | + | 0.935529i | \(0.385076\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.0549 | 0.766259 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.31164 | 0.0500421 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 44.2344 | 1.68520 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.1021 | 0.460387 | 0.230194 | − | 0.973145i | \(-0.426064\pi\) | ||||
0.230194 | + | 0.973145i | \(0.426064\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −15.2175 | −0.578066 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.1750 | 0.423894 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.63559 | 0.213463 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.14114 | 0.0809852 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.5740 | 0.625992 | 0.312996 | − | 0.949754i | \(-0.398667\pi\) | ||||
0.312996 | + | 0.949754i | \(0.398667\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.07874 | −0.342411 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.04314 | 0.0392870 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 56.6681 | 2.13122 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.7084 | −0.627497 | −0.313749 | − | 0.949506i | \(-0.601585\pi\) | ||||
−0.313749 | + | 0.949506i | \(0.601585\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.4747 | −0.805363 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −54.0694 | −2.02492 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.98821 | −0.373538 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.23501 | 0.0834679 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.86279 | −0.181351 | −0.0906756 | − | 0.995880i | \(-0.528903\pi\) | ||||
−0.0906756 | + | 0.995880i | \(0.528903\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.200881 | 0.00748119 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.06164 | 0.0394827 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.25234 | −0.269345 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.7576 | 1.02947 | 0.514736 | − | 0.857349i | \(-0.327890\pi\) | ||||
0.514736 | + | 0.857349i | \(0.327890\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.1002 | −0.966676 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.55575 | 0.242473 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.0117 | −0.517532 | −0.258766 | − | 0.965940i | \(-0.583316\pi\) | ||||
−0.258766 | + | 0.965940i | \(0.583316\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.49472 | 0.128905 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.01821 | 0.148013 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.27744 | 0.157348 | 0.0786740 | − | 0.996900i | \(-0.474931\pi\) | ||||
0.0786740 | + | 0.996900i | \(0.474931\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.909998 | 0.0334296 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.2413 | 0.375717 | 0.187858 | − | 0.982196i | \(-0.439845\pi\) | ||||
0.187858 | + | 0.982196i | \(0.439845\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.4827 | 0.970250 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −29.0213 | −1.06183 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −71.2591 | −2.60375 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.2639 | 1.39627 | 0.698134 | − | 0.715967i | \(-0.254014\pi\) | ||||
0.698134 | + | 0.715967i | \(0.254014\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.83244 | 0.0667779 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 31.6330 | 1.15124 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.3797 | −1.24955 | −0.624776 | − | 0.780804i | \(-0.714810\pi\) | ||||
−0.624776 | + | 0.780804i | \(0.714810\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.821529 | 0.0298196 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.3794 | −0.992501 | −0.496250 | − | 0.868179i | \(-0.665290\pi\) | ||||
−0.496250 | + | 0.868179i | \(0.665290\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 68.3744 | 2.47532 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.6921 | −0.495039 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.0940 | −0.472796 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.1105 | 0.580959 | 0.290479 | − | 0.956881i | \(-0.406185\pi\) | ||||
0.290479 | + | 0.956881i | \(0.406185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.538558 | −0.0193957 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.40536 | 0.0505473 | 0.0252737 | − | 0.999681i | \(-0.491954\pi\) | ||||
0.0252737 | + | 0.999681i | \(0.491954\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.4037 | 0.912529 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.99179 | −0.214954 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.74376 | −0.0624765 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.62358 | 0.165445 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.88192 | 0.0672545 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.62705 | −0.0580719 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.58377 | 0.270332 | 0.135166 | − | 0.990823i | \(-0.456843\pi\) | ||||
0.135166 | + | 0.990823i | \(0.456843\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.72280 | −0.0969343 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.3785 | 0.653463 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.0819 | −1.24579 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.15558 | −0.0409842 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.4257 | −0.829782 | −0.414891 | − | 0.909871i | \(-0.636180\pi\) | ||||
−0.414891 | + | 0.909871i | \(0.636180\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.3483 | −0.649115 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −45.2178 | −1.59769 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.9755 | 0.493185 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 45.9964 | 1.62116 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.09378 | −0.0737047 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.5024 | −0.404404 | −0.202202 | − | 0.979344i | \(-0.564810\pi\) | ||||
−0.202202 | + | 0.979344i | \(0.564810\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.7550 | −1.64179 | −0.820895 | − | 0.571079i | \(-0.806525\pi\) | ||||
−0.820895 | + | 0.571079i | \(0.806525\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.05271 | 0.0369202 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.50428 | −0.157778 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.02847 | −0.0709672 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −107.030 | −3.73995 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.4924 | 0.435986 | 0.217993 | − | 0.975950i | \(-0.430049\pi\) | ||||
0.217993 | + | 0.975950i | \(0.430049\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.669106 | 0.0233236 | 0.0116618 | − | 0.999932i | \(-0.496288\pi\) | ||||
0.0116618 | + | 0.999932i | \(0.496288\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.385983 | −0.0134382 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.4167 | 0.466543 | 0.233272 | − | 0.972412i | \(-0.425057\pi\) | ||||
0.233272 | + | 0.972412i | \(0.425057\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.8478 | 0.689343 | 0.344671 | − | 0.938723i | \(-0.387990\pi\) | ||||
0.344671 | + | 0.938723i | \(0.387990\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.69825 | −0.0936012 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −61.4700 | −2.12981 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.4927 | 0.674571 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.59207 | −0.227855 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.5515 | −0.398802 | −0.199401 | − | 0.979918i | \(-0.563900\pi\) | ||||
−0.199401 | + | 0.979918i | \(0.563900\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.0902 | −0.796213 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.75289 | 0.0603726 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −51.7891 | −1.78160 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.10098 | −0.175272 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.48297 | −0.0508953 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −57.6462 | −1.97609 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.0519 | −0.618085 | −0.309043 | − | 0.951048i | \(-0.600009\pi\) | ||||
−0.309043 | + | 0.951048i | \(0.600009\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.23659 | 0.144888 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.15199 | 0.141829 | 0.0709146 | − | 0.997482i | \(-0.477408\pi\) | ||||
0.0709146 | + | 0.997482i | \(0.477408\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.08887 | 0.173630 | 0.0868149 | − | 0.996224i | \(-0.472331\pi\) | ||||
0.0868149 | + | 0.996224i | \(0.472331\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.15084 | −0.0392206 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.9500 | −0.406782 | −0.203391 | − | 0.979098i | \(-0.565196\pi\) | ||||
−0.203391 | + | 0.979098i | \(0.565196\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.8915 | 0.506327 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.848109 | 0.0288033 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.19839 | −0.244189 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.2615 | 0.957606 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.6111 | 0.629889 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −57.8307 | −1.95503 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.5552 | 1.13308 | 0.566538 | − | 0.824035i | \(-0.308282\pi\) | ||||
0.566538 | + | 0.824035i | \(0.308282\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.845346 | 0.0285128 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.5508 | −1.06297 | −0.531486 | − | 0.847067i | \(-0.678366\pi\) | ||||
−0.531486 | + | 0.847067i | \(0.678366\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 58.9397 | 1.98348 | 0.991740 | − | 0.128263i | \(-0.0409401\pi\) | ||||
0.991740 | + | 0.128263i | \(0.0409401\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.342067 | 0.0114985 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.3167 | −0.615014 | −0.307507 | − | 0.951546i | \(-0.599495\pi\) | ||||
−0.307507 | + | 0.951546i | \(0.599495\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 81.0948 | 2.71983 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.84962 | −0.296473 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.67729 | 0.189983 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.6792 | −0.758082 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.77811 | 0.192925 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.7011 | −0.690420 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.3260 | 0.677156 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.33875 | −0.0445508 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.54777 | −0.217655 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.7843 | −0.391292 | −0.195646 | − | 0.980675i | \(-0.562680\pi\) | ||||
−0.195646 | + | 0.980675i | \(0.562680\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 33.1418 | 1.09924 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.83787 | −0.226549 | −0.113274 | − | 0.993564i | \(-0.536134\pi\) | ||||
−0.113274 | + | 0.993564i | \(0.536134\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.72806 | −0.321952 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.916478 | 0.0302978 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −62.1384 | −2.05199 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.7520 | 1.47623 | 0.738116 | − | 0.674673i | \(-0.235715\pi\) | ||||
0.738116 | + | 0.674673i | \(0.235715\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.90122 | 0.0626473 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.5193 | 1.07039 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.0842 | 0.890525 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.117483 | 0.00385866 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.54839 | −0.214846 | −0.107423 | − | 0.994213i | \(-0.534260\pi\) | ||||
−0.107423 | + | 0.994213i | \(0.534260\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.0200 | 0.623354 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.451495 | 0.0147813 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.58964 | −0.150097 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.9825 | 0.554793 | 0.277396 | − | 0.960756i | \(-0.410529\pi\) | ||||
0.277396 | + | 0.960756i | \(0.410529\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.35202 | 0.142023 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.4202 | −1.44806 | −0.724029 | − | 0.689770i | \(-0.757712\pi\) | ||||
−0.724029 | + | 0.689770i | \(0.757712\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.0721 | −0.360558 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.60781 | 0.182422 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.6101 | −1.18967 | −0.594834 | − | 0.803849i | \(-0.702782\pi\) | ||||
−0.594834 | + | 0.803849i | \(0.702782\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 98.2947 | 3.19078 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.52732 | −0.0819540 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.9783 | 0.614768 | 0.307384 | − | 0.951586i | \(-0.400546\pi\) | ||||
0.307384 | + | 0.951586i | \(0.400546\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.8776 | −0.481428 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.314532 | 0.0101674 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 72.0359 | 2.32616 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.5126 | 1.33911 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −41.6753 | −1.34297 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −29.1807 | −0.939360 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.43383 | −0.142582 | −0.0712912 | − | 0.997456i | \(-0.522712\pi\) | ||||
−0.0712912 | + | 0.997456i | \(0.522712\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.418149 | 0.0134329 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 59.2517 | 1.90148 | 0.950738 | − | 0.309995i | \(-0.100327\pi\) | ||||
0.950738 | + | 0.309995i | \(0.100327\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 40.1400 | 1.28683 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.71476 | −0.0869419 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.2522 | 0.583939 | 0.291970 | − | 0.956428i | \(-0.405689\pi\) | ||||
0.291970 | + | 0.956428i | \(0.405689\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.1572 | −0.484425 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 39.9881 | 1.27672 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.0170 | 0.574654 | 0.287327 | − | 0.957833i | \(-0.407233\pi\) | ||||
0.287327 | + | 0.957833i | \(0.407233\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.3647 | −0.776323 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.74690 | 0.119265 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.8799 | −0.409558 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.6175 | −1.09966 | −0.549831 | − | 0.835276i | \(-0.685308\pi\) | ||||
−0.549831 | + | 0.835276i | \(0.685308\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.00417 | −0.0318663 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.9838 | 0.443317 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.73230 | 0.213214 | 0.106607 | − | 0.994301i | \(-0.466001\pi\) | ||||
0.106607 | + | 0.994301i | \(0.466001\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.02815 | −0.222361 |
(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 | 3344.2.a.y.1.3 | 6 | ||
4.3 | odd | 2 | 1672.2.a.h.1.4 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1672.2.a.h.1.4 | ✓ | 6 | 4.3 | odd | 2 | ||
3344.2.a.y.1.3 | 6 | 1.1 | even | 1 | trivial |