Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2033,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("3024.2033");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.ca (of order \(6\), degree \(2\), not 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 10.0.288778218147.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 2609.4 | ||
Root | \(0.187540 - 0.324828i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.2609 |
Dual form | 3024.2.ca.b.2033.4 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.723774 | + | 1.25361i | 0.323682 | + | 0.560633i | 0.981245 | − | 0.192766i | \(-0.0617460\pi\) |
−0.657563 | + | 0.753400i | \(0.728413\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.182786 | − | 2.63943i | −0.0690867 | − | 0.997611i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.55933 | − | 0.900281i | −0.470156 | − | 0.271445i | 0.246149 | − | 0.969232i | \(-0.420835\pi\) |
−0.716305 | + | 0.697787i | \(0.754168\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.88867 | − | 1.09042i | −0.523823 | − | 0.302429i | 0.214675 | − | 0.976686i | \(-0.431131\pi\) |
−0.738497 | + | 0.674256i | \(0.764464\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.95230 | − | 3.38149i | −0.473503 | − | 0.820131i | 0.526037 | − | 0.850462i | \(-0.323677\pi\) |
−0.999540 | + | 0.0303308i | \(0.990344\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.47456 | + | 2.00604i | 0.797118 | + | 0.460216i | 0.842462 | − | 0.538755i | \(-0.181105\pi\) |
−0.0453446 | + | 0.998971i | \(0.514439\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.91522 | + | 2.83781i | −1.02490 | + | 0.591723i | −0.915518 | − | 0.402277i | \(-0.868219\pi\) |
−0.109377 | + | 0.994000i | \(0.534886\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.45230 | − | 2.51546i | 0.290460 | − | 0.503092i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.49418 | + | 4.90412i | −1.57733 | + | 0.910672i | −0.582100 | + | 0.813117i | \(0.697769\pi\) |
−0.995230 | + | 0.0975551i | \(0.968898\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.83050i | − | 0.508374i | −0.967155 | − | 0.254187i | \(-0.918192\pi\) | ||
0.967155 | − | 0.254187i | \(-0.0818078\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.17653 | − | 2.13949i | 0.536931 | − | 0.361641i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.411767 | + | 0.713202i | −0.0676941 | + | 0.117250i | −0.897886 | − | 0.440228i | \(-0.854898\pi\) |
0.830192 | + | 0.557478i | \(0.188231\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.90617 | + | 10.2298i | −0.922389 | + | 1.59762i | −0.126681 | + | 0.991943i | \(0.540433\pi\) |
−0.795708 | + | 0.605681i | \(0.792901\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.76766 | + | 6.52578i | 0.574563 | + | 0.995172i | 0.996089 | + | 0.0883555i | \(0.0281612\pi\) |
−0.421526 | + | 0.906816i | \(0.638506\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.33839 | 0.341089 | 0.170545 | − | 0.985350i | \(-0.445447\pi\) | ||||
0.170545 | + | 0.985350i | \(0.445447\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.93318 | + | 0.964903i | −0.990454 | + | 0.137843i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.996713 | + | 0.575453i | −0.136909 | + | 0.0790445i | −0.566890 | − | 0.823793i | \(-0.691854\pi\) |
0.429981 | + | 0.902838i | \(0.358520\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.60640i | − | 0.351447i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.79110 | −1.27469 | −0.637346 | − | 0.770577i | \(-0.719968\pi\) | ||||
−0.637346 | + | 0.770577i | \(0.719968\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.35536i | 0.301573i | 0.988566 | + | 0.150786i | \(0.0481806\pi\) | ||||
−0.988566 | + | 0.150786i | \(0.951819\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 3.15688i | − | 0.391563i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.312805 | 0.0382152 | 0.0191076 | − | 0.999817i | \(-0.493917\pi\) | ||||
0.0191076 | + | 0.999817i | \(0.493917\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.94933i | 0.231343i | 0.993288 | + | 0.115671i | \(0.0369019\pi\) | ||||
−0.993288 | + | 0.115671i | \(0.963098\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.42847 | − | 1.40208i | 0.284231 | − | 0.164101i | −0.351106 | − | 0.936336i | \(-0.614194\pi\) |
0.635337 | + | 0.772235i | \(0.280861\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.09120 | + | 4.28031i | −0.238315 | + | 0.487786i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.4317 | −1.39867 | −0.699336 | − | 0.714793i | \(-0.746521\pi\) | ||||
−0.699336 | + | 0.714793i | \(0.746521\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.60916 | + | 6.25124i | 0.396157 | + | 0.686163i | 0.993248 | − | 0.116010i | \(-0.0370104\pi\) |
−0.597092 | + | 0.802173i | \(0.703677\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.82605 | − | 4.89486i | 0.306528 | − | 0.530923i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.28999 | − | 9.16253i | 0.560737 | − | 0.971226i | −0.436695 | − | 0.899610i | \(-0.643851\pi\) |
0.997432 | − | 0.0716161i | \(-0.0228156\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.53287 | + | 5.18433i | −0.265517 | + | 0.543465i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.80767i | 0.595854i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.4322 | + | 7.75510i | −1.36384 | + | 0.787411i | −0.990132 | − | 0.140137i | \(-0.955246\pi\) |
−0.373704 | + | 0.927548i | \(0.621912\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.97309 | − | 3.41749i | 0.196330 | − | 0.340053i | −0.751006 | − | 0.660295i | \(-0.770431\pi\) |
0.947336 | + | 0.320242i | \(0.103764\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.59853 | + | 2.07761i | −0.354573 | + | 0.204713i | −0.666698 | − | 0.745328i | \(-0.732293\pi\) |
0.312124 | + | 0.950041i | \(0.398959\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.91092 | − | 2.83532i | −0.474757 | − | 0.274101i | 0.243472 | − | 0.969908i | \(-0.421714\pi\) |
−0.718229 | + | 0.695807i | \(0.755047\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.99916 | + | 10.3908i | 0.574615 | + | 0.995262i | 0.996083 | + | 0.0884193i | \(0.0281815\pi\) |
−0.421468 | + | 0.906843i | \(0.638485\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.27800 | − | 3.62461i | −0.590585 | − | 0.340974i | 0.174744 | − | 0.984614i | \(-0.444090\pi\) |
−0.765329 | + | 0.643640i | \(0.777424\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.11502 | − | 4.10786i | −0.663479 | − | 0.383060i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.56834 | + | 5.77105i | −0.785458 | + | 0.529032i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.87899 | − | 6.71861i | −0.352635 | − | 0.610782i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.4423 | 1.02343 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.881336 | 0.0782059 | 0.0391030 | − | 0.999235i | \(-0.487550\pi\) | ||||
0.0391030 | + | 0.999235i | \(0.487550\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.48721 | − | 2.57592i | −0.129938 | − | 0.225059i | 0.793714 | − | 0.608291i | \(-0.208144\pi\) |
−0.923652 | + | 0.383232i | \(0.874811\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.65969 | − | 9.53752i | 0.404046 | − | 0.827008i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.3045 | + | 5.94930i | 0.880372 | + | 0.508283i | 0.870781 | − | 0.491671i | \(-0.163614\pi\) |
0.00959114 | + | 0.999954i | \(0.496947\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.4143 | − | 6.01268i | −0.883327 | − | 0.509989i | −0.0115731 | − | 0.999933i | \(-0.503684\pi\) |
−0.871754 | + | 0.489944i | \(0.837017\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.96338 | + | 3.40067i | 0.164186 | + | 0.284378i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.2957 | − | 7.09895i | −1.02111 | − | 0.589536i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.13061 | + | 3.53951i | −0.502239 | + | 0.289968i | −0.729638 | − | 0.683834i | \(-0.760311\pi\) |
0.227399 | + | 0.973802i | \(0.426978\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.79093 | − | 13.4943i | 0.634017 | − | 1.09815i | −0.352706 | − | 0.935734i | \(-0.614738\pi\) |
0.986723 | − | 0.162415i | \(-0.0519283\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.54836 | − | 2.04865i | 0.285011 | − | 0.164551i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.08628i | − | 0.166503i | −0.996529 | − | 0.0832517i | \(-0.973469\pi\) | ||
0.996529 | − | 0.0832517i | \(-0.0265305\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.38862 | + | 12.4547i | 0.661116 | + | 0.981566i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.58983 | − | 9.68188i | 0.437830 | − | 0.758343i | −0.559692 | − | 0.828700i | \(-0.689081\pi\) |
0.997522 | + | 0.0703575i | \(0.0224140\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.960750 | + | 1.66407i | −0.0743450 | + | 0.128769i | −0.900801 | − | 0.434232i | \(-0.857020\pi\) |
0.826456 | + | 0.563001i | \(0.190353\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.12195 | − | 7.13943i | −0.317073 | − | 0.549187i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.2258 | −1.15760 | −0.578798 | − | 0.815471i | \(-0.696478\pi\) | ||||
−0.578798 | + | 0.815471i | \(0.696478\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.90484 | − | 3.37346i | −0.521957 | − | 0.255009i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.299401 | − | 0.172859i | 0.0223783 | − | 0.0129201i | −0.488769 | − | 0.872413i | \(-0.662554\pi\) |
0.511147 | + | 0.859493i | \(0.329221\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.27661i | 0.243548i | 0.992558 | + | 0.121774i | \(0.0388583\pi\) | ||||
−0.992558 | + | 0.121774i | \(0.961142\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.19211 | −0.0876454 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.03048i | 0.514120i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 7.39120i | − | 0.534808i | −0.963584 | − | 0.267404i | \(-0.913834\pi\) | ||
0.963584 | − | 0.267404i | \(-0.0861659\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.0285 | 0.937812 | 0.468906 | − | 0.883248i | \(-0.344648\pi\) | ||||
0.468906 | + | 0.883248i | \(0.344648\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.03035i | 0.287151i | 0.989639 | + | 0.143575i | \(0.0458599\pi\) | ||||
−0.989639 | + | 0.143575i | \(0.954140\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.2096 | + | 8.20390i | −1.00729 | + | 0.581559i | −0.910397 | − | 0.413736i | \(-0.864224\pi\) |
−0.0968925 | + | 0.995295i | \(0.530890\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.4967 | + | 21.5234i | 1.01747 | + | 1.51065i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.0989 | −1.19424 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.61199 | − | 6.25615i | −0.249847 | − | 0.432747i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.00827 | − | 10.4066i | 0.413627 | − | 0.716422i | −0.581657 | − | 0.813434i | \(-0.697595\pi\) |
0.995283 | + | 0.0970121i | \(0.0309286\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.45387 | + | 9.44638i | −0.371951 | + | 0.644238i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.47092 | + | 0.517377i | −0.507159 | + | 0.0351219i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.51535i | 0.572804i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.7932 | + | 13.1597i | −1.52635 | + | 0.881237i | −0.526836 | + | 0.849967i | \(0.676622\pi\) |
−0.999511 | + | 0.0312693i | \(0.990045\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.40410 | − | 9.36018i | 0.358683 | − | 0.621257i | −0.629058 | − | 0.777358i | \(-0.716559\pi\) |
0.987741 | + | 0.156101i | \(0.0498926\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.39777 | + | 4.84846i | −0.554941 | + | 0.320395i | −0.751112 | − | 0.660174i | \(-0.770482\pi\) |
0.196172 | + | 0.980570i | \(0.437149\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.92897 | − | 1.11369i | −0.126371 | − | 0.0729605i | 0.435482 | − | 0.900198i | \(-0.356578\pi\) |
−0.561853 | + | 0.827237i | \(0.689911\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.69247 | + | 2.93144i | 0.110404 | + | 0.191226i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.9697 | − | 9.22008i | −1.03299 | − | 0.596398i | −0.115151 | − | 0.993348i | \(-0.536735\pi\) |
−0.917840 | + | 0.396950i | \(0.870068\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.60475 | + | 3.23591i | 0.361034 | + | 0.208443i | 0.669534 | − | 0.742781i | \(-0.266494\pi\) |
−0.308500 | + | 0.951224i | \(0.599827\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.22767 | − | 7.99316i | −0.397871 | − | 0.510664i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.37486 | − | 7.57748i | −0.278366 | − | 0.482143i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.416679 | −0.0263005 | −0.0131503 | − | 0.999914i | \(-0.504186\pi\) | ||||
−0.0131503 | + | 0.999914i | \(0.504186\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.2193 | 0.642481 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.5642 | + | 18.2977i | 0.658976 | + | 1.14138i | 0.980881 | + | 0.194607i | \(0.0623433\pi\) |
−0.321906 | + | 0.946772i | \(0.604323\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.95771 | + | 0.956467i | 0.121646 | + | 0.0594320i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.2653 | − | 11.1228i | −1.18795 | − | 0.685862i | −0.230108 | − | 0.973165i | \(-0.573908\pi\) |
−0.957840 | + | 0.287304i | \(0.907241\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.44279 | − | 0.832996i | −0.0886299 | − | 0.0511705i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.5164 | − | 25.1432i | −0.885083 | − | 1.53301i | −0.845619 | − | 0.533788i | \(-0.820768\pi\) |
−0.0394642 | − | 0.999221i | \(-0.512565\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.8174 | − | 12.0189i | −1.26456 | − | 0.730097i | −0.290610 | − | 0.956842i | \(-0.593858\pi\) |
−0.973954 | + | 0.226745i | \(0.927192\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.52924 | + | 2.61496i | −0.273124 | + | 0.157688i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.03243 | + | 6.98437i | −0.242285 | + | 0.419650i | −0.961365 | − | 0.275278i | \(-0.911230\pi\) |
0.719080 | + | 0.694928i | \(0.244564\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0876 | − | 6.97879i | 0.721087 | − | 0.416320i | −0.0940658 | − | 0.995566i | \(-0.529986\pi\) |
0.815153 | + | 0.579246i | \(0.196653\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5375i | 0.923609i | 0.886982 | + | 0.461805i | \(0.152798\pi\) | ||||
−0.886982 | + | 0.461805i | \(0.847202\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.0804 | + | 13.7191i | 1.65753 | + | 0.809810i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.877036 | − | 1.51907i | 0.0515904 | − | 0.0893571i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.73712 | − | 11.6690i | 0.393587 | − | 0.681712i | −0.599333 | − | 0.800500i | \(-0.704567\pi\) |
0.992920 | + | 0.118788i | \(0.0379008\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.08655 | − | 12.2743i | −0.412595 | − | 0.714635i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.3776 | 0.715818 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.5357 | − | 11.1373i | 0.953099 | − | 0.641943i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.95271 | + | 1.70475i | −0.169072 | + | 0.0976136i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.62791i | 0.492421i | 0.969216 | + | 0.246210i | \(0.0791854\pi\) | ||||
−0.969216 | + | 0.246210i | \(0.920815\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.2440 | −0.921113 | −0.460556 | − | 0.887630i | \(-0.652350\pi\) | ||||
−0.460556 | + | 0.887630i | \(0.652350\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.77692i | 0.383054i | 0.981487 | + | 0.191527i | \(0.0613440\pi\) | ||||
−0.981487 | + | 0.191527i | \(0.938656\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.9676i | 1.23382i | 0.787033 | + | 0.616911i | \(0.211616\pi\) | ||||
−0.787033 | + | 0.616911i | \(0.788384\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.6603 | 0.988789 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 15.6655i | − | 0.871654i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.48584 | + | 3.16725i | −0.304299 | + | 0.175687i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.427426 | − | 6.17202i | −0.0235648 | − | 0.340274i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.6036 | 0.802685 | 0.401342 | − | 0.915928i | \(-0.368544\pi\) | ||||
0.401342 | + | 0.915928i | \(0.368544\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.226400 | + | 0.392137i | 0.0123696 | + | 0.0214247i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.2629 | + | 28.1681i | −0.885894 | + | 1.53441i | −0.0412090 | + | 0.999151i | \(0.513121\pi\) |
−0.844685 | + | 0.535263i | \(0.820212\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.54825 | + | 4.41370i | −0.137995 | + | 0.239015i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.81408 | + | 18.1233i | 0.205941 | + | 0.978564i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.18703i | 0.171089i | 0.996334 | + | 0.0855444i | \(0.0272630\pi\) | ||||
−0.996334 | + | 0.0855444i | \(0.972737\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.48224 | − | 3.74252i | 0.346986 | − | 0.200333i | −0.316371 | − | 0.948636i | \(-0.602464\pi\) |
0.663357 | + | 0.748303i | \(0.269131\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.69040 | − | 9.85606i | 0.302869 | − | 0.524585i | −0.673915 | − | 0.738809i | \(-0.735389\pi\) |
0.976785 | + | 0.214223i | \(0.0687220\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.44370 | + | 1.41087i | −0.129698 | + | 0.0748814i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.77569 | + | 2.75725i | 0.252051 | + | 0.145522i | 0.620703 | − | 0.784046i | \(-0.286847\pi\) |
−0.368652 | + | 0.929568i | \(0.620181\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.45164 | − | 2.51432i | −0.0764022 | − | 0.132332i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.51533 | + | 2.02958i | 0.184001 | + | 0.106233i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.2753 | + | 10.5512i | 0.953962 | + | 0.550770i | 0.894309 | − | 0.447449i | \(-0.147667\pi\) |
0.0596526 | + | 0.998219i | \(0.481001\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.70105 | + | 2.52557i | 0.0883143 | + | 0.131121i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.68498 | − | 13.3108i | −0.397913 | − | 0.689206i | 0.595555 | − | 0.803314i | \(-0.296932\pi\) |
−0.993468 | + | 0.114109i | \(0.963599\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.3903 | 1.10166 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.3630 | 1.66238 | 0.831188 | − | 0.555991i | \(-0.187661\pi\) | ||||
0.831188 | + | 0.555991i | \(0.187661\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.91730 | + | 17.1773i | 0.506750 | + | 0.877718i | 0.999969 | + | 0.00781236i | \(0.00248678\pi\) |
−0.493219 | + | 0.869905i | \(0.664180\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.87941 | + | 0.476414i | −0.350607 | + | 0.0242803i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.41918 | − | 2.55141i | −0.224061 | − | 0.129362i | 0.383768 | − | 0.923429i | \(-0.374626\pi\) |
−0.607829 | + | 0.794068i | \(0.707960\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.1920 | + | 11.0805i | 0.970581 | + | 0.560365i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.99772 | − | 15.5845i | −0.452724 | − | 0.784141i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.5288 | − | 6.65615i | −0.578613 | − | 0.334062i | 0.181969 | − | 0.983304i | \(-0.441753\pi\) |
−0.760582 | + | 0.649242i | \(0.775086\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.1750 | + | 8.18392i | −0.707864 | + | 0.408685i | −0.810270 | − | 0.586057i | \(-0.800679\pi\) |
0.102406 | + | 0.994743i | \(0.467346\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.08645 | + | 5.34589i | −0.153747 | + | 0.266298i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.28416 | − | 0.741412i | 0.0636536 | − | 0.0367504i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.33710i | − | 0.214456i | −0.994234 | − | 0.107228i | \(-0.965803\pi\) | ||
0.994234 | − | 0.107228i | \(-0.0341975\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.78968 | + | 25.8429i | 0.0880644 | + | 1.27165i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.22443 | + | 9.04898i | −0.256457 | + | 0.444197i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.41294 | − | 16.3037i | 0.459852 | − | 0.796487i | −0.539100 | − | 0.842241i | \(-0.681236\pi\) |
0.998953 | + | 0.0457540i | \(0.0145690\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.913453 | + | 1.58215i | 0.0445190 | + | 0.0771092i | 0.887426 | − | 0.460950i | \(-0.152491\pi\) |
−0.842907 | + | 0.538059i | \(0.819158\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.3413 | −0.550135 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.21680 | − | 0.430527i | 0.300852 | − | 0.0208347i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.4526 | − | 7.18954i | 0.599823 | − | 0.346308i | −0.169149 | − | 0.985590i | \(-0.554102\pi\) |
0.768972 | + | 0.639283i | \(0.220769\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.22130i | 0.106749i | 0.998575 | + | 0.0533745i | \(0.0169977\pi\) | ||||
−0.998575 | + | 0.0533745i | \(0.983002\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.7710 | −1.08928 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 10.0448i | − | 0.479413i | −0.970845 | − | 0.239706i | \(-0.922949\pi\) | ||
0.970845 | − | 0.239706i | \(-0.0770512\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 13.8934i | − | 0.660097i | −0.943964 | − | 0.330049i | \(-0.892935\pi\) | ||
0.943964 | − | 0.330049i | \(-0.107065\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.3150 | 0.726002 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.5630i | 0.498498i | 0.968439 | + | 0.249249i | \(0.0801837\pi\) | ||||
−0.968439 | + | 0.249249i | \(0.919816\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.4194 | − | 10.6344i | 0.867334 | − | 0.500755i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.33237 | + | 0.577035i | −0.390628 | + | 0.0270518i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.11307 | 0.239179 | 0.119590 | − | 0.992823i | \(-0.461842\pi\) | ||||
0.119590 | + | 0.992823i | \(0.461842\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.16691 | − | 7.21730i | −0.194072 | − | 0.336143i | 0.752524 | − | 0.658565i | \(-0.228836\pi\) |
−0.946596 | + | 0.322422i | \(0.895503\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.0143 | + | 17.3452i | −0.465403 | + | 0.806102i | −0.999220 | − | 0.0394986i | \(-0.987424\pi\) |
0.533817 | + | 0.845600i | \(0.320757\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.3896 | − | 17.9953i | 0.480773 | − | 0.832723i | −0.518984 | − | 0.854784i | \(-0.673690\pi\) |
0.999757 | + | 0.0220611i | \(0.00702284\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.0571765 | − | 0.825627i | −0.00264016 | − | 0.0381239i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 13.5678i | − | 0.623848i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.0922 | − | 5.82674i | 0.463062 | − | 0.267349i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.0308 | + | 27.7662i | −0.732468 | + | 1.26867i | 0.223357 | + | 0.974737i | \(0.428298\pi\) |
−0.955825 | + | 0.293935i | \(0.905035\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.55538 | − | 0.898002i | 0.0709194 | − | 0.0409454i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.4438 | − | 11.2259i | −0.882897 | − | 0.509741i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.8375 | − | 20.5032i | −0.536408 | − | 0.929087i | −0.999094 | − | 0.0425641i | \(-0.986447\pi\) |
0.462685 | − | 0.886523i | \(-0.346886\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.4664 | + | 8.92951i | 0.697987 | + | 0.402983i | 0.806597 | − | 0.591101i | \(-0.201307\pi\) |
−0.108610 | + | 0.994084i | \(0.534640\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.1664 | + | 19.1486i | 1.49374 | + | 0.862411i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.14511 | − | 0.356310i | 0.230790 | − | 0.0159827i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.5602 | − | 20.0229i | −0.517506 | − | 0.896346i | −0.999793 | − | 0.0203330i | \(-0.993527\pi\) |
0.482288 | − | 0.876013i | \(-0.339806\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.9995 | 0.624206 | 0.312103 | − | 0.950048i | \(-0.398967\pi\) | ||||
0.312103 | + | 0.950048i | \(0.398967\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.71228 | 0.254193 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.79171 | + | 11.7636i | 0.301037 | + | 0.521411i | 0.976371 | − | 0.216100i | \(-0.0693339\pi\) |
−0.675334 | + | 0.737512i | \(0.736001\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.14458 | − | 6.15350i | −0.183345 | − | 0.272215i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.20904 | − | 3.00744i | −0.229538 | − | 0.132524i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.64633 | − | 2.10521i | −0.160365 | − | 0.0925870i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.9477 | + | 27.6222i | 0.698682 | + | 1.21015i | 0.968924 | + | 0.247360i | \(0.0795630\pi\) |
−0.270242 | + | 0.962792i | \(0.587104\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.20531 | + | 0.695886i | 0.0527046 | + | 0.0304290i | 0.526121 | − | 0.850410i | \(-0.323646\pi\) |
−0.473416 | + | 0.880839i | \(0.656979\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.57131 | + | 5.52600i | −0.416933 | + | 0.240716i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.60628 | − | 7.97832i | 0.200273 | − | 0.346883i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.3096 | − | 12.8805i | 0.966337 | − | 0.557915i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 8.20854i | − | 0.354886i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.6798 | + | 4.73720i | 0.503085 | + | 0.204046i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.9736 | − | 22.4709i | 0.557779 | − | 0.966101i | −0.439903 | − | 0.898045i | \(-0.644987\pi\) |
0.997682 | − | 0.0680555i | \(-0.0216795\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.68407 | + | 15.0413i | −0.371985 | + | 0.644296i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.32438 | + | 16.1503i | 0.398682 | + | 0.690537i | 0.993564 | − | 0.113276i | \(-0.0361345\pi\) |
−0.594882 | + | 0.803813i | \(0.702801\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.3514 | −1.67642 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.27234 | + | 32.8125i | 0.0966296 | + | 1.39533i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.3567 | − | 20.9905i | 1.54048 | − | 0.889398i | 0.541674 | − | 0.840589i | \(-0.317791\pi\) |
0.998808 | − | 0.0488092i | \(-0.0155426\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 16.4334i | − | 0.695058i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 38.6011 | 1.62684 | 0.813422 | − | 0.581675i | \(-0.197602\pi\) | ||||
0.813422 | + | 0.581675i | \(0.197602\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 10.4936i | − | 0.441468i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 35.1560i | − | 1.47382i | −0.675993 | − | 0.736908i | \(-0.736285\pi\) | ||
0.675993 | − | 0.736908i | \(-0.263715\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.3532 | 1.47948 | 0.739742 | − | 0.672891i | \(-0.234948\pi\) | ||||
0.739742 | + | 0.672891i | \(0.234948\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.4854i | 0.687489i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.2557 | − | 13.4267i | 0.968147 | − | 0.558960i | 0.0694761 | − | 0.997584i | \(-0.477867\pi\) |
0.898671 | + | 0.438624i | \(0.144534\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.8400 | − | 10.6688i | 0.657155 | − | 0.442615i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.07228 | 0.0858249 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.6788 | − | 27.1565i | −0.647134 | − | 1.12087i | −0.983804 | − | 0.179246i | \(-0.942634\pi\) |
0.336671 | − | 0.941622i | \(-0.390699\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.67809 | − | 9.83474i | 0.233962 | − | 0.405234i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.56131 | + | 7.90043i | −0.187311 | + | 0.324432i | −0.944353 | − | 0.328935i | \(-0.893310\pi\) |
0.757042 | + | 0.653366i | \(0.226644\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.4362 | − | 6.56445i | −0.550831 | − | 0.269116i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.28537i | 0.0525186i | 0.999655 | + | 0.0262593i | \(0.00835956\pi\) | ||||
−0.999655 | + | 0.0262593i | \(0.991640\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.7126 | − | 9.64903i | 0.681721 | − | 0.393592i | −0.118782 | − | 0.992920i | \(-0.537899\pi\) |
0.800503 | + | 0.599328i | \(0.204566\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.61502 | − | 9.72551i | 0.228283 | − | 0.395398i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.7319 | + | 19.4751i | −1.36913 | + | 0.790470i | −0.990817 | − | 0.135206i | \(-0.956830\pi\) |
−0.378317 | + | 0.925676i | \(0.623497\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.41645 | − | 2.54984i | −0.178670 | − | 0.103155i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.65018 | − | 6.32229i | −0.147429 | − | 0.255355i | 0.782847 | − | 0.622214i | \(-0.213767\pi\) |
−0.930277 | + | 0.366859i | \(0.880433\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.3641 | − | 22.1495i | −1.54448 | − | 0.891706i | −0.998548 | − | 0.0538763i | \(-0.982842\pi\) |
−0.545932 | − | 0.837829i | \(-0.683824\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.408449 | + | 0.235818i | 0.0164169 | + | 0.00947832i | 0.508186 | − | 0.861247i | \(-0.330316\pi\) |
−0.491769 | + | 0.870726i | \(0.663650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.1508 | − | 12.2878i | −1.00764 | − | 0.492299i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.02013 | + | 1.76692i | 0.0408052 | + | 0.0706768i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.21558 | 0.128213 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.2247 | −0.407038 | −0.203519 | − | 0.979071i | \(-0.565238\pi\) | ||||
−0.203519 | + | 0.979071i | \(0.565238\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.637888 | + | 1.10485i | 0.0253138 | + | 0.0438448i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.1466 | + | 5.73772i | 0.560510 | + | 0.227337i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.4584 | − | 25.0907i | −1.71651 | − | 0.991025i | −0.925091 | − | 0.379745i | \(-0.876012\pi\) |
−0.791414 | − | 0.611280i | \(-0.790655\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.18633 | + | 5.30373i | 0.362274 | + | 0.209159i | 0.670078 | − | 0.742291i | \(-0.266261\pi\) |
−0.307804 | + | 0.951450i | \(0.599594\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.9203 | − | 25.8427i | −0.586577 | − | 1.01598i | −0.994677 | − | 0.103044i | \(-0.967142\pi\) |
0.408100 | − | 0.912937i | \(-0.366191\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.2676 | + | 8.81474i | 0.599305 | + | 0.346009i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.5327 | − | 17.6281i | 1.19484 | − | 0.689839i | 0.235437 | − | 0.971890i | \(-0.424348\pi\) |
0.959400 | + | 0.282050i | \(0.0910144\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.15280 | − | 3.72877i | 0.0841170 | − | 0.145695i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.3751 | − | 16.9597i | 1.14429 | − | 0.660656i | 0.196801 | − | 0.980443i | \(-0.436945\pi\) |
0.947489 | + | 0.319787i | \(0.103611\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.7674i | 0.613281i | 0.951825 | + | 0.306641i | \(0.0992050\pi\) | ||||
−0.951825 | + | 0.306641i | \(0.900795\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.3289 | − | 1.06156i | 0.594430 | − | 0.0411656i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.8339 | − | 48.2097i | 1.07773 | − | 1.86669i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.12048 | − | 3.67279i | 0.0818604 | − | 0.141786i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.35627 | − | 12.7414i | −0.283563 | − | 0.491146i | 0.688696 | − | 0.725050i | \(-0.258183\pi\) |
−0.972260 | + | 0.233904i | \(0.924850\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.98434 | −0.153131 | −0.0765654 | − | 0.997065i | \(-0.524395\pi\) | ||||
−0.0765654 | + | 0.997065i | \(0.524395\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.9243 | + | 34.0359i | 0.879753 | + | 1.30618i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.2812 | − | 11.1320i | 0.737774 | − | 0.425954i | −0.0834856 | − | 0.996509i | \(-0.526605\pi\) |
0.821259 | + | 0.570555i | \(0.193272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.2238i | 0.658088i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.50995 | 0.0956215 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 48.3823i | 1.84055i | 0.391271 | + | 0.920275i | \(0.372035\pi\) | ||||
−0.391271 | + | 0.920275i | \(0.627965\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 17.4073i | − | 0.660297i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46.1225 | 1.74701 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 23.3129i | − | 0.880514i | −0.897872 | − | 0.440257i | \(-0.854887\pi\) | ||
0.897872 | − | 0.440257i | \(-0.145113\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.86142 | + | 1.65204i | −0.107920 | + | 0.0623079i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.38088 | − | 4.58316i | −0.352804 | − | 0.172367i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.6777 | 0.663899 | 0.331949 | − | 0.943297i | \(-0.392294\pi\) | ||||
0.331949 | + | 0.943297i | \(0.392294\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.03242 | + | 13.9126i | 0.300817 | + | 0.521030i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.84208 | + | 4.92263i | −0.106288 | + | 0.184096i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.2102 | + | 26.3449i | −0.567246 | + | 0.982498i | 0.429591 | + | 0.903024i | \(0.358658\pi\) |
−0.996837 | + | 0.0794749i | \(0.974676\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.14147 | + | 9.11830i | 0.228720 | + | 0.339583i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28.4890i | 1.05806i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.5219 | − | 22.2406i | 1.42870 | − | 0.824859i | 0.431680 | − | 0.902027i | \(-0.357921\pi\) |
0.997018 | + | 0.0771674i | \(0.0245876\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.7112 | − | 25.4806i | 0.544114 | − | 0.942433i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.2270 | + | 22.6477i | −1.44888 | + | 0.836512i | −0.998415 | − | 0.0562818i | \(-0.982075\pi\) |
−0.450466 | + | 0.892794i | \(0.648742\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.487767 | − | 0.281612i | −0.0179671 | − | 0.0103733i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.3086 | + | 17.8550i | 0.379208 | + | 0.656808i | 0.990947 | − | 0.134252i | \(-0.0428631\pi\) |
−0.611739 | + | 0.791060i | \(0.709530\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.69885 | + | 4.44493i | 0.282443 | + | 0.163069i | 0.634529 | − | 0.772899i | \(-0.281194\pi\) |
−0.352086 | + | 0.935968i | \(0.614527\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.87435 | − | 5.12361i | −0.325131 | − | 0.187714i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.58599 | + | 13.4803i | −0.240647 | + | 0.492559i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.5008 | − | 21.6521i | −0.456162 | − | 0.790095i | 0.542592 | − | 0.839996i | \(-0.317443\pi\) |
−0.998754 | + | 0.0499007i | \(0.984110\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.5555 | 0.820878 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.1262 | −0.985919 | −0.492959 | − | 0.870052i | \(-0.664085\pi\) | ||||
−0.492959 | + | 0.870052i | \(0.664085\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.58366 | + | 2.74298i | 0.0574075 | + | 0.0994328i | 0.893301 | − | 0.449459i | \(-0.148383\pi\) |
−0.835893 | + | 0.548892i | \(0.815050\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.3293 | − | 17.7337i | 0.953186 | − | 0.642002i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.4922 | + | 10.6765i | 0.667713 | + | 0.385504i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.48873 | − | 1.43687i | −0.0897460 | − | 0.0518149i | 0.454455 | − | 0.890770i | \(-0.349834\pi\) |
−0.544201 | + | 0.838955i | \(0.683167\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.15679 | + | 10.6639i | 0.221444 | + | 0.383553i | 0.955247 | − | 0.295810i | \(-0.0955895\pi\) |
−0.733802 | + | 0.679363i | \(0.762256\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.12002 | − | 4.11075i | −0.255759 | − | 0.147662i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −41.0426 | + | 23.6960i | −1.47051 | + | 0.848997i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.75494 | − | 3.03965i | 0.0627968 | − | 0.108767i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.61539 | − | 1.51000i | 0.0933473 | − | 0.0538941i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 3.81570i | − | 0.136015i | −0.997685 | − | 0.0680076i | \(-0.978336\pi\) | ||
0.997685 | − | 0.0680076i | \(-0.0216642\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.41936 | + | 17.2329i | −0.299358 | + | 0.612730i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.56834 | − | 4.44849i | 0.0912044 | − | 0.157971i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.5682 | − | 42.5535i | 0.870252 | − | 1.50732i | 0.00851609 | − | 0.999964i | \(-0.497289\pi\) |
0.861736 | − | 0.507357i | \(-0.169377\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.56524 | − | 7.90724i | −0.161507 | − | 0.279738i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.04906 | −0.178177 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.54188 | + | 19.5305i | −0.336307 | + | 0.688359i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.4929 | − | 22.8012i | 1.38850 | − | 0.801648i | 0.395350 | − | 0.918531i | \(-0.370623\pi\) |
0.993146 | + | 0.116882i | \(0.0372900\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.1391i | 1.37436i | 0.726488 | + | 0.687180i | \(0.241151\pi\) | ||||
−0.726488 | + | 0.687180i | \(0.758849\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.1831 | 0.566870 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.2322i | 1.05769i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.8906i | 0.414985i | 0.978237 | + | 0.207492i | \(0.0665302\pi\) | ||||
−0.978237 | + | 0.207492i | \(0.933470\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.02389 | −0.105406 | −0.0527031 | − | 0.998610i | \(-0.516784\pi\) | ||||
−0.0527031 | + | 0.998610i | \(0.516784\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 15.2436i | − | 0.530071i | −0.964239 | − | 0.265035i | \(-0.914616\pi\) | ||
0.964239 | − | 0.265035i | \(-0.0853836\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.7306 | + | 17.1649i | −1.03259 | + | 0.596163i | −0.917724 | − | 0.397218i | \(-0.869976\pi\) |
−0.114861 | + | 0.993382i | \(0.536642\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.7985 | + | 21.5607i | 0.582032 | + | 0.747033i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.78146 | −0.0962565 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.16024 | + | 10.6698i | 0.212675 | + | 0.368364i | 0.952551 | − | 0.304379i | \(-0.0984491\pi\) |
−0.739876 | + | 0.672744i | \(0.765116\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.6008 | − | 58.1983i | 1.15865 | − | 2.00684i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.96672 | − | 10.3347i | 0.205262 | − | 0.355523i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.0243 | + | 11.4664i | −0.584961 | + | 0.393990i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.67406i | − | 0.160225i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.92537 | − | 2.26631i | 0.134402 | − | 0.0775971i | −0.431291 | − | 0.902213i | \(-0.641942\pi\) |
0.565693 | + | 0.824616i | \(0.308609\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.1307 | − | 27.9392i | 0.551014 | − | 0.954384i | −0.447188 | − | 0.894440i | \(-0.647574\pi\) |
0.998202 | − | 0.0599442i | \(-0.0190923\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.2711 | + | 8.81675i | −0.521042 | + | 0.300824i | −0.737361 | − | 0.675499i | \(-0.763928\pi\) |
0.216319 | + | 0.976323i | \(0.430595\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.4091 | + | 15.2473i | 0.898975 | + | 0.519023i | 0.876867 | − | 0.480732i | \(-0.159629\pi\) |
0.0221074 | + | 0.999756i | \(0.492962\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.0200 | − | 19.0873i | −0.374693 | − | 0.648987i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.3851 | + | 11.1920i | 0.657594 | + | 0.379662i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.590785 | − | 0.341090i | −0.0200180 | − | 0.0115574i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.09150 | − | 30.2011i | −0.0707055 | − | 1.02098i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.40363 | − | 7.62730i | −0.148700 | − | 0.257556i | 0.782047 | − | 0.623219i | \(-0.214176\pi\) |
−0.930747 | + | 0.365663i | \(0.880842\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.6776 | −1.30308 | −0.651540 | − | 0.758614i | \(-0.725877\pi\) | ||||
−0.651540 | + | 0.758614i | \(0.725877\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.4489 | −1.26026 | −0.630128 | − | 0.776491i | \(-0.716998\pi\) | ||||
−0.630128 | + | 0.776491i | \(0.716998\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.7025 | + | 23.7335i | 0.460086 | + | 0.796892i | 0.998965 | − | 0.0454915i | \(-0.0144854\pi\) |
−0.538879 | + | 0.842383i | \(0.681152\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.161096 | − | 2.32622i | −0.00540299 | − | 0.0780191i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.12487 | + | 4.69090i | 0.271888 | + | 0.156975i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.433397 | + | 0.250222i | 0.0144869 | + | 0.00836400i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.8811 | + | 24.0428i | 0.462962 | + | 0.801873i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.89177 | + | 2.24691i | 0.129654 | + | 0.0748556i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.10760 | + | 2.37152i | −0.136541 | + | 0.0788321i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.8216 | + | 20.4757i | −0.392531 | + | 0.679883i | −0.992783 | − | 0.119928i | \(-0.961734\pi\) |
0.600252 | + | 0.799811i | \(0.295067\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.92249 | + | 2.26465i | −0.129958 | + | 0.0750313i | −0.563570 | − | 0.826069i | \(-0.690572\pi\) |
0.433612 | + | 0.901100i | \(0.357239\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 12.9970i | − | 0.430139i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.52711 | + | 4.39622i | −0.215544 | + | 0.145176i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.9149 | + | 29.2975i | −0.557971 | + | 0.966434i | 0.439695 | + | 0.898147i | \(0.355087\pi\) |
−0.997666 | + | 0.0682866i | \(0.978247\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.12559 | − | 3.68164i | 0.0699648 | − | 0.121183i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.19602 | + | 2.07157i | 0.0393249 | + | 0.0681127i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32.9164 | −1.07995 | −0.539976 | − | 0.841680i | \(-0.681567\pi\) | ||||
−0.539976 | + | 0.841680i | \(0.681567\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.0253 | − | 10.5556i | −0.852946 | − | 0.345946i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.81350 | + | 5.08848i | −0.288232 | + | 0.166411i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.1057i | 1.24486i | 0.782676 | + | 0.622430i | \(0.213854\pi\) | ||||
−0.782676 | + | 0.622430i | \(0.786146\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.8771 | 0.647975 | 0.323987 | − | 0.946061i | \(-0.394976\pi\) | ||||
0.323987 | + | 0.946061i | \(0.394976\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 67.0423i | − | 2.18320i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 20.7495i | − | 0.674267i | −0.941457 | − | 0.337134i | \(-0.890543\pi\) | ||
0.941457 | − | 0.337134i | \(-0.109457\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.11544 | −0.198516 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.8345i | 0.415751i | 0.978155 | + | 0.207876i | \(0.0666549\pi\) | ||||
−0.978155 | + | 0.207876i | \(0.933345\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.26571 | − | 5.34956i | 0.299831 | − | 0.173108i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.8192 | − | 28.2854i | 0.446247 | − | 0.913384i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.9882 | 0.741556 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.42969 | + | 16.3327i | 0.303552 | + | 0.525768i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.8941 | − | 30.9936i | 0.575437 | − | 0.996685i | −0.420557 | − | 0.907266i | \(-0.638165\pi\) |
0.995994 | − | 0.0894195i | \(-0.0285012\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.5129 | + | 25.1370i | −0.465740 | + | 0.806686i | −0.999235 | − | 0.0391177i | \(-0.987545\pi\) |
0.533494 | + | 0.845804i | \(0.320879\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.9665 | + | 28.5868i | −0.447744 | + | 0.916450i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 8.93090i | − | 0.285725i | −0.989743 | − | 0.142862i | \(-0.954369\pi\) | ||
0.989743 | − | 0.142862i | \(-0.0456306\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.4977 | + | 9.52495i | −0.527268 | + | 0.304419i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.1346 | + | 45.2665i | −0.833566 | + | 1.44378i | 0.0616269 | + | 0.998099i | \(0.480371\pi\) |
−0.895193 | + | 0.445679i | \(0.852962\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.05250 | + | 2.91707i | −0.160986 | + | 0.0929454i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −37.0378 | − | 21.3838i | −1.17773 | − | 0.679964i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.9151 | + | 37.9581i | 0.696158 | + | 1.20578i | 0.969789 | + | 0.243946i | \(0.0784418\pi\) |
−0.273631 | + | 0.961835i | \(0.588225\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.5690 | − | 11.8755i | −0.652082 | − | 0.376480i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.9689 | − | 22.4987i | −1.23416 | − | 0.712542i | −0.266264 | − | 0.963900i | \(-0.585789\pi\) |
−0.967894 | + | 0.251358i | \(0.919123\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))