Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(79,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.ci (of order \(18\), degree \(6\), 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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{18})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 3 x^{16} + 100 x^{15} - 171 x^{14} - 471 x^{13} + 1537 x^{12} + 321 x^{11} - 3936 x^{10} - 1317 x^{9} + 4941 x^{8} + 21078 x^{7} - 14829 x^{6} + \cdots + 1367631 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 127.2 | ||
Root | \(-0.489413 + 1.79677i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.127 |
Dual form | 912.2.ci.f.79.2 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −0.939693 | − | 0.342020i | −0.542532 | − | 0.197465i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.0537040 | − | 0.304570i | −0.0240172 | − | 0.136208i | 0.970441 | − | 0.241336i | \(-0.0775857\pi\) |
−0.994459 | + | 0.105128i | \(0.966475\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.22544 | − | 2.43956i | −1.59707 | − | 0.922067i | −0.992049 | − | 0.125854i | \(-0.959833\pi\) |
−0.605017 | − | 0.796212i | \(-0.706834\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.766044 | + | 0.642788i | 0.255348 | + | 0.214263i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.67322 | + | 0.966032i | −0.504494 | + | 0.291270i | −0.730567 | − | 0.682841i | \(-0.760744\pi\) |
0.226074 | + | 0.974110i | \(0.427411\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.49685 | + | 4.11257i | 0.415153 | + | 1.14062i | 0.954414 | + | 0.298485i | \(0.0964811\pi\) |
−0.539262 | + | 0.842138i | \(0.681297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0537040 | + | 0.304570i | −0.0138663 | + | 0.0786398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.57294 | + | 2.99805i | −0.866564 | + | 0.727134i | −0.963372 | − | 0.268169i | \(-0.913581\pi\) |
0.0968075 | + | 0.995303i | \(0.469137\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.42972 | + | 2.69017i | 0.786832 | + | 0.617167i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.13624 | + | 3.73762i | 0.684383 | + | 0.815616i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.72421 | + | 1.36199i | 1.61061 | + | 0.283994i | 0.905257 | − | 0.424864i | \(-0.139678\pi\) |
0.705352 | + | 0.708858i | \(0.250789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.60858 | − | 1.67739i | 0.921717 | − | 0.335477i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.500000 | − | 0.866025i | −0.0962250 | − | 0.166667i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.51775 | − | 6.57580i | 1.02462 | − | 1.22109i | 0.0496481 | − | 0.998767i | \(-0.484190\pi\) |
0.974972 | − | 0.222328i | \(-0.0713655\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.67069 | − | 2.89373i | 0.300066 | − | 0.519729i | −0.676085 | − | 0.736824i | \(-0.736325\pi\) |
0.976151 | + | 0.217095i | \(0.0696581\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.90271 | − | 0.335499i | 0.331220 | − | 0.0584030i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.516095 | + | 1.41796i | −0.0872359 | + | 0.239679i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.17512i | − | 0.193189i | −0.995324 | − | 0.0965943i | \(-0.969205\pi\) | ||
0.995324 | − | 0.0965943i | \(-0.0307949\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.37651i | − | 0.700802i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.68090 | + | 10.1132i | −0.574860 | + | 1.57942i | 0.221867 | + | 0.975077i | \(0.428785\pi\) |
−0.796727 | + | 0.604339i | \(0.793437\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.64198 | + | 0.465852i | −0.402898 | + | 0.0710418i | −0.371425 | − | 0.928463i | \(-0.621131\pi\) |
−0.0314728 | + | 0.999505i | \(0.510020\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.154634 | − | 0.267835i | 0.0230515 | − | 0.0399265i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.72472 | + | 6.82246i | −0.835036 | + | 0.995157i | 0.164925 | + | 0.986306i | \(0.447262\pi\) |
−0.999961 | + | 0.00885122i | \(0.997183\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.40289 | + | 14.5542i | 1.20041 | + | 2.07918i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.38286 | − | 1.59523i | 0.613722 | − | 0.223377i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.3935 | + | 2.00898i | 1.56501 | + | 0.275954i | 0.887939 | − | 0.459961i | \(-0.152137\pi\) |
0.677074 | + | 0.735915i | \(0.263248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.384083 | + | 0.457733i | 0.0517898 | + | 0.0617207i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.30279 | − | 3.70097i | −0.305012 | − | 0.490205i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.80526 | − | 2.35389i | 0.365213 | − | 0.306450i | −0.441651 | − | 0.897187i | \(-0.645607\pi\) |
0.806865 | + | 0.590737i | \(0.201163\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0154881 | + | 0.0878376i | −0.00198305 | + | 0.0112465i | −0.985783 | − | 0.168022i | \(-0.946262\pi\) |
0.983800 | + | 0.179269i | \(0.0573731\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.66876 | − | 4.58487i | −0.210244 | − | 0.577639i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.17218 | − | 0.676759i | 0.145391 | − | 0.0839417i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.50277 | − | 2.93917i | −0.427931 | − | 0.359077i | 0.403239 | − | 0.915095i | \(-0.367884\pi\) |
−0.831171 | + | 0.556018i | \(0.812329\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.79255 | − | 3.92168i | −0.817728 | − | 0.472115i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.43826 | + | 13.8280i | 0.289368 | + | 1.64109i | 0.689252 | + | 0.724521i | \(0.257939\pi\) |
−0.399885 | + | 0.916566i | \(0.630950\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.0620 | − | 4.02625i | −1.29471 | − | 0.471237i | −0.399443 | − | 0.916758i | \(-0.630796\pi\) |
−0.895272 | + | 0.445521i | \(0.853019\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.90435 | −0.566306 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.42677 | 1.07428 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.56918 | − | 1.66304i | −0.514073 | − | 0.187107i | 0.0719402 | − | 0.997409i | \(-0.477081\pi\) |
−0.586013 | + | 0.810302i | \(0.699303\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.173648 | + | 0.984808i | 0.0192942 | + | 0.109423i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.83589 | + | 5.67875i | 1.07963 | + | 0.623324i | 0.930796 | − | 0.365538i | \(-0.119115\pi\) |
0.148833 | + | 0.988862i | \(0.452448\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.10500 | + | 0.927204i | 0.119854 | + | 0.100569i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.43404 | + | 4.29205i | −0.797013 | + | 0.460156i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.29457 | + | 11.7992i | 0.455224 | + | 1.25072i | 0.929003 | + | 0.370073i | \(0.120667\pi\) |
−0.473779 | + | 0.880644i | \(0.657110\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.70800 | − | 21.0291i | 0.388704 | − | 2.20445i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.55965 | + | 2.14780i | −0.265424 | + | 0.222717i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.635157 | − | 1.18906i | 0.0651657 | − | 0.121995i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0001 | − | 11.9176i | −1.01535 | − | 1.21005i | −0.977537 | − | 0.210764i | \(-0.932405\pi\) |
−0.0378147 | − | 0.999285i | \(-0.512040\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.90271 | − | 0.335499i | −0.191230 | − | 0.0337190i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.72450 | + | 0.627668i | −0.171595 | + | 0.0624553i | −0.426389 | − | 0.904540i | \(-0.640214\pi\) |
0.254794 | + | 0.966995i | \(0.417992\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.82401 | + | 8.35543i | 0.475324 | + | 0.823285i | 0.999601 | − | 0.0282629i | \(-0.00899757\pi\) |
−0.524277 | + | 0.851548i | \(0.675664\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.969941 | − | 1.15593i | 0.0946565 | − | 0.112807i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.55236 | + | 9.61698i | −0.536767 | + | 0.929708i | 0.462308 | + | 0.886719i | \(0.347021\pi\) |
−0.999076 | + | 0.0429890i | \(0.986312\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.1146 | − | 1.78347i | 0.968802 | − | 0.170826i | 0.333211 | − | 0.942852i | \(-0.391868\pi\) |
0.635590 | + | 0.772026i | \(0.280757\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.401915 | + | 1.10425i | −0.0381481 | + | 0.104811i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.00185i | − | 0.470535i | −0.971931 | − | 0.235267i | \(-0.924403\pi\) | ||
0.971931 | − | 0.235267i | \(-0.0755966\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.42571i | − | 0.226199i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.49685 | + | 4.11257i | −0.138384 | + | 0.380208i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 22.4111 | − | 3.95169i | 2.05443 | − | 0.362251i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.63356 | + | 6.29352i | −0.330324 | + | 0.572138i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.91783 | − | 8.24435i | 0.623760 | − | 0.743368i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.53155 | − | 2.65273i | −0.136986 | − | 0.237267i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.78923 | + | 2.10711i | −0.513711 | + | 0.186976i | −0.585851 | − | 0.810419i | \(-0.699240\pi\) |
0.0721394 | + | 0.997395i | \(0.477017\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.64198 | + | 0.465852i | 0.232613 | + | 0.0410160i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.89310 | + | 8.21488i | 0.602253 | + | 0.717737i | 0.977911 | − | 0.209021i | \(-0.0670278\pi\) |
−0.375658 | + | 0.926758i | \(0.622583\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.92925 | − | 19.7342i | −0.687553 | − | 1.71117i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.236914 | + | 0.198794i | −0.0203903 | + | 0.0171095i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.36935 | + | 7.76599i | −0.116992 | + | 0.663494i | 0.868753 | + | 0.495246i | \(0.164922\pi\) |
−0.985745 | + | 0.168248i | \(0.946189\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.10120 | + | 5.77301i | 0.178222 | + | 0.489660i | 0.996349 | − | 0.0853774i | \(-0.0272096\pi\) |
−0.818127 | + | 0.575038i | \(0.804987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.71289 | − | 4.45304i | 0.649543 | − | 0.375014i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.47744 | − | 5.43522i | −0.541671 | − | 0.454516i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.29912 | − | 1.32740i | −0.190931 | − | 0.110234i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.91829 | − | 16.5505i | −0.240697 | − | 1.36506i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.3028 | − | 3.74990i | −0.844036 | − | 0.307204i | −0.116430 | − | 0.993199i | \(-0.537145\pi\) |
−0.727606 | + | 0.685995i | \(0.759367\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.66027 | −0.135110 | −0.0675552 | − | 0.997716i | \(-0.521520\pi\) | ||||
−0.0675552 | + | 0.997716i | \(0.521520\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.66414 | −0.377073 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.971067 | − | 0.353439i | −0.0779980 | − | 0.0283889i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.28210 | + | 12.9424i | 0.182132 | + | 1.03292i | 0.929586 | + | 0.368606i | \(0.120165\pi\) |
−0.747454 | + | 0.664313i | \(0.768724\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.0192 | − | 5.78462i | −0.794578 | − | 0.458750i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −29.3155 | − | 24.5987i | −2.31039 | − | 1.93865i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.53822 | + | 4.35219i | −0.590439 | + | 0.340890i | −0.765271 | − | 0.643708i | \(-0.777395\pi\) |
0.174832 | + | 0.984598i | \(0.444062\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.204366 | − | 0.561492i | −0.0159099 | − | 0.0437121i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.27477 | + | 12.9009i | −0.176027 | + | 0.998300i | 0.760924 | + | 0.648841i | \(0.224746\pi\) |
−0.936951 | + | 0.349459i | \(0.886365\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.71411 | + | 3.95561i | −0.362624 | + | 0.304278i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.898110 | + | 4.26537i | 0.0686802 | + | 0.326181i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.41217 | − | 5.25822i | −0.335451 | − | 0.399775i | 0.571780 | − | 0.820407i | \(-0.306253\pi\) |
−0.907232 | + | 0.420632i | \(0.861808\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −23.5654 | − | 4.15521i | −1.78138 | − | 0.314105i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.44116 | + | 1.25248i | −0.258653 | + | 0.0941420i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.0507409 | − | 0.0878858i | −0.00379255 | − | 0.00656889i | 0.864123 | − | 0.503281i | \(-0.167874\pi\) |
−0.867915 | + | 0.496712i | \(0.834541\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.7409 | − | 13.9923i | 0.872695 | − | 1.04004i | −0.126151 | − | 0.992011i | \(-0.540262\pi\) |
0.998846 | − | 0.0480268i | \(-0.0152933\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0445963 | − | 0.0772431i | 0.00329665 | − | 0.00570997i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.357907 | + | 0.0631087i | −0.0263138 | + | 0.00463984i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.08208 | − | 8.46796i | 0.225384 | − | 0.619238i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.87912i | 0.354904i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.24962i | 0.307492i | 0.988110 | + | 0.153746i | \(0.0491337\pi\) | ||||
−0.988110 | + | 0.153746i | \(0.950866\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.483847 | + | 1.32936i | −0.0348281 | + | 0.0956894i | −0.955888 | − | 0.293732i | \(-0.905103\pi\) |
0.921060 | + | 0.389421i | \(0.127325\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.33296 | + | 0.235036i | −0.0954549 | + | 0.0168313i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.55243 | − | 14.8132i | 0.609335 | − | 1.05540i | −0.382015 | − | 0.924156i | \(-0.624770\pi\) |
0.991350 | − | 0.131243i | \(-0.0418970\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.4265 | − | 18.3846i | 1.09356 | − | 1.30325i | 0.144027 | − | 0.989574i | \(-0.453995\pi\) |
0.949530 | − | 0.313677i | \(-0.101561\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.28627 | + | 3.95994i | 0.161261 | + | 0.279312i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −39.3570 | + | 14.3248i | −2.76232 | + | 1.00540i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.27786 | + | 0.577975i | 0.228936 | + | 0.0403675i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.04162 | + | 6.00837i | 0.350417 | + | 0.417610i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.33746 | − | 1.18802i | −0.576714 | − | 0.0821769i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.76878 | − | 4.00148i | 0.328296 | − | 0.275473i | −0.463709 | − | 0.885988i | \(-0.653482\pi\) |
0.792005 | + | 0.610514i | \(0.209037\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.43826 | − | 13.8280i | 0.167067 | − | 0.947482i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.283770 | + | 0.779651i | 0.0193529 | + | 0.0531718i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.1188 | + | 8.15151i | −0.958449 | + | 0.553361i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.01786 | + | 7.56688i | 0.609371 | + | 0.511323i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.6779 | − | 10.2063i | −1.18914 | − | 0.686551i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.85361 | − | 10.5124i | −0.124127 | − | 0.703960i | −0.981822 | − | 0.189801i | \(-0.939216\pi\) |
0.857695 | − | 0.514158i | \(-0.171896\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.60858 | + | 1.67739i | 0.307239 | + | 0.111826i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.02146 | −0.399658 | −0.199829 | − | 0.979831i | \(-0.564039\pi\) | ||||
−0.199829 | + | 0.979831i | \(0.564039\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.01550 | 0.0671064 | 0.0335532 | − | 0.999437i | \(-0.489318\pi\) | ||||
0.0335532 | + | 0.999437i | \(0.489318\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.85827 | − | 3.22414i | −0.582831 | − | 0.212133i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.117889 | + | 0.668580i | 0.00772315 | + | 0.0438002i | 0.988426 | − | 0.151705i | \(-0.0484764\pi\) |
−0.980703 | + | 0.195505i | \(0.937365\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.38536 | + | 1.37719i | 0.155604 | + | 0.0898378i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.72483 | + | 3.12550i | 0.241954 | + | 0.203023i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.1517 | − | 11.6346i | 1.30350 | − | 0.752578i | 0.322500 | − | 0.946570i | \(-0.395477\pi\) |
0.981003 | + | 0.193992i | \(0.0621435\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.09156 | − | 8.49400i | −0.199145 | − | 0.547147i | 0.799416 | − | 0.600778i | \(-0.205143\pi\) |
−0.998561 | + | 0.0536317i | \(0.982920\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.173648 | − | 0.984808i | 0.0111395 | − | 0.0631754i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.98152 | − | 3.34089i | 0.254370 | − | 0.213442i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.92973 | + | 18.1318i | −0.377300 | + | 1.15370i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.30047 | − | 8.70036i | −0.462648 | − | 0.551363i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.1936 | + | 4.08966i | 1.46397 | + | 0.258137i | 0.848152 | − | 0.529753i | \(-0.177715\pi\) |
0.615816 | + | 0.787890i | \(0.288827\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.2400 | + | 5.18294i | −0.895261 | + | 0.325848i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.721236 | − | 1.24922i | −0.0451656 | − | 0.0782291i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.52214 | + | 8.96454i | −0.469219 | + | 0.559193i | −0.947806 | − | 0.318847i | \(-0.896704\pi\) |
0.478588 | + | 0.878040i | \(0.341149\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.86678 | + | 4.96540i | −0.178133 | + | 0.308535i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.45368 | − | 1.49061i | 0.523270 | − | 0.0922666i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.36698 | − | 6.50322i | 0.145954 | − | 0.401006i | −0.845076 | − | 0.534647i | \(-0.820445\pi\) |
0.991030 | + | 0.133641i | \(0.0426669\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.57800i | − | 0.219795i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 12.5565i | − | 0.768445i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.0460123 | + | 0.126418i | −0.00280542 | + | 0.00770783i | −0.941087 | − | 0.338163i | \(-0.890194\pi\) |
0.938282 | + | 0.345871i | \(0.112417\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0397 | − | 1.94659i | 0.670611 | − | 0.118247i | 0.172033 | − | 0.985091i | \(-0.444967\pi\) |
0.498579 | + | 0.866844i | \(0.333855\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.6768 | + | 18.4927i | −0.646186 | + | 1.11923i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.09075 | + | 7.25867i | −0.367286 | + | 0.437714i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.6972 | − | 23.7242i | −0.822982 | − | 1.42545i | −0.903452 | − | 0.428690i | \(-0.858975\pi\) |
0.0804693 | − | 0.996757i | \(-0.474358\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.13988 | − | 1.14282i | 0.187980 | − | 0.0684190i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.81377 | − | 0.672470i | −0.227510 | − | 0.0401162i | 0.0587307 | − | 0.998274i | \(-0.481295\pi\) |
−0.286241 | + | 0.958158i | \(0.592406\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.7694 | + | 17.6015i | 0.877949 | + | 1.04630i | 0.998563 | + | 0.0535994i | \(0.0170694\pi\) |
−0.120613 | + | 0.992700i | \(0.538486\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.00354 | + | 0.900119i | −0.0594443 | + | 0.0533184i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 40.2252 | − | 33.7529i | 2.37442 | − | 1.99237i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.825554 | − | 4.68195i | 0.0485620 | − | 0.275409i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.32092 | + | 14.6191i | 0.311918 | + | 0.856987i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.37553 | + | 4.25827i | −0.430883 | + | 0.248770i | −0.699723 | − | 0.714414i | \(-0.746693\pi\) |
0.268840 | + | 0.963185i | \(0.413360\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.867579 | − | 0.727985i | −0.0505124 | − | 0.0423849i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.67322 | + | 0.966032i | 0.0970899 | + | 0.0560549i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.96075 | + | 33.8051i | 0.344719 | + | 1.95500i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.3000 | + | 4.47684i | 0.708960 | + | 0.258040i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.83518 | 0.105428 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.0275845 | 0.00157948 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.73075 | − | 3.17773i | −0.498290 | − | 0.181363i | 0.0806347 | − | 0.996744i | \(-0.474305\pi\) |
−0.578925 | + | 0.815381i | \(0.696527\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.67536 | − | 9.50144i | −0.0953080 | − | 0.540518i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.9799 | + | 6.91660i | 0.679318 | + | 0.392204i | 0.799598 | − | 0.600536i | \(-0.205046\pi\) |
−0.120280 | + | 0.992740i | \(0.538379\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.5289 | + | 9.67394i | 0.651655 | + | 0.546803i | 0.907573 | − | 0.419895i | \(-0.137933\pi\) |
−0.255918 | + | 0.966699i | \(0.582378\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.30680 | + | 0.754480i | −0.0736297 | + | 0.0425101i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.66678 | + | 18.3168i | 0.374443 | + | 1.02878i | 0.973623 | + | 0.228161i | \(0.0732712\pi\) |
−0.599180 | + | 0.800614i | \(0.704507\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.87996 | + | 16.3331i | −0.161247 | + | 0.914476i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.50672 | − | 7.13798i | 0.474799 | − | 0.398403i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.3194 | + | 0.670666i | −1.13060 | + | 0.0373168i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.7968 | + | 16.4423i | 0.765306 | + | 0.912057i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.1146 | − | 1.78347i | −0.559338 | − | 0.0986264i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 40.8332 | − | 14.8621i | 2.25121 | − | 0.819373i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.61585 | + | 9.72694i | 0.308675 | + | 0.534641i | 0.978073 | − | 0.208263i | \(-0.0667811\pi\) |
−0.669398 | + | 0.742904i | \(0.733448\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.755353 | − | 0.900194i | 0.0413931 | − | 0.0493304i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.707072 | + | 1.22469i | −0.0386315 | + | 0.0669117i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.3862 | + | 2.18402i | −0.674720 | + | 0.118971i | −0.500502 | − | 0.865736i | \(-0.666851\pi\) |
−0.174219 | + | 0.984707i | \(0.555740\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.71073 | + | 4.70021i | −0.0929144 | + | 0.255280i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.45578i | 0.349600i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 47.8436i | − | 2.58331i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.829642 | + | 2.27942i | −0.0446664 | + | 0.122720i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.60502 | − | 0.459335i | 0.139845 | − | 0.0246584i | −0.103288 | − | 0.994652i | \(-0.532936\pi\) |
0.243132 | + | 0.969993i | \(0.421825\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.38187 | − | 4.12552i | 0.127499 | − | 0.220834i | −0.795208 | − | 0.606336i | \(-0.792639\pi\) |
0.922707 | + | 0.385502i | \(0.125972\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.81317 | − | 3.35260i | 0.150156 | − | 0.178949i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.924355 | − | 1.60103i | −0.0491984 | − | 0.0852142i | 0.840377 | − | 0.542002i | \(-0.182333\pi\) |
−0.889576 | + | 0.456787i | \(0.849000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.08067 | − | 1.48524i | 0.216579 | − | 0.0788285i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −22.4111 | − | 3.95169i | −1.18612 | − | 0.209146i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.12135 | − | 8.48690i | −0.375851 | − | 0.447921i | 0.544649 | − | 0.838664i | \(-0.316663\pi\) |
−0.920500 | + | 0.390743i | \(0.872218\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.52597 | + | 18.4531i | 0.238209 | + | 0.971214i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.56694 | − | 4.67122i | 0.292189 | − | 0.245175i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.632202 | + | 3.58540i | −0.0330910 | + | 0.187668i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.71428 | + | 26.6898i | 0.507081 | + | 1.39319i | 0.884234 | + | 0.467043i | \(0.154681\pi\) |
−0.377153 | + | 0.926151i | \(0.623097\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.32037 | + | 5.38112i | −0.485199 | + | 0.280130i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −43.2414 | − | 36.2838i | −2.24498 | − | 1.88376i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.1406 | − | 9.89614i | −0.887508 | − | 0.512403i | −0.0143814 | − | 0.999897i | \(-0.504578\pi\) |
−0.873127 | + | 0.487494i | \(0.837911\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.531903 | + | 3.01657i | 0.0274674 | + | 0.155775i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 35.3027 | + | 12.8491i | 1.81818 | + | 0.661764i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.4749 | −0.948991 | −0.474496 | − | 0.880258i | \(-0.657370\pi\) | ||||
−0.474496 | + | 0.880258i | \(0.657370\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.16077 | 0.315626 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.81762 | − | 3.20935i | −0.450559 | − | 0.163990i | 0.106766 | − | 0.994284i | \(-0.465950\pi\) |
−0.557326 | + | 0.830294i | \(0.688173\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.506255 | − | 2.87112i | −0.0258011 | − | 0.146326i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.32332 | − | 1.34137i | −0.118101 | − | 0.0681856i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.7806 | + | 18.2761i | 1.10432 | + | 0.926634i | 0.997708 | − | 0.0676671i | \(-0.0215556\pi\) |
0.106611 | + | 0.994301i | \(0.466000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −31.6814 | + | 18.2913i | −1.60220 | + | 0.925029i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.66774 | − | 10.0770i | −0.185013 | − | 0.508319i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.261131 | + | 1.48095i | −0.0131389 | + | 0.0745146i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.2230 | − | 23.6819i | 1.41647 | − | 1.18856i | 0.463274 | − | 0.886215i | \(-0.346675\pi\) |
0.953198 | − | 0.302346i | \(-0.0977698\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.701578 | + | 21.2560i | 0.0351228 | + | 1.06413i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.62124 | − | 5.50738i | −0.230774 | − | 0.275025i | 0.638214 | − | 0.769859i | \(-0.279673\pi\) |
−0.868988 | + | 0.494834i | \(0.835229\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.4015 | + | 2.53937i | 0.717388 | + | 0.126495i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.290618 | − | 0.105776i | 0.0144409 | − | 0.00525606i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.13520 | + | 1.96623i | 0.0562700 | + | 0.0974625i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.20702 | − | 1.43847i | 0.0596834 | − | 0.0711279i | −0.735377 | − | 0.677658i | \(-0.762995\pi\) |
0.795060 | + | 0.606531i | \(0.207439\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.94290 | − | 6.82930i | 0.194489 | − | 0.336864i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.5959 | + | 3.10263i | −0.865837 | + | 0.152670i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.20135 | − | 3.30069i | 0.0589722 | − | 0.162025i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 6.14351i | − | 0.300849i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 39.3106i | − | 1.92045i | −0.279226 | − | 0.960225i | \(-0.590078\pi\) | ||
0.279226 | − | 0.960225i | \(-0.409922\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.70770 | + | 12.9343i | −0.229439 | + | 0.630379i | −0.999975 | − | 0.00701724i | \(-0.997766\pi\) |
0.770536 | + | 0.637396i | \(0.219989\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.77078 | + | 1.54653i | −0.426450 | + | 0.0751946i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.4373 | + | 19.8100i | −0.554790 | + | 0.960924i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.279729 | − | 0.333368i | 0.0135370 | − | 0.0161328i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.22785 | + | 7.32285i | 0.204122 | + | 0.353550i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.7538 | + | 6.46186i | −0.855171 | + | 0.311257i | −0.732147 | − | 0.681147i | \(-0.761482\pi\) |
−0.123024 | + | 0.992404i | \(0.539259\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.8391 | − | 5.08511i | −1.38592 | − | 0.244375i | −0.569574 | − | 0.821940i | \(-0.692892\pi\) |
−0.816345 | + | 0.577565i | \(0.804003\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.70647 | + | 2.03369i | 0.0818189 | + | 0.0975080i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.8279 | + | 25.4507i | 1.09201 | + | 1.21747i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.42847 | + | 7.07233i | −0.402269 | + | 0.337544i | −0.821370 | − | 0.570396i | \(-0.806790\pi\) |
0.419101 | + | 0.907940i | \(0.362345\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.91829 | + | 16.5505i | −0.138966 | + | 0.788118i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.70401 | − | 4.68173i | −0.0809600 | − | 0.222436i | 0.892608 | − | 0.450834i | \(-0.148873\pi\) |
−0.973568 | + | 0.228398i | \(0.926651\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.36306 | − | 1.94167i | 0.159425 | − | 0.0920438i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.39890 | + | 7.04751i | 0.397254 | + | 0.333336i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.3367 | + | 14.0508i | 1.14852 | + | 0.663099i | 0.948527 | − | 0.316697i | \(-0.102574\pi\) |
0.199995 | + | 0.979797i | \(0.435907\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.61072 | − | 20.4774i | −0.170022 | − | 0.964245i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.56014 | + | 0.567844i | 0.0733017 | + | 0.0266797i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.60398 | −0.309599 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.8941 | 0.930607 | 0.465304 | − | 0.885151i | \(-0.345945\pi\) | ||||
0.465304 | + | 0.885151i | \(0.345945\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.38286 | + | 1.59523i | 0.204574 | + | 0.0744589i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.56088 | + | 8.85219i | 0.0726974 | + | 0.412287i | 0.999339 | + | 0.0363424i | \(0.0115707\pi\) |
−0.926642 | + | 0.375945i | \(0.877318\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.60293 | − | 3.23485i | −0.260390 | − | 0.150336i | 0.364122 | − | 0.931351i | \(-0.381369\pi\) |
−0.624513 | + | 0.781015i | \(0.714702\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.791621 | + | 0.664249i | 0.0367105 | + | 0.0308038i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.56688 | + | 1.48199i | −0.118781 | + | 0.0685781i | −0.558213 | − | 0.829697i | \(-0.688513\pi\) |
0.439432 | + | 0.898276i | \(0.355180\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.63046 | + | 20.9645i | 0.352342 | + | 0.968051i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.28210 | − | 12.9424i | 0.105154 | − | 0.596356i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.97058 | − | 3.33171i | 0.182567 | − | 0.153192i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20.3186 | + | 6.64491i | 0.932282 | + | 0.304889i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.43656 | + | 8.86255i | 0.340497 | + | 0.405788i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −23.4427 | − | 4.13358i | −1.07112 | − | 0.188868i | −0.389837 | − | 0.920884i | \(-0.627469\pi\) |
−0.681288 | + | 0.732016i | \(0.738580\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.83277 | − | 1.75898i | 0.220355 | − | 0.0802028i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 19.1344 | + | 33.1417i | 0.870643 | + | 1.50800i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.09271 | + | 3.68574i | −0.140433 | + | 0.167361i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.96250 | − | 3.39914i | 0.0889292 | − | 0.154030i | −0.818130 | − | 0.575034i | \(-0.804989\pi\) |
0.907059 | + | 0.421004i | \(0.138322\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.57215 | − | 1.51150i | 0.387646 | − | 0.0683525i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0457 | − | 33.0952i | 0.543613 | − | 1.49356i | −0.298578 | − | 0.954385i | \(-0.596512\pi\) |
0.842191 | − | 0.539179i | \(-0.181265\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 40.0374i | 1.80319i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.597528i | 0.0268569i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23.4316 | − | 64.3778i | 1.05105 | − | 2.88774i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 42.8558 | − | 7.55664i | 1.91849 | − | 0.338281i | 0.919937 | − | 0.392066i | \(-0.128240\pi\) |
0.998553 | + | 0.0537847i | \(0.0171285\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.54995 | − | 11.3448i | 0.292630 | − | 0.506850i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.5162 | + | 20.8750i | −0.781008 | + | 0.930769i | −0.998979 | − | 0.0451861i | \(-0.985612\pi\) |
0.217970 | + | 0.975955i | \(0.430056\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.283782 | + | 0.491525i | 0.0126281 | + | 0.0218726i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.78271 | − | 2.10474i | 0.256819 | − | 0.0934746i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.8085 | + | 5.25604i | 1.32124 | + | 0.232970i | 0.789401 | − | 0.613877i | \(-0.210391\pi\) |
0.531836 | + | 0.846847i | \(0.321502\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.9197 | + | 43.9992i | 1.63323 | + | 1.94641i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.614895 | − | 4.31531i | 0.0271483 | − | 0.190526i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.28575 | − | 1.91797i | 0.100722 | − | 0.0845159i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.98799 | − | 16.9457i | 0.131411 | − | 0.745272i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.34767 | + | 6.45016i | 0.103051 | + | 0.283131i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.1911 | + | 18.5856i | −1.41032 | + | 0.814248i | −0.995418 | − | 0.0956187i | \(-0.969517\pi\) |
−0.414901 | + | 0.909867i | \(0.636184\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.31904 | − | 1.94591i | −0.101405 | − | 0.0850886i | 0.590676 | − | 0.806909i | \(-0.298861\pi\) |
−0.692080 | + | 0.721820i | \(0.743306\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.7230 | + | 11.9645i | 0.904428 | + | 0.522172i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.70625 | + | 15.3479i | 0.117886 | + | 0.668566i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 36.1955 | + | 13.1741i | 1.57372 | + | 0.572786i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.66200 | 0.158917 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −47.1010 | −2.04017 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.22723 | + | 1.17462i | 0.139525 | + | 0.0507831i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.0176221 | + | 0.0999401i | 0.000760451 | + | 0.00431273i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −28.1197 | − | 16.2349i | −1.21120 | − | 0.699288i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.33536 | + | 6.15510i | 0.315372 | + | 0.264628i | 0.786708 | − | 0.617325i | \(-0.211784\pi\) |
−0.471336 | + | 0.881954i | \(0.656228\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.8185 | + | 9.13281i | −0.678837 | + | 0.391926i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.08639 | − | 2.98482i | −0.0465357 | − | 0.127856i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.835008 | − | 4.73557i | 0.0357024 | − | 0.202478i | −0.961739 | − | 0.273967i | \(-0.911664\pi\) |
0.997441 | + | 0.0714891i | \(0.0227751\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.0683255 | + | 0.0573319i | −0.00291606 | + | 0.00244687i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.6143 | − | 7.70946i | 1.55982 | − | 0.328434i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.2497 | + | 18.1739i | 0.648483 | + | 0.772831i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.357907 | + | 0.0631087i | 0.0151923 | + | 0.00267881i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.1305 | + | 5.14308i | −0.598728 | + | 0.217919i | −0.623564 | − | 0.781772i | \(-0.714316\pi\) |
0.0248360 | + | 0.999692i | \(0.492094\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.87051 | − | 10.1680i | −0.248296 | − | 0.430062i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.79242 | + | 6.90314i | −0.244556 | + | 0.291451i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.563769 | + | 0.976476i | −0.0237600 | + | 0.0411536i | −0.877661 | − | 0.479282i | \(-0.840897\pi\) |
0.853901 | + | 0.520436i | \(0.174230\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.52342 | + | 0.268620i | −0.0640906 | + | 0.0113009i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.66876 | − | 4.58487i | 0.0700812 | − | 0.192546i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.03677i | 0.336919i | 0.985709 | + | 0.168460i | \(0.0538792\pi\) | ||||
−0.985709 | + | 0.168460i | \(0.946121\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.88393i | 0.371781i | 0.982570 | + | 0.185890i | \(0.0595169\pi\) | ||||
−0.982570 | + | 0.185890i | \(0.940483\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.45346 | − | 3.99334i | 0.0607190 | − | 0.166824i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 37.8822 | − | 6.67966i | 1.57980 | − | 0.278561i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.0755 | + | 17.4513i | −0.419450 | + | 0.726508i | −0.995884 | − | 0.0906351i | \(-0.971110\pi\) |
0.576434 | + | 0.817143i | \(0.304444\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.909335 | − | 1.08370i | 0.0377907 | − | 0.0450372i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.7073 | − | 47.9905i | −1.14949 | − | 1.99098i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.0045 | + | 7.64501i | −0.869917 | + | 0.316624i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.33296 | + | 0.235036i | 0.0551109 | + | 0.00971754i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.9114 | + | 17.7707i | 0.615458 | + | 0.733474i | 0.980282 | − | 0.197602i | \(-0.0633155\pi\) |
−0.364825 | + | 0.931076i | \(0.618871\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.5146 | − | 5.43023i | 0.556861 | − | 0.223749i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.1031 | + | 10.9948i | −0.538989 | + | 0.452265i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.99379 | − | 16.9786i | 0.122940 | − | 0.697229i | −0.859570 | − | 0.511019i | \(-0.829268\pi\) |
0.982510 | − | 0.186211i | \(-0.0596207\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.40714 | − | 6.61355i | −0.0986829 | − | 0.271129i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.7841 | + | 11.9997i | −0.850636 | + | 0.491115i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.4281 | − | 19.6585i | −0.957246 | − | 0.803225i | 0.0232565 | − | 0.999730i | \(-0.492597\pi\) |
−0.980503 | + | 0.196504i | \(0.937041\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.6795 | + | 15.4034i | 1.08828 | + | 0.628318i | 0.933118 | − | 0.359571i | \(-0.117077\pi\) |
0.155161 | + | 0.987889i | \(0.450410\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.794013 | − | 4.50307i | −0.0323347 | − | 0.183379i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.11196 | + | 0.768689i | 0.0858632 | + | 0.0312517i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.8497 | −1.08979 | −0.544897 | − | 0.838503i | \(-0.683431\pi\) | ||||
−0.544897 | + | 0.838503i | \(0.683431\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 41.8828 | 1.69718 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.6269 | − | 13.3311i | −1.48177 | − | 0.539319i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.87921 | − | 27.6714i | −0.197069 | − | 1.11764i | −0.909441 | − | 0.415833i | \(-0.863490\pi\) |
0.712372 | − | 0.701802i | \(-0.247621\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.88250 | − | 1.66421i | −0.116234 | − | 0.0671075i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.01928 | − | 3.37258i | −0.161810 | − | 0.135775i | 0.558287 | − | 0.829648i | \(-0.311459\pi\) |
−0.720098 | + | 0.693873i | \(0.755903\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.7817 | + | 14.3077i | −0.996062 | + | 0.575077i | −0.907081 | − | 0.420956i | \(-0.861695\pi\) |
−0.0889816 | + | 0.996033i | \(0.528361\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.68259 | − | 7.37035i | −0.107649 | − | 0.295762i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.6385 | − | 60.3338i | 0.426222 | − | 2.41722i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.0591 | − | 15.1534i | 0.722363 | − | 0.606134i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.42832 | + | 3.96795i | 0.296659 | + | 0.158465i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.52307 | + | 4.19863i | 0.140474 | + | 0.167410i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.25046 | − | 0.396817i | −0.0895893 | − | 0.0157970i | 0.128674 | − | 0.991687i | \(-0.458928\pi\) |
−0.218263 | + | 0.975890i | \(0.570039\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.84977 | + | 2.12914i | −0.232508 | + | 0.0846258i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.952668 | + | 1.65007i | 0.0378055 | + | 0.0654810i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −47.2775 | + | 56.3431i | −1.87320 | + | 2.23239i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.02068 | + | 12.1602i | −0.277734 | + | 0.481049i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.3186 | + | 3.40639i | −0.763039 | + | 0.134544i | −0.541607 | − | 0.840632i | \(-0.682184\pi\) |
−0.221432 | + | 0.975176i | \(0.571073\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.4853 | + | 34.3032i | −0.492374 | + | 1.35279i | 0.406128 | + | 0.913816i | \(0.366879\pi\) |
−0.898502 | + | 0.438970i | \(0.855344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 0.829687i | − | 0.0326689i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 33.1703i | − | 1.30406i | −0.758193 | − | 0.652030i | \(-0.773918\pi\) | ||
0.758193 | − | 0.652030i | \(-0.226082\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.41987 | + | 6.64853i | −0.0949882 | + | 0.260978i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.0554 | − | 2.83099i | 0.629259 | − | 0.110955i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.3118 | + | 19.5927i | −0.442666 | + | 0.766720i | −0.997886 | − | 0.0649835i | \(-0.979301\pi\) |
0.555220 | + | 0.831703i | \(0.312634\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.13182 | − | 2.54061i | 0.0832972 | − | 0.0992697i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.88599 | − | 10.1948i | −0.229634 | − | 0.397738i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.1922 | + | 14.2648i | −1.52671 | + | 0.555678i | −0.962814 | − | 0.270166i | \(-0.912922\pi\) |
−0.563899 | + | 0.825844i | \(0.690699\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.4769 | − | 4.13960i | −0.913144 | − | 0.161012i | −0.302713 | − | 0.953082i | \(-0.597892\pi\) |
−0.610431 | + | 0.792070i | \(0.709004\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.1210 | + | 15.6370i | 0.509577 | + | 0.607290i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.58461 | + | 3.47482i | −0.216562 | + | 0.134748i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 51.5764 | − | 43.2777i | 1.99705 | − | 1.67572i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.85361 | + | 10.5124i | −0.0716648 | + | 0.406431i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0589389 | − | 0.161933i | −0.00227531 | − | 0.00625137i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.3177 | − | 18.0813i | 1.20721 | − | 0.696982i | 0.245059 | − | 0.969508i | \(-0.421193\pi\) |
0.962148 | + | 0.272527i | \(0.0878593\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.75695 | − | 3.15246i | −0.144605 | − | 0.121338i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.1741 | − | 7.60605i | −0.506320 | − | 0.292324i | 0.225000 | − | 0.974359i | \(-0.427762\pi\) |
−0.731320 | + | 0.682035i | \(0.761095\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.1809 | + | 74.7528i | 0.505838 | + | 2.86875i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.65832 | + | 2.05946i | 0.216827 | + | 0.0789186i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.959626 | −0.0367191 | −0.0183595 | − | 0.999831i | \(-0.505844\pi\) | ||||
−0.0183595 | + | 0.999831i | \(0.505844\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.43883 | 0.0931830 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.954261 | − | 0.347323i | −0.0364073 | − | 0.0132512i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.79230 | + | 49.8636i | 0.334960 | + | 1.89965i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.625152 | + | 0.360932i | 0.0237819 | + | 0.0137305i | 0.511844 | − | 0.859079i | \(-0.328963\pi\) |
−0.488062 | + | 0.872809i | \(0.662296\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.22132 | + | 6.05941i | 0.274315 | + | 0.230178i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.64545 | − | 0.949998i | 0.0624153 | − | 0.0360355i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.1682 | − | 47.1693i | −0.650293 | − | 1.78667i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.117889 | − | 0.668580i | 0.00445896 | − | 0.0252880i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.66025 | − | 5.58862i | 0.251554 | − | 0.211079i | −0.508287 | − | 0.861188i | \(-0.669721\pi\) |
0.759841 | + | 0.650109i | \(0.225277\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.16127 | − | 4.03033i | 0.119230 | − | 0.152007i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.77048 | − | 2.10997i | −0.0666801 | − | 0.0794662i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.81802 | + | 1.55485i | 0.331636 | + | 0.0584763i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.7859 | + | 7.92940i | −0.818185 | + | 0.297795i | −0.717001 | − | 0.697073i | \(-0.754486\pi\) |
−0.101185 | + | 0.994868i | \(0.532263\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.43121 | − | 4.21098i | −0.0911774 | − | 0.157924i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.8460 | − | 20.0763i | 0.630888 | − | 0.751863i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.30754 | + | 2.26473i | −0.0488993 | + | 0.0846961i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.9156 | + | 4.04064i | −0.855800 | + | 0.150901i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.209863 | + | 0.576593i | −0.00782656 | + | 0.0215033i | −0.943544 | − | 0.331246i | \(-0.892531\pi\) |
0.935718 | + | 0.352749i | \(0.114753\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 47.0738i | − | 1.75312i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.03912i | 0.336169i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.3988 | − | 39.5605i | 0.534760 | − | 1.46924i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.7510 | − | 2.07202i | 0.435821 | − | 0.0768470i | 0.0485666 | − | 0.998820i | \(-0.484535\pi\) |
0.387254 | + | 0.921973i | \(0.373424\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.500000 | + | 0.866025i | −0.0185185 | + | 0.0320750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.04298 | − | 9.58525i | 0.297480 | − | 0.354523i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.25030 | − | 12.5579i | −0.267796 | − | 0.463836i | 0.700496 | − | 0.713656i | \(-0.252962\pi\) |
−0.968292 | + | 0.249820i | \(0.919629\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.88406 | + | 1.77765i | −0.180151 | + | 0.0655697i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.70023 | + | 1.53408i | 0.320477 | + | 0.0565087i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.4373 | + | 16.0140i | 0.494300 | + | 0.589084i | 0.954306 | − | 0.298832i | \(-0.0965970\pi\) |
−0.460005 | + | 0.887916i | \(0.652153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.7736 | − | 15.0102i | 0.432512 | − | 0.551414i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.1026 | − | 17.7072i | 0.774179 | − | 0.649613i | −0.167597 | − | 0.985856i | \(-0.553601\pi\) |
0.941775 | + | 0.336242i | \(0.109156\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.588810 | + | 3.33931i | −0.0215723 | + | 0.122343i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.88450 | + | 10.6726i | 0.142126 | + | 0.390489i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 46.9224 | − | 27.0906i | 1.71451 | − | 0.989870i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.44207 | + | 7.08374i | 0.308055 | + | 0.258489i | 0.783688 | − | 0.621155i | \(-0.213336\pi\) |
−0.475632 | + | 0.879644i | \(0.657781\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.3961 | − | 11.7757i | −0.743276 | − | 0.429130i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.0891629 | + | 0.505668i | 0.00324497 | + | 0.0184031i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.41383 | + | 1.60650i | 0.160423 | + | 0.0583893i | 0.420983 | − | 0.907068i | \(-0.361685\pi\) |
−0.260560 | + | 0.965458i | \(0.583907\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.1539 | 0.550051 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.2111 | −0.623903 | −0.311951 | − | 0.950098i | \(-0.600983\pi\) | ||||
−0.311951 | + | 0.950098i | \(0.600983\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −47.0895 | − | 17.1392i | −1.70475 | − | 0.620479i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.250483 | + | 1.42056i | 0.00905622 | + | 0.0513604i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.8796 | + | 8.01339i | 0.501163 | + | 0.289347i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.4711 | − | 28.0856i | −1.20700 | − | 1.01279i | −0.999402 | − | 0.0345770i | \(-0.988992\pi\) |
−0.207596 | − | 0.978215i | \(-0.566564\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.1346 | − | 5.85119i | 0.364987 | − | 0.210725i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.71914 | + | 10.2183i | 0.133768 | + | 0.367525i | 0.988434 | − | 0.151654i | \(-0.0484599\pi\) |
−0.854665 | + | 0.519179i | \(0.826238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.84563 | − | 16.1384i | 0.102218 | − | 0.579708i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.39215 | − | 3.68546i | 0.157568 | − | 0.132215i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −39.8307 | + | 24.7832i | −1.42708 | + | 0.887950i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.4381 | − | 20.7819i | −0.623983 | − | 0.743634i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.45368 | − | 1.49061i | −0.302110 | − | 0.0532701i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.81933 | − | 1.39012i | 0.136318 | − | 0.0496156i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.3719 | + | 28.3569i | 0.583594 | + | 1.01082i | 0.995049 | + | 0.0993850i | \(0.0316875\pi\) |
−0.411455 | + | 0.911430i | \(0.634979\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.44846 | + | 5.30147i | −0.158369 | + | 0.188737i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.2023 | + | 21.1350i | −0.433864 | + | 0.751475i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.384422 | + | 0.0677840i | −0.0136512 | + | 0.00240708i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.22375 | + | 3.36222i | −0.0434019 | + | 0.119246i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.9518i | 1.06095i | 0.847701 | + | 0.530474i | \(0.177986\pi\) | ||||
−0.847701 | + | 0.530474i | \(0.822014\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 41.5392i | − | 1.46955i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.29457 | + | 11.7992i | −0.151741 | + | 0.416906i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.3987 | − | 3.94949i | 0.790433 | − | 0.139375i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.91766 | + | 10.2497i | −0.208570 | + | 0.361254i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.0864749 | − | 0.103057i | 0.00304406 | − | 0.00362777i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.12900 | + | 10.6157i | 0.215484 | + | 0.373230i | 0.953422 | − | 0.301639i | \(-0.0975337\pi\) |
−0.737938 | + | 0.674868i | \(0.764200\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.4324 | − | 6.34486i | 0.612133 | − | 0.222798i | −0.0173033 | − | 0.999850i | \(-0.505508\pi\) |
0.629436 | + | 0.777052i | \(0.283286\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.0397 | − | 1.94659i | −0.387178 | − | 0.0682699i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.73038 | + | 2.06219i | 0.0606127 | + | 0.0722353i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.3145 | − | 5.50963i | −0.360858 | − | 0.192758i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.3577 | − | 13.7258i | 0.571585 | − | 0.479617i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.28063 | + | 29.9479i | −0.184295 | + | 1.04519i | 0.742562 | + | 0.669777i | \(0.233610\pi\) |
−0.926857 | + | 0.375413i | \(0.877501\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.26735 | − | 3.48202i | −0.0441770 | − | 0.121375i | 0.915642 | − | 0.401994i | \(-0.131683\pi\) |
−0.959819 | + | 0.280618i | \(0.909460\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.20605 | − | 4.73776i | 0.285698 | − | 0.164948i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.7645 | + | 9.03246i | 0.374317 | + | 0.314089i | 0.810467 | − | 0.585785i | \(-0.199214\pi\) |
−0.436149 | + | 0.899874i | \(0.643658\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.3753 | + | 7.14490i | 0.429813 | + | 0.248153i | 0.699267 | − | 0.714861i | \(-0.253510\pi\) |
−0.269454 | + | 0.963013i | \(0.586843\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.75697 | + | 26.9781i | 0.165018 | + | 0.935861i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −73.6573 | − | 26.8091i | −2.55208 | − | 0.928879i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.05139 | 0.140204 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.34139 | −0.115495 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.4254 | − | 11.8019i | −1.11945 | − | 0.407447i | −0.284999 | − | 0.958528i | \(-0.591993\pi\) |
−0.834452 | + | 0.551081i | \(0.814215\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.75975 | − | 44.0077i | −0.267578 | − | 1.51751i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.35377 | + | 1.93630i | 0.115510 | + | 0.0666897i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.45793 | + | 1.22335i | 0.0501543 | + | 0.0420844i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.7068 | − | 17.7286i | 1.05510 | − | 0.609161i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.85863 | − | 21.5914i | −0.269707 | − | 0.741015i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.60050 | − | 9.07687i | 0.0548644 | − | 0.311151i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.3538 | + | 17.0789i | −0.696902 | + | 0.584770i | −0.920890 | − | 0.389821i | \(-0.872537\pi\) |
0.223988 | + | 0.974592i | \(0.428092\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.25087 | − | 0.502605i | 0.0427790 | − | 0.0171887i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.2820 | + | 13.4453i | 0.385384 | + | 0.459283i | 0.923506 | − | 0.383584i | \(-0.125310\pi\) |
−0.538122 | + | 0.842867i | \(0.680866\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.34593 | − | 1.47161i | −0.284759 | − | 0.0502107i | 0.0294441 | − | 0.999566i | \(-0.490626\pi\) |
−0.314203 | + | 0.949356i | \(0.601737\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −49.3435 | + | 17.9596i | −1.68162 | + | 0.612060i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.29230 | − | 5.70244i | −0.112071 | − | 0.194113i | 0.804534 | − | 0.593907i | \(-0.202415\pi\) |
−0.916605 | + | 0.399793i | \(0.869082\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.36455 | + | 1.62620i | −0.0463960 | + | 0.0552926i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.37709 | + | 4.11723i | −0.0807301 | + | 0.139829i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.25178 | − | 1.63134i | 0.313845 | − | 0.0553394i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.84443 | − | 18.8049i | 0.231915 | − | 0.637180i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 15.5573i | − | 0.526536i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.9453i | 0.505242i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.1004 | + | 38.7406i | −0.476138 | + | 1.30818i | 0.436609 | + | 0.899651i | \(0.356179\pi\) |
−0.912747 | + | 0.408526i | \(0.866043\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.38714 | − | 1.47888i | 0.282891 | − | 0.0498814i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.8429 | − | 34.3689i | 0.668525 | − | 1.15792i | −0.309792 | − | 0.950804i | \(-0.600259\pi\) |
0.978317 | − | 0.207114i | \(-0.0664072\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.92126 | − | 2.28967i | 0.0646557 | − | 0.0770536i | −0.732747 | − | 0.680501i | \(-0.761762\pi\) |
0.797403 | + | 0.603447i | \(0.206207\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.566272 | + | 0.980811i | 0.0190350 | + | 0.0329696i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.6929 | − | 5.71174i | 0.526915 | − | 0.191781i | −0.0648453 | − | 0.997895i | \(-0.520655\pi\) |
0.591760 | + | 0.806114i | \(0.298433\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.6025 | + | 5.21971i | 0.992835 | + | 0.175064i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.24191 | − | 1.48005i | −0.0416055 | − | 0.0495834i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −37.9878 | + | 7.99865i | −1.27121 | + | 0.267664i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.0240424 | + | 0.0201740i | −0.000803650 | + | 0.000674342i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.96075 | − | 33.8051i | 0.199024 | − | 1.12872i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.81009 | − | 26.9530i | −0.327185 | − | 0.898933i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −46.7311 | + | 26.9802i | −1.55684 | + | 0.898842i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.0271 | − | 8.41370i | −0.333679 | − | 0.279990i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.89217 | − | 2.82450i | −0.162621 | − | 0.0938894i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.35444 | − | 36.0378i | −0.210996 | − | 1.19662i | −0.887722 | − | 0.460380i | \(-0.847713\pi\) |
0.676726 | − | 0.736235i | \(-0.263398\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.72450 | − | 0.627668i | −0.0571982 | − | 0.0208184i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.5093 | −1.30900 | −0.654500 | − | 0.756062i | \(-0.727121\pi\) | ||||
−0.654500 | + | 0.756062i | \(0.727121\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.9434 | −0.726222 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0259210 | − | 0.00943446i | −0.000856921 | − | 0.000311894i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.08570 | − | 51.5276i | −0.300036 | − | 1.70159i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.6452 | − | 6.14598i | −0.351151 | − | 0.202737i | 0.314041 | − | 0.949409i | \(-0.398317\pi\) |
−0.665192 | + | 0.746672i | \(0.731650\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.11737 | + | 5.97218i | 0.234525 | + | 0.196790i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −53.2191 | + | 30.7261i | −1.75173 | + | 1.01136i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.97113 | − | 5.41564i | −0.0648104 | − | 0.178065i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.67536 | + | 9.50144i | −0.0550261 | + | 0.312068i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.0512 | + | 11.7903i | −0.461003 | + | 0.386828i | −0.843500 | − | 0.537129i | \(-0.819509\pi\) |
0.382497 | + | 0.923957i | \(0.375064\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.3338 | + | 72.5222i | −0.338677 | + | 2.37682i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.89181 | − | 10.5968i | −0.291105 | − | 0.346925i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.74461 | − | 0.483949i | −0.0897584 | − | 0.0158268i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.4279 | − | 8.16308i | 0.732686 | − | 0.266676i | 0.0513849 | − | 0.998679i | \(-0.483636\pi\) |
0.681302 | + | 0.732003i | \(0.261414\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.52499 | − | 13.0337i | −0.245569 | − | 0.425337i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.40953 | + | 10.0221i | −0.274143 | + | 0.326711i | −0.885496 | − | 0.464647i | \(-0.846181\pi\) |
0.611353 | + | 0.791358i | \(0.290626\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −42.2061 | + | 73.1031i | −1.37442 | + | 2.38056i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.48604 | − | 0.262028i | 0.0483407 | − | 0.00852377i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.00032 | − | 2.74836i | 0.0325061 | − | 0.0893098i | −0.922378 | − | 0.386289i | \(-0.873757\pi\) |
0.954884 | + | 0.296979i | \(0.0959791\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 51.5202i | − | 1.67242i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 19.4924i | − | 0.632083i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.8554 | − | 35.3200i | 0.416429 | − | 1.14413i | −0.537282 | − | 0.843403i | \(-0.680549\pi\) |
0.953711 | − | 0.300726i | \(-0.0972289\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.29431 | − | 0.228222i | 0.0418829 | − | 0.00738508i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.29251 | − | 14.3630i | 0.268059 | − | 0.464291i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.7317 | − | 29.4741i | 0.798629 | − | 0.951769i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.91756 | + | 17.1777i | 0.319921 | + | 0.554120i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.4350 | + | 3.79804i | −0.336264 | + | 0.122390i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.430868 | + | 0.0759737i | 0.0138701 | + | 0.00244568i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.7153 | − | 34.2216i | −0.923423 | − | 1.10049i | −0.994678 | − | 0.103035i | \(-0.967145\pi\) |
0.0712544 | − | 0.997458i | \(-0.477300\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.3234 | + | 6.31944i | 0.620757 | + | 0.203010i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.13072 | − | 2.62699i | 0.100470 | − | 0.0843040i | −0.591169 | − | 0.806548i | \(-0.701333\pi\) |
0.691639 | + | 0.722244i | \(0.256889\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.20509 | − | 29.5195i | 0.166867 | − | 0.946352i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.34110 | − | 20.1695i | −0.235103 | − | 0.645941i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.2562 | − | 22.6646i | 1.25592 | − | 0.725104i | 0.283639 | − | 0.958931i | \(-0.408458\pi\) |
0.972278 | + | 0.233827i | \(0.0751251\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.5842 | − | 15.5940i | −0.593953 | − | 0.498386i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.89462 | + | 5.13531i | 0.283983 | + | 0.163958i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.11745 | − | 40.3651i | −0.227011 | − | 1.28745i | −0.858802 | − | 0.512307i | \(-0.828791\pi\) |
0.631791 | − | 0.775139i | \(-0.282320\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.97097 | − | 1.80929i | −0.158388 | − | 0.0576487i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −43.4538 | −1.38315 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.0417 | −0.669087 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.1089 | − | 15.6904i | −1.36940 | − | 0.498421i | −0.450452 | − | 0.892801i | \(-0.648737\pi\) |
−0.918948 | + | 0.394380i | \(0.870959\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.95036 | − | 11.0611i | −0.0618929 | − | 0.351012i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.42788 | − | 3.71114i | −0.203777 | − | 0.117651i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.05855 | − | 5.92283i | −0.223547 | − | 0.187578i | 0.524135 | − | 0.851635i | \(-0.324389\pi\) |
−0.747682 | + | 0.664057i | \(0.768833\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.01768 | + | 0.587560i | −0.0321981 | + | 0.0185896i |
(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 | 912.2.ci.f.127.2 | yes | 18 | |
4.3 | odd | 2 | 912.2.ci.e.127.2 | yes | 18 | ||
19.3 | odd | 18 | 912.2.ci.e.79.2 | ✓ | 18 | ||
76.3 | even | 18 | inner | 912.2.ci.f.79.2 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.ci.e.79.2 | ✓ | 18 | 19.3 | odd | 18 | ||
912.2.ci.e.127.2 | yes | 18 | 4.3 | odd | 2 | ||
912.2.ci.f.79.2 | yes | 18 | 76.3 | even | 18 | inner | |
912.2.ci.f.127.2 | yes | 18 | 1.1 | even | 1 | trivial |