Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(107,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.f (of order \(4\), degree \(2\), 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: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 107.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.107 |
Dual form | 450.2.f.b.143.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | − | 2.00000i | −0.755929 | − | 0.755929i | 0.219650 | − | 0.975579i | \(-0.429509\pi\) |
−0.975579 | + | 0.219650i | \(0.929509\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.82843i | 0.852803i | 0.904534 | + | 0.426401i | \(0.140219\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | − | 3.00000i | 0.832050 | − | 0.832050i | −0.155747 | − | 0.987797i | \(-0.549778\pi\) |
0.987797 | + | 0.155747i | \(0.0497784\pi\) | |||||||
\(14\) | 2.82843 | 0.755929 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.82843 | − | 2.82843i | 0.685994 | − | 0.685994i | −0.275350 | − | 0.961344i | \(-0.588794\pi\) |
0.961344 | + | 0.275350i | \(0.0887937\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 8.00000i | − | 1.83533i | −0.397360 | − | 0.917663i | \(-0.630073\pi\) | ||
0.397360 | − | 0.917663i | \(-0.369927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | − | 2.00000i | −0.426401 | − | 0.426401i | ||||
\(23\) | −2.82843 | − | 2.82843i | −0.589768 | − | 0.589768i | 0.347801 | − | 0.937568i | \(-0.386929\pi\) |
−0.937568 | + | 0.347801i | \(0.886929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.24264i | 0.832050i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | + | 2.00000i | −0.377964 | + | 0.377964i | ||||
\(29\) | 1.41421 | 0.262613 | 0.131306 | − | 0.991342i | \(-0.458083\pi\) | ||||
0.131306 | + | 0.991342i | \(0.458083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.00000i | 0.685994i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | + | 3.00000i | 0.493197 | + | 0.493197i | 0.909312 | − | 0.416115i | \(-0.136609\pi\) |
−0.416115 | + | 0.909312i | \(0.636609\pi\) | |||||||
\(38\) | 5.65685 | + | 5.65685i | 0.917663 | + | 0.917663i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.89949i | − | 1.54604i | −0.634381 | − | 0.773021i | \(-0.718745\pi\) | ||
0.634381 | − | 0.773021i | \(-0.281255\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(44\) | 2.82843 | 0.426401 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.00000 | 0.589768 | ||||||||
\(47\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.00000 | − | 3.00000i | −0.416025 | − | 0.416025i | ||||
\(53\) | 2.82843 | + | 2.82843i | 0.388514 | + | 0.388514i | 0.874157 | − | 0.485643i | \(-0.161414\pi\) |
−0.485643 | + | 0.874157i | \(0.661414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 2.82843i | − | 0.377964i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.00000 | + | 1.00000i | −0.131306 | + | 0.131306i | ||||
\(59\) | −2.82843 | −0.368230 | −0.184115 | − | 0.982905i | \(-0.558942\pi\) | ||||
−0.184115 | + | 0.982905i | \(0.558942\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | −2.82843 | + | 2.82843i | −0.359211 | + | 0.359211i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | + | 4.00000i | 0.488678 | + | 0.488678i | 0.907889 | − | 0.419211i | \(-0.137693\pi\) |
−0.419211 | + | 0.907889i | \(0.637693\pi\) | |||||||
\(68\) | −2.82843 | − | 2.82843i | −0.342997 | − | 0.342997i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.65685i | 0.671345i | 0.941979 | + | 0.335673i | \(0.108964\pi\) | ||||
−0.941979 | + | 0.335673i | \(0.891036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | + | 1.00000i | −0.117041 | + | 0.117041i | −0.763202 | − | 0.646160i | \(-0.776374\pi\) |
0.646160 | + | 0.763202i | \(0.276374\pi\) | |||||||
\(74\) | −4.24264 | −0.493197 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.00000 | −0.917663 | ||||||||
\(77\) | 5.65685 | − | 5.65685i | 0.644658 | − | 0.644658i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000i | 1.35011i | 0.737769 | + | 0.675053i | \(0.235879\pi\) | ||||
−0.737769 | + | 0.675053i | \(0.764121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.00000 | + | 7.00000i | 0.773021 | + | 0.773021i | ||||
\(83\) | −8.48528 | − | 8.48528i | −0.931381 | − | 0.931381i | 0.0664117 | − | 0.997792i | \(-0.478845\pi\) |
−0.997792 | + | 0.0664117i | \(0.978845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.00000 | + | 2.00000i | −0.213201 | + | 0.213201i | ||||
\(89\) | −9.89949 | −1.04934 | −0.524672 | − | 0.851304i | \(-0.675812\pi\) | ||||
−0.524672 | + | 0.851304i | \(0.675812\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.0000 | −1.25794 | ||||||||
\(92\) | −2.82843 | + | 2.82843i | −0.294884 | + | 0.294884i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.00000 | + | 3.00000i | 0.304604 | + | 0.304604i | 0.842812 | − | 0.538208i | \(-0.180899\pi\) |
−0.538208 | + | 0.842812i | \(0.680899\pi\) | |||||||
\(98\) | −0.707107 | − | 0.707107i | −0.0714286 | − | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.41421i | 0.140720i | 0.997522 | + | 0.0703598i | \(0.0224147\pi\) | ||||
−0.997522 | + | 0.0703598i | \(0.977585\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | − | 2.00000i | 0.197066 | − | 0.197066i | −0.601675 | − | 0.798741i | \(-0.705500\pi\) |
0.798741 | + | 0.601675i | \(0.205500\pi\) | |||||||
\(104\) | 4.24264 | 0.416025 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | −14.1421 | + | 14.1421i | −1.36717 | + | 1.36717i | −0.502726 | + | 0.864446i | \(0.667670\pi\) |
−0.864446 | + | 0.502726i | \(0.832330\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000i | 0.766261i | 0.923694 | + | 0.383131i | \(0.125154\pi\) | ||||
−0.923694 | + | 0.383131i | \(0.874846\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.00000 | + | 2.00000i | 0.188982 | + | 0.188982i | ||||
\(113\) | −1.41421 | − | 1.41421i | −0.133038 | − | 0.133038i | 0.637452 | − | 0.770490i | \(-0.279988\pi\) |
−0.770490 | + | 0.637452i | \(0.779988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 1.41421i | − | 0.131306i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.00000 | − | 2.00000i | 0.184115 | − | 0.184115i | ||||
\(119\) | −11.3137 | −1.03713 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 4.00000i | − | 0.359211i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.0000 | − | 14.0000i | −1.24230 | − | 1.24230i | −0.959045 | − | 0.283254i | \(-0.908586\pi\) |
−0.283254 | − | 0.959045i | \(-0.591414\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 14.1421i | − | 1.23560i | −0.786334 | − | 0.617802i | \(-0.788023\pi\) | ||
0.786334 | − | 0.617802i | \(-0.211977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.0000 | + | 16.0000i | −1.38738 | + | 1.38738i | ||||
\(134\) | −5.65685 | −0.488678 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.00000 | 0.342997 | ||||||||
\(137\) | −4.24264 | + | 4.24264i | −0.362473 | + | 0.362473i | −0.864723 | − | 0.502249i | \(-0.832506\pi\) |
0.502249 | + | 0.864723i | \(0.332506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.00000i | − | 0.339276i | −0.985506 | − | 0.169638i | \(-0.945740\pi\) | ||
0.985506 | − | 0.169638i | \(-0.0542598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.00000 | − | 4.00000i | −0.335673 | − | 0.335673i | ||||
\(143\) | 8.48528 | + | 8.48528i | 0.709575 | + | 0.709575i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 1.41421i | − | 0.117041i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.00000 | − | 3.00000i | 0.246598 | − | 0.246598i | ||||
\(149\) | 21.2132 | 1.73785 | 0.868927 | − | 0.494941i | \(-0.164810\pi\) | ||||
0.868927 | + | 0.494941i | \(0.164810\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 5.65685 | − | 5.65685i | 0.458831 | − | 0.458831i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.00000i | 0.644658i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | + | 9.00000i | 0.718278 | + | 0.718278i | 0.968252 | − | 0.249974i | \(-0.0804222\pi\) |
−0.249974 | + | 0.968252i | \(0.580422\pi\) | |||||||
\(158\) | −8.48528 | − | 8.48528i | −0.675053 | − | 0.675053i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.3137i | 0.891645i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.0000 | − | 16.0000i | 1.25322 | − | 1.25322i | 0.298947 | − | 0.954270i | \(-0.403365\pi\) |
0.954270 | − | 0.298947i | \(-0.0966354\pi\) | |||||||
\(164\) | −9.89949 | −0.773021 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.0000 | 0.931381 | ||||||||
\(167\) | −2.82843 | + | 2.82843i | −0.218870 | + | 0.218870i | −0.808022 | − | 0.589152i | \(-0.799462\pi\) |
0.589152 | + | 0.808022i | \(0.299462\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.89949 | + | 9.89949i | 0.752645 | + | 0.752645i | 0.974972 | − | 0.222327i | \(-0.0713654\pi\) |
−0.222327 | + | 0.974972i | \(0.571365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 2.82843i | − | 0.213201i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.00000 | − | 7.00000i | 0.524672 | − | 0.524672i | ||||
\(179\) | 2.82843 | 0.211407 | 0.105703 | − | 0.994398i | \(-0.466291\pi\) | ||||
0.105703 | + | 0.994398i | \(0.466291\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | 8.48528 | − | 8.48528i | 0.628971 | − | 0.628971i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 4.00000i | − | 0.294884i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00000 | + | 8.00000i | 0.585018 | + | 0.585018i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.6274i | 1.63726i | 0.574320 | + | 0.818631i | \(0.305267\pi\) | ||||
−0.574320 | + | 0.818631i | \(0.694733\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.00000 | + | 9.00000i | −0.647834 | + | 0.647834i | −0.952469 | − | 0.304635i | \(-0.901466\pi\) |
0.304635 | + | 0.952469i | \(0.401466\pi\) | |||||||
\(194\) | −4.24264 | −0.304604 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 12.7279 | − | 12.7279i | 0.906827 | − | 0.906827i | −0.0891879 | − | 0.996015i | \(-0.528427\pi\) |
0.996015 | + | 0.0891879i | \(0.0284272\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.00000 | − | 1.00000i | −0.0703598 | − | 0.0703598i | ||||
\(203\) | −2.82843 | − | 2.82843i | −0.198517 | − | 0.198517i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.82843i | 0.197066i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.00000 | + | 3.00000i | −0.208013 | + | 0.208013i | ||||
\(209\) | 22.6274 | 1.56517 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 2.82843 | − | 2.82843i | 0.194257 | − | 0.194257i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 20.0000i | − | 1.36717i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.00000 | − | 8.00000i | −0.543075 | − | 0.543075i | ||||
\(218\) | −5.65685 | − | 5.65685i | −0.383131 | − | 0.383131i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 16.9706i | − | 1.14156i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.00000 | + | 6.00000i | −0.401790 | + | 0.401790i | −0.878863 | − | 0.477074i | \(-0.841698\pi\) |
0.477074 | + | 0.878863i | \(0.341698\pi\) | |||||||
\(224\) | −2.82843 | −0.188982 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.00000 | 0.133038 | ||||||||
\(227\) | 5.65685 | − | 5.65685i | 0.375459 | − | 0.375459i | −0.494002 | − | 0.869461i | \(-0.664466\pi\) |
0.869461 | + | 0.494002i | \(0.164466\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.00000i | − | 0.396491i | −0.980152 | − | 0.198246i | \(-0.936476\pi\) | ||
0.980152 | − | 0.198246i | \(-0.0635244\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.00000 | + | 1.00000i | 0.0656532 | + | 0.0656532i | ||||
\(233\) | 8.48528 | + | 8.48528i | 0.555889 | + | 0.555889i | 0.928134 | − | 0.372245i | \(-0.121412\pi\) |
−0.372245 | + | 0.928134i | \(0.621412\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.82843i | 0.184115i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.00000 | − | 8.00000i | 0.518563 | − | 0.518563i | ||||
\(239\) | 16.9706 | 1.09773 | 0.548867 | − | 0.835910i | \(-0.315059\pi\) | ||||
0.548867 | + | 0.835910i | \(0.315059\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.0000 | 1.41714 | 0.708572 | − | 0.705638i | \(-0.249340\pi\) | ||||
0.708572 | + | 0.705638i | \(0.249340\pi\) | |||||||
\(242\) | −2.12132 | + | 2.12132i | −0.136364 | + | 0.136364i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.0000 | − | 24.0000i | −1.52708 | − | 1.52708i | ||||
\(248\) | 2.82843 | + | 2.82843i | 0.179605 | + | 0.179605i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.48528i | 0.535586i | 0.963476 | + | 0.267793i | \(0.0862944\pi\) | ||||
−0.963476 | + | 0.267793i | \(0.913706\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | − | 8.00000i | 0.502956 | − | 0.502956i | ||||
\(254\) | 19.7990 | 1.24230 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.89949 | − | 9.89949i | 0.617514 | − | 0.617514i | −0.327379 | − | 0.944893i | \(-0.606166\pi\) |
0.944893 | + | 0.327379i | \(0.106166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 12.0000i | − | 0.745644i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.0000 | + | 10.0000i | 0.617802 | + | 0.617802i | ||||
\(263\) | 19.7990 | + | 19.7990i | 1.22086 | + | 1.22086i | 0.967327 | + | 0.253531i | \(0.0815919\pi\) |
0.253531 | + | 0.967327i | \(0.418408\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 22.6274i | − | 1.38738i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.00000 | − | 4.00000i | 0.244339 | − | 0.244339i | ||||
\(269\) | −15.5563 | −0.948487 | −0.474244 | − | 0.880394i | \(-0.657278\pi\) | ||||
−0.474244 | + | 0.880394i | \(0.657278\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | −2.82843 | + | 2.82843i | −0.171499 | + | 0.171499i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 6.00000i | − | 0.362473i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.00000 | − | 9.00000i | −0.540758 | − | 0.540758i | 0.382993 | − | 0.923751i | \(-0.374893\pi\) |
−0.923751 | + | 0.382993i | \(0.874893\pi\) | |||||||
\(278\) | 2.82843 | + | 2.82843i | 0.169638 | + | 0.169638i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.7279i | − | 0.759284i | −0.925133 | − | 0.379642i | \(-0.876047\pi\) | ||
0.925133 | − | 0.379642i | \(-0.123953\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.00000 | + | 8.00000i | −0.475551 | + | 0.475551i | −0.903705 | − | 0.428155i | \(-0.859164\pi\) |
0.428155 | + | 0.903705i | \(0.359164\pi\) | |||||||
\(284\) | 5.65685 | 0.335673 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.0000 | −0.709575 | ||||||||
\(287\) | −19.7990 | + | 19.7990i | −1.16870 | + | 1.16870i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000i | 0.0588235i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.00000 | + | 1.00000i | 0.0585206 | + | 0.0585206i | ||||
\(293\) | −12.7279 | − | 12.7279i | −0.743573 | − | 0.743573i | 0.229691 | − | 0.973264i | \(-0.426229\pi\) |
−0.973264 | + | 0.229691i | \(0.926229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.24264i | 0.246598i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.0000 | + | 15.0000i | −0.868927 | + | 0.868927i | ||||
\(299\) | −16.9706 | −0.981433 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.65685 | − | 5.65685i | 0.325515 | − | 0.325515i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.00000i | 0.458831i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(308\) | −5.65685 | − | 5.65685i | −0.322329 | − | 0.322329i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.6274i | 1.28308i | 0.767088 | + | 0.641542i | \(0.221705\pi\) | ||||
−0.767088 | + | 0.641542i | \(0.778295\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.0000 | − | 21.0000i | 1.18699 | − | 1.18699i | 0.209095 | − | 0.977895i | \(-0.432948\pi\) |
0.977895 | − | 0.209095i | \(-0.0670517\pi\) | |||||||
\(314\) | −12.7279 | −0.718278 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.0000 | 0.675053 | ||||||||
\(317\) | −8.48528 | + | 8.48528i | −0.476581 | + | 0.476581i | −0.904036 | − | 0.427456i | \(-0.859410\pi\) |
0.427456 | + | 0.904036i | \(0.359410\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000i | 0.223957i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.00000 | − | 8.00000i | −0.445823 | − | 0.445823i | ||||
\(323\) | −22.6274 | − | 22.6274i | −1.25902 | − | 1.25902i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 22.6274i | 1.25322i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.00000 | − | 7.00000i | 0.386510 | − | 0.386510i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.0000 | 0.879440 | 0.439720 | − | 0.898135i | \(-0.355078\pi\) | ||||
0.439720 | + | 0.898135i | \(0.355078\pi\) | |||||||
\(332\) | −8.48528 | + | 8.48528i | −0.465690 | + | 0.465690i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 4.00000i | − | 0.218870i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.0000 | + | 21.0000i | 1.14394 | + | 1.14394i | 0.987722 | + | 0.156221i | \(0.0499311\pi\) |
0.156221 | + | 0.987722i | \(0.450069\pi\) | |||||||
\(338\) | 3.53553 | + | 3.53553i | 0.192308 | + | 0.192308i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.3137i | 0.612672i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0000 | + | 12.0000i | −0.647939 | + | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.0000 | −0.752645 | ||||||||
\(347\) | 11.3137 | − | 11.3137i | 0.607352 | − | 0.607352i | −0.334901 | − | 0.942253i | \(-0.608703\pi\) |
0.942253 | + | 0.334901i | \(0.108703\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.0000i | 0.856460i | 0.903670 | + | 0.428230i | \(0.140863\pi\) | ||||
−0.903670 | + | 0.428230i | \(0.859137\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.00000 | + | 2.00000i | 0.106600 | + | 0.106600i | ||||
\(353\) | 8.48528 | + | 8.48528i | 0.451626 | + | 0.451626i | 0.895894 | − | 0.444268i | \(-0.146536\pi\) |
−0.444268 | + | 0.895894i | \(0.646536\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.89949i | 0.524672i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.00000 | + | 2.00000i | −0.105703 | + | 0.105703i | ||||
\(359\) | 11.3137 | 0.597115 | 0.298557 | − | 0.954392i | \(-0.403495\pi\) | ||||
0.298557 | + | 0.954392i | \(0.403495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −45.0000 | −2.36842 | ||||||||
\(362\) | −5.65685 | + | 5.65685i | −0.297318 | + | 0.297318i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.0000i | 0.628971i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.0000 | + | 22.0000i | 1.14839 | + | 1.14839i | 0.986869 | + | 0.161521i | \(0.0516401\pi\) |
0.161521 | + | 0.986869i | \(0.448360\pi\) | |||||||
\(368\) | 2.82843 | + | 2.82843i | 0.147442 | + | 0.147442i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 11.3137i | − | 0.587378i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | − | 5.00000i | 0.258890 | − | 0.258890i | −0.565712 | − | 0.824603i | \(-0.691399\pi\) |
0.824603 | + | 0.565712i | \(0.191399\pi\) | |||||||
\(374\) | −11.3137 | −0.585018 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.24264 | − | 4.24264i | 0.218507 | − | 0.218507i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 20.0000i | − | 1.02733i | −0.857991 | − | 0.513665i | \(-0.828287\pi\) | ||
0.857991 | − | 0.513665i | \(-0.171713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16.0000 | − | 16.0000i | −0.818631 | − | 0.818631i | ||||
\(383\) | −16.9706 | − | 16.9706i | −0.867155 | − | 0.867155i | 0.125001 | − | 0.992157i | \(-0.460106\pi\) |
−0.992157 | + | 0.125001i | \(0.960106\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 12.7279i | − | 0.647834i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.00000 | − | 3.00000i | 0.152302 | − | 0.152302i | ||||
\(389\) | −21.2132 | −1.07555 | −0.537776 | − | 0.843088i | \(-0.680735\pi\) | ||||
−0.537776 | + | 0.843088i | \(0.680735\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | −0.707107 | + | 0.707107i | −0.0357143 | + | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.0000i | 0.906827i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.00000 | − | 7.00000i | −0.351320 | − | 0.351320i | 0.509281 | − | 0.860601i | \(-0.329912\pi\) |
−0.860601 | + | 0.509281i | \(0.829912\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 12.7279i | − | 0.635602i | −0.948157 | − | 0.317801i | \(-0.897056\pi\) | ||
0.948157 | − | 0.317801i | \(-0.102944\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0000 | − | 12.0000i | 0.597763 | − | 0.597763i | ||||
\(404\) | 1.41421 | 0.0703598 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.00000 | 0.198517 | ||||||||
\(407\) | −8.48528 | + | 8.48528i | −0.420600 | + | 0.420600i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.0000i | 1.18672i | 0.804936 | + | 0.593362i | \(0.202200\pi\) | ||||
−0.804936 | + | 0.593362i | \(0.797800\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.00000 | − | 2.00000i | −0.0985329 | − | 0.0985329i | ||||
\(413\) | 5.65685 | + | 5.65685i | 0.278356 | + | 0.278356i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 4.24264i | − | 0.208013i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −16.0000 | + | 16.0000i | −0.782586 | + | 0.782586i | ||||
\(419\) | −25.4558 | −1.24360 | −0.621800 | − | 0.783176i | \(-0.713598\pi\) | ||||
−0.621800 | + | 0.783176i | \(0.713598\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 2.82843 | − | 2.82843i | 0.137686 | − | 0.137686i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.00000i | 0.194257i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 14.1421 | + | 14.1421i | 0.683586 | + | 0.683586i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 39.5980i | − | 1.90737i | −0.300811 | − | 0.953684i | \(-0.597257\pi\) | ||
0.300811 | − | 0.953684i | \(-0.402743\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.0000 | + | 23.0000i | −1.10531 | + | 1.10531i | −0.111551 | + | 0.993759i | \(0.535582\pi\) |
−0.993759 | + | 0.111551i | \(0.964418\pi\) | |||||||
\(434\) | 11.3137 | 0.543075 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.00000 | 0.383131 | ||||||||
\(437\) | −22.6274 | + | 22.6274i | −1.08242 | + | 1.08242i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000i | 0.381819i | 0.981608 | + | 0.190910i | \(0.0611437\pi\) | ||||
−0.981608 | + | 0.190910i | \(0.938856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.0000 | + | 12.0000i | 0.570782 | + | 0.570782i | ||||
\(443\) | −16.9706 | − | 16.9706i | −0.806296 | − | 0.806296i | 0.177775 | − | 0.984071i | \(-0.443110\pi\) |
−0.984071 | + | 0.177775i | \(0.943110\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 8.48528i | − | 0.401790i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.00000 | − | 2.00000i | 0.0944911 | − | 0.0944911i | ||||
\(449\) | 1.41421 | 0.0667409 | 0.0333704 | − | 0.999443i | \(-0.489376\pi\) | ||||
0.0333704 | + | 0.999443i | \(0.489376\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.0000 | 1.31847 | ||||||||
\(452\) | −1.41421 | + | 1.41421i | −0.0665190 | + | 0.0665190i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.00000i | 0.375459i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.0000 | + | 15.0000i | 0.701670 | + | 0.701670i | 0.964769 | − | 0.263099i | \(-0.0847444\pi\) |
−0.263099 | + | 0.964769i | \(0.584744\pi\) | |||||||
\(458\) | 4.24264 | + | 4.24264i | 0.198246 | + | 0.198246i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 18.3848i | − | 0.856264i | −0.903716 | − | 0.428132i | \(-0.859172\pi\) | ||
0.903716 | − | 0.428132i | \(-0.140828\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.0000 | + | 14.0000i | −0.650635 | + | 0.650635i | −0.953146 | − | 0.302511i | \(-0.902175\pi\) |
0.302511 | + | 0.953146i | \(0.402175\pi\) | |||||||
\(464\) | −1.41421 | −0.0656532 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.0000 | −0.555889 | ||||||||
\(467\) | 19.7990 | − | 19.7990i | 0.916188 | − | 0.916188i | −0.0805616 | − | 0.996750i | \(-0.525671\pi\) |
0.996750 | + | 0.0805616i | \(0.0256714\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 16.0000i | − | 0.738811i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.00000 | − | 2.00000i | −0.0920575 | − | 0.0920575i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11.3137i | 0.518563i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.0000 | + | 12.0000i | −0.548867 | + | 0.548867i | ||||
\(479\) | 5.65685 | 0.258468 | 0.129234 | − | 0.991614i | \(-0.458748\pi\) | ||||
0.129234 | + | 0.991614i | \(0.458748\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | 0.820729 | ||||||||
\(482\) | −15.5563 | + | 15.5563i | −0.708572 | + | 0.708572i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 3.00000i | − | 0.136364i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.0000 | + | 18.0000i | 0.815658 | + | 0.815658i | 0.985476 | − | 0.169818i | \(-0.0543179\pi\) |
−0.169818 | + | 0.985476i | \(0.554318\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.82843i | − | 0.127645i | −0.997961 | − | 0.0638226i | \(-0.979671\pi\) | ||
0.997961 | − | 0.0638226i | \(-0.0203292\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.00000 | − | 4.00000i | 0.180151 | − | 0.180151i | ||||
\(494\) | 33.9411 | 1.52708 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 11.3137 | − | 11.3137i | 0.507489 | − | 0.507489i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.0000i | 1.43252i | 0.697835 | + | 0.716258i | \(0.254147\pi\) | ||||
−0.697835 | + | 0.716258i | \(0.745853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.00000 | − | 6.00000i | −0.267793 | − | 0.267793i | ||||
\(503\) | 16.9706 | + | 16.9706i | 0.756680 | + | 0.756680i | 0.975717 | − | 0.219037i | \(-0.0702914\pi\) |
−0.219037 | + | 0.975717i | \(0.570291\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 11.3137i | 0.502956i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.0000 | + | 14.0000i | −0.621150 | + | 0.621150i | ||||
\(509\) | −24.0416 | −1.06563 | −0.532813 | − | 0.846233i | \(-0.678865\pi\) | ||||
−0.532813 | + | 0.846233i | \(0.678865\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.00000 | 0.176950 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.0000i | 0.617514i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 8.48528 | + | 8.48528i | 0.372822 | + | 0.372822i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.6985i | 1.30111i | 0.759457 | + | 0.650557i | \(0.225465\pi\) | ||||
−0.759457 | + | 0.650557i | \(0.774535\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.0000 | − | 24.0000i | 1.04945 | − | 1.04945i | 0.0507346 | − | 0.998712i | \(-0.483844\pi\) |
0.998712 | − | 0.0507346i | \(-0.0161562\pi\) | |||||||
\(524\) | −14.1421 | −0.617802 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.0000 | −1.22086 | ||||||||
\(527\) | 11.3137 | − | 11.3137i | 0.492833 | − | 0.492833i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 7.00000i | − | 0.304348i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16.0000 | + | 16.0000i | 0.693688 | + | 0.693688i | ||||
\(533\) | −29.6985 | − | 29.6985i | −1.28638 | − | 1.28638i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.65685i | 0.244339i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11.0000 | − | 11.0000i | 0.474244 | − | 0.474244i | ||||
\(539\) | −2.82843 | −0.121829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.00000 | −0.343947 | −0.171973 | − | 0.985102i | \(-0.555014\pi\) | ||||
−0.171973 | + | 0.985102i | \(0.555014\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 4.00000i | − | 0.171499i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | − | 12.0000i | −0.513083 | − | 0.513083i | 0.402387 | − | 0.915470i | \(-0.368181\pi\) |
−0.915470 | + | 0.402387i | \(0.868181\pi\) | |||||||
\(548\) | 4.24264 | + | 4.24264i | 0.181237 | + | 0.181237i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 11.3137i | − | 0.481980i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.0000 | − | 24.0000i | 1.02058 | − | 1.02058i | ||||
\(554\) | 12.7279 | 0.540758 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.00000 | −0.169638 | ||||||||
\(557\) | 8.48528 | − | 8.48528i | 0.359533 | − | 0.359533i | −0.504108 | − | 0.863641i | \(-0.668179\pi\) |
0.863641 | + | 0.504108i | \(0.168179\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.00000 | + | 9.00000i | 0.379642 | + | 0.379642i | ||||
\(563\) | 16.9706 | + | 16.9706i | 0.715224 | + | 0.715224i | 0.967623 | − | 0.252399i | \(-0.0812196\pi\) |
−0.252399 | + | 0.967623i | \(0.581220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 11.3137i | − | 0.475551i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.00000 | + | 4.00000i | −0.167836 | + | 0.167836i | ||||
\(569\) | −18.3848 | −0.770730 | −0.385365 | − | 0.922764i | \(-0.625924\pi\) | ||||
−0.385365 | + | 0.922764i | \(0.625924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.00000 | 0.334790 | 0.167395 | − | 0.985890i | \(-0.446465\pi\) | ||||
0.167395 | + | 0.985890i | \(0.446465\pi\) | |||||||
\(572\) | 8.48528 | − | 8.48528i | 0.354787 | − | 0.354787i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 28.0000i | − | 1.16870i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.0000 | − | 31.0000i | −1.29055 | − | 1.29055i | −0.934448 | − | 0.356098i | \(-0.884107\pi\) |
−0.356098 | − | 0.934448i | \(-0.615893\pi\) | |||||||
\(578\) | −0.707107 | − | 0.707107i | −0.0294118 | − | 0.0294118i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 33.9411i | 1.40812i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.00000 | + | 8.00000i | −0.331326 | + | 0.331326i | ||||
\(584\) | −1.41421 | −0.0585206 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.0000 | 0.743573 | ||||||||
\(587\) | 25.4558 | − | 25.4558i | 1.05068 | − | 1.05068i | 0.0520296 | − | 0.998646i | \(-0.483431\pi\) |
0.998646 | − | 0.0520296i | \(-0.0165690\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 32.0000i | − | 1.31854i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.00000 | − | 3.00000i | −0.123299 | − | 0.123299i | ||||
\(593\) | −24.0416 | − | 24.0416i | −0.987271 | − | 0.987271i | 0.0126486 | − | 0.999920i | \(-0.495974\pi\) |
−0.999920 | + | 0.0126486i | \(0.995974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 21.2132i | − | 0.868927i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.0000 | − | 12.0000i | 0.490716 | − | 0.490716i | ||||
\(599\) | 39.5980 | 1.61793 | 0.808965 | − | 0.587857i | \(-0.200028\pi\) | ||||
0.808965 | + | 0.587857i | \(0.200028\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.00000 | 0.326327 | 0.163163 | − | 0.986599i | \(-0.447830\pi\) | ||||
0.163163 | + | 0.986599i | \(0.447830\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.00000i | 0.325515i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.00000 | + | 6.00000i | 0.243532 | + | 0.243532i | 0.818310 | − | 0.574777i | \(-0.194911\pi\) |
−0.574777 | + | 0.818310i | \(0.694911\pi\) | |||||||
\(608\) | −5.65685 | − | 5.65685i | −0.229416 | − | 0.229416i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.00000 | − | 3.00000i | 0.121169 | − | 0.121169i | −0.643922 | − | 0.765091i | \(-0.722694\pi\) |
0.765091 | + | 0.643922i | \(0.222694\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.00000 | 0.322329 | ||||||||
\(617\) | −25.4558 | + | 25.4558i | −1.02481 | + | 1.02481i | −0.0251295 | + | 0.999684i | \(0.508000\pi\) |
−0.999684 | + | 0.0251295i | \(0.992000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 12.0000i | − | 0.482321i | −0.970485 | − | 0.241160i | \(-0.922472\pi\) | ||
0.970485 | − | 0.241160i | \(-0.0775280\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −16.0000 | − | 16.0000i | −0.641542 | − | 0.641542i | ||||
\(623\) | 19.7990 | + | 19.7990i | 0.793230 | + | 0.793230i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 29.6985i | 1.18699i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.00000 | − | 9.00000i | 0.359139 | − | 0.359139i | ||||
\(629\) | 16.9706 | 0.676661 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0000 | −0.796187 | −0.398094 | − | 0.917345i | \(-0.630328\pi\) | ||||
−0.398094 | + | 0.917345i | \(0.630328\pi\) | |||||||
\(632\) | −8.48528 | + | 8.48528i | −0.337526 | + | 0.337526i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 12.0000i | − | 0.476581i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00000 | + | 3.00000i | 0.118864 | + | 0.118864i | ||||
\(638\) | −2.82843 | − | 2.82843i | −0.111979 | − | 0.111979i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.3848i | 0.726155i | 0.931759 | + | 0.363078i | \(0.118274\pi\) | ||||
−0.931759 | + | 0.363078i | \(0.881726\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.0000 | + | 12.0000i | −0.473234 | + | 0.473234i | −0.902959 | − | 0.429726i | \(-0.858610\pi\) |
0.429726 | + | 0.902959i | \(0.358610\pi\) | |||||||
\(644\) | 11.3137 | 0.445823 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 32.0000 | 1.25902 | ||||||||
\(647\) | −11.3137 | + | 11.3137i | −0.444788 | + | 0.444788i | −0.893617 | − | 0.448830i | \(-0.851841\pi\) |
0.448830 | + | 0.893617i | \(0.351841\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 8.00000i | − | 0.314027i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.0000 | − | 16.0000i | −0.626608 | − | 0.626608i | ||||
\(653\) | 25.4558 | + | 25.4558i | 0.996164 | + | 0.996164i | 0.999993 | − | 0.00382851i | \(-0.00121866\pi\) |
−0.00382851 | + | 0.999993i | \(0.501219\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.89949i | 0.386510i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.82843 | 0.110180 | 0.0550899 | − | 0.998481i | \(-0.482455\pi\) | ||||
0.0550899 | + | 0.998481i | \(0.482455\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.0000 | 1.24466 | 0.622328 | − | 0.782757i | \(-0.286187\pi\) | ||||
0.622328 | + | 0.782757i | \(0.286187\pi\) | |||||||
\(662\) | −11.3137 | + | 11.3137i | −0.439720 | + | 0.439720i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 12.0000i | − | 0.465690i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.00000 | − | 4.00000i | −0.154881 | − | 0.154881i | ||||
\(668\) | 2.82843 | + | 2.82843i | 0.109435 | + | 0.109435i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.0000 | + | 25.0000i | −0.963679 | + | 0.963679i | −0.999363 | − | 0.0356839i | \(-0.988639\pi\) |
0.0356839 | + | 0.999363i | \(0.488639\pi\) | |||||||
\(674\) | −29.6985 | −1.14394 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.00000 | −0.192308 | ||||||||
\(677\) | −14.1421 | + | 14.1421i | −0.543526 | + | 0.543526i | −0.924561 | − | 0.381034i | \(-0.875568\pi\) |
0.381034 | + | 0.924561i | \(0.375568\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 12.0000i | − | 0.460518i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.00000 | − | 8.00000i | −0.306336 | − | 0.306336i | ||||
\(683\) | −8.48528 | − | 8.48528i | −0.324680 | − | 0.324680i | 0.525879 | − | 0.850559i | \(-0.323736\pi\) |
−0.850559 | + | 0.525879i | \(0.823736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 16.9706i | − | 0.647939i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.9706 | 0.646527 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | 9.89949 | − | 9.89949i | 0.376322 | − | 0.376322i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.0000i | 0.607352i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.0000 | − | 28.0000i | −1.06058 | − | 1.06058i | ||||
\(698\) | −11.3137 | − | 11.3137i | −0.428230 | − | 0.428230i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 35.3553i | − | 1.33535i | −0.744452 | − | 0.667676i | \(-0.767289\pi\) | ||
0.744452 | − | 0.667676i | \(-0.232711\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0000 | − | 24.0000i | 0.905177 | − | 0.905177i | ||||
\(704\) | −2.82843 | −0.106600 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.0000 | −0.451626 | ||||||||
\(707\) | 2.82843 | − | 2.82843i | 0.106374 | − | 0.106374i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 26.0000i | − | 0.976450i | −0.872718 | − | 0.488225i | \(-0.837644\pi\) | ||
0.872718 | − | 0.488225i | \(-0.162356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.00000 | − | 7.00000i | −0.262336 | − | 0.262336i | ||||
\(713\) | −11.3137 | − | 11.3137i | −0.423702 | − | 0.423702i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 2.82843i | − | 0.105703i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.00000 | + | 8.00000i | −0.298557 | + | 0.298557i | ||||
\(719\) | 22.6274 | 0.843860 | 0.421930 | − | 0.906628i | \(-0.361353\pi\) | ||||
0.421930 | + | 0.906628i | \(0.361353\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 31.8198 | − | 31.8198i | 1.18421 | − | 1.18421i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 8.00000i | − | 0.297318i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.00000 | + | 6.00000i | 0.222528 | + | 0.222528i | 0.809562 | − | 0.587034i | \(-0.199705\pi\) |
−0.587034 | + | 0.809562i | \(0.699705\pi\) | |||||||
\(728\) | −8.48528 | − | 8.48528i | −0.314485 | − | 0.314485i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.0000 | − | 11.0000i | 0.406294 | − | 0.406294i | −0.474150 | − | 0.880444i | \(-0.657245\pi\) |
0.880444 | + | 0.474150i | \(0.157245\pi\) | |||||||
\(734\) | −31.1127 | −1.14839 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | −11.3137 | + | 11.3137i | −0.416746 | + | 0.416746i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.00000i | 0.294285i | 0.989115 | + | 0.147142i | \(0.0470076\pi\) | ||||
−0.989115 | + | 0.147142i | \(0.952992\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.00000 | + | 8.00000i | 0.293689 | + | 0.293689i | ||||
\(743\) | 28.2843 | + | 28.2843i | 1.03765 | + | 1.03765i | 0.999263 | + | 0.0383863i | \(0.0122217\pi\) |
0.0383863 | + | 0.999263i | \(0.487778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.07107i | 0.258890i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.00000 | − | 8.00000i | 0.292509 | − | 0.292509i | ||||
\(749\) | 56.5685 | 2.06697 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.0000 | −0.437886 | −0.218943 | − | 0.975738i | \(-0.570261\pi\) | ||||
−0.218943 | + | 0.975738i | \(0.570261\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.00000i | 0.218507i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0000 | − | 15.0000i | −0.545184 | − | 0.545184i | 0.379860 | − | 0.925044i | \(-0.375972\pi\) |
−0.925044 | + | 0.379860i | \(0.875972\pi\) | |||||||
\(758\) | 14.1421 | + | 14.1421i | 0.513665 | + | 0.513665i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.0122i | 1.48669i | 0.668908 | + | 0.743345i | \(0.266762\pi\) | ||||
−0.668908 | + | 0.743345i | \(0.733238\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.0000 | − | 16.0000i | 0.579239 | − | 0.579239i | ||||
\(764\) | 22.6274 | 0.818631 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | 0.867155 | ||||||||
\(767\) | −8.48528 | + | 8.48528i | −0.306386 | + | 0.306386i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 40.0000i | − | 1.44244i | −0.692708 | − | 0.721218i | \(-0.743582\pi\) | ||
0.692708 | − | 0.721218i | \(-0.256418\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.00000 | + | 9.00000i | 0.323917 | + | 0.323917i | ||||
\(773\) | −8.48528 | − | 8.48528i | −0.305194 | − | 0.305194i | 0.537848 | − | 0.843042i | \(-0.319238\pi\) |
−0.843042 | + | 0.537848i | \(0.819238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.24264i | 0.152302i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.0000 | − | 15.0000i | 0.537776 | − | 0.537776i | ||||
\(779\) | −79.1960 | −2.83749 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.0000 | −0.572525 | ||||||||
\(782\) | 11.3137 | − | 11.3137i | 0.404577 | − | 0.404577i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0000 | + | 20.0000i | 0.712923 | + | 0.712923i | 0.967146 | − | 0.254223i | \(-0.0818196\pi\) |
−0.254223 | + | 0.967146i | \(0.581820\pi\) | |||||||
\(788\) | −12.7279 | − | 12.7279i | −0.453413 | − | 0.453413i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.65685i | 0.201135i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 9.89949 | 0.351320 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.2132 | − | 21.2132i | 0.751410 | − | 0.751410i | −0.223332 | − | 0.974742i | \(-0.571693\pi\) |
0.974742 | + | 0.223332i | \(0.0716935\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.00000 | + | 9.00000i | 0.317801 | + | 0.317801i | ||||
\(803\) | −2.82843 | − | 2.82843i | −0.0998130 | − | 0.0998130i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16.9706i | 0.597763i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.00000 | + | 1.00000i | −0.0351799 | + | 0.0351799i | ||||
\(809\) | −1.41421 | −0.0497211 | −0.0248606 | − | 0.999691i | \(-0.507914\pi\) | ||||
−0.0248606 | + | 0.999691i | \(0.507914\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | −2.82843 | + | 2.82843i | −0.0992583 | + | 0.0992583i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 12.0000i | − | 0.420600i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −16.9706 | − | 16.9706i | −0.593362 | − | 0.593362i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.0122i | 1.43134i | 0.698441 | + | 0.715668i | \(0.253877\pi\) | ||||
−0.698441 | + | 0.715668i | \(0.746123\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.0000 | + | 38.0000i | −1.32460 | + | 1.32460i | −0.414587 | + | 0.910010i | \(0.636074\pi\) |
−0.910010 | + | 0.414587i | \(0.863926\pi\) | |||||||
\(824\) | 2.82843 | 0.0985329 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | 33.9411 | − | 33.9411i | 1.18025 | − | 1.18025i | 0.200569 | − | 0.979680i | \(-0.435721\pi\) |
0.979680 | − | 0.200569i | \(-0.0642791\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 56.0000i | 1.94496i | 0.232986 | + | 0.972480i | \(0.425151\pi\) | ||||
−0.232986 | + | 0.972480i | \(0.574849\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.00000 | + | 3.00000i | 0.104006 | + | 0.104006i | ||||
\(833\) | 2.82843 | + | 2.82843i | 0.0979992 | + | 0.0979992i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 22.6274i | − | 0.782586i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18.0000 | − | 18.0000i | 0.621800 | − | 0.621800i | ||||
\(839\) | 45.2548 | 1.56237 | 0.781185 | − | 0.624299i | \(-0.214615\pi\) | ||||
0.781185 | + | 0.624299i | \(0.214615\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0000 | −0.931034 | ||||||||
\(842\) | 7.07107 | − | 7.07107i | 0.243685 | − | 0.243685i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.00000i | 0.137686i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.00000 | − | 6.00000i | −0.206162 | − | 0.206162i | ||||
\(848\) | −2.82843 | − | 2.82843i | −0.0971286 | − | 0.0971286i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 16.9706i | − | 0.581743i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.0000 | + | 19.0000i | −0.650548 | + | 0.650548i | −0.953125 | − | 0.302577i | \(-0.902153\pi\) |
0.302577 | + | 0.953125i | \(0.402153\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20.0000 | −0.683586 | ||||||||
\(857\) | −8.48528 | + | 8.48528i | −0.289852 | + | 0.289852i | −0.837022 | − | 0.547170i | \(-0.815705\pi\) |
0.547170 | + | 0.837022i | \(0.315705\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.0000i | 1.50126i | 0.660722 | + | 0.750630i | \(0.270250\pi\) | ||||
−0.660722 | + | 0.750630i | \(0.729750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.0000 | + | 28.0000i | 0.953684 | + | 0.953684i | ||||
\(863\) | 31.1127 | + | 31.1127i | 1.05909 | + | 1.05909i | 0.998141 | + | 0.0609476i | \(0.0194123\pi\) |
0.0609476 | + | 0.998141i | \(0.480588\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 32.5269i | − | 1.10531i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.00000 | + | 8.00000i | −0.271538 | + | 0.271538i | ||||
\(869\) | −33.9411 | −1.15137 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.0000 | 0.813209 | ||||||||
\(872\) | −5.65685 | + | 5.65685i | −0.191565 | + | 0.191565i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 32.0000i | − | 1.08242i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.0000 | + | 15.0000i | 0.506514 | + | 0.506514i | 0.913455 | − | 0.406941i | \(-0.133404\pi\) |
−0.406941 | + | 0.913455i | \(0.633404\pi\) | |||||||
\(878\) | −5.65685 | − | 5.65685i | −0.190910 | − | 0.190910i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 52.3259i | − | 1.76290i | −0.472273 | − | 0.881452i | \(-0.656566\pi\) | ||
0.472273 | − | 0.881452i | \(-0.343434\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.0000 | + | 16.0000i | −0.538443 | + | 0.538443i | −0.923071 | − | 0.384629i | \(-0.874330\pi\) |
0.384629 | + | 0.923071i | \(0.374330\pi\) | |||||||
\(884\) | −16.9706 | −0.570782 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.0000 | 0.806296 | ||||||||
\(887\) | −25.4558 | + | 25.4558i | −0.854724 | + | 0.854724i | −0.990711 | − | 0.135987i | \(-0.956579\pi\) |
0.135987 | + | 0.990711i | \(0.456579\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 56.0000i | 1.87818i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.00000 | + | 6.00000i | 0.200895 | + | 0.200895i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.82843i | 0.0944911i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.00000 | + | 1.00000i | −0.0333704 | + | 0.0333704i | ||||
\(899\) | 5.65685 | 0.188667 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.0000 | 0.533037 | ||||||||
\(902\) | −19.7990 | + | 19.7990i | −0.659234 | + | 0.659234i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 2.00000i | − | 0.0665190i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.00000 | − | 4.00000i | −0.132818 | − | 0.132818i | 0.637573 | − | 0.770390i | \(-0.279939\pi\) |
−0.770390 | + | 0.637573i | \(0.779939\pi\) | |||||||
\(908\) | −5.65685 | − | 5.65685i | −0.187729 | − | 0.187729i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 11.3137i | − | 0.374840i | −0.982280 | − | 0.187420i | \(-0.939987\pi\) | ||
0.982280 | − | 0.187420i | \(-0.0600125\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.0000 | − | 24.0000i | 0.794284 | − | 0.794284i | ||||
\(914\) | −21.2132 | −0.701670 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.00000 | −0.198246 | ||||||||
\(917\) | −28.2843 | + | 28.2843i | −0.934029 | + | 0.934029i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.0000i | 0.659739i | 0.944027 | + | 0.329870i | \(0.107005\pi\) | ||||
−0.944027 | + | 0.329870i | \(0.892995\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.0000 | + | 13.0000i | 0.428132 | + | 0.428132i | ||||
\(923\) | 16.9706 | + | 16.9706i | 0.558593 | + | 0.558593i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 19.7990i | − | 0.650635i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.00000 | − | 1.00000i | 0.0328266 | − | 0.0328266i | ||||
\(929\) | −32.5269 | −1.06717 | −0.533587 | − | 0.845745i | \(-0.679156\pi\) | ||||
−0.533587 | + | 0.845745i | \(0.679156\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.00000 | 0.262189 | ||||||||
\(932\) | 8.48528 | − | 8.48528i | 0.277945 | − | 0.277945i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28.0000i | 0.916188i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.0000 | + | 11.0000i | 0.359354 | + | 0.359354i | 0.863575 | − | 0.504221i | \(-0.168220\pi\) |
−0.504221 | + | 0.863575i | \(0.668220\pi\) | |||||||
\(938\) | 11.3137 | + | 11.3137i | 0.369406 | + | 0.369406i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.6985i | 0.968143i | 0.875028 | + | 0.484071i | \(0.160843\pi\) | ||||
−0.875028 | + | 0.484071i | \(0.839157\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.0000 | + | 28.0000i | −0.911805 | + | 0.911805i | ||||
\(944\) | 2.82843 | 0.0920575 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.65685 | − | 5.65685i | 0.183823 | − | 0.183823i | −0.609196 | − | 0.793019i | \(-0.708508\pi\) |
0.793019 | + | 0.609196i | \(0.208508\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00000i | 0.194768i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.00000 | − | 8.00000i | −0.259281 | − | 0.259281i | ||||
\(953\) | −4.24264 | − | 4.24264i | −0.137433 | − | 0.137433i | 0.635044 | − | 0.772476i | \(-0.280982\pi\) |
−0.772476 | + | 0.635044i | \(0.780982\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 16.9706i | − | 0.548867i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.00000 | + | 4.00000i | −0.129234 | + | 0.129234i | ||||
\(959\) | 16.9706 | 0.548008 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | −12.7279 | + | 12.7279i | −0.410365 | + | 0.410365i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 22.0000i | − | 0.708572i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.0000 | − | 10.0000i | −0.321578 | − | 0.321578i | 0.527794 | − | 0.849372i | \(-0.323019\pi\) |
−0.849372 | + | 0.527794i | \(0.823019\pi\) | |||||||
\(968\) | 2.12132 | + | 2.12132i | 0.0681818 | + | 0.0681818i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 36.7696i | − | 1.17999i | −0.807406 | − | 0.589996i | \(-0.799129\pi\) | ||
0.807406 | − | 0.589996i | \(-0.200871\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.00000 | + | 8.00000i | −0.256468 | + | 0.256468i | ||||
\(974\) | −25.4558 | −0.815658 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.48528 | + | 8.48528i | −0.271468 | + | 0.271468i | −0.829691 | − | 0.558223i | \(-0.811483\pi\) |
0.558223 | + | 0.829691i | \(0.311483\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 28.0000i | − | 0.894884i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.00000 | + | 2.00000i | 0.0638226 | + | 0.0638226i | ||||
\(983\) | −5.65685 | − | 5.65685i | −0.180426 | − | 0.180426i | 0.611116 | − | 0.791541i | \(-0.290721\pi\) |
−0.791541 | + | 0.611116i | \(0.790721\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.65685i | 0.180151i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24.0000 | + | 24.0000i | −0.763542 | + | 0.763542i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.0000 | −1.01651 | −0.508257 | − | 0.861206i | \(-0.669710\pi\) | ||||
−0.508257 | + | 0.861206i | \(0.669710\pi\) | |||||||
\(992\) | 2.82843 | − | 2.82843i | 0.0898027 | − | 0.0898027i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 16.0000i | 0.507489i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.0000 | − | 13.0000i | −0.411714 | − | 0.411714i | 0.470621 | − | 0.882335i | \(-0.344030\pi\) |
−0.882335 | + | 0.470621i | \(0.844030\pi\) | |||||||
\(998\) | −22.6274 | − | 22.6274i | −0.716258 | − | 0.716258i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))