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 | 293.2 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.293 |
Dual form | 450.2.p.d.407.2 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.258819 | − | 0.965926i | 0.183013 | − | 0.683013i | ||||
\(3\) | 1.67303 | − | 0.448288i | 0.965926 | − | 0.258819i | ||||
\(4\) | −0.866025 | − | 0.500000i | −0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 1.73205i | − | 0.707107i | ||||||
\(7\) | −1.67303 | − | 0.448288i | −0.632347 | − | 0.169437i | −0.0716124 | − | 0.997433i | \(-0.522814\pi\) |
−0.560734 | + | 0.827996i | \(0.689481\pi\) | |||||||
\(8\) | −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 | \(0.158432\pi\) | |||||||
\(12\) | −1.67303 | − | 0.448288i | −0.482963 | − | 0.129410i | ||||
\(13\) | 3.34607 | − | 0.896575i | 0.928032 | − | 0.248665i | 0.237016 | − | 0.971506i | \(-0.423830\pi\) |
0.691015 | + | 0.722840i | \(0.257164\pi\) | |||||||
\(14\) | −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 | −0.999567 | − | 0.0294245i | \(-0.990633\pi\) |
−0.0294245 | − | 0.999567i | \(-0.509367\pi\) | |||||||
\(18\) | −0.776457 | − | 2.89778i | −0.183013 | − | 0.683013i | ||||
\(19\) | − | 2.00000i | − | 0.458831i | −0.973329 | − | 0.229416i | \(-0.926318\pi\) | ||
0.973329 | − | 0.229416i | \(-0.0736815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | −0.654654 | ||||||||
\(22\) | −0.896575 | − | 3.34607i | −0.191151 | − | 0.713384i | ||||
\(23\) | −0.776457 | − | 2.89778i | −0.161903 | − | 0.604228i | −0.998415 | − | 0.0562805i | \(-0.982076\pi\) |
0.836512 | − | 0.547948i | \(-0.184591\pi\) | |||||||
\(24\) | −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 | \(0.130677\pi\) |
−0.112823 | + | 0.993615i | \(0.535989\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.00000 | + | 8.66025i | −0.898027 | + | 1.55543i | −0.0680129 | + | 0.997684i | \(0.521666\pi\) |
−0.830014 | + | 0.557743i | \(0.811667\pi\) | |||||||
\(32\) | 0.965926 | − | 0.258819i | 0.170753 | − | 0.0457532i | ||||
\(33\) | 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 | \(-0.841910\pi\) |
0.476488 | + | 0.879181i | \(0.341910\pi\) | |||||||
\(38\) | −1.93185 | − | 0.517638i | −0.313388 | − | 0.0839720i | ||||
\(39\) | 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 | \(0.430270\pi\) | |||||||
\(42\) | −0.776457 | + | 2.89778i | −0.119810 | + | 0.447137i | ||||
\(43\) | −2.68973 | + | 10.0382i | −0.410179 | + | 1.53081i | 0.384120 | + | 0.923283i | \(0.374505\pi\) |
−0.794299 | + | 0.607527i | \(0.792162\pi\) | |||||||
\(44\) | −3.46410 | −0.522233 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | −0.442326 | ||||||||
\(47\) | 0.776457 | − | 2.89778i | 0.113258 | − | 0.422684i | −0.885893 | − | 0.463890i | \(-0.846453\pi\) |
0.999151 | + | 0.0412058i | \(0.0131199\pi\) | |||||||
\(48\) | 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 | ||||
\(52\) | −3.34607 | − | 0.896575i | −0.464016 | − | 0.124333i | ||||
\(53\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(54\) | −2.59808 | − | 4.50000i | −0.353553 | − | 0.612372i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.50000 | − | 0.866025i | 0.200446 | − | 0.115728i | ||||
\(57\) | −0.896575 | − | 3.34607i | −0.118754 | − | 0.443197i | ||||
\(58\) | 8.36516 | − | 2.24144i | 1.09840 | − | 0.294315i | ||||
\(59\) | 3.46410 | − | 6.00000i | 0.450988 | − | 0.781133i | −0.547460 | − | 0.836832i | \(-0.684405\pi\) |
0.998448 | + | 0.0556984i | \(0.0177385\pi\) | |||||||
\(60\) | 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 | ||||
\(63\) | −5.01910 | + | 1.34486i | −0.632347 | + | 0.169437i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.00000 | − | 5.19615i | −0.369274 | − | 0.639602i | ||||
\(67\) | 3.13801 | + | 11.7112i | 0.383369 | + | 1.43075i | 0.840721 | + | 0.541468i | \(0.182131\pi\) |
−0.457352 | + | 0.889286i | \(0.651202\pi\) | |||||||
\(68\) | 1.55291 | + | 5.79555i | 0.188319 | + | 0.702814i | ||||
\(69\) | −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 | \(-0.0659005\pi\) | |||||||
\(72\) | −0.776457 | + | 2.89778i | −0.0915064 | + | 0.341506i | ||||
\(73\) | −9.79796 | − | 9.79796i | −1.14676 | − | 1.14676i | −0.987185 | − | 0.159579i | \(-0.948986\pi\) |
−0.159579 | − | 0.987185i | \(-0.551014\pi\) | |||||||
\(74\) | 1.73205 | + | 3.00000i | 0.201347 | + | 0.348743i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | + | 1.73205i | −0.114708 | + | 0.198680i | ||||
\(77\) | −5.79555 | + | 1.55291i | −0.660465 | + | 0.176971i | ||||
\(78\) | −1.55291 | − | 5.79555i | −0.175833 | − | 0.656217i | ||||
\(79\) | −3.46410 | + | 2.00000i | −0.389742 | + | 0.225018i | −0.682048 | − | 0.731307i | \(-0.738911\pi\) |
0.292306 | + | 0.956325i | \(0.405577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.50000 | − | 7.79423i | 0.500000 | − | 0.866025i | ||||
\(82\) | 6.12372 | − | 6.12372i | 0.676252 | − | 0.676252i | ||||
\(83\) | −2.89778 | − | 0.776457i | −0.318072 | − | 0.0852272i | 0.0962507 | − | 0.995357i | \(-0.469315\pi\) |
−0.414323 | + | 0.910130i | \(0.635982\pi\) | |||||||
\(84\) | 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 | ||||
\(88\) | −0.896575 | + | 3.34607i | −0.0955753 | + | 0.356692i | ||||
\(89\) | −1.73205 | −0.183597 | −0.0917985 | − | 0.995778i | \(-0.529262\pi\) | ||||
−0.0917985 | + | 0.995778i | \(0.529262\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | −0.628971 | ||||||||
\(92\) | −0.776457 | + | 2.89778i | −0.0809513 | + | 0.302114i | ||||
\(93\) | −4.48288 | + | 16.7303i | −0.464853 | + | 1.73485i | ||||
\(94\) | −2.59808 | − | 1.50000i | −0.267971 | − | 0.154713i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.50000 | − | 0.866025i | 0.153093 | − | 0.0883883i | ||||
\(97\) | 6.69213 | + | 1.79315i | 0.679483 | + | 0.182067i | 0.582023 | − | 0.813173i | \(-0.302261\pi\) |
0.0974602 | + | 0.995239i | \(0.468928\pi\) | |||||||
\(98\) | −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 | ||||
\(103\) | −3.34607 | + | 0.896575i | −0.329698 | + | 0.0883422i | −0.419871 | − | 0.907584i | \(-0.637925\pi\) |
0.0901732 | + | 0.995926i | \(0.471258\pi\) | |||||||
\(104\) | −1.73205 | + | 3.00000i | −0.169842 | + | 0.294174i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.12132 | + | 2.12132i | 0.205076 | + | 0.205076i | 0.802171 | − | 0.597095i | \(-0.203678\pi\) |
−0.597095 | + | 0.802171i | \(0.703678\pi\) | |||||||
\(108\) | −5.01910 | + | 1.34486i | −0.482963 | + | 0.129410i | ||||
\(109\) | 5.00000i | 0.478913i | 0.970907 | + | 0.239457i | \(0.0769693\pi\) | ||||
−0.970907 | + | 0.239457i | \(0.923031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.00000 | + | 5.19615i | −0.284747 | + | 0.493197i | ||||
\(112\) | −0.448288 | − | 1.67303i | −0.0423592 | − | 0.158087i | ||||
\(113\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(114\) | −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 | ||||
\(122\) | 12.5570 | − | 3.36465i | 1.13686 | − | 0.304621i | ||||
\(123\) | 14.4889 | + | 3.88229i | 1.30642 | + | 0.350054i | ||||
\(124\) | 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 | \(-0.675950\pi\) |
0.851077 | + | 0.525041i | \(0.175950\pi\) | |||||||
\(128\) | −0.965926 | − | 0.258819i | −0.0853766 | − | 0.0228766i | ||||
\(129\) | 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 | \(0.764541\pi\) | |||||||
\(132\) | −5.79555 | + | 1.55291i | −0.504438 | + | 0.135164i | ||||
\(133\) | −0.896575 | + | 3.34607i | −0.0777430 | + | 0.290141i | ||||
\(134\) | 12.1244 | 1.04738 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.00000 | 0.514496 | ||||||||
\(137\) | −3.10583 | + | 11.5911i | −0.265349 | + | 0.990295i | 0.696688 | + | 0.717375i | \(0.254656\pi\) |
−0.962037 | + | 0.272921i | \(0.912010\pi\) | |||||||
\(138\) | −5.01910 | + | 1.34486i | −0.427254 | + | 0.114482i | ||||
\(139\) | −3.46410 | − | 2.00000i | −0.293821 | − | 0.169638i | 0.345843 | − | 0.938293i | \(-0.387593\pi\) |
−0.639664 | + | 0.768655i | \(0.720926\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 5.19615i | − | 0.437595i | ||||||
\(142\) | −3.34607 | − | 0.896575i | −0.280796 | − | 0.0752389i | ||||
\(143\) | 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 | ||||
\(147\) | −6.69213 | − | 1.79315i | −0.551958 | − | 0.147897i | ||||
\(148\) | 3.34607 | − | 0.896575i | 0.275045 | − | 0.0736980i | ||||
\(149\) | −2.59808 | + | 4.50000i | −0.212843 | + | 0.368654i | −0.952603 | − | 0.304216i | \(-0.901606\pi\) |
0.739760 | + | 0.672870i | \(0.234939\pi\) | |||||||
\(150\) | 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 | ||||
\(153\) | −17.3867 | − | 4.65874i | −1.40563 | − | 0.376637i | ||||
\(154\) | 6.00000i | 0.483494i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.00000 | −0.480384 | ||||||||
\(157\) | 5.37945 | + | 20.0764i | 0.429327 | + | 1.60227i | 0.754288 | + | 0.656543i | \(0.227982\pi\) |
−0.324961 | + | 0.945727i | \(0.605351\pi\) | |||||||
\(158\) | 1.03528 | + | 3.86370i | 0.0823622 | + | 0.307380i | ||||
\(159\) | 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 | \(-0.487293\pi\) |
−0.999203 | + | 0.0399091i | \(0.987293\pi\) | |||||||
\(164\) | −4.33013 | − | 7.50000i | −0.338126 | − | 0.585652i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.50000 | + | 2.59808i | −0.116423 | + | 0.201650i | ||||
\(167\) | −8.69333 | + | 2.32937i | −0.672710 | + | 0.180252i | −0.578975 | − | 0.815345i | \(-0.696547\pi\) |
−0.0937349 | + | 0.995597i | \(0.529881\pi\) | |||||||
\(168\) | 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 | ||||
\(173\) | 23.1822 | + | 6.21166i | 1.76251 | + | 0.472264i | 0.987223 | − | 0.159344i | \(-0.0509379\pi\) |
0.775288 | + | 0.631607i | \(0.217605\pi\) | |||||||
\(174\) | 12.9904 | − | 7.50000i | 0.984798 | − | 0.568574i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000 | + | 1.73205i | 0.226134 | + | 0.130558i | ||||
\(177\) | 3.10583 | − | 11.5911i | 0.233448 | − | 0.871241i | ||||
\(178\) | −0.448288 | + | 1.67303i | −0.0336006 | + | 0.125399i | ||||
\(179\) | −24.2487 | −1.81243 | −0.906217 | − | 0.422813i | \(-0.861043\pi\) | ||||
−0.906217 | + | 0.422813i | \(0.861043\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.00000 | 0.520306 | 0.260153 | − | 0.965567i | \(-0.416227\pi\) | ||||
0.260153 | + | 0.965567i | \(0.416227\pi\) | |||||||
\(182\) | −1.55291 | + | 5.79555i | −0.115110 | + | 0.429595i | ||||
\(183\) | 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 | ||||
\(187\) | −20.0764 | − | 5.37945i | −1.46813 | − | 0.393385i | ||||
\(188\) | −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 | \(0.548901\pi\) | |||||||
\(192\) | −0.448288 | − | 1.67303i | −0.0323524 | − | 0.120741i | ||||
\(193\) | 16.7303 | − | 4.48288i | 1.20428 | − | 0.322685i | 0.399762 | − | 0.916619i | \(-0.369093\pi\) |
0.804513 | + | 0.593934i | \(0.202426\pi\) | |||||||
\(194\) | 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 | 0.336966 | − | 0.941517i | \(-0.390599\pi\) |
−0.941517 | + | 0.336966i | \(0.890599\pi\) | |||||||
\(198\) | −7.34847 | − | 7.34847i | −0.522233 | − | 0.522233i | ||||
\(199\) | − | 10.0000i | − | 0.708881i | −0.935079 | − | 0.354441i | \(-0.884671\pi\) | ||
0.935079 | − | 0.354441i | \(-0.115329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.5000 | + | 18.1865i | 0.740613 | + | 1.28278i | ||||
\(202\) | −3.58630 | − | 13.3843i | −0.252331 | − | 0.941713i | ||||
\(203\) | −3.88229 | − | 14.4889i | −0.272483 | − | 1.01692i | ||||
\(204\) | 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 | ||||||||
\(213\) | −1.55291 | − | 5.79555i | −0.106404 | − | 0.397105i | ||||
\(214\) | 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 | ||||
\(218\) | 4.82963 | + | 1.29410i | 0.327104 | + | 0.0876472i | ||||
\(219\) | −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 | ||||
\(223\) | −4.03459 | + | 15.0573i | −0.270176 | + | 1.00831i | 0.688829 | + | 0.724923i | \(0.258125\pi\) |
−0.959005 | + | 0.283387i | \(0.908542\pi\) | |||||||
\(224\) | −1.73205 | −0.115728 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.21166 | − | 23.1822i | 0.412282 | − | 1.53866i | −0.377936 | − | 0.925832i | \(-0.623366\pi\) |
0.790218 | − | 0.612826i | \(-0.209967\pi\) | |||||||
\(228\) | −0.896575 | + | 3.34607i | −0.0593772 | + | 0.221599i | ||||
\(229\) | 4.33013 | + | 2.50000i | 0.286143 | + | 0.165205i | 0.636201 | − | 0.771523i | \(-0.280505\pi\) |
−0.350058 | + | 0.936728i | \(0.613838\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.00000 | + | 5.19615i | −0.592157 | + | 0.341882i | ||||
\(232\) | −8.36516 | − | 2.24144i | −0.549200 | − | 0.147158i | ||||
\(233\) | 4.24264 | − | 4.24264i | 0.277945 | − | 0.277945i | −0.554343 | − | 0.832288i | \(-0.687031\pi\) |
0.832288 | + | 0.554343i | \(0.187031\pi\) | |||||||
\(234\) | −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 | ||||
\(238\) | 10.0382 | − | 2.68973i | 0.650680 | − | 0.174349i | ||||
\(239\) | 10.3923 | − | 18.0000i | 0.672222 | − | 1.16432i | −0.305050 | − | 0.952336i | \(-0.598673\pi\) |
0.977273 | − | 0.211987i | \(-0.0679934\pi\) | |||||||
\(240\) | 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 | ||||
\(243\) | 4.03459 | − | 15.0573i | 0.258819 | − | 0.965926i | ||||
\(244\) | − | 13.0000i | − | 0.832240i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.50000 | − | 12.9904i | 0.478183 | − | 0.828236i | ||||
\(247\) | −1.79315 | − | 6.69213i | −0.114095 | − | 0.425810i | ||||
\(248\) | −2.58819 | − | 9.65926i | −0.164350 | − | 0.613364i | ||||
\(249\) | −5.19615 | −0.329293 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.3923i | 0.655956i | 0.944685 | + | 0.327978i | \(0.106367\pi\) | ||||
−0.944685 | + | 0.327978i | \(0.893633\pi\) | |||||||
\(252\) | 5.01910 | + | 1.34486i | 0.316173 | + | 0.0847184i | ||||
\(253\) | −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 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(258\) | 17.3867 | + | 4.65874i | 1.08245 | + | 0.290041i | ||||
\(259\) | 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 | ||||
\(263\) | −23.1822 | − | 6.21166i | −1.42948 | − | 0.383027i | −0.540641 | − | 0.841253i | \(-0.681818\pi\) |
−0.888836 | + | 0.458226i | \(0.848485\pi\) | |||||||
\(264\) | 6.00000i | 0.369274i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.00000 | + | 1.73205i | 0.183942 | + | 0.106199i | ||||
\(267\) | −2.89778 | + | 0.776457i | −0.177341 | + | 0.0475184i | ||||
\(268\) | 3.13801 | − | 11.7112i | 0.191685 | − | 0.715377i | ||||
\(269\) | −1.73205 | −0.105605 | −0.0528025 | − | 0.998605i | \(-0.516815\pi\) | ||||
−0.0528025 | + | 0.998605i | \(0.516815\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0000 | −0.607457 | −0.303728 | − | 0.952759i | \(-0.598232\pi\) | ||||
−0.303728 | + | 0.952759i | \(0.598232\pi\) | |||||||
\(272\) | 1.55291 | − | 5.79555i | 0.0941593 | − | 0.351407i | ||||
\(273\) | −10.0382 | + | 2.68973i | −0.607539 | + | 0.162790i | ||||
\(274\) | 10.3923 | + | 6.00000i | 0.627822 | + | 0.362473i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.19615i | 0.312772i | ||||||||
\(277\) | −10.0382 | − | 2.68973i | −0.603137 | − | 0.161610i | −0.0556866 | − | 0.998448i | \(-0.517735\pi\) |
−0.547450 | + | 0.836838i | \(0.684401\pi\) | |||||||
\(278\) | −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 | \(0.283799\pi\) | |||||||
\(282\) | −5.01910 | − | 1.34486i | −0.298883 | − | 0.0800854i | ||||
\(283\) | 5.01910 | − | 1.34486i | 0.298354 | − | 0.0799438i | −0.106537 | − | 0.994309i | \(-0.533976\pi\) |
0.404891 | + | 0.914365i | \(0.367309\pi\) | |||||||
\(284\) | −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 | ||||||||
\(292\) | 3.58630 | + | 13.3843i | 0.209872 | + | 0.783255i | ||||
\(293\) | 7.76457 | + | 28.9778i | 0.453611 | + | 1.69290i | 0.692139 | + | 0.721764i | \(0.256668\pi\) |
−0.238528 | + | 0.971136i | \(0.576665\pi\) | |||||||
\(294\) | −3.46410 | + | 6.00000i | −0.202031 | + | 0.349927i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 3.46410i | − | 0.201347i | ||||||
\(297\) | 4.65874 | − | 17.3867i | 0.270328 | − | 1.00888i | ||||
\(298\) | 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 | ||||
\(302\) | −9.65926 | + | 2.58819i | −0.555828 | + | 0.148934i | ||||
\(303\) | 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 | \(-0.797374\pi\) |
0.594440 | + | 0.804140i | \(0.297374\pi\) | |||||||
\(308\) | 5.79555 | + | 1.55291i | 0.330232 | + | 0.0884855i | ||||
\(309\) | −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 | \(0.907963\pi\) | |||||||
\(312\) | −1.55291 | + | 5.79555i | −0.0879165 | + | 0.328109i | ||||
\(313\) | 0.896575 | − | 3.34607i | 0.0506774 | − | 0.189131i | −0.935947 | − | 0.352141i | \(-0.885454\pi\) |
0.986624 | + | 0.163010i | \(0.0521204\pi\) | |||||||
\(314\) | 20.7846 | 1.17294 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.00000 | 0.225018 | ||||||||
\(317\) | −1.55291 | + | 5.79555i | −0.0872204 | + | 0.325511i | −0.995725 | − | 0.0923631i | \(-0.970558\pi\) |
0.908505 | + | 0.417874i | \(0.137225\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.9808 | + | 15.0000i | 1.45464 | + | 0.839839i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.50000 | + | 2.59808i | 0.251166 | + | 0.145010i | ||||
\(322\) | 5.01910 | + | 1.34486i | 0.279703 | + | 0.0749463i | ||||
\(323\) | −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 | ||||
\(327\) | 2.24144 | + | 8.36516i | 0.123952 | + | 0.462595i | ||||
\(328\) | −8.36516 | + | 2.24144i | −0.461889 | + | 0.123763i | ||||
\(329\) | −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 | ||||
\(333\) | −2.68973 | + | 10.0382i | −0.147396 | + | 0.550090i | ||||
\(334\) | 9.00000i | 0.492458i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.50000 | − | 2.59808i | −0.0818317 | − | 0.141737i | ||||
\(337\) | 3.58630 | + | 13.3843i | 0.195358 | + | 0.729087i | 0.992174 | + | 0.124864i | \(0.0398496\pi\) |
−0.796815 | + | 0.604223i | \(0.793484\pi\) | |||||||
\(338\) | 0.258819 | + | 0.965926i | 0.0140779 | + | 0.0525394i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 34.6410i | 1.87592i | ||||||||
\(342\) | −5.79555 | + | 1.55291i | −0.313388 | + | 0.0839720i | ||||
\(343\) | 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 | ||||
\(347\) | 11.5911 | − | 3.10583i | 0.622243 | − | 0.166730i | 0.0660960 | − | 0.997813i | \(-0.478946\pi\) |
0.556147 | + | 0.831084i | \(0.312279\pi\) | |||||||
\(348\) | −3.88229 | − | 14.4889i | −0.208112 | − | 0.776686i | ||||
\(349\) | 0.866025 | − | 0.500000i | 0.0463573 | − | 0.0267644i | −0.476642 | − | 0.879097i | \(-0.658146\pi\) |
0.523000 | + | 0.852333i | \(0.324813\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.00000 | − | 15.5885i | 0.480384 | − | 0.832050i | ||||
\(352\) | 2.44949 | − | 2.44949i | 0.130558 | − | 0.130558i | ||||
\(353\) | −23.1822 | − | 6.21166i | −1.23387 | − | 0.330613i | −0.417782 | − | 0.908547i | \(-0.637192\pi\) |
−0.816083 | + | 0.577934i | \(0.803859\pi\) | |||||||
\(354\) | −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 | ||||
\(358\) | −6.27603 | + | 23.4225i | −0.331698 | + | 1.23792i | ||||
\(359\) | 17.3205 | 0.914141 | 0.457071 | − | 0.889430i | \(-0.348899\pi\) | ||||
0.457071 | + | 0.889430i | \(0.348899\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 1.81173 | − | 6.76148i | 0.0952226 | − | 0.355376i | ||||
\(363\) | 0.448288 | − | 1.67303i | 0.0235290 | − | 0.0878114i | ||||
\(364\) | 5.19615 | + | 3.00000i | 0.272352 | + | 0.157243i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 19.5000 | − | 11.2583i | 1.01928 | − | 0.588482i | ||||
\(367\) | −3.34607 | − | 0.896575i | −0.174663 | − | 0.0468009i | 0.170427 | − | 0.985370i | \(-0.445485\pi\) |
−0.345091 | + | 0.938569i | \(0.612152\pi\) | |||||||
\(368\) | 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 | ||||
\(373\) | 13.3843 | − | 3.58630i | 0.693011 | − | 0.185692i | 0.104913 | − | 0.994481i | \(-0.466544\pi\) |
0.588098 | + | 0.808790i | \(0.299877\pi\) | |||||||
\(374\) | −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 | ||||
\(378\) | 2.32937 | + | 8.69333i | 0.119810 | + | 0.447137i | ||||
\(379\) | − | 8.00000i | − | 0.410932i | −0.978664 | − | 0.205466i | \(-0.934129\pi\) | ||
0.978664 | − | 0.205466i | \(-0.0658711\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.50000 | − | 7.79423i | 0.230542 | − | 0.399310i | ||||
\(382\) | 4.48288 | + | 16.7303i | 0.229364 | + | 0.855998i | ||||
\(383\) | −6.21166 | − | 23.1822i | −0.317401 | − | 1.18456i | −0.921733 | − | 0.387824i | \(-0.873227\pi\) |
0.604333 | − | 0.796732i | \(-0.293440\pi\) | |||||||
\(384\) | −1.73205 | −0.0883883 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 17.3205i | − | 0.881591i | ||||||
\(387\) | 8.06918 | + | 30.1146i | 0.410179 | + | 1.53081i | ||||
\(388\) | −4.89898 | − | 4.89898i | −0.248708 | − | 0.248708i | ||||
\(389\) | −12.9904 | − | 22.5000i | −0.658638 | − | 1.14080i | −0.980968 | − | 0.194168i | \(-0.937799\pi\) |
0.322330 | − | 0.946627i | \(-0.395534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | + | 15.5885i | −0.455150 | + | 0.788342i | ||||
\(392\) | 3.86370 | − | 1.03528i | 0.195146 | − | 0.0522893i | ||||
\(393\) | −11.5911 | − | 3.10583i | −0.584694 | − | 0.156668i | ||||
\(394\) | −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 | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(398\) | −9.65926 | − | 2.58819i | −0.484175 | − | 0.129734i | ||||
\(399\) | 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 | \(0.840350\pi\) | |||||||
\(402\) | 20.2844 | − | 5.43520i | 1.01170 | − | 0.271083i | ||||
\(403\) | −8.96575 | + | 33.4607i | −0.446616 | + | 1.66679i | ||||
\(404\) | −13.8564 | −0.689382 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.0000 | −0.744438 | ||||||||
\(407\) | −3.10583 | + | 11.5911i | −0.153950 | + | 0.574550i | ||||
\(408\) | 10.0382 | − | 2.68973i | 0.496965 | − | 0.133161i | ||||
\(409\) | 1.73205 | + | 1.00000i | 0.0856444 | + | 0.0494468i | 0.542211 | − | 0.840243i | \(-0.317588\pi\) |
−0.456566 | + | 0.889689i | \(0.650921\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.7846i | 1.02523i | ||||||||
\(412\) | 3.34607 | + | 0.896575i | 0.164849 | + | 0.0441711i | ||||
\(413\) | −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 | ||||
\(417\) | −6.69213 | − | 1.79315i | −0.327715 | − | 0.0878110i | ||||
\(418\) | −6.69213 | + | 1.79315i | −0.327323 | + | 0.0877059i | ||||
\(419\) | 5.19615 | − | 9.00000i | 0.253849 | − | 0.439679i | −0.710734 | − | 0.703461i | \(-0.751637\pi\) |
0.964582 | + | 0.263783i | \(0.0849701\pi\) | |||||||
\(420\) | 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 | ||||
\(423\) | −2.32937 | − | 8.69333i | −0.113258 | − | 0.422684i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.00000 | −0.290701 | ||||||||
\(427\) | −5.82774 | − | 21.7494i | −0.282024 | − | 1.05253i | ||||
\(428\) | −0.776457 | − | 2.89778i | −0.0375315 | − | 0.140069i | ||||
\(429\) | 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 | \(0.946637\pi\) | |||||||
\(432\) | 5.01910 | + | 1.34486i | 0.241481 | + | 0.0647048i | ||||
\(433\) | 7.34847 | + | 7.34847i | 0.353145 | + | 0.353145i | 0.861278 | − | 0.508133i | \(-0.169664\pi\) |
−0.508133 | + | 0.861278i | \(0.669664\pi\) | |||||||
\(434\) | −8.66025 | − | 15.0000i | −0.415705 | − | 0.720023i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.50000 | − | 4.33013i | 0.119728 | − | 0.207375i | ||||
\(437\) | −5.79555 | + | 1.55291i | −0.277239 | + | 0.0742860i | ||||
\(438\) | −16.9706 | + | 16.9706i | −0.810885 | + | 0.810885i | ||||
\(439\) | 17.3205 | − | 10.0000i | 0.826663 | − | 0.477274i | −0.0260459 | − | 0.999661i | \(-0.508292\pi\) |
0.852709 | + | 0.522387i | \(0.174958\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.0000 | −0.571429 | ||||||||
\(442\) | −14.6969 | + | 14.6969i | −0.699062 | + | 0.699062i | ||||
\(443\) | 8.69333 | + | 2.32937i | 0.413033 | + | 0.110672i | 0.459351 | − | 0.888255i | \(-0.348082\pi\) |
−0.0463181 | + | 0.998927i | \(0.514749\pi\) | |||||||
\(444\) | 5.19615 | − | 3.00000i | 0.246598 | − | 0.142374i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.5000 | + | 7.79423i | 0.639244 | + | 0.369067i | ||||
\(447\) | −2.32937 | + | 8.69333i | −0.110175 | + | 0.411181i | ||||
\(448\) | −0.448288 | + | 1.67303i | −0.0211796 | + | 0.0790434i | ||||
\(449\) | 13.8564 | 0.653924 | 0.326962 | − | 0.945037i | \(-0.393975\pi\) | ||||
0.326962 | + | 0.945037i | \(0.393975\pi\) | |||||||
\(450\) | 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 | ||||
\(457\) | 30.1146 | + | 8.06918i | 1.40870 | + | 0.377460i | 0.881461 | − | 0.472256i | \(-0.156560\pi\) |
0.527240 | + | 0.849717i | \(0.323227\pi\) | |||||||
\(458\) | 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 | \(0.242221\pi\) | |||||||
\(462\) | 2.68973 | + | 10.0382i | 0.125137 | + | 0.467019i | ||||
\(463\) | −16.7303 | + | 4.48288i | −0.777524 | + | 0.208337i | −0.625693 | − | 0.780069i | \(-0.715184\pi\) |
−0.151831 | + | 0.988406i | \(0.548517\pi\) | |||||||
\(464\) | −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 | 0.980264 | + | 0.197692i | \(0.0633445\pi\) |
0.197692 | + | 0.980264i | \(0.436655\pi\) | |||||||
\(468\) | −10.0382 | + | 2.68973i | −0.464016 | + | 0.124333i | ||||
\(469\) | − | 21.0000i | − | 0.969690i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.0000 | + | 31.1769i | 0.829396 | + | 1.43656i | ||||
\(472\) | 1.79315 | + | 6.69213i | 0.0825365 | + | 0.308030i | ||||
\(473\) | 9.31749 | + | 34.7733i | 0.428418 | + | 1.59888i | ||||
\(474\) | 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 | \(0.0515575\pi\) |
−0.353796 | + | 0.935323i | \(0.615109\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.00000 | + | 10.3923i | −0.273576 | + | 0.473848i | ||||
\(482\) | −16.4207 | + | 4.39992i | −0.747944 | + | 0.200411i | ||||
\(483\) | 2.32937 | + | 8.69333i | 0.105990 | + | 0.395560i | ||||
\(484\) | −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 | \(-0.935146\pi\) |
0.202337 | + | 0.979316i | \(0.435146\pi\) | |||||||
\(488\) | −12.5570 | − | 3.36465i | −0.568430 | − | 0.152310i | ||||
\(489\) | −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 | ||||
\(493\) | 13.4486 | − | 50.1910i | 0.605696 | − | 2.26049i | ||||
\(494\) | −6.92820 | −0.311715 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.0000 | −0.449013 | ||||||||
\(497\) | −1.55291 | + | 5.79555i | −0.0696577 | + | 0.259966i | ||||
\(498\) | −1.34486 | + | 5.01910i | −0.0602648 | + | 0.224911i | ||||
\(499\) | −38.1051 | − | 22.0000i | −1.70582 | − | 0.984855i | −0.939599 | − | 0.342277i | \(-0.888802\pi\) |
−0.766220 | − | 0.642578i | \(-0.777865\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.5000 | + | 7.79423i | −0.603136 | + | 0.348220i | ||||
\(502\) | 10.0382 | + | 2.68973i | 0.448027 | + | 0.120048i | ||||
\(503\) | −6.36396 | + | 6.36396i | −0.283755 | + | 0.283755i | −0.834605 | − | 0.550850i | \(-0.814304\pi\) |
0.550850 | + | 0.834605i | \(0.314304\pi\) | |||||||
\(504\) | 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 | ||||
\(508\) | −5.01910 | + | 1.34486i | −0.222686 | + | 0.0596687i | ||||
\(509\) | −2.59808 | + | 4.50000i | −0.115158 | + | 0.199459i | −0.917843 | − | 0.396944i | \(-0.870071\pi\) |
0.802685 | + | 0.596403i | \(0.203404\pi\) | |||||||
\(510\) | 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 | ||||
\(517\) | −2.68973 | − | 10.0382i | −0.118294 | − | 0.441479i | ||||
\(518\) | −1.55291 | − | 5.79555i | −0.0682311 | − | 0.254642i | ||||
\(519\) | 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 | \(-0.164601\pi\) |
−0.494371 | + | 0.869251i | \(0.664601\pi\) | |||||||
\(524\) | 3.46410 | + | 6.00000i | 0.151330 | + | 0.262111i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.0000 | + | 20.7846i | −0.523225 | + | 0.906252i | ||||
\(527\) | 57.9555 | − | 15.5291i | 2.52458 | − | 0.676460i | ||||
\(528\) | 5.79555 | + | 1.55291i | 0.252219 | + | 0.0675819i | ||||
\(529\) | 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 | ||||
\(533\) | 28.9778 | + | 7.76457i | 1.25517 | + | 0.336321i | ||||
\(534\) | 3.00000i | 0.129823i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.5000 | − | 6.06218i | −0.453531 | − | 0.261846i | ||||
\(537\) | −40.5689 | + | 10.8704i | −1.75068 | + | 0.469092i | ||||
\(538\) | −0.448288 | + | 1.67303i | −0.0193271 | + | 0.0721296i | ||||
\(539\) | −13.8564 | −0.596838 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.0000 | −1.84871 | −0.924357 | − | 0.381528i | \(-0.875398\pi\) | ||||
−0.924357 | + | 0.381528i | \(0.875398\pi\) | |||||||
\(542\) | −2.58819 | + | 9.65926i | −0.111172 | + | 0.414901i | ||||
\(543\) | 11.7112 | − | 3.13801i | 0.502577 | − | 0.134665i | ||||
\(544\) | −5.19615 | − | 3.00000i | −0.222783 | − | 0.128624i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.3923i | 0.444750i | ||||||||
\(547\) | 1.67303 | + | 0.448288i | 0.0715337 | + | 0.0191674i | 0.294408 | − | 0.955680i | \(-0.404877\pi\) |
−0.222875 | + | 0.974847i | \(0.571544\pi\) | |||||||
\(548\) | 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 | ||||
\(552\) | 5.01910 | + | 1.34486i | 0.213627 | + | 0.0572412i | ||||
\(553\) | 6.69213 | − | 1.79315i | 0.284578 | − | 0.0762525i | ||||
\(554\) | −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 | −0.996635 | − | 0.0819634i | \(-0.973881\pi\) |
−0.0819634 | − | 0.996635i | \(-0.526119\pi\) | |||||||
\(558\) | 28.9778 | + | 7.76457i | 1.22673 | + | 0.328701i | ||||
\(559\) | 36.0000i | 1.52264i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −36.0000 | −1.51992 | ||||||||
\(562\) | −1.34486 | − | 5.01910i | −0.0567296 | − | 0.211718i | ||||
\(563\) | −5.43520 | − | 20.2844i | −0.229066 | − | 0.854887i | −0.980734 | − | 0.195346i | \(-0.937417\pi\) |
0.751668 | − | 0.659542i | \(-0.229250\pi\) | |||||||
\(564\) | −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 | 0.929456 | − | 0.368933i | \(-0.120277\pi\) |
−0.784233 | + | 0.620466i | \(0.786943\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | − | 3.46410i | 0.0836974 | − | 0.144968i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) |
0.904835 | + | 0.425762i | \(0.139994\pi\) | |||||||
\(572\) | −11.5911 | + | 3.10583i | −0.484649 | + | 0.129861i | ||||
\(573\) | −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 | 0.0199346 | − | 0.999801i | \(-0.493654\pi\) |
0.999801 | − | 0.0199346i | \(-0.00634581\pi\) | |||||||
\(578\) | 18.3526 | + | 4.91756i | 0.763367 | + | 0.204544i | ||||
\(579\) | 25.9808 | − | 15.0000i | 1.07972 | − | 0.623379i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.50000 | + | 2.59808i | 0.186691 | + | 0.107786i | ||||
\(582\) | 3.10583 | − | 11.5911i | 0.128741 | − | 0.480467i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 13.8564 | 0.573382 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.0000 | 1.23929 | ||||||||
\(587\) | −0.776457 | + | 2.89778i | −0.0320478 | + | 0.119604i | −0.980097 | − | 0.198520i | \(-0.936386\pi\) |
0.948049 | + | 0.318125i | \(0.103053\pi\) | |||||||
\(588\) | 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 | ||||
\(592\) | −3.34607 | − | 0.896575i | −0.137522 | − | 0.0368490i | ||||
\(593\) | −12.7279 | + | 12.7279i | −0.522673 | + | 0.522673i | −0.918378 | − | 0.395705i | \(-0.870500\pi\) |
0.395705 | + | 0.918378i | \(0.370500\pi\) | |||||||
\(594\) | −15.5885 | − | 9.00000i | −0.639602 | − | 0.369274i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.50000 | − | 2.59808i | 0.184327 | − | 0.106421i | ||||
\(597\) | −4.48288 | − | 16.7303i | −0.183472 | − | 0.684727i | ||||
\(598\) | −10.0382 | + | 2.68973i | −0.410492 | + | 0.109991i | ||||
\(599\) | −13.8564 | + | 24.0000i | −0.566157 | + | 0.980613i | 0.430784 | + | 0.902455i | \(0.358237\pi\) |
−0.996941 | + | 0.0781581i | \(0.975096\pi\) | |||||||
\(600\) | 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 | ||||
\(607\) | −10.3106 | − | 38.4797i | −0.418495 | − | 1.56184i | −0.777730 | − | 0.628598i | \(-0.783629\pi\) |
0.359235 | − | 0.933247i | \(-0.383038\pi\) | |||||||
\(608\) | −0.517638 | − | 1.93185i | −0.0209930 | − | 0.0783469i | ||||
\(609\) | −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 | \(-0.363745\pi\) |
−0.909774 | + | 0.415104i | \(0.863745\pi\) | |||||||
\(614\) | 2.59808 | + | 4.50000i | 0.104850 | + | 0.181605i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.00000 | − | 5.19615i | 0.120873 | − | 0.209359i | ||||
\(617\) | −34.7733 | + | 9.31749i | −1.39992 | + | 0.375108i | −0.878317 | − | 0.478079i | \(-0.841333\pi\) |
−0.521605 | + | 0.853187i | \(0.674666\pi\) | |||||||
\(618\) | 1.55291 | + | 5.79555i | 0.0624674 | + | 0.233131i | ||||
\(619\) | −19.0526 | + | 11.0000i | −0.765787 | + | 0.442127i | −0.831370 | − | 0.555720i | \(-0.812443\pi\) |
0.0655827 | + | 0.997847i | \(0.479109\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.5000 | − | 7.79423i | −0.541736 | − | 0.312772i | ||||
\(622\) | −17.1464 | + | 17.1464i | −0.687509 | + | 0.687509i | ||||
\(623\) | 2.89778 | + | 0.776457i | 0.116097 | + | 0.0311081i | ||||
\(624\) | 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 | ||||
\(628\) | 5.37945 | − | 20.0764i | 0.214664 | − | 0.801135i | ||||
\(629\) | 20.7846 | 0.828737 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 1.03528 | − | 3.86370i | 0.0411811 | − | 0.153690i | ||||
\(633\) | 9.86233 | − | 36.8067i | 0.391992 | − | 1.46294i | ||||
\(634\) | 5.19615 | + | 3.00000i | 0.206366 | + | 0.119145i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.3843 | − | 3.58630i | −0.530304 | − | 0.142094i | ||||
\(638\) | 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 | ||||
\(643\) | −5.01910 | + | 1.34486i | −0.197934 | + | 0.0530362i | −0.356424 | − | 0.934324i | \(-0.616004\pi\) |
0.158490 | + | 0.987361i | \(0.449337\pi\) | |||||||
\(644\) | 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 | 0.935941 | − | 0.352157i | \(-0.114552\pi\) |
−0.352157 | + | 0.935941i | \(0.614552\pi\) | |||||||
\(648\) | 2.32937 | + | 8.69333i | 0.0915064 | + | 0.341506i | ||||
\(649\) | − | 24.0000i | − | 0.942082i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.0000 | − | 25.9808i | 0.587896 | − | 1.01827i | ||||
\(652\) | 4.48288 | + | 16.7303i | 0.175563 | + | 0.655210i | ||||
\(653\) | −4.65874 | − | 17.3867i | −0.182311 | − | 0.680393i | −0.995190 | − | 0.0979610i | \(-0.968768\pi\) |
0.812880 | − | 0.582432i | \(-0.197899\pi\) | |||||||
\(654\) | 8.66025 | 0.338643 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.66025i | 0.338126i | ||||||||
\(657\) | −40.1528 | − | 10.7589i | −1.56651 | − | 0.419745i | ||||
\(658\) | 3.67423 | + | 3.67423i | 0.143237 | + | 0.143237i | ||||
\(659\) | 10.3923 | + | 18.0000i | 0.404827 | + | 0.701180i | 0.994301 | − | 0.106606i | \(-0.0339985\pi\) |
−0.589475 | + | 0.807787i | \(0.700665\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.0000 | + | 19.0526i | −0.427850 | + | 0.741059i | −0.996682 | − | 0.0813955i | \(-0.974062\pi\) |
0.568831 | + | 0.822454i | \(0.307396\pi\) | |||||||
\(662\) | −7.72741 | + | 2.07055i | −0.300334 | + | 0.0804743i | ||||
\(663\) | −34.7733 | − | 9.31749i | −1.35048 | − | 0.361861i | ||||
\(664\) | 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 | ||||
\(668\) | 8.69333 | + | 2.32937i | 0.336355 | + | 0.0901261i | ||||
\(669\) | 27.0000i | 1.04388i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.0000 | + | 22.5167i | 1.50558 | + | 0.869246i | ||||
\(672\) | −2.89778 | + | 0.776457i | −0.111784 | + | 0.0299525i | ||||
\(673\) | 9.86233 | − | 36.8067i | 0.380165 | − | 1.41879i | −0.465485 | − | 0.885056i | \(-0.654120\pi\) |
0.845649 | − | 0.533739i | \(-0.179213\pi\) | |||||||
\(674\) | 13.8564 | 0.533729 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 1.55291 | − | 5.79555i | 0.0596833 | − | 0.222741i | −0.929642 | − | 0.368464i | \(-0.879884\pi\) |
0.989326 | + | 0.145722i | \(0.0465506\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.3923 | − | 6.00000i | −0.398820 | − | 0.230259i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 41.5692i | − | 1.59294i | ||||||
\(682\) | 33.4607 | + | 8.96575i | 1.28127 | + | 0.343316i | ||||
\(683\) | 8.48528 | − | 8.48528i | 0.324680 | − | 0.324680i | −0.525879 | − | 0.850559i | \(-0.676264\pi\) |
0.850559 | + | 0.525879i | \(0.176264\pi\) | |||||||
\(684\) | 6.00000i | 0.229416i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.5000 | − | 9.52628i | 0.629973 | − | 0.363715i | ||||
\(687\) | 8.36516 | + | 2.24144i | 0.319151 | + | 0.0855162i | ||||
\(688\) | −10.0382 | + | 2.68973i | −0.382703 | + | 0.102545i | ||||
\(689\) | 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 | ||||||||
\(697\) | −13.4486 | − | 50.1910i | −0.509403 | − | 1.90112i | ||||
\(698\) | −0.258819 | − | 0.965926i | −0.00979645 | − | 0.0365608i | ||||
\(699\) | 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 | ||||
\(707\) | −23.1822 | + | 6.21166i | −0.871857 | + | 0.233613i | ||||
\(708\) | −8.48528 | + | 8.48528i | −0.318896 | + | 0.318896i | ||||
\(709\) | −35.5070 | + | 20.5000i | −1.33349 | + | 0.769894i | −0.985834 | − | 0.167727i | \(-0.946357\pi\) |
−0.347661 | + | 0.937620i | \(0.613024\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.00000 | + | 10.3923i | −0.225018 | + | 0.389742i | ||||
\(712\) | 1.22474 | − | 1.22474i | 0.0458993 | − | 0.0458993i | ||||
\(713\) | 28.9778 | + | 7.76457i | 1.08523 | + | 0.290785i | ||||
\(714\) | 15.5885 | − | 9.00000i | 0.583383 | − | 0.336817i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 21.0000 | + | 12.1244i | 0.784807 | + | 0.453108i | ||||
\(717\) | 9.31749 | − | 34.7733i | 0.347968 | − | 1.29863i | ||||
\(718\) | 4.48288 | − | 16.7303i | 0.167299 | − | 0.624370i | ||||
\(719\) | −6.92820 | −0.258378 | −0.129189 | − | 0.991620i | \(-0.541237\pi\) | ||||
−0.129189 | + | 0.991620i | \(0.541237\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | 0.223452 | ||||||||
\(722\) | 3.88229 | − | 14.4889i | 0.144484 | − | 0.539221i | ||||
\(723\) | −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 | ||||
\(727\) | −5.01910 | − | 1.34486i | −0.186148 | − | 0.0498782i | 0.164541 | − | 0.986370i | \(-0.447386\pi\) |
−0.350689 | + | 0.936492i | \(0.614052\pi\) | |||||||
\(728\) | 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 | ||||
\(732\) | −5.82774 | − | 21.7494i | −0.215399 | − | 0.803882i | ||||
\(733\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(734\) | −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 | ||||
\(738\) | 6.72432 | − | 25.0955i | 0.247525 | − | 0.923778i | ||||
\(739\) | 4.00000i | 0.147142i | 0.997290 | + | 0.0735712i | \(0.0234396\pi\) | ||||
−0.997290 | + | 0.0735712i | \(0.976560\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.00000 | − | 10.3923i | −0.220416 | − | 0.381771i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.98811 | + | 26.0800i | 0.256369 | + | 0.956782i | 0.967324 | + | 0.253544i | \(0.0815964\pi\) |
−0.710955 | + | 0.703238i | \(0.751737\pi\) | |||||||
\(744\) | −8.66025 | − | 15.0000i | −0.317500 | − | 0.549927i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 13.8564i | − | 0.507319i | ||||||
\(747\) | −8.69333 | + | 2.32937i | −0.318072 | + | 0.0852272i | ||||
\(748\) | 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 | \(0.155049\pi\) | |||||||
\(752\) | 2.89778 | − | 0.776457i | 0.105671 | − | 0.0283145i | ||||
\(753\) | 4.65874 | + | 17.3867i | 0.169774 | + | 0.633605i | ||||
\(754\) | 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 | −0.172327 | + | 0.985040i | \(0.555129\pi\) |
−0.985040 | + | 0.172327i | \(0.944871\pi\) | |||||||
\(758\) | −7.72741 | − | 2.07055i | −0.280672 | − | 0.0752058i | ||||
\(759\) | −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 | ||||
\(763\) | 2.24144 | − | 8.36516i | 0.0811455 | − | 0.302839i | ||||
\(764\) | 17.3205 | 0.626634 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.0000 | −0.867155 | ||||||||
\(767\) | 6.21166 | − | 23.1822i | 0.224290 | − | 0.837061i | ||||
\(768\) | −0.448288 | + | 1.67303i | −0.0161762 | + | 0.0603704i | ||||
\(769\) | −19.9186 | − | 11.5000i | −0.718283 | − | 0.414701i | 0.0958377 | − | 0.995397i | \(-0.469447\pi\) |
−0.814120 | + | 0.580696i | \(0.802780\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.7303 | − | 4.48288i | −0.602138 | − | 0.161342i | ||||
\(773\) | 25.4558 | − | 25.4558i | 0.915583 | − | 0.915583i | −0.0811212 | − | 0.996704i | \(-0.525850\pi\) |
0.996704 | + | 0.0811212i | \(0.0258501\pi\) | |||||||
\(774\) | 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 | ||||
\(778\) | −25.0955 | + | 6.72432i | −0.899717 | + | 0.241078i | ||||
\(779\) | 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 | ||||
\(783\) | 43.4667 | + | 11.6469i | 1.55337 | + | 0.416225i | ||||
\(784\) | − | 4.00000i | − | 0.142857i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.00000 | + | 10.3923i | −0.214013 | + | 0.370681i | ||||
\(787\) | −0.896575 | − | 3.34607i | −0.0319595 | − | 0.119274i | 0.948103 | − | 0.317962i | \(-0.102999\pi\) |
−0.980063 | + | 0.198688i | \(0.936332\pi\) | |||||||
\(788\) | 3.10583 | + | 11.5911i | 0.110641 | + | 0.412916i | ||||
\(789\) | −41.5692 | −1.47990 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.68973 | + | 10.0382i | 0.0955753 | + | 0.356692i | ||||
\(793\) | 31.8434 | + | 31.8434i | 1.13079 | + | 1.13079i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.00000 | + | 8.66025i | −0.177220 | + | 0.306955i | ||||
\(797\) | 40.5689 | − | 10.8704i | 1.43702 | − | 0.385049i | 0.545533 | − | 0.838089i | \(-0.316327\pi\) |
0.891490 | + | 0.453040i | \(0.149660\pi\) | |||||||
\(798\) | 5.79555 | + | 1.55291i | 0.205160 | + | 0.0549726i | ||||
\(799\) | −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 | ||||
\(803\) | −46.3644 | − | 12.4233i | −1.63617 | − | 0.438409i | ||||
\(804\) | − | 21.0000i | − | 0.740613i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 30.0000 | + | 17.3205i | 1.05670 | + | 0.610089i | ||||
\(807\) | −2.89778 | + | 0.776457i | −0.102007 | + | 0.0273326i | ||||
\(808\) | −3.58630 | + | 13.3843i | −0.126166 | + | 0.470857i | ||||
\(809\) | 6.92820 | 0.243583 | 0.121791 | − | 0.992556i | \(-0.461136\pi\) | ||||
0.121791 | + | 0.992556i | \(0.461136\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.00000 | 0.140459 | 0.0702295 | − | 0.997531i | \(-0.477627\pi\) | ||||
0.0702295 | + | 0.997531i | \(0.477627\pi\) | |||||||
\(812\) | −3.88229 | + | 14.4889i | −0.136242 | + | 0.508460i | ||||
\(813\) | −16.7303 | + | 4.48288i | −0.586758 | + | 0.157221i | ||||
\(814\) | 10.3923 | + | 6.00000i | 0.364250 | + | 0.210300i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 10.3923i | − | 0.363803i | ||||||
\(817\) | 20.0764 | + | 5.37945i | 0.702384 | + | 0.188203i | ||||
\(818\) | 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 | \(0.441215\pi\) | |||||||
\(822\) | 20.0764 | + | 5.37945i | 0.700245 | + | 0.187630i | ||||
\(823\) | −28.4416 | + | 7.62089i | −0.991410 | + | 0.265648i | −0.717843 | − | 0.696205i | \(-0.754870\pi\) |
−0.273567 | + | 0.961853i | \(0.588204\pi\) | |||||||
\(824\) | 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 | −0.993609 | − | 0.112874i | \(-0.963994\pi\) |
−0.112874 | − | 0.993609i | \(-0.536006\pi\) | |||||||
\(828\) | 2.32937 | + | 8.69333i | 0.0809513 | + | 0.302114i | ||||
\(829\) | − | 29.0000i | − | 1.00721i | −0.863934 | − | 0.503606i | \(-0.832006\pi\) | ||
0.863934 | − | 0.503606i | \(-0.167994\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.0000 | −0.624413 | ||||||||
\(832\) | −0.896575 | − | 3.34607i | −0.0310832 | − | 0.116004i | ||||
\(833\) | 6.21166 | + | 23.1822i | 0.215221 | + | 0.803216i | ||||
\(834\) | −3.46410 | + | 6.00000i | −0.119952 | + | 0.207763i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.92820i | 0.239617i | ||||||||
\(837\) | 13.4486 | + | 50.1910i | 0.464853 | + | 1.73485i | ||||
\(838\) | −7.34847 | − | 7.34847i | −0.253849 | − | 0.253849i | ||||
\(839\) | 19.0526 | + | 33.0000i | 0.657767 | + | 1.13929i | 0.981192 | + | 0.193033i | \(0.0618323\pi\) |
−0.323425 | + | 0.946254i | \(0.604834\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.0000 | + | 39.8372i | −0.793103 | + | 1.37370i | ||||
\(842\) | −9.65926 | + | 2.58819i | −0.332880 | + | 0.0891949i | ||||
\(843\) | 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 | ||||
\(852\) | −1.55291 | + | 5.79555i | −0.0532020 | + | 0.198552i | ||||
\(853\) | 4.48288 | − | 16.7303i | 0.153491 | − | 0.572835i | −0.845739 | − | 0.533597i | \(-0.820840\pi\) |
0.999230 | − | 0.0392388i | \(-0.0124933\pi\) | |||||||
\(854\) | −22.5167 | −0.770504 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.00000 | −0.102538 | ||||||||
\(857\) | −10.8704 | + | 40.5689i | −0.371326 | + | 1.38581i | 0.487314 | + | 0.873227i | \(0.337977\pi\) |
−0.858640 | + | 0.512580i | \(0.828690\pi\) | |||||||
\(858\) | −14.6969 | − | 14.6969i | −0.501745 | − | 0.501745i | ||||
\(859\) | 19.0526 | + | 11.0000i | 0.650065 | + | 0.375315i | 0.788481 | − | 0.615059i | \(-0.210868\pi\) |
−0.138416 | + | 0.990374i | \(0.544201\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.5000 | − | 12.9904i | −0.766798 | − | 0.442711i | ||||
\(862\) | 6.69213 | + | 1.79315i | 0.227935 | + | 0.0610750i | ||||
\(863\) | −10.6066 | + | 10.6066i | −0.361053 | + | 0.361053i | −0.864201 | − | 0.503148i | \(-0.832175\pi\) |
0.503148 | + | 0.864201i | \(0.332175\pi\) | |||||||
\(864\) | 2.59808 | − | 4.50000i | 0.0883883 | − | 0.153093i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.00000 | − | 5.19615i | 0.305832 | − | 0.176572i | ||||
\(867\) | 8.51747 | + | 31.7876i | 0.289268 | + | 1.07956i | ||||
\(868\) | −16.7303 | + | 4.48288i | −0.567864 | + | 0.152159i | ||||
\(869\) | −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 | ||||
\(873\) | 20.0764 | − | 5.37945i | 0.679483 | − | 0.182067i | ||||
\(874\) | 6.00000i | 0.202953i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.0000 | + | 20.7846i | 0.405442 | + | 0.702247i | ||||
\(877\) | 4.48288 | + | 16.7303i | 0.151376 | + | 0.564943i | 0.999388 | + | 0.0349667i | \(0.0111325\pi\) |
−0.848012 | + | 0.529976i | \(0.822201\pi\) | |||||||
\(878\) | −5.17638 | − | 19.3185i | −0.174694 | − | 0.651968i | ||||
\(879\) | 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 | \(-0.00928869\pi\) | |||||||
\(882\) | −3.10583 | + | 11.5911i | −0.104579 | + | 0.390293i | ||||
\(883\) | 30.6186 | + | 30.6186i | 1.03040 | + | 1.03040i | 0.999523 | + | 0.0308754i | \(0.00982951\pi\) |
0.0308754 | + | 0.999523i | \(0.490170\pi\) | |||||||
\(884\) | 10.3923 | + | 18.0000i | 0.349531 | + | 0.605406i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.50000 | − | 7.79423i | 0.151180 | − | 0.261852i | ||||
\(887\) | 23.1822 | − | 6.21166i | 0.778383 | − | 0.208567i | 0.152311 | − | 0.988333i | \(-0.451328\pi\) |
0.626072 | + | 0.779766i | \(0.284662\pi\) | |||||||
\(888\) | −1.55291 | − | 5.79555i | −0.0521124 | − | 0.194486i | ||||
\(889\) | −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 | ||||
\(893\) | −5.79555 | − | 1.55291i | −0.193941 | − | 0.0519663i | ||||
\(894\) | 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 | ||||
\(898\) | 3.58630 | − | 13.3843i | 0.119676 | − | 0.446639i | ||||
\(899\) | −86.6025 | −2.88836 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 7.76457 | − | 28.9778i | 0.258532 | − | 0.964854i | ||||
\(903\) | 8.06918 | − | 30.1146i | 0.268525 | − | 1.00215i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −15.0000 | + | 8.66025i | −0.498342 | + | 0.287718i | ||||
\(907\) | 8.36516 | + | 2.24144i | 0.277761 | + | 0.0744257i | 0.395010 | − | 0.918677i | \(-0.370741\pi\) |
−0.117250 | + | 0.993102i | \(0.537408\pi\) | |||||||
\(908\) | −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 | ||||
\(913\) | −10.0382 | + | 2.68973i | −0.332216 | + | 0.0890170i | ||||
\(914\) | 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 | ||||
\(918\) | −8.06918 | + | 30.1146i | −0.266323 | + | 0.993929i | ||||
\(919\) | 40.0000i | 1.31948i | 0.751495 | + | 0.659739i | \(0.229333\pi\) | ||||
−0.751495 | + | 0.659739i | \(0.770667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.50000 | + | 7.79423i | −0.148280 | + | 0.256829i | ||||
\(922\) | −3.13801 | − | 11.7112i | −0.103345 | − | 0.385689i | ||||
\(923\) | −3.10583 | − | 11.5911i | −0.102230 | − | 0.381526i | ||||
\(924\) | 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 | 0.803587 | − | 0.595187i | \(-0.202922\pi\) |
−0.917241 | + | 0.398333i | \(0.869589\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.00000 | + | 6.92820i | −0.131095 | + | 0.227063i | ||||
\(932\) | −5.79555 | + | 1.55291i | −0.189840 | + | 0.0508674i | ||||
\(933\) | −40.5689 | − | 10.8704i | −1.32817 | − | 0.355881i | ||||
\(934\) | 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 | \(-0.822674\pi\) |
0.528714 | + | 0.848800i | \(0.322674\pi\) | |||||||
\(938\) | −20.2844 | − | 5.43520i | −0.662311 | − | 0.177466i | ||||
\(939\) | − | 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 | \(0.693658\pi\) | |||||||
\(942\) | 34.7733 | − | 9.31749i | 1.13298 | − | 0.303580i | ||||
\(943\) | 6.72432 | − | 25.0955i | 0.218974 | − | 0.817222i | ||||
\(944\) | 6.92820 | 0.225494 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 36.0000 | 1.17046 | ||||||||
\(947\) | −6.98811 | + | 26.0800i | −0.227083 | + | 0.847486i | 0.754476 | + | 0.656328i | \(0.227891\pi\) |
−0.981559 | + | 0.191158i | \(0.938776\pi\) | |||||||
\(948\) | 6.69213 | − | 1.79315i | 0.217350 | − | 0.0582388i | ||||
\(949\) | −41.5692 | − | 24.0000i | −1.34939 | − | 0.779073i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.3923i | 0.336994i | ||||||||
\(952\) | −10.0382 | − | 2.68973i | −0.325340 | − | 0.0871745i | ||||
\(953\) | −29.6985 | + | 29.6985i | −0.962028 | + | 0.962028i | −0.999305 | − | 0.0372767i | \(-0.988132\pi\) |
0.0372767 | + | 0.999305i | \(0.488132\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18.0000 | + | 10.3923i | −0.582162 | + | 0.336111i | ||||
\(957\) | 50.1910 | + | 13.4486i | 1.62244 | + | 0.434733i | ||||
\(958\) | 26.7685 | − | 7.17260i | 0.864852 | − | 0.231736i | ||||
\(959\) | 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 | ||||
\(963\) | 8.69333 | + | 2.32937i | 0.280139 | + | 0.0750629i | ||||
\(964\) | 17.0000i | 0.547533i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.00000 | 0.289570 | ||||||||
\(967\) | 13.8969 | + | 51.8640i | 0.446895 | + | 1.66783i | 0.710885 | + | 0.703309i | \(0.248295\pi\) |
−0.263990 | + | 0.964525i | \(0.585039\pi\) | |||||||
\(968\) | 0.258819 | + | 0.965926i | 0.00831876 | + | 0.0310460i | ||||
\(969\) | −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 | ||||
\(977\) | −40.5689 | + | 10.8704i | −1.29791 | + | 0.347775i | −0.840661 | − | 0.541562i | \(-0.817833\pi\) |
−0.457253 | + | 0.889337i | \(0.651167\pi\) | |||||||
\(978\) | −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 | ||||
\(983\) | −8.69333 | − | 2.32937i | −0.277274 | − | 0.0742954i | 0.117502 | − | 0.993073i | \(-0.462511\pi\) |
−0.394776 | + | 0.918777i | \(0.629178\pi\) | |||||||
\(984\) | −12.9904 | + | 7.50000i | −0.414118 | + | 0.239091i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −45.0000 | − | 25.9808i | −1.43309 | − | 0.827396i | ||||
\(987\) | −2.32937 | + | 8.69333i | −0.0741447 | + | 0.276712i | ||||
\(988\) | −1.79315 | + | 6.69213i | −0.0570477 | + | 0.212905i | ||||
\(989\) | 31.1769 | 0.991368 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | −2.58819 | + | 9.65926i | −0.0821751 | + | 0.306682i | ||||
\(993\) | −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 | ||||
\(997\) | 40.1528 | + | 10.7589i | 1.27165 | + | 0.340738i | 0.830663 | − | 0.556775i | \(-0.187961\pi\) |
0.440988 | + | 0.897513i | \(0.354628\pi\) | |||||||
\(998\) | −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.293.2 | yes | 8 | |
3.2 | odd | 2 | 1350.2.q.b.1043.1 | 8 | |||
5.2 | odd | 4 | inner | 450.2.p.d.257.2 | yes | 8 | |
5.3 | odd | 4 | inner | 450.2.p.d.257.1 | ✓ | 8 | |
5.4 | even | 2 | inner | 450.2.p.d.293.1 | yes | 8 | |
9.2 | odd | 6 | inner | 450.2.p.d.443.2 | yes | 8 | |
9.7 | even | 3 | 1350.2.q.b.143.1 | 8 | |||
15.2 | even | 4 | 1350.2.q.b.557.1 | 8 | |||
15.8 | even | 4 | 1350.2.q.b.557.2 | 8 | |||
15.14 | odd | 2 | 1350.2.q.b.1043.2 | 8 | |||
45.2 | even | 12 | inner | 450.2.p.d.407.2 | yes | 8 | |
45.7 | odd | 12 | 1350.2.q.b.1007.1 | 8 | |||
45.29 | odd | 6 | inner | 450.2.p.d.443.1 | yes | 8 | |
45.34 | even | 6 | 1350.2.q.b.143.2 | 8 | |||
45.38 | even | 12 | inner | 450.2.p.d.407.1 | yes | 8 | |
45.43 | odd | 12 | 1350.2.q.b.1007.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.p.d.257.1 | ✓ | 8 | 5.3 | odd | 4 | inner | |
450.2.p.d.257.2 | yes | 8 | 5.2 | odd | 4 | inner | |
450.2.p.d.293.1 | yes | 8 | 5.4 | even | 2 | inner | |
450.2.p.d.293.2 | yes | 8 | 1.1 | even | 1 | trivial | |
450.2.p.d.407.1 | yes | 8 | 45.38 | even | 12 | inner | |
450.2.p.d.407.2 | yes | 8 | 45.2 | even | 12 | inner | |
450.2.p.d.443.1 | yes | 8 | 45.29 | odd | 6 | inner | |
450.2.p.d.443.2 | yes | 8 | 9.2 | odd | 6 | inner | |
1350.2.q.b.143.1 | 8 | 9.7 | even | 3 | |||
1350.2.q.b.143.2 | 8 | 45.34 | even | 6 | |||
1350.2.q.b.557.1 | 8 | 15.2 | even | 4 | |||
1350.2.q.b.557.2 | 8 | 15.8 | even | 4 | |||
1350.2.q.b.1007.1 | 8 | 45.7 | odd | 12 | |||
1350.2.q.b.1007.2 | 8 | 45.43 | odd | 12 | |||
1350.2.q.b.1043.1 | 8 | 3.2 | odd | 2 | |||
1350.2.q.b.1043.2 | 8 | 15.14 | odd | 2 |