Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(107,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([3, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.q (of order \(12\), degree \(4\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 107.2 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.107 |
Dual form | 950.2.q.d.293.2 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.965926 | + | 0.258819i | 0.683013 | + | 0.183013i | ||||
\(3\) | 0.517638 | − | 1.93185i | 0.298858 | − | 1.11536i | −0.639246 | − | 0.769002i | \(-0.720753\pi\) |
0.938104 | − | 0.346353i | \(-0.112580\pi\) | |||||||
\(4\) | 0.866025 | + | 0.500000i | 0.433013 | + | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | − | 1.73205i | 0.408248 | − | 0.707107i | ||||
\(7\) | 1.22474 | + | 1.22474i | 0.462910 | + | 0.462910i | 0.899608 | − | 0.436698i | \(-0.143852\pi\) |
−0.436698 | + | 0.899608i | \(0.643852\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | −0.866025 | − | 0.500000i | −0.288675 | − | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | 0.904534 | 0.452267 | − | 0.891883i | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | 1.41421 | − | 1.41421i | 0.408248 | − | 0.408248i | ||||
\(13\) | 1.93185 | − | 0.517638i | 0.535799 | − | 0.143567i | 0.0192343 | − | 0.999815i | \(-0.493877\pi\) |
0.516565 | + | 0.856248i | \(0.327210\pi\) | |||||||
\(14\) | 0.866025 | + | 1.50000i | 0.231455 | + | 0.400892i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(18\) | −0.707107 | − | 0.707107i | −0.166667 | − | 0.166667i | ||||
\(19\) | −2.59808 | + | 3.50000i | −0.596040 | + | 0.802955i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00000 | − | 1.73205i | 0.654654 | − | 0.377964i | ||||
\(22\) | 2.89778 | + | 0.776457i | 0.617808 | + | 0.165541i | ||||
\(23\) | −1.34486 | − | 5.01910i | −0.280423 | − | 1.04655i | −0.952119 | − | 0.305727i | \(-0.901100\pi\) |
0.671696 | − | 0.740827i | \(-0.265566\pi\) | |||||||
\(24\) | 1.73205 | − | 1.00000i | 0.353553 | − | 0.204124i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 2.82843 | − | 2.82843i | 0.544331 | − | 0.544331i | ||||
\(28\) | 0.448288 | + | 1.67303i | 0.0847184 | + | 0.316173i | ||||
\(29\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.46410i | 0.622171i | 0.950382 | + | 0.311086i | \(0.100693\pi\) | ||||
−0.950382 | + | 0.311086i | \(0.899307\pi\) | |||||||
\(32\) | 0.258819 | + | 0.965926i | 0.0457532 | + | 0.170753i | ||||
\(33\) | 1.55291 | − | 5.79555i | 0.270328 | − | 1.00888i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 0.707107 | − | 0.707107i | 0.116248 | − | 0.116248i | −0.646590 | − | 0.762838i | \(-0.723806\pi\) |
0.762838 | + | 0.646590i | \(0.223806\pi\) | |||||||
\(38\) | −3.41542 | + | 2.70831i | −0.554054 | + | 0.439346i | ||||
\(39\) | − | 4.00000i | − | 0.640513i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.50000 | + | 2.59808i | −0.702782 | + | 0.405751i | −0.808383 | − | 0.588657i | \(-0.799657\pi\) |
0.105601 | + | 0.994409i | \(0.466323\pi\) | |||||||
\(42\) | 3.34607 | − | 0.896575i | 0.516309 | − | 0.138345i | ||||
\(43\) | −6.69213 | − | 1.79315i | −1.02054 | − | 0.273453i | −0.290513 | − | 0.956871i | \(-0.593826\pi\) |
−0.730027 | + | 0.683418i | \(0.760493\pi\) | |||||||
\(44\) | 2.59808 | + | 1.50000i | 0.391675 | + | 0.226134i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 5.19615i | − | 0.766131i | ||||||
\(47\) | 10.0382 | − | 2.68973i | 1.46422 | − | 0.392337i | 0.563276 | − | 0.826269i | \(-0.309541\pi\) |
0.900946 | + | 0.433932i | \(0.142874\pi\) | |||||||
\(48\) | 1.93185 | − | 0.517638i | 0.278839 | − | 0.0747146i | ||||
\(49\) | − | 4.00000i | − | 0.571429i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.93185 | + | 0.517638i | 0.267900 | + | 0.0717835i | ||||
\(53\) | 2.89778 | − | 0.776457i | 0.398040 | − | 0.106655i | −0.0542455 | − | 0.998528i | \(-0.517275\pi\) |
0.452286 | + | 0.891873i | \(0.350609\pi\) | |||||||
\(54\) | 3.46410 | − | 2.00000i | 0.471405 | − | 0.272166i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.73205i | 0.231455i | ||||||||
\(57\) | 5.41662 | + | 6.83083i | 0.717449 | + | 0.904766i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.19615 | − | 9.00000i | −0.676481 | − | 1.17170i | −0.976034 | − | 0.217620i | \(-0.930171\pi\) |
0.299552 | − | 0.954080i | \(-0.403163\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | + | 3.46410i | −0.256074 | + | 0.443533i | −0.965187 | − | 0.261562i | \(-0.915762\pi\) |
0.709113 | + | 0.705095i | \(0.249096\pi\) | |||||||
\(62\) | −0.896575 | + | 3.34607i | −0.113865 | + | 0.424951i | ||||
\(63\) | −0.448288 | − | 1.67303i | −0.0564789 | − | 0.210782i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.00000 | − | 5.19615i | 0.369274 | − | 0.639602i | ||||
\(67\) | 0.517638 | + | 1.93185i | 0.0632396 | + | 0.236013i | 0.990310 | − | 0.138874i | \(-0.0443482\pi\) |
−0.927071 | + | 0.374887i | \(0.877682\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.3923 | −1.25109 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.00000 | + | 5.19615i | −1.06810 | + | 0.616670i | −0.927663 | − | 0.373419i | \(-0.878185\pi\) |
−0.140441 | + | 0.990089i | \(0.544852\pi\) | |||||||
\(72\) | −0.258819 | − | 0.965926i | −0.0305021 | − | 0.113835i | ||||
\(73\) | −3.34607 | − | 0.896575i | −0.391627 | − | 0.104936i | 0.0576314 | − | 0.998338i | \(-0.481645\pi\) |
−0.449259 | + | 0.893402i | \(0.648312\pi\) | |||||||
\(74\) | 0.866025 | − | 0.500000i | 0.100673 | − | 0.0581238i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00000 | + | 1.73205i | −0.458831 | + | 0.198680i | ||||
\(77\) | 3.67423 | + | 3.67423i | 0.418718 | + | 0.418718i | ||||
\(78\) | 1.03528 | − | 3.86370i | 0.117222 | − | 0.437478i | ||||
\(79\) | −1.73205 | − | 3.00000i | −0.194871 | − | 0.337526i | 0.751987 | − | 0.659178i | \(-0.229095\pi\) |
−0.946858 | + | 0.321651i | \(0.895762\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.50000 | − | 9.52628i | −0.611111 | − | 1.05848i | ||||
\(82\) | −5.01910 | + | 1.34486i | −0.554267 | + | 0.148515i | ||||
\(83\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(84\) | 3.46410 | 0.377964 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.00000 | − | 3.46410i | −0.646997 | − | 0.373544i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.12132 | + | 2.12132i | 0.226134 | + | 0.226134i | ||||
\(89\) | −2.59808 | + | 4.50000i | −0.275396 | + | 0.476999i | −0.970235 | − | 0.242166i | \(-0.922142\pi\) |
0.694839 | + | 0.719165i | \(0.255475\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.00000 | + | 1.73205i | 0.314485 | + | 0.181568i | ||||
\(92\) | 1.34486 | − | 5.01910i | 0.140212 | − | 0.523277i | ||||
\(93\) | 6.69213 | + | 1.79315i | 0.693942 | + | 0.185941i | ||||
\(94\) | 10.3923 | 1.07188 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.00000 | 0.204124 | ||||||||
\(97\) | −7.72741 | − | 2.07055i | −0.784599 | − | 0.210233i | −0.155788 | − | 0.987791i | \(-0.549792\pi\) |
−0.628811 | + | 0.777558i | \(0.716458\pi\) | |||||||
\(98\) | 1.03528 | − | 3.86370i | 0.104579 | − | 0.390293i | ||||
\(99\) | −2.59808 | − | 1.50000i | −0.261116 | − | 0.150756i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.00000 | + | 15.5885i | −0.895533 | + | 1.55111i | −0.0623905 | + | 0.998052i | \(0.519872\pi\) |
−0.833143 | + | 0.553058i | \(0.813461\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.94975 | − | 4.94975i | −0.487713 | − | 0.487713i | 0.419871 | − | 0.907584i | \(-0.362075\pi\) |
−0.907584 | + | 0.419871i | \(0.862075\pi\) | |||||||
\(104\) | 1.73205 | + | 1.00000i | 0.169842 | + | 0.0980581i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | 0.291386 | ||||||||
\(107\) | 4.24264 | − | 4.24264i | 0.410152 | − | 0.410152i | −0.471640 | − | 0.881791i | \(-0.656338\pi\) |
0.881791 | + | 0.471640i | \(0.156338\pi\) | |||||||
\(108\) | 3.86370 | − | 1.03528i | 0.371785 | − | 0.0996195i | ||||
\(109\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.00000 | − | 1.73205i | −0.0949158 | − | 0.164399i | ||||
\(112\) | −0.448288 | + | 1.67303i | −0.0423592 | + | 0.158087i | ||||
\(113\) | 12.7279 | + | 12.7279i | 1.19734 | + | 1.19734i | 0.974959 | + | 0.222383i | \(0.0713835\pi\) |
0.222383 | + | 0.974959i | \(0.428617\pi\) | |||||||
\(114\) | 3.46410 | + | 8.00000i | 0.324443 | + | 0.749269i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.93185 | − | 0.517638i | −0.178600 | − | 0.0478557i | ||||
\(118\) | −2.68973 | − | 10.0382i | −0.247609 | − | 0.924091i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | −2.82843 | + | 2.82843i | −0.256074 | + | 0.256074i | ||||
\(123\) | 2.68973 | + | 10.0382i | 0.242524 | + | 0.905114i | ||||
\(124\) | −1.73205 | + | 3.00000i | −0.155543 | + | 0.269408i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 1.73205i | − | 0.154303i | ||||||
\(127\) | −1.81173 | − | 6.76148i | −0.160765 | − | 0.599984i | −0.998542 | − | 0.0539720i | \(-0.982812\pi\) |
0.837777 | − | 0.546012i | \(-0.183855\pi\) | |||||||
\(128\) | −0.258819 | + | 0.965926i | −0.0228766 | + | 0.0853766i | ||||
\(129\) | −6.92820 | + | 12.0000i | −0.609994 | + | 1.05654i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.50000 | + | 12.9904i | 0.655278 | + | 1.13497i | 0.981824 | + | 0.189794i | \(0.0607819\pi\) |
−0.326546 | + | 0.945181i | \(0.605885\pi\) | |||||||
\(132\) | 4.24264 | − | 4.24264i | 0.369274 | − | 0.369274i | ||||
\(133\) | −7.46859 | + | 1.10463i | −0.647609 | + | 0.0957833i | ||||
\(134\) | 2.00000i | 0.172774i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(138\) | −10.0382 | − | 2.68973i | −0.854508 | − | 0.228965i | ||||
\(139\) | 17.3205 | + | 10.0000i | 1.46911 | + | 0.848189i | 0.999400 | − | 0.0346338i | \(-0.0110265\pi\) |
0.469706 | + | 0.882823i | \(0.344360\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 20.7846i | − | 1.75038i | ||||||
\(142\) | −10.0382 | + | 2.68973i | −0.842387 | + | 0.225717i | ||||
\(143\) | 5.79555 | − | 1.55291i | 0.484649 | − | 0.129861i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.00000 | − | 1.73205i | −0.248282 | − | 0.143346i | ||||
\(147\) | −7.72741 | − | 2.07055i | −0.637346 | − | 0.170776i | ||||
\(148\) | 0.965926 | − | 0.258819i | 0.0793986 | − | 0.0212748i | ||||
\(149\) | −5.19615 | + | 3.00000i | −0.425685 | + | 0.245770i | −0.697507 | − | 0.716578i | \(-0.745707\pi\) |
0.271821 | + | 0.962348i | \(0.412374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.7846i | 1.69143i | 0.533637 | + | 0.845714i | \(0.320825\pi\) | ||||
−0.533637 | + | 0.845714i | \(0.679175\pi\) | |||||||
\(152\) | −4.31199 | + | 0.637756i | −0.349749 | + | 0.0517289i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.59808 | + | 4.50000i | 0.209359 | + | 0.362620i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | − | 3.46410i | 0.160128 | − | 0.277350i | ||||
\(157\) | −4.93117 | + | 18.4034i | −0.393550 | + | 1.46875i | 0.430686 | + | 0.902502i | \(0.358272\pi\) |
−0.824236 | + | 0.566246i | \(0.808395\pi\) | |||||||
\(158\) | −0.896575 | − | 3.34607i | −0.0713277 | − | 0.266199i | ||||
\(159\) | − | 6.00000i | − | 0.475831i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.50000 | − | 7.79423i | 0.354650 | − | 0.614271i | ||||
\(162\) | −2.84701 | − | 10.6252i | −0.223682 | − | 0.834793i | ||||
\(163\) | −17.1464 | + | 17.1464i | −1.34301 | + | 1.34301i | −0.449966 | + | 0.893045i | \(0.648564\pi\) |
−0.893045 | + | 0.449966i | \(0.851436\pi\) | |||||||
\(164\) | −5.19615 | −0.405751 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.43520 | − | 20.2844i | −0.420588 | − | 1.56966i | −0.773372 | − | 0.633952i | \(-0.781432\pi\) |
0.352784 | − | 0.935705i | \(-0.385235\pi\) | |||||||
\(168\) | 3.34607 | + | 0.896575i | 0.258155 | + | 0.0691723i | ||||
\(169\) | −7.79423 | + | 4.50000i | −0.599556 | + | 0.346154i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | − | 1.73205i | 0.305888 | − | 0.132453i | ||||
\(172\) | −4.89898 | − | 4.89898i | −0.373544 | − | 0.373544i | ||||
\(173\) | −3.88229 | + | 14.4889i | −0.295165 | + | 1.10157i | 0.645922 | + | 0.763404i | \(0.276473\pi\) |
−0.941086 | + | 0.338166i | \(0.890193\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.50000 | + | 2.59808i | 0.113067 | + | 0.195837i | ||||
\(177\) | −20.0764 | + | 5.37945i | −1.50903 | + | 0.404344i | ||||
\(178\) | −3.67423 | + | 3.67423i | −0.275396 | + | 0.275396i | ||||
\(179\) | 5.19615 | 0.388379 | 0.194189 | − | 0.980964i | \(-0.437792\pi\) | ||||
0.194189 | + | 0.980964i | \(0.437792\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.0000 | − | 10.3923i | −1.33793 | − | 0.772454i | −0.351429 | − | 0.936214i | \(-0.614304\pi\) |
−0.986500 | + | 0.163760i | \(0.947638\pi\) | |||||||
\(182\) | 2.44949 | + | 2.44949i | 0.181568 | + | 0.181568i | ||||
\(183\) | 5.65685 | + | 5.65685i | 0.418167 | + | 0.418167i | ||||
\(184\) | 2.59808 | − | 4.50000i | 0.191533 | − | 0.331744i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.00000 | + | 3.46410i | 0.439941 | + | 0.254000i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 10.0382 | + | 2.68973i | 0.732111 | + | 0.196168i | ||||
\(189\) | 6.92820 | 0.503953 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.0000 | 1.73658 | 0.868290 | − | 0.496058i | \(-0.165220\pi\) | ||||
0.868290 | + | 0.496058i | \(0.165220\pi\) | |||||||
\(192\) | 1.93185 | + | 0.517638i | 0.139419 | + | 0.0373573i | ||||
\(193\) | −0.517638 | + | 1.93185i | −0.0372604 | + | 0.139058i | −0.982050 | − | 0.188619i | \(-0.939599\pi\) |
0.944790 | + | 0.327677i | \(0.106266\pi\) | |||||||
\(194\) | −6.92820 | − | 4.00000i | −0.497416 | − | 0.287183i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | − | 3.46410i | 0.142857 | − | 0.247436i | ||||
\(197\) | −3.67423 | − | 3.67423i | −0.261778 | − | 0.261778i | 0.563998 | − | 0.825776i | \(-0.309263\pi\) |
−0.825776 | + | 0.563998i | \(0.809263\pi\) | |||||||
\(198\) | −2.12132 | − | 2.12132i | −0.150756 | − | 0.150756i | ||||
\(199\) | 6.92820 | + | 4.00000i | 0.491127 | + | 0.283552i | 0.725042 | − | 0.688705i | \(-0.241820\pi\) |
−0.233915 | + | 0.972257i | \(0.575154\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | −12.7279 | + | 12.7279i | −0.895533 | + | 0.895533i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.50000 | − | 6.06218i | −0.243857 | − | 0.422372i | ||||
\(207\) | −1.34486 | + | 5.01910i | −0.0934745 | + | 0.348851i | ||||
\(208\) | 1.41421 | + | 1.41421i | 0.0980581 | + | 0.0980581i | ||||
\(209\) | −7.79423 | + | 10.5000i | −0.539138 | + | 0.726300i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.5000 | − | 11.2583i | 1.34244 | − | 0.775055i | 0.355271 | − | 0.934763i | \(-0.384389\pi\) |
0.987164 | + | 0.159708i | \(0.0510552\pi\) | |||||||
\(212\) | 2.89778 | + | 0.776457i | 0.199020 | + | 0.0533273i | ||||
\(213\) | 5.37945 | + | 20.0764i | 0.368594 | + | 1.37561i | ||||
\(214\) | 5.19615 | − | 3.00000i | 0.355202 | − | 0.205076i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.00000 | 0.272166 | ||||||||
\(217\) | −4.24264 | + | 4.24264i | −0.288009 | + | 0.288009i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.46410 | + | 6.00000i | −0.234082 | + | 0.405442i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.517638 | − | 1.93185i | −0.0347416 | − | 0.129657i | ||||
\(223\) | 5.95284 | − | 22.2163i | 0.398632 | − | 1.48771i | −0.416874 | − | 0.908964i | \(-0.636874\pi\) |
0.815506 | − | 0.578749i | \(-0.196459\pi\) | |||||||
\(224\) | −0.866025 | + | 1.50000i | −0.0578638 | + | 0.100223i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.00000 | + | 15.5885i | 0.598671 | + | 1.03693i | ||||
\(227\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(228\) | 1.27551 | + | 8.62398i | 0.0844729 | + | 0.571137i | ||||
\(229\) | − | 20.0000i | − | 1.32164i | −0.750546 | − | 0.660819i | \(-0.770209\pi\) | ||
0.750546 | − | 0.660819i | \(-0.229791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.00000 | − | 5.19615i | 0.592157 | − | 0.341882i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.0382 | − | 2.68973i | −0.657624 | − | 0.176210i | −0.0854505 | − | 0.996342i | \(-0.527233\pi\) |
−0.572174 | + | 0.820133i | \(0.693900\pi\) | |||||||
\(234\) | −1.73205 | − | 1.00000i | −0.113228 | − | 0.0653720i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 10.3923i | − | 0.676481i | ||||||
\(237\) | −6.69213 | + | 1.79315i | −0.434701 | + | 0.116478i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 24.0000i | − | 1.55243i | −0.630468 | − | 0.776215i | \(-0.717137\pi\) | ||
0.630468 | − | 0.776215i | \(-0.282863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.0000 | − | 6.92820i | −0.772988 | − | 0.446285i | 0.0609515 | − | 0.998141i | \(-0.480586\pi\) |
−0.833939 | + | 0.551856i | \(0.813920\pi\) | |||||||
\(242\) | −1.93185 | − | 0.517638i | −0.124184 | − | 0.0332750i | ||||
\(243\) | −9.65926 | + | 2.58819i | −0.619642 | + | 0.166032i | ||||
\(244\) | −3.46410 | + | 2.00000i | −0.221766 | + | 0.128037i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.3923i | 0.662589i | ||||||||
\(247\) | −3.20736 | + | 8.10634i | −0.204080 | + | 0.515794i | ||||
\(248\) | −2.44949 | + | 2.44949i | −0.155543 | + | 0.155543i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | + | 20.7846i | −0.757433 | + | 1.31191i | 0.186722 | + | 0.982413i | \(0.440214\pi\) |
−0.944156 | + | 0.329500i | \(0.893120\pi\) | |||||||
\(252\) | 0.448288 | − | 1.67303i | 0.0282395 | − | 0.105391i | ||||
\(253\) | −4.03459 | − | 15.0573i | −0.253652 | − | 0.946644i | ||||
\(254\) | − | 7.00000i | − | 0.439219i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(258\) | −9.79796 | + | 9.79796i | −0.609994 | + | 0.609994i | ||||
\(259\) | 1.73205 | 0.107624 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.88229 | + | 14.4889i | 0.239848 | + | 0.895126i | ||||
\(263\) | 25.0955 | + | 6.72432i | 1.54745 | + | 0.414639i | 0.928665 | − | 0.370918i | \(-0.120957\pi\) |
0.618789 | + | 0.785557i | \(0.287624\pi\) | |||||||
\(264\) | 5.19615 | − | 3.00000i | 0.319801 | − | 0.184637i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.50000 | − | 0.866025i | −0.459855 | − | 0.0530994i | ||||
\(267\) | 7.34847 | + | 7.34847i | 0.449719 | + | 0.449719i | ||||
\(268\) | −0.517638 | + | 1.93185i | −0.0316198 | + | 0.118007i | ||||
\(269\) | −10.3923 | − | 18.0000i | −0.633630 | − | 1.09748i | −0.986804 | − | 0.161922i | \(-0.948231\pi\) |
0.353174 | − | 0.935558i | \(-0.385102\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.00000 | − | 1.73205i | −0.0607457 | − | 0.105215i | 0.834053 | − | 0.551684i | \(-0.186015\pi\) |
−0.894799 | + | 0.446469i | \(0.852681\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.89898 | − | 4.89898i | 0.296500 | − | 0.296500i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.00000 | − | 5.19615i | −0.541736 | − | 0.312772i | ||||
\(277\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(278\) | 14.1421 | + | 14.1421i | 0.848189 | + | 0.848189i | ||||
\(279\) | 1.73205 | − | 3.00000i | 0.103695 | − | 0.179605i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.5000 | + | 7.79423i | 0.805342 | + | 0.464965i | 0.845336 | − | 0.534235i | \(-0.179400\pi\) |
−0.0399934 | + | 0.999200i | \(0.512734\pi\) | |||||||
\(282\) | 5.37945 | − | 20.0764i | 0.320342 | − | 1.19553i | ||||
\(283\) | −30.1146 | − | 8.06918i | −1.79013 | − | 0.479663i | −0.797759 | − | 0.602977i | \(-0.793981\pi\) |
−0.992368 | + | 0.123314i | \(0.960648\pi\) | |||||||
\(284\) | −10.3923 | −0.616670 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.00000 | 0.354787 | ||||||||
\(287\) | −8.69333 | − | 2.32937i | −0.513151 | − | 0.137498i | ||||
\(288\) | 0.258819 | − | 0.965926i | 0.0152511 | − | 0.0569177i | ||||
\(289\) | 14.7224 | + | 8.50000i | 0.866025 | + | 0.500000i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.00000 | + | 13.8564i | −0.468968 | + | 0.812277i | ||||
\(292\) | −2.44949 | − | 2.44949i | −0.143346 | − | 0.143346i | ||||
\(293\) | −6.36396 | − | 6.36396i | −0.371787 | − | 0.371787i | 0.496341 | − | 0.868128i | \(-0.334677\pi\) |
−0.868128 | + | 0.496341i | \(0.834677\pi\) | |||||||
\(294\) | −6.92820 | − | 4.00000i | −0.404061 | − | 0.233285i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | 8.48528 | − | 8.48528i | 0.492366 | − | 0.492366i | ||||
\(298\) | −5.79555 | + | 1.55291i | −0.335727 | + | 0.0899579i | ||||
\(299\) | −5.19615 | − | 9.00000i | −0.300501 | − | 0.520483i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00000 | − | 10.3923i | −0.345834 | − | 0.599002i | ||||
\(302\) | −5.37945 | + | 20.0764i | −0.309553 | + | 1.15527i | ||||
\(303\) | 25.4558 | + | 25.4558i | 1.46240 | + | 1.46240i | ||||
\(304\) | −4.33013 | − | 0.500000i | −0.248350 | − | 0.0286770i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.3185 | − | 5.17638i | −1.10257 | − | 0.295432i | −0.338757 | − | 0.940874i | \(-0.610006\pi\) |
−0.763809 | + | 0.645442i | \(0.776673\pi\) | |||||||
\(308\) | 1.34486 | + | 5.01910i | 0.0766307 | + | 0.285990i | ||||
\(309\) | −12.1244 | + | 7.00000i | −0.689730 | + | 0.398216i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 2.82843 | − | 2.82843i | 0.160128 | − | 0.160128i | ||||
\(313\) | −2.68973 | − | 10.0382i | −0.152032 | − | 0.567392i | −0.999341 | − | 0.0362920i | \(-0.988445\pi\) |
0.847309 | − | 0.531100i | \(-0.178221\pi\) | |||||||
\(314\) | −9.52628 | + | 16.5000i | −0.537599 | + | 0.931149i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 3.46410i | − | 0.194871i | ||||||
\(317\) | −6.98811 | − | 26.0800i | −0.392492 | − | 1.46480i | −0.826011 | − | 0.563654i | \(-0.809395\pi\) |
0.433519 | − | 0.901144i | \(-0.357272\pi\) | |||||||
\(318\) | 1.55291 | − | 5.79555i | 0.0870831 | − | 0.324999i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.00000 | − | 10.3923i | −0.334887 | − | 0.580042i | ||||
\(322\) | 6.36396 | − | 6.36396i | 0.354650 | − | 0.354650i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | − | 11.0000i | − | 0.611111i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −21.0000 | + | 12.1244i | −1.16308 | + | 0.671506i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.01910 | − | 1.34486i | −0.277133 | − | 0.0742576i | ||||
\(329\) | 15.5885 | + | 9.00000i | 0.859419 | + | 0.496186i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 19.0526i | − | 1.04722i | −0.851957 | − | 0.523612i | \(-0.824584\pi\) | ||
0.851957 | − | 0.523612i | \(-0.175416\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.965926 | + | 0.258819i | −0.0529324 | + | 0.0141832i | ||||
\(334\) | − | 21.0000i | − | 1.14907i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.00000 | + | 1.73205i | 0.163663 | + | 0.0944911i | ||||
\(337\) | 1.93185 | + | 0.517638i | 0.105235 | + | 0.0281975i | 0.311052 | − | 0.950393i | \(-0.399319\pi\) |
−0.205817 | + | 0.978590i | \(0.565985\pi\) | |||||||
\(338\) | −8.69333 | + | 2.32937i | −0.472855 | + | 0.126701i | ||||
\(339\) | 31.1769 | − | 18.0000i | 1.69330 | − | 0.977626i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.3923i | 0.562775i | ||||||||
\(342\) | 4.31199 | − | 0.637756i | 0.233166 | − | 0.0344859i | ||||
\(343\) | 13.4722 | − | 13.4722i | 0.727430 | − | 0.727430i | ||||
\(344\) | −3.46410 | − | 6.00000i | −0.186772 | − | 0.323498i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.50000 | + | 12.9904i | −0.403202 | + | 0.698367i | ||||
\(347\) | −2.68973 | + | 10.0382i | −0.144392 | + | 0.538879i | 0.855390 | + | 0.517985i | \(0.173318\pi\) |
−0.999782 | + | 0.0208935i | \(0.993349\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.00000i | − | 0.214115i | −0.994253 | − | 0.107058i | \(-0.965857\pi\) | ||
0.994253 | − | 0.107058i | \(-0.0341429\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.00000 | − | 6.92820i | 0.213504 | − | 0.369800i | ||||
\(352\) | 0.776457 | + | 2.89778i | 0.0413853 | + | 0.154452i | ||||
\(353\) | −7.34847 | + | 7.34847i | −0.391120 | + | 0.391120i | −0.875086 | − | 0.483967i | \(-0.839196\pi\) |
0.483967 | + | 0.875086i | \(0.339196\pi\) | |||||||
\(354\) | −20.7846 | −1.10469 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.50000 | + | 2.59808i | −0.238500 | + | 0.137698i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.01910 | + | 1.34486i | 0.265268 | + | 0.0710782i | ||||
\(359\) | 5.19615 | − | 3.00000i | 0.274242 | − | 0.158334i | −0.356572 | − | 0.934268i | \(-0.616054\pi\) |
0.630814 | + | 0.775934i | \(0.282721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.50000 | − | 18.1865i | −0.289474 | − | 0.957186i | ||||
\(362\) | −14.6969 | − | 14.6969i | −0.772454 | − | 0.772454i | ||||
\(363\) | −1.03528 | + | 3.86370i | −0.0543379 | + | 0.202792i | ||||
\(364\) | 1.73205 | + | 3.00000i | 0.0907841 | + | 0.157243i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.00000 | + | 6.92820i | 0.209083 | + | 0.362143i | ||||
\(367\) | −3.34607 | + | 0.896575i | −0.174663 | + | 0.0468009i | −0.345091 | − | 0.938569i | \(-0.612152\pi\) |
0.170427 | + | 0.985370i | \(0.445485\pi\) | |||||||
\(368\) | 3.67423 | − | 3.67423i | 0.191533 | − | 0.191533i | ||||
\(369\) | 5.19615 | 0.270501 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.50000 | + | 2.59808i | 0.233628 | + | 0.134885i | ||||
\(372\) | 4.89898 | + | 4.89898i | 0.254000 | + | 0.254000i | ||||
\(373\) | −21.9203 | − | 21.9203i | −1.13499 | − | 1.13499i | −0.989335 | − | 0.145655i | \(-0.953471\pi\) |
−0.145655 | − | 0.989335i | \(-0.546529\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.00000 | + | 5.19615i | 0.464140 | + | 0.267971i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 6.69213 | + | 1.79315i | 0.344206 | + | 0.0922297i | ||||
\(379\) | 3.46410 | 0.177939 | 0.0889695 | − | 0.996034i | \(-0.471643\pi\) | ||||
0.0889695 | + | 0.996034i | \(0.471643\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.0000 | −0.717242 | ||||||||
\(382\) | 23.1822 | + | 6.21166i | 1.18611 | + | 0.317816i | ||||
\(383\) | 6.21166 | − | 23.1822i | 0.317401 | − | 1.18456i | −0.604333 | − | 0.796732i | \(-0.706560\pi\) |
0.921733 | − | 0.387824i | \(-0.126773\pi\) | |||||||
\(384\) | 1.73205 | + | 1.00000i | 0.0883883 | + | 0.0510310i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.00000 | + | 1.73205i | −0.0508987 | + | 0.0881591i | ||||
\(387\) | 4.89898 | + | 4.89898i | 0.249029 | + | 0.249029i | ||||
\(388\) | −5.65685 | − | 5.65685i | −0.287183 | − | 0.287183i | ||||
\(389\) | 25.9808 | + | 15.0000i | 1.31728 | + | 0.760530i | 0.983290 | − | 0.182047i | \(-0.0582724\pi\) |
0.333987 | + | 0.942578i | \(0.391606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2.82843 | − | 2.82843i | 0.142857 | − | 0.142857i | ||||
\(393\) | 28.9778 | − | 7.76457i | 1.46174 | − | 0.391671i | ||||
\(394\) | −2.59808 | − | 4.50000i | −0.130889 | − | 0.226707i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.50000 | − | 2.59808i | −0.0753778 | − | 0.130558i | ||||
\(397\) | −0.448288 | + | 1.67303i | −0.0224989 | + | 0.0839671i | −0.976262 | − | 0.216591i | \(-0.930506\pi\) |
0.953764 | + | 0.300558i | \(0.0971729\pi\) | |||||||
\(398\) | 5.65685 | + | 5.65685i | 0.283552 | + | 0.283552i | ||||
\(399\) | −1.73205 | + | 15.0000i | −0.0867110 | + | 0.750939i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.0000 | − | 10.3923i | 0.898877 | − | 0.518967i | 0.0220414 | − | 0.999757i | \(-0.492983\pi\) |
0.876836 | + | 0.480790i | \(0.159650\pi\) | |||||||
\(402\) | 3.86370 | + | 1.03528i | 0.192704 | + | 0.0516349i | ||||
\(403\) | 1.79315 | + | 6.69213i | 0.0893232 | + | 0.333359i | ||||
\(404\) | −15.5885 | + | 9.00000i | −0.775555 | + | 0.447767i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.12132 | − | 2.12132i | 0.105150 | − | 0.105150i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.1865 | + | 31.5000i | −0.899266 | + | 1.55757i | −0.0708321 | + | 0.997488i | \(0.522565\pi\) |
−0.828434 | + | 0.560087i | \(0.810768\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.81173 | − | 6.76148i | −0.0892577 | − | 0.333114i | ||||
\(413\) | 4.65874 | − | 17.3867i | 0.229242 | − | 0.855542i | ||||
\(414\) | −2.59808 | + | 4.50000i | −0.127688 | + | 0.221163i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.00000 | + | 1.73205i | 0.0490290 | + | 0.0849208i | ||||
\(417\) | 28.2843 | − | 28.2843i | 1.38509 | − | 1.38509i | ||||
\(418\) | −10.2462 | + | 8.12493i | −0.501160 | + | 0.397403i | ||||
\(419\) | 9.00000i | 0.439679i | 0.975536 | + | 0.219839i | \(0.0705533\pi\) | ||||
−0.975536 | + | 0.219839i | \(0.929447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.00000 | − | 5.19615i | 0.438633 | − | 0.253245i | −0.264385 | − | 0.964417i | \(-0.585169\pi\) |
0.703018 | + | 0.711172i | \(0.251835\pi\) | |||||||
\(422\) | 21.7494 | − | 5.82774i | 1.05875 | − | 0.283690i | ||||
\(423\) | −10.0382 | − | 2.68973i | −0.488074 | − | 0.130779i | ||||
\(424\) | 2.59808 | + | 1.50000i | 0.126174 | + | 0.0728464i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 20.7846i | 1.00702i | ||||||||
\(427\) | −6.69213 | + | 1.79315i | −0.323855 | + | 0.0867767i | ||||
\(428\) | 5.79555 | − | 1.55291i | 0.280139 | − | 0.0750629i | ||||
\(429\) | − | 12.0000i | − | 0.579365i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.00000 | − | 5.19615i | −0.433515 | − | 0.250290i | 0.267328 | − | 0.963606i | \(-0.413859\pi\) |
−0.700843 | + | 0.713316i | \(0.747193\pi\) | |||||||
\(432\) | 3.86370 | + | 1.03528i | 0.185893 | + | 0.0498097i | ||||
\(433\) | −27.0459 | + | 7.24693i | −1.29974 | + | 0.348265i | −0.841353 | − | 0.540485i | \(-0.818241\pi\) |
−0.458391 | + | 0.888751i | \(0.651574\pi\) | |||||||
\(434\) | −5.19615 | + | 3.00000i | −0.249423 | + | 0.144005i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.0609 | + | 8.33298i | 1.00748 | + | 0.398620i | ||||
\(438\) | −4.89898 | + | 4.89898i | −0.234082 | + | 0.234082i | ||||
\(439\) | 12.1244 | + | 21.0000i | 0.578664 | + | 1.00228i | 0.995633 | + | 0.0933546i | \(0.0297590\pi\) |
−0.416969 | + | 0.908921i | \(0.636908\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.00000 | + | 3.46410i | −0.0952381 | + | 0.164957i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(444\) | − | 2.00000i | − | 0.0949158i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.5000 | − | 19.9186i | 0.544541 | − | 0.943172i | ||||
\(447\) | 3.10583 | + | 11.5911i | 0.146901 | + | 0.548241i | ||||
\(448\) | −1.22474 | + | 1.22474i | −0.0578638 | + | 0.0578638i | ||||
\(449\) | −5.19615 | −0.245222 | −0.122611 | − | 0.992455i | \(-0.539127\pi\) | ||||
−0.122611 | + | 0.992455i | \(0.539127\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.5000 | + | 7.79423i | −0.635690 | + | 0.367016i | ||||
\(452\) | 4.65874 | + | 17.3867i | 0.219129 | + | 0.817800i | ||||
\(453\) | 40.1528 | + | 10.7589i | 1.88654 | + | 0.505497i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.00000 | + | 8.66025i | −0.0468293 | + | 0.405554i | ||||
\(457\) | 26.9444 | + | 26.9444i | 1.26041 | + | 1.26041i | 0.950897 | + | 0.309509i | \(0.100165\pi\) |
0.309509 | + | 0.950897i | \(0.399835\pi\) | |||||||
\(458\) | 5.17638 | − | 19.3185i | 0.241876 | − | 0.902695i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.00000 | − | 15.5885i | −0.419172 | − | 0.726027i | 0.576685 | − | 0.816967i | \(-0.304346\pi\) |
−0.995856 | + | 0.0909401i | \(0.971013\pi\) | |||||||
\(462\) | 10.0382 | − | 2.68973i | 0.467019 | − | 0.125137i | ||||
\(463\) | 23.2702 | − | 23.2702i | 1.08146 | − | 1.08146i | 0.0850817 | − | 0.996374i | \(-0.472885\pi\) |
0.996374 | − | 0.0850817i | \(-0.0271151\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.00000 | − | 5.19615i | −0.416917 | − | 0.240707i | ||||
\(467\) | 29.3939 | + | 29.3939i | 1.36019 | + | 1.36019i | 0.873673 | + | 0.486513i | \(0.161731\pi\) |
0.486513 | + | 0.873673i | \(0.338269\pi\) | |||||||
\(468\) | −1.41421 | − | 1.41421i | −0.0653720 | − | 0.0653720i | ||||
\(469\) | −1.73205 | + | 3.00000i | −0.0799787 | + | 0.138527i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 33.0000 | + | 19.0526i | 1.52056 | + | 0.877896i | ||||
\(472\) | 2.68973 | − | 10.0382i | 0.123805 | − | 0.462045i | ||||
\(473\) | −20.0764 | − | 5.37945i | −0.923113 | − | 0.247348i | ||||
\(474\) | −6.92820 | −0.318223 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.89778 | − | 0.776457i | −0.132680 | − | 0.0355515i | ||||
\(478\) | 6.21166 | − | 23.1822i | 0.284115 | − | 1.06033i | ||||
\(479\) | 5.19615 | + | 3.00000i | 0.237418 | + | 0.137073i | 0.613990 | − | 0.789314i | \(-0.289564\pi\) |
−0.376571 | + | 0.926388i | \(0.622897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.00000 | − | 1.73205i | 0.0455961 | − | 0.0789747i | ||||
\(482\) | −9.79796 | − | 9.79796i | −0.446285 | − | 0.446285i | ||||
\(483\) | −12.7279 | − | 12.7279i | −0.579141 | − | 0.579141i | ||||
\(484\) | −1.73205 | − | 1.00000i | −0.0787296 | − | 0.0454545i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10.0000 | −0.453609 | ||||||||
\(487\) | 17.6777 | − | 17.6777i | 0.801052 | − | 0.801052i | −0.182208 | − | 0.983260i | \(-0.558325\pi\) |
0.983260 | + | 0.182208i | \(0.0583245\pi\) | |||||||
\(488\) | −3.86370 | + | 1.03528i | −0.174902 | + | 0.0468648i | ||||
\(489\) | 24.2487 | + | 42.0000i | 1.09656 | + | 1.89931i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.5000 | + | 18.1865i | 0.473858 | + | 0.820747i | 0.999552 | − | 0.0299272i | \(-0.00952753\pi\) |
−0.525694 | + | 0.850674i | \(0.676194\pi\) | |||||||
\(492\) | −2.68973 | + | 10.0382i | −0.121262 | + | 0.452557i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −5.19615 | + | 7.00000i | −0.233786 | + | 0.314945i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.00000 | + | 1.73205i | −0.134704 | + | 0.0777714i | ||||
\(497\) | −17.3867 | − | 4.65874i | −0.779899 | − | 0.208973i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.06218 | + | 3.50000i | −0.271380 | + | 0.156682i | −0.629515 | − | 0.776989i | \(-0.716746\pi\) |
0.358134 | + | 0.933670i | \(0.383413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −42.0000 | −1.87642 | ||||||||
\(502\) | −16.9706 | + | 16.9706i | −0.757433 | + | 0.757433i | ||||
\(503\) | −1.34486 | − | 5.01910i | −0.0599645 | − | 0.223791i | 0.929441 | − | 0.368972i | \(-0.120290\pi\) |
−0.989405 | + | 0.145181i | \(0.953623\pi\) | |||||||
\(504\) | 0.866025 | − | 1.50000i | 0.0385758 | − | 0.0668153i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 15.5885i | − | 0.692991i | ||||||
\(507\) | 4.65874 | + | 17.3867i | 0.206902 | + | 0.772169i | ||||
\(508\) | 1.81173 | − | 6.76148i | 0.0803827 | − | 0.299992i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.00000 | − | 5.19615i | −0.132712 | − | 0.229864i | ||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 2.55103 | + | 17.2480i | 0.112631 | + | 0.761516i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −12.0000 | + | 6.92820i | −0.528271 | + | 0.304997i | ||||
\(517\) | 30.1146 | − | 8.06918i | 1.32444 | − | 0.354882i | ||||
\(518\) | 1.67303 | + | 0.448288i | 0.0735088 | + | 0.0196966i | ||||
\(519\) | 25.9808 | + | 15.0000i | 1.14043 | + | 0.658427i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 20.7846i | − | 0.910590i | −0.890341 | − | 0.455295i | \(-0.849534\pi\) | ||
0.890341 | − | 0.455295i | \(-0.150466\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.0459 | + | 7.24693i | −1.18264 | + | 0.316886i | −0.795971 | − | 0.605334i | \(-0.793039\pi\) |
−0.386664 | + | 0.922221i | \(0.626373\pi\) | |||||||
\(524\) | 15.0000i | 0.655278i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.5000 | + | 12.9904i | 0.981047 | + | 0.566408i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 5.79555 | − | 1.55291i | 0.252219 | − | 0.0675819i | ||||
\(529\) | −3.46410 | + | 2.00000i | −0.150613 | + | 0.0869565i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.3923i | 0.450988i | ||||||||
\(532\) | −7.02030 | − | 2.77766i | −0.304369 | − | 0.120427i | ||||
\(533\) | −7.34847 | + | 7.34847i | −0.318298 | + | 0.318298i | ||||
\(534\) | 5.19615 | + | 9.00000i | 0.224860 | + | 0.389468i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.00000 | + | 1.73205i | −0.0431934 | + | 0.0748132i | ||||
\(537\) | 2.68973 | − | 10.0382i | 0.116070 | − | 0.433180i | ||||
\(538\) | −5.37945 | − | 20.0764i | −0.231925 | − | 0.865555i | ||||
\(539\) | − | 12.0000i | − | 0.516877i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | − | 8.66025i | 0.214967 | − | 0.372333i | −0.738296 | − | 0.674477i | \(-0.764369\pi\) |
0.953262 | + | 0.302144i | \(0.0977023\pi\) | |||||||
\(542\) | −0.517638 | − | 1.93185i | −0.0222345 | − | 0.0829801i | ||||
\(543\) | −29.3939 | + | 29.3939i | −1.26141 | + | 1.26141i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.00000 | − | 3.46410i | 0.256776 | − | 0.148250i | ||||
\(547\) | 5.69402 | + | 21.2504i | 0.243459 | + | 0.908600i | 0.974152 | + | 0.225894i | \(0.0725303\pi\) |
−0.730693 | + | 0.682706i | \(0.760803\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.46410 | − | 2.00000i | 0.147844 | − | 0.0853579i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −7.34847 | − | 7.34847i | −0.312772 | − | 0.312772i | ||||
\(553\) | 1.55291 | − | 5.79555i | 0.0660366 | − | 0.246452i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.0000 | + | 17.3205i | 0.424094 | + | 0.734553i | ||||
\(557\) | 5.01910 | − | 1.34486i | 0.212666 | − | 0.0569837i | −0.150913 | − | 0.988547i | \(-0.548221\pi\) |
0.363579 | + | 0.931563i | \(0.381555\pi\) | |||||||
\(558\) | 2.44949 | − | 2.44949i | 0.103695 | − | 0.103695i | ||||
\(559\) | −13.8564 | −0.586064 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.0227 | + | 11.0227i | 0.464965 | + | 0.464965i | ||||
\(563\) | 16.9706 | + | 16.9706i | 0.715224 | + | 0.715224i | 0.967623 | − | 0.252399i | \(-0.0812196\pi\) |
−0.252399 | + | 0.967623i | \(0.581220\pi\) | |||||||
\(564\) | 10.3923 | − | 18.0000i | 0.437595 | − | 0.757937i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −27.0000 | − | 15.5885i | −1.13489 | − | 0.655232i | ||||
\(567\) | 4.93117 | − | 18.4034i | 0.207089 | − | 0.772868i | ||||
\(568\) | −10.0382 | − | 2.68973i | −0.421193 | − | 0.112858i | ||||
\(569\) | 5.19615 | 0.217834 | 0.108917 | − | 0.994051i | \(-0.465262\pi\) | ||||
0.108917 | + | 0.994051i | \(0.465262\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | 5.79555 | + | 1.55291i | 0.242324 | + | 0.0649306i | ||||
\(573\) | 12.4233 | − | 46.3644i | 0.518991 | − | 1.93690i | ||||
\(574\) | −7.79423 | − | 4.50000i | −0.325325 | − | 0.187826i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −7.34847 | − | 7.34847i | −0.305921 | − | 0.305921i | 0.537404 | − | 0.843325i | \(-0.319405\pi\) |
−0.843325 | + | 0.537404i | \(0.819405\pi\) | |||||||
\(578\) | 12.0208 | + | 12.0208i | 0.500000 | + | 0.500000i | ||||
\(579\) | 3.46410 | + | 2.00000i | 0.143963 | + | 0.0831172i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −11.3137 | + | 11.3137i | −0.468968 | + | 0.468968i | ||||
\(583\) | 8.69333 | − | 2.32937i | 0.360041 | − | 0.0964727i | ||||
\(584\) | −1.73205 | − | 3.00000i | −0.0716728 | − | 0.124141i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.50000 | − | 7.79423i | −0.185893 | − | 0.321977i | ||||
\(587\) | 5.37945 | − | 20.0764i | 0.222034 | − | 0.828641i | −0.761537 | − | 0.648121i | \(-0.775555\pi\) |
0.983571 | − | 0.180520i | \(-0.0577782\pi\) | |||||||
\(588\) | −5.65685 | − | 5.65685i | −0.233285 | − | 0.233285i | ||||
\(589\) | −12.1244 | − | 9.00000i | −0.499575 | − | 0.370839i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.00000 | + | 5.19615i | −0.370211 | + | 0.213741i | ||||
\(592\) | 0.965926 | + | 0.258819i | 0.0396993 | + | 0.0106374i | ||||
\(593\) | 10.7589 | + | 40.1528i | 0.441815 | + | 1.64888i | 0.724210 | + | 0.689579i | \(0.242204\pi\) |
−0.282395 | + | 0.959298i | \(0.591129\pi\) | |||||||
\(594\) | 10.3923 | − | 6.00000i | 0.426401 | − | 0.246183i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 11.3137 | − | 11.3137i | 0.463039 | − | 0.463039i | ||||
\(598\) | −2.68973 | − | 10.0382i | −0.109991 | − | 0.410492i | ||||
\(599\) | 10.3923 | − | 18.0000i | 0.424618 | − | 0.735460i | −0.571767 | − | 0.820416i | \(-0.693742\pi\) |
0.996385 | + | 0.0849563i | \(0.0270751\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.5167i | 0.918474i | 0.888314 | + | 0.459237i | \(0.151877\pi\) | ||||
−0.888314 | + | 0.459237i | \(0.848123\pi\) | |||||||
\(602\) | −3.10583 | − | 11.5911i | −0.126584 | − | 0.472418i | ||||
\(603\) | 0.517638 | − | 1.93185i | 0.0210799 | − | 0.0786711i | ||||
\(604\) | −10.3923 | + | 18.0000i | −0.422857 | + | 0.732410i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 18.0000 | + | 31.1769i | 0.731200 | + | 1.26648i | ||||
\(607\) | −7.77817 | + | 7.77817i | −0.315706 | + | 0.315706i | −0.847115 | − | 0.531409i | \(-0.821663\pi\) |
0.531409 | + | 0.847115i | \(0.321663\pi\) | |||||||
\(608\) | −4.05317 | − | 1.60368i | −0.164378 | − | 0.0650379i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.0000 | − | 10.3923i | 0.728202 | − | 0.420428i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.01910 | − | 1.34486i | −0.202719 | − | 0.0543185i | 0.156030 | − | 0.987752i | \(-0.450130\pi\) |
−0.358750 | + | 0.933434i | \(0.616797\pi\) | |||||||
\(614\) | −17.3205 | − | 10.0000i | −0.698999 | − | 0.403567i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.19615i | 0.209359i | ||||||||
\(617\) | 30.1146 | − | 8.06918i | 1.21237 | − | 0.324853i | 0.404677 | − | 0.914460i | \(-0.367384\pi\) |
0.807690 | + | 0.589607i | \(0.200717\pi\) | |||||||
\(618\) | −13.5230 | + | 3.62347i | −0.543973 | + | 0.145757i | ||||
\(619\) | − | 31.0000i | − | 1.24600i | −0.782224 | − | 0.622998i | \(-0.785915\pi\) | ||
0.782224 | − | 0.622998i | \(-0.214085\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.0000 | − | 10.3923i | −0.722315 | − | 0.417029i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.69333 | + | 2.32937i | −0.348291 | + | 0.0933243i | ||||
\(624\) | 3.46410 | − | 2.00000i | 0.138675 | − | 0.0800641i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 10.3923i | − | 0.415360i | ||||||
\(627\) | 16.2499 | + | 20.4925i | 0.648957 | + | 0.818391i | ||||
\(628\) | −13.4722 | + | 13.4722i | −0.537599 | + | 0.537599i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.0000 | − | 22.5167i | 0.517522 | − | 0.896374i | −0.482271 | − | 0.876022i | \(-0.660188\pi\) |
0.999793 | − | 0.0203520i | \(-0.00647871\pi\) | |||||||
\(632\) | 0.896575 | − | 3.34607i | 0.0356639 | − | 0.133099i | ||||
\(633\) | −11.6555 | − | 43.4988i | −0.463264 | − | 1.72892i | ||||
\(634\) | − | 27.0000i | − | 1.07231i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.00000 | − | 5.19615i | 0.118958 | − | 0.206041i | ||||
\(637\) | −2.07055 | − | 7.72741i | −0.0820383 | − | 0.306171i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.3923 | 0.411113 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.0000 | − | 10.3923i | 0.710957 | − | 0.410471i | −0.100458 | − | 0.994941i | \(-0.532031\pi\) |
0.811415 | + | 0.584470i | \(0.198698\pi\) | |||||||
\(642\) | −3.10583 | − | 11.5911i | −0.122577 | − | 0.457465i | ||||
\(643\) | 33.4607 | + | 8.96575i | 1.31956 | + | 0.353575i | 0.848813 | − | 0.528694i | \(-0.177318\pi\) |
0.470747 | + | 0.882268i | \(0.343985\pi\) | |||||||
\(644\) | 7.79423 | − | 4.50000i | 0.307136 | − | 0.177325i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.67423 | + | 3.67423i | 0.144449 | + | 0.144449i | 0.775633 | − | 0.631184i | \(-0.217431\pi\) |
−0.631184 | + | 0.775633i | \(0.717431\pi\) | |||||||
\(648\) | 2.84701 | − | 10.6252i | 0.111841 | − | 0.417397i | ||||
\(649\) | −15.5885 | − | 27.0000i | −0.611900 | − | 1.05984i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.00000 | + | 10.3923i | 0.235159 | + | 0.407307i | ||||
\(652\) | −23.4225 | + | 6.27603i | −0.917294 | + | 0.245788i | ||||
\(653\) | −11.0227 | + | 11.0227i | −0.431352 | + | 0.431352i | −0.889088 | − | 0.457736i | \(-0.848660\pi\) |
0.457736 | + | 0.889088i | \(0.348660\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.50000 | − | 2.59808i | −0.175695 | − | 0.101438i | ||||
\(657\) | 2.44949 | + | 2.44949i | 0.0955637 | + | 0.0955637i | ||||
\(658\) | 12.7279 | + | 12.7279i | 0.496186 | + | 0.496186i | ||||
\(659\) | 7.79423 | − | 13.5000i | 0.303620 | − | 0.525885i | −0.673333 | − | 0.739339i | \(-0.735138\pi\) |
0.976953 | + | 0.213454i | \(0.0684713\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.00000 | − | 5.19615i | −0.350059 | − | 0.202107i | 0.314652 | − | 0.949207i | \(-0.398112\pi\) |
−0.664711 | + | 0.747100i | \(0.731446\pi\) | |||||||
\(662\) | 4.93117 | − | 18.4034i | 0.191655 | − | 0.715267i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.00000 | −0.0387492 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 5.43520 | − | 20.2844i | 0.210294 | − | 0.784829i | ||||
\(669\) | −39.8372 | − | 23.0000i | −1.54019 | − | 0.889231i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.00000 | + | 10.3923i | −0.231627 | + | 0.401190i | ||||
\(672\) | 2.44949 | + | 2.44949i | 0.0944911 | + | 0.0944911i | ||||
\(673\) | −22.6274 | − | 22.6274i | −0.872223 | − | 0.872223i | 0.120492 | − | 0.992714i | \(-0.461553\pi\) |
−0.992714 | + | 0.120492i | \(0.961553\pi\) | |||||||
\(674\) | 1.73205 | + | 1.00000i | 0.0667161 | + | 0.0385186i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 23.3345 | − | 23.3345i | 0.896819 | − | 0.896819i | −0.0983348 | − | 0.995153i | \(-0.531352\pi\) |
0.995153 | + | 0.0983348i | \(0.0313516\pi\) | |||||||
\(678\) | 34.7733 | − | 9.31749i | 1.33546 | − | 0.357836i | ||||
\(679\) | −6.92820 | − | 12.0000i | −0.265880 | − | 0.460518i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.68973 | + | 10.0382i | −0.102995 | + | 0.384382i | ||||
\(683\) | 25.4558 | + | 25.4558i | 0.974041 | + | 0.974041i | 0.999671 | − | 0.0256307i | \(-0.00815939\pi\) |
−0.0256307 | + | 0.999671i | \(0.508159\pi\) | |||||||
\(684\) | 4.33013 | + | 0.500000i | 0.165567 | + | 0.0191180i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.5000 | − | 9.52628i | 0.629973 | − | 0.363715i | ||||
\(687\) | −38.6370 | − | 10.3528i | −1.47409 | − | 0.394982i | ||||
\(688\) | −1.79315 | − | 6.69213i | −0.0683632 | − | 0.255135i | ||||
\(689\) | 5.19615 | − | 3.00000i | 0.197958 | − | 0.114291i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.0000 | −0.646710 | −0.323355 | − | 0.946278i | \(-0.604811\pi\) | ||||
−0.323355 | + | 0.946278i | \(0.604811\pi\) | |||||||
\(692\) | −10.6066 | + | 10.6066i | −0.403202 | + | 0.403202i | ||||
\(693\) | −1.34486 | − | 5.01910i | −0.0510871 | − | 0.190660i | ||||
\(694\) | −5.19615 | + | 9.00000i | −0.197243 | + | 0.341635i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.03528 | − | 3.86370i | 0.0391858 | − | 0.146243i | ||||
\(699\) | −10.3923 | + | 18.0000i | −0.393073 | + | 0.680823i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.00000 | − | 10.3923i | −0.226617 | − | 0.392512i | 0.730186 | − | 0.683248i | \(-0.239433\pi\) |
−0.956803 | + | 0.290736i | \(0.906100\pi\) | |||||||
\(702\) | 5.65685 | − | 5.65685i | 0.213504 | − | 0.213504i | ||||
\(703\) | 0.637756 | + | 4.31199i | 0.0240534 | + | 0.162630i | ||||
\(704\) | 3.00000i | 0.113067i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.00000 | + | 5.19615i | −0.338719 | + | 0.195560i | ||||
\(707\) | −30.1146 | + | 8.06918i | −1.13258 | + | 0.303473i | ||||
\(708\) | −20.0764 | − | 5.37945i | −0.754517 | − | 0.202172i | ||||
\(709\) | −27.7128 | − | 16.0000i | −1.04078 | − | 0.600893i | −0.120723 | − | 0.992686i | \(-0.538521\pi\) |
−0.920053 | + | 0.391794i | \(0.871855\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.46410i | 0.129914i | ||||||||
\(712\) | −5.01910 | + | 1.34486i | −0.188099 | + | 0.0504009i | ||||
\(713\) | 17.3867 | − | 4.65874i | 0.651136 | − | 0.174471i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.50000 | + | 2.59808i | 0.168173 | + | 0.0970947i | ||||
\(717\) | −46.3644 | − | 12.4233i | −1.73151 | − | 0.463957i | ||||
\(718\) | 5.79555 | − | 1.55291i | 0.216288 | − | 0.0579542i | ||||
\(719\) | 15.5885 | − | 9.00000i | 0.581351 | − | 0.335643i | −0.180319 | − | 0.983608i | \(-0.557713\pi\) |
0.761670 | + | 0.647965i | \(0.224380\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 12.1244i | − | 0.451535i | ||||||
\(722\) | −0.605571 | − | 18.9903i | −0.0225370 | − | 0.706748i | ||||
\(723\) | −19.5959 | + | 19.5959i | −0.728780 | + | 0.728780i | ||||
\(724\) | −10.3923 | − | 18.0000i | −0.386227 | − | 0.668965i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.00000 | + | 3.46410i | −0.0742270 | + | 0.128565i | ||||
\(727\) | −6.27603 | + | 23.4225i | −0.232765 | + | 0.868691i | 0.746379 | + | 0.665522i | \(0.231791\pi\) |
−0.979144 | + | 0.203169i | \(0.934876\pi\) | |||||||
\(728\) | 0.896575 | + | 3.34607i | 0.0332293 | + | 0.124013i | ||||
\(729\) | − | 13.0000i | − | 0.481481i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 2.07055 | + | 7.72741i | 0.0765298 | + | 0.285613i | ||||
\(733\) | −33.0681 | + | 33.0681i | −1.22140 | + | 1.22140i | −0.254264 | + | 0.967135i | \(0.581833\pi\) |
−0.967135 | + | 0.254264i | \(0.918167\pi\) | |||||||
\(734\) | −3.46410 | −0.127862 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.50000 | − | 2.59808i | 0.165872 | − | 0.0957664i | ||||
\(737\) | 1.55291 | + | 5.79555i | 0.0572023 | + | 0.213482i | ||||
\(738\) | 5.01910 | + | 1.34486i | 0.184756 | + | 0.0495051i | ||||
\(739\) | −14.7224 | + | 8.50000i | −0.541573 | + | 0.312678i | −0.745716 | − | 0.666264i | \(-0.767893\pi\) |
0.204143 | + | 0.978941i | \(0.434559\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.0000 | + | 10.3923i | 0.514303 | + | 0.381771i | ||||
\(742\) | 3.67423 | + | 3.67423i | 0.134885 | + | 0.134885i | ||||
\(743\) | 5.43520 | − | 20.2844i | 0.199398 | − | 0.744164i | −0.791686 | − | 0.610928i | \(-0.790796\pi\) |
0.991084 | − | 0.133236i | \(-0.0425368\pi\) | |||||||
\(744\) | 3.46410 | + | 6.00000i | 0.127000 | + | 0.219971i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.5000 | − | 26.8468i | −0.567495 | − | 0.982931i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.3923 | 0.379727 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.0000 | + | 22.5167i | 1.42313 | + | 0.821645i | 0.996565 | − | 0.0828123i | \(-0.0263902\pi\) |
0.426565 | + | 0.904457i | \(0.359724\pi\) | |||||||
\(752\) | 7.34847 | + | 7.34847i | 0.267971 | + | 0.267971i | ||||
\(753\) | 33.9411 | + | 33.9411i | 1.23688 | + | 1.23688i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 6.00000 | + | 3.46410i | 0.218218 | + | 0.125988i | ||||
\(757\) | −5.82774 | + | 21.7494i | −0.211813 | + | 0.790496i | 0.775451 | + | 0.631407i | \(0.217522\pi\) |
−0.987264 | + | 0.159089i | \(0.949144\pi\) | |||||||
\(758\) | 3.34607 | + | 0.896575i | 0.121535 | + | 0.0325651i | ||||
\(759\) | −31.1769 | −1.13165 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0000 | 0.761249 | 0.380625 | − | 0.924730i | \(-0.375709\pi\) | ||||
0.380625 | + | 0.924730i | \(0.375709\pi\) | |||||||
\(762\) | −13.5230 | − | 3.62347i | −0.489885 | − | 0.131264i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 20.7846 | + | 12.0000i | 0.751961 | + | 0.434145i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.0000 | − | 20.7846i | 0.433578 | − | 0.750978i | ||||
\(767\) | −14.6969 | − | 14.6969i | −0.530676 | − | 0.530676i | ||||
\(768\) | 1.41421 | + | 1.41421i | 0.0510310 | + | 0.0510310i | ||||
\(769\) | 29.4449 | + | 17.0000i | 1.06181 | + | 0.613036i | 0.925932 | − | 0.377690i | \(-0.123282\pi\) |
0.135877 | + | 0.990726i | \(0.456615\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.41421 | + | 1.41421i | −0.0508987 | + | 0.0508987i | ||||
\(773\) | 20.2844 | − | 5.43520i | 0.729581 | − | 0.195491i | 0.125138 | − | 0.992139i | \(-0.460063\pi\) |
0.604443 | + | 0.796649i | \(0.293396\pi\) | |||||||
\(774\) | 3.46410 | + | 6.00000i | 0.124515 | + | 0.215666i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.00000 | − | 6.92820i | −0.143592 | − | 0.248708i | ||||
\(777\) | 0.896575 | − | 3.34607i | 0.0321645 | − | 0.120039i | ||||
\(778\) | 21.2132 | + | 21.2132i | 0.760530 | + | 0.760530i | ||||
\(779\) | 2.59808 | − | 22.5000i | 0.0930857 | − | 0.806146i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.0000 | + | 15.5885i | −0.966136 | + | 0.557799i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.46410 | − | 2.00000i | 0.123718 | − | 0.0714286i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 30.0000 | 1.07006 | ||||||||
\(787\) | −11.3137 | + | 11.3137i | −0.403290 | + | 0.403290i | −0.879391 | − | 0.476101i | \(-0.842050\pi\) |
0.476101 | + | 0.879391i | \(0.342050\pi\) | |||||||
\(788\) | −1.34486 | − | 5.01910i | −0.0479088 | − | 0.178798i | ||||
\(789\) | 25.9808 | − | 45.0000i | 0.924940 | − | 1.60204i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.1769i | 1.10852i | ||||||||
\(792\) | −0.776457 | − | 2.89778i | −0.0275902 | − | 0.102968i | ||||
\(793\) | −2.07055 | + | 7.72741i | −0.0735275 | + | 0.274408i | ||||
\(794\) | −0.866025 | + | 1.50000i | −0.0307341 | + | 0.0532330i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.00000 | + | 6.92820i | 0.141776 | + | 0.245564i | ||||
\(797\) | −10.6066 | + | 10.6066i | −0.375705 | + | 0.375705i | −0.869550 | − | 0.493845i | \(-0.835591\pi\) |
0.493845 | + | 0.869550i | \(0.335591\pi\) | |||||||
\(798\) | −5.55532 | + | 14.0406i | −0.196656 | + | 0.497032i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.50000 | − | 2.59808i | 0.159000 | − | 0.0917985i | ||||
\(802\) | 20.0764 | − | 5.37945i | 0.708922 | − | 0.189955i | ||||
\(803\) | −10.0382 | − | 2.68973i | −0.354240 | − | 0.0949184i | ||||
\(804\) | 3.46410 | + | 2.00000i | 0.122169 | + | 0.0705346i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.92820i | 0.244036i | ||||||||
\(807\) | −40.1528 | + | 10.7589i | −1.41344 | + | 0.378731i | ||||
\(808\) | −17.3867 | + | 4.65874i | −0.611661 | + | 0.163894i | ||||
\(809\) | 42.0000i | 1.47664i | 0.674450 | + | 0.738321i | \(0.264381\pi\) | ||||
−0.674450 | + | 0.738321i | \(0.735619\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.5000 | − | 23.3827i | −1.42215 | − | 0.821077i | −0.425665 | − | 0.904881i | \(-0.639960\pi\) |
−0.996482 | + | 0.0838036i | \(0.973293\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.86370 | + | 1.03528i | −0.135506 | + | 0.0363087i | ||||
\(814\) | 2.59808 | − | 1.50000i | 0.0910625 | − | 0.0525750i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.6627 | − | 18.7637i | 0.827853 | − | 0.656459i | ||||
\(818\) | −25.7196 | + | 25.7196i | −0.899266 | + | 0.899266i | ||||
\(819\) | −1.73205 | − | 3.00000i | −0.0605228 | − | 0.104828i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.00000 | + | 5.19615i | −0.104701 | + | 0.181347i | −0.913616 | − | 0.406578i | \(-0.866722\pi\) |
0.808915 | + | 0.587925i | \(0.200055\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.34486 | + | 5.01910i | 0.0468790 | + | 0.174955i | 0.985396 | − | 0.170278i | \(-0.0544666\pi\) |
−0.938517 | + | 0.345233i | \(0.887800\pi\) | |||||||
\(824\) | − | 7.00000i | − | 0.243857i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.00000 | − | 15.5885i | 0.313150 | − | 0.542392i | ||||
\(827\) | 9.31749 | + | 34.7733i | 0.324001 | + | 1.20919i | 0.915313 | + | 0.402744i | \(0.131944\pi\) |
−0.591312 | + | 0.806443i | \(0.701390\pi\) | |||||||
\(828\) | −3.67423 | + | 3.67423i | −0.127688 | + | 0.127688i | ||||
\(829\) | −27.7128 | −0.962506 | −0.481253 | − | 0.876582i | \(-0.659818\pi\) | ||||
−0.481253 | + | 0.876582i | \(0.659818\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.517638 | + | 1.93185i | 0.0179459 | + | 0.0669749i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 34.6410 | − | 20.0000i | 1.19952 | − | 0.692543i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.0000 | + | 5.19615i | −0.415029 | + | 0.179713i | ||||
\(837\) | 9.79796 | + | 9.79796i | 0.338667 | + | 0.338667i | ||||
\(838\) | −2.32937 | + | 8.69333i | −0.0804668 | + | 0.300306i | ||||
\(839\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.5000 | + | 25.1147i | 0.500000 | + | 0.866025i | ||||
\(842\) | 10.0382 | − | 2.68973i | 0.345939 | − | 0.0926941i | ||||
\(843\) | 22.0454 | − | 22.0454i | 0.759284 | − | 0.759284i | ||||
\(844\) | 22.5167 | 0.775055 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.00000 | − | 5.19615i | −0.309426 | − | 0.178647i | ||||
\(847\) | −2.44949 | − | 2.44949i | −0.0841655 | − | 0.0841655i | ||||
\(848\) | 2.12132 | + | 2.12132i | 0.0728464 | + | 0.0728464i | ||||
\(849\) | −31.1769 | + | 54.0000i | −1.06999 | + | 1.85328i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.50000 | − | 2.59808i | −0.154258 | − | 0.0890609i | ||||
\(852\) | −5.37945 | + | 20.0764i | −0.184297 | + | 0.687806i | ||||
\(853\) | −13.3843 | − | 3.58630i | −0.458268 | − | 0.122793i | 0.0222973 | − | 0.999751i | \(-0.492902\pi\) |
−0.480566 | + | 0.876959i | \(0.659569\pi\) | |||||||
\(854\) | −6.92820 | −0.237078 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.00000 | 0.205076 | ||||||||
\(857\) | −46.3644 | − | 12.4233i | −1.58378 | − | 0.424372i | −0.643686 | − | 0.765290i | \(-0.722596\pi\) |
−0.940093 | + | 0.340917i | \(0.889262\pi\) | |||||||
\(858\) | 3.10583 | − | 11.5911i | 0.106031 | − | 0.395714i | ||||
\(859\) | −9.52628 | − | 5.50000i | −0.325032 | − | 0.187658i | 0.328601 | − | 0.944469i | \(-0.393423\pi\) |
−0.653633 | + | 0.756811i | \(0.726756\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.00000 | + | 15.5885i | −0.306719 | + | 0.531253i | ||||
\(862\) | −7.34847 | − | 7.34847i | −0.250290 | − | 0.250290i | ||||
\(863\) | 10.6066 | + | 10.6066i | 0.361053 | + | 0.361053i | 0.864201 | − | 0.503148i | \(-0.167825\pi\) |
−0.503148 | + | 0.864201i | \(0.667825\pi\) | |||||||
\(864\) | 3.46410 | + | 2.00000i | 0.117851 | + | 0.0680414i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −28.0000 | −0.951479 | ||||||||
\(867\) | 24.0416 | − | 24.0416i | 0.816497 | − | 0.816497i | ||||
\(868\) | −5.79555 | + | 1.55291i | −0.196714 | + | 0.0527093i | ||||
\(869\) | −5.19615 | − | 9.00000i | −0.176267 | − | 0.305304i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.00000 | + | 3.46410i | 0.0677674 | + | 0.117377i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.65685 | + | 5.65685i | 0.191456 | + | 0.191456i | ||||
\(874\) | 18.1865 | + | 13.5000i | 0.615169 | + | 0.456644i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.00000 | + | 3.46410i | −0.202721 | + | 0.117041i | ||||
\(877\) | −45.3985 | − | 12.1645i | −1.53300 | − | 0.410766i | −0.609003 | − | 0.793168i | \(-0.708430\pi\) |
−0.923996 | + | 0.382402i | \(0.875097\pi\) | |||||||
\(878\) | 6.27603 | + | 23.4225i | 0.211806 | + | 0.790470i | ||||
\(879\) | −15.5885 | + | 9.00000i | −0.525786 | + | 0.303562i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.0000 | 0.505363 | 0.252681 | − | 0.967550i | \(-0.418688\pi\) | ||||
0.252681 | + | 0.967550i | \(0.418688\pi\) | |||||||
\(882\) | −2.82843 | + | 2.82843i | −0.0952381 | + | 0.0952381i | ||||
\(883\) | −9.86233 | − | 36.8067i | −0.331894 | − | 1.23864i | −0.907198 | − | 0.420705i | \(-0.861783\pi\) |
0.575304 | − | 0.817940i | \(-0.304884\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(888\) | 0.517638 | − | 1.93185i | 0.0173708 | − | 0.0648287i | ||||
\(889\) | 6.06218 | − | 10.5000i | 0.203319 | − | 0.352159i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.5000 | − | 28.5788i | −0.552771 | − | 0.957427i | ||||
\(892\) | 16.2635 | − | 16.2635i | 0.544541 | − | 0.544541i | ||||
\(893\) | −16.6660 | + | 42.1218i | −0.557705 | + | 1.40955i | ||||
\(894\) | 12.0000i | 0.401340i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.50000 | + | 0.866025i | −0.0501115 | + | 0.0289319i | ||||
\(897\) | −20.0764 | + | 5.37945i | −0.670331 | + | 0.179615i | ||||
\(898\) | −5.01910 | − | 1.34486i | −0.167489 | − | 0.0448787i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −15.0573 | + | 4.03459i | −0.501353 | + | 0.134337i | ||||
\(903\) | −23.1822 | + | 6.21166i | −0.771456 | + | 0.206711i | ||||
\(904\) | 18.0000i | 0.598671i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 36.0000 | + | 20.7846i | 1.19602 | + | 0.690522i | ||||
\(907\) | −42.5007 | − | 11.3880i | −1.41121 | − | 0.378134i | −0.528856 | − | 0.848712i | \(-0.677379\pi\) |
−0.882358 | + | 0.470578i | \(0.844045\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.5885 | − | 9.00000i | 0.517036 | − | 0.298511i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 31.1769i | − | 1.03294i | −0.856306 | − | 0.516469i | \(-0.827246\pi\) | ||
0.856306 | − | 0.516469i | \(-0.172754\pi\) | |||||||
\(912\) | −3.20736 | + | 8.10634i | −0.106206 | + | 0.268428i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 19.0526 | + | 33.0000i | 0.630203 | + | 1.09154i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.0000 | − | 17.3205i | 0.330409 | − | 0.572286i | ||||
\(917\) | −6.72432 | + | 25.0955i | −0.222056 | + | 0.828726i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.0000i | 1.51740i | 0.651440 | + | 0.758700i | \(0.274165\pi\) | ||||
−0.651440 | + | 0.758700i | \(0.725835\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.0000 | + | 34.6410i | −0.659022 | + | 1.14146i | ||||
\(922\) | −4.65874 | − | 17.3867i | −0.153428 | − | 0.572599i | ||||
\(923\) | −14.6969 | + | 14.6969i | −0.483756 | + | 0.483756i | ||||
\(924\) | 10.3923 | 0.341882 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 28.5000 | − | 16.4545i | 0.936568 | − | 0.540728i | ||||
\(927\) | 1.81173 | + | 6.76148i | 0.0595051 | + | 0.222076i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.1865 | + | 10.5000i | −0.596681 | + | 0.344494i | −0.767735 | − | 0.640768i | \(-0.778616\pi\) |
0.171054 | + | 0.985262i | \(0.445283\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.0000 | + | 10.3923i | 0.458831 | + | 0.340594i | ||||
\(932\) | −7.34847 | − | 7.34847i | −0.240707 | − | 0.240707i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.7846 | + | 36.0000i | 0.680093 | + | 1.17796i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.00000 | − | 1.73205i | −0.0326860 | − | 0.0566139i | ||||
\(937\) | −36.8067 | + | 9.86233i | −1.20242 | + | 0.322188i | −0.803785 | − | 0.594920i | \(-0.797184\pi\) |
−0.398638 | + | 0.917108i | \(0.630517\pi\) | |||||||
\(938\) | −2.44949 | + | 2.44949i | −0.0799787 | + | 0.0799787i | ||||
\(939\) | −20.7846 | −0.678280 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.0000 | + | 20.7846i | 1.17357 | + | 0.677559i | 0.954517 | − | 0.298155i | \(-0.0963712\pi\) |
0.219049 | + | 0.975714i | \(0.429705\pi\) | |||||||
\(942\) | 26.9444 | + | 26.9444i | 0.877896 | + | 0.877896i | ||||
\(943\) | 19.0919 | + | 19.0919i | 0.621717 | + | 0.621717i | ||||
\(944\) | 5.19615 | − | 9.00000i | 0.169120 | − | 0.292925i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18.0000 | − | 10.3923i | −0.585230 | − | 0.337883i | ||||
\(947\) | 10.7589 | − | 40.1528i | 0.349617 | − | 1.30479i | −0.537507 | − | 0.843259i | \(-0.680634\pi\) |
0.887124 | − | 0.461531i | \(-0.152700\pi\) | |||||||
\(948\) | −6.69213 | − | 1.79315i | −0.217350 | − | 0.0582388i | ||||
\(949\) | −6.92820 | −0.224899 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −54.0000 | −1.75107 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.31749 | − | 34.7733i | 0.301823 | − | 1.12642i | −0.633823 | − | 0.773478i | \(-0.718515\pi\) |
0.935646 | − | 0.352940i | \(-0.114818\pi\) | |||||||
\(954\) | −2.59808 | − | 1.50000i | −0.0841158 | − | 0.0485643i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.0000 | − | 20.7846i | 0.388108 | − | 0.672222i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.24264 | + | 4.24264i | 0.137073 | + | 0.137073i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | 1.41421 | − | 1.41421i | 0.0455961 | − | 0.0455961i | ||||
\(963\) | −5.79555 | + | 1.55291i | −0.186759 | + | 0.0500420i | ||||
\(964\) | −6.92820 | − | 12.0000i | −0.223142 | − | 0.386494i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −9.00000 | − | 15.5885i | −0.289570 | − | 0.501550i | ||||
\(967\) | 9.86233 | − | 36.8067i | 0.317151 | − | 1.18362i | −0.604819 | − | 0.796363i | \(-0.706755\pi\) |
0.921970 | − | 0.387261i | \(-0.126579\pi\) | |||||||
\(968\) | −1.41421 | − | 1.41421i | −0.0454545 | − | 0.0454545i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.00000 | − | 5.19615i | 0.288824 | − | 0.166752i | −0.348588 | − | 0.937276i | \(-0.613339\pi\) |
0.637411 | + | 0.770524i | \(0.280005\pi\) | |||||||
\(972\) | −9.65926 | − | 2.58819i | −0.309821 | − | 0.0830162i | ||||
\(973\) | 8.96575 | + | 33.4607i | 0.287429 | + | 1.07270i | ||||
\(974\) | 21.6506 | − | 12.5000i | 0.693731 | − | 0.400526i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | −0.128037 | ||||||||
\(977\) | −33.9411 | + | 33.9411i | −1.08587 | + | 1.08587i | −0.0899242 | + | 0.995949i | \(0.528662\pi\) |
−0.995949 | + | 0.0899242i | \(0.971338\pi\) | |||||||
\(978\) | 12.5521 | + | 46.8449i | 0.401371 | + | 1.49794i | ||||
\(979\) | −7.79423 | + | 13.5000i | −0.249105 | + | 0.431462i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.43520 | + | 20.2844i | 0.173444 | + | 0.647303i | ||||
\(983\) | 5.43520 | − | 20.2844i | 0.173356 | − | 0.646973i | −0.823470 | − | 0.567360i | \(-0.807965\pi\) |
0.996826 | − | 0.0796132i | \(-0.0253685\pi\) | |||||||
\(984\) | −5.19615 | + | 9.00000i | −0.165647 | + | 0.286910i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 25.4558 | − | 25.4558i | 0.810268 | − | 0.810268i | ||||
\(988\) | −6.83083 | + | 5.41662i | −0.217318 | + | 0.172326i | ||||
\(989\) | 36.0000i | 1.14473i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.00000 | + | 3.46410i | −0.190596 | + | 0.110041i | −0.592262 | − | 0.805746i | \(-0.701765\pi\) |
0.401665 | + | 0.915786i | \(0.368431\pi\) | |||||||
\(992\) | −3.34607 | + | 0.896575i | −0.106238 | + | 0.0284663i | ||||
\(993\) | −36.8067 | − | 9.86233i | −1.16803 | − | 0.312972i | ||||
\(994\) | −15.5885 | − | 9.00000i | −0.494436 | − | 0.285463i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.36516 | − | 2.24144i | 0.264927 | − | 0.0709871i | −0.123910 | − | 0.992293i | \(-0.539543\pi\) |
0.388837 | + | 0.921306i | \(0.372877\pi\) | |||||||
\(998\) | −6.76148 | + | 1.81173i | −0.214031 | + | 0.0573494i | ||||
\(999\) | − | 4.00000i | − | 0.126554i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 950.2.q.d.107.2 | yes | 8 | |
5.2 | odd | 4 | inner | 950.2.q.d.943.1 | yes | 8 | |
5.3 | odd | 4 | inner | 950.2.q.d.943.2 | yes | 8 | |
5.4 | even | 2 | inner | 950.2.q.d.107.1 | ✓ | 8 | |
19.8 | odd | 6 | inner | 950.2.q.d.407.2 | yes | 8 | |
95.8 | even | 12 | inner | 950.2.q.d.293.2 | yes | 8 | |
95.27 | even | 12 | inner | 950.2.q.d.293.1 | yes | 8 | |
95.84 | odd | 6 | inner | 950.2.q.d.407.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.q.d.107.1 | ✓ | 8 | 5.4 | even | 2 | inner | |
950.2.q.d.107.2 | yes | 8 | 1.1 | even | 1 | trivial | |
950.2.q.d.293.1 | yes | 8 | 95.27 | even | 12 | inner | |
950.2.q.d.293.2 | yes | 8 | 95.8 | even | 12 | inner | |
950.2.q.d.407.1 | yes | 8 | 95.84 | odd | 6 | inner | |
950.2.q.d.407.2 | yes | 8 | 19.8 | odd | 6 | inner | |
950.2.q.d.943.1 | yes | 8 | 5.2 | odd | 4 | inner | |
950.2.q.d.943.2 | yes | 8 | 5.3 | odd | 4 | inner |