Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(440,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("441.440");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.c (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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 440.3 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.440 |
Dual form | 441.2.c.a.440.1 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.44949 | −1.09545 | −0.547723 | − | 0.836660i | \(-0.684505\pi\) | ||||
−0.547723 | + | 0.836660i | \(0.684505\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843i | 1.00000i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 3.46410i | − 1.09545i | ||||||||
\(11\) | 1.41421i | 0.426401i | 0.977008 | + | 0.213201i | \(0.0683888\pi\) | ||||
−0.977008 | + | 0.213201i | \(0.931611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.19615i | 1.44115i | 0.693375 | + | 0.720577i | \(0.256123\pi\) | ||||
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | −4.89898 | −1.18818 | −0.594089 | − | 0.804400i | \(-0.702487\pi\) | ||||
−0.594089 | + | 0.804400i | \(0.702487\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.73205i | − 0.397360i | −0.980064 | − | 0.198680i | \(-0.936335\pi\) | ||||
0.980064 | − | 0.198680i | \(-0.0636654\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | 5.65685i | 1.17954i | 0.807573 | + | 0.589768i | \(0.200781\pi\) | ||||
−0.807573 | + | 0.589768i | \(0.799219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −7.34847 | −1.44115 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 2.82843i | − 0.525226i | −0.964901 | − | 0.262613i | \(-0.915416\pi\) | ||||
0.964901 | − | 0.262613i | \(-0.0845842\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.73205i | 0.311086i | 0.987829 | + | 0.155543i | \(0.0497126\pi\) | ||||
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 6.92820i | − 1.18818i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | 2.44949 | 0.397360 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 6.92820i | − 1.09545i | ||||||||
\(41\) | 7.34847 | 1.14764 | 0.573819 | − | 0.818982i | \(-0.305461\pi\) | ||||
0.573819 | + | 0.818982i | \(0.305461\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.00000 | −1.17954 | ||||||||
\(47\) | 12.2474 | 1.78647 | 0.893237 | − | 0.449586i | \(-0.148429\pi\) | ||||
0.893237 | + | 0.449586i | \(0.148429\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.41421i | 0.200000i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 2.82843i | − 0.388514i | −0.980951 | − | 0.194257i | \(-0.937770\pi\) | ||||
0.980951 | − | 0.194257i | \(-0.0622296\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 3.46410i | − 0.467099i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.00000 | 0.525226 | ||||||||
\(59\) | −4.89898 | −0.637793 | −0.318896 | − | 0.947790i | \(-0.603312\pi\) | ||||
−0.318896 | + | 0.947790i | \(0.603312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.46410i | 0.443533i | 0.975100 | + | 0.221766i | \(0.0711822\pi\) | ||||
−0.975100 | + | 0.221766i | \(0.928818\pi\) | |||||||
\(62\) | −2.44949 | −0.311086 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | − 12.7279i | − 1.57870i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.0000 | 1.34386 | 0.671932 | − | 0.740613i | \(-0.265465\pi\) | ||||
0.671932 | + | 0.740613i | \(0.265465\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 7.07107i | − 0.839181i | −0.907713 | − | 0.419591i | \(-0.862174\pi\) | ||||
0.907713 | − | 0.419591i | \(-0.137826\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.73205i | 0.202721i | 0.994850 | + | 0.101361i | \(0.0323196\pi\) | ||||
−0.994850 | + | 0.101361i | \(0.967680\pi\) | |||||||
\(74\) | − 1.41421i | − 0.164399i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.00000 | 0.562544 | 0.281272 | − | 0.959628i | \(-0.409244\pi\) | ||||
0.281272 | + | 0.959628i | \(0.409244\pi\) | |||||||
\(80\) | 9.79796 | 1.09545 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.3923i | 1.14764i | ||||||||
\(83\) | −7.34847 | −0.806599 | −0.403300 | − | 0.915068i | \(-0.632137\pi\) | ||||
−0.403300 | + | 0.915068i | \(0.632137\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0000 | 1.30158 | ||||||||
\(86\) | − 1.41421i | − 0.152499i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.00000 | −0.426401 | ||||||||
\(89\) | 4.89898 | 0.519291 | 0.259645 | − | 0.965704i | \(-0.416394\pi\) | ||||
0.259645 | + | 0.965704i | \(0.416394\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 17.3205i | 1.78647i | ||||||||
\(95\) | 4.24264i | 0.435286i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3923i | 1.05518i | 0.849500 | + | 0.527589i | \(0.176904\pi\) | ||||
−0.849500 | + | 0.527589i | \(0.823096\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.1464 | 1.70613 | 0.853067 | − | 0.521802i | \(-0.174740\pi\) | ||||
0.853067 | + | 0.521802i | \(0.174740\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.66025i | 0.853320i | 0.904412 | + | 0.426660i | \(0.140310\pi\) | ||||
−0.904412 | + | 0.426660i | \(0.859690\pi\) | |||||||
\(104\) | −14.6969 | −1.44115 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.00000 | 0.388514 | ||||||||
\(107\) | − 2.82843i | − 0.273434i | −0.990610 | − | 0.136717i | \(-0.956345\pi\) | ||||
0.990610 | − | 0.136717i | \(-0.0436552\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | −0.0957826 | −0.0478913 | − | 0.998853i | \(-0.515250\pi\) | ||||
−0.0478913 | + | 0.998853i | \(0.515250\pi\) | |||||||
\(110\) | 4.89898 | 0.467099 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.41421i | 0.133038i | 0.997785 | + | 0.0665190i | \(0.0211893\pi\) | ||||
−0.997785 | + | 0.0665190i | \(0.978811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 13.8564i | − 1.29212i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 6.92820i | − 0.637793i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | −4.89898 | −0.443533 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.79796 | 0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.0000 | 0.976092 | 0.488046 | − | 0.872818i | \(-0.337710\pi\) | ||||
0.488046 | + | 0.872818i | \(0.337710\pi\) | |||||||
\(128\) | − 11.3137i | − 1.00000i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 18.0000 | 1.57870 | ||||||||
\(131\) | −2.44949 | −0.214013 | −0.107006 | − | 0.994258i | \(-0.534127\pi\) | ||||
−0.107006 | + | 0.994258i | \(0.534127\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 15.5563i | 1.34386i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 13.8564i | − 1.18818i | ||||||||
\(137\) | − 11.3137i | − 0.966595i | −0.875456 | − | 0.483298i | \(-0.839439\pi\) | ||||
0.875456 | − | 0.483298i | \(-0.160561\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.19615i | 0.440732i | 0.975417 | + | 0.220366i | \(0.0707252\pi\) | ||||
−0.975417 | + | 0.220366i | \(0.929275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.0000 | 0.839181 | ||||||||
\(143\) | −7.34847 | −0.614510 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.92820i | 0.575356i | ||||||||
\(146\) | −2.44949 | −0.202721 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.65685i | 0.463428i | 0.972784 | + | 0.231714i | \(0.0744333\pi\) | ||||
−0.972784 | + | 0.231714i | \(0.925567\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.0000 | −1.79033 | −0.895167 | − | 0.445730i | \(-0.852944\pi\) | ||||
−0.895167 | + | 0.445730i | \(0.852944\pi\) | |||||||
\(152\) | 4.89898 | 0.397360 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 4.24264i | − 0.340777i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.3205i | 1.38233i | 0.722698 | + | 0.691164i | \(0.242902\pi\) | ||||
−0.722698 | + | 0.691164i | \(0.757098\pi\) | |||||||
\(158\) | 7.07107i | 0.562544i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0000 | −0.783260 | −0.391630 | − | 0.920123i | \(-0.628089\pi\) | ||||
−0.391630 | + | 0.920123i | \(0.628089\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 10.3923i | − 0.806599i | ||||||||
\(167\) | 7.34847 | 0.568642 | 0.284321 | − | 0.958729i | \(-0.408232\pi\) | ||||
0.284321 | + | 0.958729i | \(0.408232\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.0000 | −1.07692 | ||||||||
\(170\) | 16.9706i | 1.30158i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.79796 | −0.744925 | −0.372463 | − | 0.928047i | \(-0.621486\pi\) | ||||
−0.372463 | + | 0.928047i | \(0.621486\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 5.65685i | − 0.426401i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.92820i | 0.519291i | ||||||||
\(179\) | 9.89949i | 0.739923i | 0.929047 | + | 0.369961i | \(0.120629\pi\) | ||||
−0.929047 | + | 0.369961i | \(0.879371\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 15.5885i | − 1.15868i | −0.815086 | − | 0.579340i | \(-0.803310\pi\) | ||||
0.815086 | − | 0.579340i | \(-0.196690\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.0000 | −1.17954 | ||||||||
\(185\) | 2.44949 | 0.180090 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 6.92820i | − 0.506640i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.00000 | −0.435286 | ||||||||
\(191\) | 1.41421i | 0.102329i | 0.998690 | + | 0.0511645i | \(0.0162933\pi\) | ||||
−0.998690 | + | 0.0511645i | \(0.983707\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.0000 | 0.791797 | 0.395899 | − | 0.918294i | \(-0.370433\pi\) | ||||
0.395899 | + | 0.918294i | \(0.370433\pi\) | |||||||
\(194\) | −14.6969 | −1.05518 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 19.7990i | − 1.41062i | −0.708899 | − | 0.705310i | \(-0.750808\pi\) | ||||
0.708899 | − | 0.705310i | \(-0.249192\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 13.8564i | − 0.982255i | −0.871088 | − | 0.491127i | \(-0.836585\pi\) | ||||
0.871088 | − | 0.491127i | \(-0.163415\pi\) | |||||||
\(200\) | 2.82843i | 0.200000i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 24.2487i | 1.70613i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.0000 | −1.25717 | ||||||||
\(206\) | −12.2474 | −0.853320 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 20.7846i | − 1.44115i | ||||||||
\(209\) | 2.44949 | 0.169435 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.0000 | −1.51454 | −0.757271 | − | 0.653101i | \(-0.773468\pi\) | ||||
−0.757271 | + | 0.653101i | \(0.773468\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.00000 | 0.273434 | ||||||||
\(215\) | 2.44949 | 0.167054 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 1.41421i | − 0.0957826i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 25.4558i | − 1.71235i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 20.7846i | − 1.39184i | −0.718119 | − | 0.695920i | \(-0.754997\pi\) | ||||
0.718119 | − | 0.695920i | \(-0.245003\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.00000 | −0.133038 | ||||||||
\(227\) | −26.9444 | −1.78836 | −0.894181 | − | 0.447706i | \(-0.852241\pi\) | ||||
−0.894181 | + | 0.447706i | \(0.852241\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 22.5167i | − 1.48794i | −0.668211 | − | 0.743971i | \(-0.732940\pi\) | ||||
0.668211 | − | 0.743971i | \(-0.267060\pi\) | |||||||
\(230\) | 19.5959 | 1.29212 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.00000 | 0.525226 | ||||||||
\(233\) | 9.89949i | 0.648537i | 0.945965 | + | 0.324269i | \(0.105118\pi\) | ||||
−0.945965 | + | 0.324269i | \(0.894882\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −30.0000 | −1.95698 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.8701i | 1.73808i | 0.494742 | + | 0.869040i | \(0.335262\pi\) | ||||
−0.494742 | + | 0.869040i | \(0.664738\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 13.8564i | − 0.892570i | −0.894891 | − | 0.446285i | \(-0.852747\pi\) | ||||
0.894891 | − | 0.446285i | \(-0.147253\pi\) | |||||||
\(242\) | 12.7279i | 0.818182i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.00000 | 0.572656 | ||||||||
\(248\) | −4.89898 | −0.311086 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.8564i | 0.876356i | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.00000 | −0.502956 | ||||||||
\(254\) | 15.5563i | 0.976092i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.44949 | −0.152795 | −0.0763975 | − | 0.997077i | \(-0.524342\pi\) | ||||
−0.0763975 | + | 0.997077i | \(0.524342\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 3.46410i | − 0.214013i | ||||||||
\(263\) | 14.1421i | 0.872041i | 0.899937 | + | 0.436021i | \(0.143613\pi\) | ||||
−0.899937 | + | 0.436021i | \(0.856387\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.92820i | 0.425596i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.1464 | 1.04544 | 0.522718 | − | 0.852506i | \(-0.324918\pi\) | ||||
0.522718 | + | 0.852506i | \(0.324918\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.8564i | 0.841717i | 0.907126 | + | 0.420858i | \(0.138271\pi\) | ||||
−0.907126 | + | 0.420858i | \(0.861729\pi\) | |||||||
\(272\) | 19.5959 | 1.18818 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.0000 | 0.966595 | ||||||||
\(275\) | 1.41421i | 0.0852803i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.0000 | 1.38194 | 0.690968 | − | 0.722885i | \(-0.257185\pi\) | ||||
0.690968 | + | 0.722885i | \(0.257185\pi\) | |||||||
\(278\) | −7.34847 | −0.440732 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.6274i | 1.34984i | 0.737892 | + | 0.674919i | \(0.235822\pi\) | ||||
−0.737892 | + | 0.674919i | \(0.764178\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.73205i | 0.102960i | 0.998674 | + | 0.0514799i | \(0.0163938\pi\) | ||||
−0.998674 | + | 0.0514799i | \(0.983606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − 10.3923i | − 0.614510i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00000 | 0.411765 | ||||||||
\(290\) | −9.79796 | −0.575356 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.6969 | −0.858604 | −0.429302 | − | 0.903161i | \(-0.641240\pi\) | ||||
−0.429302 | + | 0.903161i | \(0.641240\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0000 | 0.698667 | ||||||||
\(296\) | − 2.82843i | − 0.164399i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.00000 | −0.463428 | ||||||||
\(299\) | −29.3939 | −1.69989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 31.1127i | − 1.79033i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.92820i | 0.397360i | ||||||||
\(305\) | − 8.48528i | − 0.485866i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.5885i | 0.889680i | 0.895610 | + | 0.444840i | \(0.146740\pi\) | ||||
−0.895610 | + | 0.444840i | \(0.853260\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.00000 | 0.340777 | ||||||||
\(311\) | 17.1464 | 0.972285 | 0.486142 | − | 0.873880i | \(-0.338404\pi\) | ||||
0.486142 | + | 0.873880i | \(0.338404\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 12.1244i | − 0.685309i | −0.939461 | − | 0.342655i | \(-0.888674\pi\) | ||||
0.939461 | − | 0.342655i | \(-0.111326\pi\) | |||||||
\(314\) | −24.4949 | −1.38233 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.1421i | 0.794301i | 0.917753 | + | 0.397151i | \(0.130001\pi\) | ||||
−0.917753 | + | 0.397151i | \(0.869999\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | 0.223957 | ||||||||
\(320\) | 19.5959 | 1.09545 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.48528i | 0.472134i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.19615i | 0.288231i | ||||||||
\(326\) | − 14.1421i | − 0.783260i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 20.7846i | 1.14764i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.0000 | −1.70391 | −0.851957 | − | 0.523612i | \(-0.824584\pi\) | ||||
−0.851957 | + | 0.523612i | \(0.824584\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.3923i | 0.568642i | ||||||||
\(335\) | −26.9444 | −1.47213 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.0000 | 1.25289 | 0.626445 | − | 0.779466i | \(-0.284509\pi\) | ||||
0.626445 | + | 0.779466i | \(0.284509\pi\) | |||||||
\(338\) | − 19.7990i | − 1.07692i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.44949 | −0.132647 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 2.82843i | − 0.152499i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 13.8564i | − 0.744925i | ||||||||
\(347\) | 31.1127i | 1.67022i | 0.550085 | + | 0.835109i | \(0.314595\pi\) | ||||
−0.550085 | + | 0.835109i | \(0.685405\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.3923i | 0.556287i | 0.960539 | + | 0.278144i | \(0.0897191\pi\) | ||||
−0.960539 | + | 0.278144i | \(0.910281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.1464 | 0.912612 | 0.456306 | − | 0.889823i | \(-0.349172\pi\) | ||||
0.456306 | + | 0.889823i | \(0.349172\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.3205i | 0.919277i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.0000 | −0.739923 | ||||||||
\(359\) | − 28.2843i | − 1.49279i | −0.665505 | − | 0.746393i | \(-0.731784\pi\) | ||||
0.665505 | − | 0.746393i | \(-0.268216\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.0000 | 0.842105 | ||||||||
\(362\) | 22.0454 | 1.15868 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 4.24264i | − 0.222070i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.73205i | 0.0904123i | 0.998978 | + | 0.0452062i | \(0.0143945\pi\) | ||||
−0.998978 | + | 0.0452062i | \(0.985606\pi\) | |||||||
\(368\) | − 22.6274i | − 1.17954i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.46410i | 0.180090i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.0000 | 1.50156 | 0.750782 | − | 0.660551i | \(-0.229677\pi\) | ||||
0.750782 | + | 0.660551i | \(0.229677\pi\) | |||||||
\(374\) | 9.79796 | 0.506640 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 34.6410i | 1.78647i | ||||||||
\(377\) | 14.6969 | 0.756931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.00000 | −0.359566 | −0.179783 | − | 0.983706i | \(-0.557540\pi\) | ||||
−0.179783 | + | 0.983706i | \(0.557540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.00000 | −0.102329 | ||||||||
\(383\) | 19.5959 | 1.00130 | 0.500652 | − | 0.865648i | \(-0.333094\pi\) | ||||
0.500652 | + | 0.865648i | \(0.333094\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.5563i | 0.791797i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.8701i | 1.36237i | 0.732113 | + | 0.681183i | \(0.238534\pi\) | ||||
−0.732113 | + | 0.681183i | \(0.761466\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 27.7128i | − 1.40150i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 28.0000 | 1.41062 | ||||||||
\(395\) | −12.2474 | −0.616236 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1.73205i | − 0.0869291i | −0.999055 | − | 0.0434646i | \(-0.986160\pi\) | ||||
0.999055 | − | 0.0434646i | \(-0.0138396\pi\) | |||||||
\(398\) | 19.5959 | 0.982255 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | − 19.7990i | − 0.988714i | −0.869259 | − | 0.494357i | \(-0.835403\pi\) | ||||
0.869259 | − | 0.494357i | \(-0.164597\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.00000 | −0.448322 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.41421i | − 0.0701000i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.9090i | 1.62724i | 0.581394 | + | 0.813622i | \(0.302507\pi\) | ||||
−0.581394 | + | 0.813622i | \(0.697493\pi\) | |||||||
\(410\) | − 25.4558i | − 1.25717i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.0000 | 0.883585 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.46410i | 0.169435i | ||||||||
\(419\) | −36.7423 | −1.79498 | −0.897491 | − | 0.441034i | \(-0.854612\pi\) | ||||
−0.897491 | + | 0.441034i | \(0.854612\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | −0.0487370 | −0.0243685 | − | 0.999703i | \(-0.507758\pi\) | ||||
−0.0243685 | + | 0.999703i | \(0.507758\pi\) | |||||||
\(422\) | − 31.1127i | − 1.51454i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.00000 | 0.388514 | ||||||||
\(425\) | −4.89898 | −0.237635 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.46410i | 0.167054i | ||||||||
\(431\) | − 15.5563i | − 0.749323i | −0.927162 | − | 0.374661i | \(-0.877759\pi\) | ||||
0.927162 | − | 0.374661i | \(-0.122241\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 15.5885i | − 0.749133i | −0.927200 | − | 0.374567i | \(-0.877791\pi\) | ||||
0.927200 | − | 0.374567i | \(-0.122209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.79796 | 0.468700 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 27.7128i | − 1.32266i | −0.750095 | − | 0.661330i | \(-0.769992\pi\) | ||||
0.750095 | − | 0.661330i | \(-0.230008\pi\) | |||||||
\(440\) | 9.79796 | 0.467099 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 36.0000 | 1.71235 | ||||||||
\(443\) | 39.5980i | 1.88136i | 0.339300 | + | 0.940678i | \(0.389810\pi\) | ||||
−0.339300 | + | 0.940678i | \(0.610190\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0000 | −0.568855 | ||||||||
\(446\) | 29.3939 | 1.39184 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 7.07107i | − 0.333704i | −0.985982 | − | 0.166852i | \(-0.946640\pi\) | ||||
0.985982 | − | 0.166852i | \(-0.0533603\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.3923i | 0.489355i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 38.1051i | − 1.78836i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.00000 | 0.233890 | 0.116945 | − | 0.993138i | \(-0.462690\pi\) | ||||
0.116945 | + | 0.993138i | \(0.462690\pi\) | |||||||
\(458\) | 31.8434 | 1.48794 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.6969 | 0.684505 | 0.342252 | − | 0.939608i | \(-0.388810\pi\) | ||||
0.342252 | + | 0.939608i | \(0.388810\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.0000 | −0.604161 | −0.302081 | − | 0.953282i | \(-0.597681\pi\) | ||||
−0.302081 | + | 0.953282i | \(0.597681\pi\) | |||||||
\(464\) | 11.3137i | 0.525226i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.0000 | −0.648537 | ||||||||
\(467\) | 26.9444 | 1.24684 | 0.623419 | − | 0.781888i | \(-0.285743\pi\) | ||||
0.623419 | + | 0.781888i | \(0.285743\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 42.4264i | − 1.95698i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 13.8564i | − 0.637793i | ||||||||
\(473\) | − 1.41421i | − 0.0650256i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1.73205i | − 0.0794719i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −38.0000 | −1.73808 | ||||||||
\(479\) | −4.89898 | −0.223840 | −0.111920 | − | 0.993717i | \(-0.535700\pi\) | ||||
−0.111920 | + | 0.993717i | \(0.535700\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 5.19615i | − 0.236924i | ||||||||
\(482\) | 19.5959 | 0.892570 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 25.4558i | − 1.15589i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.0000 | 0.770344 | 0.385172 | − | 0.922845i | \(-0.374142\pi\) | ||||
0.385172 | + | 0.922845i | \(0.374142\pi\) | |||||||
\(488\) | −9.79796 | −0.443533 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 11.3137i | − 0.510581i | −0.966864 | − | 0.255290i | \(-0.917829\pi\) | ||||
0.966864 | − | 0.255290i | \(-0.0821710\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.8564i | 0.624061i | ||||||||
\(494\) | 12.7279i | 0.572656i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 6.92820i | − 0.311086i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.0000 | −1.11915 | −0.559577 | − | 0.828778i | \(-0.689036\pi\) | ||||
−0.559577 | + | 0.828778i | \(0.689036\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.0454 | −0.982956 | −0.491478 | − | 0.870890i | \(-0.663543\pi\) | ||||
−0.491478 | + | 0.870890i | \(0.663543\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −42.0000 | −1.86898 | ||||||||
\(506\) | − 11.3137i | − 0.502956i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.44949 | −0.108572 | −0.0542859 | − | 0.998525i | \(-0.517288\pi\) | ||||
−0.0542859 | + | 0.998525i | \(0.517288\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 22.6274i | − 1.00000i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 3.46410i | − 0.152795i | ||||||||
\(515\) | − 21.2132i | − 0.934765i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.3205i | 0.761755i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 36.0000 | 1.57870 | ||||||||
\(521\) | −4.89898 | −0.214628 | −0.107314 | − | 0.994225i | \(-0.534225\pi\) | ||||
−0.107314 | + | 0.994225i | \(0.534225\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.73205i | − 0.0757373i | −0.999283 | − | 0.0378686i | \(-0.987943\pi\) | ||||
0.999283 | − | 0.0378686i | \(-0.0120568\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.0000 | −0.872041 | ||||||||
\(527\) | − 8.48528i | − 0.369625i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.00000 | −0.391304 | ||||||||
\(530\) | −9.79796 | −0.425596 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 38.1838i | 1.65392i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.92820i | 0.299532i | ||||||||
\(536\) | 31.1127i | 1.34386i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24.2487i | 1.04544i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0000 | 0.730887 | 0.365444 | − | 0.930834i | \(-0.380917\pi\) | ||||
0.365444 | + | 0.930834i | \(0.380917\pi\) | |||||||
\(542\) | −19.5959 | −0.841717 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.44949 | 0.104925 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.0000 | −0.427569 | −0.213785 | − | 0.976881i | \(-0.568579\pi\) | ||||
−0.213785 | + | 0.976881i | \(0.568579\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.00000 | −0.0852803 | ||||||||
\(551\) | −4.89898 | −0.208704 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 32.5269i | 1.38194i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 15.5563i | − 0.659144i | −0.944131 | − | 0.329572i | \(-0.893096\pi\) | ||||
0.944131 | − | 0.329572i | \(-0.106904\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 5.19615i | − 0.219774i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −32.0000 | −1.34984 | ||||||||
\(563\) | −26.9444 | −1.13557 | −0.567785 | − | 0.823177i | \(-0.692200\pi\) | ||||
−0.567785 | + | 0.823177i | \(0.692200\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 3.46410i | − 0.145736i | ||||||||
\(566\) | −2.44949 | −0.102960 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 20.0000 | 0.839181 | ||||||||
\(569\) | 1.41421i | 0.0592869i | 0.999561 | + | 0.0296435i | \(0.00943719\pi\) | ||||
−0.999561 | + | 0.0296435i | \(0.990563\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.0000 | 0.460336 | 0.230168 | − | 0.973151i | \(-0.426072\pi\) | ||||
0.230168 | + | 0.973151i | \(0.426072\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.65685i | 0.235907i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.73205i | 0.0721062i | 0.999350 | + | 0.0360531i | \(0.0114785\pi\) | ||||
−0.999350 | + | 0.0360531i | \(0.988521\pi\) | |||||||
\(578\) | 9.89949i | 0.411765i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00000 | 0.165663 | ||||||||
\(584\) | −4.89898 | −0.202721 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 20.7846i | − 0.858604i | ||||||||
\(587\) | 14.6969 | 0.606608 | 0.303304 | − | 0.952894i | \(-0.401910\pi\) | ||||
0.303304 | + | 0.952894i | \(0.401910\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.00000 | 0.123613 | ||||||||
\(590\) | 16.9706i | 0.698667i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.00000 | 0.164399 | ||||||||
\(593\) | −17.1464 | −0.704119 | −0.352060 | − | 0.935978i | \(-0.614519\pi\) | ||||
−0.352060 | + | 0.935978i | \(0.614519\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 41.5692i | − 1.69989i | ||||||||
\(599\) | 5.65685i | 0.231133i | 0.993300 | + | 0.115566i | \(0.0368683\pi\) | ||||
−0.993300 | + | 0.115566i | \(0.963132\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.9808i | 1.05978i | 0.848067 | + | 0.529889i | \(0.177766\pi\) | ||||
−0.848067 | + | 0.529889i | \(0.822234\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.0454 | −0.896273 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.8372i | 1.61694i | 0.588537 | + | 0.808470i | \(0.299704\pi\) | ||||
−0.588537 | + | 0.808470i | \(0.700296\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.0000 | 0.485866 | ||||||||
\(611\) | 63.6396i | 2.57458i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.00000 | 0.323117 | 0.161558 | − | 0.986863i | \(-0.448348\pi\) | ||||
0.161558 | + | 0.986863i | \(0.448348\pi\) | |||||||
\(614\) | −22.0454 | −0.889680 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 24.0416i | − 0.967880i | −0.875101 | − | 0.483940i | \(-0.839205\pi\) | ||||
0.875101 | − | 0.483940i | \(-0.160795\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 29.4449i | − 1.18349i | −0.806126 | − | 0.591744i | \(-0.798439\pi\) | ||||
0.806126 | − | 0.591744i | \(-0.201561\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.2487i | 0.972285i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 17.1464 | 0.685309 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.89898 | 0.195335 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.0000 | 1.51276 | 0.756378 | − | 0.654135i | \(-0.226967\pi\) | ||||
0.756378 | + | 0.654135i | \(0.226967\pi\) | |||||||
\(632\) | 14.1421i | 0.562544i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −20.0000 | −0.794301 | ||||||||
\(635\) | −26.9444 | −1.06926 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.65685i | 0.223957i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 27.7128i | 1.09545i | ||||||||
\(641\) | 14.1421i | 0.558581i | 0.960207 | + | 0.279290i | \(0.0900992\pi\) | ||||
−0.960207 | + | 0.279290i | \(0.909901\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 25.9808i | − 1.02458i | −0.858812 | − | 0.512291i | \(-0.828797\pi\) | ||||
0.858812 | − | 0.512291i | \(-0.171203\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.0000 | −0.472134 | ||||||||
\(647\) | 17.1464 | 0.674096 | 0.337048 | − | 0.941488i | \(-0.390572\pi\) | ||||
0.337048 | + | 0.941488i | \(0.390572\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 6.92820i | − 0.271956i | ||||||||
\(650\) | −7.34847 | −0.288231 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 7.07107i | − 0.276712i | −0.990383 | − | 0.138356i | \(-0.955818\pi\) | ||||
0.990383 | − | 0.138356i | \(-0.0441819\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.00000 | 0.234439 | ||||||||
\(656\) | −29.3939 | −1.14764 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.6274i | 0.881439i | 0.897645 | + | 0.440720i | \(0.145277\pi\) | ||||
−0.897645 | + | 0.440720i | \(0.854723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 29.4449i | − 1.14527i | −0.819810 | − | 0.572636i | \(-0.805921\pi\) | ||||
0.819810 | − | 0.572636i | \(-0.194079\pi\) | |||||||
\(662\) | − 43.8406i | − 1.70391i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − 20.7846i | − 0.806599i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.0000 | 0.619522 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 38.1051i | − 1.47213i | ||||||||
\(671\) | −4.89898 | −0.189123 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.0000 | 1.34915 | 0.674575 | − | 0.738206i | \(-0.264327\pi\) | ||||
0.674575 | + | 0.738206i | \(0.264327\pi\) | |||||||
\(674\) | 32.5269i | 1.25289i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.79796 | −0.376566 | −0.188283 | − | 0.982115i | \(-0.560292\pi\) | ||||
−0.188283 | + | 0.982115i | \(0.560292\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 33.9411i | 1.30158i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 3.46410i | − 0.132647i | ||||||||
\(683\) | 48.0833i | 1.83985i | 0.392089 | + | 0.919927i | \(0.371753\pi\) | ||||
−0.392089 | + | 0.919927i | \(0.628247\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.7128i | 1.05885i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.00000 | 0.152499 | ||||||||
\(689\) | 14.6969 | 0.559909 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 43.3013i | − 1.64726i | −0.567129 | − | 0.823629i | \(-0.691946\pi\) | ||||
0.567129 | − | 0.823629i | \(-0.308054\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −44.0000 | −1.67022 | ||||||||
\(695\) | − 12.7279i | − 0.482798i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −36.0000 | −1.36360 | ||||||||
\(698\) | −14.6969 | −0.556287 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.65685i | 0.213656i | 0.994277 | + | 0.106828i | \(0.0340695\pi\) | ||||
−0.994277 | + | 0.106828i | \(0.965931\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.73205i | 0.0653255i | ||||||||
\(704\) | − 11.3137i | − 0.426401i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.2487i | 0.912612i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.0000 | −1.50223 | −0.751116 | − | 0.660171i | \(-0.770484\pi\) | ||||
−0.751116 | + | 0.660171i | \(0.770484\pi\) | |||||||
\(710\) | −24.4949 | −0.919277 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.8564i | 0.519291i | ||||||||
\(713\) | −9.79796 | −0.366936 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.0000 | 0.673162 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 40.0000 | 1.49279 | ||||||||
\(719\) | 26.9444 | 1.00486 | 0.502428 | − | 0.864619i | \(-0.332440\pi\) | ||||
0.502428 | + | 0.864619i | \(0.332440\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 22.6274i | 0.842105i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 2.82843i | − 0.105045i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.9808i | 0.963573i | 0.876289 | + | 0.481787i | \(0.160012\pi\) | ||||
−0.876289 | + | 0.481787i | \(0.839988\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.00000 | 0.222070 | ||||||||
\(731\) | 4.89898 | 0.181195 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.8372i | 1.47142i | 0.677297 | + | 0.735710i | \(0.263151\pi\) | ||||
−0.677297 | + | 0.735710i | \(0.736849\pi\) | |||||||
\(734\) | −2.44949 | −0.0904123 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.5563i | 0.573025i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.00000 | −0.0367856 | −0.0183928 | − | 0.999831i | \(-0.505855\pi\) | ||||
−0.0183928 | + | 0.999831i | \(0.505855\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 24.0416i | − 0.882002i | −0.897507 | − | 0.441001i | \(-0.854624\pi\) | ||||
0.897507 | − | 0.441001i | \(-0.145376\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 13.8564i | − 0.507659i | ||||||||
\(746\) | 41.0122i | 1.50156i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.0000 | 1.05823 | 0.529113 | − | 0.848552i | \(-0.322525\pi\) | ||||
0.529113 | + | 0.848552i | \(0.322525\pi\) | |||||||
\(752\) | −48.9898 | −1.78647 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 20.7846i | 0.756931i | ||||||||
\(755\) | 53.8888 | 1.96121 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | − 9.89949i | − 0.359566i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.0000 | −0.435286 | ||||||||
\(761\) | −24.4949 | −0.887939 | −0.443970 | − | 0.896042i | \(-0.646430\pi\) | ||||
−0.443970 | + | 0.896042i | \(0.646430\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.7128i | 1.00130i | ||||||||
\(767\) | − 25.4558i | − 0.919157i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 25.9808i | − 0.936890i | −0.883493 | − | 0.468445i | \(-0.844814\pi\) | ||||
0.883493 | − | 0.468445i | \(-0.155186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.9444 | −0.969122 | −0.484561 | − | 0.874757i | \(-0.661021\pi\) | ||||
−0.484561 | + | 0.874757i | \(0.661021\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.73205i | 0.0622171i | ||||||||
\(776\) | −29.3939 | −1.05518 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −38.0000 | −1.36237 | ||||||||
\(779\) | − 12.7279i | − 0.456025i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0000 | 0.357828 | ||||||||
\(782\) | 39.1918 | 1.40150 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 42.4264i | − 1.51426i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 45.0333i | − 1.60526i | −0.596474 | − | 0.802632i | \(-0.703432\pi\) | ||||
0.596474 | − | 0.802632i | \(-0.296568\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 17.3205i | − 0.616236i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.0000 | −0.639199 | ||||||||
\(794\) | 2.44949 | 0.0869291 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.3939 | 1.04118 | 0.520592 | − | 0.853805i | \(-0.325711\pi\) | ||||
0.520592 | + | 0.853805i | \(0.325711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −60.0000 | −2.12265 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28.0000 | 0.988714 | ||||||||
\(803\) | −2.44949 | −0.0864406 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 12.7279i | − 0.448322i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 48.4974i | 1.70613i | ||||||||
\(809\) | − 41.0122i | − 1.44191i | −0.692981 | − | 0.720956i | \(-0.743703\pi\) | ||||
0.692981 | − | 0.720956i | \(-0.256297\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.1769i | 1.09477i | 0.836881 | + | 0.547385i | \(0.184377\pi\) | ||||
−0.836881 | + | 0.547385i | \(0.815623\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.00000 | 0.0701000 | ||||||||
\(815\) | 24.4949 | 0.858019 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.73205i | 0.0605968i | ||||||||
\(818\) | −46.5403 | −1.62724 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 24.0416i | − 0.839059i | −0.907742 | − | 0.419529i | \(-0.862195\pi\) | ||||
0.907742 | − | 0.419529i | \(-0.137805\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.0000 | −1.18517 | −0.592583 | − | 0.805510i | \(-0.701892\pi\) | ||||
−0.592583 | + | 0.805510i | \(0.701892\pi\) | |||||||
\(824\) | −24.4949 | −0.853320 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 7.07107i | − 0.245885i | −0.992414 | − | 0.122943i | \(-0.960767\pi\) | ||||
0.992414 | − | 0.122943i | \(-0.0392331\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.73205i | 0.0601566i | 0.999548 | + | 0.0300783i | \(0.00957567\pi\) | ||||
−0.999548 | + | 0.0300783i | \(0.990424\pi\) | |||||||
\(830\) | 25.4558i | 0.883585i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 41.5692i | − 1.44115i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.0000 | −0.622916 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 51.9615i | − 1.79498i | ||||||||
\(839\) | 14.6969 | 0.507395 | 0.253697 | − | 0.967284i | \(-0.418353\pi\) | ||||
0.253697 | + | 0.967284i | \(0.418353\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | − 1.41421i | − 0.0487370i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 34.2929 | 1.17971 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11.3137i | 0.388514i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 6.92820i | − 0.237635i | ||||||||
\(851\) | − 5.65685i | − 0.193914i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 36.3731i | − 1.24539i | −0.782465 | − | 0.622695i | \(-0.786038\pi\) | ||||
0.782465 | − | 0.622695i | \(-0.213962\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.00000 | 0.273434 | ||||||||
\(857\) | 39.1918 | 1.33877 | 0.669384 | − | 0.742917i | \(-0.266558\pi\) | ||||
0.669384 | + | 0.742917i | \(0.266558\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 38.1051i | − 1.30013i | −0.759879 | − | 0.650065i | \(-0.774742\pi\) | ||||
0.759879 | − | 0.650065i | \(-0.225258\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 22.0000 | 0.749323 | ||||||||
\(863\) | − 41.0122i | − 1.39607i | −0.716063 | − | 0.698036i | \(-0.754058\pi\) | ||||
0.716063 | − | 0.698036i | \(-0.245942\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.0000 | 0.816024 | ||||||||
\(866\) | 22.0454 | 0.749133 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.07107i | 0.239870i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 57.1577i | 1.93671i | ||||||||
\(872\) | − 2.82843i | − 0.0957826i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.8564i | 0.468700i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.0000 | 0.675352 | 0.337676 | − | 0.941262i | \(-0.390359\pi\) | ||||
0.337676 | + | 0.941262i | \(0.390359\pi\) | |||||||
\(878\) | 39.1918 | 1.32266 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 13.8564i | 0.467099i | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.0000 | 0.370179 | 0.185090 | − | 0.982722i | \(-0.440742\pi\) | ||||
0.185090 | + | 0.982722i | \(0.440742\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −56.0000 | −1.88136 | ||||||||
\(887\) | 41.6413 | 1.39818 | 0.699089 | − | 0.715034i | \(-0.253589\pi\) | ||||
0.699089 | + | 0.715034i | \(0.253589\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 16.9706i | − 0.568855i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 21.2132i | − 0.709873i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 24.2487i | − 0.810545i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.0000 | 0.333704 | ||||||||
\(899\) | 4.89898 | 0.163390 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.8564i | 0.461624i | ||||||||
\(902\) | −14.6969 | −0.489355 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.00000 | −0.133038 | ||||||||
\(905\) | 38.1838i | 1.26927i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.00000 | 0.166022 | 0.0830111 | − | 0.996549i | \(-0.473546\pi\) | ||||
0.0830111 | + | 0.996549i | \(0.473546\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 53.7401i | − 1.78049i | −0.455483 | − | 0.890245i | \(-0.650533\pi\) | ||||
0.455483 | − | 0.890245i | \(-0.349467\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 10.3923i | − 0.343935i | ||||||||
\(914\) | 7.07107i | 0.233890i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.0000 | 0.560778 | 0.280389 | − | 0.959886i | \(-0.409536\pi\) | ||||
0.280389 | + | 0.959886i | \(0.409536\pi\) | |||||||
\(920\) | 39.1918 | 1.29212 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.7846i | 0.684505i | ||||||||
\(923\) | 36.7423 | 1.20939 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00000 | −0.0328798 | ||||||||
\(926\) | − 18.3848i | − 0.604161i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 56.3383 | 1.84840 | 0.924199 | − | 0.381911i | \(-0.124734\pi\) | ||||
0.924199 | + | 0.381911i | \(0.124734\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 38.1051i | 1.24684i | ||||||||
\(935\) | 16.9706i | 0.554997i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 46.7654i | − 1.52776i | −0.645359 | − | 0.763879i | \(-0.723292\pi\) | ||||
0.645359 | − | 0.763879i | \(-0.276708\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48.9898 | −1.59702 | −0.798511 | − | 0.601980i | \(-0.794379\pi\) | ||||
−0.798511 | + | 0.601980i | \(0.794379\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41.5692i | 1.35368i | ||||||||
\(944\) | 19.5959 | 0.637793 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.00000 | 0.0650256 | ||||||||
\(947\) | − 49.4975i | − 1.60845i | −0.594324 | − | 0.804226i | \(-0.702580\pi\) | ||||
0.594324 | − | 0.804226i | \(-0.297420\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.00000 | −0.292152 | ||||||||
\(950\) | 2.44949 | 0.0794719 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.65685i | 0.183243i | 0.995794 | + | 0.0916217i | \(0.0292051\pi\) | ||||
−0.995794 | + | 0.0916217i | \(0.970795\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 3.46410i | − 0.112096i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 6.92820i | − 0.223840i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | 7.34847 | 0.236924 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −26.9444 | −0.867371 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.0000 | −0.418052 | −0.209026 | − | 0.977910i | \(-0.567029\pi\) | ||||
−0.209026 | + | 0.977910i | \(0.567029\pi\) | |||||||
\(968\) | 25.4558i | 0.818182i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 36.0000 | 1.15589 | ||||||||
\(971\) | −39.1918 | −1.25773 | −0.628863 | − | 0.777516i | \(-0.716479\pi\) | ||||
−0.628863 | + | 0.777516i | \(0.716479\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 24.0416i | 0.770344i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 13.8564i | − 0.443533i | ||||||||
\(977\) | − 7.07107i | − 0.226224i | −0.993582 | − | 0.113112i | \(-0.963918\pi\) | ||||
0.993582 | − | 0.113112i | \(-0.0360818\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.92820i | 0.221426i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 16.0000 | 0.510581 | ||||||||
\(983\) | −4.89898 | −0.156253 | −0.0781266 | − | 0.996943i | \(-0.524894\pi\) | ||||
−0.0781266 | + | 0.996943i | \(0.524894\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48.4974i | 1.54526i | ||||||||
\(986\) | −19.5959 | −0.624061 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 5.65685i | − 0.179878i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.0000 | 1.11181 | 0.555906 | − | 0.831245i | \(-0.312372\pi\) | ||||
0.555906 | + | 0.831245i | \(0.312372\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33.9411i | 1.07601i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 29.4449i | − 0.932528i | −0.884646 | − | 0.466264i | \(-0.845600\pi\) | ||||
0.884646 | − | 0.466264i | \(-0.154400\pi\) | |||||||
\(998\) | − 35.3553i | − 1.11915i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))