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 | 257.1 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.257 |
Dual form | 450.2.p.d.443.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||
\(7\) | −0.448288 | + | 1.67303i | −0.169437 | + | 0.632347i | 0.827996 | + | 0.560734i | \(0.189481\pi\) |
−0.997433 | + | 0.0716124i | \(0.977186\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −2.59808 | + | 1.50000i | −0.866025 | + | 0.500000i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | − | 1.73205i | 0.904534 | − | 0.522233i | 0.0258656 | − | 0.999665i | \(-0.491766\pi\) |
0.878668 | + | 0.477432i | \(0.158432\pi\) | |||||||
\(12\) | −0.448288 | + | 1.67303i | −0.129410 | + | 0.482963i | ||||
\(13\) | 0.896575 | + | 3.34607i | 0.248665 | + | 0.928032i | 0.971506 | + | 0.237016i | \(0.0761695\pi\) |
−0.722840 | + | 0.691015i | \(0.757164\pi\) | |||||||
\(14\) | 0.866025 | − | 1.50000i | 0.231455 | − | 0.400892i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | −4.24264 | + | 4.24264i | −1.02899 | + | 1.02899i | −0.0294245 | + | 0.999567i | \(0.509367\pi\) |
−0.999567 | + | 0.0294245i | \(0.990633\pi\) | |||||||
\(18\) | 2.89778 | − | 0.776457i | 0.683013 | − | 0.183013i | ||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | −0.654654 | ||||||||
\(22\) | −3.34607 | + | 0.896575i | −0.713384 | + | 0.191151i | ||||
\(23\) | 2.89778 | − | 0.776457i | 0.604228 | − | 0.161903i | 0.0562805 | − | 0.998415i | \(-0.482076\pi\) |
0.547948 | + | 0.836512i | \(0.315409\pi\) | |||||||
\(24\) | 0.866025 | − | 1.50000i | 0.176777 | − | 0.306186i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 3.46410i | − | 0.679366i | ||||||
\(27\) | −3.67423 | − | 3.67423i | −0.707107 | − | 0.707107i | ||||
\(28\) | −1.22474 | + | 1.22474i | −0.231455 | + | 0.231455i | ||||
\(29\) | −4.33013 | − | 7.50000i | −0.804084 | − | 1.39272i | −0.916907 | − | 0.399100i | \(-0.869323\pi\) |
0.112823 | − | 0.993615i | \(-0.464011\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.00000 | + | 8.66025i | −0.898027 | + | 1.55543i | −0.0680129 | + | 0.997684i | \(0.521666\pi\) |
−0.830014 | + | 0.557743i | \(0.811667\pi\) | |||||||
\(32\) | −0.258819 | − | 0.965926i | −0.0457532 | − | 0.170753i | ||||
\(33\) | 4.24264 | + | 4.24264i | 0.738549 | + | 0.738549i | ||||
\(34\) | 5.19615 | − | 3.00000i | 0.891133 | − | 0.514496i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | 2.44949 | + | 2.44949i | 0.402694 | + | 0.402694i | 0.879181 | − | 0.476488i | \(-0.158090\pi\) |
−0.476488 | + | 0.879181i | \(0.658090\pi\) | |||||||
\(38\) | 0.517638 | − | 1.93185i | 0.0839720 | − | 0.313388i | ||||
\(39\) | −5.19615 | + | 3.00000i | −0.832050 | + | 0.480384i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.50000 | + | 4.33013i | 1.17130 | + | 0.676252i | 0.953987 | − | 0.299849i | \(-0.0969363\pi\) |
0.217317 | + | 0.976101i | \(0.430270\pi\) | |||||||
\(42\) | 2.89778 | + | 0.776457i | 0.447137 | + | 0.119810i | ||||
\(43\) | −10.0382 | − | 2.68973i | −1.53081 | − | 0.410179i | −0.607527 | − | 0.794299i | \(-0.707838\pi\) |
−0.923283 | + | 0.384120i | \(0.874505\pi\) | |||||||
\(44\) | 3.46410 | 0.522233 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | −0.442326 | ||||||||
\(47\) | −2.89778 | − | 0.776457i | −0.422684 | − | 0.113258i | 0.0412058 | − | 0.999151i | \(-0.486880\pi\) |
−0.463890 | + | 0.885893i | \(0.653547\pi\) | |||||||
\(48\) | −1.22474 | + | 1.22474i | −0.176777 | + | 0.176777i | ||||
\(49\) | 3.46410 | + | 2.00000i | 0.494872 | + | 0.285714i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.00000 | − | 5.19615i | −1.26025 | − | 0.727607i | ||||
\(52\) | −0.896575 | + | 3.34607i | −0.124333 | + | 0.464016i | ||||
\(53\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(54\) | 2.59808 | + | 4.50000i | 0.353553 | + | 0.612372i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.50000 | − | 0.866025i | 0.200446 | − | 0.115728i | ||||
\(57\) | −3.34607 | + | 0.896575i | −0.443197 | + | 0.118754i | ||||
\(58\) | 2.24144 | + | 8.36516i | 0.294315 | + | 1.09840i | ||||
\(59\) | −3.46410 | + | 6.00000i | −0.450988 | + | 0.781133i | −0.998448 | − | 0.0556984i | \(-0.982261\pi\) |
0.547460 | + | 0.836832i | \(0.315595\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | + | 11.2583i | 0.832240 | + | 1.44148i | 0.896258 | + | 0.443533i | \(0.146275\pi\) |
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 7.07107 | − | 7.07107i | 0.898027 | − | 0.898027i | ||||
\(63\) | −1.34486 | − | 5.01910i | −0.169437 | − | 0.632347i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.00000 | − | 5.19615i | −0.369274 | − | 0.639602i | ||||
\(67\) | 11.7112 | − | 3.13801i | 1.43075 | − | 0.383369i | 0.541468 | − | 0.840721i | \(-0.317869\pi\) |
0.889286 | + | 0.457352i | \(0.151202\pi\) | |||||||
\(68\) | −5.79555 | + | 1.55291i | −0.702814 | + | 0.188319i | ||||
\(69\) | 2.59808 | + | 4.50000i | 0.312772 | + | 0.541736i | ||||
\(70\) | 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 | ||||
\(73\) | 9.79796 | − | 9.79796i | 1.14676 | − | 1.14676i | 0.159579 | − | 0.987185i | \(-0.448986\pi\) |
0.987185 | − | 0.159579i | \(-0.0510137\pi\) | |||||||
\(74\) | −1.73205 | − | 3.00000i | −0.201347 | − | 0.348743i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | + | 1.73205i | −0.114708 | + | 0.198680i | ||||
\(77\) | 1.55291 | + | 5.79555i | 0.176971 | + | 0.660465i | ||||
\(78\) | 5.79555 | − | 1.55291i | 0.656217 | − | 0.175833i | ||||
\(79\) | 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 | ||||
\(82\) | −6.12372 | − | 6.12372i | −0.676252 | − | 0.676252i | ||||
\(83\) | 0.776457 | − | 2.89778i | 0.0852272 | − | 0.318072i | −0.910130 | − | 0.414323i | \(-0.864018\pi\) |
0.995357 | + | 0.0962507i | \(0.0306850\pi\) | |||||||
\(84\) | −2.59808 | − | 1.50000i | −0.283473 | − | 0.163663i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.00000 | + | 5.19615i | 0.970495 | + | 0.560316i | ||||
\(87\) | 10.6066 | − | 10.6066i | 1.13715 | − | 1.13715i | ||||
\(88\) | −3.34607 | − | 0.896575i | −0.356692 | − | 0.0955753i | ||||
\(89\) | 1.73205 | 0.183597 | 0.0917985 | − | 0.995778i | \(-0.470738\pi\) | ||||
0.0917985 | + | 0.995778i | \(0.470738\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | −0.628971 | ||||||||
\(92\) | 2.89778 | + | 0.776457i | 0.302114 | + | 0.0809513i | ||||
\(93\) | −16.7303 | − | 4.48288i | −1.73485 | − | 0.464853i | ||||
\(94\) | 2.59808 | + | 1.50000i | 0.267971 | + | 0.154713i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.50000 | − | 0.866025i | 0.153093 | − | 0.0883883i | ||||
\(97\) | 1.79315 | − | 6.69213i | 0.182067 | − | 0.679483i | −0.813173 | − | 0.582023i | \(-0.802261\pi\) |
0.995239 | − | 0.0974602i | \(-0.0310719\pi\) | |||||||
\(98\) | −2.82843 | − | 2.82843i | −0.285714 | − | 0.285714i | ||||
\(99\) | −5.19615 | + | 9.00000i | −0.522233 | + | 0.904534i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0000 | − | 6.92820i | 1.19404 | − | 0.689382i | 0.234823 | − | 0.972038i | \(-0.424549\pi\) |
0.959221 | + | 0.282656i | \(0.0912155\pi\) | |||||||
\(102\) | 7.34847 | + | 7.34847i | 0.727607 | + | 0.727607i | ||||
\(103\) | −0.896575 | − | 3.34607i | −0.0883422 | − | 0.329698i | 0.907584 | − | 0.419871i | \(-0.137925\pi\) |
−0.995926 | + | 0.0901732i | \(0.971258\pi\) | |||||||
\(104\) | 1.73205 | − | 3.00000i | 0.169842 | − | 0.294174i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.12132 | − | 2.12132i | 0.205076 | − | 0.205076i | −0.597095 | − | 0.802171i | \(-0.703678\pi\) |
0.802171 | + | 0.597095i | \(0.203678\pi\) | |||||||
\(108\) | −1.34486 | − | 5.01910i | −0.129410 | − | 0.482963i | ||||
\(109\) | − | 5.00000i | − | 0.478913i | −0.970907 | − | 0.239457i | \(-0.923031\pi\) | ||
0.970907 | − | 0.239457i | \(-0.0769693\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.00000 | + | 5.19615i | −0.284747 | + | 0.493197i | ||||
\(112\) | −1.67303 | + | 0.448288i | −0.158087 | + | 0.0423592i | ||||
\(113\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(114\) | 3.46410 | 0.324443 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 8.66025i | − | 0.804084i | ||||||
\(117\) | −7.34847 | − | 7.34847i | −0.679366 | − | 0.679366i | ||||
\(118\) | 4.89898 | − | 4.89898i | 0.450988 | − | 0.450988i | ||||
\(119\) | −5.19615 | − | 9.00000i | −0.476331 | − | 0.825029i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | −3.36465 | − | 12.5570i | −0.304621 | − | 1.13686i | ||||
\(123\) | −3.88229 | + | 14.4889i | −0.350054 | + | 1.30642i | ||||
\(124\) | −8.66025 | + | 5.00000i | −0.777714 | + | 0.449013i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.19615i | 0.462910i | ||||||||
\(127\) | −3.67423 | − | 3.67423i | −0.326036 | − | 0.326036i | 0.525041 | − | 0.851077i | \(-0.324050\pi\) |
−0.851077 | + | 0.525041i | \(0.824050\pi\) | |||||||
\(128\) | 0.258819 | − | 0.965926i | 0.0228766 | − | 0.0853766i | ||||
\(129\) | − | 18.0000i | − | 1.58481i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | − | 3.46410i | −0.524222 | − | 0.302660i | 0.214438 | − | 0.976738i | \(-0.431208\pi\) |
−0.738661 | + | 0.674078i | \(0.764541\pi\) | |||||||
\(132\) | 1.55291 | + | 5.79555i | 0.135164 | + | 0.504438i | ||||
\(133\) | −3.34607 | − | 0.896575i | −0.290141 | − | 0.0777430i | ||||
\(134\) | −12.1244 | −1.04738 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.00000 | 0.514496 | ||||||||
\(137\) | 11.5911 | + | 3.10583i | 0.990295 | + | 0.265349i | 0.717375 | − | 0.696688i | \(-0.245344\pi\) |
0.272921 | + | 0.962037i | \(0.412010\pi\) | |||||||
\(138\) | −1.34486 | − | 5.01910i | −0.114482 | − | 0.427254i | ||||
\(139\) | 3.46410 | + | 2.00000i | 0.293821 | + | 0.169638i | 0.639664 | − | 0.768655i | \(-0.279074\pi\) |
−0.345843 | + | 0.938293i | \(0.612407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 5.19615i | − | 0.437595i | ||||||
\(142\) | −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 | ||||||||
\(146\) | −12.0000 | + | 6.92820i | −0.993127 | + | 0.573382i | ||||
\(147\) | −1.79315 | + | 6.69213i | −0.147897 | + | 0.551958i | ||||
\(148\) | 0.896575 | + | 3.34607i | 0.0736980 | + | 0.275045i | ||||
\(149\) | 2.59808 | − | 4.50000i | 0.212843 | − | 0.368654i | −0.739760 | − | 0.672870i | \(-0.765061\pi\) |
0.952603 | + | 0.304216i | \(0.0983945\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | − | 8.66025i | −0.406894 | − | 0.704761i | 0.587646 | − | 0.809118i | \(-0.300055\pi\) |
−0.994540 | + | 0.104357i | \(0.966722\pi\) | |||||||
\(152\) | 1.41421 | − | 1.41421i | 0.114708 | − | 0.114708i | ||||
\(153\) | 4.65874 | − | 17.3867i | 0.376637 | − | 1.40563i | ||||
\(154\) | − | 6.00000i | − | 0.483494i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.00000 | −0.480384 | ||||||||
\(157\) | 20.0764 | − | 5.37945i | 1.60227 | − | 0.429327i | 0.656543 | − | 0.754288i | \(-0.272018\pi\) |
0.945727 | + | 0.324961i | \(0.105351\pi\) | |||||||
\(158\) | −3.86370 | + | 1.03528i | −0.307380 | + | 0.0823622i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.19615i | 0.409514i | ||||||||
\(162\) | −6.36396 | + | 6.36396i | −0.500000 | + | 0.500000i | ||||
\(163\) | 12.2474 | − | 12.2474i | 0.959294 | − | 0.959294i | −0.0399091 | − | 0.999203i | \(-0.512707\pi\) |
0.999203 | + | 0.0399091i | \(0.0127068\pi\) | |||||||
\(164\) | 4.33013 | + | 7.50000i | 0.338126 | + | 0.585652i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.50000 | + | 2.59808i | −0.116423 | + | 0.201650i | ||||
\(167\) | 2.32937 | + | 8.69333i | 0.180252 | + | 0.672710i | 0.995597 | + | 0.0937349i | \(0.0298806\pi\) |
−0.815345 | + | 0.578975i | \(0.803453\pi\) | |||||||
\(168\) | 2.12132 | + | 2.12132i | 0.163663 | + | 0.163663i | ||||
\(169\) | 0.866025 | − | 0.500000i | 0.0666173 | − | 0.0384615i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | − | 5.19615i | −0.229416 | − | 0.397360i | ||||
\(172\) | −7.34847 | − | 7.34847i | −0.560316 | − | 0.560316i | ||||
\(173\) | −6.21166 | + | 23.1822i | −0.472264 | + | 1.76251i | 0.159344 | + | 0.987223i | \(0.449062\pi\) |
−0.631607 | + | 0.775288i | \(0.717605\pi\) | |||||||
\(174\) | −12.9904 | + | 7.50000i | −0.984798 | + | 0.568574i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000 | + | 1.73205i | 0.226134 | + | 0.130558i | ||||
\(177\) | −11.5911 | − | 3.10583i | −0.871241 | − | 0.233448i | ||||
\(178\) | −1.67303 | − | 0.448288i | −0.125399 | − | 0.0336006i | ||||
\(179\) | 24.2487 | 1.81243 | 0.906217 | − | 0.422813i | \(-0.138957\pi\) | ||||
0.906217 | + | 0.422813i | \(0.138957\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.00000 | 0.520306 | 0.260153 | − | 0.965567i | \(-0.416227\pi\) | ||||
0.260153 | + | 0.965567i | \(0.416227\pi\) | |||||||
\(182\) | 5.79555 | + | 1.55291i | 0.429595 | + | 0.115110i | ||||
\(183\) | −15.9217 | + | 15.9217i | −1.17696 | + | 1.17696i | ||||
\(184\) | −2.59808 | − | 1.50000i | −0.191533 | − | 0.110581i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 15.0000 | + | 8.66025i | 1.09985 | + | 0.635001i | ||||
\(187\) | −5.37945 | + | 20.0764i | −0.393385 | + | 1.46813i | ||||
\(188\) | −2.12132 | − | 2.12132i | −0.154713 | − | 0.154713i | ||||
\(189\) | 7.79423 | − | 4.50000i | 0.566947 | − | 0.327327i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.0000 | + | 8.66025i | −1.08536 | + | 0.626634i | −0.932338 | − | 0.361588i | \(-0.882235\pi\) |
−0.153024 | + | 0.988222i | \(0.548901\pi\) | |||||||
\(192\) | −1.67303 | + | 0.448288i | −0.120741 | + | 0.0323524i | ||||
\(193\) | 4.48288 | + | 16.7303i | 0.322685 | + | 1.20428i | 0.916619 | + | 0.399762i | \(0.130907\pi\) |
−0.593934 | + | 0.804513i | \(0.702426\pi\) | |||||||
\(194\) | −3.46410 | + | 6.00000i | −0.248708 | + | 0.430775i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | + | 3.46410i | 0.142857 | + | 0.247436i | ||||
\(197\) | −8.48528 | + | 8.48528i | −0.604551 | + | 0.604551i | −0.941517 | − | 0.336966i | \(-0.890599\pi\) |
0.336966 | + | 0.941517i | \(0.390599\pi\) | |||||||
\(198\) | 7.34847 | − | 7.34847i | 0.522233 | − | 0.522233i | ||||
\(199\) | 10.0000i | 0.708881i | 0.935079 | + | 0.354441i | \(0.115329\pi\) | ||||
−0.935079 | + | 0.354441i | \(0.884671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.5000 | + | 18.1865i | 0.740613 | + | 1.28278i | ||||
\(202\) | −13.3843 | + | 3.58630i | −0.941713 | + | 0.252331i | ||||
\(203\) | 14.4889 | − | 3.88229i | 1.01692 | − | 0.272483i | ||||
\(204\) | −5.19615 | − | 9.00000i | −0.363803 | − | 0.630126i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.46410i | 0.241355i | ||||||||
\(207\) | −6.36396 | + | 6.36396i | −0.442326 | + | 0.442326i | ||||
\(208\) | −2.44949 | + | 2.44949i | −0.169842 | + | 0.169842i | ||||
\(209\) | 3.46410 | + | 6.00000i | 0.239617 | + | 0.415029i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.0000 | − | 19.0526i | 0.757271 | − | 1.31163i | −0.186966 | − | 0.982366i | \(-0.559865\pi\) |
0.944237 | − | 0.329266i | \(-0.106801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.79555 | − | 1.55291i | 0.397105 | − | 0.106404i | ||||
\(214\) | −2.59808 | + | 1.50000i | −0.177601 | + | 0.102538i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.19615i | 0.353553i | ||||||||
\(217\) | −12.2474 | − | 12.2474i | −0.831411 | − | 0.831411i | ||||
\(218\) | −1.29410 | + | 4.82963i | −0.0876472 | + | 0.327104i | ||||
\(219\) | 20.7846 | + | 12.0000i | 1.40449 | + | 0.810885i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.0000 | − | 10.3923i | −1.21081 | − | 0.699062i | ||||
\(222\) | 4.24264 | − | 4.24264i | 0.284747 | − | 0.284747i | ||||
\(223\) | −15.0573 | − | 4.03459i | −1.00831 | − | 0.270176i | −0.283387 | − | 0.959005i | \(-0.591458\pi\) |
−0.724923 | + | 0.688829i | \(0.758125\pi\) | |||||||
\(224\) | 1.73205 | 0.115728 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.1822 | − | 6.21166i | −1.53866 | − | 0.412282i | −0.612826 | − | 0.790218i | \(-0.709967\pi\) |
−0.925832 | + | 0.377936i | \(0.876634\pi\) | |||||||
\(228\) | −3.34607 | − | 0.896575i | −0.221599 | − | 0.0593772i | ||||
\(229\) | −4.33013 | − | 2.50000i | −0.286143 | − | 0.165205i | 0.350058 | − | 0.936728i | \(-0.386162\pi\) |
−0.636201 | + | 0.771523i | \(0.719495\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.00000 | + | 5.19615i | −0.592157 | + | 0.341882i | ||||
\(232\) | −2.24144 | + | 8.36516i | −0.147158 | + | 0.549200i | ||||
\(233\) | 4.24264 | + | 4.24264i | 0.277945 | + | 0.277945i | 0.832288 | − | 0.554343i | \(-0.187031\pi\) |
−0.554343 | + | 0.832288i | \(0.687031\pi\) | |||||||
\(234\) | 5.19615 | + | 9.00000i | 0.339683 | + | 0.588348i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.00000 | + | 3.46410i | −0.390567 | + | 0.225494i | ||||
\(237\) | 4.89898 | + | 4.89898i | 0.318223 | + | 0.318223i | ||||
\(238\) | 2.68973 | + | 10.0382i | 0.174349 | + | 0.650680i | ||||
\(239\) | −10.3923 | + | 18.0000i | −0.672222 | + | 1.16432i | 0.305050 | + | 0.952336i | \(0.401327\pi\) |
−0.977273 | + | 0.211987i | \(0.932007\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.50000 | − | 14.7224i | −0.547533 | − | 0.948355i | −0.998443 | − | 0.0557856i | \(-0.982234\pi\) |
0.450910 | − | 0.892570i | \(-0.351100\pi\) | |||||||
\(242\) | −0.707107 | + | 0.707107i | −0.0454545 | + | 0.0454545i | ||||
\(243\) | 15.0573 | + | 4.03459i | 0.965926 | + | 0.258819i | ||||
\(244\) | 13.0000i | 0.832240i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.50000 | − | 12.9904i | 0.478183 | − | 0.828236i | ||||
\(247\) | −6.69213 | + | 1.79315i | −0.425810 | + | 0.114095i | ||||
\(248\) | 9.65926 | − | 2.58819i | 0.613364 | − | 0.164350i | ||||
\(249\) | 5.19615 | 0.329293 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.3923i | 0.655956i | 0.944685 | + | 0.327978i | \(0.106367\pi\) | ||||
−0.944685 | + | 0.327978i | \(0.893633\pi\) | |||||||
\(252\) | 1.34486 | − | 5.01910i | 0.0847184 | − | 0.316173i | ||||
\(253\) | 7.34847 | − | 7.34847i | 0.461994 | − | 0.461994i | ||||
\(254\) | 2.59808 | + | 4.50000i | 0.163018 | + | 0.282355i | ||||
\(255\) | 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 | \(0.916667\pi\) | |||||||
\(258\) | −4.65874 | + | 17.3867i | −0.290041 | + | 1.08245i | ||||
\(259\) | −5.19615 | + | 3.00000i | −0.322873 | + | 0.186411i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.5000 | + | 12.9904i | 1.39272 | + | 0.804084i | ||||
\(262\) | 4.89898 | + | 4.89898i | 0.302660 | + | 0.302660i | ||||
\(263\) | 6.21166 | − | 23.1822i | 0.383027 | − | 1.42948i | −0.458226 | − | 0.888836i | \(-0.651515\pi\) |
0.841253 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(264\) | − | 6.00000i | − | 0.369274i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.00000 | + | 1.73205i | 0.183942 | + | 0.106199i | ||||
\(267\) | 0.776457 | + | 2.89778i | 0.0475184 | + | 0.177341i | ||||
\(268\) | 11.7112 | + | 3.13801i | 0.715377 | + | 0.191685i | ||||
\(269\) | 1.73205 | 0.105605 | 0.0528025 | − | 0.998605i | \(-0.483185\pi\) | ||||
0.0528025 | + | 0.998605i | \(0.483185\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0000 | −0.607457 | −0.303728 | − | 0.952759i | \(-0.598232\pi\) | ||||
−0.303728 | + | 0.952759i | \(0.598232\pi\) | |||||||
\(272\) | −5.79555 | − | 1.55291i | −0.351407 | − | 0.0941593i | ||||
\(273\) | −2.68973 | − | 10.0382i | −0.162790 | − | 0.607539i | ||||
\(274\) | −10.3923 | − | 6.00000i | −0.627822 | − | 0.362473i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.19615i | 0.312772i | ||||||||
\(277\) | −2.68973 | + | 10.0382i | −0.161610 | + | 0.603137i | 0.836838 | + | 0.547450i | \(0.184401\pi\) |
−0.998448 | + | 0.0556866i | \(0.982265\pi\) | |||||||
\(278\) | −2.82843 | − | 2.82843i | −0.169638 | − | 0.169638i | ||||
\(279\) | − | 30.0000i | − | 1.79605i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.50000 | − | 2.59808i | 0.268447 | − | 0.154988i | −0.359734 | − | 0.933055i | \(-0.617133\pi\) |
0.628182 | + | 0.778067i | \(0.283799\pi\) | |||||||
\(282\) | −1.34486 | + | 5.01910i | −0.0800854 | + | 0.298883i | ||||
\(283\) | 1.34486 | + | 5.01910i | 0.0799438 | + | 0.298354i | 0.994309 | − | 0.106537i | \(-0.0339761\pi\) |
−0.914365 | + | 0.404891i | \(0.867309\pi\) | |||||||
\(284\) | 1.73205 | − | 3.00000i | 0.102778 | − | 0.178017i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | − | 10.3923i | −0.354787 | − | 0.614510i | ||||
\(287\) | −10.6066 | + | 10.6066i | −0.626088 | + | 0.626088i | ||||
\(288\) | 2.12132 | + | 2.12132i | 0.125000 | + | 0.125000i | ||||
\(289\) | − | 19.0000i | − | 1.11765i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0000 | 0.703452 | ||||||||
\(292\) | 13.3843 | − | 3.58630i | 0.783255 | − | 0.209872i | ||||
\(293\) | −28.9778 | + | 7.76457i | −1.69290 | + | 0.453611i | −0.971136 | − | 0.238528i | \(-0.923335\pi\) |
−0.721764 | + | 0.692139i | \(0.756668\pi\) | |||||||
\(294\) | 3.46410 | − | 6.00000i | 0.202031 | − | 0.349927i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 3.46410i | − | 0.201347i | ||||||
\(297\) | −17.3867 | − | 4.65874i | −1.00888 | − | 0.270328i | ||||
\(298\) | −3.67423 | + | 3.67423i | −0.212843 | + | 0.212843i | ||||
\(299\) | 5.19615 | + | 9.00000i | 0.300501 | + | 0.520483i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.00000 | − | 15.5885i | 0.518751 | − | 0.898504i | ||||
\(302\) | 2.58819 | + | 9.65926i | 0.148934 | + | 0.555828i | ||||
\(303\) | 16.9706 | + | 16.9706i | 0.974933 | + | 0.974933i | ||||
\(304\) | −1.73205 | + | 1.00000i | −0.0993399 | + | 0.0573539i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −9.00000 | + | 15.5885i | −0.514496 | + | 0.891133i | ||||
\(307\) | 3.67423 | + | 3.67423i | 0.209700 | + | 0.209700i | 0.804140 | − | 0.594440i | \(-0.202626\pi\) |
−0.594440 | + | 0.804140i | \(0.702626\pi\) | |||||||
\(308\) | −1.55291 | + | 5.79555i | −0.0884855 | + | 0.330232i | ||||
\(309\) | 5.19615 | − | 3.00000i | 0.295599 | − | 0.170664i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.0000 | − | 12.1244i | −1.19080 | − | 0.687509i | −0.232313 | − | 0.972641i | \(-0.574629\pi\) |
−0.958488 | + | 0.285132i | \(0.907963\pi\) | |||||||
\(312\) | 5.79555 | + | 1.55291i | 0.328109 | + | 0.0879165i | ||||
\(313\) | 3.34607 | + | 0.896575i | 0.189131 | + | 0.0506774i | 0.352141 | − | 0.935947i | \(-0.385454\pi\) |
−0.163010 | + | 0.986624i | \(0.552120\pi\) | |||||||
\(314\) | −20.7846 | −1.17294 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.00000 | 0.225018 | ||||||||
\(317\) | 5.79555 | + | 1.55291i | 0.325511 | + | 0.0872204i | 0.417874 | − | 0.908505i | \(-0.362775\pi\) |
−0.0923631 | + | 0.995725i | \(0.529442\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.9808 | − | 15.0000i | −1.45464 | − | 0.839839i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.50000 | + | 2.59808i | 0.251166 | + | 0.145010i | ||||
\(322\) | 1.34486 | − | 5.01910i | 0.0749463 | − | 0.279703i | ||||
\(323\) | −8.48528 | − | 8.48528i | −0.472134 | − | 0.472134i | ||||
\(324\) | 7.79423 | − | 4.50000i | 0.433013 | − | 0.250000i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −15.0000 | + | 8.66025i | −0.830773 | + | 0.479647i | ||||
\(327\) | 8.36516 | − | 2.24144i | 0.462595 | − | 0.123952i | ||||
\(328\) | −2.24144 | − | 8.36516i | −0.123763 | − | 0.461889i | ||||
\(329\) | 2.59808 | − | 4.50000i | 0.143237 | − | 0.248093i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | − | 6.92820i | −0.219860 | − | 0.380808i | 0.734905 | − | 0.678170i | \(-0.237227\pi\) |
−0.954765 | + | 0.297361i | \(0.903893\pi\) | |||||||
\(332\) | 2.12132 | − | 2.12132i | 0.116423 | − | 0.116423i | ||||
\(333\) | −10.0382 | − | 2.68973i | −0.550090 | − | 0.147396i | ||||
\(334\) | − | 9.00000i | − | 0.492458i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.50000 | − | 2.59808i | −0.0818317 | − | 0.141737i | ||||
\(337\) | 13.3843 | − | 3.58630i | 0.729087 | − | 0.195358i | 0.124864 | − | 0.992174i | \(-0.460150\pi\) |
0.604223 | + | 0.796815i | \(0.293484\pi\) | |||||||
\(338\) | −0.965926 | + | 0.258819i | −0.0525394 | + | 0.0140779i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 34.6410i | 1.87592i | ||||||||
\(342\) | 1.55291 | + | 5.79555i | 0.0839720 | + | 0.313388i | ||||
\(343\) | −13.4722 | + | 13.4722i | −0.727430 | + | 0.727430i | ||||
\(344\) | 5.19615 | + | 9.00000i | 0.280158 | + | 0.485247i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.0000 | − | 20.7846i | 0.645124 | − | 1.11739i | ||||
\(347\) | −3.10583 | − | 11.5911i | −0.166730 | − | 0.622243i | −0.997813 | − | 0.0660960i | \(-0.978946\pi\) |
0.831084 | − | 0.556147i | \(-0.187721\pi\) | |||||||
\(348\) | 14.4889 | − | 3.88229i | 0.776686 | − | 0.208112i | ||||
\(349\) | −0.866025 | + | 0.500000i | −0.0463573 | + | 0.0267644i | −0.523000 | − | 0.852333i | \(-0.675187\pi\) |
0.476642 | + | 0.879097i | \(0.341854\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.00000 | − | 15.5885i | 0.480384 | − | 0.832050i | ||||
\(352\) | −2.44949 | − | 2.44949i | −0.130558 | − | 0.130558i | ||||
\(353\) | 6.21166 | − | 23.1822i | 0.330613 | − | 1.23387i | −0.577934 | − | 0.816083i | \(-0.696141\pi\) |
0.908547 | − | 0.417782i | \(-0.137192\pi\) | |||||||
\(354\) | 10.3923 | + | 6.00000i | 0.552345 | + | 0.318896i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.50000 | + | 0.866025i | 0.0794998 | + | 0.0458993i | ||||
\(357\) | 12.7279 | − | 12.7279i | 0.673633 | − | 0.673633i | ||||
\(358\) | −23.4225 | − | 6.27603i | −1.23792 | − | 0.331698i | ||||
\(359\) | −17.3205 | −0.914141 | −0.457071 | − | 0.889430i | \(-0.651101\pi\) | ||||
−0.457071 | + | 0.889430i | \(0.651101\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | −6.76148 | − | 1.81173i | −0.355376 | − | 0.0952226i | ||||
\(363\) | 1.67303 | + | 0.448288i | 0.0878114 | + | 0.0235290i | ||||
\(364\) | −5.19615 | − | 3.00000i | −0.272352 | − | 0.157243i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 19.5000 | − | 11.2583i | 1.01928 | − | 0.588482i | ||||
\(367\) | −0.896575 | + | 3.34607i | −0.0468009 | + | 0.174663i | −0.985370 | − | 0.170427i | \(-0.945485\pi\) |
0.938569 | + | 0.345091i | \(0.112152\pi\) | |||||||
\(368\) | 2.12132 | + | 2.12132i | 0.110581 | + | 0.110581i | ||||
\(369\) | −25.9808 | −1.35250 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −12.2474 | − | 12.2474i | −0.635001 | − | 0.635001i | ||||
\(373\) | 3.58630 | + | 13.3843i | 0.185692 | + | 0.693011i | 0.994481 | + | 0.104913i | \(0.0334564\pi\) |
−0.808790 | + | 0.588098i | \(0.799877\pi\) | |||||||
\(374\) | 10.3923 | − | 18.0000i | 0.537373 | − | 0.930758i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.50000 | + | 2.59808i | 0.0773566 | + | 0.133986i | ||||
\(377\) | 21.2132 | − | 21.2132i | 1.09254 | − | 1.09254i | ||||
\(378\) | −8.69333 | + | 2.32937i | −0.447137 | + | 0.119810i | ||||
\(379\) | 8.00000i | 0.410932i | 0.978664 | + | 0.205466i | \(0.0658711\pi\) | ||||
−0.978664 | + | 0.205466i | \(0.934129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.50000 | − | 7.79423i | 0.230542 | − | 0.399310i | ||||
\(382\) | 16.7303 | − | 4.48288i | 0.855998 | − | 0.229364i | ||||
\(383\) | 23.1822 | − | 6.21166i | 1.18456 | − | 0.317401i | 0.387824 | − | 0.921733i | \(-0.373227\pi\) |
0.796732 | + | 0.604333i | \(0.206560\pi\) | |||||||
\(384\) | 1.73205 | 0.0883883 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 17.3205i | − | 0.881591i | ||||||
\(387\) | 30.1146 | − | 8.06918i | 1.53081 | − | 0.410179i | ||||
\(388\) | 4.89898 | − | 4.89898i | 0.248708 | − | 0.248708i | ||||
\(389\) | 12.9904 | + | 22.5000i | 0.658638 | + | 1.14080i | 0.980968 | + | 0.194168i | \(0.0622006\pi\) |
−0.322330 | + | 0.946627i | \(0.604466\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | + | 15.5885i | −0.455150 | + | 0.788342i | ||||
\(392\) | −1.03528 | − | 3.86370i | −0.0522893 | − | 0.195146i | ||||
\(393\) | 3.10583 | − | 11.5911i | 0.156668 | − | 0.584694i | ||||
\(394\) | 10.3923 | − | 6.00000i | 0.523557 | − | 0.302276i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −9.00000 | + | 5.19615i | −0.452267 | + | 0.261116i | ||||
\(397\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(398\) | 2.58819 | − | 9.65926i | 0.129734 | − | 0.484175i | ||||
\(399\) | − | 6.00000i | − | 0.300376i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0000 | − | 10.3923i | −0.898877 | − | 0.518967i | −0.0220414 | − | 0.999757i | \(-0.507017\pi\) |
−0.876836 | + | 0.480790i | \(0.840350\pi\) | |||||||
\(402\) | −5.43520 | − | 20.2844i | −0.271083 | − | 1.01170i | ||||
\(403\) | −33.4607 | − | 8.96575i | −1.66679 | − | 0.446616i | ||||
\(404\) | 13.8564 | 0.689382 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.0000 | −0.744438 | ||||||||
\(407\) | 11.5911 | + | 3.10583i | 0.574550 | + | 0.153950i | ||||
\(408\) | 2.68973 | + | 10.0382i | 0.133161 | + | 0.496965i | ||||
\(409\) | −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 | ||||||||
\(411\) | 20.7846i | 1.02523i | ||||||||
\(412\) | 0.896575 | − | 3.34607i | 0.0441711 | − | 0.164849i | ||||
\(413\) | −8.48528 | − | 8.48528i | −0.417533 | − | 0.417533i | ||||
\(414\) | 7.79423 | − | 4.50000i | 0.383065 | − | 0.221163i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.00000 | − | 1.73205i | 0.147087 | − | 0.0849208i | ||||
\(417\) | −1.79315 | + | 6.69213i | −0.0878110 | + | 0.327715i | ||||
\(418\) | −1.79315 | − | 6.69213i | −0.0877059 | − | 0.327323i | ||||
\(419\) | −5.19615 | + | 9.00000i | −0.253849 | + | 0.439679i | −0.964582 | − | 0.263783i | \(-0.915030\pi\) |
0.710734 | + | 0.703461i | \(0.248363\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.00000 | − | 8.66025i | −0.243685 | − | 0.422075i | 0.718076 | − | 0.695965i | \(-0.245023\pi\) |
−0.961761 | + | 0.273890i | \(0.911690\pi\) | |||||||
\(422\) | −15.5563 | + | 15.5563i | −0.757271 | + | 0.757271i | ||||
\(423\) | 8.69333 | − | 2.32937i | 0.422684 | − | 0.113258i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.00000 | −0.290701 | ||||||||
\(427\) | −21.7494 | + | 5.82774i | −1.05253 | + | 0.282024i | ||||
\(428\) | 2.89778 | − | 0.776457i | 0.140069 | − | 0.0375315i | ||||
\(429\) | −10.3923 | + | 18.0000i | −0.501745 | + | 0.869048i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.92820i | 0.333720i | 0.985981 | + | 0.166860i | \(0.0533628\pi\) | ||||
−0.985981 | + | 0.166860i | \(0.946637\pi\) | |||||||
\(432\) | 1.34486 | − | 5.01910i | 0.0647048 | − | 0.241481i | ||||
\(433\) | −7.34847 | + | 7.34847i | −0.353145 | + | 0.353145i | −0.861278 | − | 0.508133i | \(-0.830336\pi\) |
0.508133 | + | 0.861278i | \(0.330336\pi\) | |||||||
\(434\) | 8.66025 | + | 15.0000i | 0.415705 | + | 0.720023i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.50000 | − | 4.33013i | 0.119728 | − | 0.207375i | ||||
\(437\) | 1.55291 | + | 5.79555i | 0.0742860 | + | 0.277239i | ||||
\(438\) | −16.9706 | − | 16.9706i | −0.810885 | − | 0.810885i | ||||
\(439\) | −17.3205 | + | 10.0000i | −0.826663 | + | 0.477274i | −0.852709 | − | 0.522387i | \(-0.825042\pi\) |
0.0260459 | + | 0.999661i | \(0.491708\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.0000 | −0.571429 | ||||||||
\(442\) | 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 | \(0.151918\pi\) | |||||||
\(444\) | −5.19615 | + | 3.00000i | −0.246598 | + | 0.142374i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.5000 | + | 7.79423i | 0.639244 | + | 0.369067i | ||||
\(447\) | 8.69333 | + | 2.32937i | 0.411181 | + | 0.110175i | ||||
\(448\) | −1.67303 | − | 0.448288i | −0.0790434 | − | 0.0211796i | ||||
\(449\) | −13.8564 | −0.653924 | −0.326962 | − | 0.945037i | \(-0.606025\pi\) | ||||
−0.326962 | + | 0.945037i | \(0.606025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.0000 | 1.41264 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.2474 | − | 12.2474i | 0.575435 | − | 0.575435i | ||||
\(454\) | 20.7846 | + | 12.0000i | 0.975470 | + | 0.563188i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.00000 | + | 1.73205i | 0.140488 | + | 0.0811107i | ||||
\(457\) | 8.06918 | − | 30.1146i | 0.377460 | − | 1.40870i | −0.472256 | − | 0.881461i | \(-0.656560\pi\) |
0.849717 | − | 0.527240i | \(-0.176773\pi\) | |||||||
\(458\) | 3.53553 | + | 3.53553i | 0.165205 | + | 0.165205i | ||||
\(459\) | 31.1769 | 1.45521 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.5000 | − | 6.06218i | 0.489034 | − | 0.282344i | −0.235140 | − | 0.971962i | \(-0.575555\pi\) |
0.724174 | + | 0.689618i | \(0.242221\pi\) | |||||||
\(462\) | 10.0382 | − | 2.68973i | 0.467019 | − | 0.125137i | ||||
\(463\) | −4.48288 | − | 16.7303i | −0.208337 | − | 0.777524i | −0.988406 | − | 0.151831i | \(-0.951483\pi\) |
0.780069 | − | 0.625693i | \(-0.215184\pi\) | |||||||
\(464\) | 4.33013 | − | 7.50000i | 0.201021 | − | 0.348179i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | − | 5.19615i | −0.138972 | − | 0.240707i | ||||
\(467\) | 25.4558 | − | 25.4558i | 1.17796 | − | 1.17796i | 0.197692 | − | 0.980264i | \(-0.436655\pi\) |
0.980264 | − | 0.197692i | \(-0.0633445\pi\) | |||||||
\(468\) | −2.68973 | − | 10.0382i | −0.124333 | − | 0.464016i | ||||
\(469\) | 21.0000i | 0.969690i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.0000 | + | 31.1769i | 0.829396 | + | 1.43656i | ||||
\(472\) | 6.69213 | − | 1.79315i | 0.308030 | − | 0.0825365i | ||||
\(473\) | −34.7733 | + | 9.31749i | −1.59888 | + | 0.428418i | ||||
\(474\) | −3.46410 | − | 6.00000i | −0.159111 | − | 0.275589i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 10.3923i | − | 0.476331i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.6969 | − | 14.6969i | 0.672222 | − | 0.672222i | ||||
\(479\) | −13.8564 | − | 24.0000i | −0.633115 | − | 1.09659i | −0.986911 | − | 0.161265i | \(-0.948443\pi\) |
0.353796 | − | 0.935323i | \(-0.384891\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.00000 | + | 10.3923i | −0.273576 | + | 0.473848i | ||||
\(482\) | 4.39992 | + | 16.4207i | 0.200411 | + | 0.747944i | ||||
\(483\) | −8.69333 | + | 2.32937i | −0.395560 | + | 0.105990i | ||||
\(484\) | 0.866025 | − | 0.500000i | 0.0393648 | − | 0.0227273i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −13.5000 | − | 7.79423i | −0.612372 | − | 0.353553i | ||||
\(487\) | 17.1464 | + | 17.1464i | 0.776979 | + | 0.776979i | 0.979316 | − | 0.202337i | \(-0.0648537\pi\) |
−0.202337 | + | 0.979316i | \(0.564854\pi\) | |||||||
\(488\) | 3.36465 | − | 12.5570i | 0.152310 | − | 0.568430i | ||||
\(489\) | 25.9808 | + | 15.0000i | 1.17489 | + | 0.678323i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | + | 6.92820i | 0.541552 | + | 0.312665i | 0.745708 | − | 0.666273i | \(-0.232111\pi\) |
−0.204155 | + | 0.978938i | \(0.565445\pi\) | |||||||
\(492\) | −10.6066 | + | 10.6066i | −0.478183 | + | 0.478183i | ||||
\(493\) | 50.1910 | + | 13.4486i | 2.26049 | + | 0.605696i | ||||
\(494\) | 6.92820 | 0.311715 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.0000 | −0.449013 | ||||||||
\(497\) | 5.79555 | + | 1.55291i | 0.259966 | + | 0.0696577i | ||||
\(498\) | −5.01910 | − | 1.34486i | −0.224911 | − | 0.0602648i | ||||
\(499\) | 38.1051 | + | 22.0000i | 1.70582 | + | 0.984855i | 0.939599 | + | 0.342277i | \(0.111198\pi\) |
0.766220 | + | 0.642578i | \(0.222135\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.5000 | + | 7.79423i | −0.603136 | + | 0.348220i | ||||
\(502\) | 2.68973 | − | 10.0382i | 0.120048 | − | 0.448027i | ||||
\(503\) | −6.36396 | − | 6.36396i | −0.283755 | − | 0.283755i | 0.550850 | − | 0.834605i | \(-0.314304\pi\) |
−0.834605 | + | 0.550850i | \(0.814304\pi\) | |||||||
\(504\) | −2.59808 | + | 4.50000i | −0.115728 | + | 0.200446i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.00000 | + | 5.19615i | −0.400099 | + | 0.230997i | ||||
\(507\) | 1.22474 | + | 1.22474i | 0.0543928 | + | 0.0543928i | ||||
\(508\) | −1.34486 | − | 5.01910i | −0.0596687 | − | 0.222686i | ||||
\(509\) | 2.59808 | − | 4.50000i | 0.115158 | − | 0.199459i | −0.802685 | − | 0.596403i | \(-0.796596\pi\) |
0.917843 | + | 0.396944i | \(0.129929\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | + | 20.7846i | 0.530849 | + | 0.919457i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 7.34847 | − | 7.34847i | 0.324443 | − | 0.324443i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.00000 | − | 15.5885i | 0.396203 | − | 0.686244i | ||||
\(517\) | −10.0382 | + | 2.68973i | −0.441479 | + | 0.118294i | ||||
\(518\) | 5.79555 | − | 1.55291i | 0.254642 | − | 0.0682311i | ||||
\(519\) | −41.5692 | −1.82469 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.19615i | 0.227648i | 0.993501 | + | 0.113824i | \(0.0363099\pi\) | ||||
−0.993501 | + | 0.113824i | \(0.963690\pi\) | |||||||
\(522\) | −18.3712 | − | 18.3712i | −0.804084 | − | 0.804084i | ||||
\(523\) | −8.57321 | + | 8.57321i | −0.374880 | + | 0.374880i | −0.869251 | − | 0.494371i | \(-0.835399\pi\) |
0.494371 | + | 0.869251i | \(0.335399\pi\) | |||||||
\(524\) | −3.46410 | − | 6.00000i | −0.151330 | − | 0.262111i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.0000 | + | 20.7846i | −0.523225 | + | 0.906252i | ||||
\(527\) | −15.5291 | − | 57.9555i | −0.676460 | − | 2.52458i | ||||
\(528\) | −1.55291 | + | 5.79555i | −0.0675819 | + | 0.252219i | ||||
\(529\) | −12.1244 | + | 7.00000i | −0.527146 | + | 0.304348i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 20.7846i | − | 0.901975i | ||||||
\(532\) | −2.44949 | − | 2.44949i | −0.106199 | − | 0.106199i | ||||
\(533\) | −7.76457 | + | 28.9778i | −0.336321 | + | 1.25517i | ||||
\(534\) | − | 3.00000i | − | 0.129823i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.5000 | − | 6.06218i | −0.453531 | − | 0.261846i | ||||
\(537\) | 10.8704 | + | 40.5689i | 0.469092 | + | 1.75068i | ||||
\(538\) | −1.67303 | − | 0.448288i | −0.0721296 | − | 0.0193271i | ||||
\(539\) | 13.8564 | 0.596838 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.0000 | −1.84871 | −0.924357 | − | 0.381528i | \(-0.875398\pi\) | ||||
−0.924357 | + | 0.381528i | \(0.875398\pi\) | |||||||
\(542\) | 9.65926 | + | 2.58819i | 0.414901 | + | 0.111172i | ||||
\(543\) | 3.13801 | + | 11.7112i | 0.134665 | + | 0.502577i | ||||
\(544\) | 5.19615 | + | 3.00000i | 0.222783 | + | 0.128624i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.3923i | 0.444750i | ||||||||
\(547\) | 0.448288 | − | 1.67303i | 0.0191674 | − | 0.0715337i | −0.955680 | − | 0.294408i | \(-0.904877\pi\) |
0.974847 | + | 0.222875i | \(0.0715441\pi\) | |||||||
\(548\) | 8.48528 | + | 8.48528i | 0.362473 | + | 0.362473i | ||||
\(549\) | −33.7750 | − | 19.5000i | −1.44148 | − | 0.832240i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.0000 | − | 8.66025i | 0.639021 | − | 0.368939i | ||||
\(552\) | 1.34486 | − | 5.01910i | 0.0572412 | − | 0.213627i | ||||
\(553\) | 1.79315 | + | 6.69213i | 0.0762525 | + | 0.284578i | ||||
\(554\) | 5.19615 | − | 9.00000i | 0.220763 | − | 0.382373i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | −25.4558 | + | 25.4558i | −1.07860 | + | 1.07860i | −0.0819634 | + | 0.996635i | \(0.526119\pi\) |
−0.996635 | + | 0.0819634i | \(0.973881\pi\) | |||||||
\(558\) | −7.76457 | + | 28.9778i | −0.328701 | + | 1.22673i | ||||
\(559\) | − | 36.0000i | − | 1.52264i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −36.0000 | −1.51992 | ||||||||
\(562\) | −5.01910 | + | 1.34486i | −0.211718 | + | 0.0567296i | ||||
\(563\) | 20.2844 | − | 5.43520i | 0.854887 | − | 0.229066i | 0.195346 | − | 0.980734i | \(-0.437417\pi\) |
0.659542 | + | 0.751668i | \(0.270750\pi\) | |||||||
\(564\) | 2.59808 | − | 4.50000i | 0.109399 | − | 0.189484i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 5.19615i | − | 0.218411i | ||||||
\(567\) | 11.0227 | + | 11.0227i | 0.462910 | + | 0.462910i | ||||
\(568\) | −2.44949 | + | 2.44949i | −0.102778 | + | 0.102778i | ||||
\(569\) | −3.46410 | − | 6.00000i | −0.145223 | − | 0.251533i | 0.784233 | − | 0.620466i | \(-0.213057\pi\) |
−0.929456 | + | 0.368933i | \(0.879723\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | − | 3.46410i | 0.0836974 | − | 0.144968i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) |
0.904835 | + | 0.425762i | \(0.139994\pi\) | |||||||
\(572\) | 3.10583 | + | 11.5911i | 0.129861 | + | 0.484649i | ||||
\(573\) | −21.2132 | − | 21.2132i | −0.886194 | − | 0.886194i | ||||
\(574\) | 12.9904 | − | 7.50000i | 0.542208 | − | 0.313044i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.50000 | − | 2.59808i | −0.0625000 | − | 0.108253i | ||||
\(577\) | −24.4949 | − | 24.4949i | −1.01974 | − | 1.01974i | −0.999801 | − | 0.0199346i | \(-0.993654\pi\) |
−0.0199346 | − | 0.999801i | \(-0.506346\pi\) | |||||||
\(578\) | −4.91756 | + | 18.3526i | −0.204544 | + | 0.763367i | ||||
\(579\) | −25.9808 | + | 15.0000i | −1.07972 | + | 0.623379i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.50000 | + | 2.59808i | 0.186691 | + | 0.107786i | ||||
\(582\) | −11.5911 | − | 3.10583i | −0.480467 | − | 0.128741i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −13.8564 | −0.573382 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.0000 | 1.23929 | ||||||||
\(587\) | 2.89778 | + | 0.776457i | 0.119604 | + | 0.0320478i | 0.318125 | − | 0.948049i | \(-0.396947\pi\) |
−0.198520 | + | 0.980097i | \(0.563614\pi\) | |||||||
\(588\) | −4.89898 | + | 4.89898i | −0.202031 | + | 0.202031i | ||||
\(589\) | −17.3205 | − | 10.0000i | −0.713679 | − | 0.412043i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.0000 | − | 10.3923i | −0.740421 | − | 0.427482i | ||||
\(592\) | −0.896575 | + | 3.34607i | −0.0368490 | + | 0.137522i | ||||
\(593\) | −12.7279 | − | 12.7279i | −0.522673 | − | 0.522673i | 0.395705 | − | 0.918378i | \(-0.370500\pi\) |
−0.918378 | + | 0.395705i | \(0.870500\pi\) | |||||||
\(594\) | 15.5885 | + | 9.00000i | 0.639602 | + | 0.369274i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.50000 | − | 2.59808i | 0.184327 | − | 0.106421i | ||||
\(597\) | −16.7303 | + | 4.48288i | −0.684727 | + | 0.183472i | ||||
\(598\) | −2.68973 | − | 10.0382i | −0.109991 | − | 0.410492i | ||||
\(599\) | 13.8564 | − | 24.0000i | 0.566157 | − | 0.980613i | −0.430784 | − | 0.902455i | \(-0.641763\pi\) |
0.996941 | − | 0.0781581i | \(-0.0249039\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.0000 | + | 32.9090i | 0.775026 | + | 1.34238i | 0.934780 | + | 0.355228i | \(0.115597\pi\) |
−0.159754 | + | 0.987157i | \(0.551070\pi\) | |||||||
\(602\) | −12.7279 | + | 12.7279i | −0.518751 | + | 0.518751i | ||||
\(603\) | −25.7196 | + | 25.7196i | −1.04738 | + | 1.04738i | ||||
\(604\) | − | 10.0000i | − | 0.406894i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.0000 | − | 20.7846i | −0.487467 | − | 0.844317i | ||||
\(607\) | −38.4797 | + | 10.3106i | −1.56184 | + | 0.418495i | −0.933247 | − | 0.359235i | \(-0.883038\pi\) |
−0.628598 | + | 0.777730i | \(0.716371\pi\) | |||||||
\(608\) | 1.93185 | − | 0.517638i | 0.0783469 | − | 0.0209930i | ||||
\(609\) | 12.9904 | + | 22.5000i | 0.526397 | + | 0.911746i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 10.3923i | − | 0.420428i | ||||||
\(612\) | 12.7279 | − | 12.7279i | 0.514496 | − | 0.514496i | ||||
\(613\) | 12.2474 | − | 12.2474i | 0.494670 | − | 0.494670i | −0.415104 | − | 0.909774i | \(-0.636255\pi\) |
0.909774 | + | 0.415104i | \(0.136255\pi\) | |||||||
\(614\) | −2.59808 | − | 4.50000i | −0.104850 | − | 0.181605i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.00000 | − | 5.19615i | 0.120873 | − | 0.209359i | ||||
\(617\) | 9.31749 | + | 34.7733i | 0.375108 | + | 1.39992i | 0.853187 | + | 0.521605i | \(0.174666\pi\) |
−0.478079 | + | 0.878317i | \(0.658667\pi\) | |||||||
\(618\) | −5.79555 | + | 1.55291i | −0.233131 | + | 0.0624674i | ||||
\(619\) | 19.0526 | − | 11.0000i | 0.765787 | − | 0.442127i | −0.0655827 | − | 0.997847i | \(-0.520891\pi\) |
0.831370 | + | 0.555720i | \(0.187557\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.5000 | − | 7.79423i | −0.541736 | − | 0.312772i | ||||
\(622\) | 17.1464 | + | 17.1464i | 0.687509 | + | 0.687509i | ||||
\(623\) | −0.776457 | + | 2.89778i | −0.0311081 | + | 0.116097i | ||||
\(624\) | −5.19615 | − | 3.00000i | −0.208013 | − | 0.120096i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.00000 | − | 1.73205i | −0.119904 | − | 0.0692267i | ||||
\(627\) | −8.48528 | + | 8.48528i | −0.338869 | + | 0.338869i | ||||
\(628\) | 20.0764 | + | 5.37945i | 0.801135 | + | 0.214664i | ||||
\(629\) | −20.7846 | −0.828737 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | −3.86370 | − | 1.03528i | −0.153690 | − | 0.0411811i | ||||
\(633\) | 36.8067 | + | 9.86233i | 1.46294 | + | 0.391992i | ||||
\(634\) | −5.19615 | − | 3.00000i | −0.206366 | − | 0.119145i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.58630 | + | 13.3843i | −0.142094 | + | 0.530304i | ||||
\(638\) | 21.2132 | + | 21.2132i | 0.839839 | + | 0.839839i | ||||
\(639\) | 5.19615 | + | 9.00000i | 0.205557 | + | 0.356034i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.5000 | − | 16.4545i | 1.12568 | − | 0.649913i | 0.182837 | − | 0.983143i | \(-0.441472\pi\) |
0.942845 | + | 0.333230i | \(0.108139\pi\) | |||||||
\(642\) | −3.67423 | − | 3.67423i | −0.145010 | − | 0.145010i | ||||
\(643\) | −1.34486 | − | 5.01910i | −0.0530362 | − | 0.197934i | 0.934324 | − | 0.356424i | \(-0.116004\pi\) |
−0.987361 | + | 0.158490i | \(0.949337\pi\) | |||||||
\(644\) | −2.59808 | + | 4.50000i | −0.102379 | + | 0.177325i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.00000 | + | 10.3923i | 0.236067 | + | 0.408880i | ||||
\(647\) | 14.8492 | − | 14.8492i | 0.583784 | − | 0.583784i | −0.352157 | − | 0.935941i | \(-0.614552\pi\) |
0.935941 | + | 0.352157i | \(0.114552\pi\) | |||||||
\(648\) | −8.69333 | + | 2.32937i | −0.341506 | + | 0.0915064i | ||||
\(649\) | 24.0000i | 0.942082i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.0000 | − | 25.9808i | 0.587896 | − | 1.01827i | ||||
\(652\) | 16.7303 | − | 4.48288i | 0.655210 | − | 0.175563i | ||||
\(653\) | 17.3867 | − | 4.65874i | 0.680393 | − | 0.182311i | 0.0979610 | − | 0.995190i | \(-0.468768\pi\) |
0.582432 | + | 0.812880i | \(0.302101\pi\) | |||||||
\(654\) | −8.66025 | −0.338643 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.66025i | 0.338126i | ||||||||
\(657\) | −10.7589 | + | 40.1528i | −0.419745 | + | 1.56651i | ||||
\(658\) | −3.67423 | + | 3.67423i | −0.143237 | + | 0.143237i | ||||
\(659\) | −10.3923 | − | 18.0000i | −0.404827 | − | 0.701180i | 0.589475 | − | 0.807787i | \(-0.299335\pi\) |
−0.994301 | + | 0.106606i | \(0.966001\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.0000 | + | 19.0526i | −0.427850 | + | 0.741059i | −0.996682 | − | 0.0813955i | \(-0.974062\pi\) |
0.568831 | + | 0.822454i | \(0.307396\pi\) | |||||||
\(662\) | 2.07055 | + | 7.72741i | 0.0804743 | + | 0.300334i | ||||
\(663\) | 9.31749 | − | 34.7733i | 0.361861 | − | 1.35048i | ||||
\(664\) | −2.59808 | + | 1.50000i | −0.100825 | + | 0.0582113i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.00000 | + | 5.19615i | 0.348743 | + | 0.201347i | ||||
\(667\) | −18.3712 | − | 18.3712i | −0.711335 | − | 0.711335i | ||||
\(668\) | −2.32937 | + | 8.69333i | −0.0901261 | + | 0.336355i | ||||
\(669\) | − | 27.0000i | − | 1.04388i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.0000 | + | 22.5167i | 1.50558 | + | 0.869246i | ||||
\(672\) | 0.776457 | + | 2.89778i | 0.0299525 | + | 0.111784i | ||||
\(673\) | 36.8067 | + | 9.86233i | 1.41879 | + | 0.380165i | 0.885056 | − | 0.465485i | \(-0.154120\pi\) |
0.533739 | + | 0.845649i | \(0.320787\pi\) | |||||||
\(674\) | −13.8564 | −0.533729 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −5.79555 | − | 1.55291i | −0.222741 | − | 0.0596833i | 0.145722 | − | 0.989326i | \(-0.453449\pi\) |
−0.368464 | + | 0.929642i | \(0.620116\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.3923 | + | 6.00000i | 0.398820 | + | 0.230259i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 41.5692i | − | 1.59294i | ||||||
\(682\) | 8.96575 | − | 33.4607i | 0.343316 | − | 1.28127i | ||||
\(683\) | 8.48528 | + | 8.48528i | 0.324680 | + | 0.324680i | 0.850559 | − | 0.525879i | \(-0.176264\pi\) |
−0.525879 | + | 0.850559i | \(0.676264\pi\) | |||||||
\(684\) | − | 6.00000i | − | 0.229416i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.5000 | − | 9.52628i | 0.629973 | − | 0.363715i | ||||
\(687\) | 2.24144 | − | 8.36516i | 0.0855162 | − | 0.319151i | ||||
\(688\) | −2.68973 | − | 10.0382i | −0.102545 | − | 0.382703i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.00000 | + | 6.92820i | 0.152167 | + | 0.263561i | 0.932024 | − | 0.362397i | \(-0.118041\pi\) |
−0.779857 | + | 0.625958i | \(0.784708\pi\) | |||||||
\(692\) | −16.9706 | + | 16.9706i | −0.645124 | + | 0.645124i | ||||
\(693\) | −12.7279 | − | 12.7279i | −0.483494 | − | 0.483494i | ||||
\(694\) | 12.0000i | 0.455514i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −15.0000 | −0.568574 | ||||||||
\(697\) | −50.1910 | + | 13.4486i | −1.90112 | + | 0.509403i | ||||
\(698\) | 0.965926 | − | 0.258819i | 0.0365608 | − | 0.00979645i | ||||
\(699\) | −5.19615 | + | 9.00000i | −0.196537 | + | 0.340411i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 12.1244i | − | 0.457931i | −0.973435 | − | 0.228965i | \(-0.926466\pi\) | ||
0.973435 | − | 0.228965i | \(-0.0735342\pi\) | |||||||
\(702\) | −12.7279 | + | 12.7279i | −0.480384 | + | 0.480384i | ||||
\(703\) | −4.89898 | + | 4.89898i | −0.184769 | + | 0.184769i | ||||
\(704\) | 1.73205 | + | 3.00000i | 0.0652791 | + | 0.113067i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.0000 | + | 20.7846i | −0.451626 | + | 0.782239i | ||||
\(707\) | 6.21166 | + | 23.1822i | 0.233613 | + | 0.871857i | ||||
\(708\) | −8.48528 | − | 8.48528i | −0.318896 | − | 0.318896i | ||||
\(709\) | 35.5070 | − | 20.5000i | 1.33349 | − | 0.769894i | 0.347661 | − | 0.937620i | \(-0.386976\pi\) |
0.985834 | + | 0.167727i | \(0.0536426\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.00000 | + | 10.3923i | −0.225018 | + | 0.389742i | ||||
\(712\) | −1.22474 | − | 1.22474i | −0.0458993 | − | 0.0458993i | ||||
\(713\) | −7.76457 | + | 28.9778i | −0.290785 | + | 1.08523i | ||||
\(714\) | −15.5885 | + | 9.00000i | −0.583383 | + | 0.336817i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 21.0000 | + | 12.1244i | 0.784807 | + | 0.453108i | ||||
\(717\) | −34.7733 | − | 9.31749i | −1.29863 | − | 0.347968i | ||||
\(718\) | 16.7303 | + | 4.48288i | 0.624370 | + | 0.167299i | ||||
\(719\) | 6.92820 | 0.258378 | 0.129189 | − | 0.991620i | \(-0.458763\pi\) | ||||
0.129189 | + | 0.991620i | \(0.458763\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | 0.223452 | ||||||||
\(722\) | −14.4889 | − | 3.88229i | −0.539221 | − | 0.144484i | ||||
\(723\) | 20.8207 | − | 20.8207i | 0.774329 | − | 0.774329i | ||||
\(724\) | 6.06218 | + | 3.50000i | 0.225299 | + | 0.130076i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.50000 | − | 0.866025i | −0.0556702 | − | 0.0321412i | ||||
\(727\) | −1.34486 | + | 5.01910i | −0.0498782 | + | 0.186148i | −0.986370 | − | 0.164541i | \(-0.947386\pi\) |
0.936492 | + | 0.350689i | \(0.114052\pi\) | |||||||
\(728\) | 4.24264 | + | 4.24264i | 0.157243 | + | 0.157243i | ||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 54.0000 | − | 31.1769i | 1.99726 | − | 1.15312i | ||||
\(732\) | −21.7494 | + | 5.82774i | −0.803882 | + | 0.215399i | ||||
\(733\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(734\) | 1.73205 | − | 3.00000i | 0.0639312 | − | 0.110732i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.50000 | − | 2.59808i | −0.0552907 | − | 0.0957664i | ||||
\(737\) | 29.6985 | − | 29.6985i | 1.09396 | − | 1.09396i | ||||
\(738\) | 25.0955 | + | 6.72432i | 0.923778 | + | 0.247525i | ||||
\(739\) | − | 4.00000i | − | 0.147142i | −0.997290 | − | 0.0735712i | \(-0.976560\pi\) | ||
0.997290 | − | 0.0735712i | \(-0.0234396\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.00000 | − | 10.3923i | −0.220416 | − | 0.381771i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.0800 | + | 6.98811i | −0.956782 | + | 0.256369i | −0.703238 | − | 0.710955i | \(-0.748263\pi\) |
−0.253544 | + | 0.967324i | \(0.581596\pi\) | |||||||
\(744\) | 8.66025 | + | 15.0000i | 0.317500 | + | 0.549927i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 13.8564i | − | 0.507319i | ||||||
\(747\) | 2.32937 | + | 8.69333i | 0.0852272 | + | 0.318072i | ||||
\(748\) | −14.6969 | + | 14.6969i | −0.537373 | + | 0.537373i | ||||
\(749\) | 2.59808 | + | 4.50000i | 0.0949316 | + | 0.164426i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | − | 1.73205i | 0.0364905 | − | 0.0632034i | −0.847203 | − | 0.531269i | \(-0.821715\pi\) |
0.883694 | + | 0.468065i | \(0.155049\pi\) | |||||||
\(752\) | −0.776457 | − | 2.89778i | −0.0283145 | − | 0.105671i | ||||
\(753\) | −17.3867 | + | 4.65874i | −0.633605 | + | 0.169774i | ||||
\(754\) | −25.9808 | + | 15.0000i | −0.946164 | + | 0.546268i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 9.00000 | 0.327327 | ||||||||
\(757\) | 31.8434 | + | 31.8434i | 1.15737 | + | 1.15737i | 0.985040 | + | 0.172327i | \(0.0551286\pi\) |
0.172327 | + | 0.985040i | \(0.444871\pi\) | |||||||
\(758\) | 2.07055 | − | 7.72741i | 0.0752058 | − | 0.280672i | ||||
\(759\) | 15.5885 | + | 9.00000i | 0.565825 | + | 0.326679i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.5000 | − | 19.9186i | −1.25062 | − | 0.722048i | −0.279391 | − | 0.960178i | \(-0.590132\pi\) |
−0.971233 | + | 0.238129i | \(0.923466\pi\) | |||||||
\(762\) | −6.36396 | + | 6.36396i | −0.230542 | + | 0.230542i | ||||
\(763\) | 8.36516 | + | 2.24144i | 0.302839 | + | 0.0811455i | ||||
\(764\) | −17.3205 | −0.626634 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.0000 | −0.867155 | ||||||||
\(767\) | −23.1822 | − | 6.21166i | −0.837061 | − | 0.224290i | ||||
\(768\) | −1.67303 | − | 0.448288i | −0.0603704 | − | 0.0161762i | ||||
\(769\) | 19.9186 | + | 11.5000i | 0.718283 | + | 0.414701i | 0.814120 | − | 0.580696i | \(-0.197220\pi\) |
−0.0958377 | + | 0.995397i | \(0.530553\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.48288 | + | 16.7303i | −0.161342 | + | 0.602138i | ||||
\(773\) | 25.4558 | + | 25.4558i | 0.915583 | + | 0.915583i | 0.996704 | − | 0.0811212i | \(-0.0258501\pi\) |
−0.0811212 | + | 0.996704i | \(0.525850\pi\) | |||||||
\(774\) | −31.1769 | −1.12063 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.00000 | + | 3.46410i | −0.215387 | + | 0.124354i | ||||
\(777\) | −7.34847 | − | 7.34847i | −0.263625 | − | 0.263625i | ||||
\(778\) | −6.72432 | − | 25.0955i | −0.241078 | − | 0.899717i | ||||
\(779\) | −8.66025 | + | 15.0000i | −0.310286 | + | 0.537431i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.00000 | − | 10.3923i | −0.214697 | − | 0.371866i | ||||
\(782\) | 12.7279 | − | 12.7279i | 0.455150 | − | 0.455150i | ||||
\(783\) | −11.6469 | + | 43.4667i | −0.416225 | + | 1.55337i | ||||
\(784\) | 4.00000i | 0.142857i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.00000 | + | 10.3923i | −0.214013 | + | 0.370681i | ||||
\(787\) | −3.34607 | + | 0.896575i | −0.119274 | + | 0.0319595i | −0.317962 | − | 0.948103i | \(-0.602999\pi\) |
0.198688 | + | 0.980063i | \(0.436332\pi\) | |||||||
\(788\) | −11.5911 | + | 3.10583i | −0.412916 | + | 0.110641i | ||||
\(789\) | 41.5692 | 1.47990 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 10.0382 | − | 2.68973i | 0.356692 | − | 0.0955753i | ||||
\(793\) | −31.8434 | + | 31.8434i | −1.13079 | + | 1.13079i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.00000 | + | 8.66025i | −0.177220 | + | 0.306955i | ||||
\(797\) | −10.8704 | − | 40.5689i | −0.385049 | − | 1.43702i | −0.838089 | − | 0.545533i | \(-0.816327\pi\) |
0.453040 | − | 0.891490i | \(-0.350340\pi\) | |||||||
\(798\) | −1.55291 | + | 5.79555i | −0.0549726 | + | 0.205160i | ||||
\(799\) | 15.5885 | − | 9.00000i | 0.551480 | − | 0.318397i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.50000 | + | 2.59808i | −0.159000 | + | 0.0917985i | ||||
\(802\) | 14.6969 | + | 14.6969i | 0.518967 | + | 0.518967i | ||||
\(803\) | 12.4233 | − | 46.3644i | 0.438409 | − | 1.63617i | ||||
\(804\) | 21.0000i | 0.740613i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 30.0000 | + | 17.3205i | 1.05670 | + | 0.610089i | ||||
\(807\) | 0.776457 | + | 2.89778i | 0.0273326 | + | 0.102007i | ||||
\(808\) | −13.3843 | − | 3.58630i | −0.470857 | − | 0.126166i | ||||
\(809\) | −6.92820 | −0.243583 | −0.121791 | − | 0.992556i | \(-0.538864\pi\) | ||||
−0.121791 | + | 0.992556i | \(0.538864\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.00000 | 0.140459 | 0.0702295 | − | 0.997531i | \(-0.477627\pi\) | ||||
0.0702295 | + | 0.997531i | \(0.477627\pi\) | |||||||
\(812\) | 14.4889 | + | 3.88229i | 0.508460 | + | 0.136242i | ||||
\(813\) | −4.48288 | − | 16.7303i | −0.157221 | − | 0.586758i | ||||
\(814\) | −10.3923 | − | 6.00000i | −0.364250 | − | 0.210300i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 10.3923i | − | 0.363803i | ||||||
\(817\) | 5.37945 | − | 20.0764i | 0.188203 | − | 0.702384i | ||||
\(818\) | 1.41421 | + | 1.41421i | 0.0494468 | + | 0.0494468i | ||||
\(819\) | 15.5885 | − | 9.00000i | 0.544705 | − | 0.314485i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.5000 | + | 9.52628i | −0.575854 | + | 0.332469i | −0.759484 | − | 0.650526i | \(-0.774548\pi\) |
0.183630 | + | 0.982995i | \(0.441215\pi\) | |||||||
\(822\) | 5.37945 | − | 20.0764i | 0.187630 | − | 0.700245i | ||||
\(823\) | −7.62089 | − | 28.4416i | −0.265648 | − | 0.991410i | −0.961853 | − | 0.273567i | \(-0.911796\pi\) |
0.696205 | − | 0.717843i | \(-0.254870\pi\) | |||||||
\(824\) | −1.73205 | + | 3.00000i | −0.0603388 | + | 0.104510i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.00000 | + | 10.3923i | 0.208767 | + | 0.361595i | ||||
\(827\) | −31.8198 | + | 31.8198i | −1.10648 | + | 1.10648i | −0.112874 | + | 0.993609i | \(0.536006\pi\) |
−0.993609 | + | 0.112874i | \(0.963994\pi\) | |||||||
\(828\) | −8.69333 | + | 2.32937i | −0.302114 | + | 0.0809513i | ||||
\(829\) | 29.0000i | 1.00721i | 0.863934 | + | 0.503606i | \(0.167994\pi\) | ||||
−0.863934 | + | 0.503606i | \(0.832006\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.0000 | −0.624413 | ||||||||
\(832\) | −3.34607 | + | 0.896575i | −0.116004 | + | 0.0310832i | ||||
\(833\) | −23.1822 | + | 6.21166i | −0.803216 | + | 0.215221i | ||||
\(834\) | 3.46410 | − | 6.00000i | 0.119952 | − | 0.207763i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.92820i | 0.239617i | ||||||||
\(837\) | 50.1910 | − | 13.4486i | 1.73485 | − | 0.464853i | ||||
\(838\) | 7.34847 | − | 7.34847i | 0.253849 | − | 0.253849i | ||||
\(839\) | −19.0526 | − | 33.0000i | −0.657767 | − | 1.13929i | −0.981192 | − | 0.193033i | \(-0.938168\pi\) |
0.323425 | − | 0.946254i | \(-0.395166\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.0000 | + | 39.8372i | −0.793103 | + | 1.37370i | ||||
\(842\) | 2.58819 | + | 9.65926i | 0.0891949 | + | 0.332880i | ||||
\(843\) | 6.36396 | + | 6.36396i | 0.219186 | + | 0.219186i | ||||
\(844\) | 19.0526 | − | 11.0000i | 0.655816 | − | 0.378636i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.00000 | −0.309426 | ||||||||
\(847\) | 1.22474 | + | 1.22474i | 0.0420827 | + | 0.0420827i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.79423 | + | 4.50000i | −0.267497 | + | 0.154440i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.00000 | + | 5.19615i | 0.308516 | + | 0.178122i | ||||
\(852\) | 5.79555 | + | 1.55291i | 0.198552 | + | 0.0532020i | ||||
\(853\) | 16.7303 | + | 4.48288i | 0.572835 | + | 0.153491i | 0.533597 | − | 0.845739i | \(-0.320840\pi\) |
0.0392388 | + | 0.999230i | \(0.487507\pi\) | |||||||
\(854\) | 22.5167 | 0.770504 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.00000 | −0.102538 | ||||||||
\(857\) | 40.5689 | + | 10.8704i | 1.38581 | + | 0.371326i | 0.873227 | − | 0.487314i | \(-0.162023\pi\) |
0.512580 | + | 0.858640i | \(0.328690\pi\) | |||||||
\(858\) | 14.6969 | − | 14.6969i | 0.501745 | − | 0.501745i | ||||
\(859\) | −19.0526 | − | 11.0000i | −0.650065 | − | 0.375315i | 0.138416 | − | 0.990374i | \(-0.455799\pi\) |
−0.788481 | + | 0.615059i | \(0.789132\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.5000 | − | 12.9904i | −0.766798 | − | 0.442711i | ||||
\(862\) | 1.79315 | − | 6.69213i | 0.0610750 | − | 0.227935i | ||||
\(863\) | −10.6066 | − | 10.6066i | −0.361053 | − | 0.361053i | 0.503148 | − | 0.864201i | \(-0.332175\pi\) |
−0.864201 | + | 0.503148i | \(0.832175\pi\) | |||||||
\(864\) | −2.59808 | + | 4.50000i | −0.0883883 | + | 0.153093i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.00000 | − | 5.19615i | 0.305832 | − | 0.176572i | ||||
\(867\) | 31.7876 | − | 8.51747i | 1.07956 | − | 0.289268i | ||||
\(868\) | −4.48288 | − | 16.7303i | −0.152159 | − | 0.567864i | ||||
\(869\) | 6.92820 | − | 12.0000i | 0.235023 | − | 0.407072i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.0000 | + | 36.3731i | 0.711558 | + | 1.23245i | ||||
\(872\) | −3.53553 | + | 3.53553i | −0.119728 | + | 0.119728i | ||||
\(873\) | 5.37945 | + | 20.0764i | 0.182067 | + | 0.679483i | ||||
\(874\) | − | 6.00000i | − | 0.202953i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.0000 | + | 20.7846i | 0.405442 | + | 0.702247i | ||||
\(877\) | 16.7303 | − | 4.48288i | 0.564943 | − | 0.151376i | 0.0349667 | − | 0.999388i | \(-0.488867\pi\) |
0.529976 | + | 0.848012i | \(0.322201\pi\) | |||||||
\(878\) | 19.3185 | − | 5.17638i | 0.651968 | − | 0.174694i | ||||
\(879\) | −25.9808 | − | 45.0000i | −0.876309 | − | 1.51781i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.73205i | − | 0.0583543i | −0.999574 | − | 0.0291771i | \(-0.990711\pi\) | ||
0.999574 | − | 0.0291771i | \(-0.00928869\pi\) | |||||||
\(882\) | 11.5911 | + | 3.10583i | 0.390293 | + | 0.104579i | ||||
\(883\) | −30.6186 | + | 30.6186i | −1.03040 | + | 1.03040i | −0.0308754 | + | 0.999523i | \(0.509830\pi\) |
−0.999523 | + | 0.0308754i | \(0.990170\pi\) | |||||||
\(884\) | −10.3923 | − | 18.0000i | −0.349531 | − | 0.605406i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.50000 | − | 7.79423i | 0.151180 | − | 0.261852i | ||||
\(887\) | −6.21166 | − | 23.1822i | −0.208567 | − | 0.778383i | −0.988333 | − | 0.152311i | \(-0.951328\pi\) |
0.779766 | − | 0.626072i | \(-0.215338\pi\) | |||||||
\(888\) | 5.79555 | − | 1.55291i | 0.194486 | − | 0.0521124i | ||||
\(889\) | 7.79423 | − | 4.50000i | 0.261410 | − | 0.150925i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 31.1769i | − | 1.04447i | ||||||
\(892\) | −11.0227 | − | 11.0227i | −0.369067 | − | 0.369067i | ||||
\(893\) | 1.55291 | − | 5.79555i | 0.0519663 | − | 0.193941i | ||||
\(894\) | −7.79423 | − | 4.50000i | −0.260678 | − | 0.150503i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.50000 | + | 0.866025i | 0.0501115 | + | 0.0289319i | ||||
\(897\) | −12.7279 | + | 12.7279i | −0.424973 | + | 0.424973i | ||||
\(898\) | 13.3843 | + | 3.58630i | 0.446639 | + | 0.119676i | ||||
\(899\) | 86.6025 | 2.88836 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −28.9778 | − | 7.76457i | −0.964854 | − | 0.258532i | ||||
\(903\) | 30.1146 | + | 8.06918i | 1.00215 | + | 0.268525i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −15.0000 | + | 8.66025i | −0.498342 | + | 0.287718i | ||||
\(907\) | 2.24144 | − | 8.36516i | 0.0744257 | − | 0.277761i | −0.918677 | − | 0.395010i | \(-0.870741\pi\) |
0.993102 | + | 0.117250i | \(0.0374077\pi\) | |||||||
\(908\) | −16.9706 | − | 16.9706i | −0.563188 | − | 0.563188i | ||||
\(909\) | −20.7846 | + | 36.0000i | −0.689382 | + | 1.19404i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0000 | + | 27.7128i | −1.59031 | + | 0.918166i | −0.597058 | + | 0.802198i | \(0.703664\pi\) |
−0.993253 | + | 0.115968i | \(0.963003\pi\) | |||||||
\(912\) | −2.44949 | − | 2.44949i | −0.0811107 | − | 0.0811107i | ||||
\(913\) | −2.68973 | − | 10.0382i | −0.0890170 | − | 0.332216i | ||||
\(914\) | −15.5885 | + | 27.0000i | −0.515620 | + | 0.893081i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.50000 | − | 4.33013i | −0.0826023 | − | 0.143071i | ||||
\(917\) | 8.48528 | − | 8.48528i | 0.280209 | − | 0.280209i | ||||
\(918\) | −30.1146 | − | 8.06918i | −0.993929 | − | 0.266323i | ||||
\(919\) | − | 40.0000i | − | 1.31948i | −0.751495 | − | 0.659739i | \(-0.770667\pi\) | ||
0.751495 | − | 0.659739i | \(-0.229333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.50000 | + | 7.79423i | −0.148280 | + | 0.256829i | ||||
\(922\) | −11.7112 | + | 3.13801i | −0.385689 | + | 0.103345i | ||||
\(923\) | 11.5911 | − | 3.10583i | 0.381526 | − | 0.102230i | ||||
\(924\) | −10.3923 | −0.341882 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.3205i | 0.569187i | ||||||||
\(927\) | 7.34847 | + | 7.34847i | 0.241355 | + | 0.241355i | ||||
\(928\) | −6.12372 | + | 6.12372i | −0.201021 | + | 0.201021i | ||||
\(929\) | 3.46410 | + | 6.00000i | 0.113653 | + | 0.196854i | 0.917241 | − | 0.398333i | \(-0.130411\pi\) |
−0.803587 | + | 0.595187i | \(0.797078\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.00000 | + | 6.92820i | −0.131095 | + | 0.227063i | ||||
\(932\) | 1.55291 | + | 5.79555i | 0.0508674 | + | 0.189840i | ||||
\(933\) | 10.8704 | − | 40.5689i | 0.355881 | − | 1.32817i | ||||
\(934\) | −31.1769 | + | 18.0000i | −1.02014 | + | 0.588978i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 10.3923i | 0.339683i | ||||||||
\(937\) | 9.79796 | + | 9.79796i | 0.320085 | + | 0.320085i | 0.848800 | − | 0.528714i | \(-0.177326\pi\) |
−0.528714 | + | 0.848800i | \(0.677326\pi\) | |||||||
\(938\) | 5.43520 | − | 20.2844i | 0.177466 | − | 0.662311i | ||||
\(939\) | 6.00000i | 0.195803i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.50000 | − | 2.59808i | −0.146696 | − | 0.0846949i | 0.424856 | − | 0.905261i | \(-0.360325\pi\) |
−0.571551 | + | 0.820566i | \(0.693658\pi\) | |||||||
\(942\) | −9.31749 | − | 34.7733i | −0.303580 | − | 1.13298i | ||||
\(943\) | 25.0955 | + | 6.72432i | 0.817222 | + | 0.218974i | ||||
\(944\) | −6.92820 | −0.225494 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 36.0000 | 1.17046 | ||||||||
\(947\) | 26.0800 | + | 6.98811i | 0.847486 | + | 0.227083i | 0.656328 | − | 0.754476i | \(-0.272109\pi\) |
0.191158 | + | 0.981559i | \(0.438776\pi\) | |||||||
\(948\) | 1.79315 | + | 6.69213i | 0.0582388 | + | 0.217350i | ||||
\(949\) | 41.5692 | + | 24.0000i | 1.34939 | + | 0.779073i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.3923i | 0.336994i | ||||||||
\(952\) | −2.68973 | + | 10.0382i | −0.0871745 | + | 0.325340i | ||||
\(953\) | −29.6985 | − | 29.6985i | −0.962028 | − | 0.962028i | 0.0372767 | − | 0.999305i | \(-0.488132\pi\) |
−0.999305 | + | 0.0372767i | \(0.988132\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18.0000 | + | 10.3923i | −0.582162 | + | 0.336111i | ||||
\(957\) | 13.4486 | − | 50.1910i | 0.434733 | − | 1.62244i | ||||
\(958\) | 7.17260 | + | 26.7685i | 0.231736 | + | 0.864852i | ||||
\(959\) | −10.3923 | + | 18.0000i | −0.335585 | + | 0.581250i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −34.5000 | − | 59.7558i | −1.11290 | − | 1.92760i | ||||
\(962\) | 8.48528 | − | 8.48528i | 0.273576 | − | 0.273576i | ||||
\(963\) | −2.32937 | + | 8.69333i | −0.0750629 | + | 0.280139i | ||||
\(964\) | − | 17.0000i | − | 0.547533i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.00000 | 0.289570 | ||||||||
\(967\) | 51.8640 | − | 13.8969i | 1.66783 | − | 0.446895i | 0.703309 | − | 0.710885i | \(-0.251705\pi\) |
0.964525 | + | 0.263990i | \(0.0850385\pi\) | |||||||
\(968\) | −0.965926 | + | 0.258819i | −0.0310460 | + | 0.00831876i | ||||
\(969\) | 10.3923 | − | 18.0000i | 0.333849 | − | 0.578243i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 38.1051i | − | 1.22285i | −0.791302 | − | 0.611426i | \(-0.790596\pi\) | ||
0.791302 | − | 0.611426i | \(-0.209404\pi\) | |||||||
\(972\) | 11.0227 | + | 11.0227i | 0.353553 | + | 0.353553i | ||||
\(973\) | −4.89898 | + | 4.89898i | −0.157054 | + | 0.157054i | ||||
\(974\) | −12.1244 | − | 21.0000i | −0.388489 | − | 0.672883i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.50000 | + | 11.2583i | −0.208060 | + | 0.360370i | ||||
\(977\) | 10.8704 | + | 40.5689i | 0.347775 | + | 1.29791i | 0.889337 | + | 0.457253i | \(0.151167\pi\) |
−0.541562 | + | 0.840661i | \(0.682167\pi\) | |||||||
\(978\) | −21.2132 | − | 21.2132i | −0.678323 | − | 0.678323i | ||||
\(979\) | 5.19615 | − | 3.00000i | 0.166070 | − | 0.0958804i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.50000 | + | 12.9904i | 0.239457 | + | 0.414751i | ||||
\(982\) | −9.79796 | − | 9.79796i | −0.312665 | − | 0.312665i | ||||
\(983\) | 2.32937 | − | 8.69333i | 0.0742954 | − | 0.277274i | −0.918777 | − | 0.394776i | \(-0.870822\pi\) |
0.993073 | + | 0.117502i | \(0.0374887\pi\) | |||||||
\(984\) | 12.9904 | − | 7.50000i | 0.414118 | − | 0.239091i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −45.0000 | − | 25.9808i | −1.43309 | − | 0.827396i | ||||
\(987\) | 8.69333 | + | 2.32937i | 0.276712 | + | 0.0741447i | ||||
\(988\) | −6.69213 | − | 1.79315i | −0.212905 | − | 0.0570477i | ||||
\(989\) | −31.1769 | −0.991368 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | 9.65926 | + | 2.58819i | 0.306682 | + | 0.0821751i | ||||
\(993\) | 9.79796 | − | 9.79796i | 0.310929 | − | 0.310929i | ||||
\(994\) | −5.19615 | − | 3.00000i | −0.164812 | − | 0.0951542i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.50000 | + | 2.59808i | 0.142588 | + | 0.0823232i | ||||
\(997\) | 10.7589 | − | 40.1528i | 0.340738 | − | 1.27165i | −0.556775 | − | 0.830663i | \(-0.687961\pi\) |
0.897513 | − | 0.440988i | \(-0.145372\pi\) | |||||||
\(998\) | −31.1127 | − | 31.1127i | −0.984855 | − | 0.984855i | ||||
\(999\) | − | 18.0000i | − | 0.569495i |
(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.d.257.1 | ✓ | 8 | |
3.2 | odd | 2 | 1350.2.q.b.557.2 | 8 | |||
5.2 | odd | 4 | inner | 450.2.p.d.293.2 | yes | 8 | |
5.3 | odd | 4 | inner | 450.2.p.d.293.1 | yes | 8 | |
5.4 | even | 2 | inner | 450.2.p.d.257.2 | yes | 8 | |
9.2 | odd | 6 | inner | 450.2.p.d.407.1 | yes | 8 | |
9.7 | even | 3 | 1350.2.q.b.1007.2 | 8 | |||
15.2 | even | 4 | 1350.2.q.b.1043.1 | 8 | |||
15.8 | even | 4 | 1350.2.q.b.1043.2 | 8 | |||
15.14 | odd | 2 | 1350.2.q.b.557.1 | 8 | |||
45.2 | even | 12 | inner | 450.2.p.d.443.2 | yes | 8 | |
45.7 | odd | 12 | 1350.2.q.b.143.1 | 8 | |||
45.29 | odd | 6 | inner | 450.2.p.d.407.2 | yes | 8 | |
45.34 | even | 6 | 1350.2.q.b.1007.1 | 8 | |||
45.38 | even | 12 | inner | 450.2.p.d.443.1 | yes | 8 | |
45.43 | odd | 12 | 1350.2.q.b.143.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.p.d.257.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
450.2.p.d.257.2 | yes | 8 | 5.4 | even | 2 | inner | |
450.2.p.d.293.1 | yes | 8 | 5.3 | odd | 4 | inner | |
450.2.p.d.293.2 | yes | 8 | 5.2 | odd | 4 | inner | |
450.2.p.d.407.1 | yes | 8 | 9.2 | odd | 6 | inner | |
450.2.p.d.407.2 | yes | 8 | 45.29 | odd | 6 | inner | |
450.2.p.d.443.1 | yes | 8 | 45.38 | even | 12 | inner | |
450.2.p.d.443.2 | yes | 8 | 45.2 | even | 12 | inner | |
1350.2.q.b.143.1 | 8 | 45.7 | odd | 12 | |||
1350.2.q.b.143.2 | 8 | 45.43 | odd | 12 | |||
1350.2.q.b.557.1 | 8 | 15.14 | odd | 2 | |||
1350.2.q.b.557.2 | 8 | 3.2 | odd | 2 | |||
1350.2.q.b.1007.1 | 8 | 45.34 | even | 6 | |||
1350.2.q.b.1007.2 | 8 | 9.7 | even | 3 | |||
1350.2.q.b.1043.1 | 8 | 15.2 | even | 4 | |||
1350.2.q.b.1043.2 | 8 | 15.8 | even | 4 |