Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(257,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.p (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: | \(3.59326809096\) |
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 | 257.2 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.257 |
Dual form | 450.2.p.b.443.2 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.965926 | + | 0.258819i | 0.683013 | + | 0.183013i | ||||
\(3\) | 0.448288 | + | 1.67303i | 0.258819 | + | 0.965926i | ||||
\(4\) | 0.866025 | + | 0.500000i | 0.433013 | + | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.73205i | 0.707107i | ||||||||
\(7\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | −2.59808 | + | 1.50000i | −0.866025 | + | 0.500000i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | + | 0.866025i | −0.452267 | + | 0.261116i | −0.708787 | − | 0.705422i | \(-0.750757\pi\) |
0.256520 | + | 0.966539i | \(0.417424\pi\) | |||||||
\(12\) | −0.448288 | + | 1.67303i | −0.129410 | + | 0.482963i | ||||
\(13\) | 1.79315 | + | 6.69213i | 0.497331 | + | 1.85606i | 0.516565 | + | 0.856248i | \(0.327210\pi\) |
−0.0192343 | + | 0.999815i | \(0.506123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 2.12132 | − | 2.12132i | 0.514496 | − | 0.514496i | −0.401405 | − | 0.915901i | \(-0.631478\pi\) |
0.915901 | + | 0.401405i | \(0.131478\pi\) | |||||||
\(18\) | −2.89778 | + | 0.776457i | −0.683013 | + | 0.183013i | ||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.67303 | + | 0.448288i | −0.356692 | + | 0.0955753i | ||||
\(23\) | 5.79555 | − | 1.55291i | 1.20846 | − | 0.323805i | 0.402300 | − | 0.915508i | \(-0.368211\pi\) |
0.806156 | + | 0.591703i | \(0.201544\pi\) | |||||||
\(24\) | −0.866025 | + | 1.50000i | −0.176777 | + | 0.306186i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.92820i | 1.35873i | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.707107 | − | 0.707107i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.73205 | − | 3.00000i | −0.321634 | − | 0.557086i | 0.659192 | − | 0.751975i | \(-0.270899\pi\) |
−0.980825 | + | 0.194889i | \(0.937565\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | + | 3.46410i | −0.359211 | + | 0.622171i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0.258819 | + | 0.965926i | 0.0457532 | + | 0.170753i | ||||
\(33\) | −2.12132 | − | 2.12132i | −0.369274 | − | 0.369274i | ||||
\(34\) | 2.59808 | − | 1.50000i | 0.445566 | − | 0.257248i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | −4.89898 | − | 4.89898i | −0.805387 | − | 0.805387i | 0.178545 | − | 0.983932i | \(-0.442861\pi\) |
−0.983932 | + | 0.178545i | \(0.942861\pi\) | |||||||
\(38\) | 1.03528 | − | 3.86370i | 0.167944 | − | 0.626775i | ||||
\(39\) | −10.3923 | + | 6.00000i | −1.66410 | + | 0.960769i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | − | 3.46410i | −0.937043 | − | 0.541002i | −0.0480106 | − | 0.998847i | \(-0.515288\pi\) |
−0.889032 | + | 0.457845i | \(0.848621\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.36516 | + | 2.24144i | 1.27568 | + | 0.341816i | 0.832203 | − | 0.554472i | \(-0.187080\pi\) |
0.443473 | + | 0.896288i | \(0.353746\pi\) | |||||||
\(44\) | −1.73205 | −0.261116 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | 11.5911 | + | 3.10583i | 1.69074 | + | 0.453032i | 0.970580 | − | 0.240779i | \(-0.0774030\pi\) |
0.720157 | + | 0.693811i | \(0.244070\pi\) | |||||||
\(48\) | −1.22474 | + | 1.22474i | −0.176777 | + | 0.176777i | ||||
\(49\) | 6.06218 | + | 3.50000i | 0.866025 | + | 0.500000i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.50000 | + | 2.59808i | 0.630126 | + | 0.363803i | ||||
\(52\) | −1.79315 | + | 6.69213i | −0.248665 | + | 0.928032i | ||||
\(53\) | −8.48528 | − | 8.48528i | −1.16554 | − | 1.16554i | −0.983243 | − | 0.182300i | \(-0.941646\pi\) |
−0.182300 | − | 0.983243i | \(-0.558354\pi\) | |||||||
\(54\) | −2.59808 | − | 4.50000i | −0.353553 | − | 0.612372i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.69213 | − | 1.79315i | 0.886394 | − | 0.237509i | ||||
\(58\) | −0.896575 | − | 3.34607i | −0.117726 | − | 0.439360i | ||||
\(59\) | 4.33013 | − | 7.50000i | 0.563735 | − | 0.976417i | −0.433432 | − | 0.901186i | \(-0.642697\pi\) |
0.997166 | − | 0.0752304i | \(-0.0239692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | − | 6.92820i | −0.512148 | − | 0.887066i | −0.999901 | − | 0.0140840i | \(-0.995517\pi\) |
0.487753 | − | 0.872982i | \(-0.337817\pi\) | |||||||
\(62\) | −2.82843 | + | 2.82843i | −0.359211 | + | 0.359211i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.50000 | − | 2.59808i | −0.184637 | − | 0.319801i | ||||
\(67\) | 3.34607 | − | 0.896575i | 0.408787 | − | 0.109534i | −0.0485648 | − | 0.998820i | \(-0.515465\pi\) |
0.457352 | + | 0.889286i | \(0.348798\pi\) | |||||||
\(68\) | 2.89778 | − | 0.776457i | 0.351407 | − | 0.0941593i | ||||
\(69\) | 5.19615 | + | 9.00000i | 0.625543 | + | 1.08347i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.46410i | − | 0.411113i | −0.978645 | − | 0.205557i | \(-0.934100\pi\) | ||
0.978645 | − | 0.205557i | \(-0.0659005\pi\) | |||||||
\(72\) | −2.89778 | − | 0.776457i | −0.341506 | − | 0.0915064i | ||||
\(73\) | −4.89898 | + | 4.89898i | −0.573382 | + | 0.573382i | −0.933072 | − | 0.359690i | \(-0.882883\pi\) |
0.359690 | + | 0.933072i | \(0.382883\pi\) | |||||||
\(74\) | −3.46410 | − | 6.00000i | −0.402694 | − | 0.697486i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | − | 3.46410i | 0.229416 | − | 0.397360i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −11.5911 | + | 3.10583i | −1.31243 | + | 0.351666i | ||||
\(79\) | 3.46410 | − | 2.00000i | 0.389742 | − | 0.225018i | −0.292306 | − | 0.956325i | \(-0.594423\pi\) |
0.682048 | + | 0.731307i | \(0.261089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.50000 | − | 7.79423i | 0.500000 | − | 0.866025i | ||||
\(82\) | −4.89898 | − | 4.89898i | −0.541002 | − | 0.541002i | ||||
\(83\) | 2.32937 | − | 8.69333i | 0.255682 | − | 0.954217i | −0.712028 | − | 0.702151i | \(-0.752223\pi\) |
0.967710 | − | 0.252066i | \(-0.0811101\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.50000 | + | 4.33013i | 0.808746 | + | 0.466930i | ||||
\(87\) | 4.24264 | − | 4.24264i | 0.454859 | − | 0.454859i | ||||
\(88\) | −1.67303 | − | 0.448288i | −0.178346 | − | 0.0477876i | ||||
\(89\) | 1.73205 | 0.183597 | 0.0917985 | − | 0.995778i | \(-0.470738\pi\) | ||||
0.0917985 | + | 0.995778i | \(0.470738\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.79555 | + | 1.55291i | 0.604228 | + | 0.161903i | ||||
\(93\) | −6.69213 | − | 1.79315i | −0.693942 | − | 0.185941i | ||||
\(94\) | 10.3923 | + | 6.00000i | 1.07188 | + | 0.618853i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.50000 | + | 0.866025i | −0.153093 | + | 0.0883883i | ||||
\(97\) | −4.03459 | + | 15.0573i | −0.409651 | + | 1.52884i | 0.385664 | + | 0.922639i | \(0.373972\pi\) |
−0.795314 | + | 0.606197i | \(0.792694\pi\) | |||||||
\(98\) | 4.94975 | + | 4.94975i | 0.500000 | + | 0.500000i | ||||
\(99\) | 2.59808 | − | 4.50000i | 0.261116 | − | 0.452267i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0000 | − | 6.92820i | 1.19404 | − | 0.689382i | 0.234823 | − | 0.972038i | \(-0.424549\pi\) |
0.959221 | + | 0.282656i | \(0.0912155\pi\) | |||||||
\(102\) | 3.67423 | + | 3.67423i | 0.363803 | + | 0.363803i | ||||
\(103\) | 1.79315 | + | 6.69213i | 0.176684 | + | 0.659395i | 0.996259 | + | 0.0864221i | \(0.0275434\pi\) |
−0.819574 | + | 0.572973i | \(0.805790\pi\) | |||||||
\(104\) | −3.46410 | + | 6.00000i | −0.339683 | + | 0.588348i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | − | 10.3923i | −0.582772 | − | 1.00939i | ||||
\(107\) | −8.48528 | + | 8.48528i | −0.820303 | + | 0.820303i | −0.986151 | − | 0.165848i | \(-0.946964\pi\) |
0.165848 | + | 0.986151i | \(0.446964\pi\) | |||||||
\(108\) | −1.34486 | − | 5.01910i | −0.129410 | − | 0.482963i | ||||
\(109\) | − | 2.00000i | − | 0.191565i | −0.995402 | − | 0.0957826i | \(-0.969465\pi\) | ||
0.995402 | − | 0.0957826i | \(-0.0305354\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00000 | − | 10.3923i | 0.569495 | − | 0.986394i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.89778 | + | 0.776457i | −0.272600 | + | 0.0730429i | −0.392529 | − | 0.919739i | \(-0.628400\pi\) |
0.119929 | + | 0.992782i | \(0.461733\pi\) | |||||||
\(114\) | 6.92820 | 0.648886 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 3.46410i | − | 0.321634i | ||||||
\(117\) | −14.6969 | − | 14.6969i | −1.35873 | − | 1.35873i | ||||
\(118\) | 6.12372 | − | 6.12372i | 0.563735 | − | 0.563735i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00000 | + | 6.92820i | −0.363636 | + | 0.629837i | ||||
\(122\) | −2.07055 | − | 7.72741i | −0.187459 | − | 0.699607i | ||||
\(123\) | 3.10583 | − | 11.5911i | 0.280043 | − | 1.04514i | ||||
\(124\) | −3.46410 | + | 2.00000i | −0.311086 | + | 0.179605i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(128\) | −0.258819 | + | 0.965926i | −0.0228766 | + | 0.0853766i | ||||
\(129\) | 15.0000i | 1.32068i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.0000 | − | 8.66025i | −1.31056 | − | 0.756650i | −0.328368 | − | 0.944550i | \(-0.606499\pi\) |
−0.982188 | + | 0.187900i | \(0.939832\pi\) | |||||||
\(132\) | −0.776457 | − | 2.89778i | −0.0675819 | − | 0.252219i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.46410 | 0.299253 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00000 | 0.257248 | ||||||||
\(137\) | −17.3867 | − | 4.65874i | −1.48544 | − | 0.398023i | −0.577247 | − | 0.816569i | \(-0.695873\pi\) |
−0.908196 | + | 0.418546i | \(0.862540\pi\) | |||||||
\(138\) | 2.68973 | + | 10.0382i | 0.228965 | + | 0.854508i | ||||
\(139\) | 11.2583 | + | 6.50000i | 0.954919 | + | 0.551323i | 0.894606 | − | 0.446857i | \(-0.147457\pi\) |
0.0603135 | + | 0.998179i | \(0.480790\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.7846i | 1.75038i | ||||||||
\(142\) | 0.896575 | − | 3.34607i | 0.0752389 | − | 0.280796i | ||||
\(143\) | −8.48528 | − | 8.48528i | −0.709575 | − | 0.709575i | ||||
\(144\) | −2.59808 | − | 1.50000i | −0.216506 | − | 0.125000i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.00000 | + | 3.46410i | −0.496564 | + | 0.286691i | ||||
\(147\) | −3.13801 | + | 11.7112i | −0.258819 | + | 0.965926i | ||||
\(148\) | −1.79315 | − | 6.69213i | −0.147396 | − | 0.550090i | ||||
\(149\) | 5.19615 | − | 9.00000i | 0.425685 | − | 0.737309i | −0.570799 | − | 0.821090i | \(-0.693366\pi\) |
0.996484 | + | 0.0837813i | \(0.0266997\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | + | 1.73205i | 0.0813788 | + | 0.140952i | 0.903842 | − | 0.427865i | \(-0.140734\pi\) |
−0.822464 | + | 0.568818i | \(0.807401\pi\) | |||||||
\(152\) | 2.82843 | − | 2.82843i | 0.229416 | − | 0.229416i | ||||
\(153\) | −2.32937 | + | 8.69333i | −0.188319 | + | 0.702814i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −12.0000 | −0.960769 | ||||||||
\(157\) | 6.69213 | − | 1.79315i | 0.534090 | − | 0.143109i | 0.0183138 | − | 0.999832i | \(-0.494170\pi\) |
0.515776 | + | 0.856723i | \(0.327504\pi\) | |||||||
\(158\) | 3.86370 | − | 1.03528i | 0.307380 | − | 0.0823622i | ||||
\(159\) | 10.3923 | − | 18.0000i | 0.824163 | − | 1.42749i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 6.36396 | − | 6.36396i | 0.500000 | − | 0.500000i | ||||
\(163\) | −1.22474 | + | 1.22474i | −0.0959294 | + | 0.0959294i | −0.753443 | − | 0.657513i | \(-0.771608\pi\) |
0.657513 | + | 0.753443i | \(0.271608\pi\) | |||||||
\(164\) | −3.46410 | − | 6.00000i | −0.270501 | − | 0.468521i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.50000 | − | 7.79423i | 0.349268 | − | 0.604949i | ||||
\(167\) | 1.55291 | + | 5.79555i | 0.120168 | + | 0.448474i | 0.999621 | − | 0.0275115i | \(-0.00875830\pi\) |
−0.879453 | + | 0.475985i | \(0.842092\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −30.3109 | + | 17.5000i | −2.33161 | + | 1.34615i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.00000 | + | 10.3923i | 0.458831 | + | 0.794719i | ||||
\(172\) | 6.12372 | + | 6.12372i | 0.466930 | + | 0.466930i | ||||
\(173\) | −4.65874 | + | 17.3867i | −0.354198 | + | 1.32188i | 0.527294 | + | 0.849683i | \(0.323207\pi\) |
−0.881491 | + | 0.472200i | \(0.843460\pi\) | |||||||
\(174\) | 5.19615 | − | 3.00000i | 0.393919 | − | 0.227429i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.50000 | − | 0.866025i | −0.113067 | − | 0.0652791i | ||||
\(177\) | 14.4889 | + | 3.88229i | 1.08905 | + | 0.291810i | ||||
\(178\) | 1.67303 | + | 0.448288i | 0.125399 | + | 0.0336006i | ||||
\(179\) | −12.1244 | −0.906217 | −0.453108 | − | 0.891455i | \(-0.649685\pi\) | ||||
−0.453108 | + | 0.891455i | \(0.649685\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.79796 | − | 9.79796i | 0.724286 | − | 0.724286i | ||||
\(184\) | 5.19615 | + | 3.00000i | 0.383065 | + | 0.221163i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.00000 | − | 3.46410i | −0.439941 | − | 0.254000i | ||||
\(187\) | −1.34486 | + | 5.01910i | −0.0983461 | + | 0.367033i | ||||
\(188\) | 8.48528 | + | 8.48528i | 0.618853 | + | 0.618853i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | − | 1.73205i | 0.217072 | − | 0.125327i | −0.387522 | − | 0.921861i | \(-0.626669\pi\) |
0.604594 | + | 0.796534i | \(0.293335\pi\) | |||||||
\(192\) | −1.67303 | + | 0.448288i | −0.120741 | + | 0.0323524i | ||||
\(193\) | −1.34486 | − | 5.01910i | −0.0968054 | − | 0.361283i | 0.900482 | − | 0.434894i | \(-0.143214\pi\) |
−0.997287 | + | 0.0736115i | \(0.976548\pi\) | |||||||
\(194\) | −7.79423 | + | 13.5000i | −0.559593 | + | 0.969244i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.50000 | + | 6.06218i | 0.250000 | + | 0.433013i | ||||
\(197\) | 4.24264 | − | 4.24264i | 0.302276 | − | 0.302276i | −0.539628 | − | 0.841904i | \(-0.681435\pi\) |
0.841904 | + | 0.539628i | \(0.181435\pi\) | |||||||
\(198\) | 3.67423 | − | 3.67423i | 0.261116 | − | 0.261116i | ||||
\(199\) | − | 26.0000i | − | 1.84309i | −0.388270 | − | 0.921546i | \(-0.626927\pi\) | ||
0.388270 | − | 0.921546i | \(-0.373073\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.00000 | + | 5.19615i | 0.211604 | + | 0.366508i | ||||
\(202\) | 13.3843 | − | 3.58630i | 0.941713 | − | 0.252331i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.59808 | + | 4.50000i | 0.181902 | + | 0.315063i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.92820i | 0.482711i | ||||||||
\(207\) | −12.7279 | + | 12.7279i | −0.884652 | + | 0.884652i | ||||
\(208\) | −4.89898 | + | 4.89898i | −0.339683 | + | 0.339683i | ||||
\(209\) | 3.46410 | + | 6.00000i | 0.239617 | + | 0.415029i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.5000 | + | 19.9186i | −0.791693 | + | 1.37125i | 0.133226 | + | 0.991086i | \(0.457467\pi\) |
−0.924918 | + | 0.380166i | \(0.875867\pi\) | |||||||
\(212\) | −3.10583 | − | 11.5911i | −0.213309 | − | 0.796081i | ||||
\(213\) | 5.79555 | − | 1.55291i | 0.397105 | − | 0.106404i | ||||
\(214\) | −10.3923 | + | 6.00000i | −0.710403 | + | 0.410152i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 5.19615i | − | 0.353553i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.517638 | − | 1.93185i | 0.0350589 | − | 0.130842i | ||||
\(219\) | −10.3923 | − | 6.00000i | −0.702247 | − | 0.405442i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.0000 | + | 10.3923i | 1.21081 | + | 0.699062i | ||||
\(222\) | 8.48528 | − | 8.48528i | 0.569495 | − | 0.569495i | ||||
\(223\) | −3.34607 | − | 0.896575i | −0.224069 | − | 0.0600391i | 0.145038 | − | 0.989426i | \(-0.453670\pi\) |
−0.369107 | + | 0.929387i | \(0.620336\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.00000 | −0.199557 | ||||||||
\(227\) | 2.89778 | + | 0.776457i | 0.192332 | + | 0.0515353i | 0.353699 | − | 0.935359i | \(-0.384924\pi\) |
−0.161367 | + | 0.986894i | \(0.551590\pi\) | |||||||
\(228\) | 6.69213 | + | 1.79315i | 0.443197 | + | 0.118754i | ||||
\(229\) | −17.3205 | − | 10.0000i | −1.14457 | − | 0.660819i | −0.197013 | − | 0.980401i | \(-0.563124\pi\) |
−0.947559 | + | 0.319582i | \(0.896457\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.896575 | − | 3.34607i | 0.0588631 | − | 0.219680i | ||||
\(233\) | 6.36396 | + | 6.36396i | 0.416917 | + | 0.416917i | 0.884140 | − | 0.467223i | \(-0.154745\pi\) |
−0.467223 | + | 0.884140i | \(0.654745\pi\) | |||||||
\(234\) | −10.3923 | − | 18.0000i | −0.679366 | − | 1.17670i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.50000 | − | 4.33013i | 0.488208 | − | 0.281867i | ||||
\(237\) | 4.89898 | + | 4.89898i | 0.318223 | + | 0.318223i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.19615 | + | 9.00000i | −0.336111 | + | 0.582162i | −0.983698 | − | 0.179830i | \(-0.942445\pi\) |
0.647586 | + | 0.761992i | \(0.275778\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00000 | + | 8.66025i | 0.322078 | + | 0.557856i | 0.980917 | − | 0.194429i | \(-0.0622852\pi\) |
−0.658838 | + | 0.752285i | \(0.728952\pi\) | |||||||
\(242\) | −5.65685 | + | 5.65685i | −0.363636 | + | 0.363636i | ||||
\(243\) | 15.0573 | + | 4.03459i | 0.965926 | + | 0.258819i | ||||
\(244\) | − | 8.00000i | − | 0.512148i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.00000 | − | 10.3923i | 0.382546 | − | 0.662589i | ||||
\(247\) | 26.7685 | − | 7.17260i | 1.70324 | − | 0.456382i | ||||
\(248\) | −3.86370 | + | 1.03528i | −0.245345 | + | 0.0657401i | ||||
\(249\) | 15.5885 | 0.987878 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.3923i | 0.655956i | 0.944685 | + | 0.327978i | \(0.106367\pi\) | ||||
−0.944685 | + | 0.327978i | \(0.893633\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.34847 | + | 7.34847i | −0.461994 | + | 0.461994i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −0.776457 | − | 2.89778i | −0.0484341 | − | 0.180758i | 0.937471 | − | 0.348063i | \(-0.113160\pi\) |
−0.985905 | + | 0.167304i | \(0.946494\pi\) | |||||||
\(258\) | −3.88229 | + | 14.4889i | −0.241701 | + | 0.902039i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.00000 | + | 5.19615i | 0.557086 | + | 0.321634i | ||||
\(262\) | −12.2474 | − | 12.2474i | −0.756650 | − | 0.756650i | ||||
\(263\) | −6.21166 | + | 23.1822i | −0.383027 | + | 1.42948i | 0.458226 | + | 0.888836i | \(0.348485\pi\) |
−0.841253 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(264\) | − | 3.00000i | − | 0.184637i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.776457 | + | 2.89778i | 0.0475184 | + | 0.177341i | ||||
\(268\) | 3.34607 | + | 0.896575i | 0.204393 | + | 0.0547671i | ||||
\(269\) | 6.92820 | 0.422420 | 0.211210 | − | 0.977441i | \(-0.432260\pi\) | ||||
0.211210 | + | 0.977441i | \(0.432260\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 2.89778 | + | 0.776457i | 0.175704 | + | 0.0470796i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.5885 | − | 9.00000i | −0.941733 | − | 0.543710i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 10.3923i | 0.625543i | ||||||||
\(277\) | −0.896575 | + | 3.34607i | −0.0538700 | + | 0.201046i | −0.987616 | − | 0.156891i | \(-0.949853\pi\) |
0.933746 | + | 0.357936i | \(0.116520\pi\) | |||||||
\(278\) | 9.19239 | + | 9.19239i | 0.551323 | + | 0.551323i | ||||
\(279\) | − | 12.0000i | − | 0.718421i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | + | 10.3923i | −1.07379 | + | 0.619953i | −0.929214 | − | 0.369541i | \(-0.879515\pi\) |
−0.144575 | + | 0.989494i | \(0.546182\pi\) | |||||||
\(282\) | −5.37945 | + | 20.0764i | −0.320342 | + | 1.19553i | ||||
\(283\) | −8.51747 | − | 31.7876i | −0.506311 | − | 1.88958i | −0.454120 | − | 0.890941i | \(-0.650046\pi\) |
−0.0521913 | − | 0.998637i | \(-0.516621\pi\) | |||||||
\(284\) | 1.73205 | − | 3.00000i | 0.102778 | − | 0.178017i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | − | 10.3923i | −0.354787 | − | 0.614510i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.12132 | − | 2.12132i | −0.125000 | − | 0.125000i | ||||
\(289\) | 8.00000i | 0.470588i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −27.0000 | −1.58277 | ||||||||
\(292\) | −6.69213 | + | 1.79315i | −0.391627 | + | 0.104936i | ||||
\(293\) | −11.5911 | + | 3.10583i | −0.677160 | + | 0.181444i | −0.580978 | − | 0.813919i | \(-0.697330\pi\) |
−0.0961820 | + | 0.995364i | \(0.530663\pi\) | |||||||
\(294\) | −6.06218 | + | 10.5000i | −0.353553 | + | 0.612372i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 6.92820i | − | 0.402694i | ||||||
\(297\) | 8.69333 | + | 2.32937i | 0.504438 | + | 0.135164i | ||||
\(298\) | 7.34847 | − | 7.34847i | 0.425685 | − | 0.425685i | ||||
\(299\) | 20.7846 | + | 36.0000i | 1.20201 | + | 2.08193i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.517638 | + | 1.93185i | 0.0297867 | + | 0.111166i | ||||
\(303\) | 16.9706 | + | 16.9706i | 0.974933 | + | 0.974933i | ||||
\(304\) | 3.46410 | − | 2.00000i | 0.198680 | − | 0.114708i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.50000 | + | 7.79423i | −0.257248 | + | 0.445566i | ||||
\(307\) | −15.9217 | − | 15.9217i | −0.908698 | − | 0.908698i | 0.0874688 | − | 0.996167i | \(-0.472122\pi\) |
−0.996167 | + | 0.0874688i | \(0.972122\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.3923 | + | 6.00000i | −0.591198 | + | 0.341328i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.00000 | − | 1.73205i | −0.170114 | − | 0.0982156i | 0.412525 | − | 0.910946i | \(-0.364647\pi\) |
−0.582640 | + | 0.812731i | \(0.697980\pi\) | |||||||
\(312\) | −11.5911 | − | 3.10583i | −0.656217 | − | 0.175833i | ||||
\(313\) | 1.67303 | + | 0.448288i | 0.0945654 | + | 0.0253387i | 0.305791 | − | 0.952099i | \(-0.401079\pi\) |
−0.211226 | + | 0.977437i | \(0.567746\pi\) | |||||||
\(314\) | 6.92820 | 0.390981 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.00000 | 0.225018 | ||||||||
\(317\) | −28.9778 | − | 7.76457i | −1.62755 | − | 0.436102i | −0.674346 | − | 0.738416i | \(-0.735574\pi\) |
−0.953208 | + | 0.302314i | \(0.902241\pi\) | |||||||
\(318\) | 14.6969 | − | 14.6969i | 0.824163 | − | 0.824163i | ||||
\(319\) | 5.19615 | + | 3.00000i | 0.290929 | + | 0.167968i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.0000 | − | 10.3923i | −1.00466 | − | 0.580042i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.48528 | − | 8.48528i | −0.472134 | − | 0.472134i | ||||
\(324\) | 7.79423 | − | 4.50000i | 0.433013 | − | 0.250000i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.50000 | + | 0.866025i | −0.0830773 | + | 0.0479647i | ||||
\(327\) | 3.34607 | − | 0.896575i | 0.185038 | − | 0.0495807i | ||||
\(328\) | −1.79315 | − | 6.69213i | −0.0990102 | − | 0.369511i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.500000 | + | 0.866025i | 0.0274825 | + | 0.0476011i | 0.879440 | − | 0.476011i | \(-0.157918\pi\) |
−0.851957 | + | 0.523612i | \(0.824584\pi\) | |||||||
\(332\) | 6.36396 | − | 6.36396i | 0.349268 | − | 0.349268i | ||||
\(333\) | 20.0764 | + | 5.37945i | 1.10018 | + | 0.294792i | ||||
\(334\) | 6.00000i | 0.328305i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.36516 | + | 2.24144i | −0.455679 | + | 0.122099i | −0.479356 | − | 0.877621i | \(-0.659130\pi\) |
0.0236762 | + | 0.999720i | \(0.492463\pi\) | |||||||
\(338\) | −33.8074 | + | 9.05867i | −1.83888 | + | 0.492727i | ||||
\(339\) | −2.59808 | − | 4.50000i | −0.141108 | − | 0.244406i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 6.92820i | − | 0.375183i | ||||||
\(342\) | 3.10583 | + | 11.5911i | 0.167944 | + | 0.626775i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.33013 | + | 7.50000i | 0.233465 | + | 0.404373i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.00000 | + | 15.5885i | −0.483843 | + | 0.838041i | ||||
\(347\) | 5.43520 | + | 20.2844i | 0.291777 | + | 1.08893i | 0.943744 | + | 0.330678i | \(0.107278\pi\) |
−0.651967 | + | 0.758248i | \(0.726056\pi\) | |||||||
\(348\) | 5.79555 | − | 1.55291i | 0.310674 | − | 0.0832449i | ||||
\(349\) | −8.66025 | + | 5.00000i | −0.463573 | + | 0.267644i | −0.713545 | − | 0.700609i | \(-0.752912\pi\) |
0.249973 | + | 0.968253i | \(0.419578\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.0000 | − | 31.1769i | 0.960769 | − | 1.66410i | ||||
\(352\) | −1.22474 | − | 1.22474i | −0.0652791 | − | 0.0652791i | ||||
\(353\) | −2.32937 | + | 8.69333i | −0.123980 | + | 0.462699i | −0.999801 | − | 0.0199361i | \(-0.993654\pi\) |
0.875821 | + | 0.482635i | \(0.160320\pi\) | |||||||
\(354\) | 12.9904 | + | 7.50000i | 0.690431 | + | 0.398621i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.50000 | + | 0.866025i | 0.0794998 | + | 0.0458993i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.7112 | − | 3.13801i | −0.618958 | − | 0.165849i | ||||
\(359\) | 13.8564 | 0.731313 | 0.365657 | − | 0.930750i | \(-0.380844\pi\) | ||||
0.365657 | + | 0.930750i | \(0.380844\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | −1.93185 | − | 0.517638i | −0.101536 | − | 0.0272065i | ||||
\(363\) | −13.3843 | − | 3.58630i | −0.702492 | − | 0.188232i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 12.0000 | − | 6.92820i | 0.627250 | − | 0.362143i | ||||
\(367\) | 6.27603 | − | 23.4225i | 0.327606 | − | 1.22264i | −0.584060 | − | 0.811710i | \(-0.698537\pi\) |
0.911666 | − | 0.410932i | \(-0.134797\pi\) | |||||||
\(368\) | 4.24264 | + | 4.24264i | 0.221163 | + | 0.221163i | ||||
\(369\) | 20.7846 | 1.08200 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.89898 | − | 4.89898i | −0.254000 | − | 0.254000i | ||||
\(373\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(374\) | −2.59808 | + | 4.50000i | −0.134343 | + | 0.232689i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.00000 | + | 10.3923i | 0.309426 | + | 0.535942i | ||||
\(377\) | 16.9706 | − | 16.9706i | 0.874028 | − | 0.874028i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 19.0000i | − | 0.975964i | −0.872854 | − | 0.487982i | \(-0.837733\pi\) | ||
0.872854 | − | 0.487982i | \(-0.162267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.34607 | − | 0.896575i | 0.171200 | − | 0.0458728i | ||||
\(383\) | 28.9778 | − | 7.76457i | 1.48070 | − | 0.396751i | 0.574111 | − | 0.818777i | \(-0.305348\pi\) |
0.906584 | + | 0.422026i | \(0.138681\pi\) | |||||||
\(384\) | −1.73205 | −0.0883883 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 5.19615i | − | 0.264477i | ||||||
\(387\) | −25.0955 | + | 6.72432i | −1.27568 | + | 0.341816i | ||||
\(388\) | −11.0227 | + | 11.0227i | −0.559593 | + | 0.559593i | ||||
\(389\) | 5.19615 | + | 9.00000i | 0.263455 | + | 0.456318i | 0.967158 | − | 0.254177i | \(-0.0818045\pi\) |
−0.703702 | + | 0.710495i | \(0.748471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.00000 | − | 15.5885i | 0.455150 | − | 0.788342i | ||||
\(392\) | 1.81173 | + | 6.76148i | 0.0915064 | + | 0.341506i | ||||
\(393\) | 7.76457 | − | 28.9778i | 0.391671 | − | 1.46174i | ||||
\(394\) | 5.19615 | − | 3.00000i | 0.261778 | − | 0.151138i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.50000 | − | 2.59808i | 0.226134 | − | 0.130558i | ||||
\(397\) | −2.44949 | − | 2.44949i | −0.122936 | − | 0.122936i | 0.642962 | − | 0.765898i | \(-0.277705\pi\) |
−0.765898 | + | 0.642962i | \(0.777705\pi\) | |||||||
\(398\) | 6.72930 | − | 25.1141i | 0.337309 | − | 1.25885i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.5000 | + | 12.9904i | 1.12360 | + | 0.648709i | 0.942317 | − | 0.334723i | \(-0.108643\pi\) |
0.181280 | + | 0.983432i | \(0.441976\pi\) | |||||||
\(402\) | 1.55291 | + | 5.79555i | 0.0774523 | + | 0.289056i | ||||
\(403\) | −26.7685 | − | 7.17260i | −1.33344 | − | 0.357293i | ||||
\(404\) | 13.8564 | 0.689382 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.5911 | + | 3.10583i | 0.574550 | + | 0.153950i | ||||
\(408\) | 1.34486 | + | 5.01910i | 0.0665807 | + | 0.248482i | ||||
\(409\) | −1.73205 | − | 1.00000i | −0.0856444 | − | 0.0494468i | 0.456566 | − | 0.889689i | \(-0.349079\pi\) |
−0.542211 | + | 0.840243i | \(0.682412\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 31.1769i | − | 1.53784i | ||||||
\(412\) | −1.79315 | + | 6.69213i | −0.0883422 | + | 0.329698i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −15.5885 | + | 9.00000i | −0.766131 | + | 0.442326i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.00000 | + | 3.46410i | −0.294174 | + | 0.169842i | ||||
\(417\) | −5.82774 | + | 21.7494i | −0.285386 | + | 1.06507i | ||||
\(418\) | 1.79315 | + | 6.69213i | 0.0877059 | + | 0.327323i | ||||
\(419\) | −2.59808 | + | 4.50000i | −0.126924 | + | 0.219839i | −0.922484 | − | 0.386037i | \(-0.873844\pi\) |
0.795559 | + | 0.605876i | \(0.207177\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.0000 | − | 24.2487i | −0.682318 | − | 1.18181i | −0.974272 | − | 0.225377i | \(-0.927639\pi\) |
0.291953 | − | 0.956433i | \(-0.405695\pi\) | |||||||
\(422\) | −16.2635 | + | 16.2635i | −0.791693 | + | 0.791693i | ||||
\(423\) | −34.7733 | + | 9.31749i | −1.69074 | + | 0.453032i | ||||
\(424\) | − | 12.0000i | − | 0.582772i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.00000 | 0.290701 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −11.5911 | + | 3.10583i | −0.560277 | + | 0.150126i | ||||
\(429\) | 10.3923 | − | 18.0000i | 0.501745 | − | 0.869048i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 24.2487i | − | 1.16802i | −0.811747 | − | 0.584010i | \(-0.801483\pi\) | ||
0.811747 | − | 0.584010i | \(-0.198517\pi\) | |||||||
\(432\) | 1.34486 | − | 5.01910i | 0.0647048 | − | 0.241481i | ||||
\(433\) | 20.8207 | − | 20.8207i | 1.00058 | − | 1.00058i | 0.000577367 | − | 1.00000i | \(-0.499816\pi\) |
1.00000 | 0.000577367i | \(-0.000183782\pi\) | ||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.00000 | − | 1.73205i | 0.0478913 | − | 0.0829502i | ||||
\(437\) | −6.21166 | − | 23.1822i | −0.297144 | − | 1.10896i | ||||
\(438\) | −8.48528 | − | 8.48528i | −0.405442 | − | 0.405442i | ||||
\(439\) | 8.66025 | − | 5.00000i | 0.413331 | − | 0.238637i | −0.278889 | − | 0.960323i | \(-0.589966\pi\) |
0.692220 | + | 0.721686i | \(0.256633\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −21.0000 | −1.00000 | ||||||||
\(442\) | 14.6969 | + | 14.6969i | 0.699062 | + | 0.699062i | ||||
\(443\) | −2.32937 | + | 8.69333i | −0.110672 | + | 0.413033i | −0.998927 | − | 0.0463181i | \(-0.985251\pi\) |
0.888255 | + | 0.459351i | \(0.151918\pi\) | |||||||
\(444\) | 10.3923 | − | 6.00000i | 0.493197 | − | 0.284747i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.00000 | − | 1.73205i | −0.142054 | − | 0.0820150i | ||||
\(447\) | 17.3867 | + | 4.65874i | 0.822361 | + | 0.220351i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.6410 | −1.63481 | −0.817405 | − | 0.576063i | \(-0.804588\pi\) | ||||
−0.817405 | + | 0.576063i | \(0.804588\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | 0.565058 | ||||||||
\(452\) | −2.89778 | − | 0.776457i | −0.136300 | − | 0.0365215i | ||||
\(453\) | −2.44949 | + | 2.44949i | −0.115087 | + | 0.115087i | ||||
\(454\) | 2.59808 | + | 1.50000i | 0.121934 | + | 0.0703985i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.00000 | + | 3.46410i | 0.280976 | + | 0.162221i | ||||
\(457\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(458\) | −14.1421 | − | 14.1421i | −0.660819 | − | 0.660819i | ||||
\(459\) | −15.5885 | −0.727607 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.0000 | − | 8.66025i | 0.698620 | − | 0.403348i | −0.108213 | − | 0.994128i | \(-0.534513\pi\) |
0.806833 | + | 0.590779i | \(0.201180\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.896575 | + | 3.34607i | 0.0416674 | + | 0.155505i | 0.983625 | − | 0.180227i | \(-0.0576832\pi\) |
−0.941958 | + | 0.335732i | \(0.891016\pi\) | |||||||
\(464\) | 1.73205 | − | 3.00000i | 0.0804084 | − | 0.139272i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.50000 | + | 7.79423i | 0.208458 | + | 0.361061i | ||||
\(467\) | 10.6066 | − | 10.6066i | 0.490815 | − | 0.490815i | −0.417748 | − | 0.908563i | \(-0.637180\pi\) |
0.908563 | + | 0.417748i | \(0.137180\pi\) | |||||||
\(468\) | −5.37945 | − | 20.0764i | −0.248665 | − | 0.928032i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.00000 | + | 10.3923i | 0.276465 | + | 0.478852i | ||||
\(472\) | 8.36516 | − | 2.24144i | 0.385038 | − | 0.103171i | ||||
\(473\) | −14.4889 | + | 3.88229i | −0.666200 | + | 0.178508i | ||||
\(474\) | 3.46410 | + | 6.00000i | 0.159111 | + | 0.275589i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 34.7733 | + | 9.31749i | 1.59216 | + | 0.426618i | ||||
\(478\) | −7.34847 | + | 7.34847i | −0.336111 | + | 0.336111i | ||||
\(479\) | −3.46410 | − | 6.00000i | −0.158279 | − | 0.274147i | 0.775969 | − | 0.630771i | \(-0.217261\pi\) |
−0.934248 | + | 0.356624i | \(0.883928\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.0000 | − | 41.5692i | 1.09431 | − | 1.89539i | ||||
\(482\) | 2.58819 | + | 9.65926i | 0.117889 | + | 0.439967i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.92820 | + | 4.00000i | −0.314918 | + | 0.181818i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 13.5000 | + | 7.79423i | 0.612372 | + | 0.353553i | ||||
\(487\) | 12.2474 | + | 12.2474i | 0.554985 | + | 0.554985i | 0.927875 | − | 0.372890i | \(-0.121633\pi\) |
−0.372890 | + | 0.927875i | \(0.621633\pi\) | |||||||
\(488\) | 2.07055 | − | 7.72741i | 0.0937295 | − | 0.349803i | ||||
\(489\) | −2.59808 | − | 1.50000i | −0.117489 | − | 0.0678323i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.5000 | − | 11.2583i | −0.880023 | − | 0.508081i | −0.00935679 | − | 0.999956i | \(-0.502978\pi\) |
−0.870666 | + | 0.491875i | \(0.836312\pi\) | |||||||
\(492\) | 8.48528 | − | 8.48528i | 0.382546 | − | 0.382546i | ||||
\(493\) | −10.0382 | − | 2.68973i | −0.452098 | − | 0.121139i | ||||
\(494\) | 27.7128 | 1.24686 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 15.0573 | + | 4.03459i | 0.674733 | + | 0.180794i | ||||
\(499\) | 4.33013 | + | 2.50000i | 0.193843 | + | 0.111915i | 0.593780 | − | 0.804627i | \(-0.297635\pi\) |
−0.399937 | + | 0.916542i | \(0.630968\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.00000 | + | 5.19615i | −0.402090 | + | 0.232147i | ||||
\(502\) | −2.68973 | + | 10.0382i | −0.120048 | + | 0.448027i | ||||
\(503\) | 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 | ||||||||
\(506\) | −9.00000 | + | 5.19615i | −0.400099 | + | 0.230997i | ||||
\(507\) | −42.8661 | − | 42.8661i | −1.90375 | − | 1.90375i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.5885 | − | 27.0000i | 0.690946 | − | 1.19675i | −0.280582 | − | 0.959830i | \(-0.590527\pi\) |
0.971528 | − | 0.236924i | \(-0.0761392\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −14.6969 | + | 14.6969i | −0.648886 | + | 0.648886i | ||||
\(514\) | − | 3.00000i | − | 0.132324i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.50000 | + | 12.9904i | −0.330169 | + | 0.571870i | ||||
\(517\) | −20.0764 | + | 5.37945i | −0.882959 | + | 0.236588i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −31.1769 | −1.36851 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 5.19615i | − | 0.227648i | −0.993501 | − | 0.113824i | \(-0.963690\pi\) | ||
0.993501 | − | 0.113824i | \(-0.0363099\pi\) | |||||||
\(522\) | 7.34847 | + | 7.34847i | 0.321634 | + | 0.321634i | ||||
\(523\) | 18.3712 | − | 18.3712i | 0.803315 | − | 0.803315i | −0.180297 | − | 0.983612i | \(-0.557706\pi\) |
0.983612 | + | 0.180297i | \(0.0577059\pi\) | |||||||
\(524\) | −8.66025 | − | 15.0000i | −0.378325 | − | 0.655278i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.0000 | + | 20.7846i | −0.523225 | + | 0.906252i | ||||
\(527\) | 3.10583 | + | 11.5911i | 0.135292 | + | 0.504917i | ||||
\(528\) | 0.776457 | − | 2.89778i | 0.0337910 | − | 0.126110i | ||||
\(529\) | 11.2583 | − | 6.50000i | 0.489493 | − | 0.282609i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 25.9808i | 1.12747i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.4233 | − | 46.3644i | 0.538113 | − | 2.00827i | ||||
\(534\) | 3.00000i | 0.129823i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.00000 | + | 1.73205i | 0.129580 | + | 0.0748132i | ||||
\(537\) | −5.43520 | − | 20.2844i | −0.234546 | − | 0.875338i | ||||
\(538\) | 6.69213 | + | 1.79315i | 0.288518 | + | 0.0773082i | ||||
\(539\) | −12.1244 | −0.522233 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.00000 | −0.171973 | −0.0859867 | − | 0.996296i | \(-0.527404\pi\) | ||||
−0.0859867 | + | 0.996296i | \(0.527404\pi\) | |||||||
\(542\) | 7.72741 | + | 2.07055i | 0.331921 | + | 0.0889378i | ||||
\(543\) | −0.896575 | − | 3.34607i | −0.0384757 | − | 0.143593i | ||||
\(544\) | 2.59808 | + | 1.50000i | 0.111392 | + | 0.0643120i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.48288 | − | 16.7303i | 0.191674 | − | 0.715337i | −0.801429 | − | 0.598090i | \(-0.795926\pi\) |
0.993103 | − | 0.117247i | \(-0.0374069\pi\) | |||||||
\(548\) | −12.7279 | − | 12.7279i | −0.543710 | − | 0.543710i | ||||
\(549\) | 20.7846 | + | 12.0000i | 0.887066 | + | 0.512148i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0000 | + | 6.92820i | −0.511217 | + | 0.295151i | ||||
\(552\) | −2.68973 | + | 10.0382i | −0.114482 | + | 0.427254i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.73205 | + | 3.00000i | −0.0735878 | + | 0.127458i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.50000 | + | 11.2583i | 0.275661 | + | 0.477460i | ||||
\(557\) | 4.24264 | − | 4.24264i | 0.179766 | − | 0.179766i | −0.611488 | − | 0.791254i | \(-0.709429\pi\) |
0.791254 | + | 0.611488i | \(0.209429\pi\) | |||||||
\(558\) | 3.10583 | − | 11.5911i | 0.131480 | − | 0.490691i | ||||
\(559\) | 60.0000i | 2.53773i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.00000 | −0.379980 | ||||||||
\(562\) | −20.0764 | + | 5.37945i | −0.846871 | + | 0.226919i | ||||
\(563\) | 20.2844 | − | 5.43520i | 0.854887 | − | 0.229066i | 0.195346 | − | 0.980734i | \(-0.437417\pi\) |
0.659542 | + | 0.751668i | \(0.270750\pi\) | |||||||
\(564\) | −10.3923 | + | 18.0000i | −0.437595 | + | 0.757937i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 32.9090i | − | 1.38327i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.44949 | − | 2.44949i | 0.102778 | − | 0.102778i | ||||
\(569\) | −16.4545 | − | 28.5000i | −0.689808 | − | 1.19478i | −0.971900 | − | 0.235395i | \(-0.924362\pi\) |
0.282092 | − | 0.959387i | \(-0.408972\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.50000 | + | 14.7224i | −0.355714 | + | 0.616115i | −0.987240 | − | 0.159240i | \(-0.949096\pi\) |
0.631526 | + | 0.775355i | \(0.282429\pi\) | |||||||
\(572\) | −3.10583 | − | 11.5911i | −0.129861 | − | 0.484649i | ||||
\(573\) | 4.24264 | + | 4.24264i | 0.177239 | + | 0.177239i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.50000 | − | 2.59808i | −0.0625000 | − | 0.108253i | ||||
\(577\) | 14.6969 | + | 14.6969i | 0.611842 | + | 0.611842i | 0.943426 | − | 0.331584i | \(-0.107583\pi\) |
−0.331584 | + | 0.943426i | \(0.607583\pi\) | |||||||
\(578\) | −2.07055 | + | 7.72741i | −0.0861236 | + | 0.321418i | ||||
\(579\) | 7.79423 | − | 4.50000i | 0.323917 | − | 0.187014i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −26.0800 | − | 6.98811i | −1.08105 | − | 0.289667i | ||||
\(583\) | 20.0764 | + | 5.37945i | 0.831479 | + | 0.222794i | ||||
\(584\) | −6.92820 | −0.286691 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.0000 | −0.495715 | ||||||||
\(587\) | −26.0800 | − | 6.98811i | −1.07644 | − | 0.288430i | −0.323301 | − | 0.946296i | \(-0.604793\pi\) |
−0.753135 | + | 0.657866i | \(0.771459\pi\) | |||||||
\(588\) | −8.57321 | + | 8.57321i | −0.353553 | + | 0.353553i | ||||
\(589\) | 13.8564 | + | 8.00000i | 0.570943 | + | 0.329634i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00000 | + | 5.19615i | 0.370211 | + | 0.213741i | ||||
\(592\) | 1.79315 | − | 6.69213i | 0.0736980 | − | 0.275045i | ||||
\(593\) | 14.8492 | + | 14.8492i | 0.609785 | + | 0.609785i | 0.942890 | − | 0.333105i | \(-0.108096\pi\) |
−0.333105 | + | 0.942890i | \(0.608096\pi\) | |||||||
\(594\) | 7.79423 | + | 4.50000i | 0.319801 | + | 0.184637i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.00000 | − | 5.19615i | 0.368654 | − | 0.212843i | ||||
\(597\) | 43.4988 | − | 11.6555i | 1.78029 | − | 0.477027i | ||||
\(598\) | 10.7589 | + | 40.1528i | 0.439964 | + | 1.64197i | ||||
\(599\) | −22.5167 | + | 39.0000i | −0.920006 | + | 1.59350i | −0.120603 | + | 0.992701i | \(0.538483\pi\) |
−0.799402 | + | 0.600796i | \(0.794850\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.50000 | − | 16.4545i | −0.387513 | − | 0.671192i | 0.604601 | − | 0.796528i | \(-0.293332\pi\) |
−0.992114 | + | 0.125336i | \(0.959999\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.34847 | + | 7.34847i | −0.299253 | + | 0.299253i | ||||
\(604\) | 2.00000i | 0.0813788i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 12.0000 | + | 20.7846i | 0.487467 | + | 0.844317i | ||||
\(607\) | 6.69213 | − | 1.79315i | 0.271625 | − | 0.0727818i | −0.120435 | − | 0.992721i | \(-0.538429\pi\) |
0.392061 | + | 0.919939i | \(0.371762\pi\) | |||||||
\(608\) | 3.86370 | − | 1.03528i | 0.156694 | − | 0.0419860i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 83.1384i | 3.36342i | ||||||||
\(612\) | −6.36396 | + | 6.36396i | −0.257248 | + | 0.257248i | ||||
\(613\) | −17.1464 | + | 17.1464i | −0.692538 | + | 0.692538i | −0.962790 | − | 0.270252i | \(-0.912893\pi\) |
0.270252 | + | 0.962790i | \(0.412893\pi\) | |||||||
\(614\) | −11.2583 | − | 19.5000i | −0.454349 | − | 0.786956i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.98811 | + | 26.0800i | 0.281331 | + | 1.04994i | 0.951479 | + | 0.307714i | \(0.0995639\pi\) |
−0.670148 | + | 0.742227i | \(0.733769\pi\) | |||||||
\(618\) | −11.5911 | + | 3.10583i | −0.466263 | + | 0.124935i | ||||
\(619\) | 32.0429 | − | 18.5000i | 1.28791 | − | 0.743578i | 0.309633 | − | 0.950856i | \(-0.399794\pi\) |
0.978282 | + | 0.207279i | \(0.0664606\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.0000 | − | 15.5885i | −1.08347 | − | 0.625543i | ||||
\(622\) | −2.44949 | − | 2.44949i | −0.0982156 | − | 0.0982156i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −10.3923 | − | 6.00000i | −0.416025 | − | 0.240192i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.50000 | + | 0.866025i | 0.0599521 | + | 0.0346133i | ||||
\(627\) | −8.48528 | + | 8.48528i | −0.338869 | + | 0.338869i | ||||
\(628\) | 6.69213 | + | 1.79315i | 0.267045 | + | 0.0715545i | ||||
\(629\) | −20.7846 | −0.828737 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00000 | 0.0796187 | 0.0398094 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398094 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(632\) | 3.86370 | + | 1.03528i | 0.153690 | + | 0.0411811i | ||||
\(633\) | −38.4797 | − | 10.3106i | −1.52943 | − | 0.409810i | ||||
\(634\) | −25.9808 | − | 15.0000i | −1.03183 | − | 0.595726i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 18.0000 | − | 10.3923i | 0.713746 | − | 0.412082i | ||||
\(637\) | −12.5521 | + | 46.8449i | −0.497331 | + | 1.85606i | ||||
\(638\) | 4.24264 | + | 4.24264i | 0.167968 | + | 0.167968i | ||||
\(639\) | 5.19615 | + | 9.00000i | 0.205557 | + | 0.356034i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.5000 | + | 9.52628i | −0.651711 | + | 0.376265i | −0.789111 | − | 0.614250i | \(-0.789459\pi\) |
0.137401 | + | 0.990516i | \(0.456125\pi\) | |||||||
\(642\) | −14.6969 | − | 14.6969i | −0.580042 | − | 0.580042i | ||||
\(643\) | 12.1038 | + | 45.1719i | 0.477326 | + | 1.78141i | 0.612376 | + | 0.790566i | \(0.290214\pi\) |
−0.135050 | + | 0.990839i | \(0.543120\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | − | 10.3923i | −0.236067 | − | 0.408880i | ||||
\(647\) | 8.48528 | − | 8.48528i | 0.333591 | − | 0.333591i | −0.520358 | − | 0.853948i | \(-0.674201\pi\) |
0.853948 | + | 0.520358i | \(0.174201\pi\) | |||||||
\(648\) | 8.69333 | − | 2.32937i | 0.341506 | − | 0.0915064i | ||||
\(649\) | 15.0000i | 0.588802i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.67303 | + | 0.448288i | −0.0655210 | + | 0.0175563i | ||||
\(653\) | 46.3644 | − | 12.4233i | 1.81438 | − | 0.486162i | 0.818314 | − | 0.574771i | \(-0.194909\pi\) |
0.996066 | + | 0.0886092i | \(0.0282422\pi\) | |||||||
\(654\) | 3.46410 | 0.135457 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 6.92820i | − | 0.270501i | ||||||
\(657\) | 5.37945 | − | 20.0764i | 0.209872 | − | 0.783255i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.79423 | − | 13.5000i | −0.303620 | − | 0.525885i | 0.673333 | − | 0.739339i | \(-0.264862\pi\) |
−0.976953 | + | 0.213454i | \(0.931529\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.0000 | + | 19.0526i | −0.427850 | + | 0.741059i | −0.996682 | − | 0.0813955i | \(-0.974062\pi\) |
0.568831 | + | 0.822454i | \(0.307396\pi\) | |||||||
\(662\) | 0.258819 | + | 0.965926i | 0.0100593 | + | 0.0375418i | ||||
\(663\) | −9.31749 | + | 34.7733i | −0.361861 | + | 1.35048i | ||||
\(664\) | 7.79423 | − | 4.50000i | 0.302475 | − | 0.174634i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18.0000 | + | 10.3923i | 0.697486 | + | 0.402694i | ||||
\(667\) | −14.6969 | − | 14.6969i | −0.569068 | − | 0.569068i | ||||
\(668\) | −1.55291 | + | 5.79555i | −0.0600841 | + | 0.224237i | ||||
\(669\) | − | 6.00000i | − | 0.231973i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000 | + | 6.92820i | 0.463255 | + | 0.267460i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.8449 | + | 12.5521i | 1.80574 | + | 0.483846i | 0.994850 | − | 0.101355i | \(-0.0323177\pi\) |
0.810888 | + | 0.585201i | \(0.198984\pi\) | |||||||
\(674\) | −8.66025 | −0.333581 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −35.0000 | −1.34615 | ||||||||
\(677\) | −5.79555 | − | 1.55291i | −0.222741 | − | 0.0596833i | 0.145722 | − | 0.989326i | \(-0.453449\pi\) |
−0.368464 | + | 0.929642i | \(0.620116\pi\) | |||||||
\(678\) | −1.34486 | − | 5.01910i | −0.0516492 | − | 0.192757i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.19615i | 0.199117i | ||||||||
\(682\) | 1.79315 | − | 6.69213i | 0.0686633 | − | 0.256255i | ||||
\(683\) | −8.48528 | − | 8.48528i | −0.324680 | − | 0.324680i | 0.525879 | − | 0.850559i | \(-0.323736\pi\) |
−0.850559 | + | 0.525879i | \(0.823736\pi\) | |||||||
\(684\) | 12.0000i | 0.458831i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.96575 | − | 33.4607i | 0.342065 | − | 1.27660i | ||||
\(688\) | 2.24144 | + | 8.36516i | 0.0854540 | + | 0.318919i | ||||
\(689\) | 41.5692 | − | 72.0000i | 1.58366 | − | 2.74298i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.5000 | + | 30.3109i | 0.665731 | + | 1.15308i | 0.979086 | + | 0.203445i | \(0.0652137\pi\) |
−0.313355 | + | 0.949636i | \(0.601453\pi\) | |||||||
\(692\) | −12.7279 | + | 12.7279i | −0.483843 | + | 0.483843i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.0000i | 0.797149i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.00000 | 0.227429 | ||||||||
\(697\) | −20.0764 | + | 5.37945i | −0.760448 | + | 0.203761i | ||||
\(698\) | −9.65926 | + | 2.58819i | −0.365608 | + | 0.0979645i | ||||
\(699\) | −7.79423 | + | 13.5000i | −0.294805 | + | 0.510617i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 27.7128i | − | 1.04670i | −0.852118 | − | 0.523349i | \(-0.824682\pi\) | ||
0.852118 | − | 0.523349i | \(-0.175318\pi\) | |||||||
\(702\) | 25.4558 | − | 25.4558i | 0.960769 | − | 0.960769i | ||||
\(703\) | −19.5959 | + | 19.5959i | −0.739074 | + | 0.739074i | ||||
\(704\) | −0.866025 | − | 1.50000i | −0.0326396 | − | 0.0565334i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.50000 | + | 7.79423i | −0.169360 | + | 0.293340i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.6066 | + | 10.6066i | 0.398621 | + | 0.398621i | ||||
\(709\) | 6.92820 | − | 4.00000i | 0.260194 | − | 0.150223i | −0.364229 | − | 0.931309i | \(-0.618667\pi\) |
0.624423 | + | 0.781086i | \(0.285334\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.00000 | + | 10.3923i | −0.225018 | + | 0.389742i | ||||
\(712\) | 1.22474 | + | 1.22474i | 0.0458993 | + | 0.0458993i | ||||
\(713\) | −6.21166 | + | 23.1822i | −0.232628 | + | 0.868181i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10.5000 | − | 6.06218i | −0.392403 | − | 0.226554i | ||||
\(717\) | −17.3867 | − | 4.65874i | −0.649317 | − | 0.173984i | ||||
\(718\) | 13.3843 | + | 3.58630i | 0.499496 | + | 0.133840i | ||||
\(719\) | −34.6410 | −1.29189 | −0.645946 | − | 0.763383i | \(-0.723537\pi\) | ||||
−0.645946 | + | 0.763383i | \(0.723537\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.89778 | + | 0.776457i | 0.107844 | + | 0.0288967i | ||||
\(723\) | −12.2474 | + | 12.2474i | −0.455488 | + | 0.455488i | ||||
\(724\) | −1.73205 | − | 1.00000i | −0.0643712 | − | 0.0371647i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −12.0000 | − | 6.92820i | −0.445362 | − | 0.257130i | ||||
\(727\) | 0.896575 | − | 3.34607i | 0.0332521 | − | 0.124099i | −0.947305 | − | 0.320334i | \(-0.896205\pi\) |
0.980557 | + | 0.196235i | \(0.0628716\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.5000 | − | 12.9904i | 0.832193 | − | 0.480467i | ||||
\(732\) | 13.3843 | − | 3.58630i | 0.494697 | − | 0.132554i | ||||
\(733\) | −5.37945 | − | 20.0764i | −0.198695 | − | 0.741538i | −0.991279 | − | 0.131777i | \(-0.957932\pi\) |
0.792585 | − | 0.609762i | \(-0.208735\pi\) | |||||||
\(734\) | 12.1244 | − | 21.0000i | 0.447518 | − | 0.775124i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | + | 5.19615i | 0.110581 | + | 0.191533i | ||||
\(737\) | −4.24264 | + | 4.24264i | −0.156280 | + | 0.156280i | ||||
\(738\) | 20.0764 | + | 5.37945i | 0.739022 | + | 0.198020i | ||||
\(739\) | 41.0000i | 1.50821i | 0.656754 | + | 0.754105i | \(0.271929\pi\) | ||||
−0.656754 | + | 0.754105i | \(0.728071\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.0000 | + | 41.5692i | 0.881662 | + | 1.52708i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.1822 | + | 6.21166i | −0.850473 | + | 0.227884i | −0.657625 | − | 0.753345i | \(-0.728439\pi\) |
−0.192848 | + | 0.981229i | \(0.561772\pi\) | |||||||
\(744\) | −3.46410 | − | 6.00000i | −0.127000 | − | 0.219971i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.98811 | + | 26.0800i | 0.255682 | + | 0.954217i | ||||
\(748\) | −3.67423 | + | 3.67423i | −0.134343 | + | 0.134343i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.0000 | − | 32.9090i | 0.693320 | − | 1.20087i | −0.277424 | − | 0.960748i | \(-0.589481\pi\) |
0.970744 | − | 0.240118i | \(-0.0771860\pi\) | |||||||
\(752\) | 3.10583 | + | 11.5911i | 0.113258 | + | 0.422684i | ||||
\(753\) | −17.3867 | + | 4.65874i | −0.633605 | + | 0.169774i | ||||
\(754\) | 20.7846 | − | 12.0000i | 0.756931 | − | 0.437014i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.3939 | + | 29.3939i | 1.06834 | + | 1.06834i | 0.997487 | + | 0.0708518i | \(0.0225717\pi\) |
0.0708518 | + | 0.997487i | \(0.477428\pi\) | |||||||
\(758\) | 4.91756 | − | 18.3526i | 0.178614 | − | 0.666596i | ||||
\(759\) | −15.5885 | − | 9.00000i | −0.565825 | − | 0.326679i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.5000 | + | 26.8468i | 1.68562 | + | 0.973195i | 0.957802 | + | 0.287429i | \(0.0928005\pi\) |
0.727822 | + | 0.685766i | \(0.240533\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.46410 | 0.125327 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.0000 | 1.08394 | ||||||||
\(767\) | 57.9555 | + | 15.5291i | 2.09265 | + | 0.560725i | ||||
\(768\) | −1.67303 | − | 0.448288i | −0.0603704 | − | 0.0161762i | ||||
\(769\) | −11.2583 | − | 6.50000i | −0.405986 | − | 0.234396i | 0.283078 | − | 0.959097i | \(-0.408645\pi\) |
−0.689063 | + | 0.724701i | \(0.741978\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.50000 | − | 2.59808i | 0.162064 | − | 0.0935674i | ||||
\(772\) | 1.34486 | − | 5.01910i | 0.0484027 | − | 0.180641i | ||||
\(773\) | 4.24264 | + | 4.24264i | 0.152597 | + | 0.152597i | 0.779277 | − | 0.626680i | \(-0.215587\pi\) |
−0.626680 | + | 0.779277i | \(0.715587\pi\) | |||||||
\(774\) | −25.9808 | −0.933859 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.5000 | + | 7.79423i | −0.484622 | + | 0.279797i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.68973 | + | 10.0382i | 0.0964314 | + | 0.359887i | ||||
\(779\) | −13.8564 | + | 24.0000i | −0.496457 | + | 0.859889i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.00000 | + | 5.19615i | 0.107348 | + | 0.185933i | ||||
\(782\) | 12.7279 | − | 12.7279i | 0.455150 | − | 0.455150i | ||||
\(783\) | −4.65874 | + | 17.3867i | −0.166490 | + | 0.621349i | ||||
\(784\) | 7.00000i | 0.250000i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 15.0000 | − | 25.9808i | 0.535032 | − | 0.926703i | ||||
\(787\) | −50.1910 | + | 13.4486i | −1.78912 | + | 0.479392i | −0.992195 | − | 0.124693i | \(-0.960205\pi\) |
−0.796920 | + | 0.604085i | \(0.793539\pi\) | |||||||
\(788\) | 5.79555 | − | 1.55291i | 0.206458 | − | 0.0553203i | ||||
\(789\) | −41.5692 | −1.47990 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.01910 | − | 1.34486i | 0.178346 | − | 0.0477876i | ||||
\(793\) | 39.1918 | − | 39.1918i | 1.39174 | − | 1.39174i | ||||
\(794\) | −1.73205 | − | 3.00000i | −0.0614682 | − | 0.106466i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.0000 | − | 22.5167i | 0.460773 | − | 0.798082i | ||||
\(797\) | 6.21166 | + | 23.1822i | 0.220028 | + | 0.821156i | 0.984336 | + | 0.176304i | \(0.0564143\pi\) |
−0.764308 | + | 0.644852i | \(0.776919\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.1769 | − | 18.0000i | 1.10296 | − | 0.636794i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.50000 | + | 2.59808i | −0.159000 | + | 0.0917985i | ||||
\(802\) | 18.3712 | + | 18.3712i | 0.648709 | + | 0.648709i | ||||
\(803\) | 3.10583 | − | 11.5911i | 0.109602 | − | 0.409041i | ||||
\(804\) | 6.00000i | 0.211604i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −24.0000 | − | 13.8564i | −0.845364 | − | 0.488071i | ||||
\(807\) | 3.10583 | + | 11.5911i | 0.109330 | + | 0.408026i | ||||
\(808\) | 13.3843 | + | 3.58630i | 0.470857 | + | 0.126166i | ||||
\(809\) | 8.66025 | 0.304478 | 0.152239 | − | 0.988344i | \(-0.451352\pi\) | ||||
0.152239 | + | 0.988344i | \(0.451352\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.0000 | −1.01833 | −0.509164 | − | 0.860670i | \(-0.670045\pi\) | ||||
−0.509164 | + | 0.860670i | \(0.670045\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.58630 | + | 13.3843i | 0.125777 | + | 0.469407i | ||||
\(814\) | 10.3923 | + | 6.00000i | 0.364250 | + | 0.210300i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.19615i | 0.181902i | ||||||||
\(817\) | 8.96575 | − | 33.4607i | 0.313672 | − | 1.17064i | ||||
\(818\) | −1.41421 | − | 1.41421i | −0.0494468 | − | 0.0494468i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.0000 | + | 17.3205i | −1.04701 | + | 0.604490i | −0.921810 | − | 0.387642i | \(-0.873290\pi\) |
−0.125197 | + | 0.992132i | \(0.539956\pi\) | |||||||
\(822\) | 8.06918 | − | 30.1146i | 0.281445 | − | 1.05037i | ||||
\(823\) | −1.79315 | − | 6.69213i | −0.0625053 | − | 0.233273i | 0.927605 | − | 0.373562i | \(-0.121864\pi\) |
−0.990111 | + | 0.140289i | \(0.955197\pi\) | |||||||
\(824\) | −3.46410 | + | 6.00000i | −0.120678 | + | 0.209020i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.3345 | + | 23.3345i | −0.811421 | + | 0.811421i | −0.984847 | − | 0.173426i | \(-0.944516\pi\) |
0.173426 | + | 0.984847i | \(0.444516\pi\) | |||||||
\(828\) | −17.3867 | + | 4.65874i | −0.604228 | + | 0.161903i | ||||
\(829\) | − | 16.0000i | − | 0.555703i | −0.960624 | − | 0.277851i | \(-0.910378\pi\) | ||
0.960624 | − | 0.277851i | \(-0.0896223\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.00000 | −0.208138 | ||||||||
\(832\) | −6.69213 | + | 1.79315i | −0.232008 | + | 0.0621663i | ||||
\(833\) | 20.2844 | − | 5.43520i | 0.702814 | − | 0.188319i | ||||
\(834\) | −11.2583 | + | 19.5000i | −0.389844 | + | 0.675230i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.92820i | 0.239617i | ||||||||
\(837\) | 20.0764 | − | 5.37945i | 0.693942 | − | 0.185941i | ||||
\(838\) | −3.67423 | + | 3.67423i | −0.126924 | + | 0.126924i | ||||
\(839\) | −3.46410 | − | 6.00000i | −0.119594 | − | 0.207143i | 0.800013 | − | 0.599983i | \(-0.204826\pi\) |
−0.919607 | + | 0.392840i | \(0.871493\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.50000 | − | 14.7224i | 0.293103 | − | 0.507670i | ||||
\(842\) | −7.24693 | − | 27.0459i | −0.249746 | − | 0.932064i | ||||
\(843\) | −25.4558 | − | 25.4558i | −0.876746 | − | 0.876746i | ||||
\(844\) | −19.9186 | + | 11.5000i | −0.685626 | + | 0.395846i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −36.0000 | −1.23771 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.10583 | − | 11.5911i | 0.106655 | − | 0.398040i | ||||
\(849\) | 49.3634 | − | 28.5000i | 1.69415 | − | 0.978117i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.0000 | − | 20.7846i | −1.23406 | − | 0.712487i | ||||
\(852\) | 5.79555 | + | 1.55291i | 0.198552 | + | 0.0532020i | ||||
\(853\) | −16.7303 | − | 4.48288i | −0.572835 | − | 0.153491i | −0.0392388 | − | 0.999230i | \(-0.512493\pi\) |
−0.533597 | + | 0.845739i | \(0.679160\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | 2.89778 | + | 0.776457i | 0.0989862 | + | 0.0265233i | 0.307972 | − | 0.951395i | \(-0.400350\pi\) |
−0.208986 | + | 0.977919i | \(0.567016\pi\) | |||||||
\(858\) | 14.6969 | − | 14.6969i | 0.501745 | − | 0.501745i | ||||
\(859\) | 27.7128 | + | 16.0000i | 0.945549 | + | 0.545913i | 0.891695 | − | 0.452636i | \(-0.149516\pi\) |
0.0538535 | + | 0.998549i | \(0.482850\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.27603 | − | 23.4225i | 0.213762 | − | 0.797772i | ||||
\(863\) | −33.9411 | − | 33.9411i | −1.15537 | − | 1.15537i | −0.985460 | − | 0.169910i | \(-0.945652\pi\) |
−0.169910 | − | 0.985460i | \(-0.554348\pi\) | |||||||
\(864\) | 2.59808 | − | 4.50000i | 0.0883883 | − | 0.153093i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 25.5000 | − | 14.7224i | 0.866525 | − | 0.500289i | ||||
\(867\) | −13.3843 | + | 3.58630i | −0.454553 | + | 0.121797i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.46410 | + | 6.00000i | −0.117512 | + | 0.203536i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000 | + | 20.7846i | 0.406604 | + | 0.704260i | ||||
\(872\) | 1.41421 | − | 1.41421i | 0.0478913 | − | 0.0478913i | ||||
\(873\) | −12.1038 | − | 45.1719i | −0.409651 | − | 1.52884i | ||||
\(874\) | − | 24.0000i | − | 0.811812i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.00000 | − | 10.3923i | −0.202721 | − | 0.351123i | ||||
\(877\) | −20.0764 | + | 5.37945i | −0.677932 | + | 0.181651i | −0.581325 | − | 0.813671i | \(-0.697466\pi\) |
−0.0966065 | + | 0.995323i | \(0.530799\pi\) | |||||||
\(878\) | 9.65926 | − | 2.58819i | 0.325984 | − | 0.0873472i | ||||
\(879\) | −10.3923 | − | 18.0000i | −0.350524 | − | 0.607125i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.6410i | 1.16709i | 0.812082 | + | 0.583543i | \(0.198334\pi\) | ||||
−0.812082 | + | 0.583543i | \(0.801666\pi\) | |||||||
\(882\) | −20.2844 | − | 5.43520i | −0.683013 | − | 0.183013i | ||||
\(883\) | −18.3712 | + | 18.3712i | −0.618239 | + | 0.618239i | −0.945080 | − | 0.326840i | \(-0.894016\pi\) |
0.326840 | + | 0.945080i | \(0.394016\pi\) | |||||||
\(884\) | 10.3923 | + | 18.0000i | 0.349531 | + | 0.605406i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.50000 | + | 7.79423i | −0.151180 | + | 0.261852i | ||||
\(887\) | −10.8704 | − | 40.5689i | −0.364992 | − | 1.36217i | −0.867431 | − | 0.497557i | \(-0.834230\pi\) |
0.502439 | − | 0.864613i | \(-0.332436\pi\) | |||||||
\(888\) | 11.5911 | − | 3.10583i | 0.388972 | − | 0.104225i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.5885i | 0.522233i | ||||||||
\(892\) | −2.44949 | − | 2.44949i | −0.0820150 | − | 0.0820150i | ||||
\(893\) | 12.4233 | − | 46.3644i | 0.415730 | − | 1.55153i | ||||
\(894\) | 15.5885 | + | 9.00000i | 0.521356 | + | 0.301005i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −50.9117 | + | 50.9117i | −1.69989 | + | 1.69989i | ||||
\(898\) | −33.4607 | − | 8.96575i | −1.11660 | − | 0.299191i | ||||
\(899\) | 13.8564 | 0.462137 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | 11.5911 | + | 3.10583i | 0.385942 | + | 0.103413i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.59808 | − | 1.50000i | −0.0864107 | − | 0.0498893i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.00000 | + | 1.73205i | −0.0996683 | + | 0.0575435i | ||||
\(907\) | 2.24144 | − | 8.36516i | 0.0744257 | − | 0.277761i | −0.918677 | − | 0.395010i | \(-0.870741\pi\) |
0.993102 | + | 0.117250i | \(0.0374077\pi\) | |||||||
\(908\) | 2.12132 | + | 2.12132i | 0.0703985 | + | 0.0703985i | ||||
\(909\) | −20.7846 | + | 36.0000i | −0.689382 | + | 1.19404i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.0000 | − | 19.0526i | 1.09334 | − | 0.631239i | 0.158875 | − | 0.987299i | \(-0.449213\pi\) |
0.934463 | + | 0.356059i | \(0.115880\pi\) | |||||||
\(912\) | 4.89898 | + | 4.89898i | 0.162221 | + | 0.162221i | ||||
\(913\) | 4.03459 | + | 15.0573i | 0.133525 | + | 0.498324i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | − | 17.3205i | −0.330409 | − | 0.572286i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −15.0573 | − | 4.03459i | −0.496965 | − | 0.133161i | ||||
\(919\) | − | 34.0000i | − | 1.12156i | −0.827966 | − | 0.560778i | \(-0.810502\pi\) | ||
0.827966 | − | 0.560778i | \(-0.189498\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.5000 | − | 33.7750i | 0.642547 | − | 1.11292i | ||||
\(922\) | 16.7303 | − | 4.48288i | 0.550984 | − | 0.147636i | ||||
\(923\) | 23.1822 | − | 6.21166i | 0.763052 | − | 0.204459i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.46410i | 0.113837i | ||||||||
\(927\) | −14.6969 | − | 14.6969i | −0.482711 | − | 0.482711i | ||||
\(928\) | 2.44949 | − | 2.44949i | 0.0804084 | − | 0.0804084i | ||||
\(929\) | −17.3205 | − | 30.0000i | −0.568267 | − | 0.984268i | −0.996737 | − | 0.0807121i | \(-0.974281\pi\) |
0.428470 | − | 0.903556i | \(-0.359053\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.0000 | − | 24.2487i | 0.458831 | − | 0.794719i | ||||
\(932\) | 2.32937 | + | 8.69333i | 0.0763011 | + | 0.284760i | ||||
\(933\) | 1.55291 | − | 5.79555i | 0.0508401 | − | 0.189738i | ||||
\(934\) | 12.9904 | − | 7.50000i | 0.425058 | − | 0.245407i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 20.7846i | − | 0.679366i | ||||||
\(937\) | −3.67423 | − | 3.67423i | −0.120032 | − | 0.120032i | 0.644539 | − | 0.764571i | \(-0.277049\pi\) |
−0.764571 | + | 0.644539i | \(0.777049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.00000i | 0.0979013i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.0000 | − | 10.3923i | −0.586783 | − | 0.338779i | 0.177041 | − | 0.984203i | \(-0.443347\pi\) |
−0.763825 | + | 0.645424i | \(0.776681\pi\) | |||||||
\(942\) | 3.10583 | + | 11.5911i | 0.101193 | + | 0.377659i | ||||
\(943\) | −40.1528 | − | 10.7589i | −1.30755 | − | 0.350358i | ||||
\(944\) | 8.66025 | 0.281867 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.0000 | −0.487692 | ||||||||
\(947\) | 14.4889 | + | 3.88229i | 0.470826 | + | 0.126157i | 0.486427 | − | 0.873721i | \(-0.338300\pi\) |
−0.0156019 | + | 0.999878i | \(0.504966\pi\) | |||||||
\(948\) | 1.79315 | + | 6.69213i | 0.0582388 | + | 0.217350i | ||||
\(949\) | −41.5692 | − | 24.0000i | −1.34939 | − | 0.779073i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 51.9615i | − | 1.68497i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.8492 | − | 14.8492i | −0.481014 | − | 0.481014i | 0.424441 | − | 0.905455i | \(-0.360471\pi\) |
−0.905455 | + | 0.424441i | \(0.860471\pi\) | |||||||
\(954\) | 31.1769 | + | 18.0000i | 1.00939 | + | 0.582772i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.00000 | + | 5.19615i | −0.291081 | + | 0.168056i | ||||
\(957\) | −2.68973 | + | 10.0382i | −0.0869465 | + | 0.324489i | ||||
\(958\) | −1.79315 | − | 6.69213i | −0.0579341 | − | 0.216213i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 33.9411 | − | 33.9411i | 1.09431 | − | 1.09431i | ||||
\(963\) | 9.31749 | − | 34.7733i | 0.300252 | − | 1.12055i | ||||
\(964\) | 10.0000i | 0.322078i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.3843 | + | 3.58630i | −0.430409 | + | 0.115328i | −0.467518 | − | 0.883984i | \(-0.654852\pi\) |
0.0371092 | + | 0.999311i | \(0.488185\pi\) | |||||||
\(968\) | −7.72741 | + | 2.07055i | −0.248368 | + | 0.0665501i | ||||
\(969\) | 10.3923 | − | 18.0000i | 0.333849 | − | 0.578243i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 12.1244i | − | 0.389089i | −0.980894 | − | 0.194545i | \(-0.937677\pi\) | ||
0.980894 | − | 0.194545i | \(-0.0623229\pi\) | |||||||
\(972\) | 11.0227 | + | 11.0227i | 0.353553 | + | 0.353553i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.66025 | + | 15.0000i | 0.277492 | + | 0.480631i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.00000 | − | 6.92820i | 0.128037 | − | 0.221766i | ||||
\(977\) | −1.55291 | − | 5.79555i | −0.0496821 | − | 0.185416i | 0.936625 | − | 0.350332i | \(-0.113931\pi\) |
−0.986308 | + | 0.164916i | \(0.947265\pi\) | |||||||
\(978\) | −2.12132 | − | 2.12132i | −0.0678323 | − | 0.0678323i | ||||
\(979\) | −2.59808 | + | 1.50000i | −0.0830349 | + | 0.0479402i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.00000 | + | 5.19615i | 0.0957826 | + | 0.165900i | ||||
\(982\) | −15.9217 | − | 15.9217i | −0.508081 | − | 0.508081i | ||||
\(983\) | −10.8704 | + | 40.5689i | −0.346712 | + | 1.29395i | 0.543888 | + | 0.839158i | \(0.316952\pi\) |
−0.890600 | + | 0.454788i | \(0.849715\pi\) | |||||||
\(984\) | 10.3923 | − | 6.00000i | 0.331295 | − | 0.191273i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.00000 | − | 5.19615i | −0.286618 | − | 0.165479i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 26.7685 | + | 7.17260i | 0.851620 | + | 0.228191i | ||||
\(989\) | 51.9615 | 1.65228 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.0000 | 1.01651 | 0.508257 | − | 0.861206i | \(-0.330290\pi\) | ||||
0.508257 | + | 0.861206i | \(0.330290\pi\) | |||||||
\(992\) | −3.86370 | − | 1.03528i | −0.122673 | − | 0.0328701i | ||||
\(993\) | −1.22474 | + | 1.22474i | −0.0388661 | + | 0.0388661i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 13.5000 | + | 7.79423i | 0.427764 | + | 0.246970i | ||||
\(997\) | −2.68973 | + | 10.0382i | −0.0851845 | + | 0.317913i | −0.995349 | − | 0.0963340i | \(-0.969288\pi\) |
0.910165 | + | 0.414247i | \(0.135955\pi\) | |||||||
\(998\) | 3.53553 | + | 3.53553i | 0.111915 | + | 0.111915i | ||||
\(999\) | 36.0000i | 1.13899i |
(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 | 450.2.p.b.257.2 | yes | 8 | |
3.2 | odd | 2 | 1350.2.q.e.557.1 | 8 | |||
5.2 | odd | 4 | inner | 450.2.p.b.293.1 | yes | 8 | |
5.3 | odd | 4 | inner | 450.2.p.b.293.2 | yes | 8 | |
5.4 | even | 2 | inner | 450.2.p.b.257.1 | ✓ | 8 | |
9.2 | odd | 6 | inner | 450.2.p.b.407.2 | yes | 8 | |
9.7 | even | 3 | 1350.2.q.e.1007.1 | 8 | |||
15.2 | even | 4 | 1350.2.q.e.1043.2 | 8 | |||
15.8 | even | 4 | 1350.2.q.e.1043.1 | 8 | |||
15.14 | odd | 2 | 1350.2.q.e.557.2 | 8 | |||
45.2 | even | 12 | inner | 450.2.p.b.443.1 | yes | 8 | |
45.7 | odd | 12 | 1350.2.q.e.143.2 | 8 | |||
45.29 | odd | 6 | inner | 450.2.p.b.407.1 | yes | 8 | |
45.34 | even | 6 | 1350.2.q.e.1007.2 | 8 | |||
45.38 | even | 12 | inner | 450.2.p.b.443.2 | yes | 8 | |
45.43 | odd | 12 | 1350.2.q.e.143.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.p.b.257.1 | ✓ | 8 | 5.4 | even | 2 | inner | |
450.2.p.b.257.2 | yes | 8 | 1.1 | even | 1 | trivial | |
450.2.p.b.293.1 | yes | 8 | 5.2 | odd | 4 | inner | |
450.2.p.b.293.2 | yes | 8 | 5.3 | odd | 4 | inner | |
450.2.p.b.407.1 | yes | 8 | 45.29 | odd | 6 | inner | |
450.2.p.b.407.2 | yes | 8 | 9.2 | odd | 6 | inner | |
450.2.p.b.443.1 | yes | 8 | 45.2 | even | 12 | inner | |
450.2.p.b.443.2 | yes | 8 | 45.38 | even | 12 | inner | |
1350.2.q.e.143.1 | 8 | 45.43 | odd | 12 | |||
1350.2.q.e.143.2 | 8 | 45.7 | odd | 12 | |||
1350.2.q.e.557.1 | 8 | 3.2 | odd | 2 | |||
1350.2.q.e.557.2 | 8 | 15.14 | odd | 2 | |||
1350.2.q.e.1007.1 | 8 | 9.7 | even | 3 | |||
1350.2.q.e.1007.2 | 8 | 45.34 | even | 6 | |||
1350.2.q.e.1043.1 | 8 | 15.8 | even | 4 | |||
1350.2.q.e.1043.2 | 8 | 15.2 | even | 4 |