Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(64,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.h (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.2593100598870016.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{10} + 9x^{8} - 16x^{6} + 36x^{4} - 64x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 195) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 64.4 | ||
Root | \(0.721581 + 1.21627i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 585.64 |
Dual form | 585.2.h.g.64.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61036 | −1.13870 | −0.569350 | − | 0.822096i | \(-0.692805\pi\) | ||||
−0.569350 | + | 0.822096i | \(0.692805\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.593272 | 0.296636 | ||||||||
\(5\) | 1.11567 | + | 1.93785i | 0.498943 | + | 0.866635i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.86509 | 1.83883 | 0.919416 | − | 0.393285i | \(-0.128662\pi\) | ||||
0.919416 | + | 0.393285i | \(0.128662\pi\) | |||||||
\(8\) | 2.26534 | 0.800920 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.79664 | − | 3.12065i | −0.568146 | − | 0.986836i | ||||
\(11\) | 0.989386i | 0.298311i | 0.988814 | + | 0.149156i | \(0.0476555\pi\) | ||||
−0.988814 | + | 0.149156i | \(0.952344\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.822183 | + | 3.51056i | 0.228033 | + | 0.973653i | ||||
\(14\) | −7.83457 | −2.09388 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.83457 | −1.20864 | ||||||||
\(17\) | − | 3.83457i | − | 0.930020i | −0.885305 | − | 0.465010i | \(-0.846051\pi\) | ||
0.885305 | − | 0.465010i | \(-0.153949\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.88632i | − | 0.662168i | −0.943601 | − | 0.331084i | \(-0.892586\pi\) | ||
0.943601 | − | 0.331084i | \(-0.107414\pi\) | |||||||
\(20\) | 0.661896 | + | 1.14967i | 0.148004 | + | 0.257075i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 1.59327i | − | 0.339687i | ||||||
\(23\) | − | 4.00000i | − | 0.834058i | −0.908893 | − | 0.417029i | \(-0.863071\pi\) | ||
0.908893 | − | 0.417029i | \(-0.136929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.51056 | + | 4.32401i | −0.502112 | + | 0.864803i | ||||
\(26\) | −1.32401 | − | 5.65327i | −0.259661 | − | 1.10870i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.88632 | 0.545464 | ||||||||
\(29\) | 2.81346 | 0.522446 | 0.261223 | − | 0.965279i | \(-0.415874\pi\) | ||||
0.261223 | + | 0.965279i | \(0.415874\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.84387i | 1.22919i | 0.788841 | + | 0.614597i | \(0.210682\pi\) | ||||
−0.788841 | + | 0.614597i | \(0.789318\pi\) | |||||||
\(32\) | 3.25473 | 0.575361 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.17506i | 1.05901i | ||||||||
\(35\) | 5.42784 | + | 9.42784i | 0.917473 | + | 1.59360i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.334405 | 0.0549759 | 0.0274880 | − | 0.999622i | \(-0.491249\pi\) | ||||
0.0274880 | + | 0.999622i | \(0.491249\pi\) | |||||||
\(38\) | 4.64803i | 0.754010i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.52738 | + | 4.38991i | 0.399614 | + | 0.694105i | ||||
\(41\) | 5.85448i | 0.914316i | 0.889385 | + | 0.457158i | \(0.151133\pi\) | ||||
−0.889385 | + | 0.457158i | \(0.848867\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.83457i | − | 1.19476i | −0.801958 | − | 0.597381i | \(-0.796208\pi\) | ||
0.801958 | − | 0.597381i | \(-0.203792\pi\) | |||||||
\(44\) | 0.586975i | 0.0884898i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.44146i | 0.949741i | ||||||||
\(47\) | 0.989386 | 0.144317 | 0.0721584 | − | 0.997393i | \(-0.477011\pi\) | ||||
0.0721584 | + | 0.997393i | \(0.477011\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.6691 | 2.38131 | ||||||||
\(50\) | 4.04291 | − | 6.96324i | 0.571754 | − | 0.984750i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.487778 | + | 2.08271i | 0.0676426 | + | 0.288820i | ||||
\(53\) | 7.02112i | 0.964424i | 0.876054 | + | 0.482212i | \(0.160167\pi\) | ||||
−0.876054 | + | 0.482212i | \(0.839833\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.91729 | + | 1.10383i | −0.258527 | + | 0.148840i | ||||
\(56\) | 11.0211 | 1.47276 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.53069 | −0.594909 | ||||||||
\(59\) | − | 6.76203i | − | 0.880341i | −0.897914 | − | 0.440171i | \(-0.854918\pi\) | ||
0.897914 | − | 0.440171i | \(-0.145082\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.64803 | −0.851193 | −0.425596 | − | 0.904913i | \(-0.639936\pi\) | ||||
−0.425596 | + | 0.904913i | \(0.639936\pi\) | |||||||
\(62\) | − | 11.0211i | − | 1.39968i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.42784 | 0.553480 | ||||||||
\(65\) | −5.88566 | + | 5.50990i | −0.730027 | + | 0.683419i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.34901 | 0.897824 | 0.448912 | − | 0.893576i | \(-0.351812\pi\) | ||||
0.448912 | + | 0.893576i | \(0.351812\pi\) | |||||||
\(68\) | − | 2.27494i | − | 0.275877i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.74080 | − | 15.1823i | −1.04473 | − | 1.81463i | ||||
\(71\) | 9.91475i | 1.17666i | 0.808619 | + | 0.588332i | \(0.200215\pi\) | ||||
−0.808619 | + | 0.588332i | \(0.799785\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.64437 | 0.192459 | 0.0962293 | − | 0.995359i | \(-0.469322\pi\) | ||||
0.0962293 | + | 0.995359i | \(0.469322\pi\) | |||||||
\(74\) | −0.538514 | −0.0626010 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 1.71237i | − | 0.196423i | ||||||
\(77\) | 4.81346i | 0.548544i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.8346 | −1.33149 | −0.665747 | − | 0.746178i | \(-0.731887\pi\) | ||||
−0.665747 | + | 0.746178i | \(0.731887\pi\) | |||||||
\(80\) | −5.39379 | − | 9.36870i | −0.603044 | − | 1.04745i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 9.42784i | − | 1.04113i | ||||||
\(83\) | 13.2035 | 1.44927 | 0.724635 | − | 0.689132i | \(-0.242008\pi\) | ||||
0.724635 | + | 0.689132i | \(0.242008\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.43084 | − | 4.27812i | 0.805988 | − | 0.464027i | ||||
\(86\) | 12.6165i | 1.36047i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.24130i | 0.238923i | ||||||||
\(89\) | 1.89694i | 0.201075i | 0.994933 | + | 0.100537i | \(0.0320562\pi\) | ||||
−0.994933 | + | 0.100537i | \(0.967944\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | + | 17.0792i | 0.419314 | + | 1.79039i | ||||
\(92\) | − | 2.37309i | − | 0.247411i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.59327 | −0.164333 | ||||||||
\(95\) | 5.59327 | − | 3.22019i | 0.573858 | − | 0.330384i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.5697 | −1.07319 | −0.536597 | − | 0.843839i | \(-0.680290\pi\) | ||||
−0.536597 | + | 0.843839i | \(0.680290\pi\) | |||||||
\(98\) | −26.8434 | −2.71159 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.48944 | + | 2.56531i | −0.148944 | + | 0.256531i | ||||
\(101\) | −13.6691 | −1.36013 | −0.680065 | − | 0.733152i | \(-0.738049\pi\) | ||||
−0.680065 | + | 0.733152i | \(0.738049\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.2077i | 1.39992i | 0.714181 | + | 0.699961i | \(0.246799\pi\) | ||||
−0.714181 | + | 0.699961i | \(0.753201\pi\) | |||||||
\(104\) | 1.86253 | + | 7.95262i | 0.182636 | + | 0.779819i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 11.3065i | − | 1.09819i | ||||||
\(107\) | − | 14.8557i | − | 1.43615i | −0.695964 | − | 0.718077i | \(-0.745023\pi\) | ||
0.695964 | − | 0.718077i | \(-0.254977\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 20.6343i | − | 1.97641i | −0.153137 | − | 0.988205i | \(-0.548937\pi\) | ||
0.153137 | − | 0.988205i | \(-0.451063\pi\) | |||||||
\(110\) | 3.08753 | − | 1.77757i | 0.294384 | − | 0.169484i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −23.5206 | −2.22249 | ||||||||
\(113\) | 13.4615i | 1.26635i | 0.774009 | + | 0.633175i | \(0.218249\pi\) | ||||
−0.774009 | + | 0.633175i | \(0.781751\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.75142 | − | 4.46268i | 0.722823 | − | 0.416147i | ||||
\(116\) | 1.66914 | 0.154976 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.8893i | 1.00244i | ||||||||
\(119\) | − | 18.6556i | − | 1.71015i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.0211 | 0.911010 | ||||||||
\(122\) | 10.7057 | 0.969253 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.06027i | 0.364623i | ||||||||
\(125\) | −11.1803 | − | 0.0409180i | −0.999993 | − | 0.00365982i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.66914i | − | 0.325584i | −0.986660 | − | 0.162792i | \(-0.947950\pi\) | ||
0.986660 | − | 0.162792i | \(-0.0520499\pi\) | |||||||
\(128\) | −13.6399 | −1.20561 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 9.47806 | − | 8.87294i | 0.831281 | − | 0.778208i | ||||
\(131\) | −2.37309 | −0.207338 | −0.103669 | − | 0.994612i | \(-0.533058\pi\) | ||||
−0.103669 | + | 0.994612i | \(0.533058\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 14.0422i | − | 1.21762i | ||||||
\(134\) | −11.8346 | −1.02235 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 8.68663i | − | 0.744872i | ||||||
\(137\) | 7.49885 | 0.640670 | 0.320335 | − | 0.947304i | \(-0.396205\pi\) | ||||
0.320335 | + | 0.947304i | \(0.396205\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.37309 | −0.201283 | −0.100641 | − | 0.994923i | \(-0.532089\pi\) | ||||
−0.100641 | + | 0.994923i | \(0.532089\pi\) | |||||||
\(140\) | 3.22019 | + | 5.59327i | 0.272155 | + | 0.472718i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 15.9664i | − | 1.33987i | ||||||
\(143\) | −3.47330 | + | 0.813457i | −0.290452 | + | 0.0680247i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.13889 | + | 5.45207i | 0.260671 | + | 0.452770i | ||||
\(146\) | −2.64803 | −0.219152 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.198393 | 0.0163078 | ||||||||
\(149\) | 3.87571i | 0.317510i | 0.987318 | + | 0.158755i | \(0.0507481\pi\) | ||||
−0.987318 | + | 0.158755i | \(0.949252\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.84387i | 0.556946i | 0.960444 | + | 0.278473i | \(0.0898283\pi\) | ||||
−0.960444 | + | 0.278473i | \(0.910172\pi\) | |||||||
\(152\) | − | 6.53851i | − | 0.530344i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 7.75142i | − | 0.624627i | ||||||
\(155\) | −13.2624 | + | 7.63550i | −1.06526 | + | 0.613298i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.00000i | − | 0.638470i | −0.947676 | − | 0.319235i | \(-0.896574\pi\) | ||
0.947676 | − | 0.319235i | \(-0.103426\pi\) | |||||||
\(158\) | 19.0580 | 1.51617 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.63121 | + | 6.30719i | 0.287072 | + | 0.498627i | ||||
\(161\) | − | 19.4604i | − | 1.53369i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.0580 | −1.49274 | −0.746368 | − | 0.665534i | \(-0.768204\pi\) | ||||
−0.746368 | + | 0.665534i | \(0.768204\pi\) | |||||||
\(164\) | 3.47330i | 0.271219i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −21.2624 | −1.65028 | ||||||||
\(167\) | 2.96816 | 0.229683 | 0.114841 | − | 0.993384i | \(-0.463364\pi\) | ||||
0.114841 | + | 0.993384i | \(0.463364\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6480 | + | 5.77264i | −0.896002 | + | 0.444050i | ||||
\(170\) | −11.9664 | + | 6.88933i | −0.917778 | + | 0.528387i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 4.64803i | − | 0.354409i | ||||||
\(173\) | − | 24.3172i | − | 1.84880i | −0.381424 | − | 0.924400i | \(-0.624566\pi\) | ||
0.381424 | − | 0.924400i | \(-0.375434\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.2141 | + | 21.0367i | −0.923299 | + | 1.59023i | ||||
\(176\) | − | 4.78326i | − | 0.360552i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 3.05476i | − | 0.228964i | ||||||
\(179\) | 16.4153 | 1.22694 | 0.613469 | − | 0.789719i | \(-0.289773\pi\) | ||||
0.613469 | + | 0.789719i | \(0.289773\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | −6.44146 | − | 27.5037i | −0.477472 | − | 2.03871i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 9.06138i | − | 0.668014i | ||||||
\(185\) | 0.373086 | + | 0.648029i | 0.0274298 | + | 0.0476440i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.79387 | 0.277435 | ||||||||
\(188\) | 0.586975 | 0.0428095 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.00720 | + | 5.18567i | −0.653451 | + | 0.376208i | ||||
\(191\) | −12.4826 | −0.903209 | −0.451605 | − | 0.892218i | \(-0.649148\pi\) | ||||
−0.451605 | + | 0.892218i | \(0.649148\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.62314 | −0.260799 | −0.130400 | − | 0.991462i | \(-0.541626\pi\) | ||||
−0.130400 | + | 0.991462i | \(0.541626\pi\) | |||||||
\(194\) | 17.0211 | 1.22204 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.88933 | 0.706381 | ||||||||
\(197\) | −17.2290 | −1.22752 | −0.613759 | − | 0.789493i | \(-0.710343\pi\) | ||||
−0.613759 | + | 0.789493i | \(0.710343\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.87680 | −0.700148 | −0.350074 | − | 0.936722i | \(-0.613844\pi\) | ||||
−0.350074 | + | 0.936722i | \(0.613844\pi\) | |||||||
\(200\) | −5.68728 | + | 9.79538i | −0.402151 | + | 0.692638i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 22.0123 | 1.54878 | ||||||||
\(203\) | 13.6877 | 0.960691 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.3451 | + | 6.53167i | −0.792378 | + | 0.456192i | ||||
\(206\) | − | 22.8795i | − | 1.59409i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.97490 | − | 16.9720i | −0.275610 | − | 1.17680i | ||||
\(209\) | 2.85569 | 0.197532 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.8768 | 1.50606 | 0.753031 | − | 0.657986i | \(-0.228591\pi\) | ||||
0.753031 | + | 0.657986i | \(0.228591\pi\) | |||||||
\(212\) | 4.16543i | 0.286083i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 23.9231i | 1.63535i | ||||||||
\(215\) | 15.1823 | − | 8.74080i | 1.03542 | − | 0.596118i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 33.2961i | 2.26028i | ||||||||
\(218\) | 33.2288i | 2.25054i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.13747 | + | 0.654870i | −0.0766883 | + | 0.0441514i | ||||
\(221\) | 13.4615 | − | 3.15272i | 0.905518 | − | 0.212075i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.3892 | 1.23143 | 0.615714 | − | 0.787969i | \(-0.288867\pi\) | ||||
0.615714 | + | 0.787969i | \(0.288867\pi\) | |||||||
\(224\) | 15.8346 | 1.05799 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 21.6779i | − | 1.44199i | ||||||
\(227\) | 12.0295 | 0.798428 | 0.399214 | − | 0.916858i | \(-0.369283\pi\) | ||||
0.399214 | + | 0.916858i | \(0.369283\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.17395i | 0.0775768i | 0.999247 | + | 0.0387884i | \(0.0123498\pi\) | ||||
−0.999247 | + | 0.0387884i | \(0.987650\pi\) | |||||||
\(230\) | −12.4826 | + | 7.18654i | −0.823078 | + | 0.473867i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.37345 | 0.418437 | ||||||||
\(233\) | − | 15.0211i | − | 0.984066i | −0.870577 | − | 0.492033i | \(-0.836254\pi\) | ||
0.870577 | − | 0.492033i | \(-0.163746\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.10383 | + | 1.91729i | 0.0720059 | + | 0.125070i | ||||
\(236\) | − | 4.01172i | − | 0.261141i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 30.0422i | 1.94735i | ||||||||
\(239\) | 18.4710i | 1.19479i | 0.801947 | + | 0.597395i | \(0.203797\pi\) | ||||
−0.801947 | + | 0.597395i | \(0.796203\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 10.9041i | − | 0.702397i | −0.936301 | − | 0.351199i | \(-0.885774\pi\) | ||
0.936301 | − | 0.351199i | \(-0.114226\pi\) | |||||||
\(242\) | −16.1376 | −1.03737 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.94409 | −0.252494 | ||||||||
\(245\) | 18.5973 | + | 32.3024i | 1.18814 | + | 2.06372i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.1326 | − | 2.37309i | 0.644722 | − | 0.150996i | ||||
\(248\) | 15.5037i | 0.984487i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 18.0043 | + | 0.0658929i | 1.13869 | + | 0.00416744i | ||||
\(251\) | 16.8135 | 1.06126 | 0.530628 | − | 0.847605i | \(-0.321956\pi\) | ||||
0.530628 | + | 0.847605i | \(0.321956\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.95754 | 0.248809 | ||||||||
\(254\) | 5.90866i | 0.370742i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.1095 | 0.819345 | ||||||||
\(257\) | − | 8.64803i | − | 0.539449i | −0.962938 | − | 0.269725i | \(-0.913067\pi\) | ||
0.962938 | − | 0.269725i | \(-0.0869327\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.62691 | 0.101091 | ||||||||
\(260\) | −3.49180 | + | 3.26887i | −0.216552 | + | 0.202726i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.82153 | 0.236095 | ||||||||
\(263\) | 0.813457i | 0.0501599i | 0.999685 | + | 0.0250799i | \(0.00798403\pi\) | ||||
−0.999685 | + | 0.0250799i | \(0.992016\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.6059 | + | 7.83325i | −0.835804 | + | 0.481193i | ||||
\(266\) | 22.6131i | 1.38650i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.35996 | 0.266327 | ||||||||
\(269\) | −23.2288 | −1.41628 | −0.708142 | − | 0.706070i | \(-0.750466\pi\) | ||||
−0.708142 | + | 0.706070i | \(0.750466\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.5953i | 0.886600i | 0.896373 | + | 0.443300i | \(0.146192\pi\) | ||||
−0.896373 | + | 0.443300i | \(0.853808\pi\) | |||||||
\(272\) | 18.5385i | 1.12406i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.0759 | −0.729530 | ||||||||
\(275\) | −4.27812 | − | 2.48391i | −0.257980 | − | 0.149785i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 17.6269i | − | 1.05910i | −0.848279 | − | 0.529549i | \(-0.822361\pi\) | ||
0.848279 | − | 0.529549i | \(-0.177639\pi\) | |||||||
\(278\) | 3.82153 | 0.229200 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.2959 | + | 21.3573i | 0.734823 | + | 1.27634i | ||||
\(281\) | − | 9.64835i | − | 0.575572i | −0.957695 | − | 0.287786i | \(-0.907081\pi\) | ||
0.957695 | − | 0.287786i | \(-0.0929193\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4.00000i | − | 0.237775i | −0.992908 | − | 0.118888i | \(-0.962067\pi\) | ||
0.992908 | − | 0.118888i | \(-0.0379328\pi\) | |||||||
\(284\) | 5.88214i | 0.349041i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.59327 | − | 1.30996i | 0.330737 | − | 0.0774596i | ||||
\(287\) | 28.4826i | 1.68127i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.29606 | 0.135062 | ||||||||
\(290\) | −5.05476 | − | 8.77981i | −0.296826 | − | 0.515568i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.975556 | 0.0570901 | ||||||||
\(293\) | −17.8978 | −1.04560 | −0.522802 | − | 0.852454i | \(-0.675113\pi\) | ||||
−0.522802 | + | 0.852454i | \(0.675113\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.1038 | − | 7.54420i | 0.762934 | − | 0.439240i | ||||
\(296\) | 0.757543 | 0.0440313 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 6.24130i | − | 0.361549i | ||||||
\(299\) | 14.0422 | − | 3.28873i | 0.812083 | − | 0.190192i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 38.1159i | − | 2.19697i | ||||||
\(302\) | − | 11.0211i | − | 0.634194i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 13.9541i | 0.800324i | ||||||||
\(305\) | −7.41701 | − | 12.8829i | −0.424697 | − | 0.737673i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.49145 | 0.541706 | 0.270853 | − | 0.962621i | \(-0.412694\pi\) | ||||
0.270853 | + | 0.962621i | \(0.412694\pi\) | |||||||
\(308\) | 2.85569i | 0.162718i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 21.3573 | − | 12.2959i | 1.21301 | − | 0.698362i | ||||
\(311\) | −34.5248 | −1.95772 | −0.978862 | − | 0.204523i | \(-0.934436\pi\) | ||||
−0.978862 | + | 0.204523i | \(0.934436\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 5.39420i | − | 0.304898i | −0.988311 | − | 0.152449i | \(-0.951284\pi\) | ||
0.988311 | − | 0.152449i | \(-0.0487160\pi\) | |||||||
\(314\) | 12.8829i | 0.727025i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.02112 | −0.394969 | ||||||||
\(317\) | −5.01494 | −0.281667 | −0.140833 | − | 0.990033i | \(-0.544978\pi\) | ||||
−0.140833 | + | 0.990033i | \(0.544978\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.78360i | 0.155851i | ||||||||
\(320\) | 4.94002 | + | 8.58052i | 0.276155 | + | 0.479665i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 31.3383i | 1.74641i | ||||||||
\(323\) | −11.0678 | −0.615829 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.2438 | − | 5.25832i | −0.956516 | − | 0.291679i | ||||
\(326\) | 30.6903 | 1.69978 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13.2624i | 0.732294i | ||||||||
\(329\) | 4.81346 | 0.265374 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 17.7480i | − | 0.975519i | −0.872978 | − | 0.487759i | \(-0.837814\pi\) | ||
0.872978 | − | 0.487759i | \(-0.162186\pi\) | |||||||
\(332\) | 7.83325 | 0.429906 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.77981 | −0.261540 | ||||||||
\(335\) | 8.19907 | + | 14.2413i | 0.447963 | + | 0.778085i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 18.2749i | − | 0.995500i | −0.867321 | − | 0.497750i | \(-0.834160\pi\) | ||
0.867321 | − | 0.497750i | \(-0.165840\pi\) | |||||||
\(338\) | 18.7576 | − | 9.29606i | 1.02028 | − | 0.505639i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.40851 | − | 2.53809i | 0.239085 | − | 0.137647i | ||||
\(341\) | −6.77123 | −0.366682 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 47.0413 | 2.53999 | ||||||||
\(344\) | − | 17.7480i | − | 0.956908i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 39.1595i | 2.10523i | ||||||||
\(347\) | − | 21.6269i | − | 1.16099i | −0.814263 | − | 0.580497i | \(-0.802858\pi\) | ||
0.814263 | − | 0.580497i | \(-0.197142\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12.8829i | − | 0.689606i | −0.938675 | − | 0.344803i | \(-0.887946\pi\) | ||
0.938675 | − | 0.344803i | \(-0.112054\pi\) | |||||||
\(350\) | 19.6691 | − | 33.8768i | 1.05136 | − | 1.81079i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.22019i | 0.171636i | ||||||||
\(353\) | 10.7876 | 0.574165 | 0.287083 | − | 0.957906i | \(-0.407315\pi\) | ||||
0.287083 | + | 0.957906i | \(0.407315\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.2133 | + | 11.0616i | −1.01974 | + | 0.587089i | ||||
\(356\) | 1.12540i | 0.0596460i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −26.4346 | −1.39711 | ||||||||
\(359\) | 15.3183i | 0.808467i | 0.914656 | + | 0.404234i | \(0.132462\pi\) | ||||
−0.914656 | + | 0.404234i | \(0.867538\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.6691 | 0.561534 | ||||||||
\(362\) | 9.66218 | 0.507833 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.37309 | + | 10.1326i | 0.124384 | + | 0.531093i | ||||
\(365\) | 1.83457 | + | 3.18654i | 0.0960259 | + | 0.166791i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.165428i | 0.00863527i | 0.999991 | + | 0.00431764i | \(0.00137435\pi\) | ||||
−0.999991 | + | 0.00431764i | \(0.998626\pi\) | |||||||
\(368\) | 19.3383i | 1.00808i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.600805 | − | 1.04356i | −0.0312343 | − | 0.0542522i | ||||
\(371\) | 34.1584i | 1.77342i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.30974i | − | 0.0678158i | −0.999425 | − | 0.0339079i | \(-0.989205\pi\) | ||
0.999425 | − | 0.0339079i | \(-0.0107953\pi\) | |||||||
\(374\) | −6.10951 | −0.315915 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.24130 | 0.115586 | ||||||||
\(377\) | 2.31318 | + | 9.87680i | 0.119135 | + | 0.508681i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.266399i | 0.0136840i | 0.999977 | + | 0.00684201i | \(0.00217790\pi\) | ||||
−0.999977 | + | 0.00684201i | \(0.997822\pi\) | |||||||
\(380\) | 3.31833 | − | 1.91044i | 0.170227 | − | 0.0980037i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 20.1015 | 1.02848 | ||||||||
\(383\) | −9.91475 | −0.506620 | −0.253310 | − | 0.967385i | \(-0.581519\pi\) | ||||
−0.253310 | + | 0.967385i | \(0.581519\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.32778 | + | 5.37023i | −0.475388 | + | 0.273692i | ||||
\(386\) | 5.83457 | 0.296972 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.27072 | −0.318348 | ||||||||
\(389\) | −15.2288 | −0.772129 | −0.386065 | − | 0.922472i | \(-0.626166\pi\) | ||||
−0.386065 | + | 0.922472i | \(0.626166\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.3383 | −0.775691 | ||||||||
\(392\) | 37.7614 | 1.90724 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 27.7450 | 1.39777 | ||||||||
\(395\) | −13.2035 | − | 22.9337i | −0.664339 | − | 1.15392i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.3533 | −0.670184 | −0.335092 | − | 0.942185i | \(-0.608767\pi\) | ||||
−0.335092 | + | 0.942185i | \(0.608767\pi\) | |||||||
\(398\) | 15.9052 | 0.797258 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.1375 | − | 20.9048i | 0.606874 | − | 1.04524i | ||||
\(401\) | − | 33.0663i | − | 1.65125i | −0.564219 | − | 0.825625i | \(-0.690822\pi\) | ||
0.564219 | − | 0.825625i | \(-0.309178\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.0258 | + | 5.62691i | −1.19681 | + | 0.280297i | ||||
\(404\) | −8.10951 | −0.403463 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −22.0422 | −1.09394 | ||||||||
\(407\) | 0.330856i | 0.0163999i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.2967i | 0.954161i | 0.878860 | + | 0.477080i | \(0.158305\pi\) | ||||
−0.878860 | + | 0.477080i | \(0.841695\pi\) | |||||||
\(410\) | 18.2698 | − | 10.5184i | 0.902280 | − | 0.519465i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.42900i | 0.415267i | ||||||||
\(413\) | − | 32.8979i | − | 1.61880i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.7307 | + | 25.5864i | 0.723104 | + | 1.25599i | ||||
\(416\) | 2.67599 | + | 11.4259i | 0.131201 | + | 0.560202i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.59870 | −0.224930 | ||||||||
\(419\) | −16.4153 | −0.801941 | −0.400970 | − | 0.916091i | \(-0.631327\pi\) | ||||
−0.400970 | + | 0.916091i | \(0.631327\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 2.78360i | − | 0.135664i | −0.997697 | − | 0.0678321i | \(-0.978392\pi\) | ||
0.997697 | − | 0.0678321i | \(-0.0216082\pi\) | |||||||
\(422\) | −35.2296 | −1.71495 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 15.9052i | 0.772427i | ||||||||
\(425\) | 16.5807 | + | 9.62691i | 0.804284 | + | 0.466974i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −32.3433 | −1.56520 | ||||||||
\(428\) | − | 8.81346i | − | 0.426015i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −24.4490 | + | 14.0759i | −1.17903 | + | 0.678799i | ||||
\(431\) | − | 8.74080i | − | 0.421030i | −0.977591 | − | 0.210515i | \(-0.932486\pi\) | ||
0.977591 | − | 0.210515i | \(-0.0675140\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 22.6903i | − | 1.09042i | −0.838298 | − | 0.545212i | \(-0.816449\pi\) | ||
0.838298 | − | 0.545212i | \(-0.183551\pi\) | |||||||
\(434\) | − | 53.6188i | − | 2.57378i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 12.2418i | − | 0.586274i | ||||||
\(437\) | −11.5453 | −0.552286 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.62691 | −0.459468 | −0.229734 | − | 0.973254i | \(-0.573786\pi\) | ||||
−0.229734 | + | 0.973254i | \(0.573786\pi\) | |||||||
\(440\) | −4.34331 | + | 2.50055i | −0.207059 | + | 0.119209i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −21.6779 | + | 5.07703i | −1.03111 | + | 0.241490i | ||||
\(443\) | − | 28.8979i | − | 1.37298i | −0.727139 | − | 0.686491i | \(-0.759150\pi\) | ||
0.727139 | − | 0.686491i | \(-0.240850\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.67599 | + | 2.11636i | −0.174258 | + | 0.100325i | ||||
\(446\) | −29.6132 | −1.40223 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 21.5419 | 1.01776 | ||||||||
\(449\) | 11.9963i | 0.566138i | 0.959100 | + | 0.283069i | \(0.0913526\pi\) | ||||
−0.959100 | + | 0.283069i | \(0.908647\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.79234 | −0.272751 | ||||||||
\(452\) | 7.98632i | 0.375645i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −19.3719 | −0.909170 | ||||||||
\(455\) | −28.6343 | + | 26.8062i | −1.34240 | + | 1.25669i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.44919 | −0.114568 | −0.0572841 | − | 0.998358i | \(-0.518244\pi\) | ||||
−0.0572841 | + | 0.998358i | \(0.518244\pi\) | |||||||
\(458\) | − | 1.89049i | − | 0.0883366i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.59870 | − | 2.64758i | 0.214415 | − | 0.123444i | ||||
\(461\) | 15.5847i | 0.725850i | 0.931818 | + | 0.362925i | \(0.118222\pi\) | ||||
−0.931818 | + | 0.362925i | \(0.881778\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.5953 | 0.678300 | 0.339150 | − | 0.940732i | \(-0.389861\pi\) | ||||
0.339150 | + | 0.940732i | \(0.389861\pi\) | |||||||
\(464\) | −13.6019 | −0.631450 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.1895i | 1.12056i | ||||||||
\(467\) | 21.2961i | 0.985464i | 0.870181 | + | 0.492732i | \(0.164002\pi\) | ||||
−0.870181 | + | 0.492732i | \(0.835998\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 35.7536 | 1.65095 | ||||||||
\(470\) | −1.77757 | − | 3.08753i | −0.0819930 | − | 0.142417i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 15.3183i | − | 0.705083i | ||||||
\(473\) | 7.75142 | 0.356411 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.4805 | + | 7.24628i | 0.572645 | + | 0.332482i | ||||
\(476\) | − | 11.0678i | − | 0.507292i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 29.7450i | − | 1.36051i | ||||||
\(479\) | − | 15.8511i | − | 0.724254i | −0.932129 | − | 0.362127i | \(-0.882051\pi\) | ||
0.932129 | − | 0.362127i | \(-0.117949\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.274943 | + | 1.17395i | 0.0125363 | + | 0.0535275i | ||||
\(482\) | 17.5596i | 0.799819i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.94524 | 0.270238 | ||||||||
\(485\) | −11.7923 | − | 20.4826i | −0.535463 | − | 0.930067i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.03904 | −0.273655 | −0.136828 | − | 0.990595i | \(-0.543691\pi\) | ||||
−0.136828 | + | 0.990595i | \(0.543691\pi\) | |||||||
\(488\) | −15.0601 | −0.681738 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −29.9484 | − | 52.0186i | −1.35293 | − | 2.34996i | ||||
\(491\) | 4.89792 | 0.221040 | 0.110520 | − | 0.993874i | \(-0.464748\pi\) | ||||
0.110520 | + | 0.993874i | \(0.464748\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 10.7884i | − | 0.485885i | ||||||
\(494\) | −16.3172 | + | 3.82153i | −0.734144 | + | 0.171939i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 33.0872i | − | 1.48566i | ||||||
\(497\) | 48.2362i | 2.16369i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 38.0132i | − | 1.70170i | −0.525405 | − | 0.850852i | \(-0.676086\pi\) | ||
0.525405 | − | 0.850852i | \(-0.323914\pi\) | |||||||
\(500\) | −6.63293 | − | 0.0242755i | −0.296634 | − | 0.00108563i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −27.0758 | −1.20845 | ||||||||
\(503\) | − | 8.15174i | − | 0.363468i | −0.983348 | − | 0.181734i | \(-0.941829\pi\) | ||
0.983348 | − | 0.181734i | \(-0.0581710\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.2503 | − | 26.4888i | −0.678628 | − | 1.17874i | ||||
\(506\) | −6.37309 | −0.283318 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 2.17680i | − | 0.0965798i | ||||||
\(509\) | − | 19.5422i | − | 0.866193i | −0.901347 | − | 0.433097i | \(-0.857421\pi\) | ||
0.901347 | − | 0.433097i | \(-0.142579\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.00000 | 0.353899 | ||||||||
\(512\) | 6.16871 | 0.272621 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.9265i | 0.614270i | ||||||||
\(515\) | −27.5324 | + | 15.8511i | −1.21322 | + | 0.698482i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.978885i | 0.0430513i | ||||||||
\(518\) | −2.61992 | −0.115113 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −13.3331 | + | 12.4818i | −0.584693 | + | 0.547364i | ||||
\(521\) | −6.89792 | −0.302203 | −0.151102 | − | 0.988518i | \(-0.548282\pi\) | ||||
−0.151102 | + | 0.988518i | \(0.548282\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.5459i | 0.942138i | 0.882096 | + | 0.471069i | \(0.156132\pi\) | ||||
−0.882096 | + | 0.471069i | \(0.843868\pi\) | |||||||
\(524\) | −1.40788 | −0.0615037 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 1.30996i | − | 0.0571170i | ||||||
\(527\) | 26.2433 | 1.14318 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 21.9104 | − | 12.6144i | 0.951729 | − | 0.547934i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 8.33086i | − | 0.361188i | ||||||
\(533\) | −20.5525 | + | 4.81346i | −0.890227 | + | 0.208494i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.7882 | − | 16.5741i | 1.24462 | − | 0.716559i | ||||
\(536\) | 16.6480 | 0.719085 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 37.4068 | 1.61272 | ||||||||
\(539\) | 16.4922i | 0.710370i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.369126i | 0.0158700i | 0.999969 | + | 0.00793499i | \(0.00252581\pi\) | ||||
−0.999969 | + | 0.00793499i | \(0.997474\pi\) | |||||||
\(542\) | − | 23.5037i | − | 1.00957i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 12.4805i | − | 0.535097i | ||||||
\(545\) | 39.9863 | − | 23.0211i | 1.71283 | − | 0.986116i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.5459i | 0.921238i | 0.887598 | + | 0.460619i | \(0.152373\pi\) | ||||
−0.887598 | + | 0.460619i | \(0.847627\pi\) | |||||||
\(548\) | 4.44885 | 0.190046 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.88933 | + | 4.00000i | 0.293762 | + | 0.170561i | ||||
\(551\) | − | 8.12054i | − | 0.345947i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −57.5763 | −2.44839 | ||||||||
\(554\) | 28.3857i | 1.20599i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.40788 | −0.0597076 | ||||||||
\(557\) | −1.22106 | −0.0517382 | −0.0258691 | − | 0.999665i | \(-0.508235\pi\) | ||||
−0.0258691 | + | 0.999665i | \(0.508235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.5037 | − | 6.44146i | 1.16328 | − | 0.272445i | ||||
\(560\) | −26.2413 | − | 45.5796i | −1.10890 | − | 1.92609i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.5374i | 0.655404i | ||||||||
\(563\) | − | 8.48260i | − | 0.357499i | −0.983895 | − | 0.178750i | \(-0.942795\pi\) | ||
0.983895 | − | 0.178750i | \(-0.0572052\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.0864 | + | 15.0186i | −1.09746 | + | 0.631837i | ||||
\(566\) | 6.44146i | 0.270755i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 22.4603i | 0.942414i | ||||||||
\(569\) | 2.33086 | 0.0977146 | 0.0488573 | − | 0.998806i | \(-0.484442\pi\) | ||||
0.0488573 | + | 0.998806i | \(0.484442\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.8768 | −1.25031 | −0.625153 | − | 0.780503i | \(-0.714963\pi\) | ||||
−0.625153 | + | 0.780503i | \(0.714963\pi\) | |||||||
\(572\) | −2.06061 | + | 0.482601i | −0.0861584 | + | 0.0201786i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 45.8673i | − | 1.91447i | ||||||
\(575\) | 17.2961 | + | 10.0422i | 0.721295 | + | 0.418790i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.1024 | −1.50296 | −0.751482 | − | 0.659753i | \(-0.770661\pi\) | ||||
−0.751482 | + | 0.659753i | \(0.770661\pi\) | |||||||
\(578\) | −3.69749 | −0.153795 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.86222 | + | 3.23456i | 0.0773243 | + | 0.134308i | ||||
\(581\) | 64.2362 | 2.66497 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.94659 | −0.287699 | ||||||||
\(584\) | 3.72506 | 0.154144 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.8220 | 1.19063 | ||||||||
\(587\) | −8.87681 | −0.366385 | −0.183193 | − | 0.983077i | \(-0.558643\pi\) | ||||
−0.183193 | + | 0.983077i | \(0.558643\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.7536 | 0.813933 | ||||||||
\(590\) | −21.1019 | + | 12.1489i | −0.868753 | + | 0.500163i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.61671 | −0.0664462 | ||||||||
\(593\) | −26.2904 | −1.07962 | −0.539809 | − | 0.841788i | \(-0.681504\pi\) | ||||
−0.539809 | + | 0.841788i | \(0.681504\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 36.1517 | − | 20.8135i | 1.48208 | − | 0.853269i | ||||
\(596\) | 2.29935i | 0.0941849i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −22.6131 | + | 5.29606i | −0.924718 | + | 0.216572i | ||||
\(599\) | 12.4153 | 0.507276 | 0.253638 | − | 0.967299i | \(-0.418373\pi\) | ||||
0.253638 | + | 0.967299i | \(0.418373\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.02112 | −0.204816 | −0.102408 | − | 0.994743i | \(-0.532655\pi\) | ||||
−0.102408 | + | 0.994743i | \(0.532655\pi\) | |||||||
\(602\) | 61.3805i | 2.50168i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.06027i | 0.165210i | ||||||||
\(605\) | 11.1803 | + | 19.4195i | 0.454542 | + | 0.789513i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 13.8768i | − | 0.563242i | −0.959526 | − | 0.281621i | \(-0.909128\pi\) | ||
0.959526 | − | 0.281621i | \(-0.0908721\pi\) | |||||||
\(608\) | − | 9.39420i | − | 0.380985i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.9441 | + | 20.7462i | 0.483602 | + | 0.839988i | ||||
\(611\) | 0.813457 | + | 3.47330i | 0.0329089 | + | 0.140515i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.4928 | −1.39315 | −0.696575 | − | 0.717484i | \(-0.745294\pi\) | ||||
−0.696575 | + | 0.717484i | \(0.745294\pi\) | |||||||
\(614\) | −15.2847 | −0.616840 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.9041i | 0.439340i | ||||||||
\(617\) | −23.5068 | −0.946349 | −0.473174 | − | 0.880969i | \(-0.656892\pi\) | ||||
−0.473174 | + | 0.880969i | \(0.656892\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.01782i | 0.322263i | 0.986933 | + | 0.161132i | \(0.0515144\pi\) | ||||
−0.986933 | + | 0.161132i | \(0.948486\pi\) | |||||||
\(620\) | −7.86821 | + | 4.52993i | −0.315995 | + | 0.181926i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 55.5975 | 2.22926 | ||||||||
\(623\) | 9.22877i | 0.369743i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.3942 | − | 21.7114i | −0.495768 | − | 0.868455i | ||||
\(626\) | 8.68663i | 0.347187i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 4.74617i | − | 0.189393i | ||||||
\(629\) | − | 1.28230i | − | 0.0511287i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 28.1193i | − | 1.11941i | −0.828691 | − | 0.559707i | \(-0.810914\pi\) | ||
0.828691 | − | 0.559707i | \(-0.189086\pi\) | |||||||
\(632\) | −26.8094 | −1.06642 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.07587 | 0.320734 | ||||||||
\(635\) | 7.11027 | − | 4.09356i | 0.282162 | − | 0.162448i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.7051 | + | 58.5180i | 0.543016 | + | 2.31857i | ||||
\(638\) | − | 4.48260i | − | 0.177468i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −15.2176 | − | 26.4321i | −0.601530 | − | 1.04482i | ||||
\(641\) | 40.5248 | 1.60063 | 0.800317 | − | 0.599577i | \(-0.204664\pi\) | ||||
0.800317 | + | 0.599577i | \(0.204664\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.1895 | 0.953939 | 0.476970 | − | 0.878920i | \(-0.341735\pi\) | ||||
0.476970 | + | 0.878920i | \(0.341735\pi\) | |||||||
\(644\) | − | 11.5453i | − | 0.454948i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.8232 | 0.701244 | ||||||||
\(647\) | − | 26.1095i | − | 1.02647i | −0.858248 | − | 0.513235i | \(-0.828447\pi\) | ||
0.858248 | − | 0.513235i | \(-0.171553\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.69026 | 0.262616 | ||||||||
\(650\) | 27.7689 | + | 8.46781i | 1.08918 | + | 0.332135i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.3065 | −0.442799 | ||||||||
\(653\) | 24.7153i | 0.967185i | 0.875293 | + | 0.483592i | \(0.160668\pi\) | ||||
−0.875293 | + | 0.483592i | \(0.839332\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.64758 | − | 4.59870i | −0.103450 | − | 0.179686i | ||||
\(656\) | − | 28.3039i | − | 1.10508i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.75142 | −0.302182 | ||||||||
\(659\) | 33.7787 | 1.31583 | 0.657915 | − | 0.753092i | \(-0.271439\pi\) | ||||
0.657915 | + | 0.753092i | \(0.271439\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 4.96782i | − | 0.193226i | −0.995322 | − | 0.0966129i | \(-0.969199\pi\) | ||
0.995322 | − | 0.0966129i | \(-0.0308009\pi\) | |||||||
\(662\) | 28.5807i | 1.11082i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 29.9104 | 1.16075 | ||||||||
\(665\) | 27.2118 | − | 15.6665i | 1.05523 | − | 0.607521i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 11.2538i | − | 0.435750i | ||||||
\(668\) | 1.76092 | 0.0681322 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.2035 | − | 22.9337i | −0.510095 | − | 0.886005i | ||||
\(671\) | − | 6.57747i | − | 0.253920i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.33086i | 0.321131i | 0.987025 | + | 0.160565i | \(0.0513318\pi\) | ||||
−0.987025 | + | 0.160565i | \(0.948668\pi\) | |||||||
\(674\) | 29.4293i | 1.13357i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.91044 | + | 3.42475i | −0.265786 | + | 0.131721i | ||||
\(677\) | − | 12.2327i | − | 0.470141i | −0.971978 | − | 0.235071i | \(-0.924468\pi\) | ||
0.971978 | − | 0.235071i | \(-0.0755322\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −51.4227 | −1.97342 | ||||||||
\(680\) | 16.8334 | − | 9.69142i | 0.645532 | − | 0.371649i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.9041 | 0.417541 | ||||||||
\(683\) | 30.8488 | 1.18040 | 0.590198 | − | 0.807259i | \(-0.299050\pi\) | ||||
0.590198 | + | 0.807259i | \(0.299050\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.36624 | + | 14.5317i | 0.319658 | + | 0.555227i | ||||
\(686\) | −75.7536 | −2.89229 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 37.8768i | 1.44404i | ||||||||
\(689\) | −24.6480 | + | 5.77264i | −0.939015 | + | 0.219920i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.0235i | 1.48452i | 0.670110 | + | 0.742262i | \(0.266247\pi\) | ||||
−0.670110 | + | 0.742262i | \(0.733753\pi\) | |||||||
\(692\) | − | 14.4267i | − | 0.548420i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 34.8272i | 1.32202i | ||||||||
\(695\) | −2.64758 | − | 4.59870i | −0.100429 | − | 0.174438i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.4494 | 0.850333 | ||||||||
\(698\) | 20.7462i | 0.785254i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.24628 | + | 12.4805i | −0.273884 | + | 0.471719i | ||||
\(701\) | 1.60186 | 0.0605014 | 0.0302507 | − | 0.999542i | \(-0.490369\pi\) | ||||
0.0302507 | + | 0.999542i | \(0.490369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.965202i | − | 0.0364033i | ||||||
\(704\) | 4.38085i | 0.165109i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.3719 | −0.653801 | ||||||||
\(707\) | −66.5017 | −2.50105 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 39.2899i | − | 1.47556i | −0.675040 | − | 0.737781i | \(-0.735874\pi\) | ||
0.675040 | − | 0.737781i | \(-0.264126\pi\) | |||||||
\(710\) | 30.9405 | − | 17.8132i | 1.16118 | − | 0.668517i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.29721i | 0.161045i | ||||||||
\(713\) | 27.3755 | 1.02522 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.45142 | − | 5.82319i | −0.203871 | − | 0.217775i | ||||
\(716\) | 9.73874 | 0.363954 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 24.6680i | − | 0.920601i | ||||||
\(719\) | −4.48260 | −0.167173 | −0.0835864 | − | 0.996501i | \(-0.526637\pi\) | ||||
−0.0835864 | + | 0.996501i | \(0.526637\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 69.1216i | 2.57422i | ||||||||
\(722\) | −17.1812 | −0.639418 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.55963 | −0.132293 | ||||||||
\(725\) | −7.06335 | + | 12.1654i | −0.262326 | + | 0.451813i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 7.58468i | − | 0.281300i | −0.990059 | − | 0.140650i | \(-0.955081\pi\) | ||
0.990059 | − | 0.140650i | \(-0.0449193\pi\) | |||||||
\(728\) | 9.06138 | + | 38.6903i | 0.335837 | + | 1.43396i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.95433 | − | 5.13149i | −0.109345 | − | 0.189925i | ||||
\(731\) | −30.0422 | −1.11115 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.9979 | 1.29268 | 0.646339 | − | 0.763050i | \(-0.276299\pi\) | ||||
0.646339 | + | 0.763050i | \(0.276299\pi\) | |||||||
\(734\) | − | 0.266399i | − | 0.00983298i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 13.0189i | − | 0.479884i | ||||||
\(737\) | 7.27100i | 0.267831i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.6734i | 0.981196i | 0.871386 | + | 0.490598i | \(0.163222\pi\) | ||||
−0.871386 | + | 0.490598i | \(0.836778\pi\) | |||||||
\(740\) | 0.221341 | + | 0.384457i | 0.00813667 | + | 0.0141329i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 55.0074i | − | 2.01939i | ||||||
\(743\) | −28.2012 | −1.03460 | −0.517300 | − | 0.855804i | \(-0.673063\pi\) | ||||
−0.517300 | + | 0.855804i | \(0.673063\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.51056 | + | 4.32401i | −0.275166 | + | 0.158420i | ||||
\(746\) | 2.10916i | 0.0772218i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.25080 | 0.0822973 | ||||||||
\(749\) | − | 72.2743i | − | 2.64085i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.74617 | 0.173190 | 0.0865951 | − | 0.996244i | \(-0.472401\pi\) | ||||
0.0865951 | + | 0.996244i | \(0.472401\pi\) | |||||||
\(752\) | −4.78326 | −0.174427 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.72506 | − | 15.9052i | −0.135659 | − | 0.579235i | ||||
\(755\) | −13.2624 | + | 7.63550i | −0.482669 | + | 0.277884i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.9863i | 1.16256i | 0.813703 | + | 0.581281i | \(0.197448\pi\) | ||||
−0.813703 | + | 0.581281i | \(0.802552\pi\) | |||||||
\(758\) | − | 0.429000i | − | 0.0155820i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.6707 | − | 7.29483i | 0.459614 | − | 0.264611i | ||||
\(761\) | − | 37.0238i | − | 1.34211i | −0.741406 | − | 0.671056i | \(-0.765841\pi\) | ||
0.741406 | − | 0.671056i | \(-0.234159\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 100.388i | − | 3.63429i | ||||||
\(764\) | −7.40557 | −0.267924 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.9664 | 0.576888 | ||||||||
\(767\) | 23.7385 | − | 5.55963i | 0.857147 | − | 0.200747i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.7680i | 1.28983i | 0.764255 | + | 0.644914i | \(0.223107\pi\) | ||||
−0.764255 | + | 0.644914i | \(0.776893\pi\) | |||||||
\(770\) | 15.0211 | − | 8.64803i | 0.541323 | − | 0.311653i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.14951 | −0.0773624 | ||||||||
\(773\) | 40.4833 | 1.45608 | 0.728041 | − | 0.685533i | \(-0.240431\pi\) | ||||
0.728041 | + | 0.685533i | \(0.240431\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.5930 | − | 17.1819i | −1.06301 | − | 0.617193i | ||||
\(776\) | −23.9441 | −0.859543 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.5239 | 0.879223 | ||||||||
\(779\) | 16.8979 | 0.605431 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.80952 | −0.351012 | ||||||||
\(782\) | 24.7002 | 0.883278 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −80.5882 | −2.87815 | ||||||||
\(785\) | 15.5028 | − | 8.92537i | 0.553320 | − | 0.318560i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.53391 | 0.197262 | 0.0986312 | − | 0.995124i | \(-0.468554\pi\) | ||||
0.0986312 | + | 0.995124i | \(0.468554\pi\) | |||||||
\(788\) | −10.2215 | −0.364126 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 21.2624 | + | 36.9316i | 0.756483 | + | 1.31397i | ||||
\(791\) | 65.4914i | 2.32861i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.46590 | − | 23.3383i | −0.194100 | − | 0.828767i | ||||
\(794\) | 21.5037 | 0.763138 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.85963 | −0.207689 | ||||||||
\(797\) | 50.8420i | 1.80092i | 0.434943 | + | 0.900458i | \(0.356769\pi\) | ||||
−0.434943 | + | 0.900458i | \(0.643231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.79387i | − | 0.134218i | ||||||
\(800\) | −8.17119 | + | 14.0735i | −0.288895 | + | 0.497573i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 53.2487i | 1.88028i | ||||||||
\(803\) | 1.62691i | 0.0574125i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 37.7114 | − | 21.7114i | 1.32915 | − | 0.765225i | ||||
\(806\) | 38.6903 | − | 9.06138i | 1.36281 | − | 0.319173i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −30.9653 | −1.08936 | ||||||||
\(809\) | −15.2288 | −0.535415 | −0.267708 | − | 0.963500i | \(-0.586266\pi\) | ||||
−0.267708 | + | 0.963500i | \(0.586266\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.6843i | 0.831669i | 0.909440 | + | 0.415835i | \(0.136510\pi\) | ||||
−0.909440 | + | 0.415835i | \(0.863490\pi\) | |||||||
\(812\) | 8.12054 | 0.284975 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 0.532799i | − | 0.0186746i | ||||||
\(815\) | −21.2624 | − | 36.9316i | −0.744790 | − | 1.29366i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.6131 | −0.791132 | ||||||||
\(818\) | − | 31.0747i | − | 1.08650i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.73074 | + | 3.87506i | −0.235048 | + | 0.135323i | ||||
\(821\) | 42.7965i | 1.49361i | 0.665045 | + | 0.746803i | \(0.268412\pi\) | ||||
−0.665045 | + | 0.746803i | \(0.731588\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.8420i | 1.63281i | 0.577480 | + | 0.816405i | \(0.304036\pi\) | ||||
−0.577480 | + | 0.816405i | \(0.695964\pi\) | |||||||
\(824\) | 32.1852i | 1.12123i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 52.9776i | 1.84333i | ||||||||
\(827\) | 49.9818 | 1.73804 | 0.869019 | − | 0.494779i | \(-0.164751\pi\) | ||||
0.869019 | + | 0.494779i | \(0.164751\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.0285 | −0.695620 | −0.347810 | − | 0.937565i | \(-0.613075\pi\) | ||||
−0.347810 | + | 0.937565i | \(0.613075\pi\) | |||||||
\(830\) | −23.7219 | − | 41.2035i | −0.823398 | − | 1.43019i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.64050 | + | 15.5442i | 0.126212 | + | 0.538898i | ||||
\(833\) | − | 63.9190i | − | 2.21466i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.31149 | + | 5.75186i | 0.114599 | + | 0.199051i | ||||
\(836\) | 1.69420 | 0.0585951 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26.4346 | 0.913169 | ||||||||
\(839\) | − | 1.63054i | − | 0.0562924i | −0.999604 | − | 0.0281462i | \(-0.991040\pi\) | ||
0.999604 | − | 0.0281462i | \(-0.00896039\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0845 | −0.727050 | ||||||||
\(842\) | 4.48260i | 0.154481i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.9789 | 0.446752 | ||||||||
\(845\) | −24.1819 | − | 16.1318i | −0.831883 | − | 0.554951i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.7537 | 1.67520 | ||||||||
\(848\) | − | 33.9441i | − | 1.16564i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −26.7010 | − | 15.5028i | −0.915838 | − | 0.531743i | ||||
\(851\) | − | 1.33762i | − | 0.0458531i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.0324 | 0.514700 | 0.257350 | − | 0.966318i | \(-0.417151\pi\) | ||||
0.257350 | + | 0.966318i | \(0.417151\pi\) | |||||||
\(854\) | 52.0845 | 1.78229 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 33.6532i | − | 1.15024i | ||||||
\(857\) | 26.6058i | 0.908837i | 0.890788 | + | 0.454418i | \(0.150153\pi\) | ||||
−0.890788 | + | 0.454418i | \(0.849847\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.58074 | −0.156293 | −0.0781465 | − | 0.996942i | \(-0.524900\pi\) | ||||
−0.0781465 | + | 0.996942i | \(0.524900\pi\) | |||||||
\(860\) | 9.00720 | − | 5.18567i | 0.307143 | − | 0.176830i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.0759i | 0.479426i | ||||||||
\(863\) | 21.7874 | 0.741651 | 0.370826 | − | 0.928703i | \(-0.379075\pi\) | ||||
0.370826 | + | 0.928703i | \(0.379075\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 47.1231 | − | 27.1300i | 1.60223 | − | 0.922446i | ||||
\(866\) | 36.5396i | 1.24167i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 19.7536i | 0.670481i | ||||||||
\(869\) | − | 11.7090i | − | 0.397199i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.04223 | + | 25.7991i | 0.204733 | + | 0.874169i | ||||
\(872\) | − | 46.7439i | − | 1.58295i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.5921 | 0.628888 | ||||||||
\(875\) | −54.3930 | − | 0.199070i | −1.83882 | − | 0.00672980i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.9578 | −0.808997 | −0.404498 | − | 0.914539i | \(-0.632554\pi\) | ||||
−0.404498 | + | 0.914539i | \(0.632554\pi\) | |||||||
\(878\) | 15.5028 | 0.523195 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.26926 | − | 5.33654i | 0.312467 | − | 0.179895i | ||||
\(881\) | −24.9230 | −0.839676 | −0.419838 | − | 0.907599i | \(-0.637913\pi\) | ||||
−0.419838 | + | 0.907599i | \(0.637913\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.88074i | 0.298861i | 0.988772 | + | 0.149430i | \(0.0477440\pi\) | ||||
−0.988772 | + | 0.149430i | \(0.952256\pi\) | |||||||
\(884\) | 7.98632 | − | 1.87042i | 0.268609 | − | 0.0629090i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 46.5362i | 1.56341i | ||||||||
\(887\) | 10.0422i | 0.337185i | 0.985686 | + | 0.168593i | \(0.0539222\pi\) | ||||
−0.985686 | + | 0.168593i | \(0.946078\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 17.8507i | − | 0.598694i | ||||||
\(890\) | 5.91967 | − | 3.40810i | 0.198428 | − | 0.114240i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.9098 | 0.365286 | ||||||||
\(893\) | − | 2.85569i | − | 0.0955619i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.3141 | + | 31.8105i | 0.612172 | + | 1.06331i | ||||
\(896\) | −66.3594 | −2.21691 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 19.3183i | − | 0.644661i | ||||||
\(899\) | 19.2549i | 0.642188i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.9230 | 0.896934 | ||||||||
\(902\) | 9.32778 | 0.310581 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 30.4949i | 1.01425i | ||||||||
\(905\) | −6.69402 | − | 11.6271i | −0.222517 | − | 0.386499i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.9652i | 1.22741i | 0.789536 | + | 0.613705i | \(0.210321\pi\) | ||||
−0.789536 | + | 0.613705i | \(0.789679\pi\) | |||||||
\(908\) | 7.13678 | 0.236842 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 46.1116 | − | 43.1677i | 1.52859 | − | 1.43100i | ||||
\(911\) | 44.4826 | 1.47377 | 0.736887 | − | 0.676016i | \(-0.236295\pi\) | ||||
0.736887 | + | 0.676016i | \(0.236295\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.0633i | 0.432334i | ||||||||
\(914\) | 3.94409 | 0.130459 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.696471i | 0.0230120i | ||||||||
\(917\) | −11.5453 | −0.381259 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.8346 | −0.390387 | −0.195193 | − | 0.980765i | \(-0.562533\pi\) | ||||
−0.195193 | + | 0.980765i | \(0.562533\pi\) | |||||||
\(920\) | 17.5596 | − | 10.1095i | 0.578924 | − | 0.333301i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 25.0970i | − | 0.826525i | ||||||
\(923\) | −34.8063 | + | 8.15174i | −1.14566 | + | 0.268318i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.839544 | + | 1.44597i | −0.0276040 | + | 0.0475433i | ||||
\(926\) | −23.5037 | −0.772380 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.15704 | 0.300595 | ||||||||
\(929\) | − | 5.69081i | − | 0.186709i | −0.995633 | − | 0.0933547i | \(-0.970241\pi\) | ||
0.995633 | − | 0.0933547i | \(-0.0297591\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 48.1125i | − | 1.57682i | ||||||
\(932\) | − | 8.91160i | − | 0.291909i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 34.2944i | − | 1.12215i | ||||||
\(935\) | 4.23271 | + | 7.35197i | 0.138424 | + | 0.240435i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 25.9441i | − | 0.847556i | −0.905766 | − | 0.423778i | \(-0.860704\pi\) | ||
0.905766 | − | 0.423778i | \(-0.139296\pi\) | |||||||
\(938\) | −57.5763 | −1.87993 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.654870 | + | 1.13747i | 0.0213595 | + | 0.0371002i | ||||
\(941\) | 15.2573i | 0.497375i | 0.968584 | + | 0.248687i | \(0.0799991\pi\) | ||||
−0.968584 | + | 0.248687i | \(0.920001\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.4179 | 0.762592 | ||||||||
\(944\) | 32.6915i | 1.06402i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.4826 | −0.405844 | ||||||||
\(947\) | −19.5089 | −0.633955 | −0.316978 | − | 0.948433i | \(-0.602668\pi\) | ||||
−0.316978 | + | 0.948433i | \(0.602668\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.35197 | + | 5.77264i | 0.0438868 | + | 0.187388i | ||||
\(950\) | −20.0981 | − | 11.6691i | −0.652070 | − | 0.378597i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 42.2613i | − | 1.36970i | ||||||
\(953\) | − | 5.39420i | − | 0.174735i | −0.996176 | − | 0.0873677i | \(-0.972155\pi\) | ||
0.996176 | − | 0.0873677i | \(-0.0278455\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.9265 | − | 24.1895i | −0.450650 | − | 0.782753i | ||||
\(956\) | 10.9583i | 0.354417i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25.5260i | 0.824707i | ||||||||
\(959\) | 36.4826 | 1.17808 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.8385 | −0.510920 | ||||||||
\(962\) | −0.442758 | − | 1.89049i | −0.0142751 | − | 0.0609517i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 6.46912i | − | 0.208356i | ||||||
\(965\) | −4.04223 | − | 7.02112i | −0.130124 | − | 0.226018i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.7590 | 0.474616 | 0.237308 | − | 0.971434i | \(-0.423735\pi\) | ||||
0.237308 | + | 0.971434i | \(0.423735\pi\) | |||||||
\(968\) | 22.7013 | 0.729647 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 18.9900 | + | 32.9844i | 0.609731 | + | 1.05907i | ||||
\(971\) | −14.1940 | −0.455506 | −0.227753 | − | 0.973719i | \(-0.573138\pi\) | ||||
−0.227753 | + | 0.973719i | \(0.573138\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.5453 | −0.370125 | ||||||||
\(974\) | 9.72506 | 0.311611 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.1404 | 1.02879 | ||||||||
\(977\) | 1.42652 | 0.0456384 | 0.0228192 | − | 0.999740i | \(-0.492736\pi\) | ||||
0.0228192 | + | 0.999740i | \(0.492736\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.87680 | −0.0599829 | ||||||||
\(980\) | 11.0332 | + | 19.1641i | 0.352444 | + | 0.612174i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.88743 | −0.251698 | ||||||||
\(983\) | 27.8738 | 0.889037 | 0.444519 | − | 0.895770i | \(-0.353375\pi\) | ||||
0.444519 | + | 0.895770i | \(0.353375\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.2219 | − | 33.3874i | −0.612462 | − | 1.06381i | ||||
\(986\) | 17.3733i | 0.553277i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.01138 | − | 1.40788i | 0.191248 | − | 0.0447908i | ||||
\(989\) | −31.3383 | −0.996500 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.0845 | −1.14626 | −0.573130 | − | 0.819464i | \(-0.694271\pi\) | ||||
−0.573130 | + | 0.819464i | \(0.694271\pi\) | |||||||
\(992\) | 22.2749i | 0.707230i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 77.6778i | − | 2.46379i | ||||||
\(995\) | −11.0193 | − | 19.1398i | −0.349334 | − | 0.606773i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 2.92297i | − | 0.0925714i | −0.998928 | − | 0.0462857i | \(-0.985262\pi\) | ||
0.998928 | − | 0.0462857i | \(-0.0147385\pi\) | |||||||
\(998\) | 61.2151i | 1.93773i | ||||||||
\(999\) | 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 | 585.2.h.g.64.4 | 12 | ||
3.2 | odd | 2 | 195.2.h.c.64.9 | yes | 12 | ||
5.4 | even | 2 | inner | 585.2.h.g.64.10 | 12 | ||
12.11 | even | 2 | 3120.2.r.n.2209.9 | 12 | |||
13.12 | even | 2 | inner | 585.2.h.g.64.9 | 12 | ||
15.2 | even | 4 | 975.2.b.j.376.5 | 6 | |||
15.8 | even | 4 | 975.2.b.l.376.2 | 6 | |||
15.14 | odd | 2 | 195.2.h.c.64.4 | yes | 12 | ||
39.38 | odd | 2 | 195.2.h.c.64.3 | ✓ | 12 | ||
60.59 | even | 2 | 3120.2.r.n.2209.4 | 12 | |||
65.64 | even | 2 | inner | 585.2.h.g.64.3 | 12 | ||
156.155 | even | 2 | 3120.2.r.n.2209.10 | 12 | |||
195.38 | even | 4 | 975.2.b.l.376.5 | 6 | |||
195.77 | even | 4 | 975.2.b.j.376.2 | 6 | |||
195.194 | odd | 2 | 195.2.h.c.64.10 | yes | 12 | ||
780.779 | even | 2 | 3120.2.r.n.2209.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.h.c.64.3 | ✓ | 12 | 39.38 | odd | 2 | ||
195.2.h.c.64.4 | yes | 12 | 15.14 | odd | 2 | ||
195.2.h.c.64.9 | yes | 12 | 3.2 | odd | 2 | ||
195.2.h.c.64.10 | yes | 12 | 195.194 | odd | 2 | ||
585.2.h.g.64.3 | 12 | 65.64 | even | 2 | inner | ||
585.2.h.g.64.4 | 12 | 1.1 | even | 1 | trivial | ||
585.2.h.g.64.9 | 12 | 13.12 | even | 2 | inner | ||
585.2.h.g.64.10 | 12 | 5.4 | even | 2 | inner | ||
975.2.b.j.376.2 | 6 | 195.77 | even | 4 | |||
975.2.b.j.376.5 | 6 | 15.2 | even | 4 | |||
975.2.b.l.376.2 | 6 | 15.8 | even | 4 | |||
975.2.b.l.376.5 | 6 | 195.38 | even | 4 | |||
3120.2.r.n.2209.3 | 12 | 780.779 | even | 2 | |||
3120.2.r.n.2209.4 | 12 | 60.59 | even | 2 | |||
3120.2.r.n.2209.9 | 12 | 12.11 | even | 2 | |||
3120.2.r.n.2209.10 | 12 | 156.155 | even | 2 |