Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,2,Mod(97,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("980.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.82533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 802 x^{12} - 2264 x^{11} + 5402 x^{10} - 10642 x^{9} + \cdots + 196 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 293.6 | ||
Root | \(0.500000 + 1.61777i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.293 |
Dual form | 980.2.m.a.97.6 |
$q$-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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 1.11777 | − | 1.11777i | 0.645346 | − | 0.645346i | −0.306518 | − | 0.951865i | \(-0.599164\pi\) |
0.951865 | + | 0.306518i | \(0.0991641\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.524151 | + | 2.17377i | 0.234408 | + | 0.972138i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.501168i | 0.167056i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.685455 | 0.206672 | 0.103336 | − | 0.994646i | \(-0.467048\pi\) | ||||
0.103336 | + | 0.994646i | \(0.467048\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.04830 | + | 1.04830i | −0.290747 | + | 0.290747i | −0.837375 | − | 0.546628i | \(-0.815911\pi\) |
0.546628 | + | 0.837375i | \(0.315911\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.01566 | + | 1.84390i | 0.778640 | + | 0.476092i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.965868 | + | 0.965868i | 0.234257 | + | 0.234257i | 0.814467 | − | 0.580210i | \(-0.197029\pi\) |
−0.580210 | + | 0.814467i | \(0.697029\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.11898 | 0.715543 | 0.357771 | − | 0.933809i | \(-0.383537\pi\) | ||||
0.357771 | + | 0.933809i | \(0.383537\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.25058 | + | 3.25058i | 0.677794 | + | 0.677794i | 0.959501 | − | 0.281707i | \(-0.0909006\pi\) |
−0.281707 | + | 0.959501i | \(0.590901\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.45053 | + | 2.27877i | −0.890106 | + | 0.455753i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.91351 | + | 3.91351i | 0.753155 | + | 0.753155i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.90106i | − | 1.46719i | −0.679587 | − | 0.733595i | \(-0.737841\pi\) | ||
0.679587 | − | 0.733595i | \(-0.262159\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.81863i | 1.58387i | 0.610604 | + | 0.791936i | \(0.290927\pi\) | ||||
−0.610604 | + | 0.791936i | \(0.709073\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.766183 | − | 0.766183i | 0.133375 | − | 0.133375i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.35839 | − | 6.35839i | 1.04531 | − | 1.04531i | 0.0463890 | − | 0.998923i | \(-0.485229\pi\) |
0.998923 | − | 0.0463890i | \(-0.0147714\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.34353i | 0.375265i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.2469i | 1.60029i | 0.599805 | + | 0.800146i | \(0.295245\pi\) | ||||
−0.599805 | + | 0.800146i | \(0.704755\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.73689 | + | 3.73689i | 0.569871 | + | 0.569871i | 0.932092 | − | 0.362221i | \(-0.117982\pi\) |
−0.362221 | + | 0.932092i | \(0.617982\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.08942 | + | 0.262688i | −0.162402 | + | 0.0391592i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.93346 | − | 4.93346i | −0.719620 | − | 0.719620i | 0.248908 | − | 0.968527i | \(-0.419928\pi\) |
−0.968527 | + | 0.248908i | \(0.919928\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.15924 | 0.302354 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.54501 | − | 6.54501i | −0.899026 | − | 0.899026i | 0.0963237 | − | 0.995350i | \(-0.469292\pi\) |
−0.995350 | + | 0.0963237i | \(0.969292\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.359282 | + | 1.49002i | 0.0484456 | + | 0.200914i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.48631 | − | 3.48631i | 0.461773 | − | 0.461773i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.20860 | −0.547912 | −0.273956 | − | 0.961742i | \(-0.588332\pi\) | ||||
−0.273956 | + | 0.961742i | \(0.588332\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.13247i | 0.529108i | 0.964371 | + | 0.264554i | \(0.0852247\pi\) | ||||
−0.964371 | + | 0.264554i | \(0.914775\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.82824 | − | 1.72930i | −0.350799 | − | 0.214493i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.93604 | + | 2.93604i | −0.358694 | + | 0.358694i | −0.863331 | − | 0.504637i | \(-0.831626\pi\) |
0.504637 | + | 0.863331i | \(0.331626\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.26683 | 0.874823 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.5889 | 1.49402 | 0.747011 | − | 0.664812i | \(-0.231488\pi\) | ||||
0.747011 | + | 0.664812i | \(0.231488\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.08131 | − | 9.08131i | 1.06289 | − | 1.06289i | 0.0650023 | − | 0.997885i | \(-0.479295\pi\) |
0.997885 | − | 0.0650023i | \(-0.0207055\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.42754 | + | 7.52182i | −0.280308 | + | 0.868545i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 14.0313i | − | 1.57865i | −0.613978 | − | 0.789323i | \(-0.710432\pi\) | ||
0.613978 | − | 0.789323i | \(-0.289568\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.24532 | 0.805036 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.99595 | + | 3.99595i | −0.438612 | + | 0.438612i | −0.891545 | − | 0.452933i | \(-0.850378\pi\) |
0.452933 | + | 0.891545i | \(0.350378\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.59331 | + | 2.60583i | −0.172819 | + | 0.282642i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.83159 | − | 8.83159i | −0.946846 | − | 0.946846i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.5990 | −1.22949 | −0.614745 | − | 0.788726i | \(-0.710741\pi\) | ||||
−0.614745 | + | 0.788726i | \(0.710741\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.85722 | + | 9.85722i | 1.02215 | + | 1.02215i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.63482 | + | 6.77993i | 0.167729 | + | 0.695607i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.60010 | + | 2.60010i | 0.264000 | + | 0.264000i | 0.826677 | − | 0.562677i | \(-0.190228\pi\) |
−0.562677 | + | 0.826677i | \(0.690228\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.343528i | 0.0345259i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.06878i | 0.305355i | 0.988276 | + | 0.152677i | \(0.0487896\pi\) | ||||
−0.988276 | + | 0.152677i | \(0.951210\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.7098 | − | 11.7098i | 1.15380 | − | 1.15380i | 0.168012 | − | 0.985785i | \(-0.446265\pi\) |
0.985785 | − | 0.168012i | \(-0.0537348\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.74942 | − | 3.74942i | 0.362470 | − | 0.362470i | −0.502252 | − | 0.864721i | \(-0.667495\pi\) |
0.864721 | + | 0.502252i | \(0.167495\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 16.5615i | − | 1.58630i | −0.609025 | − | 0.793151i | \(-0.708439\pi\) | ||
0.609025 | − | 0.793151i | \(-0.291561\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 14.2145i | − | 1.34918i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.21561 | − | 7.21561i | −0.678787 | − | 0.678787i | 0.280939 | − | 0.959726i | \(-0.409354\pi\) |
−0.959726 | + | 0.280939i | \(0.909354\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.36222 | + | 8.76981i | −0.500029 | + | 0.817789i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.525376 | − | 0.525376i | −0.0485711 | − | 0.0485711i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5302 | −0.957287 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.4537 | + | 11.4537i | 1.03274 | + | 1.03274i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.28626 | − | 8.48000i | −0.651703 | − | 0.758474i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.13026 | + | 2.13026i | −0.189030 | + | 0.189030i | −0.795277 | − | 0.606247i | \(-0.792674\pi\) |
0.606247 | + | 0.795277i | \(0.292674\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.35400 | 0.735528 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.9460i | 0.956356i | 0.878263 | + | 0.478178i | \(0.158703\pi\) | ||||
−0.878263 | + | 0.478178i | \(0.841297\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.45579 | + | 10.5583i | −0.555626 | + | 0.908717i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.956158 | − | 0.956158i | 0.0816901 | − | 0.0816901i | −0.665081 | − | 0.746771i | \(-0.731603\pi\) |
0.746771 | + | 0.665081i | \(0.231603\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.703180 | −0.0596429 | −0.0298215 | − | 0.999555i | \(-0.509494\pi\) | ||||
−0.0298215 | + | 0.999555i | \(0.509494\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.0290 | −0.928808 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.718564 | + | 0.718564i | −0.0600894 | + | 0.0600894i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.1751 | − | 4.14135i | 1.42631 | − | 0.343921i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.3033i | 0.926002i | 0.886358 | + | 0.463001i | \(0.153227\pi\) | ||||
−0.886358 | + | 0.463001i | \(0.846773\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.90340 | −0.643169 | −0.321585 | − | 0.946881i | \(-0.604215\pi\) | ||||
−0.321585 | + | 0.946881i | \(0.604215\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.484063 | + | 0.484063i | −0.0391341 | + | 0.0391341i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.1696 | + | 4.62229i | −1.53974 | + | 0.371272i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.64962 | − | 1.64962i | −0.131654 | − | 0.131654i | 0.638209 | − | 0.769863i | \(-0.279675\pi\) |
−0.769863 | + | 0.638209i | \(0.779675\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.6317 | −1.16037 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.799253 | + | 0.799253i | 0.0626023 | + | 0.0626023i | 0.737715 | − | 0.675112i | \(-0.235905\pi\) |
−0.675112 | + | 0.737715i | \(0.735905\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.06710 | + | 1.26391i | 0.160923 | + | 0.0983951i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.76281 | − | 5.76281i | −0.445940 | − | 0.445940i | 0.448062 | − | 0.894002i | \(-0.352114\pi\) |
−0.894002 | + | 0.448062i | \(0.852114\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8021i | 0.830933i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.56313i | 0.119536i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.3652 | − | 12.3652i | 0.940106 | − | 0.940106i | −0.0581991 | − | 0.998305i | \(-0.518536\pi\) |
0.998305 | + | 0.0581991i | \(0.0185358\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.70425 | + | 4.70425i | −0.353593 | + | 0.353593i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.07389i | 0.0802666i | 0.999194 | + | 0.0401333i | \(0.0127783\pi\) | ||||
−0.999194 | + | 0.0401333i | \(0.987222\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 8.93607i | − | 0.664213i | −0.943242 | − | 0.332106i | \(-0.892241\pi\) | ||
0.943242 | − | 0.332106i | \(-0.107759\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.61916 | + | 4.61916i | 0.341458 | + | 0.341458i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.1544 | + | 10.4889i | 1.26122 | + | 0.771159i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.662059 | + | 0.662059i | 0.0484145 | + | 0.0484145i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.3795 | −1.76404 | −0.882020 | − | 0.471212i | \(-0.843817\pi\) | ||||
−0.882020 | + | 0.471212i | \(0.843817\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.38737 | − | 6.38737i | −0.459773 | − | 0.459773i | 0.438808 | − | 0.898581i | \(-0.355401\pi\) |
−0.898581 | + | 0.438808i | \(0.855401\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.09429 | + | 1.22836i | −0.364809 | + | 0.0879649i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.78673 | − | 1.78673i | 0.127299 | − | 0.127299i | −0.640587 | − | 0.767886i | \(-0.721309\pi\) |
0.767886 | + | 0.640587i | \(0.221309\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.34400 | −0.662379 | −0.331189 | − | 0.943564i | \(-0.607450\pi\) | ||||
−0.331189 | + | 0.943564i | \(0.607450\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.56365i | 0.462964i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.2743 | + | 5.37091i | −1.55571 | + | 0.375121i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.62909 | + | 1.62909i | −0.113230 | + | 0.113230i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.13792 | 0.147883 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.84703 | −0.677898 | −0.338949 | − | 0.940805i | \(-0.610071\pi\) | ||||
−0.338949 | + | 0.940805i | \(0.610071\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.0715 | − | 14.0715i | 0.964162 | − | 0.964162i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.16444 | + | 10.0818i | −0.420411 | + | 0.687575i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 20.3017i | − | 1.37186i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.02504 | −0.136219 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.338625 | + | 0.338625i | −0.0226760 | + | 0.0226760i | −0.718354 | − | 0.695678i | \(-0.755104\pi\) |
0.695678 | + | 0.718354i | \(0.255104\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.14205 | − | 2.23047i | −0.0761364 | − | 0.148698i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.80638 | − | 9.80638i | −0.650872 | − | 0.650872i | 0.302331 | − | 0.953203i | \(-0.402235\pi\) |
−0.953203 | + | 0.302331i | \(0.902235\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.66291 | −0.175970 | −0.0879850 | − | 0.996122i | \(-0.528043\pi\) | ||||
−0.0879850 | + | 0.996122i | \(0.528043\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.3874 | + | 13.3874i | 0.877036 | + | 0.877036i | 0.993227 | − | 0.116191i | \(-0.0370685\pi\) |
−0.116191 | + | 0.993227i | \(0.537068\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.13832 | − | 13.3101i | 0.530886 | − | 0.868254i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.6838 | − | 15.6838i | −1.01877 | − | 1.01877i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.74416i | 0.371559i | 0.982591 | + | 0.185779i | \(0.0594809\pi\) | ||||
−0.982591 | + | 0.185779i | \(0.940519\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 10.1861i | − | 0.656146i | −0.944652 | − | 0.328073i | \(-0.893601\pi\) | ||
0.944652 | − | 0.328073i | \(-0.106399\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.64191 | + | 3.64191i | −0.233628 | + | 0.233628i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.26963 | + | 3.26963i | −0.208042 | + | 0.208042i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.93312i | 0.566113i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 7.28871i | − | 0.460059i | −0.973184 | − | 0.230030i | \(-0.926118\pi\) | ||
0.973184 | − | 0.230030i | \(-0.0738823\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.22813 | + | 2.22813i | 0.140081 | + | 0.140081i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.13177 | + | 4.69369i | 0.0708742 | + | 0.293930i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.63856 | − | 8.63856i | −0.538859 | − | 0.538859i | 0.384335 | − | 0.923194i | \(-0.374431\pi\) |
−0.923194 | + | 0.384335i | \(0.874431\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.95976 | 0.245103 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.2080 | + | 15.2080i | 0.937766 | + | 0.937766i | 0.998174 | − | 0.0604077i | \(-0.0192401\pi\) |
−0.0604077 | + | 0.998174i | \(0.519240\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.7968 | − | 17.6579i | 0.663239 | − | 1.08472i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.9650 | + | 12.9650i | −0.793446 | + | 0.793446i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.4753 | −1.61423 | −0.807114 | − | 0.590396i | \(-0.798972\pi\) | ||||
−0.807114 | + | 0.590396i | \(0.798972\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 17.8483i | − | 1.08421i | −0.840312 | − | 0.542103i | \(-0.817628\pi\) | ||
0.840312 | − | 0.542103i | \(-0.182372\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.05064 | + | 1.56199i | −0.183960 | + | 0.0941916i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.7630 | − | 18.7630i | 1.12736 | − | 1.12736i | 0.136751 | − | 0.990605i | \(-0.456334\pi\) |
0.990605 | − | 0.136751i | \(-0.0436661\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.41962 | −0.264596 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.7465 | −1.11832 | −0.559161 | − | 0.829059i | \(-0.688877\pi\) | ||||
−0.559161 | + | 0.829059i | \(0.688877\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.462374 | − | 0.462374i | 0.0274853 | − | 0.0274853i | −0.693231 | − | 0.720716i | \(-0.743813\pi\) |
0.720716 | + | 0.693231i | \(0.243813\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.40578 | + | 5.75107i | 0.557150 | + | 0.340664i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 15.1342i | − | 0.890247i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.81264 | 0.340743 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.72555 | − | 1.72555i | 0.100808 | − | 0.100808i | −0.654904 | − | 0.755712i | \(-0.727291\pi\) |
0.755712 | + | 0.654904i | \(0.227291\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.20594 | − | 9.14851i | −0.128435 | − | 0.532647i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.68253 | + | 2.68253i | 0.155656 | + | 0.155656i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.81519 | −0.394133 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.43020 | + | 3.43020i | 0.197060 | + | 0.197060i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.98302 | + | 2.16604i | −0.514366 | + | 0.124027i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.5555 | + | 18.5555i | 1.05902 | + | 1.05902i | 0.998145 | + | 0.0608747i | \(0.0193890\pi\) |
0.0608747 | + | 0.998145i | \(0.480611\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 26.1777i | − | 1.48920i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 4.96809i | − | 0.281714i | −0.990030 | − | 0.140857i | \(-0.955014\pi\) | ||
0.990030 | − | 0.140857i | \(-0.0449858\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.65395 | − | 8.65395i | 0.489150 | − | 0.489150i | −0.418888 | − | 0.908038i | \(-0.637580\pi\) |
0.908038 | + | 0.418888i | \(0.137580\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.3182 | − | 18.3182i | 1.02885 | − | 1.02885i | 0.0292785 | − | 0.999571i | \(-0.490679\pi\) |
0.999571 | − | 0.0292785i | \(-0.00932098\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 5.41582i | − | 0.303228i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 8.38199i | − | 0.467837i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.01252 | + | 3.01252i | 0.167621 | + | 0.167621i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.27667 | − | 7.05434i | 0.126287 | − | 0.391304i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.5120 | − | 18.5120i | −1.02371 | − | 1.02371i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.1663 | 0.833613 | 0.416806 | − | 0.908995i | \(-0.363149\pi\) | ||||
0.416806 | + | 0.908995i | \(0.363149\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.18662 | + | 3.18662i | 0.174626 | + | 0.174626i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.92120 | − | 4.84334i | −0.432781 | − | 0.264620i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.7442 | − | 12.7442i | 0.694218 | − | 0.694218i | −0.268939 | − | 0.963157i | \(-0.586673\pi\) |
0.963157 | + | 0.268939i | \(0.0866729\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.1308 | −0.876106 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.04477i | 0.327343i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.80892 | + | 15.7964i | 0.205065 | + | 0.850449i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.27723 | − | 4.27723i | 0.229614 | − | 0.229614i | −0.582918 | − | 0.812531i | \(-0.698089\pi\) |
0.812531 | + | 0.582918i | \(0.198089\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.80171 | 0.310558 | 0.155279 | − | 0.987871i | \(-0.450372\pi\) | ||||
0.155279 | + | 0.987871i | \(0.450372\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.20509 | −0.437955 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.37164 | + | 8.37164i | −0.445577 | + | 0.445577i | −0.893881 | − | 0.448304i | \(-0.852028\pi\) |
0.448304 | + | 0.893881i | \(0.352028\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.59846 | + | 27.3652i | 0.350210 | + | 1.45240i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.87602i | 0.257346i | 0.991687 | + | 0.128673i | \(0.0410718\pi\) | ||||
−0.991687 | + | 0.128673i | \(0.958928\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.27197 | −0.487998 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.7703 | + | 11.7703i | −0.617781 | + | 0.617781i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.5006 | + | 14.9807i | 1.28242 | + | 0.784125i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.37569 | + | 4.37569i | 0.228409 | + | 0.228409i | 0.812028 | − | 0.583619i | \(-0.198364\pi\) |
−0.583619 | + | 0.812028i | \(0.698364\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.13541 | −0.267339 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.2192 | − | 23.2192i | −1.20225 | − | 1.20225i | −0.973482 | − | 0.228763i | \(-0.926532\pi\) |
−0.228763 | − | 0.973482i | \(-0.573468\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.6231 | − | 1.33433i | −0.910053 | − | 0.0689045i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.28270 | + | 8.28270i | 0.426581 | + | 0.426581i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.53089i | 0.335469i | 0.985832 | + | 0.167735i | \(0.0536452\pi\) | ||||
−0.985832 | + | 0.167735i | \(0.946355\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.76229i | 0.243980i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.607781 | + | 0.607781i | −0.0310561 | + | 0.0310561i | −0.722464 | − | 0.691408i | \(-0.756991\pi\) |
0.691408 | + | 0.722464i | \(0.256991\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.87281 | + | 1.87281i | −0.0952004 | + | 0.0952004i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.3550i | 1.33625i | 0.744049 | + | 0.668125i | \(0.232903\pi\) | ||||
−0.744049 | + | 0.668125i | \(0.767097\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.27927i | 0.317556i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.2351 | + | 12.2351i | 0.617181 | + | 0.617181i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.5008 | − | 7.35454i | 1.53466 | − | 0.370047i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.66846 | − | 7.66846i | −0.384869 | − | 0.384869i | 0.487984 | − | 0.872853i | \(-0.337732\pi\) |
−0.872853 | + | 0.487984i | \(0.837732\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.00000 | 0.149813 | 0.0749064 | − | 0.997191i | \(-0.476134\pi\) | ||||
0.0749064 | + | 0.997191i | \(0.476134\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.24459 | − | 9.24459i | −0.460506 | − | 0.460506i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.79765 | + | 15.7497i | 0.188707 | + | 0.782606i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.35839 | − | 4.35839i | 0.216037 | − | 0.216037i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.39075 | 0.167662 | 0.0838308 | − | 0.996480i | \(-0.473284\pi\) | ||||
0.0838308 | + | 0.996480i | \(0.473284\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2.13753i | − | 0.105437i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.7807 | − | 6.59178i | −0.529206 | − | 0.323578i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.785995 | + | 0.785995i | −0.0384904 | + | 0.0384904i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.03776 | 0.0506978 | 0.0253489 | − | 0.999679i | \(-0.491930\pi\) | ||||
0.0253489 | + | 0.999679i | \(0.491930\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.683118 | −0.0332931 | −0.0166466 | − | 0.999861i | \(-0.505299\pi\) | ||||
−0.0166466 | + | 0.999861i | \(0.505299\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.47250 | − | 2.47250i | 0.120217 | − | 0.120217i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.49961 | − | 2.09764i | −0.315278 | − | 0.101750i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.60638i | 0.0775569i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.6855 | −0.900047 | −0.450023 | − | 0.893017i | \(-0.648584\pi\) | ||||
−0.450023 | + | 0.893017i | \(0.648584\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.43170 | + | 7.43170i | −0.357145 | + | 0.357145i | −0.862759 | − | 0.505615i | \(-0.831266\pi\) |
0.505615 | + | 0.862759i | \(0.331266\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.5687 | − | 23.8269i | 0.698517 | − | 1.14241i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.1385 | + | 10.1385i | 0.484990 | + | 0.484990i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.1027 | 1.29354 | 0.646772 | − | 0.762684i | \(-0.276119\pi\) | ||||
0.646772 | + | 0.762684i | \(0.276119\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.5312 | + | 26.5312i | 1.26053 | + | 1.26053i | 0.950835 | + | 0.309699i | \(0.100228\pi\) |
0.309699 | + | 0.950835i | \(0.399772\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.07962 | − | 25.2135i | −0.288202 | − | 1.19523i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.6345 | + | 12.6345i | 0.597592 | + | 0.597592i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.36931i | 0.300586i | 0.988641 | + | 0.150293i | \(0.0480217\pi\) | ||||
−0.988641 | + | 0.150293i | \(0.951978\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.02376i | 0.330736i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.83420 | + | 8.83420i | −0.415067 | + | 0.415067i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.5160 | − | 10.5160i | 0.491919 | − | 0.491919i | −0.416991 | − | 0.908910i | \(-0.636915\pi\) |
0.908910 | + | 0.416991i | \(0.136915\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.55987i | 0.352865i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.8860i | 1.95082i | 0.220390 | + | 0.975412i | \(0.429267\pi\) | ||||
−0.220390 | + | 0.975412i | \(0.570733\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.8985 | + | 17.8985i | 0.831813 | + | 0.831813i | 0.987765 | − | 0.155952i | \(-0.0498445\pi\) |
−0.155952 | + | 0.987765i | \(0.549845\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16.2606 | + | 26.5940i | −0.754069 | + | 1.23327i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.8630 | + | 28.8630i | 1.33562 | + | 1.33562i | 0.900255 | + | 0.435363i | \(0.143380\pi\) |
0.435363 | + | 0.900255i | \(0.356620\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.68779 | −0.169924 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.56147 | + | 2.56147i | 0.117777 | + | 0.117777i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.8811 | + | 7.10742i | −0.636909 | + | 0.326111i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.28015 | − | 3.28015i | 0.150188 | − | 0.150188i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.88101 | 0.223019 | 0.111509 | − | 0.993763i | \(-0.464431\pi\) | ||||
0.111509 | + | 0.993763i | \(0.464431\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.3310i | 0.607843i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.28917 | + | 7.01486i | −0.194761 | + | 0.318528i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.0326 | + | 25.0326i | −1.13433 | + | 1.13433i | −0.144887 | + | 0.989448i | \(0.546282\pi\) |
−0.989448 | + | 0.144887i | \(0.953718\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.78677 | 0.0808003 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.8068 | 1.16464 | 0.582322 | − | 0.812958i | \(-0.302144\pi\) | ||||
0.582322 | + | 0.812958i | \(0.302144\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.63138 | − | 7.63138i | 0.343700 | − | 0.343700i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.746751 | + | 0.180061i | −0.0335640 | + | 0.00809313i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 13.0869i | − | 0.585852i | −0.956135 | − | 0.292926i | \(-0.905371\pi\) | ||
0.956135 | − | 0.292926i | \(-0.0946290\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.8830 | −0.575571 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.2498 | − | 15.2498i | 0.679955 | − | 0.679955i | −0.280035 | − | 0.959990i | \(-0.590346\pi\) |
0.959990 | + | 0.280035i | \(0.0903460\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.67081 | + | 1.60850i | −0.296847 | + | 0.0715775i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.0743 | + | 12.0743i | 0.536239 | + | 0.536239i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.529424 | −0.0234663 | −0.0117332 | − | 0.999931i | \(-0.503735\pi\) | ||||
−0.0117332 | + | 0.999931i | \(0.503735\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.2062 | + | 12.2062i | 0.538915 | + | 0.538915i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 31.5920 | + | 19.3166i | 1.39211 | + | 0.851192i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.38167 | − | 3.38167i | −0.148726 | − | 0.148726i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 27.6429i | − | 1.21339i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 3.62652i | − | 0.158881i | −0.996840 | − | 0.0794404i | \(-0.974687\pi\) | ||
0.996840 | − | 0.0794404i | \(-0.0253133\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.5942 | − | 14.5942i | 0.638160 | − | 0.638160i | −0.311941 | − | 0.950101i | \(-0.600979\pi\) |
0.950101 | + | 0.311941i | \(0.100979\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.51763 | + | 8.51763i | −0.371034 | + | 0.371034i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1.86740i | − | 0.0811915i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 2.10922i | − | 0.0915321i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.7418 | − | 10.7418i | −0.465280 | − | 0.465280i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.1156 | + | 6.18510i | 0.437336 | + | 0.267405i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.20037 | + | 1.20037i | 0.0517998 | + | 0.0517998i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.5486 | 1.18441 | 0.592204 | − | 0.805788i | \(-0.298258\pi\) | ||||
0.592204 | + | 0.805788i | \(0.298258\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.98849 | − | 9.98849i | −0.428647 | − | 0.428647i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 36.0008 | − | 8.68072i | 1.54210 | − | 0.371841i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.00886 | − | 5.00886i | 0.214164 | − | 0.214164i | −0.591870 | − | 0.806034i | \(-0.701610\pi\) |
0.806034 | + | 0.591870i | \(0.201610\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.07106 | −0.0883907 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 24.6432i | − | 1.04984i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 30.8989 | − | 7.45053i | 1.31159 | − | 0.316257i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.38343 | − | 7.38343i | 0.312846 | − | 0.312846i | −0.533165 | − | 0.846011i | \(-0.678998\pi\) |
0.846011 | + | 0.533165i | \(0.178998\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.83479 | −0.331376 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.48006 | 0.0624883 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.5473 | + | 19.5473i | −0.823822 | + | 0.823822i | −0.986654 | − | 0.162832i | \(-0.947937\pi\) |
0.162832 | + | 0.986654i | \(0.447937\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.9030 | − | 19.4671i | 0.500762 | − | 0.818988i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.1287i | 0.466538i | 0.972412 | + | 0.233269i | \(0.0749422\pi\) | ||||
−0.972412 | + | 0.233269i | \(0.925058\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.6948 | 0.866051 | 0.433025 | − | 0.901382i | \(-0.357446\pi\) | ||||
0.433025 | + | 0.901382i | \(0.357446\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.2508 | + | 27.2508i | −1.13842 | + | 1.13842i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.8741 | − | 7.05950i | −0.912215 | − | 0.294402i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.12665 | − | 5.12665i | −0.213425 | − | 0.213425i | 0.592295 | − | 0.805721i | \(-0.298222\pi\) |
−0.805721 | + | 0.592295i | \(0.798222\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.2793 | −0.593426 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.48631 | − | 4.48631i | −0.185804 | − | 0.185804i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.866669 | − | 1.41742i | 0.0358324 | − | 0.0586032i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.87340 | − | 5.87340i | −0.242421 | − | 0.242421i | 0.575430 | − | 0.817851i | \(-0.304835\pi\) |
−0.817851 | + | 0.575430i | \(0.804835\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.5051i | 1.13333i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 3.99432i | − | 0.164304i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.3128 | + | 19.3128i | −0.793082 | + | 0.793082i | −0.981994 | − | 0.188912i | \(-0.939504\pi\) |
0.188912 | + | 0.981994i | \(0.439504\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.4445 | + | 10.4445i | −0.427464 | + | 0.427464i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 25.3620i | − | 1.03626i | −0.855301 | − | 0.518131i | \(-0.826628\pi\) | ||
0.855301 | − | 0.518131i | \(-0.173372\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 13.8045i | − | 0.563099i | −0.959547 | − | 0.281550i | \(-0.909152\pi\) | ||
0.959547 | − | 0.281550i | \(-0.0908484\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.47145 | − | 1.47145i | −0.0599221 | − | 0.0599221i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.51939 | − | 22.8901i | −0.224395 | − | 0.930615i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.8422 | + | 15.8422i | 0.643016 | + | 0.643016i | 0.951296 | − | 0.308280i | \(-0.0997532\pi\) |
−0.308280 | + | 0.951296i | \(0.599753\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.3435 | 0.418454 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.5361 | + | 23.5361i | 0.950614 | + | 0.950614i | 0.998837 | − | 0.0482227i | \(-0.0153557\pi\) |
−0.0482227 | + | 0.998837i | \(0.515356\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.8942 | + | 30.9011i | −0.761886 | + | 1.24605i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.1167 | − | 21.1167i | 0.850125 | − | 0.850125i | −0.140023 | − | 0.990148i | \(-0.544718\pi\) |
0.990148 | + | 0.140023i | \(0.0447177\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.4621 | 1.46554 | 0.732768 | − | 0.680478i | \(-0.238228\pi\) | ||||
0.732768 | + | 0.680478i | \(0.238228\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 25.4424i | 1.02097i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.6144 | − | 20.2834i | 0.584578 | − | 0.811338i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.38971 | − | 2.38971i | 0.0954357 | − | 0.0954357i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.2827 | 0.489744 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.0247 | 1.87203 | 0.936013 | − | 0.351966i | \(-0.114487\pi\) | ||||
0.936013 | + | 0.351966i | \(0.114487\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.0067 | + | 11.0067i | −0.437479 | + | 0.437479i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.74727 | − | 3.51411i | −0.228073 | − | 0.139453i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.30914i | 0.249586i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.1052 | −0.636118 | −0.318059 | − | 0.948071i | \(-0.603031\pi\) | ||||
−0.318059 | + | 0.948071i | \(0.603031\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.1021 | − | 29.1021i | 1.14768 | − | 1.14768i | 0.160667 | − | 0.987009i | \(-0.448635\pi\) |
0.987009 | − | 0.160667i | \(-0.0513646\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.37876 | + | 18.1596i | 0.172413 | + | 0.715035i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.1956 | − | 30.1956i | −1.18711 | − | 1.18711i | −0.977862 | − | 0.209251i | \(-0.932898\pi\) |
−0.209251 | − | 0.977862i | \(-0.567102\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.88480 | −0.113238 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.5747 | − | 23.5747i | −0.922550 | − | 0.922550i | 0.0746587 | − | 0.997209i | \(-0.476213\pi\) |
−0.997209 | + | 0.0746587i | \(0.976213\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.7941 | + | 5.73736i | −0.929711 | + | 0.224177i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.55127 | + | 4.55127i | 0.177562 | + | 0.177562i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.01773i | 0.0785996i | 0.999227 | + | 0.0392998i | \(0.0125127\pi\) | ||||
−0.999227 | + | 0.0392998i | \(0.987487\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 0.473111i | − | 0.0184019i | −0.999958 | − | 0.00920095i | \(-0.997071\pi\) | ||
0.999958 | − | 0.00920095i | \(-0.00292879\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.26354 | + | 2.26354i | −0.0879086 | + | 0.0879086i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.6831 | − | 25.6831i | 0.994452 | − | 0.994452i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.757012i | 0.0292678i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.83262i | 0.109352i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.1663 | − | 15.1663i | −0.584616 | − | 0.584616i | 0.351552 | − | 0.936168i | \(-0.385654\pi\) |
−0.936168 | + | 0.351552i | \(0.885654\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −26.3352 | − | 8.49922i | −1.01364 | − | 0.327135i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.0449 | − | 10.0449i | −0.386058 | − | 0.386058i | 0.487221 | − | 0.873279i | \(-0.338011\pi\) |
−0.873279 | + | 0.487221i | \(0.838011\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.9226 | −0.840076 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.8058 | − | 14.8058i | −0.566527 | − | 0.566527i | 0.364626 | − | 0.931154i | \(-0.381197\pi\) |
−0.931154 | + | 0.364626i | \(0.881197\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.57964 | + | 1.57729i | 0.0985628 | + | 0.0602653i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.97653 | + | 2.97653i | −0.113562 | + | 0.113562i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.7223 | 0.522778 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.47007i | 0.246133i | 0.992398 | + | 0.123067i | \(0.0392729\pi\) | ||||
−0.992398 | + | 0.123067i | \(0.960727\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.368573 | − | 1.52855i | −0.0139808 | − | 0.0579812i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.89712 | + | 9.89712i | −0.374880 | + | 0.374880i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.9281 | 1.13198 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.5423 | 0.587026 | 0.293513 | − | 0.955955i | \(-0.405176\pi\) | ||||
0.293513 | + | 0.955955i | \(0.405176\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.8317 | − | 19.8317i | 0.747966 | − | 0.747966i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.78086 | − | 23.9744i | −0.217720 | − | 0.902930i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 8.97963i | − | 0.337237i | −0.985681 | − | 0.168619i | \(-0.946069\pi\) | ||
0.985681 | − | 0.168619i | \(-0.0539306\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.03206 | 0.263723 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.6657 | + | 28.6657i | −1.07354 | + | 1.07354i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.93863 | − | 1.18536i | −0.0725006 | − | 0.0443298i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.42066 | + | 6.42066i | 0.239784 | + | 0.239784i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.5516 | −1.51232 | −0.756160 | − | 0.654387i | \(-0.772927\pi\) | ||||
−0.756160 | + | 0.654387i | \(0.772927\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.3858 | − | 11.3858i | −0.423441 | − | 0.423441i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.0047 | + | 35.1639i | 0.668677 | + | 1.30596i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.9052 | + | 11.9052i | 0.441540 | + | 0.441540i | 0.892529 | − | 0.450990i | \(-0.148929\pi\) |
−0.450990 | + | 0.892529i | \(0.648929\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.8776i | 1.10658i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.21869i | 0.266993i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.37977 | + | 4.37977i | −0.161770 | + | 0.161770i | −0.783351 | − | 0.621580i | \(-0.786491\pi\) |
0.621580 | + | 0.783351i | \(0.286491\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.01252 | + | 2.01252i | −0.0741322 | + | 0.0741322i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 39.6402i | − | 1.45819i | −0.684413 | − | 0.729095i | \(-0.739941\pi\) | ||
0.684413 | − | 0.729095i | \(-0.260059\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.30942i | 0.268518i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.7507 | − | 15.7507i | −0.577837 | − | 0.577837i | 0.356470 | − | 0.934307i | \(-0.383980\pi\) |
−0.934307 | + | 0.356470i | \(0.883980\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.5707 | + | 5.92464i | −0.900202 | + | 0.217062i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.00264 | − | 2.00264i | −0.0732728 | − | 0.0732728i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.3346 | −0.669039 | −0.334520 | − | 0.942389i | \(-0.608574\pi\) | ||||
−0.334520 | + | 0.942389i | \(0.608574\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.14712 | − | 8.14712i | −0.296898 | − | 0.296898i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.14258 | − | 17.1802i | −0.150764 | − | 0.625250i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.1143 | + | 14.1143i | −0.512994 | + | 0.512994i | −0.915443 | − | 0.402449i | \(-0.868159\pi\) |
0.402449 | + | 0.915443i | \(0.368159\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.98108 | 0.180802 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.6443i | 0.422107i | 0.977475 | + | 0.211054i | \(0.0676894\pi\) | ||||
−0.977475 | + | 0.211054i | \(0.932311\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.30596 | − | 0.798518i | −0.0472171 | − | 0.0288705i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.41188 | − | 4.41188i | 0.159304 | − | 0.159304i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −45.3371 | −1.63490 | −0.817448 | − | 0.576002i | \(-0.804612\pi\) | ||||
−0.817448 | + | 0.576002i | \(0.804612\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.3119 | −0.695501 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.16153 | + | 5.16153i | −0.185647 | + | 0.185647i | −0.793811 | − | 0.608164i | \(-0.791906\pi\) |
0.608164 | + | 0.793811i | \(0.291906\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.0956 | − | 39.2476i | −0.721855 | − | 1.40981i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31.9598i | 1.14508i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.62909 | 0.308773 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30.9209 | − | 30.9209i | 1.10502 | − | 1.10502i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.72123 | − | 4.45053i | 0.0971250 | − | 0.158846i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.6593 | + | 21.6593i | 0.772071 | + | 0.772071i | 0.978468 | − | 0.206397i | \(-0.0661738\pi\) |
−0.206397 | + | 0.978468i | \(0.566174\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 33.9982 | 1.21037 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.33207 | − | 4.33207i | −0.153836 | − | 0.153836i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.66921 | − | 31.8058i | −0.271999 | − | 1.12804i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.7751 | − | 30.7751i | −1.09011 | − | 1.09011i | −0.995516 | − | 0.0945938i | \(-0.969845\pi\) |
−0.0945938 | − | 0.995516i | \(-0.530155\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 9.53015i | − | 0.337153i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 5.81304i | − | 0.205394i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.22483 | − | 6.22483i | 0.219670 | − | 0.219670i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.5934 | + | 29.5934i | −1.04174 | + | 1.04174i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.6597i | 0.515407i | 0.966224 | + | 0.257703i | \(0.0829657\pi\) | ||||
−0.966224 | + | 0.257703i | \(0.917034\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 0.360507i | − | 0.0126591i | −0.999980 | − | 0.00632956i | \(-0.997985\pi\) | ||
0.999980 | − | 0.00632956i | \(-0.00201477\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.9503 | − | 19.9503i | −0.699688 | − | 0.699688i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.31846 | + | 2.15632i | −0.0461836 | + | 0.0755326i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.6553 | + | 11.6553i | 0.407767 | + | 0.407767i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.2813 | 0.777623 | 0.388812 | − | 0.921317i | \(-0.372886\pi\) | ||||
0.388812 | + | 0.921317i | \(0.372886\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.18136 | − | 8.18136i | −0.285184 | − | 0.285184i | 0.549988 | − | 0.835173i | \(-0.314632\pi\) |
−0.835173 | + | 0.549988i | \(0.814632\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.66397 | + | 5.15587i | −0.0579319 | + | 0.179504i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.7972 | + | 24.7972i | −0.862283 | + | 0.862283i | −0.991603 | − | 0.129320i | \(-0.958721\pi\) |
0.129320 | + | 0.991603i | \(0.458721\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.3974 | −0.882089 | −0.441044 | − | 0.897485i | \(-0.645392\pi\) | ||||
−0.441044 | + | 0.897485i | \(0.645392\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 41.9454i | − | 1.45507i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.50643 | − | 15.5476i | 0.328984 | − | 0.538047i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −34.5118 | + | 34.5118i | −1.19290 | + | 1.19290i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.36253 | −0.150611 | −0.0753057 | − | 0.997160i | \(-0.523993\pi\) | ||||
−0.0753057 | + | 0.997160i | \(0.523993\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −33.4268 | −1.15265 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.9543 | + | 20.9543i | −0.721705 | + | 0.721705i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.4813 | + | 5.66195i | −0.807781 | + | 0.194777i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 1.03366i | − | 0.0354750i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 41.3369 | 1.41701 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.8935 | − | 36.8935i | 1.26321 | − | 1.26321i | 0.313683 | − | 0.949528i | \(-0.398437\pi\) |
0.949528 | − | 0.313683i | \(-0.101563\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.39789 | + | 0.819319i | −0.116205 | + | 0.0280201i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.0587 | − | 18.0587i | −0.616873 | − | 0.616873i | 0.327855 | − | 0.944728i | \(-0.393674\pi\) |
−0.944728 | + | 0.327855i | \(0.893674\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.7639 | 1.11789 | 0.558944 | − | 0.829205i | \(-0.311207\pi\) | ||||
0.558944 | + | 0.829205i | \(0.311207\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.0139 | − | 17.0139i | −0.579159 | − | 0.579159i | 0.355513 | − | 0.934672i | \(-0.384306\pi\) |
−0.934672 | + | 0.355513i | \(0.884306\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.3602 | + | 20.3978i | 1.13428 | + | 0.693545i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.9166 | − | 16.9166i | −0.574518 | − | 0.574518i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 9.61784i | − | 0.326263i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 6.15572i | − | 0.208578i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.30309 | + | 1.30309i | −0.0441029 | + | 0.0441029i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.1895 | + | 34.1895i | −1.15450 | + | 1.15450i | −0.168857 | + | 0.985641i | \(0.554007\pi\) |
−0.985641 | + | 0.168857i | \(0.945993\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 3.85755i | − | 0.130112i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.63541i | − | 0.122480i | −0.998123 | − | 0.0612400i | \(-0.980494\pi\) | ||
0.998123 | − | 0.0612400i | \(-0.0195055\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.50117 | − | 7.50117i | −0.252434 | − | 0.252434i | 0.569534 | − | 0.821968i | \(-0.307124\pi\) |
−0.821968 | + | 0.569534i | \(0.807124\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.6917 | − | 7.76021i | −0.426627 | − | 0.260857i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.98966 | + | 7.98966i | 0.268267 | + | 0.268267i | 0.828401 | − | 0.560135i | \(-0.189251\pi\) |
−0.560135 | + | 0.828401i | \(0.689251\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.96634 | 0.166379 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.3874 | − | 15.3874i | −0.514919 | − | 0.514919i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.33440 | + | 0.562883i | −0.0780303 | + | 0.0188151i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.61784 | + | 7.61784i | −0.254352 | + | 0.254352i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 69.6765 | 2.32384 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 12.6432i | − | 0.421207i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.4249 | − | 4.68385i | 0.645707 | − | 0.155697i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.4009 | − | 11.4009i | 0.378561 | − | 0.378561i | −0.492022 | − | 0.870583i | \(-0.663742\pi\) |
0.870583 | + | 0.492022i | \(0.163742\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.53798 | −0.0510114 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.2211 | −1.03440 | −0.517201 | − | 0.855864i | \(-0.673026\pi\) | ||||
−0.517201 | + | 0.855864i | \(0.673026\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.73904 | + | 2.73904i | −0.0906490 | + | 0.0906490i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.61984 | + | 12.4621i | −0.251904 | + | 0.411985i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.3844i | 1.62904i | 0.580135 | + | 0.814520i | \(0.303000\pi\) | ||||
−0.580135 | + | 0.814520i | \(0.697000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 41.4817 | 1.36687 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.1969 | + | 13.1969i | −0.434382 | + | 0.434382i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.8089 | + | 42.7875i | −0.454034 | + | 1.40684i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.86856 | + | 5.86856i | 0.192749 | + | 0.192749i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.9421 | 1.73697 | 0.868487 | − | 0.495711i | \(-0.165093\pi\) | ||||
0.868487 | + | 0.495711i | \(0.165093\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.55319 | − | 5.55319i | −0.181803 | − | 0.181803i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.09214 | + | 1.78618i | −0.0357169 | + | 0.0584144i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.9004 | − | 28.9004i | −0.944134 | − | 0.944134i | 0.0543857 | − | 0.998520i | \(-0.482680\pi\) |
−0.998520 | + | 0.0543857i | \(0.982680\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 19.3463i | − | 0.631343i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.9805i | 1.17293i | 0.809975 | + | 0.586465i | \(0.199481\pi\) | ||||
−0.809975 | + | 0.586465i | \(0.800519\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33.3083 | + | 33.3083i | −1.08467 | + | 1.08467i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.6841 | + | 13.6841i | −0.444675 | + | 0.444675i | −0.893580 | − | 0.448905i | \(-0.851814\pi\) |
0.448905 | + | 0.893580i | \(0.351814\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.0399i | 0.618062i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 40.9511i | − | 1.32793i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.7055 | + | 13.7055i | 0.443965 | + | 0.443965i | 0.893342 | − | 0.449377i | \(-0.148354\pi\) |
−0.449377 | + | 0.893342i | \(0.648354\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.7786 | − | 52.9954i | −0.413504 | − | 1.71489i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.05366 | − | 6.05366i | −0.195687 | − | 0.195687i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −46.7682 | −1.50865 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.87909 | + | 1.87909i | 0.0605528 | + | 0.0605528i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.5367 | − | 17.2326i | 0.339189 | − | 0.554737i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.8117 | + | 26.8117i | −0.862207 | + | 0.862207i | −0.991594 | − | 0.129387i | \(-0.958699\pi\) |
0.129387 | + | 0.991594i | \(0.458699\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.73463 | 0.216347 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.20717i | 0.0708313i | 0.999373 | + | 0.0354157i | \(0.0112755\pi\) | ||||
−0.999373 | + | 0.0354157i | \(0.988724\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.34035 | − | 10.4299i | −0.171028 | − | 0.334026i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.3487 | − | 38.3487i | 1.22688 | − | 1.22688i | 0.261749 | − | 0.965136i | \(-0.415701\pi\) |
0.965136 | − | 0.261749i | \(-0.0842992\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.95058 | −0.254102 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.30009 | 0.265001 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.9302 | − | 24.9302i | 0.795149 | − | 0.795149i | −0.187177 | − | 0.982326i | \(-0.559934\pi\) |
0.982326 | + | 0.187177i | \(0.0599339\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.82045 | + | 2.94742i | 0.153592 | + | 0.0939126i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.2942i | 0.772510i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.32206 | 0.264359 | 0.132179 | − | 0.991226i | \(-0.457802\pi\) | ||||
0.132179 | + | 0.991226i | \(0.457802\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.9524 | − | 16.9524i | 0.537969 | − | 0.537969i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.89767 | − | 20.3117i | −0.155267 | − | 0.643924i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.3341 | + | 22.3341i | 0.707330 | + | 0.707330i | 0.965973 | − | 0.258643i | \(-0.0832754\pi\) |
−0.258643 | + | 0.965973i | \(0.583275\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 49.7672 | 1.57457 |
(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 | 980.2.m.a.293.6 | 16 | ||
5.2 | odd | 4 | inner | 980.2.m.a.97.3 | 16 | ||
7.2 | even | 3 | 140.2.u.a.73.3 | yes | 16 | ||
7.3 | odd | 6 | 140.2.u.a.33.3 | yes | 16 | ||
7.4 | even | 3 | 980.2.v.a.313.2 | 16 | |||
7.5 | odd | 6 | 980.2.v.a.913.2 | 16 | |||
7.6 | odd | 2 | inner | 980.2.m.a.293.3 | 16 | ||
21.2 | odd | 6 | 1260.2.dq.a.73.2 | 16 | |||
21.17 | even | 6 | 1260.2.dq.a.1153.1 | 16 | |||
28.3 | even | 6 | 560.2.ci.d.33.2 | 16 | |||
28.23 | odd | 6 | 560.2.ci.d.353.2 | 16 | |||
35.2 | odd | 12 | 140.2.u.a.17.3 | ✓ | 16 | ||
35.3 | even | 12 | 700.2.bc.b.257.2 | 16 | |||
35.9 | even | 6 | 700.2.bc.b.493.2 | 16 | |||
35.12 | even | 12 | 980.2.v.a.717.2 | 16 | |||
35.17 | even | 12 | 140.2.u.a.117.3 | yes | 16 | ||
35.23 | odd | 12 | 700.2.bc.b.157.2 | 16 | |||
35.24 | odd | 6 | 700.2.bc.b.593.2 | 16 | |||
35.27 | even | 4 | inner | 980.2.m.a.97.6 | 16 | ||
35.32 | odd | 12 | 980.2.v.a.117.2 | 16 | |||
105.2 | even | 12 | 1260.2.dq.a.577.1 | 16 | |||
105.17 | odd | 12 | 1260.2.dq.a.397.2 | 16 | |||
140.87 | odd | 12 | 560.2.ci.d.257.2 | 16 | |||
140.107 | even | 12 | 560.2.ci.d.17.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.2.u.a.17.3 | ✓ | 16 | 35.2 | odd | 12 | ||
140.2.u.a.33.3 | yes | 16 | 7.3 | odd | 6 | ||
140.2.u.a.73.3 | yes | 16 | 7.2 | even | 3 | ||
140.2.u.a.117.3 | yes | 16 | 35.17 | even | 12 | ||
560.2.ci.d.17.2 | 16 | 140.107 | even | 12 | |||
560.2.ci.d.33.2 | 16 | 28.3 | even | 6 | |||
560.2.ci.d.257.2 | 16 | 140.87 | odd | 12 | |||
560.2.ci.d.353.2 | 16 | 28.23 | odd | 6 | |||
700.2.bc.b.157.2 | 16 | 35.23 | odd | 12 | |||
700.2.bc.b.257.2 | 16 | 35.3 | even | 12 | |||
700.2.bc.b.493.2 | 16 | 35.9 | even | 6 | |||
700.2.bc.b.593.2 | 16 | 35.24 | odd | 6 | |||
980.2.m.a.97.3 | 16 | 5.2 | odd | 4 | inner | ||
980.2.m.a.97.6 | 16 | 35.27 | even | 4 | inner | ||
980.2.m.a.293.3 | 16 | 7.6 | odd | 2 | inner | ||
980.2.m.a.293.6 | 16 | 1.1 | even | 1 | trivial | ||
980.2.v.a.117.2 | 16 | 35.32 | odd | 12 | |||
980.2.v.a.313.2 | 16 | 7.4 | even | 3 | |||
980.2.v.a.717.2 | 16 | 35.12 | even | 12 | |||
980.2.v.a.913.2 | 16 | 7.5 | odd | 6 | |||
1260.2.dq.a.73.2 | 16 | 21.2 | odd | 6 | |||
1260.2.dq.a.397.2 | 16 | 105.17 | odd | 12 | |||
1260.2.dq.a.577.1 | 16 | 105.2 | even | 12 | |||
1260.2.dq.a.1153.1 | 16 | 21.17 | even | 6 |