Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(263,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.263");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.g (of order \(3\), degree \(2\), not 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.1485512441856.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 24x^{6} + 455x^{4} + 2904x^{2} + 14641 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 373.2 | ||
Root | \(-1.34203 + 2.32446i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.373 |
Dual form | 637.2.g.h.263.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | 0.633316 | − | 0.773893i | \(-0.281693\pi\) |
−0.986869 | + | 0.161521i | \(0.948360\pi\) | |||||||
\(3\) | −1.41421 | −0.816497 | −0.408248 | − | 0.912871i | \(-0.633860\pi\) | ||||
−0.408248 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 2.04914 | − | 3.54921i | 0.916401 | − | 1.58725i | 0.111565 | − | 0.993757i | \(-0.464414\pi\) |
0.804836 | − | 0.593497i | \(-0.202253\pi\) | |||||||
\(6\) | 0.707107 | + | 1.22474i | 0.288675 | + | 0.500000i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −4.09827 | −1.29599 | ||||||||
\(11\) | −3.79583 | −1.14449 | −0.572243 | − | 0.820084i | \(-0.693927\pi\) | ||||
−0.572243 | + | 0.820084i | \(0.693927\pi\) | |||||||
\(12\) | −0.707107 | + | 1.22474i | −0.204124 | + | 0.353553i | ||||
\(13\) | 0.634922 | − | 3.54921i | 0.176096 | − | 0.984373i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.89792 | + | 5.01934i | −0.748239 | + | 1.29599i | ||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | −0.634922 | + | 1.09972i | −0.153991 | + | 0.266721i | −0.932691 | − | 0.360676i | \(-0.882546\pi\) |
0.778700 | + | 0.627396i | \(0.215879\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | 2.82843 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(20\) | −2.04914 | − | 3.54921i | −0.458201 | − | 0.793627i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.89792 | + | 3.28729i | 0.404637 | + | 0.700852i | ||||
\(23\) | 3.89792 | + | 6.75139i | 0.812772 | + | 1.40776i | 0.910917 | + | 0.412590i | \(0.135376\pi\) |
−0.0981454 | + | 0.995172i | \(0.531291\pi\) | |||||||
\(24\) | 4.24264 | 0.866025 | ||||||||
\(25\) | −5.89792 | − | 10.2155i | −1.17958 | − | 2.04310i | ||||
\(26\) | −3.39116 | + | 1.22474i | −0.665062 | + | 0.240192i | ||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.397916 | + | 0.689210i | −0.0738911 | + | 0.127983i | −0.900604 | − | 0.434642i | \(-0.856875\pi\) |
0.826712 | + | 0.562625i | \(0.190208\pi\) | |||||||
\(30\) | 5.79583 | 1.05817 | ||||||||
\(31\) | −0.707107 | − | 1.22474i | −0.127000 | − | 0.219971i | 0.795513 | − | 0.605937i | \(-0.207202\pi\) |
−0.922513 | + | 0.385966i | \(0.873868\pi\) | |||||||
\(32\) | −2.50000 | + | 4.33013i | −0.441942 | + | 0.765466i | ||||
\(33\) | 5.36812 | 0.934469 | ||||||||
\(34\) | 1.26984 | 0.217777 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −1.39792 | − | 2.42126i | −0.229816 | − | 0.398053i | 0.727937 | − | 0.685643i | \(-0.240479\pi\) |
−0.957753 | + | 0.287591i | \(0.907146\pi\) | |||||||
\(38\) | −1.41421 | − | 2.44949i | −0.229416 | − | 0.397360i | ||||
\(39\) | −0.897916 | + | 5.01934i | −0.143782 | + | 0.803737i | ||||
\(40\) | −6.14741 | + | 10.6476i | −0.971990 | + | 1.68354i | ||||
\(41\) | 1.48640 | − | 2.57452i | 0.232136 | − | 0.402072i | −0.726300 | − | 0.687378i | \(-0.758762\pi\) |
0.958437 | + | 0.285306i | \(0.0920951\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.89792 | − | 6.75139i | −0.594427 | − | 1.02958i | −0.993628 | − | 0.112714i | \(-0.964046\pi\) |
0.399201 | − | 0.916863i | \(-0.369288\pi\) | |||||||
\(44\) | −1.89792 | + | 3.28729i | −0.286122 | + | 0.495577i | ||||
\(45\) | −2.04914 | + | 3.54921i | −0.305467 | + | 0.529085i | ||||
\(46\) | 3.89792 | − | 6.75139i | 0.574716 | − | 0.995438i | ||||
\(47\) | 1.41421 | − | 2.44949i | 0.206284 | − | 0.357295i | −0.744257 | − | 0.667893i | \(-0.767196\pi\) |
0.950541 | + | 0.310599i | \(0.100530\pi\) | |||||||
\(48\) | −0.707107 | − | 1.22474i | −0.102062 | − | 0.176777i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.89792 | + | 10.2155i | −0.834091 | + | 1.44469i | ||||
\(51\) | 0.897916 | − | 1.55524i | 0.125733 | − | 0.217777i | ||||
\(52\) | −2.75624 | − | 2.32446i | −0.382222 | − | 0.322345i | ||||
\(53\) | 6.29583 | + | 10.9047i | 0.864799 | + | 1.49788i | 0.867247 | + | 0.497879i | \(0.165888\pi\) |
−0.00244768 | + | 0.999997i | \(0.500779\pi\) | |||||||
\(54\) | −2.82843 | − | 4.89898i | −0.384900 | − | 0.666667i | ||||
\(55\) | −7.77817 | + | 13.4722i | −1.04881 | + | 1.81659i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 0.795832 | 0.104498 | ||||||||
\(59\) | −6.21959 | + | 10.7726i | −0.809722 | + | 1.40248i | 0.103335 | + | 0.994647i | \(0.467049\pi\) |
−0.913057 | + | 0.407833i | \(0.866285\pi\) | |||||||
\(60\) | 2.89792 | + | 5.01934i | 0.374119 | + | 0.647994i | ||||
\(61\) | −8.34091 | −1.06794 | −0.533972 | − | 0.845502i | \(-0.679301\pi\) | ||||
−0.533972 | + | 0.845502i | \(0.679301\pi\) | |||||||
\(62\) | −0.707107 | + | 1.22474i | −0.0898027 | + | 0.155543i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | −11.2958 | − | 9.52628i | −1.40108 | − | 1.18159i | ||||
\(66\) | −2.68406 | − | 4.64893i | −0.330385 | − | 0.572243i | ||||
\(67\) | −3.79583 | −0.463735 | −0.231867 | − | 0.972747i | \(-0.574484\pi\) | ||||
−0.231867 | + | 0.972747i | \(0.574484\pi\) | |||||||
\(68\) | 0.634922 | + | 1.09972i | 0.0769956 | + | 0.133360i | ||||
\(69\) | −5.51249 | − | 9.54790i | −0.663625 | − | 1.14943i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | − | 5.19615i | −0.356034 | − | 0.616670i | 0.631260 | − | 0.775571i | \(-0.282538\pi\) |
−0.987294 | + | 0.158901i | \(0.949205\pi\) | |||||||
\(72\) | 3.00000 | 0.353553 | ||||||||
\(73\) | −6.29178 | − | 10.8977i | −0.736397 | − | 1.27548i | −0.954108 | − | 0.299463i | \(-0.903192\pi\) |
0.217711 | − | 0.976013i | \(-0.430141\pi\) | |||||||
\(74\) | −1.39792 | + | 2.42126i | −0.162504 | + | 0.281466i | ||||
\(75\) | 8.34091 | + | 14.4469i | 0.963126 | + | 1.66818i | ||||
\(76\) | 1.41421 | − | 2.44949i | 0.162221 | − | 0.280976i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.79583 | − | 1.73205i | 0.543021 | − | 0.196116i | ||||
\(79\) | 1.10208 | − | 1.90887i | 0.123994 | − | 0.214764i | −0.797345 | − | 0.603524i | \(-0.793763\pi\) |
0.921339 | + | 0.388759i | \(0.127096\pi\) | |||||||
\(80\) | 4.09827 | 0.458201 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | −2.97280 | −0.328290 | ||||||||
\(83\) | 9.89949 | 1.08661 | 0.543305 | − | 0.839535i | \(-0.317173\pi\) | ||||
0.543305 | + | 0.839535i | \(0.317173\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.60208 | + | 4.50694i | 0.282236 | + | 0.488847i | ||||
\(86\) | −3.89792 | + | 6.75139i | −0.420323 | + | 0.728021i | ||||
\(87\) | 0.562738 | − | 0.974691i | 0.0603318 | − | 0.104498i | ||||
\(88\) | 11.3875 | 1.21391 | ||||||||
\(89\) | −7.48944 | − | 12.9721i | −0.793879 | − | 1.37504i | −0.923549 | − | 0.383481i | \(-0.874725\pi\) |
0.129670 | − | 0.991557i | \(-0.458608\pi\) | |||||||
\(90\) | 4.09827 | 0.431996 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.79583 | 0.812772 | ||||||||
\(93\) | 1.00000 | + | 1.73205i | 0.103695 | + | 0.179605i | ||||
\(94\) | −2.82843 | −0.291730 | ||||||||
\(95\) | 5.79583 | − | 10.0387i | 0.594640 | − | 1.02995i | ||||
\(96\) | 3.53553 | − | 6.12372i | 0.360844 | − | 0.625000i | ||||
\(97\) | −2.12132 | − | 3.67423i | −0.215387 | − | 0.373062i | 0.738005 | − | 0.674795i | \(-0.235768\pi\) |
−0.953392 | + | 0.301733i | \(0.902435\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.79583 | 0.381495 | ||||||||
\(100\) | −11.7958 | −1.17958 | ||||||||
\(101\) | 9.75513 | 0.970671 | 0.485336 | − | 0.874328i | \(-0.338697\pi\) | ||||
0.485336 | + | 0.874328i | \(0.338697\pi\) | |||||||
\(102\) | −1.79583 | −0.177814 | ||||||||
\(103\) | 2.68406 | − | 4.64893i | 0.264468 | − | 0.458072i | −0.702956 | − | 0.711233i | \(-0.748137\pi\) |
0.967424 | + | 0.253161i | \(0.0814703\pi\) | |||||||
\(104\) | −1.90477 | + | 10.6476i | −0.186778 | + | 1.04409i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.29583 | − | 10.9047i | 0.611505 | − | 1.05916i | ||||
\(107\) | 3.00000 | + | 5.19615i | 0.290021 | + | 0.502331i | 0.973814 | − | 0.227345i | \(-0.0730044\pi\) |
−0.683793 | + | 0.729676i | \(0.739671\pi\) | |||||||
\(108\) | 2.82843 | − | 4.89898i | 0.272166 | − | 0.471405i | ||||
\(109\) | −0.795832 | − | 1.37842i | −0.0762268 | − | 0.132029i | 0.825392 | − | 0.564560i | \(-0.190954\pi\) |
−0.901619 | + | 0.432531i | \(0.857621\pi\) | |||||||
\(110\) | 15.5563 | 1.48324 | ||||||||
\(111\) | 1.97695 | + | 3.42418i | 0.187644 | + | 0.325009i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.29583 | − | 2.24445i | −0.121902 | − | 0.211140i | 0.798616 | − | 0.601841i | \(-0.205566\pi\) |
−0.920518 | + | 0.390701i | \(0.872233\pi\) | |||||||
\(114\) | 2.00000 | + | 3.46410i | 0.187317 | + | 0.324443i | ||||
\(115\) | 31.9494 | 2.97930 | ||||||||
\(116\) | 0.397916 | + | 0.689210i | 0.0369456 | + | 0.0639916i | ||||
\(117\) | −0.634922 | + | 3.54921i | −0.0586986 | + | 0.328124i | ||||
\(118\) | 12.4392 | 1.14512 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 8.69375 | − | 15.0580i | 0.793627 | − | 1.37460i | ||||
\(121\) | 3.40834 | 0.309849 | ||||||||
\(122\) | 4.17046 | + | 7.22344i | 0.377575 | + | 0.653980i | ||||
\(123\) | −2.10208 | + | 3.64092i | −0.189539 | + | 0.328290i | ||||
\(124\) | −1.41421 | −0.127000 | ||||||||
\(125\) | −27.8512 | −2.49108 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.79583 | − | 10.0387i | 0.514297 | − | 0.890788i | −0.485566 | − | 0.874200i | \(-0.661386\pi\) |
0.999862 | − | 0.0165881i | \(-0.00528038\pi\) | |||||||
\(128\) | 1.50000 | + | 2.59808i | 0.132583 | + | 0.229640i | ||||
\(129\) | 5.51249 | + | 9.54790i | 0.485347 | + | 0.840646i | ||||
\(130\) | −2.60208 | + | 14.5456i | −0.228218 | + | 1.27573i | ||||
\(131\) | 2.68406 | − | 4.64893i | 0.234507 | − | 0.406178i | −0.724622 | − | 0.689146i | \(-0.757986\pi\) |
0.959129 | + | 0.282968i | \(0.0913190\pi\) | |||||||
\(132\) | 2.68406 | − | 4.64893i | 0.233617 | − | 0.404637i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.89792 | + | 3.28729i | 0.163955 | + | 0.283978i | ||||
\(135\) | 11.5917 | − | 20.0773i | 0.997652 | − | 1.72798i | ||||
\(136\) | 1.90477 | − | 3.29915i | 0.163332 | − | 0.282900i | ||||
\(137\) | 9.39792 | − | 16.2777i | 0.802918 | − | 1.39069i | −0.114769 | − | 0.993392i | \(-0.536613\pi\) |
0.917688 | − | 0.397303i | \(-0.130054\pi\) | |||||||
\(138\) | −5.51249 | + | 9.54790i | −0.469254 | + | 0.812772i | ||||
\(139\) | −0.851476 | − | 1.47480i | −0.0722212 | − | 0.125091i | 0.827653 | − | 0.561240i | \(-0.189675\pi\) |
−0.899875 | + | 0.436149i | \(0.856342\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | + | 3.46410i | −0.168430 | + | 0.291730i | ||||
\(142\) | −3.00000 | + | 5.19615i | −0.251754 | + | 0.436051i | ||||
\(143\) | −2.41006 | + | 13.4722i | −0.201539 | + | 1.12660i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 1.63077 | + | 2.82457i | 0.135428 | + | 0.234568i | ||||
\(146\) | −6.29178 | + | 10.8977i | −0.520711 | + | 0.901898i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.79583 | −0.229816 | ||||||||
\(149\) | −14.5917 | −1.19540 | −0.597698 | − | 0.801721i | \(-0.703918\pi\) | ||||
−0.597698 | + | 0.801721i | \(0.703918\pi\) | |||||||
\(150\) | 8.34091 | − | 14.4469i | 0.681033 | − | 1.17958i | ||||
\(151\) | −0.795832 | − | 1.37842i | −0.0647639 | − | 0.112174i | 0.831825 | − | 0.555037i | \(-0.187296\pi\) |
−0.896589 | + | 0.442863i | \(0.853963\pi\) | |||||||
\(152\) | −8.48528 | −0.688247 | ||||||||
\(153\) | 0.634922 | − | 1.09972i | 0.0513304 | − | 0.0889069i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.79583 | −0.465532 | ||||||||
\(156\) | 3.89792 | + | 3.28729i | 0.312083 | + | 0.263194i | ||||
\(157\) | −0.0721845 | − | 0.125027i | −0.00576095 | − | 0.00997825i | 0.863131 | − | 0.504981i | \(-0.168500\pi\) |
−0.868892 | + | 0.495003i | \(0.835167\pi\) | |||||||
\(158\) | −2.20417 | −0.175354 | ||||||||
\(159\) | −8.90365 | − | 15.4216i | −0.706105 | − | 1.22301i | ||||
\(160\) | 10.2457 | + | 17.7460i | 0.809992 | + | 1.40295i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.50000 | + | 4.33013i | 0.196419 | + | 0.340207i | ||||
\(163\) | 15.3875 | 1.20524 | 0.602621 | − | 0.798028i | \(-0.294123\pi\) | ||||
0.602621 | + | 0.798028i | \(0.294123\pi\) | |||||||
\(164\) | −1.48640 | − | 2.57452i | −0.116068 | − | 0.201036i | ||||
\(165\) | 11.0000 | − | 19.0526i | 0.856349 | − | 1.48324i | ||||
\(166\) | −4.94975 | − | 8.57321i | −0.384175 | − | 0.665410i | ||||
\(167\) | 0.851476 | − | 1.47480i | 0.0658892 | − | 0.114123i | −0.831199 | − | 0.555975i | \(-0.812345\pi\) |
0.897088 | + | 0.441852i | \(0.145678\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.1937 | − | 4.50694i | −0.937981 | − | 0.346688i | ||||
\(170\) | 2.60208 | − | 4.50694i | 0.199571 | − | 0.345667i | ||||
\(171\) | −2.82843 | −0.216295 | ||||||||
\(172\) | −7.79583 | −0.594427 | ||||||||
\(173\) | 17.8073 | 1.35386 | 0.676932 | − | 0.736046i | \(-0.263309\pi\) | ||||
0.676932 | + | 0.736046i | \(0.263309\pi\) | |||||||
\(174\) | −1.12548 | −0.0853221 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.89792 | − | 3.28729i | −0.143061 | − | 0.247789i | ||||
\(177\) | 8.79583 | − | 15.2348i | 0.661135 | − | 1.14512i | ||||
\(178\) | −7.48944 | + | 12.9721i | −0.561357 | + | 0.972299i | ||||
\(179\) | −19.5917 | −1.46435 | −0.732175 | − | 0.681117i | \(-0.761495\pi\) | ||||
−0.732175 | + | 0.681117i | \(0.761495\pi\) | |||||||
\(180\) | 2.04914 | + | 3.54921i | 0.152734 | + | 0.264542i | ||||
\(181\) | −3.80953 | −0.283160 | −0.141580 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141580 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.7958 | 0.871973 | ||||||||
\(184\) | −11.6937 | − | 20.2542i | −0.862074 | − | 1.49316i | ||||
\(185\) | −11.4581 | −0.842415 | ||||||||
\(186\) | 1.00000 | − | 1.73205i | 0.0733236 | − | 0.127000i | ||||
\(187\) | 2.41006 | − | 4.17434i | 0.176241 | − | 0.305258i | ||||
\(188\) | −1.41421 | − | 2.44949i | −0.103142 | − | 0.178647i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.5917 | −0.840948 | ||||||||
\(191\) | −16.2042 | −1.17249 | −0.586246 | − | 0.810133i | \(-0.699395\pi\) | ||||
−0.586246 | + | 0.810133i | \(0.699395\pi\) | |||||||
\(192\) | −9.89949 | −0.714435 | ||||||||
\(193\) | 22.5917 | 1.62618 | 0.813092 | − | 0.582136i | \(-0.197783\pi\) | ||||
0.813092 | + | 0.582136i | \(0.197783\pi\) | |||||||
\(194\) | −2.12132 | + | 3.67423i | −0.152302 | + | 0.263795i | ||||
\(195\) | 15.9747 | + | 13.4722i | 1.14397 | + | 0.964764i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.00000 | − | 6.92820i | 0.284988 | − | 0.493614i | −0.687618 | − | 0.726073i | \(-0.741344\pi\) |
0.972606 | + | 0.232458i | \(0.0746770\pi\) | |||||||
\(198\) | −1.89792 | − | 3.28729i | −0.134879 | − | 0.233617i | ||||
\(199\) | 2.53969 | − | 4.39887i | 0.180034 | − | 0.311828i | −0.761858 | − | 0.647744i | \(-0.775713\pi\) |
0.941892 | + | 0.335916i | \(0.109046\pi\) | |||||||
\(200\) | 17.6937 | + | 30.6465i | 1.25114 | + | 2.16703i | ||||
\(201\) | 5.36812 | 0.378638 | ||||||||
\(202\) | −4.87756 | − | 8.44819i | −0.343184 | − | 0.594412i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.897916 | − | 1.55524i | −0.0628667 | − | 0.108888i | ||||
\(205\) | −6.09166 | − | 10.5511i | −0.425460 | − | 0.736919i | ||||
\(206\) | −5.36812 | −0.374014 | ||||||||
\(207\) | −3.89792 | − | 6.75139i | −0.270924 | − | 0.469254i | ||||
\(208\) | 3.39116 | − | 1.22474i | 0.235135 | − | 0.0849208i | ||||
\(209\) | −10.7362 | −0.742641 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.89792 | + | 6.75139i | −0.268344 | + | 0.464785i | −0.968434 | − | 0.249269i | \(-0.919810\pi\) |
0.700091 | + | 0.714054i | \(0.253143\pi\) | |||||||
\(212\) | 12.5917 | 0.864799 | ||||||||
\(213\) | 4.24264 | + | 7.34847i | 0.290701 | + | 0.503509i | ||||
\(214\) | 3.00000 | − | 5.19615i | 0.205076 | − | 0.355202i | ||||
\(215\) | −31.9494 | −2.17893 | ||||||||
\(216\) | −16.9706 | −1.15470 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.795832 | + | 1.37842i | −0.0539005 | + | 0.0933584i | ||||
\(219\) | 8.89792 | + | 15.4116i | 0.601265 | + | 1.04142i | ||||
\(220\) | 7.77817 | + | 13.4722i | 0.524404 | + | 0.908295i | ||||
\(221\) | 3.50000 | + | 2.95171i | 0.235435 | + | 0.198553i | ||||
\(222\) | 1.97695 | − | 3.42418i | 0.132684 | − | 0.229816i | ||||
\(223\) | −2.82843 | + | 4.89898i | −0.189405 | + | 0.328060i | −0.945052 | − | 0.326920i | \(-0.893989\pi\) |
0.755647 | + | 0.654979i | \(0.227323\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.89792 | + | 10.2155i | 0.393194 | + | 0.681033i | ||||
\(226\) | −1.29583 | + | 2.24445i | −0.0861974 | + | 0.149298i | ||||
\(227\) | 3.67990 | − | 6.37378i | 0.244244 | − | 0.423043i | −0.717675 | − | 0.696378i | \(-0.754794\pi\) |
0.961919 | + | 0.273336i | \(0.0881270\pi\) | |||||||
\(228\) | −2.00000 | + | 3.46410i | −0.132453 | + | 0.229416i | ||||
\(229\) | 6.36396 | − | 11.0227i | 0.420542 | − | 0.728401i | −0.575450 | − | 0.817837i | \(-0.695173\pi\) |
0.995993 | + | 0.0894361i | \(0.0285065\pi\) | |||||||
\(230\) | −15.9747 | − | 27.6690i | −1.05334 | − | 1.82444i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.19375 | − | 2.06763i | 0.0783733 | − | 0.135747i | ||||
\(233\) | −8.59166 | + | 14.8812i | −0.562859 | + | 0.974900i | 0.434387 | + | 0.900726i | \(0.356965\pi\) |
−0.997245 | + | 0.0741732i | \(0.976368\pi\) | |||||||
\(234\) | 3.39116 | − | 1.22474i | 0.221687 | − | 0.0800641i | ||||
\(235\) | −5.79583 | − | 10.0387i | −0.378078 | − | 0.654851i | ||||
\(236\) | 6.21959 | + | 10.7726i | 0.404861 | + | 0.701240i | ||||
\(237\) | −1.55858 | + | 2.69954i | −0.101241 | + | 0.175354i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.2042 | −0.660053 | −0.330026 | − | 0.943972i | \(-0.607058\pi\) | ||||
−0.330026 | + | 0.943972i | \(0.607058\pi\) | |||||||
\(240\) | −5.79583 | −0.374119 | ||||||||
\(241\) | 5.58467 | − | 9.67293i | 0.359740 | − | 0.623088i | −0.628177 | − | 0.778070i | \(-0.716199\pi\) |
0.987917 | + | 0.154982i | \(0.0495320\pi\) | |||||||
\(242\) | −1.70417 | − | 2.95171i | −0.109548 | − | 0.189743i | ||||
\(243\) | −9.89949 | −0.635053 | ||||||||
\(244\) | −4.17046 | + | 7.22344i | −0.266986 | + | 0.462433i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.20417 | 0.268048 | ||||||||
\(247\) | 1.79583 | − | 10.0387i | 0.114266 | − | 0.638746i | ||||
\(248\) | 2.12132 | + | 3.67423i | 0.134704 | + | 0.233314i | ||||
\(249\) | −14.0000 | −0.887214 | ||||||||
\(250\) | 13.9256 | + | 24.1198i | 0.880731 | + | 1.52547i | ||||
\(251\) | −8.34091 | − | 14.4469i | −0.526474 | − | 0.911879i | −0.999524 | − | 0.0308439i | \(-0.990181\pi\) |
0.473050 | − | 0.881035i | \(-0.343153\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.7958 | − | 25.6271i | −0.930206 | − | 1.61116i | ||||
\(254\) | −11.5917 | −0.727326 | ||||||||
\(255\) | −3.67990 | − | 6.37378i | −0.230444 | − | 0.399142i | ||||
\(256\) | 8.50000 | − | 14.7224i | 0.531250 | − | 0.920152i | ||||
\(257\) | 4.31483 | + | 7.47350i | 0.269151 | + | 0.466184i | 0.968643 | − | 0.248457i | \(-0.0799235\pi\) |
−0.699492 | + | 0.714641i | \(0.746590\pi\) | |||||||
\(258\) | 5.51249 | − | 9.54790i | 0.343192 | − | 0.594427i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −13.8979 | + | 5.01934i | −0.861912 | + | 0.311286i | ||||
\(261\) | 0.397916 | − | 0.689210i | 0.0246304 | − | 0.0426610i | ||||
\(262\) | −5.36812 | −0.331643 | ||||||||
\(263\) | 3.38749 | 0.208882 | 0.104441 | − | 0.994531i | \(-0.466695\pi\) | ||||
0.104441 | + | 0.994531i | \(0.466695\pi\) | |||||||
\(264\) | −16.1043 | −0.991154 | ||||||||
\(265\) | 51.6041 | 3.17001 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.5917 | + | 18.3453i | 0.648199 | + | 1.12271i | ||||
\(268\) | −1.89792 | + | 3.28729i | −0.115934 | + | 0.200803i | ||||
\(269\) | 6.21959 | − | 10.7726i | 0.379215 | − | 0.656820i | −0.611733 | − | 0.791064i | \(-0.709527\pi\) |
0.990948 | + | 0.134244i | \(0.0428607\pi\) | |||||||
\(270\) | −23.1833 | −1.41089 | ||||||||
\(271\) | 8.75928 | + | 15.1715i | 0.532088 | + | 0.921604i | 0.999298 | + | 0.0374577i | \(0.0119260\pi\) |
−0.467210 | + | 0.884147i | \(0.654741\pi\) | |||||||
\(272\) | −1.26984 | −0.0769956 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.7958 | −1.13550 | ||||||||
\(275\) | 22.3875 | + | 38.7763i | 1.35002 | + | 2.33830i | ||||
\(276\) | −11.0250 | −0.663625 | ||||||||
\(277\) | −16.0917 | + | 27.8716i | −0.966854 | + | 1.67464i | −0.262306 | + | 0.964985i | \(0.584483\pi\) |
−0.704548 | + | 0.709656i | \(0.748850\pi\) | |||||||
\(278\) | −0.851476 | + | 1.47480i | −0.0510681 | + | 0.0884526i | ||||
\(279\) | 0.707107 | + | 1.22474i | 0.0423334 | + | 0.0733236i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.7958 | 1.47920 | 0.739598 | − | 0.673049i | \(-0.235016\pi\) | ||||
0.739598 | + | 0.673049i | \(0.235016\pi\) | |||||||
\(282\) | 4.00000 | 0.238197 | ||||||||
\(283\) | 15.8451 | 0.941893 | 0.470946 | − | 0.882162i | \(-0.343913\pi\) | ||||
0.470946 | + | 0.882162i | \(0.343913\pi\) | |||||||
\(284\) | −6.00000 | −0.356034 | ||||||||
\(285\) | −8.19654 | + | 14.1968i | −0.485521 | + | 0.840948i | ||||
\(286\) | 12.8723 | − | 4.64893i | 0.761155 | − | 0.274897i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.50000 | − | 4.33013i | 0.147314 | − | 0.255155i | ||||
\(289\) | 7.69375 | + | 13.3260i | 0.452573 | + | 0.783880i | ||||
\(290\) | 1.63077 | − | 2.82457i | 0.0957619 | − | 0.165865i | ||||
\(291\) | 3.00000 | + | 5.19615i | 0.175863 | + | 0.304604i | ||||
\(292\) | −12.5836 | −0.736397 | ||||||||
\(293\) | −1.48640 | − | 2.57452i | −0.0868363 | − | 0.150405i | 0.819336 | − | 0.573314i | \(-0.194342\pi\) |
−0.906172 | + | 0.422909i | \(0.861009\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.4896 | + | 44.1492i | 1.48406 | + | 2.57047i | ||||
\(296\) | 4.19375 | + | 7.26378i | 0.243757 | + | 0.422199i | ||||
\(297\) | −21.4725 | −1.24596 | ||||||||
\(298\) | 7.29583 | + | 12.6368i | 0.422636 | + | 0.732027i | ||||
\(299\) | 26.4370 | − | 9.54790i | 1.52889 | − | 0.552170i | ||||
\(300\) | 16.6818 | 0.963126 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.795832 | + | 1.37842i | −0.0457950 | + | 0.0793192i | ||||
\(303\) | −13.7958 | −0.792550 | ||||||||
\(304\) | 1.41421 | + | 2.44949i | 0.0811107 | + | 0.140488i | ||||
\(305\) | −17.0917 | + | 29.6036i | −0.978666 | + | 1.69510i | ||||
\(306\) | −1.26984 | −0.0725922 | ||||||||
\(307\) | 20.0583 | 1.14478 | 0.572392 | − | 0.819980i | \(-0.306015\pi\) | ||||
0.572392 | + | 0.819980i | \(0.306015\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.79583 | + | 6.57457i | −0.215937 | + | 0.374014i | ||||
\(310\) | 2.89792 | + | 5.01934i | 0.164591 | + | 0.285079i | ||||
\(311\) | −14.4161 | − | 24.9695i | −0.817464 | − | 1.41589i | −0.907545 | − | 0.419955i | \(-0.862046\pi\) |
0.0900809 | − | 0.995934i | \(-0.471287\pi\) | |||||||
\(312\) | 2.69375 | − | 15.0580i | 0.152503 | − | 0.852492i | ||||
\(313\) | 7.63381 | − | 13.2221i | 0.431488 | − | 0.747359i | −0.565514 | − | 0.824739i | \(-0.691322\pi\) |
0.997002 | + | 0.0773795i | \(0.0246553\pi\) | |||||||
\(314\) | −0.0721845 | + | 0.125027i | −0.00407360 | + | 0.00705569i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.10208 | − | 1.90887i | −0.0619971 | − | 0.107382i | ||||
\(317\) | −3.29583 | + | 5.70855i | −0.185112 | + | 0.320624i | −0.943614 | − | 0.331047i | \(-0.892598\pi\) |
0.758502 | + | 0.651671i | \(0.225932\pi\) | |||||||
\(318\) | −8.90365 | + | 15.4216i | −0.499292 | + | 0.864799i | ||||
\(319\) | 1.51042 | − | 2.61613i | 0.0845674 | − | 0.146475i | ||||
\(320\) | 14.3440 | − | 24.8445i | 0.801851 | − | 1.38885i | ||||
\(321\) | −4.24264 | − | 7.34847i | −0.236801 | − | 0.410152i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.79583 | + | 3.11047i | −0.0999227 | + | 0.173071i | ||||
\(324\) | −2.50000 | + | 4.33013i | −0.138889 | + | 0.240563i | ||||
\(325\) | −40.0016 | + | 14.4469i | −2.21889 | + | 0.801369i | ||||
\(326\) | −7.69375 | − | 13.3260i | −0.426117 | − | 0.738057i | ||||
\(327\) | 1.12548 | + | 1.94938i | 0.0622390 | + | 0.107801i | ||||
\(328\) | −4.45919 | + | 7.72355i | −0.246218 | + | 0.426462i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −22.0000 | −1.21106 | ||||||||
\(331\) | 29.3875 | 1.61528 | 0.807641 | − | 0.589674i | \(-0.200744\pi\) | ||||
0.807641 | + | 0.589674i | \(0.200744\pi\) | |||||||
\(332\) | 4.94975 | − | 8.57321i | 0.271653 | − | 0.470516i | ||||
\(333\) | 1.39792 | + | 2.42126i | 0.0766053 | + | 0.132684i | ||||
\(334\) | −1.70295 | −0.0931814 | ||||||||
\(335\) | −7.77817 | + | 13.4722i | −0.424967 | + | 0.736065i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.9792 | 0.979387 | 0.489694 | − | 0.871895i | \(-0.337109\pi\) | ||||
0.489694 | + | 0.871895i | \(0.337109\pi\) | |||||||
\(338\) | 2.19375 | + | 12.8136i | 0.119324 | + | 0.696966i | ||||
\(339\) | 1.83258 | + | 3.17413i | 0.0995322 | + | 0.172395i | ||||
\(340\) | 5.20417 | 0.282236 | ||||||||
\(341\) | 2.68406 | + | 4.64893i | 0.145350 | + | 0.251753i | ||||
\(342\) | 1.41421 | + | 2.44949i | 0.0764719 | + | 0.132453i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11.6937 | + | 20.2542i | 0.630485 | + | 1.09203i | ||||
\(345\) | −45.1833 | −2.43259 | ||||||||
\(346\) | −8.90365 | − | 15.4216i | −0.478663 | − | 0.829069i | ||||
\(347\) | 16.4896 | − | 28.5608i | 0.885207 | − | 1.53322i | 0.0397307 | − | 0.999210i | \(-0.487350\pi\) |
0.845476 | − | 0.534013i | \(-0.179317\pi\) | |||||||
\(348\) | −0.562738 | − | 0.974691i | −0.0301659 | − | 0.0522489i | ||||
\(349\) | 13.2907 | − | 23.0201i | 0.711433 | − | 1.23224i | −0.252887 | − | 0.967496i | \(-0.581380\pi\) |
0.964319 | − | 0.264742i | \(-0.0852867\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.59166 | − | 20.0773i | 0.191709 | − | 1.07165i | ||||
\(352\) | 9.48958 | − | 16.4364i | 0.505796 | − | 0.876065i | ||||
\(353\) | −5.22375 | −0.278032 | −0.139016 | − | 0.990290i | \(-0.544394\pi\) | ||||
−0.139016 | + | 0.990290i | \(0.544394\pi\) | |||||||
\(354\) | −17.5917 | −0.934986 | ||||||||
\(355\) | −24.5896 | −1.30508 | ||||||||
\(356\) | −14.9789 | −0.793879 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.79583 | + | 16.9669i | 0.517726 | + | 0.896727i | ||||
\(359\) | 2.00000 | − | 3.46410i | 0.105556 | − | 0.182828i | −0.808409 | − | 0.588621i | \(-0.799671\pi\) |
0.913965 | + | 0.405793i | \(0.133004\pi\) | |||||||
\(360\) | 6.14741 | − | 10.6476i | 0.323997 | − | 0.561179i | ||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 1.90477 | + | 3.29915i | 0.100112 | + | 0.173400i | ||||
\(363\) | −4.82012 | −0.252990 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −51.5708 | −2.69934 | ||||||||
\(366\) | −5.89792 | − | 10.2155i | −0.308289 | − | 0.533972i | ||||
\(367\) | −21.2132 | −1.10732 | −0.553660 | − | 0.832743i | \(-0.686769\pi\) | ||||
−0.553660 | + | 0.832743i | \(0.686769\pi\) | |||||||
\(368\) | −3.89792 | + | 6.75139i | −0.203193 | + | 0.351940i | ||||
\(369\) | −1.48640 | + | 2.57452i | −0.0773788 | + | 0.134024i | ||||
\(370\) | 5.72904 | + | 9.92299i | 0.297839 | + | 0.515871i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.00000 | 0.103695 | ||||||||
\(373\) | 6.59166 | 0.341303 | 0.170652 | − | 0.985331i | \(-0.445413\pi\) | ||||
0.170652 | + | 0.985331i | \(0.445413\pi\) | |||||||
\(374\) | −4.82012 | −0.249242 | ||||||||
\(375\) | 39.3875 | 2.03396 | ||||||||
\(376\) | −4.24264 | + | 7.34847i | −0.218797 | + | 0.378968i | ||||
\(377\) | 2.19350 | + | 1.84988i | 0.112971 | + | 0.0952737i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.6937 | + | 21.9862i | −0.652034 | + | 1.12936i | 0.330595 | + | 0.943773i | \(0.392751\pi\) |
−0.982629 | + | 0.185583i | \(0.940583\pi\) | |||||||
\(380\) | −5.79583 | − | 10.0387i | −0.297320 | − | 0.514973i | ||||
\(381\) | −8.19654 | + | 14.1968i | −0.419922 | + | 0.727326i | ||||
\(382\) | 8.10208 | + | 14.0332i | 0.414539 | + | 0.718002i | ||||
\(383\) | −12.1504 | −0.620859 | −0.310429 | − | 0.950596i | \(-0.600473\pi\) | ||||
−0.310429 | + | 0.950596i | \(0.600473\pi\) | |||||||
\(384\) | −2.12132 | − | 3.67423i | −0.108253 | − | 0.187500i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.2958 | − | 19.5650i | −0.574943 | − | 0.995830i | ||||
\(387\) | 3.89792 | + | 6.75139i | 0.198142 | + | 0.343192i | ||||
\(388\) | −4.24264 | −0.215387 | ||||||||
\(389\) | 0.193747 | + | 0.335580i | 0.00982338 | + | 0.0170146i | 0.870895 | − | 0.491469i | \(-0.163540\pi\) |
−0.861072 | + | 0.508483i | \(0.830206\pi\) | |||||||
\(390\) | 3.67990 | − | 20.5706i | 0.186339 | − | 1.04163i | ||||
\(391\) | −9.89949 | −0.500639 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.79583 | + | 6.57457i | −0.191474 | + | 0.331643i | ||||
\(394\) | −8.00000 | −0.403034 | ||||||||
\(395\) | −4.51664 | − | 7.82305i | −0.227257 | − | 0.393620i | ||||
\(396\) | 1.89792 | − | 3.28729i | 0.0953739 | − | 0.165192i | ||||
\(397\) | −7.07107 | −0.354887 | −0.177443 | − | 0.984131i | \(-0.556783\pi\) | ||||
−0.177443 | + | 0.984131i | \(0.556783\pi\) | |||||||
\(398\) | −5.07938 | −0.254606 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.89792 | − | 10.2155i | 0.294896 | − | 0.510774i | ||||
\(401\) | 2.19375 | + | 3.79968i | 0.109551 | + | 0.189747i | 0.915588 | − | 0.402117i | \(-0.131726\pi\) |
−0.806038 | + | 0.591864i | \(0.798392\pi\) | |||||||
\(402\) | −2.68406 | − | 4.64893i | −0.133869 | − | 0.231867i | ||||
\(403\) | −4.79583 | + | 1.73205i | −0.238897 | + | 0.0862796i | ||||
\(404\) | 4.87756 | − | 8.44819i | 0.242668 | − | 0.420313i | ||||
\(405\) | −10.2457 | + | 17.7460i | −0.509112 | + | 0.881808i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.30625 | + | 9.19070i | 0.263021 | + | 0.455566i | ||||
\(408\) | −2.69375 | + | 4.66571i | −0.133360 | + | 0.230987i | ||||
\(409\) | 9.39420 | − | 16.2712i | 0.464513 | − | 0.804561i | −0.534666 | − | 0.845063i | \(-0.679563\pi\) |
0.999179 | + | 0.0405026i | \(0.0128959\pi\) | |||||||
\(410\) | −6.09166 | + | 10.5511i | −0.300846 | + | 0.521080i | ||||
\(411\) | −13.2907 | + | 23.0201i | −0.655580 | + | 1.13550i | ||||
\(412\) | −2.68406 | − | 4.64893i | −0.132234 | − | 0.229036i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.89792 | + | 6.75139i | −0.191572 | + | 0.331813i | ||||
\(415\) | 20.2854 | − | 35.1354i | 0.995772 | − | 1.72473i | ||||
\(416\) | 13.7812 | + | 11.6223i | 0.675680 | + | 0.569831i | ||||
\(417\) | 1.20417 | + | 2.08568i | 0.0589684 | + | 0.102136i | ||||
\(418\) | 5.36812 | + | 9.29785i | 0.262563 | + | 0.454773i | ||||
\(419\) | −12.8576 | + | 22.2699i | −0.628133 | + | 1.08796i | 0.359794 | + | 0.933032i | \(0.382847\pi\) |
−0.987926 | + | 0.154926i | \(0.950486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.5917 | 0.613680 | 0.306840 | − | 0.951761i | \(-0.400728\pi\) | ||||
0.306840 | + | 0.951761i | \(0.400728\pi\) | |||||||
\(422\) | 7.79583 | 0.379495 | ||||||||
\(423\) | −1.41421 | + | 2.44949i | −0.0687614 | + | 0.119098i | ||||
\(424\) | −18.8875 | − | 32.7141i | −0.917258 | − | 1.58874i | ||||
\(425\) | 14.9789 | 0.726582 | ||||||||
\(426\) | 4.24264 | − | 7.34847i | 0.205557 | − | 0.356034i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.00000 | 0.290021 | ||||||||
\(429\) | 3.40834 | − | 19.0526i | 0.164556 | − | 0.919866i | ||||
\(430\) | 15.9747 | + | 27.6690i | 0.770369 | + | 1.33432i | ||||
\(431\) | 33.1833 | 1.59838 | 0.799192 | − | 0.601075i | \(-0.205261\pi\) | ||||
0.799192 | + | 0.601075i | \(0.205261\pi\) | |||||||
\(432\) | 2.82843 | + | 4.89898i | 0.136083 | + | 0.235702i | ||||
\(433\) | −10.2457 | − | 17.7460i | −0.492376 | − | 0.852820i | 0.507586 | − | 0.861601i | \(-0.330538\pi\) |
−0.999961 | + | 0.00878126i | \(0.997205\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.30625 | − | 3.99455i | −0.110576 | − | 0.191524i | ||||
\(436\) | −1.59166 | −0.0762268 | ||||||||
\(437\) | 11.0250 | + | 19.0958i | 0.527396 | + | 0.913476i | ||||
\(438\) | 8.89792 | − | 15.4116i | 0.425159 | − | 0.736397i | ||||
\(439\) | −10.0291 | − | 17.3710i | −0.478664 | − | 0.829070i | 0.521037 | − | 0.853534i | \(-0.325545\pi\) |
−0.999701 | + | 0.0244638i | \(0.992212\pi\) | |||||||
\(440\) | 23.3345 | − | 40.4166i | 1.11243 | − | 1.92678i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.806253 | − | 4.50694i | 0.0383495 | − | 0.214373i | ||||
\(443\) | −5.00000 | + | 8.66025i | −0.237557 | + | 0.411461i | −0.960013 | − | 0.279956i | \(-0.909680\pi\) |
0.722456 | + | 0.691417i | \(0.243013\pi\) | |||||||
\(444\) | 3.95390 | 0.187644 | ||||||||
\(445\) | −61.3875 | −2.91005 | ||||||||
\(446\) | 5.65685 | 0.267860 | ||||||||
\(447\) | 20.6357 | 0.976036 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.7958 | − | 20.4310i | −0.556680 | − | 0.964198i | −0.997771 | − | 0.0667352i | \(-0.978742\pi\) |
0.441091 | − | 0.897462i | \(-0.354592\pi\) | |||||||
\(450\) | 5.89792 | − | 10.2155i | 0.278030 | − | 0.481563i | ||||
\(451\) | −5.64212 | + | 9.77243i | −0.265677 | + | 0.460166i | ||||
\(452\) | −2.59166 | −0.121902 | ||||||||
\(453\) | 1.12548 | + | 1.94938i | 0.0528795 | + | 0.0915899i | ||||
\(454\) | −7.35981 | −0.345413 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.0000 | 0.561951 | ||||||||
\(457\) | −2.29583 | − | 3.97650i | −0.107394 | − | 0.186013i | 0.807320 | − | 0.590115i | \(-0.200917\pi\) |
−0.914714 | + | 0.404102i | \(0.867584\pi\) | |||||||
\(458\) | −12.7279 | −0.594737 | ||||||||
\(459\) | −3.59166 | + | 6.22094i | −0.167644 | + | 0.290369i | ||||
\(460\) | 15.9747 | − | 27.6690i | 0.744825 | − | 1.29007i | ||||
\(461\) | 12.0930 | + | 20.9457i | 0.563227 | + | 0.975538i | 0.997212 | + | 0.0746180i | \(0.0237737\pi\) |
−0.433985 | + | 0.900920i | \(0.642893\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.3875 | −0.808065 | −0.404033 | − | 0.914745i | \(-0.632392\pi\) | ||||
−0.404033 | + | 0.914745i | \(0.632392\pi\) | |||||||
\(464\) | −0.795832 | −0.0369456 | ||||||||
\(465\) | 8.19654 | 0.380106 | ||||||||
\(466\) | 17.1833 | 0.796002 | ||||||||
\(467\) | −15.9747 | + | 27.6690i | −0.739222 | + | 1.28037i | 0.213624 | + | 0.976916i | \(0.431473\pi\) |
−0.952846 | + | 0.303454i | \(0.901860\pi\) | |||||||
\(468\) | 2.75624 | + | 2.32446i | 0.127407 | + | 0.107448i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.79583 | + | 10.0387i | −0.267342 | + | 0.463050i | ||||
\(471\) | 0.102084 | + | 0.176815i | 0.00470379 | + | 0.00814721i | ||||
\(472\) | 18.6588 | − | 32.3179i | 0.858840 | − | 1.48755i | ||||
\(473\) | 14.7958 | + | 25.6271i | 0.680313 | + | 1.17834i | ||||
\(474\) | 3.11716 | 0.143176 | ||||||||
\(475\) | −16.6818 | − | 28.8938i | −0.765415 | − | 1.32574i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.29583 | − | 10.9047i | −0.288266 | − | 0.499292i | ||||
\(478\) | 5.10208 | + | 8.83707i | 0.233364 | + | 0.404198i | ||||
\(479\) | 20.9245 | 0.956063 | 0.478032 | − | 0.878343i | \(-0.341350\pi\) | ||||
0.478032 | + | 0.878343i | \(0.341350\pi\) | |||||||
\(480\) | −14.4896 | − | 25.0967i | −0.661356 | − | 1.14550i | ||||
\(481\) | −9.48113 | + | 3.42418i | −0.432302 | + | 0.156129i | ||||
\(482\) | −11.1693 | −0.508749 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.70417 | − | 2.95171i | 0.0774622 | − | 0.134168i | ||||
\(485\) | −17.3875 | −0.789525 | ||||||||
\(486\) | 4.94975 | + | 8.57321i | 0.224525 | + | 0.388889i | ||||
\(487\) | −0.204168 | + | 0.353630i | −0.00925176 | + | 0.0160245i | −0.870614 | − | 0.491966i | \(-0.836278\pi\) |
0.861362 | + | 0.507991i | \(0.169612\pi\) | |||||||
\(488\) | 25.0227 | 1.13273 | ||||||||
\(489\) | −21.7612 | −0.984076 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.79583 | + | 8.30662i | −0.216433 | + | 0.374873i | −0.953715 | − | 0.300712i | \(-0.902776\pi\) |
0.737282 | + | 0.675585i | \(0.236109\pi\) | |||||||
\(492\) | 2.10208 | + | 3.64092i | 0.0947693 | + | 0.164145i | ||||
\(493\) | −0.505291 | − | 0.875190i | −0.0227572 | − | 0.0394166i | ||||
\(494\) | −9.59166 | + | 3.46410i | −0.431549 | + | 0.155857i | ||||
\(495\) | 7.77817 | − | 13.4722i | 0.349603 | − | 0.605530i | ||||
\(496\) | 0.707107 | − | 1.22474i | 0.0317500 | − | 0.0549927i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.00000 | + | 12.1244i | 0.313678 | + | 0.543305i | ||||
\(499\) | −12.8979 | + | 22.3398i | −0.577390 | + | 1.00007i | 0.418387 | + | 0.908269i | \(0.362595\pi\) |
−0.995777 | + | 0.0918002i | \(0.970738\pi\) | |||||||
\(500\) | −13.9256 | + | 24.1198i | −0.622771 | + | 1.07867i | ||||
\(501\) | −1.20417 | + | 2.08568i | −0.0537983 | + | 0.0931814i | ||||
\(502\) | −8.34091 | + | 14.4469i | −0.372273 | + | 0.644796i | ||||
\(503\) | 12.8576 | + | 22.2699i | 0.573290 | + | 0.992967i | 0.996225 | + | 0.0868074i | \(0.0276665\pi\) |
−0.422935 | + | 0.906160i | \(0.639000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.9896 | − | 34.6230i | 0.889525 | − | 1.54070i | ||||
\(506\) | −14.7958 | + | 25.6271i | −0.657755 | + | 1.13926i | ||||
\(507\) | 17.2446 | + | 6.37378i | 0.765858 | + | 0.283069i | ||||
\(508\) | −5.79583 | − | 10.0387i | −0.257148 | − | 0.445394i | ||||
\(509\) | 3.04498 | + | 5.27406i | 0.134966 | + | 0.233769i | 0.925585 | − | 0.378541i | \(-0.123574\pi\) |
−0.790618 | + | 0.612309i | \(0.790241\pi\) | |||||||
\(510\) | −3.67990 | + | 6.37378i | −0.162949 | + | 0.282236i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | 16.0000 | 0.706417 | ||||||||
\(514\) | 4.31483 | − | 7.47350i | 0.190319 | − | 0.329642i | ||||
\(515\) | −11.0000 | − | 19.0526i | −0.484718 | − | 0.839556i | ||||
\(516\) | 11.0250 | 0.485347 | ||||||||
\(517\) | −5.36812 | + | 9.29785i | −0.236089 | + | 0.408919i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.1833 | −1.10543 | ||||||||
\(520\) | 33.8875 | + | 28.5788i | 1.48606 | + | 1.25326i | ||||
\(521\) | 2.33787 | + | 4.04932i | 0.102424 | + | 0.177404i | 0.912683 | − | 0.408669i | \(-0.134007\pi\) |
−0.810259 | + | 0.586072i | \(0.800673\pi\) | |||||||
\(522\) | −0.795832 | −0.0348326 | ||||||||
\(523\) | 21.0688 | + | 36.4923i | 0.921276 | + | 1.59570i | 0.797444 | + | 0.603393i | \(0.206185\pi\) |
0.123832 | + | 0.992303i | \(0.460482\pi\) | |||||||
\(524\) | −2.68406 | − | 4.64893i | −0.117254 | − | 0.203089i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.69375 | − | 2.93366i | −0.0738509 | − | 0.127913i | ||||
\(527\) | 1.79583 | 0.0782276 | ||||||||
\(528\) | 2.68406 | + | 4.64893i | 0.116809 | + | 0.202318i | ||||
\(529\) | −18.8875 | + | 32.7141i | −0.821195 | + | 1.42235i | ||||
\(530\) | −25.8020 | − | 44.6904i | −1.12077 | − | 1.94123i | ||||
\(531\) | 6.21959 | − | 10.7726i | 0.269907 | − | 0.467493i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.19375 | − | 6.91015i | −0.354911 | − | 0.299312i | ||||
\(534\) | 10.5917 | − | 18.3453i | 0.458346 | − | 0.793879i | ||||
\(535\) | 24.5896 | 1.06310 | ||||||||
\(536\) | 11.3875 | 0.491865 | ||||||||
\(537\) | 27.7068 | 1.19564 | ||||||||
\(538\) | −12.4392 | −0.536291 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −11.5917 | − | 20.0773i | −0.498826 | − | 0.863992i | ||||
\(541\) | −3.29583 | + | 5.70855i | −0.141699 | + | 0.245430i | −0.928136 | − | 0.372240i | \(-0.878590\pi\) |
0.786438 | + | 0.617670i | \(0.211923\pi\) | |||||||
\(542\) | 8.75928 | − | 15.1715i | 0.376243 | − | 0.651673i | ||||
\(543\) | 5.38749 | 0.231200 | ||||||||
\(544\) | −3.17461 | − | 5.49859i | −0.136110 | − | 0.235750i | ||||
\(545\) | −6.52307 | −0.279418 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.9792 | 0.469435 | 0.234717 | − | 0.972064i | \(-0.424584\pi\) | ||||
0.234717 | + | 0.972064i | \(0.424584\pi\) | |||||||
\(548\) | −9.39792 | − | 16.2777i | −0.401459 | − | 0.695347i | ||||
\(549\) | 8.34091 | 0.355981 | ||||||||
\(550\) | 22.3875 | − | 38.7763i | 0.954606 | − | 1.65343i | ||||
\(551\) | −1.12548 | + | 1.94938i | −0.0479469 | + | 0.0830464i | ||||
\(552\) | 16.5375 | + | 28.6437i | 0.703881 | + | 1.21916i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 32.1833 | 1.36734 | ||||||||
\(555\) | 16.2042 | 0.687829 | ||||||||
\(556\) | −1.70295 | −0.0722212 | ||||||||
\(557\) | 1.40834 | 0.0596732 | 0.0298366 | − | 0.999555i | \(-0.490501\pi\) | ||||
0.0298366 | + | 0.999555i | \(0.490501\pi\) | |||||||
\(558\) | 0.707107 | − | 1.22474i | 0.0299342 | − | 0.0518476i | ||||
\(559\) | −26.4370 | + | 9.54790i | −1.11816 | + | 0.403833i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.40834 | + | 5.90341i | −0.143900 | + | 0.249242i | ||||
\(562\) | −12.3979 | − | 21.4738i | −0.522975 | − | 0.905818i | ||||
\(563\) | 6.21959 | − | 10.7726i | 0.262125 | − | 0.454013i | −0.704682 | − | 0.709524i | \(-0.748910\pi\) |
0.966806 | + | 0.255511i | \(0.0822435\pi\) | |||||||
\(564\) | 2.00000 | + | 3.46410i | 0.0842152 | + | 0.145865i | ||||
\(565\) | −10.6213 | −0.446843 | ||||||||
\(566\) | −7.92254 | − | 13.7222i | −0.333009 | − | 0.576789i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.00000 | + | 15.5885i | 0.377632 | + | 0.654077i | ||||
\(569\) | −12.7958 | − | 22.1630i | −0.536429 | − | 0.929123i | −0.999093 | − | 0.0425886i | \(-0.986440\pi\) |
0.462664 | − | 0.886534i | \(-0.346894\pi\) | |||||||
\(570\) | 16.3931 | 0.686631 | ||||||||
\(571\) | 11.5917 | + | 20.0773i | 0.485096 | + | 0.840211i | 0.999853 | − | 0.0171250i | \(-0.00545132\pi\) |
−0.514757 | + | 0.857336i | \(0.672118\pi\) | |||||||
\(572\) | 10.4622 | + | 8.82327i | 0.437448 | + | 0.368919i | ||||
\(573\) | 22.9162 | 0.957336 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 45.9792 | − | 79.6382i | 1.91746 | − | 3.32114i | ||||
\(576\) | −7.00000 | −0.291667 | ||||||||
\(577\) | 12.3670 | + | 21.4203i | 0.514845 | + | 0.891738i | 0.999852 | + | 0.0172271i | \(0.00548384\pi\) |
−0.485007 | + | 0.874510i | \(0.661183\pi\) | |||||||
\(578\) | 7.69375 | − | 13.3260i | 0.320018 | − | 0.554287i | ||||
\(579\) | −31.9494 | −1.32777 | ||||||||
\(580\) | 3.26153 | 0.135428 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.00000 | − | 5.19615i | 0.124354 | − | 0.215387i | ||||
\(583\) | −23.8979 | − | 41.3924i | −0.989751 | − | 1.71430i | ||||
\(584\) | 18.8753 | + | 32.6930i | 0.781067 | + | 1.35285i | ||||
\(585\) | 11.2958 | + | 9.52628i | 0.467025 | + | 0.393863i | ||||
\(586\) | −1.48640 | + | 2.57452i | −0.0614025 | + | 0.106352i | ||||
\(587\) | 8.34091 | − | 14.4469i | 0.344266 | − | 0.596287i | −0.640954 | − | 0.767579i | \(-0.721461\pi\) |
0.985220 | + | 0.171293i | \(0.0547944\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | − | 3.46410i | −0.0824086 | − | 0.142736i | ||||
\(590\) | 25.4896 | − | 44.1492i | 1.04939 | − | 1.81760i | ||||
\(591\) | −5.65685 | + | 9.79796i | −0.232692 | + | 0.403034i | ||||
\(592\) | 1.39792 | − | 2.42126i | 0.0574540 | − | 0.0995132i | ||||
\(593\) | −4.17046 | + | 7.22344i | −0.171260 | + | 0.296631i | −0.938861 | − | 0.344297i | \(-0.888117\pi\) |
0.767601 | + | 0.640929i | \(0.221451\pi\) | |||||||
\(594\) | 10.7362 | + | 18.5957i | 0.440513 | + | 0.762991i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.29583 | + | 12.6368i | −0.298849 | + | 0.517621i | ||||
\(597\) | −3.59166 | + | 6.22094i | −0.146997 | + | 0.254606i | ||||
\(598\) | −21.4872 | − | 18.1211i | −0.878677 | − | 0.741028i | ||||
\(599\) | 16.7958 | + | 29.0912i | 0.686259 | + | 1.18864i | 0.973039 | + | 0.230639i | \(0.0740817\pi\) |
−0.286780 | + | 0.957996i | \(0.592585\pi\) | |||||||
\(600\) | −25.0227 | − | 43.3407i | −1.02155 | − | 1.76937i | ||||
\(601\) | −12.0930 | + | 20.9457i | −0.493284 | + | 0.854393i | −0.999970 | − | 0.00773797i | \(-0.997537\pi\) |
0.506686 | + | 0.862130i | \(0.330870\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.79583 | 0.154578 | ||||||||
\(604\) | −1.59166 | −0.0647639 | ||||||||
\(605\) | 6.98415 | − | 12.0969i | 0.283946 | − | 0.491809i | ||||
\(606\) | 6.89792 | + | 11.9475i | 0.280209 | + | 0.485336i | ||||
\(607\) | −4.79064 | −0.194446 | −0.0972231 | − | 0.995263i | \(-0.530996\pi\) | ||||
−0.0972231 | + | 0.995263i | \(0.530996\pi\) | |||||||
\(608\) | −7.07107 | + | 12.2474i | −0.286770 | + | 0.496700i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 34.1833 | 1.38404 | ||||||||
\(611\) | −7.79583 | − | 6.57457i | −0.315386 | − | 0.265979i | ||||
\(612\) | −0.634922 | − | 1.09972i | −0.0256652 | − | 0.0444535i | ||||
\(613\) | 41.9792 | 1.69552 | 0.847761 | − | 0.530378i | \(-0.177950\pi\) | ||||
0.847761 | + | 0.530378i | \(0.177950\pi\) | |||||||
\(614\) | −10.0291 | − | 17.3710i | −0.404743 | − | 0.701035i | ||||
\(615\) | 8.61491 | + | 14.9215i | 0.347387 | + | 0.601692i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.19375 | − | 3.79968i | −0.0883169 | − | 0.152969i | 0.818483 | − | 0.574531i | \(-0.194815\pi\) |
−0.906800 | + | 0.421561i | \(0.861482\pi\) | |||||||
\(618\) | 7.59166 | 0.305381 | ||||||||
\(619\) | −16.9558 | − | 29.3684i | −0.681512 | − | 1.18041i | −0.974519 | − | 0.224303i | \(-0.927989\pi\) |
0.293007 | − | 0.956110i | \(-0.405344\pi\) | |||||||
\(620\) | −2.89792 | + | 5.01934i | −0.116383 | + | 0.201581i | ||||
\(621\) | 22.0499 | + | 38.1916i | 0.884834 | + | 1.53258i | ||||
\(622\) | −14.4161 | + | 24.9695i | −0.578034 | + | 1.00118i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.79583 | + | 1.73205i | −0.191987 | + | 0.0693375i | ||||
\(625\) | −27.5812 | + | 47.7721i | −1.10325 | + | 1.91088i | ||||
\(626\) | −15.2676 | −0.610216 | ||||||||
\(627\) | 15.1833 | 0.606364 | ||||||||
\(628\) | −0.144369 | −0.00576095 | ||||||||
\(629\) | 3.55027 | 0.141559 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.7958 | + | 34.2874i | 0.788060 | + | 1.36496i | 0.927154 | + | 0.374680i | \(0.122247\pi\) |
−0.139095 | + | 0.990279i | \(0.544419\pi\) | |||||||
\(632\) | −3.30625 | + | 5.72660i | −0.131516 | + | 0.227792i | ||||
\(633\) | 5.51249 | − | 9.54790i | 0.219102 | − | 0.379495i | ||||
\(634\) | 6.59166 | 0.261788 | ||||||||
\(635\) | −23.7529 | − | 41.1412i | −0.942605 | − | 1.63264i | ||||
\(636\) | −17.8073 | −0.706105 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.02084 | −0.119596 | ||||||||
\(639\) | 3.00000 | + | 5.19615i | 0.118678 | + | 0.205557i | ||||
\(640\) | 12.2948 | 0.485995 | ||||||||
\(641\) | 2.39792 | − | 4.15331i | 0.0947120 | − | 0.164046i | −0.814776 | − | 0.579775i | \(-0.803140\pi\) |
0.909488 | + | 0.415729i | \(0.136474\pi\) | |||||||
\(642\) | −4.24264 | + | 7.34847i | −0.167444 | + | 0.290021i | ||||
\(643\) | 2.82843 | + | 4.89898i | 0.111542 | + | 0.193197i | 0.916392 | − | 0.400281i | \(-0.131088\pi\) |
−0.804850 | + | 0.593478i | \(0.797754\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 45.1833 | 1.77909 | ||||||||
\(646\) | 3.59166 | 0.141312 | ||||||||
\(647\) | −38.7318 | −1.52270 | −0.761351 | − | 0.648339i | \(-0.775464\pi\) | ||||
−0.761351 | + | 0.648339i | \(0.775464\pi\) | |||||||
\(648\) | 15.0000 | 0.589256 | ||||||||
\(649\) | 23.6085 | − | 40.8912i | 0.926716 | − | 1.60512i | ||||
\(650\) | 32.5122 | + | 27.4190i | 1.27523 | + | 1.07546i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.69375 | − | 13.3260i | 0.301310 | − | 0.521885i | ||||
\(653\) | 6.59166 | + | 11.4171i | 0.257952 | + | 0.446785i | 0.965693 | − | 0.259686i | \(-0.0836191\pi\) |
−0.707741 | + | 0.706472i | \(0.750286\pi\) | |||||||
\(654\) | 1.12548 | − | 1.94938i | 0.0440096 | − | 0.0762268i | ||||
\(655\) | −11.0000 | − | 19.0526i | −0.429806 | − | 0.744445i | ||||
\(656\) | 2.97280 | 0.116068 | ||||||||
\(657\) | 6.29178 | + | 10.8977i | 0.245466 | + | 0.425159i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.20417 | + | 15.9421i | 0.358543 | + | 0.621016i | 0.987718 | − | 0.156249i | \(-0.0499401\pi\) |
−0.629174 | + | 0.777264i | \(0.716607\pi\) | |||||||
\(660\) | −11.0000 | − | 19.0526i | −0.428174 | − | 0.741620i | ||||
\(661\) | −7.50417 | −0.291879 | −0.145939 | − | 0.989294i | \(-0.546620\pi\) | ||||
−0.145939 | + | 0.989294i | \(0.546620\pi\) | |||||||
\(662\) | −14.6937 | − | 25.4503i | −0.571089 | − | 0.989155i | ||||
\(663\) | −4.94975 | − | 4.17434i | −0.192232 | − | 0.162118i | ||||
\(664\) | −29.6985 | −1.15252 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.39792 | − | 2.42126i | 0.0541681 | − | 0.0938220i | ||||
\(667\) | −6.20417 | −0.240226 | ||||||||
\(668\) | −0.851476 | − | 1.47480i | −0.0329446 | − | 0.0570617i | ||||
\(669\) | 4.00000 | − | 6.92820i | 0.154649 | − | 0.267860i | ||||
\(670\) | 15.5563 | 0.600994 | ||||||||
\(671\) | 31.6607 | 1.22225 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.9896 | − | 20.7666i | 0.462164 | − | 0.800492i | −0.536904 | − | 0.843643i | \(-0.680406\pi\) |
0.999069 | + | 0.0431511i | \(0.0137397\pi\) | |||||||
\(674\) | −8.98958 | − | 15.5704i | −0.346266 | − | 0.599750i | ||||
\(675\) | −33.3636 | − | 57.7875i | −1.28417 | − | 2.22424i | ||||
\(676\) | −10.0000 | + | 8.30662i | −0.384615 | + | 0.319486i | ||||
\(677\) | 3.82427 | − | 6.62383i | 0.146979 | − | 0.254575i | −0.783131 | − | 0.621857i | \(-0.786378\pi\) |
0.930109 | + | 0.367283i | \(0.119712\pi\) | |||||||
\(678\) | 1.83258 | − | 3.17413i | 0.0703799 | − | 0.121902i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −7.80625 | − | 13.5208i | −0.299356 | − | 0.518500i | ||||
\(681\) | −5.20417 | + | 9.01388i | −0.199424 | + | 0.345413i | ||||
\(682\) | 2.68406 | − | 4.64893i | 0.102778 | − | 0.178017i | ||||
\(683\) | 3.38749 | − | 5.86731i | 0.129619 | − | 0.224506i | −0.793910 | − | 0.608035i | \(-0.791958\pi\) |
0.923529 | + | 0.383529i | \(0.125291\pi\) | |||||||
\(684\) | −1.41421 | + | 2.44949i | −0.0540738 | + | 0.0936586i | ||||
\(685\) | −38.5152 | − | 66.7103i | −1.47159 | − | 2.54887i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.00000 | + | 15.5885i | −0.343371 | + | 0.594737i | ||||
\(688\) | 3.89792 | − | 6.75139i | 0.148607 | − | 0.257394i | ||||
\(689\) | 42.7004 | − | 15.4216i | 1.62676 | − | 0.587515i | ||||
\(690\) | 22.5917 | + | 39.1299i | 0.860050 | + | 1.48965i | ||||
\(691\) | −1.26984 | − | 2.19944i | −0.0483072 | − | 0.0836705i | 0.840861 | − | 0.541251i | \(-0.182049\pi\) |
−0.889168 | + | 0.457581i | \(0.848716\pi\) | |||||||
\(692\) | 8.90365 | − | 15.4216i | 0.338466 | − | 0.586240i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −32.9792 | −1.25187 | ||||||||
\(695\) | −6.97916 | −0.264735 | ||||||||
\(696\) | −1.68821 | + | 2.92407i | −0.0639916 | + | 0.110837i | ||||
\(697\) | 1.88749 | + | 3.26924i | 0.0714940 | + | 0.123831i | ||||
\(698\) | −26.5813 | −1.00612 | ||||||||
\(699\) | 12.1504 | − | 21.0452i | 0.459572 | − | 0.796002i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.5917 | −1.11766 | −0.558831 | − | 0.829282i | \(-0.688750\pi\) | ||||
−0.558831 | + | 0.829282i | \(0.688750\pi\) | |||||||
\(702\) | −19.1833 | + | 6.92820i | −0.724028 | + | 0.261488i | ||||
\(703\) | −3.95390 | − | 6.84836i | −0.149124 | − | 0.258291i | ||||
\(704\) | −26.5708 | −1.00143 | ||||||||
\(705\) | 8.19654 | + | 14.1968i | 0.308700 | + | 0.534684i | ||||
\(706\) | 2.61187 | + | 4.52390i | 0.0982992 | + | 0.170259i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −8.79583 | − | 15.2348i | −0.330568 | − | 0.572560i | ||||
\(709\) | −9.20417 | −0.345670 | −0.172835 | − | 0.984951i | \(-0.555293\pi\) | ||||
−0.172835 | + | 0.984951i | \(0.555293\pi\) | |||||||
\(710\) | 12.2948 | + | 21.2952i | 0.461416 | + | 0.799196i | ||||
\(711\) | −1.10208 | + | 1.90887i | −0.0413314 | + | 0.0715881i | ||||
\(712\) | 22.4683 | + | 38.9163i | 0.842036 | + | 1.45845i | ||||
\(713\) | 5.51249 | − | 9.54790i | 0.206444 | − | 0.357572i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 42.8771 | + | 36.1602i | 1.60351 | + | 1.35231i | ||||
\(716\) | −9.79583 | + | 16.9669i | −0.366087 | + | 0.634082i | ||||
\(717\) | 14.4309 | 0.538931 | ||||||||
\(718\) | −4.00000 | −0.149279 | ||||||||
\(719\) | −1.99169 | −0.0742775 | −0.0371387 | − | 0.999310i | \(-0.511824\pi\) | ||||
−0.0371387 | + | 0.999310i | \(0.511824\pi\) | |||||||
\(720\) | −4.09827 | −0.152734 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.50000 | + | 9.52628i | 0.204689 | + | 0.354531i | ||||
\(723\) | −7.89792 | + | 13.6796i | −0.293727 | + | 0.508749i | ||||
\(724\) | −1.90477 | + | 3.29915i | −0.0707901 | + | 0.122612i | ||||
\(725\) | 9.38749 | 0.348643 | ||||||||
\(726\) | 2.41006 | + | 4.17434i | 0.0894456 | + | 0.154924i | ||||
\(727\) | −32.4974 | −1.20526 | −0.602632 | − | 0.798020i | \(-0.705881\pi\) | ||||
−0.602632 | + | 0.798020i | \(0.705881\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 25.7854 | + | 44.6616i | 0.954361 | + | 1.65300i | ||||
\(731\) | 9.89949 | 0.366146 | ||||||||
\(732\) | 5.89792 | − | 10.2155i | 0.217993 | − | 0.377575i | ||||
\(733\) | −16.6096 | + | 28.7687i | −0.613491 | + | 1.06260i | 0.377156 | + | 0.926150i | \(0.376902\pi\) |
−0.990647 | + | 0.136448i | \(0.956431\pi\) | |||||||
\(734\) | 10.6066 | + | 18.3712i | 0.391497 | + | 0.678092i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −38.9792 | −1.43679 | ||||||||
\(737\) | 14.4083 | 0.530738 | ||||||||
\(738\) | 2.97280 | 0.109430 | ||||||||
\(739\) | −23.1833 | −0.852812 | −0.426406 | − | 0.904532i | \(-0.640221\pi\) | ||||
−0.426406 | + | 0.904532i | \(0.640221\pi\) | |||||||
\(740\) | −5.72904 | + | 9.92299i | −0.210604 | + | 0.364776i | ||||
\(741\) | −2.53969 | + | 14.1968i | −0.0932978 | + | 0.521534i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.5917 | − | 25.2735i | 0.535316 | − | 0.927195i | −0.463832 | − | 0.885923i | \(-0.653526\pi\) |
0.999148 | − | 0.0412716i | \(-0.0131409\pi\) | |||||||
\(744\) | −3.00000 | − | 5.19615i | −0.109985 | − | 0.190500i | ||||
\(745\) | −29.9003 | + | 51.7888i | −1.09546 | + | 1.89740i | ||||
\(746\) | −3.29583 | − | 5.70855i | −0.120669 | − | 0.209005i | ||||
\(747\) | −9.89949 | −0.362204 | ||||||||
\(748\) | −2.41006 | − | 4.17434i | −0.0881205 | − | 0.152629i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −19.6937 | − | 34.1106i | −0.719114 | − | 1.24554i | ||||
\(751\) | 3.89792 | + | 6.75139i | 0.142237 | + | 0.246362i | 0.928339 | − | 0.371735i | \(-0.121237\pi\) |
−0.786102 | + | 0.618097i | \(0.787904\pi\) | |||||||
\(752\) | 2.82843 | 0.103142 | ||||||||
\(753\) | 11.7958 | + | 20.4310i | 0.429864 | + | 0.744546i | ||||
\(754\) | 0.505291 | − | 2.82457i | 0.0184016 | − | 0.102865i | ||||
\(755\) | −6.52307 | −0.237399 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.59166 | + | 11.4171i | −0.239578 | + | 0.414961i | −0.960593 | − | 0.277958i | \(-0.910342\pi\) |
0.721015 | + | 0.692919i | \(0.243676\pi\) | |||||||
\(758\) | 25.3875 | 0.922115 | ||||||||
\(759\) | 20.9245 | + | 36.2422i | 0.759510 | + | 1.31551i | ||||
\(760\) | −17.3875 | + | 30.1160i | −0.630711 | + | 1.09242i | ||||
\(761\) | 17.8073 | 0.645514 | 0.322757 | − | 0.946482i | \(-0.395390\pi\) | ||||
0.322757 | + | 0.946482i | \(0.395390\pi\) | |||||||
\(762\) | 16.3931 | 0.593859 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −8.10208 | + | 14.0332i | −0.293123 | + | 0.507704i | ||||
\(765\) | −2.60208 | − | 4.50694i | −0.0940786 | − | 0.162949i | ||||
\(766\) | 6.07522 | + | 10.5226i | 0.219507 | + | 0.380197i | ||||
\(767\) | 34.2854 | + | 28.9144i | 1.23797 | + | 1.04404i | ||||
\(768\) | −12.0208 | + | 20.8207i | −0.433764 | + | 0.751301i | ||||
\(769\) | 2.12132 | − | 3.67423i | 0.0764968 | − | 0.132496i | −0.825239 | − | 0.564783i | \(-0.808960\pi\) |
0.901736 | + | 0.432287i | \(0.142293\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.10208 | − | 10.5691i | −0.219761 | − | 0.380638i | ||||
\(772\) | 11.2958 | − | 19.5650i | 0.406546 | − | 0.704158i | ||||
\(773\) | 17.3889 | − | 30.1185i | 0.625436 | − | 1.08329i | −0.363020 | − | 0.931781i | \(-0.618254\pi\) |
0.988456 | − | 0.151506i | \(-0.0484124\pi\) | |||||||
\(774\) | 3.89792 | − | 6.75139i | 0.140108 | − | 0.242674i | ||||
\(775\) | −8.34091 | + | 14.4469i | −0.299614 | + | 0.518947i | ||||
\(776\) | 6.36396 | + | 11.0227i | 0.228453 | + | 0.395692i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.193747 | − | 0.335580i | 0.00694618 | − | 0.0120311i | ||||
\(779\) | 4.20417 | − | 7.28183i | 0.150630 | − | 0.260899i | ||||
\(780\) | 19.6546 | − | 7.09841i | 0.703748 | − | 0.254164i | ||||
\(781\) | 11.3875 | + | 19.7237i | 0.407477 | + | 0.705770i | ||||
\(782\) | 4.94975 | + | 8.57321i | 0.177003 | + | 0.306578i | ||||
\(783\) | −2.25095 | + | 3.89876i | −0.0804424 | + | 0.139330i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.591663 | −0.0211174 | ||||||||
\(786\) | 7.59166 | 0.270786 | ||||||||
\(787\) | −21.1985 | + | 36.7168i | −0.755644 | + | 1.30881i | 0.189410 | + | 0.981898i | \(0.439342\pi\) |
−0.945054 | + | 0.326915i | \(0.893991\pi\) | |||||||
\(788\) | −4.00000 | − | 6.92820i | −0.142494 | − | 0.246807i | ||||
\(789\) | −4.79064 | −0.170551 | ||||||||
\(790\) | −4.51664 | + | 7.82305i | −0.160695 | + | 0.278332i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −11.3875 | −0.404637 | ||||||||
\(793\) | −5.29583 | + | 29.6036i | −0.188060 | + | 1.05126i | ||||
\(794\) | 3.53553 | + | 6.12372i | 0.125471 | + | 0.217323i | ||||
\(795\) | −72.9792 | −2.58830 | ||||||||
\(796\) | −2.53969 | − | 4.39887i | −0.0900169 | − | 0.155914i | ||||
\(797\) | 0.418369 | + | 0.724636i | 0.0148194 | + | 0.0256679i | 0.873340 | − | 0.487111i | \(-0.161949\pi\) |
−0.858521 | + | 0.512779i | \(0.828616\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.79583 | + | 3.11047i | 0.0635320 | + | 0.110041i | ||||
\(800\) | 58.9792 | 2.08523 | ||||||||
\(801\) | 7.48944 | + | 12.9721i | 0.264626 | + | 0.458346i | ||||
\(802\) | 2.19375 | − | 3.79968i | 0.0774639 | − | 0.134171i | ||||
\(803\) | 23.8825 | + | 41.3657i | 0.842796 | + | 1.45977i | ||||
\(804\) | 2.68406 | − | 4.64893i | 0.0946594 | − | 0.163955i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.89792 | + | 3.28729i | 0.137298 | + | 0.115790i | ||||
\(807\) | −8.79583 | + | 15.2348i | −0.309628 | + | 0.536291i | ||||
\(808\) | −29.2654 | −1.02955 | ||||||||
\(809\) | −37.3667 | −1.31374 | −0.656871 | − | 0.754003i | \(-0.728120\pi\) | ||||
−0.656871 | + | 0.754003i | \(0.728120\pi\) | |||||||
\(810\) | 20.4914 | 0.719993 | ||||||||
\(811\) | 52.0372 | 1.82727 | 0.913636 | − | 0.406533i | \(-0.133262\pi\) | ||||
0.913636 | + | 0.406533i | \(0.133262\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.3875 | − | 21.4558i | −0.434448 | − | 0.752487i | ||||
\(814\) | 5.30625 | − | 9.19070i | 0.185984 | − | 0.322134i | ||||
\(815\) | 31.5311 | − | 54.6134i | 1.10449 | − | 1.91302i | ||||
\(816\) | 1.79583 | 0.0628667 | ||||||||
\(817\) | −11.0250 | − | 19.0958i | −0.385715 | − | 0.668078i | ||||
\(818\) | −18.7884 | −0.656921 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.1833 | −0.425460 | ||||||||
\(821\) | −18.1833 | − | 31.4944i | −0.634602 | − | 1.09916i | −0.986599 | − | 0.163162i | \(-0.947831\pi\) |
0.351997 | − | 0.936001i | \(-0.385503\pi\) | |||||||
\(822\) | 26.5813 | 0.927130 | ||||||||
\(823\) | 10.3875 | − | 17.9917i | 0.362085 | − | 0.627150i | −0.626219 | − | 0.779648i | \(-0.715398\pi\) |
0.988304 | + | 0.152497i | \(0.0487316\pi\) | |||||||
\(824\) | −8.05217 | + | 13.9468i | −0.280511 | + | 0.485859i | ||||
\(825\) | −31.6607 | − | 54.8379i | −1.10228 | − | 1.90921i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.9792 | −0.729517 | −0.364758 | − | 0.931102i | \(-0.618848\pi\) | ||||
−0.364758 | + | 0.931102i | \(0.618848\pi\) | |||||||
\(828\) | −7.79583 | −0.270924 | ||||||||
\(829\) | 27.2737 | 0.947254 | 0.473627 | − | 0.880725i | \(-0.342944\pi\) | ||||
0.473627 | + | 0.880725i | \(0.342944\pi\) | |||||||
\(830\) | −40.5708 | −1.40823 | ||||||||
\(831\) | 22.7570 | − | 39.4164i | 0.789433 | − | 1.36734i | ||||
\(832\) | 4.44446 | − | 24.8445i | 0.154084 | − | 0.861326i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.20417 | − | 2.08568i | 0.0416969 | − | 0.0722212i | ||||
\(835\) | −3.48958 | − | 6.04413i | −0.120762 | − | 0.209166i | ||||
\(836\) | −5.36812 | + | 9.29785i | −0.185660 | + | 0.321573i | ||||
\(837\) | −4.00000 | − | 6.92820i | −0.138260 | − | 0.239474i | ||||
\(838\) | 25.7151 | 0.888314 | ||||||||
\(839\) | 2.82843 | + | 4.89898i | 0.0976481 | + | 0.169132i | 0.910711 | − | 0.413045i | \(-0.135535\pi\) |
−0.813063 | + | 0.582176i | \(0.802201\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.1833 | + | 24.5662i | 0.489080 | + | 0.847112i | ||||
\(842\) | −6.29583 | − | 10.9047i | −0.216969 | − | 0.375801i | ||||
\(843\) | −35.0666 | −1.20776 | ||||||||
\(844\) | 3.89792 | + | 6.75139i | 0.134172 | + | 0.232392i | ||||
\(845\) | −40.9827 | + | 34.0428i | −1.40985 | + | 1.17111i | ||||
\(846\) | 2.82843 | 0.0972433 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.29583 | + | 10.9047i | −0.216200 | + | 0.374469i | ||||
\(849\) | −22.4083 | −0.769052 | ||||||||
\(850\) | −7.48944 | − | 12.9721i | −0.256886 | − | 0.444939i | ||||
\(851\) | 10.8979 | − | 18.8757i | 0.373576 | − | 0.647052i | ||||
\(852\) | 8.48528 | 0.290701 | ||||||||
\(853\) | 33.5080 | 1.14729 | 0.573646 | − | 0.819103i | \(-0.305528\pi\) | ||||
0.573646 | + | 0.819103i | \(0.305528\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.79583 | + | 10.0387i | −0.198213 | + | 0.343315i | ||||
\(856\) | −9.00000 | − | 15.5885i | −0.307614 | − | 0.532803i | ||||
\(857\) | −8.70183 | − | 15.0720i | −0.297249 | − | 0.514850i | 0.678257 | − | 0.734825i | \(-0.262736\pi\) |
−0.975506 | + | 0.219975i | \(0.929402\pi\) | |||||||
\(858\) | −18.2042 | + | 6.57457i | −0.621480 | + | 0.224452i | ||||
\(859\) | 5.09412 | − | 8.82327i | 0.173809 | − | 0.301046i | −0.765939 | − | 0.642913i | \(-0.777726\pi\) |
0.939748 | + | 0.341867i | \(0.111059\pi\) | |||||||
\(860\) | −15.9747 | + | 27.6690i | −0.544733 | + | 0.943506i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.5917 | − | 28.7376i | −0.565114 | − | 0.978807i | ||||
\(863\) | −4.10208 | + | 7.10502i | −0.139637 | + | 0.241858i | −0.927359 | − | 0.374173i | \(-0.877927\pi\) |
0.787723 | + | 0.616030i | \(0.211260\pi\) | |||||||
\(864\) | −14.1421 | + | 24.4949i | −0.481125 | + | 0.833333i | ||||
\(865\) | 36.4896 | − | 63.2018i | 1.24068 | − | 2.14893i | ||||
\(866\) | −10.2457 | + | 17.7460i | −0.348162 | + | 0.603035i | ||||
\(867\) | −10.8806 | − | 18.8458i | −0.369525 | − | 0.640035i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.18333 | + | 7.24573i | −0.141910 | + | 0.245795i | ||||
\(870\) | −2.30625 | + | 3.99455i | −0.0781893 | + | 0.135428i | ||||
\(871\) | −2.41006 | + | 13.4722i | −0.0816617 | + | 0.456488i | ||||
\(872\) | 2.38749 | + | 4.13526i | 0.0808508 | + | 0.140038i | ||||
\(873\) | 2.12132 | + | 3.67423i | 0.0717958 | + | 0.124354i | ||||
\(874\) | 11.0250 | − | 19.0958i | 0.372925 | − | 0.645925i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 17.7958 | 0.601265 | ||||||||
\(877\) | 4.79583 | 0.161944 | 0.0809719 | − | 0.996716i | \(-0.474198\pi\) | ||||
0.0809719 | + | 0.996716i | \(0.474198\pi\) | |||||||
\(878\) | −10.0291 | + | 17.3710i | −0.338467 | + | 0.586241i | ||||
\(879\) | 2.10208 | + | 3.64092i | 0.0709015 | + | 0.122805i | ||||
\(880\) | −15.5563 | −0.524404 | ||||||||
\(881\) | 5.29593 | − | 9.17282i | 0.178424 | − | 0.309040i | −0.762917 | − | 0.646497i | \(-0.776233\pi\) |
0.941341 | + | 0.337457i | \(0.109567\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.3875 | −1.52741 | −0.763705 | − | 0.645565i | \(-0.776622\pi\) | ||||
−0.763705 | + | 0.645565i | \(0.776622\pi\) | |||||||
\(884\) | 4.30625 | − | 1.55524i | 0.144835 | − | 0.0523082i | ||||
\(885\) | −36.0477 | − | 62.4365i | −1.21173 | − | 2.09878i | ||||
\(886\) | 10.0000 | 0.335957 | ||||||||
\(887\) | −21.0688 | − | 36.4923i | −0.707422 | − | 1.22529i | −0.965810 | − | 0.259250i | \(-0.916525\pi\) |
0.258388 | − | 0.966041i | \(-0.416809\pi\) | |||||||
\(888\) | −5.93085 | − | 10.2725i | −0.199026 | − | 0.344724i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 30.6937 | + | 53.1631i | 1.02886 | + | 1.78203i | ||||
\(891\) | 18.9792 | 0.635826 | ||||||||
\(892\) | 2.82843 | + | 4.89898i | 0.0947027 | + | 0.164030i | ||||
\(893\) | 4.00000 | − | 6.92820i | 0.133855 | − | 0.231843i | ||||
\(894\) | −10.3179 | − | 17.8711i | −0.345081 | − | 0.597698i | ||||
\(895\) | −40.1460 | + | 69.5349i | −1.34193 | + | 2.32429i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −37.3875 | + | 13.5028i | −1.24833 | + | 0.450845i | ||||
\(898\) | −11.7958 | + | 20.4310i | −0.393632 | + | 0.681791i | ||||
\(899\) | 1.12548 | 0.0375367 | ||||||||
\(900\) | 11.7958 | 0.393194 | ||||||||
\(901\) | −15.9895 | −0.532686 | ||||||||
\(902\) | 11.2842 | 0.375724 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.88749 | + | 6.73334i | 0.129296 | + | 0.223947i | ||||
\(905\) | −7.80625 | + | 13.5208i | −0.259489 | + | 0.449447i | ||||
\(906\) | 1.12548 | − | 1.94938i | 0.0373914 | − | 0.0647639i | ||||
\(907\) | 20.6125 | 0.684427 | 0.342214 | − | 0.939622i | \(-0.388823\pi\) | ||||
0.342214 | + | 0.939622i | \(0.388823\pi\) | |||||||
\(908\) | −3.67990 | − | 6.37378i | −0.122122 | − | 0.211521i | ||||
\(909\) | −9.75513 | −0.323557 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.81667 | −0.159584 | −0.0797918 | − | 0.996812i | \(-0.525426\pi\) | ||||
−0.0797918 | + | 0.996812i | \(0.525426\pi\) | |||||||
\(912\) | −2.00000 | − | 3.46410i | −0.0662266 | − | 0.114708i | ||||
\(913\) | −37.5768 | −1.24361 | ||||||||
\(914\) | −2.29583 | + | 3.97650i | −0.0759394 | + | 0.131531i | ||||
\(915\) | 24.1713 | − | 41.8659i | 0.799077 | − | 1.38404i | ||||
\(916\) | −6.36396 | − | 11.0227i | −0.210271 | − | 0.364200i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 7.18333 | 0.237085 | ||||||||
\(919\) | 10.0000 | 0.329870 | 0.164935 | − | 0.986304i | \(-0.447259\pi\) | ||||
0.164935 | + | 0.986304i | \(0.447259\pi\) | |||||||
\(920\) | −95.8483 | −3.16003 | ||||||||
\(921\) | −28.3667 | −0.934713 | ||||||||
\(922\) | 12.0930 | − | 20.9457i | 0.398262 | − | 0.689810i | ||||
\(923\) | −20.3470 | + | 7.34847i | −0.669729 | + | 0.241878i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.4896 | + | 28.5608i | −0.542174 | + | 0.939073i | ||||
\(926\) | 8.69375 | + | 15.0580i | 0.285694 | + | 0.494837i | ||||
\(927\) | −2.68406 | + | 4.64893i | −0.0881560 | + | 0.152691i | ||||
\(928\) | −1.98958 | − | 3.44605i | −0.0653111 | − | 0.113122i | ||||
\(929\) | 21.3576 | 0.700719 | 0.350360 | − | 0.936615i | \(-0.386059\pi\) | ||||
0.350360 | + | 0.936615i | \(0.386059\pi\) | |||||||
\(930\) | −4.09827 | − | 7.09841i | −0.134388 | − | 0.232766i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8.59166 | + | 14.8812i | 0.281429 | + | 0.487450i | ||||
\(933\) | 20.3875 | + | 35.3122i | 0.667457 | + | 1.15607i | ||||
\(934\) | 31.9494 | 1.04542 | ||||||||
\(935\) | −9.87707 | − | 17.1076i | −0.323015 | − | 0.559478i | ||||
\(936\) | 1.90477 | − | 10.6476i | 0.0622593 | − | 0.348028i | ||||
\(937\) | 13.7090 | 0.447854 | 0.223927 | − | 0.974606i | \(-0.428112\pi\) | ||||
0.223927 | + | 0.974606i | \(0.428112\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.7958 | + | 18.6989i | −0.352309 | + | 0.610216i | ||||
\(940\) | −11.5917 | −0.378078 | ||||||||
\(941\) | 1.83258 | + | 3.17413i | 0.0597405 | + | 0.103474i | 0.894349 | − | 0.447370i | \(-0.147639\pi\) |
−0.834608 | + | 0.550844i | \(0.814306\pi\) | |||||||
\(942\) | 0.102084 | − | 0.176815i | 0.00332608 | − | 0.00576095i | ||||
\(943\) | 23.1754 | 0.754695 | ||||||||
\(944\) | −12.4392 | −0.404861 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.7958 | − | 25.6271i | 0.481054 | − | 0.833210i | ||||
\(947\) | −18.8979 | − | 32.7322i | −0.614100 | − | 1.06365i | −0.990542 | − | 0.137212i | \(-0.956186\pi\) |
0.376442 | − | 0.926440i | \(-0.377147\pi\) | |||||||
\(948\) | 1.55858 | + | 2.69954i | 0.0506204 | + | 0.0876771i | ||||
\(949\) | −42.6729 | + | 15.4116i | −1.38522 | + | 0.500283i | ||||
\(950\) | −16.6818 | + | 28.8938i | −0.541230 | + | 0.937438i | ||||
\(951\) | 4.66101 | − | 8.07311i | 0.151144 | − | 0.261788i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.5917 | + | 37.3979i | 0.699423 | + | 1.21144i | 0.968667 | + | 0.248364i | \(0.0798928\pi\) |
−0.269244 | + | 0.963072i | \(0.586774\pi\) | |||||||
\(954\) | −6.29583 | + | 10.9047i | −0.203835 | + | 0.353053i | ||||
\(955\) | −33.2045 | + | 57.5120i | −1.07447 | + | 1.86104i | ||||
\(956\) | −5.10208 | + | 8.83707i | −0.165013 | + | 0.285811i | ||||
\(957\) | −2.13606 | + | 3.69976i | −0.0690490 | + | 0.119596i | ||||
\(958\) | −10.4622 | − | 18.1211i | −0.338019 | − | 0.585467i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −20.2854 | + | 35.1354i | −0.654709 | + | 1.13399i | ||||
\(961\) | 14.5000 | − | 25.1147i | 0.467742 | − | 0.810153i | ||||
\(962\) | 7.70599 | + | 6.49881i | 0.248451 | + | 0.209530i | ||||
\(963\) | −3.00000 | − | 5.19615i | −0.0966736 | − | 0.167444i | ||||
\(964\) | −5.58467 | − | 9.67293i | −0.179870 | − | 0.311544i | ||||
\(965\) | 46.2934 | − | 80.1825i | 1.49024 | − | 2.58117i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.3875 | −0.559144 | −0.279572 | − | 0.960125i | \(-0.590193\pi\) | ||||
−0.279572 | + | 0.960125i | \(0.590193\pi\) | |||||||
\(968\) | −10.2250 | −0.328644 | ||||||||
\(969\) | 2.53969 | − | 4.39887i | 0.0815866 | − | 0.141312i | ||||
\(970\) | 8.69375 | + | 15.0580i | 0.279139 | + | 0.483484i | ||||
\(971\) | 22.6274 | 0.726148 | 0.363074 | − | 0.931760i | \(-0.381727\pi\) | ||||
0.363074 | + | 0.931760i | \(0.381727\pi\) | |||||||
\(972\) | −4.94975 | + | 8.57321i | −0.158763 | + | 0.274986i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.408337 | 0.0130840 | ||||||||
\(975\) | 56.5708 | − | 20.4310i | 1.81172 | − | 0.654315i | ||||
\(976\) | −4.17046 | − | 7.22344i | −0.133493 | − | 0.231217i | ||||
\(977\) | −28.3875 | −0.908196 | −0.454098 | − | 0.890952i | \(-0.650038\pi\) | ||||
−0.454098 | + | 0.890952i | \(0.650038\pi\) | |||||||
\(978\) | 10.8806 | + | 18.8458i | 0.347923 | + | 0.602621i | ||||
\(979\) | 28.4286 | + | 49.2398i | 0.908583 | + | 1.57371i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.795832 | + | 1.37842i | 0.0254089 | + | 0.0440096i | ||||
\(982\) | 9.59166 | 0.306082 | ||||||||
\(983\) | 0.433107 | + | 0.750163i | 0.0138140 | + | 0.0239265i | 0.872850 | − | 0.487989i | \(-0.162269\pi\) |
−0.859036 | + | 0.511916i | \(0.828936\pi\) | |||||||
\(984\) | 6.30625 | − | 10.9228i | 0.201036 | − | 0.348205i | ||||
\(985\) | −16.3931 | − | 28.3937i | −0.522327 | − | 0.904697i | ||||
\(986\) | −0.505291 | + | 0.875190i | −0.0160918 | + | 0.0278717i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.79583 | − | 6.57457i | −0.248018 | − | 0.209165i | ||||
\(989\) | 30.3875 | − | 52.6327i | 0.966266 | − | 1.67362i | ||||
\(990\) | −15.5563 | −0.494413 | ||||||||
\(991\) | 27.7958 | 0.882964 | 0.441482 | − | 0.897270i | \(-0.354453\pi\) | ||||
0.441482 | + | 0.897270i | \(0.354453\pi\) | |||||||
\(992\) | 7.07107 | 0.224507 | ||||||||
\(993\) | −41.5602 | −1.31887 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.4083 | − | 18.0278i | −0.329966 | − | 0.571519i | ||||
\(996\) | −7.00000 | + | 12.1244i | −0.221803 | + | 0.384175i | ||||
\(997\) | 0.634922 | − | 1.09972i | 0.0201082 | − | 0.0348284i | −0.855796 | − | 0.517313i | \(-0.826932\pi\) |
0.875904 | + | 0.482485i | \(0.160266\pi\) | |||||||
\(998\) | 25.7958 | 0.816553 | ||||||||
\(999\) | −7.90781 | − | 13.6967i | −0.250192 | − | 0.433345i |
(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 | 637.2.g.h.373.2 | 8 | ||
7.2 | even | 3 | 637.2.f.g.295.3 | yes | 8 | ||
7.3 | odd | 6 | 637.2.h.k.165.1 | 8 | |||
7.4 | even | 3 | 637.2.h.k.165.4 | 8 | |||
7.5 | odd | 6 | 637.2.f.g.295.2 | ✓ | 8 | ||
7.6 | odd | 2 | inner | 637.2.g.h.373.3 | 8 | ||
13.3 | even | 3 | 637.2.h.k.471.4 | 8 | |||
91.3 | odd | 6 | inner | 637.2.g.h.263.3 | 8 | ||
91.9 | even | 3 | 8281.2.a.bv.1.1 | 4 | |||
91.16 | even | 3 | 637.2.f.g.393.3 | yes | 8 | ||
91.30 | even | 6 | 8281.2.a.bn.1.2 | 4 | |||
91.55 | odd | 6 | 637.2.h.k.471.1 | 8 | |||
91.61 | odd | 6 | 8281.2.a.bv.1.4 | 4 | |||
91.68 | odd | 6 | 637.2.f.g.393.2 | yes | 8 | ||
91.81 | even | 3 | inner | 637.2.g.h.263.2 | 8 | ||
91.82 | odd | 6 | 8281.2.a.bn.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.f.g.295.2 | ✓ | 8 | 7.5 | odd | 6 | ||
637.2.f.g.295.3 | yes | 8 | 7.2 | even | 3 | ||
637.2.f.g.393.2 | yes | 8 | 91.68 | odd | 6 | ||
637.2.f.g.393.3 | yes | 8 | 91.16 | even | 3 | ||
637.2.g.h.263.2 | 8 | 91.81 | even | 3 | inner | ||
637.2.g.h.263.3 | 8 | 91.3 | odd | 6 | inner | ||
637.2.g.h.373.2 | 8 | 1.1 | even | 1 | trivial | ||
637.2.g.h.373.3 | 8 | 7.6 | odd | 2 | inner | ||
637.2.h.k.165.1 | 8 | 7.3 | odd | 6 | |||
637.2.h.k.165.4 | 8 | 7.4 | even | 3 | |||
637.2.h.k.471.1 | 8 | 91.55 | odd | 6 | |||
637.2.h.k.471.4 | 8 | 13.3 | even | 3 | |||
8281.2.a.bn.1.2 | 4 | 91.30 | even | 6 | |||
8281.2.a.bn.1.3 | 4 | 91.82 | odd | 6 | |||
8281.2.a.bv.1.1 | 4 | 91.9 | even | 3 | |||
8281.2.a.bv.1.4 | 4 | 91.61 | odd | 6 |