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 | 373.1 | ||
Root | \(2.04914 - 3.54921i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.373 |
Dual form | 637.2.g.h.263.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||
\(5\) | −1.34203 | + | 2.32446i | −0.600174 | + | 1.03953i | 0.392621 | + | 0.919700i | \(0.371569\pi\) |
−0.992794 | + | 0.119831i | \(0.961765\pi\) | |||||||
\(6\) | 0.707107 | + | 1.22474i | 0.288675 | + | 0.500000i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.68406 | 0.848774 | ||||||||
\(11\) | 5.79583 | 1.74751 | 0.873754 | − | 0.486367i | \(-0.161678\pi\) | ||||
0.873754 | + | 0.486367i | \(0.161678\pi\) | |||||||
\(12\) | −0.707107 | + | 1.22474i | −0.204124 | + | 0.353553i | ||||
\(13\) | −2.75624 | + | 2.32446i | −0.764444 | + | 0.644690i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.89792 | − | 3.28729i | 0.490040 | − | 0.848774i | ||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 2.75624 | − | 4.77395i | 0.668487 | − | 1.15785i | −0.309840 | − | 0.950789i | \(-0.600276\pi\) |
0.978327 | − | 0.207065i | \(-0.0663911\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | 2.82843 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(20\) | 1.34203 | + | 2.32446i | 0.300087 | + | 0.519766i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.89792 | − | 5.01934i | −0.617838 | − | 1.07013i | ||||
\(23\) | −0.897916 | − | 1.55524i | −0.187228 | − | 0.324289i | 0.757097 | − | 0.653303i | \(-0.226617\pi\) |
−0.944325 | + | 0.329014i | \(0.893284\pi\) | |||||||
\(24\) | 4.24264 | 0.866025 | ||||||||
\(25\) | −1.10208 | − | 1.90887i | −0.220417 | − | 0.381773i | ||||
\(26\) | 3.39116 | + | 1.22474i | 0.665062 | + | 0.240192i | ||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.39792 | − | 7.61741i | 0.816672 | − | 1.41452i | −0.0914483 | − | 0.995810i | \(-0.529150\pi\) |
0.908121 | − | 0.418708i | \(-0.137517\pi\) | |||||||
\(30\) | −3.79583 | −0.693021 | ||||||||
\(31\) | −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 | ||||
\(33\) | −8.19654 | −1.42684 | ||||||||
\(34\) | −5.51249 | −0.945383 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 3.39792 | + | 5.88536i | 0.558614 | + | 0.967548i | 0.997613 | + | 0.0690599i | \(0.0220000\pi\) |
−0.438999 | + | 0.898488i | \(0.644667\pi\) | |||||||
\(38\) | −1.41421 | − | 2.44949i | −0.229416 | − | 0.397360i | ||||
\(39\) | 3.89792 | − | 3.28729i | 0.624166 | − | 0.526387i | ||||
\(40\) | 4.02609 | − | 6.97339i | 0.636580 | − | 1.10259i | ||||
\(41\) | 4.87756 | − | 8.44819i | 0.761747 | − | 1.31939i | −0.180202 | − | 0.983630i | \(-0.557675\pi\) |
0.941949 | − | 0.335755i | \(-0.108992\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.897916 | + | 1.55524i | 0.136931 | + | 0.237171i | 0.926333 | − | 0.376705i | \(-0.122943\pi\) |
−0.789403 | + | 0.613876i | \(0.789610\pi\) | |||||||
\(44\) | 2.89792 | − | 5.01934i | 0.436877 | − | 0.756694i | ||||
\(45\) | 1.34203 | − | 2.32446i | 0.200058 | − | 0.346510i | ||||
\(46\) | −0.897916 | + | 1.55524i | −0.132390 | + | 0.229307i | ||||
\(47\) | 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 | ||||||||
\(50\) | −1.10208 | + | 1.90887i | −0.155858 | + | 0.269954i | ||||
\(51\) | −3.89792 | + | 6.75139i | −0.545817 | + | 0.945383i | ||||
\(52\) | 0.634922 | + | 3.54921i | 0.0880479 | + | 0.492187i | ||||
\(53\) | −3.29583 | − | 5.70855i | −0.452717 | − | 0.784129i | 0.545836 | − | 0.837892i | \(-0.316212\pi\) |
−0.998554 | + | 0.0537624i | \(0.982879\pi\) | |||||||
\(54\) | −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 | ||||||||
\(58\) | −8.79583 | −1.15495 | ||||||||
\(59\) | 0.562738 | − | 0.974691i | 0.0732622 | − | 0.126894i | −0.827067 | − | 0.562103i | \(-0.809992\pi\) |
0.900329 | + | 0.435209i | \(0.143326\pi\) | |||||||
\(60\) | −1.89792 | − | 3.28729i | −0.245020 | − | 0.424387i | ||||
\(61\) | −1.55858 | −0.199556 | −0.0997780 | − | 0.995010i | \(-0.531813\pi\) | ||||
−0.0997780 | + | 0.995010i | \(0.531813\pi\) | |||||||
\(62\) | −0.707107 | + | 1.22474i | −0.0898027 | + | 0.155543i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | −1.70417 | − | 9.52628i | −0.211376 | − | 1.18159i | ||||
\(66\) | 4.09827 | + | 7.09841i | 0.504462 | + | 0.873754i | ||||
\(67\) | 5.79583 | 0.708074 | 0.354037 | − | 0.935232i | \(-0.384809\pi\) | ||||
0.354037 | + | 0.935232i | \(0.384809\pi\) | |||||||
\(68\) | −2.75624 | − | 4.77395i | −0.334244 | − | 0.578927i | ||||
\(69\) | 1.26984 | + | 2.19944i | 0.152871 | + | 0.264781i | ||||
\(70\) | 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 | ||||||||
\(73\) | −2.90061 | − | 5.02401i | −0.339491 | − | 0.588015i | 0.644846 | − | 0.764312i | \(-0.276921\pi\) |
−0.984337 | + | 0.176297i | \(0.943588\pi\) | |||||||
\(74\) | 3.39792 | − | 5.88536i | 0.395000 | − | 0.684160i | ||||
\(75\) | 1.55858 | + | 2.69954i | 0.179970 | + | 0.311716i | ||||
\(76\) | 1.41421 | − | 2.44949i | 0.162221 | − | 0.280976i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.79583 | − | 1.73205i | −0.543021 | − | 0.196116i | ||||
\(79\) | 5.89792 | − | 10.2155i | 0.663567 | − | 1.14933i | −0.316104 | − | 0.948724i | \(-0.602375\pi\) |
0.979672 | − | 0.200608i | \(-0.0642917\pi\) | |||||||
\(80\) | −2.68406 | −0.300087 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | −9.75513 | −1.07727 | ||||||||
\(83\) | 9.89949 | 1.08661 | 0.543305 | − | 0.839535i | \(-0.317173\pi\) | ||||
0.543305 | + | 0.839535i | \(0.317173\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.39792 | + | 12.8136i | 0.802417 | + | 1.38983i | ||||
\(86\) | 0.897916 | − | 1.55524i | 0.0968247 | − | 0.167705i | ||||
\(87\) | −6.21959 | + | 10.7726i | −0.666810 | + | 1.15495i | ||||
\(88\) | −17.3875 | −1.85351 | ||||||||
\(89\) | 6.07522 | + | 10.5226i | 0.643972 | + | 1.11539i | 0.984538 | + | 0.175172i | \(0.0560482\pi\) |
−0.340565 | + | 0.940221i | \(0.610618\pi\) | |||||||
\(90\) | −2.68406 | −0.282925 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.79583 | −0.187228 | ||||||||
\(93\) | 1.00000 | + | 1.73205i | 0.103695 | + | 0.179605i | ||||
\(94\) | −2.82843 | −0.291730 | ||||||||
\(95\) | −3.79583 | + | 6.57457i | −0.389444 | + | 0.674537i | ||||
\(96\) | 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 | ||||||||
\(99\) | −5.79583 | −0.582503 | ||||||||
\(100\) | −2.20417 | −0.220417 | ||||||||
\(101\) | 2.97280 | 0.295804 | 0.147902 | − | 0.989002i | \(-0.452748\pi\) | ||||
0.147902 | + | 0.989002i | \(0.452748\pi\) | |||||||
\(102\) | 7.79583 | 0.771902 | ||||||||
\(103\) | −4.09827 | + | 7.09841i | −0.403815 | + | 0.699428i | −0.994183 | − | 0.107707i | \(-0.965649\pi\) |
0.590368 | + | 0.807134i | \(0.298983\pi\) | |||||||
\(104\) | 8.26873 | − | 6.97339i | 0.810815 | − | 0.683797i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.29583 | + | 5.70855i | −0.320119 | + | 0.554463i | ||||
\(107\) | 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 | ||||
\(109\) | 8.79583 | + | 15.2348i | 0.842488 | + | 1.45923i | 0.887785 | + | 0.460258i | \(0.152243\pi\) |
−0.0452972 | + | 0.998974i | \(0.514423\pi\) | |||||||
\(110\) | 15.5563 | 1.48324 | ||||||||
\(111\) | −4.80538 | − | 8.32316i | −0.456106 | − | 0.789999i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.29583 | + | 14.3688i | 0.780406 | + | 1.35170i | 0.931705 | + | 0.363215i | \(0.118321\pi\) |
−0.151299 | + | 0.988488i | \(0.548346\pi\) | |||||||
\(114\) | 2.00000 | + | 3.46410i | 0.187317 | + | 0.324443i | ||||
\(115\) | 4.82012 | 0.449478 | ||||||||
\(116\) | −4.39792 | − | 7.61741i | −0.408336 | − | 0.707259i | ||||
\(117\) | 2.75624 | − | 2.32446i | 0.254815 | − | 0.214897i | ||||
\(118\) | −1.12548 | −0.103608 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −5.69375 | + | 9.86186i | −0.519766 | + | 0.900260i | ||||
\(121\) | 22.5917 | 2.05379 | ||||||||
\(122\) | 0.779291 | + | 1.34977i | 0.0705537 | + | 0.122203i | ||||
\(123\) | −6.89792 | + | 11.9475i | −0.621964 | + | 1.07727i | ||||
\(124\) | −1.41421 | −0.127000 | ||||||||
\(125\) | −7.50417 | −0.671194 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.79583 | + | 6.57457i | −0.336826 | + | 0.583399i | −0.983834 | − | 0.179084i | \(-0.942687\pi\) |
0.647008 | + | 0.762483i | \(0.276020\pi\) | |||||||
\(128\) | 1.50000 | + | 2.59808i | 0.132583 | + | 0.229640i | ||||
\(129\) | −1.26984 | − | 2.19944i | −0.111804 | − | 0.193649i | ||||
\(130\) | −7.39792 | + | 6.23899i | −0.648840 | + | 0.547196i | ||||
\(131\) | −4.09827 | + | 7.09841i | −0.358068 | + | 0.620191i | −0.987638 | − | 0.156752i | \(-0.949898\pi\) |
0.629570 | + | 0.776944i | \(0.283231\pi\) | |||||||
\(132\) | −4.09827 | + | 7.09841i | −0.356709 | + | 0.617838i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.89792 | − | 5.01934i | −0.250342 | − | 0.433605i | ||||
\(135\) | −7.59166 | + | 13.1491i | −0.653386 | + | 1.13170i | ||||
\(136\) | −8.26873 | + | 14.3219i | −0.709038 | + | 1.22809i | ||||
\(137\) | 4.60208 | − | 7.97104i | 0.393183 | − | 0.681012i | −0.599685 | − | 0.800236i | \(-0.704707\pi\) |
0.992867 | + | 0.119224i | \(0.0380407\pi\) | |||||||
\(138\) | 1.26984 | − | 2.19944i | 0.108096 | − | 0.187228i | ||||
\(139\) | −7.63381 | − | 13.2221i | −0.647491 | − | 1.12149i | −0.983720 | − | 0.179707i | \(-0.942485\pi\) |
0.336229 | − | 0.941780i | \(-0.390848\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | + | 3.46410i | −0.168430 | + | 0.291730i | ||||
\(142\) | −3.00000 | + | 5.19615i | −0.251754 | + | 0.436051i | ||||
\(143\) | −15.9747 | + | 13.4722i | −1.33587 | + | 1.12660i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 11.8043 | + | 20.4456i | 0.980291 | + | 1.69791i | ||||
\(146\) | −2.90061 | + | 5.02401i | −0.240056 | + | 0.415790i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.79583 | 0.558614 | ||||||||
\(149\) | 4.59166 | 0.376164 | 0.188082 | − | 0.982153i | \(-0.439773\pi\) | ||||
0.188082 | + | 0.982153i | \(0.439773\pi\) | |||||||
\(150\) | 1.55858 | − | 2.69954i | 0.127258 | − | 0.220417i | ||||
\(151\) | 8.79583 | + | 15.2348i | 0.715795 | + | 1.23979i | 0.962652 | + | 0.270741i | \(0.0872687\pi\) |
−0.246858 | + | 0.969052i | \(0.579398\pi\) | |||||||
\(152\) | −8.48528 | −0.688247 | ||||||||
\(153\) | −2.75624 | + | 4.77395i | −0.222829 | + | 0.385951i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.79583 | 0.304889 | ||||||||
\(156\) | −0.897916 | − | 5.01934i | −0.0718908 | − | 0.401869i | ||||
\(157\) | −3.46335 | − | 5.99870i | −0.276405 | − | 0.478748i | 0.694083 | − | 0.719895i | \(-0.255810\pi\) |
−0.970489 | + | 0.241146i | \(0.922477\pi\) | |||||||
\(158\) | −11.7958 | −0.938426 | ||||||||
\(159\) | 4.66101 | + | 8.07311i | 0.369642 | + | 0.640239i | ||||
\(160\) | −6.71015 | − | 11.6223i | −0.530484 | − | 0.918825i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.50000 | + | 4.33013i | 0.196419 | + | 0.340207i | ||||
\(163\) | −13.3875 | −1.04859 | −0.524295 | − | 0.851537i | \(-0.675671\pi\) | ||||
−0.524295 | + | 0.851537i | \(0.675671\pi\) | |||||||
\(164\) | −4.87756 | − | 8.44819i | −0.380874 | − | 0.659693i | ||||
\(165\) | 11.0000 | − | 19.0526i | 0.856349 | − | 1.48324i | ||||
\(166\) | −4.94975 | − | 8.57321i | −0.384175 | − | 0.665410i | ||||
\(167\) | 7.63381 | − | 13.2221i | 0.590722 | − | 1.02316i | −0.403414 | − | 0.915018i | \(-0.632176\pi\) |
0.994135 | − | 0.108142i | \(-0.0344902\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.19375 | − | 12.8136i | 0.168750 | − | 0.985659i | ||||
\(170\) | 7.39792 | − | 12.8136i | 0.567394 | − | 0.982756i | ||||
\(171\) | −2.82843 | −0.216295 | ||||||||
\(172\) | 1.79583 | 0.136931 | ||||||||
\(173\) | −9.32202 | −0.708740 | −0.354370 | − | 0.935105i | \(-0.615305\pi\) | ||||
−0.354370 | + | 0.935105i | \(0.615305\pi\) | |||||||
\(174\) | 12.4392 | 0.943012 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.89792 | + | 5.01934i | 0.218439 | + | 0.378347i | ||||
\(177\) | −0.795832 | + | 1.37842i | −0.0598184 | + | 0.103608i | ||||
\(178\) | 6.07522 | − | 10.5226i | 0.455357 | − | 0.788702i | ||||
\(179\) | −0.408337 | −0.0305205 | −0.0152603 | − | 0.999884i | \(-0.504858\pi\) | ||||
−0.0152603 | + | 0.999884i | \(0.504858\pi\) | |||||||
\(180\) | −1.34203 | − | 2.32446i | −0.100029 | − | 0.173255i | ||||
\(181\) | 16.5375 | 1.22922 | 0.614610 | − | 0.788831i | \(-0.289314\pi\) | ||||
0.614610 | + | 0.788831i | \(0.289314\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.20417 | 0.162937 | ||||||||
\(184\) | 2.69375 | + | 4.66571i | 0.198586 | + | 0.343960i | ||||
\(185\) | −18.2404 | −1.34106 | ||||||||
\(186\) | 1.00000 | − | 1.73205i | 0.0733236 | − | 0.127000i | ||||
\(187\) | 15.9747 | − | 27.6690i | 1.16819 | − | 2.02336i | ||||
\(188\) | −1.41421 | − | 2.44949i | −0.103142 | − | 0.178647i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.59166 | 0.550757 | ||||||||
\(191\) | −25.7958 | −1.86652 | −0.933260 | − | 0.359200i | \(-0.883049\pi\) | ||||
−0.933260 | + | 0.359200i | \(0.883049\pi\) | |||||||
\(192\) | −9.89949 | −0.714435 | ||||||||
\(193\) | 3.40834 | 0.245337 | 0.122669 | − | 0.992448i | \(-0.460855\pi\) | ||||
0.122669 | + | 0.992448i | \(0.460855\pi\) | |||||||
\(194\) | −2.12132 | + | 3.67423i | −0.152302 | + | 0.263795i | ||||
\(195\) | 2.41006 | + | 13.4722i | 0.172588 | + | 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 | \(0.0746770\pi\) | |||||||
\(198\) | 2.89792 | + | 5.01934i | 0.205946 | + | 0.356709i | ||||
\(199\) | −11.0250 | + | 19.0958i | −0.781539 | + | 1.35367i | 0.149505 | + | 0.988761i | \(0.452232\pi\) |
−0.931045 | + | 0.364905i | \(0.881101\pi\) | |||||||
\(200\) | 3.30625 | + | 5.72660i | 0.233787 | + | 0.404932i | ||||
\(201\) | −8.19654 | −0.578140 | ||||||||
\(202\) | −1.48640 | − | 2.57452i | −0.104583 | − | 0.181142i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.89792 | + | 6.75139i | 0.272909 | + | 0.472692i | ||||
\(205\) | 13.0917 | + | 22.6754i | 0.914361 | + | 1.58372i | ||||
\(206\) | 8.19654 | 0.571080 | ||||||||
\(207\) | 0.897916 | + | 1.55524i | 0.0624095 | + | 0.108096i | ||||
\(208\) | −3.39116 | − | 1.22474i | −0.235135 | − | 0.0849208i | ||||
\(209\) | 16.3931 | 1.13393 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.897916 | − | 1.55524i | 0.0618151 | − | 0.107067i | −0.833462 | − | 0.552577i | \(-0.813644\pi\) |
0.895277 | + | 0.445510i | \(0.146978\pi\) | |||||||
\(212\) | −6.59166 | −0.452717 | ||||||||
\(213\) | 4.24264 | + | 7.34847i | 0.290701 | + | 0.503509i | ||||
\(214\) | 3.00000 | − | 5.19615i | 0.205076 | − | 0.355202i | ||||
\(215\) | −4.82012 | −0.328729 | ||||||||
\(216\) | −16.9706 | −1.15470 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.79583 | − | 15.2348i | 0.595729 | − | 1.03183i | ||||
\(219\) | 4.10208 | + | 7.10502i | 0.277193 | + | 0.480113i | ||||
\(220\) | 7.77817 | + | 13.4722i | 0.524404 | + | 0.908295i | ||||
\(221\) | 3.50000 | + | 19.5650i | 0.235435 | + | 1.31608i | ||||
\(222\) | −4.80538 | + | 8.32316i | −0.322516 | + | 0.558614i | ||||
\(223\) | −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 | ||||||||
\(225\) | 1.10208 | + | 1.90887i | 0.0734723 | + | 0.127258i | ||||
\(226\) | 8.29583 | − | 14.3688i | 0.551831 | − | 0.955798i | ||||
\(227\) | 10.4622 | − | 18.1211i | 0.694403 | − | 1.20274i | −0.275979 | − | 0.961164i | \(-0.589002\pi\) |
0.970382 | − | 0.241577i | \(-0.0776647\pi\) | |||||||
\(228\) | −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 | \(0.0285065\pi\) | |||||||
\(230\) | −2.41006 | − | 4.17434i | −0.158915 | − | 0.275248i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.1937 | + | 22.8522i | −0.866212 | + | 1.50032i | ||||
\(233\) | 10.5917 | − | 18.3453i | 0.693883 | − | 1.20184i | −0.276673 | − | 0.960964i | \(-0.589232\pi\) |
0.970556 | − | 0.240876i | \(-0.0774348\pi\) | |||||||
\(234\) | −3.39116 | − | 1.22474i | −0.221687 | − | 0.0800641i | ||||
\(235\) | 3.79583 | + | 6.57457i | 0.247613 | + | 0.428878i | ||||
\(236\) | −0.562738 | − | 0.974691i | −0.0366311 | − | 0.0634470i | ||||
\(237\) | −8.34091 | + | 14.4469i | −0.541800 | + | 0.938426i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.7958 | −1.28049 | −0.640243 | − | 0.768172i | \(-0.721166\pi\) | ||||
−0.640243 | + | 0.768172i | \(0.721166\pi\) | |||||||
\(240\) | 3.79583 | 0.245020 | ||||||||
\(241\) | 2.19350 | − | 3.79926i | 0.141296 | − | 0.244732i | −0.786689 | − | 0.617350i | \(-0.788206\pi\) |
0.927985 | + | 0.372618i | \(0.121540\pi\) | |||||||
\(242\) | −11.2958 | − | 19.5650i | −0.726124 | − | 1.25768i | ||||
\(243\) | −9.89949 | −0.635053 | ||||||||
\(244\) | −0.779291 | + | 1.34977i | −0.0498890 | + | 0.0864103i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13.7958 | 0.879590 | ||||||||
\(247\) | −7.79583 | + | 6.57457i | −0.496037 | + | 0.418330i | ||||
\(248\) | 2.12132 | + | 3.67423i | 0.134704 | + | 0.233314i | ||||
\(249\) | −14.0000 | −0.887214 | ||||||||
\(250\) | 3.75209 | + | 6.49881i | 0.237303 | + | 0.411021i | ||||
\(251\) | −1.55858 | − | 2.69954i | −0.0983769 | − | 0.170394i | 0.812636 | − | 0.582771i | \(-0.198032\pi\) |
−0.911013 | + | 0.412378i | \(0.864698\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.20417 | − | 9.01388i | −0.327183 | − | 0.566698i | ||||
\(254\) | 7.59166 | 0.476343 | ||||||||
\(255\) | −10.4622 | − | 18.1211i | −0.655170 | − | 1.13479i | ||||
\(256\) | 8.50000 | − | 14.7224i | 0.531250 | − | 0.920152i | ||||
\(257\) | 7.70599 | + | 13.3472i | 0.480686 | + | 0.832573i | 0.999754 | − | 0.0221596i | \(-0.00705419\pi\) |
−0.519068 | + | 0.854733i | \(0.673721\pi\) | |||||||
\(258\) | −1.26984 | + | 2.19944i | −0.0790571 | + | 0.136931i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −9.10208 | − | 3.28729i | −0.564487 | − | 0.203869i | ||||
\(261\) | −4.39792 | + | 7.61741i | −0.272224 | + | 0.471506i | ||||
\(262\) | 8.19654 | 0.506384 | ||||||||
\(263\) | −25.3875 | −1.56546 | −0.782730 | − | 0.622361i | \(-0.786173\pi\) | ||||
−0.782730 | + | 0.622361i | \(0.786173\pi\) | |||||||
\(264\) | 24.5896 | 1.51339 | ||||||||
\(265\) | 17.6924 | 1.08684 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.59166 | − | 14.8812i | −0.525801 | − | 0.910714i | ||||
\(268\) | 2.89792 | − | 5.01934i | 0.177018 | − | 0.306605i | ||||
\(269\) | −0.562738 | + | 0.974691i | −0.0343107 | + | 0.0594279i | −0.882671 | − | 0.469992i | \(-0.844257\pi\) |
0.848360 | + | 0.529420i | \(0.177590\pi\) | |||||||
\(270\) | 15.1833 | 0.924028 | ||||||||
\(271\) | −11.5877 | − | 20.0705i | −0.703903 | − | 1.21920i | −0.967086 | − | 0.254450i | \(-0.918106\pi\) |
0.263183 | − | 0.964746i | \(-0.415228\pi\) | |||||||
\(272\) | 5.51249 | 0.334244 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.20417 | −0.556044 | ||||||||
\(275\) | −6.38749 | − | 11.0635i | −0.385180 | − | 0.667152i | ||||
\(276\) | 2.53969 | 0.152871 | ||||||||
\(277\) | 3.09166 | − | 5.35492i | 0.185760 | − | 0.321746i | −0.758072 | − | 0.652170i | \(-0.773859\pi\) |
0.943832 | + | 0.330425i | \(0.107192\pi\) | |||||||
\(278\) | −7.63381 | + | 13.2221i | −0.457845 | + | 0.793011i | ||||
\(279\) | 0.707107 | + | 1.22474i | 0.0423334 | + | 0.0733236i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.2042 | 0.907005 | 0.453502 | − | 0.891255i | \(-0.350174\pi\) | ||||
0.453502 | + | 0.891255i | \(0.350174\pi\) | |||||||
\(282\) | 4.00000 | 0.238197 | ||||||||
\(283\) | 29.4097 | 1.74823 | 0.874114 | − | 0.485721i | \(-0.161443\pi\) | ||||
0.874114 | + | 0.485721i | \(0.161443\pi\) | |||||||
\(284\) | −6.00000 | −0.356034 | ||||||||
\(285\) | 5.36812 | − | 9.29785i | 0.317980 | − | 0.550757i | ||||
\(286\) | 19.6546 | + | 7.09841i | 1.16220 | + | 0.419738i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.50000 | − | 4.33013i | 0.147314 | − | 0.255155i | ||||
\(289\) | −6.69375 | − | 11.5939i | −0.393750 | − | 0.681995i | ||||
\(290\) | 11.8043 | − | 20.4456i | 0.693170 | − | 1.20061i | ||||
\(291\) | 3.00000 | + | 5.19615i | 0.175863 | + | 0.304604i | ||||
\(292\) | −5.80122 | −0.339491 | ||||||||
\(293\) | −4.87756 | − | 8.44819i | −0.284950 | − | 0.493548i | 0.687647 | − | 0.726045i | \(-0.258644\pi\) |
−0.972597 | + | 0.232497i | \(0.925310\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.51042 | + | 2.61613i | 0.0879401 | + | 0.152317i | ||||
\(296\) | −10.1937 | − | 17.6561i | −0.592500 | − | 1.02624i | ||||
\(297\) | 32.7862 | 1.90245 | ||||||||
\(298\) | −2.29583 | − | 3.97650i | −0.132994 | − | 0.230352i | ||||
\(299\) | 6.08996 | + | 2.19944i | 0.352192 | + | 0.127197i | ||||
\(300\) | 3.11716 | 0.179970 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.79583 | − | 15.2348i | 0.506143 | − | 0.876666i | ||||
\(303\) | −4.20417 | −0.241523 | ||||||||
\(304\) | 1.41421 | + | 2.44949i | 0.0811107 | + | 0.140488i | ||||
\(305\) | 2.09166 | − | 3.62287i | 0.119768 | − | 0.207445i | ||||
\(306\) | 5.51249 | 0.315128 | ||||||||
\(307\) | −34.2004 | −1.95192 | −0.975960 | − | 0.217951i | \(-0.930063\pi\) | ||||
−0.975960 | + | 0.217951i | \(0.930063\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.79583 | − | 10.0387i | 0.329713 | − | 0.571080i | ||||
\(310\) | −1.89792 | − | 3.28729i | −0.107794 | − | 0.186705i | ||||
\(311\) | 5.93085 | + | 10.2725i | 0.336308 | + | 0.582502i | 0.983735 | − | 0.179625i | \(-0.0574884\pi\) |
−0.647427 | + | 0.762127i | \(0.724155\pi\) | |||||||
\(312\) | −11.6937 | + | 9.86186i | −0.662028 | + | 0.558318i | ||||
\(313\) | 0.851476 | − | 1.47480i | 0.0481283 | − | 0.0833606i | −0.840958 | − | 0.541101i | \(-0.818008\pi\) |
0.889086 | + | 0.457740i | \(0.151341\pi\) | |||||||
\(314\) | −3.46335 | + | 5.99870i | −0.195448 | + | 0.338526i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.89792 | − | 10.2155i | −0.331784 | − | 0.574666i | ||||
\(317\) | 6.29583 | − | 10.9047i | 0.353609 | − | 0.612469i | −0.633270 | − | 0.773931i | \(-0.718288\pi\) |
0.986879 | + | 0.161462i | \(0.0516210\pi\) | |||||||
\(318\) | 4.66101 | − | 8.07311i | 0.261376 | − | 0.452717i | ||||
\(319\) | 25.4896 | − | 44.1492i | 1.42714 | − | 2.47188i | ||||
\(320\) | −9.39420 | + | 16.2712i | −0.525152 | + | 0.909590i | ||||
\(321\) | −4.24264 | − | 7.34847i | −0.236801 | − | 0.410152i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.79583 | − | 13.5028i | 0.433772 | − | 0.751315i | ||||
\(324\) | −2.50000 | + | 4.33013i | −0.138889 | + | 0.240563i | ||||
\(325\) | 7.47470 | + | 2.69954i | 0.414622 | + | 0.149744i | ||||
\(326\) | 6.69375 | + | 11.5939i | 0.370732 | + | 0.642127i | ||||
\(327\) | −12.4392 | − | 21.5453i | −0.687888 | − | 1.19146i | ||||
\(328\) | −14.6327 | + | 25.3446i | −0.807955 | + | 1.39942i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −22.0000 | −1.21106 | ||||||||
\(331\) | 0.612505 | 0.0336663 | 0.0168332 | − | 0.999858i | \(-0.494642\pi\) | ||||
0.0168332 | + | 0.999858i | \(0.494642\pi\) | |||||||
\(332\) | 4.94975 | − | 8.57321i | 0.271653 | − | 0.470516i | ||||
\(333\) | −3.39792 | − | 5.88536i | −0.186205 | − | 0.322516i | ||||
\(334\) | −15.2676 | −0.835407 | ||||||||
\(335\) | −7.77817 | + | 13.4722i | −0.424967 | + | 0.736065i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.9792 | −1.63307 | −0.816534 | − | 0.577297i | \(-0.804108\pi\) | ||||
−0.816534 | + | 0.577297i | \(0.804108\pi\) | |||||||
\(338\) | −12.1937 | + | 4.50694i | −0.663252 | + | 0.245145i | ||||
\(339\) | −11.7321 | − | 20.3206i | −0.637199 | − | 1.10366i | ||||
\(340\) | 14.7958 | 0.802417 | ||||||||
\(341\) | −4.09827 | − | 7.09841i | −0.221934 | − | 0.384401i | ||||
\(342\) | 1.41421 | + | 2.44949i | 0.0764719 | + | 0.132453i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.69375 | − | 4.66571i | −0.145237 | − | 0.251558i | ||||
\(345\) | −6.81667 | −0.366997 | ||||||||
\(346\) | 4.66101 | + | 8.07311i | 0.250577 | + | 0.434013i | ||||
\(347\) | −7.48958 | + | 12.9723i | −0.402062 | + | 0.696391i | −0.993975 | − | 0.109611i | \(-0.965040\pi\) |
0.591913 | + | 0.806002i | \(0.298373\pi\) | |||||||
\(348\) | 6.21959 | + | 10.7726i | 0.333405 | + | 0.577475i | ||||
\(349\) | 6.50833 | − | 11.2728i | 0.348383 | − | 0.603417i | −0.637579 | − | 0.770385i | \(-0.720064\pi\) |
0.985962 | + | 0.166968i | \(0.0533976\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.5917 | + | 13.1491i | −0.832221 | + | 0.701849i | ||||
\(352\) | −14.4896 | + | 25.0967i | −0.772297 | + | 1.33766i | ||||
\(353\) | 15.1232 | 0.804929 | 0.402464 | − | 0.915436i | \(-0.368154\pi\) | ||||
0.402464 | + | 0.915436i | \(0.368154\pi\) | |||||||
\(354\) | 1.59166 | 0.0845959 | ||||||||
\(355\) | 16.1043 | 0.854730 | ||||||||
\(356\) | 12.1504 | 0.643972 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.204168 | + | 0.353630i | 0.0107906 | + | 0.0186899i | ||||
\(359\) | 2.00000 | − | 3.46410i | 0.105556 | − | 0.182828i | −0.808409 | − | 0.588621i | \(-0.799671\pi\) |
0.913965 | + | 0.405793i | \(0.133004\pi\) | |||||||
\(360\) | −4.02609 | + | 6.97339i | −0.212193 | + | 0.367530i | ||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | −8.26873 | − | 14.3219i | −0.434595 | − | 0.752740i | ||||
\(363\) | −31.9494 | −1.67691 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.5708 | 0.815014 | ||||||||
\(366\) | −1.10208 | − | 1.90887i | −0.0576069 | − | 0.0997780i | ||||
\(367\) | −21.2132 | −1.10732 | −0.553660 | − | 0.832743i | \(-0.686769\pi\) | ||||
−0.553660 | + | 0.832743i | \(0.686769\pi\) | |||||||
\(368\) | 0.897916 | − | 1.55524i | 0.0468071 | − | 0.0810723i | ||||
\(369\) | −4.87756 | + | 8.44819i | −0.253916 | + | 0.439795i | ||||
\(370\) | 9.12020 | + | 15.7967i | 0.474137 | + | 0.821229i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.00000 | 0.103695 | ||||||||
\(373\) | −12.5917 | −0.651972 | −0.325986 | − | 0.945375i | \(-0.605696\pi\) | ||||
−0.325986 | + | 0.945375i | \(0.605696\pi\) | |||||||
\(374\) | −31.9494 | −1.65207 | ||||||||
\(375\) | 10.6125 | 0.548027 | ||||||||
\(376\) | −4.24264 | + | 7.34847i | −0.218797 | + | 0.378968i | ||||
\(377\) | 5.58467 | + | 31.2182i | 0.287625 | + | 1.60782i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.69375 | − | 2.93366i | 0.0870020 | − | 0.150692i | −0.819241 | − | 0.573450i | \(-0.805605\pi\) |
0.906243 | + | 0.422758i | \(0.138938\pi\) | |||||||
\(380\) | 3.79583 | + | 6.57457i | 0.194722 | + | 0.337268i | ||||
\(381\) | 5.36812 | − | 9.29785i | 0.275017 | − | 0.476343i | ||||
\(382\) | 12.8979 | + | 22.3398i | 0.659915 | + | 1.14301i | ||||
\(383\) | 14.9789 | 0.765385 | 0.382692 | − | 0.923876i | \(-0.374997\pi\) | ||||
0.382692 | + | 0.923876i | \(0.374997\pi\) | |||||||
\(384\) | −2.12132 | − | 3.67423i | −0.108253 | − | 0.187500i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.70417 | − | 2.95171i | −0.0867399 | − | 0.150238i | ||||
\(387\) | −0.897916 | − | 1.55524i | −0.0456436 | − | 0.0790571i | ||||
\(388\) | −4.24264 | −0.215387 | ||||||||
\(389\) | −14.1937 | − | 24.5843i | −0.719652 | − | 1.24647i | −0.961138 | − | 0.276069i | \(-0.910968\pi\) |
0.241486 | − | 0.970404i | \(-0.422365\pi\) | |||||||
\(390\) | 10.4622 | − | 8.82327i | 0.529776 | − | 0.446784i | ||||
\(391\) | −9.89949 | −0.500639 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.79583 | − | 10.0387i | 0.292361 | − | 0.506384i | ||||
\(394\) | −8.00000 | −0.403034 | ||||||||
\(395\) | 15.8303 | + | 27.4190i | 0.796511 | + | 1.37960i | ||||
\(396\) | −2.89792 | + | 5.01934i | −0.145626 | + | 0.252231i | ||||
\(397\) | −7.07107 | −0.354887 | −0.177443 | − | 0.984131i | \(-0.556783\pi\) | ||||
−0.177443 | + | 0.984131i | \(0.556783\pi\) | |||||||
\(398\) | 22.0499 | 1.10526 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.10208 | − | 1.90887i | 0.0551042 | − | 0.0954433i | ||||
\(401\) | −12.1937 | − | 21.1202i | −0.608927 | − | 1.05469i | −0.991418 | − | 0.130733i | \(-0.958267\pi\) |
0.382491 | − | 0.923959i | \(-0.375066\pi\) | |||||||
\(402\) | 4.09827 | + | 7.09841i | 0.204403 | + | 0.354037i | ||||
\(403\) | 4.79583 | + | 1.73205i | 0.238897 | + | 0.0862796i | ||||
\(404\) | 1.48640 | − | 2.57452i | 0.0739511 | − | 0.128087i | ||||
\(405\) | 6.71015 | − | 11.6223i | 0.333430 | − | 0.577517i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.6937 | + | 34.1106i | 0.976183 | + | 1.69080i | ||||
\(408\) | 11.6937 | − | 20.2542i | 0.578927 | − | 1.00273i | ||||
\(409\) | −14.3440 | + | 24.8445i | −0.709263 | + | 1.22848i | 0.255868 | + | 0.966712i | \(0.417639\pi\) |
−0.965131 | + | 0.261767i | \(0.915695\pi\) | |||||||
\(410\) | 13.0917 | − | 22.6754i | 0.646551 | − | 1.11986i | ||||
\(411\) | −6.50833 | + | 11.2728i | −0.321032 | + | 0.556044i | ||||
\(412\) | 4.09827 | + | 7.09841i | 0.201907 | + | 0.349714i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.897916 | − | 1.55524i | 0.0441302 | − | 0.0764357i | ||||
\(415\) | −13.2854 | + | 23.0110i | −0.652155 | + | 1.12957i | ||||
\(416\) | −3.17461 | − | 17.7460i | −0.155648 | − | 0.870071i | ||||
\(417\) | 10.7958 | + | 18.6989i | 0.528674 | + | 0.915690i | ||||
\(418\) | −8.19654 | − | 14.1968i | −0.400906 | − | 0.694390i | ||||
\(419\) | 14.2718 | − | 24.7194i | 0.697221 | − | 1.20762i | −0.272205 | − | 0.962239i | \(-0.587753\pi\) |
0.969426 | − | 0.245384i | \(-0.0789139\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.59166 | −0.321258 | −0.160629 | − | 0.987015i | \(-0.551352\pi\) | ||||
−0.160629 | + | 0.987015i | \(0.551352\pi\) | |||||||
\(422\) | −1.79583 | −0.0874197 | ||||||||
\(423\) | −1.41421 | + | 2.44949i | −0.0687614 | + | 0.119098i | ||||
\(424\) | 9.88749 | + | 17.1256i | 0.480179 | + | 0.831695i | ||||
\(425\) | −12.1504 | −0.589383 | ||||||||
\(426\) | 4.24264 | − | 7.34847i | 0.205557 | − | 0.356034i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.00000 | 0.290021 | ||||||||
\(429\) | 22.5917 | − | 19.0526i | 1.09074 | − | 0.919866i | ||||
\(430\) | 2.41006 | + | 4.17434i | 0.116223 | + | 0.201305i | ||||
\(431\) | −5.18333 | −0.249672 | −0.124836 | − | 0.992177i | \(-0.539840\pi\) | ||||
−0.124836 | + | 0.992177i | \(0.539840\pi\) | |||||||
\(432\) | 2.82843 | + | 4.89898i | 0.136083 | + | 0.235702i | ||||
\(433\) | 6.71015 | + | 11.6223i | 0.322469 | + | 0.558533i | 0.980997 | − | 0.194024i | \(-0.0621539\pi\) |
−0.658528 | + | 0.752556i | \(0.728821\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.6937 | − | 28.9144i | −0.800404 | − | 1.38634i | ||||
\(436\) | 17.5917 | 0.842488 | ||||||||
\(437\) | −2.53969 | − | 4.39887i | −0.121490 | − | 0.210427i | ||||
\(438\) | 4.10208 | − | 7.10502i | 0.196005 | − | 0.339491i | ||||
\(439\) | 17.1002 | + | 29.6184i | 0.816148 | + | 1.41361i | 0.908501 | + | 0.417883i | \(0.137228\pi\) |
−0.0923531 | + | 0.995726i | \(0.529439\pi\) | |||||||
\(440\) | 23.3345 | − | 40.4166i | 1.11243 | − | 1.92678i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.1937 | − | 12.8136i | 0.722693 | − | 0.609479i | ||||
\(443\) | −5.00000 | + | 8.66025i | −0.237557 | + | 0.411461i | −0.960013 | − | 0.279956i | \(-0.909680\pi\) |
0.722456 | + | 0.691417i | \(0.243013\pi\) | |||||||
\(444\) | −9.61076 | −0.456106 | ||||||||
\(445\) | −32.6125 | −1.54598 | ||||||||
\(446\) | 5.65685 | 0.267860 | ||||||||
\(447\) | −6.49359 | −0.307136 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.20417 | − | 3.81773i | −0.104021 | − | 0.180170i | 0.809317 | − | 0.587372i | \(-0.199838\pi\) |
−0.913338 | + | 0.407203i | \(0.866504\pi\) | |||||||
\(450\) | 1.10208 | − | 1.90887i | 0.0519527 | − | 0.0899848i | ||||
\(451\) | 28.2695 | − | 48.9643i | 1.33116 | − | 2.30564i | ||||
\(452\) | 16.5917 | 0.780406 | ||||||||
\(453\) | −12.4392 | − | 21.5453i | −0.584444 | − | 1.01229i | ||||
\(454\) | −20.9245 | −0.982034 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.0000 | 0.561951 | ||||||||
\(457\) | 7.29583 | + | 12.6368i | 0.341285 | + | 0.591122i | 0.984672 | − | 0.174419i | \(-0.0558047\pi\) |
−0.643387 | + | 0.765541i | \(0.722471\pi\) | |||||||
\(458\) | −12.7279 | −0.594737 | ||||||||
\(459\) | 15.5917 | − | 27.0056i | 0.727757 | − | 1.26051i | ||||
\(460\) | 2.41006 | − | 4.17434i | 0.112370 | − | 0.194630i | ||||
\(461\) | 15.4842 | + | 26.8194i | 0.721169 | + | 1.24910i | 0.960531 | + | 0.278172i | \(0.0897284\pi\) |
−0.239362 | + | 0.970930i | \(0.576938\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.3875 | 0.529222 | 0.264611 | − | 0.964355i | \(-0.414756\pi\) | ||||
0.264611 | + | 0.964355i | \(0.414756\pi\) | |||||||
\(464\) | 8.79583 | 0.408336 | ||||||||
\(465\) | −5.36812 | −0.248940 | ||||||||
\(466\) | −21.1833 | −0.981299 | ||||||||
\(467\) | −2.41006 | + | 4.17434i | −0.111524 | + | 0.193166i | −0.916385 | − | 0.400298i | \(-0.868907\pi\) |
0.804861 | + | 0.593464i | \(0.202240\pi\) | |||||||
\(468\) | −0.634922 | − | 3.54921i | −0.0293493 | − | 0.164062i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.79583 | − | 6.57457i | 0.175089 | − | 0.303262i | ||||
\(471\) | 4.89792 | + | 8.48344i | 0.225684 | + | 0.390896i | ||||
\(472\) | −1.68821 | + | 2.92407i | −0.0777063 | + | 0.134591i | ||||
\(473\) | 5.20417 | + | 9.01388i | 0.239288 | + | 0.414459i | ||||
\(474\) | 16.6818 | 0.766222 | ||||||||
\(475\) | −3.11716 | − | 5.39909i | −0.143025 | − | 0.247727i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.29583 | + | 5.70855i | 0.150906 | + | 0.261376i | ||||
\(478\) | 9.89792 | + | 17.1437i | 0.452720 | + | 0.784134i | ||||
\(479\) | 7.35981 | 0.336278 | 0.168139 | − | 0.985763i | \(-0.446224\pi\) | ||||
0.168139 | + | 0.985763i | \(0.446224\pi\) | |||||||
\(480\) | 9.48958 | + | 16.4364i | 0.433138 | + | 0.750217i | ||||
\(481\) | −23.0458 | − | 8.32316i | −1.05080 | − | 0.379503i | ||||
\(482\) | −4.38701 | −0.199823 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.2958 | − | 19.5650i | 0.513447 | − | 0.889316i | ||||
\(485\) | 11.3875 | 0.517079 | ||||||||
\(486\) | 4.94975 | + | 8.57321i | 0.224525 | + | 0.388889i | ||||
\(487\) | −9.79583 | + | 16.9669i | −0.443891 | + | 0.768843i | −0.997974 | − | 0.0636190i | \(-0.979736\pi\) |
0.554083 | + | 0.832462i | \(0.313069\pi\) | |||||||
\(488\) | 4.67575 | 0.211661 | ||||||||
\(489\) | 18.9328 | 0.856170 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.79583 | − | 8.30662i | 0.216433 | − | 0.374873i | −0.737282 | − | 0.675585i | \(-0.763891\pi\) |
0.953715 | + | 0.300712i | \(0.0972244\pi\) | |||||||
\(492\) | 6.89792 | + | 11.9475i | 0.310982 | + | 0.538637i | ||||
\(493\) | −24.2434 | − | 41.9909i | −1.09187 | − | 1.89117i | ||||
\(494\) | 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 | ||||
\(499\) | −8.10208 | + | 14.0332i | −0.362699 | + | 0.628213i | −0.988404 | − | 0.151847i | \(-0.951478\pi\) |
0.625705 | + | 0.780060i | \(0.284811\pi\) | |||||||
\(500\) | −3.75209 | + | 6.49881i | −0.167798 | + | 0.290635i | ||||
\(501\) | −10.7958 | + | 18.6989i | −0.482322 | + | 0.835407i | ||||
\(502\) | −1.55858 | + | 2.69954i | −0.0695629 | + | 0.120487i | ||||
\(503\) | −14.2718 | − | 24.7194i | −0.636347 | − | 1.10218i | −0.986228 | − | 0.165391i | \(-0.947111\pi\) |
0.349881 | − | 0.936794i | \(-0.386222\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.98958 | + | 6.91015i | −0.177534 | + | 0.307498i | ||||
\(506\) | −5.20417 | + | 9.01388i | −0.231354 | + | 0.400716i | ||||
\(507\) | −3.10243 | + | 18.1211i | −0.137784 | + | 0.804787i | ||||
\(508\) | 3.79583 | + | 6.57457i | 0.168413 | + | 0.291700i | ||||
\(509\) | 13.2185 | + | 22.8951i | 0.585899 | + | 1.01481i | 0.994763 | + | 0.102211i | \(0.0325917\pi\) |
−0.408864 | + | 0.912595i | \(0.634075\pi\) | |||||||
\(510\) | −10.4622 | + | 18.1211i | −0.463275 | + | 0.802417i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | 16.0000 | 0.706417 | ||||||||
\(514\) | 7.70599 | − | 13.3472i | 0.339897 | − | 0.588718i | ||||
\(515\) | −11.0000 | − | 19.0526i | −0.484718 | − | 0.839556i | ||||
\(516\) | −2.53969 | −0.111804 | ||||||||
\(517\) | 8.19654 | − | 14.1968i | 0.360484 | − | 0.624376i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.1833 | 0.578684 | ||||||||
\(520\) | 5.11251 | + | 28.5788i | 0.224198 | + | 1.25326i | ||||
\(521\) | 12.5114 | + | 21.6703i | 0.548133 | + | 0.949394i | 0.998403 | + | 0.0565015i | \(0.0179946\pi\) |
−0.450269 | + | 0.892893i | \(0.648672\pi\) | |||||||
\(522\) | 8.79583 | 0.384983 | ||||||||
\(523\) | 14.2865 | + | 24.7450i | 0.624705 | + | 1.08202i | 0.988598 | + | 0.150580i | \(0.0481142\pi\) |
−0.363893 | + | 0.931441i | \(0.618552\pi\) | |||||||
\(524\) | 4.09827 | + | 7.09841i | 0.179034 | + | 0.310096i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.6937 | + | 21.9862i | 0.553474 | + | 0.958645i | ||||
\(527\) | −7.79583 | −0.339592 | ||||||||
\(528\) | −4.09827 | − | 7.09841i | −0.178354 | − | 0.308919i | ||||
\(529\) | 9.88749 | − | 17.1256i | 0.429891 | − | 0.744593i | ||||
\(530\) | −8.84620 | − | 15.3221i | −0.384255 | − | 0.665548i | ||||
\(531\) | −0.562738 | + | 0.974691i | −0.0244207 | + | 0.0422980i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.19375 | + | 34.6230i | 0.268281 | + | 1.49969i | ||||
\(534\) | −8.59166 | + | 14.8812i | −0.371798 | + | 0.643972i | ||||
\(535\) | −16.1043 | −0.696252 | ||||||||
\(536\) | −17.3875 | −0.751025 | ||||||||
\(537\) | 0.577476 | 0.0249199 | ||||||||
\(538\) | 1.12548 | 0.0485227 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.59166 | + | 13.1491i | 0.326693 | + | 0.565849i | ||||
\(541\) | 6.29583 | − | 10.9047i | 0.270679 | − | 0.468830i | −0.698357 | − | 0.715750i | \(-0.746085\pi\) |
0.969036 | + | 0.246920i | \(0.0794185\pi\) | |||||||
\(542\) | −11.5877 | + | 20.0705i | −0.497735 | + | 0.862102i | ||||
\(543\) | −23.3875 | −1.00365 | ||||||||
\(544\) | 13.7812 | + | 23.8698i | 0.590865 | + | 1.02341i | ||||
\(545\) | −47.2170 | −2.02256 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.9792 | −1.58111 | −0.790557 | − | 0.612388i | \(-0.790209\pi\) | ||||
−0.790557 | + | 0.612388i | \(0.790209\pi\) | |||||||
\(548\) | −4.60208 | − | 7.97104i | −0.196591 | − | 0.340506i | ||||
\(549\) | 1.55858 | 0.0665187 | ||||||||
\(550\) | −6.38749 | + | 11.0635i | −0.272364 | + | 0.471748i | ||||
\(551\) | 12.4392 | − | 21.5453i | 0.529927 | − | 0.917861i | ||||
\(552\) | −3.80953 | − | 6.59831i | −0.162145 | − | 0.280843i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.18333 | −0.262704 | ||||||||
\(555\) | 25.7958 | 1.09497 | ||||||||
\(556\) | −15.2676 | −0.647491 | ||||||||
\(557\) | 20.5917 | 0.872497 | 0.436248 | − | 0.899826i | \(-0.356307\pi\) | ||||
0.436248 | + | 0.899826i | \(0.356307\pi\) | |||||||
\(558\) | 0.707107 | − | 1.22474i | 0.0299342 | − | 0.0518476i | ||||
\(559\) | −6.08996 | − | 2.19944i | −0.257578 | − | 0.0930262i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.5917 | + | 39.1299i | −0.953821 | + | 1.65207i | ||||
\(562\) | −7.60208 | − | 13.1672i | −0.320675 | − | 0.555425i | ||||
\(563\) | −0.562738 | + | 0.974691i | −0.0237166 | + | 0.0410783i | −0.877640 | − | 0.479320i | \(-0.840883\pi\) |
0.853924 | + | 0.520399i | \(0.174217\pi\) | |||||||
\(564\) | 2.00000 | + | 3.46410i | 0.0842152 | + | 0.145865i | ||||
\(565\) | −44.5330 | −1.87352 | ||||||||
\(566\) | −14.7049 | − | 25.4696i | −0.618092 | − | 1.07057i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.00000 | + | 15.5885i | 0.377632 | + | 0.654077i | ||||
\(569\) | −3.20417 | − | 5.54978i | −0.134326 | − | 0.232659i | 0.791014 | − | 0.611798i | \(-0.209554\pi\) |
−0.925340 | + | 0.379139i | \(0.876220\pi\) | |||||||
\(570\) | −10.7362 | −0.449691 | ||||||||
\(571\) | −7.59166 | − | 13.1491i | −0.317701 | − | 0.550275i | 0.662307 | − | 0.749233i | \(-0.269578\pi\) |
−0.980008 | + | 0.198958i | \(0.936244\pi\) | |||||||
\(572\) | 3.67990 | + | 20.5706i | 0.153864 | + | 0.860100i | ||||
\(573\) | 36.4808 | 1.52401 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.97916 | + | 3.42800i | −0.0825366 | + | 0.142958i | ||||
\(576\) | −7.00000 | −0.291667 | ||||||||
\(577\) | −4.58883 | − | 7.94808i | −0.191035 | − | 0.330883i | 0.754558 | − | 0.656233i | \(-0.227851\pi\) |
−0.945594 | + | 0.325350i | \(0.894518\pi\) | |||||||
\(578\) | −6.69375 | + | 11.5939i | −0.278423 | + | 0.482243i | ||||
\(579\) | −4.82012 | −0.200317 | ||||||||
\(580\) | 23.6085 | 0.980291 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.00000 | − | 5.19615i | 0.124354 | − | 0.215387i | ||||
\(583\) | −19.1021 | − | 33.0858i | −0.791127 | − | 1.37027i | ||||
\(584\) | 8.70183 | + | 15.0720i | 0.360084 | + | 0.623685i | ||||
\(585\) | 1.70417 | + | 9.52628i | 0.0704587 | + | 0.393863i | ||||
\(586\) | −4.87756 | + | 8.44819i | −0.201490 | + | 0.348991i | ||||
\(587\) | 1.55858 | − | 2.69954i | 0.0643296 | − | 0.111422i | −0.832067 | − | 0.554675i | \(-0.812842\pi\) |
0.896396 | + | 0.443253i | \(0.146176\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | − | 3.46410i | −0.0824086 | − | 0.142736i | ||||
\(590\) | 1.51042 | − | 2.61613i | 0.0621831 | − | 0.107704i | ||||
\(591\) | −5.65685 | + | 9.79796i | −0.232692 | + | 0.403034i | ||||
\(592\) | −3.39792 | + | 5.88536i | −0.139653 | + | 0.241887i | ||||
\(593\) | −0.779291 | + | 1.34977i | −0.0320017 | + | 0.0554285i | −0.881583 | − | 0.472030i | \(-0.843522\pi\) |
0.849581 | + | 0.527458i | \(0.176855\pi\) | |||||||
\(594\) | −16.3931 | − | 28.3937i | −0.672617 | − | 1.16501i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.29583 | − | 3.97650i | 0.0940409 | − | 0.162884i | ||||
\(597\) | 15.5917 | − | 27.0056i | 0.638124 | − | 1.10526i | ||||
\(598\) | −1.14021 | − | 6.37378i | −0.0466268 | − | 0.260643i | ||||
\(599\) | 7.20417 | + | 12.4780i | 0.294354 | + | 0.509837i | 0.974834 | − | 0.222930i | \(-0.0715621\pi\) |
−0.680480 | + | 0.732767i | \(0.738229\pi\) | |||||||
\(600\) | −4.67575 | − | 8.09863i | −0.190887 | − | 0.330625i | ||||
\(601\) | −15.4842 | + | 26.8194i | −0.631612 | + | 1.09398i | 0.355610 | + | 0.934634i | \(0.384273\pi\) |
−0.987222 | + | 0.159350i | \(0.949060\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.79583 | −0.236025 | ||||||||
\(604\) | 17.5917 | 0.715795 | ||||||||
\(605\) | −30.3187 | + | 52.5135i | −1.23263 | + | 2.13498i | ||||
\(606\) | 2.10208 | + | 3.64092i | 0.0853913 | + | 0.147902i | ||||
\(607\) | 35.9033 | 1.45727 | 0.728636 | − | 0.684901i | \(-0.240155\pi\) | ||||
0.728636 | + | 0.684901i | \(0.240155\pi\) | |||||||
\(608\) | −7.07107 | + | 12.2474i | −0.286770 | + | 0.496700i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.18333 | −0.169378 | ||||||||
\(611\) | 1.79583 | + | 10.0387i | 0.0726516 | + | 0.406121i | ||||
\(612\) | 2.75624 | + | 4.77395i | 0.111415 | + | 0.192976i | ||||
\(613\) | −5.97916 | −0.241496 | −0.120748 | − | 0.992683i | \(-0.538529\pi\) | ||||
−0.120748 | + | 0.992683i | \(0.538529\pi\) | |||||||
\(614\) | 17.1002 | + | 29.6184i | 0.690108 | + | 1.19530i | ||||
\(615\) | −18.5144 | − | 32.0679i | −0.746573 | − | 1.29310i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.1937 | + | 21.1202i | 0.490902 | + | 0.850267i | 0.999945 | − | 0.0104740i | \(-0.00333405\pi\) |
−0.509043 | + | 0.860741i | \(0.670001\pi\) | |||||||
\(618\) | −11.5917 | −0.466285 | ||||||||
\(619\) | 16.9558 | + | 29.3684i | 0.681512 | + | 1.18041i | 0.974519 | + | 0.224303i | \(0.0720107\pi\) |
−0.293007 | + | 0.956110i | \(0.594656\pi\) | |||||||
\(620\) | 1.89792 | − | 3.28729i | 0.0762221 | − | 0.132021i | ||||
\(621\) | −5.07938 | − | 8.79774i | −0.203828 | − | 0.353041i | ||||
\(622\) | 5.93085 | − | 10.2725i | 0.237806 | − | 0.411891i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.79583 | + | 1.73205i | 0.191987 | + | 0.0693375i | ||||
\(625\) | 15.5812 | − | 26.9875i | 0.623250 | − | 1.07950i | ||||
\(626\) | −1.70295 | −0.0680636 | ||||||||
\(627\) | −23.1833 | −0.925853 | ||||||||
\(628\) | −6.92670 | −0.276405 | ||||||||
\(629\) | 37.4619 | 1.49370 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.2042 | + | 17.6741i | 0.406222 | + | 0.703596i | 0.994463 | − | 0.105089i | \(-0.0335128\pi\) |
−0.588241 | + | 0.808685i | \(0.700179\pi\) | |||||||
\(632\) | −17.6937 | + | 30.6465i | −0.703819 | + | 1.21905i | ||||
\(633\) | −1.26984 | + | 2.19944i | −0.0504718 | + | 0.0874197i | ||||
\(634\) | −12.5917 | −0.500079 | ||||||||
\(635\) | −10.1882 | − | 17.6465i | −0.404308 | − | 0.700281i | ||||
\(636\) | 9.32202 | 0.369642 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −50.9792 | −2.01828 | ||||||||
\(639\) | 3.00000 | + | 5.19615i | 0.118678 | + | 0.205557i | ||||
\(640\) | −8.05217 | −0.318290 | ||||||||
\(641\) | −2.39792 | + | 4.15331i | −0.0947120 | + | 0.164046i | −0.909488 | − | 0.415729i | \(-0.863526\pi\) |
0.814776 | + | 0.579775i | \(0.196860\pi\) | |||||||
\(642\) | −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 | ||||||||
\(645\) | 6.81667 | 0.268406 | ||||||||
\(646\) | −15.5917 | −0.613446 | ||||||||
\(647\) | 1.96221 | 0.0771426 | 0.0385713 | − | 0.999256i | \(-0.487719\pi\) | ||||
0.0385713 | + | 0.999256i | \(0.487719\pi\) | |||||||
\(648\) | 15.0000 | 0.589256 | ||||||||
\(649\) | 3.26153 | − | 5.64914i | 0.128026 | − | 0.221748i | ||||
\(650\) | −1.39948 | − | 7.82305i | −0.0548920 | − | 0.306845i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.69375 | + | 11.5939i | −0.262147 | + | 0.454053i | ||||
\(653\) | −12.5917 | − | 21.8094i | −0.492750 | − | 0.853468i | 0.507215 | − | 0.861819i | \(-0.330675\pi\) |
−0.999965 | + | 0.00835161i | \(0.997342\pi\) | |||||||
\(654\) | −12.4392 | + | 21.5453i | −0.486411 | + | 0.842488i | ||||
\(655\) | −11.0000 | − | 19.0526i | −0.429806 | − | 0.744445i | ||||
\(656\) | 9.75513 | 0.380874 | ||||||||
\(657\) | 2.90061 | + | 5.02401i | 0.113164 | + | 0.196005i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.7958 | + | 32.5553i | 0.732182 | + | 1.26818i | 0.955949 | + | 0.293533i | \(0.0948311\pi\) |
−0.223767 | + | 0.974643i | \(0.571836\pi\) | |||||||
\(660\) | −11.0000 | − | 19.0526i | −0.428174 | − | 0.741620i | ||||
\(661\) | −27.8512 | −1.08328 | −0.541642 | − | 0.840609i | \(-0.682197\pi\) | ||||
−0.541642 | + | 0.840609i | \(0.682197\pi\) | |||||||
\(662\) | −0.306253 | − | 0.530445i | −0.0119028 | − | 0.0206163i | ||||
\(663\) | −4.94975 | − | 27.6690i | −0.192232 | − | 1.07458i | ||||
\(664\) | −29.6985 | −1.15252 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.39792 | + | 5.88536i | −0.131667 | + | 0.228053i | ||||
\(667\) | −15.7958 | −0.611617 | ||||||||
\(668\) | −7.63381 | − | 13.2221i | −0.295361 | − | 0.511580i | ||||
\(669\) | 4.00000 | − | 6.92820i | 0.154649 | − | 0.267860i | ||||
\(670\) | 15.5563 | 0.600994 | ||||||||
\(671\) | −9.03328 | −0.348726 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.9896 | + | 20.7666i | −0.462164 | + | 0.800492i | −0.999069 | − | 0.0431511i | \(-0.986260\pi\) |
0.536904 | + | 0.843643i | \(0.319594\pi\) | |||||||
\(674\) | 14.9896 | + | 25.9627i | 0.577377 | + | 1.00005i | ||||
\(675\) | −6.23433 | − | 10.7982i | −0.239959 | − | 0.415622i | ||||
\(676\) | −10.0000 | − | 8.30662i | −0.384615 | − | 0.319486i | ||||
\(677\) | 17.3889 | − | 30.1185i | 0.668311 | − | 1.15755i | −0.310065 | − | 0.950715i | \(-0.600351\pi\) |
0.978376 | − | 0.206833i | \(-0.0663158\pi\) | |||||||
\(678\) | −11.7321 | + | 20.3206i | −0.450568 | + | 0.780406i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −22.1937 | − | 38.4407i | −0.851091 | − | 1.47413i | ||||
\(681\) | −14.7958 | + | 25.6271i | −0.566977 | + | 0.982034i | ||||
\(682\) | −4.09827 | + | 7.09841i | −0.156931 | + | 0.271812i | ||||
\(683\) | −25.3875 | + | 43.9724i | −0.971425 | + | 1.68256i | −0.280166 | + | 0.959952i | \(0.590390\pi\) |
−0.691259 | + | 0.722607i | \(0.742944\pi\) | |||||||
\(684\) | −1.41421 | + | 2.44949i | −0.0540738 | + | 0.0936586i | ||||
\(685\) | 12.3523 | + | 21.3947i | 0.471956 | + | 0.817451i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.00000 | + | 15.5885i | −0.343371 | + | 0.594737i | ||||
\(688\) | −0.897916 | + | 1.55524i | −0.0342327 | + | 0.0592928i | ||||
\(689\) | 22.3534 | + | 8.07311i | 0.851597 | + | 0.307561i | ||||
\(690\) | 3.40834 | + | 5.90341i | 0.129753 | + | 0.224739i | ||||
\(691\) | 5.51249 | + | 9.54790i | 0.209705 | + | 0.363219i | 0.951622 | − | 0.307273i | \(-0.0994164\pi\) |
−0.741917 | + | 0.670492i | \(0.766083\pi\) | |||||||
\(692\) | −4.66101 | + | 8.07311i | −0.177185 | + | 0.306893i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.9792 | 0.568601 | ||||||||
\(695\) | 40.9792 | 1.55443 | ||||||||
\(696\) | 18.6588 | − | 32.3179i | 0.707259 | − | 1.22501i | ||||
\(697\) | −26.8875 | − | 46.5705i | −1.01844 | − | 1.76398i | ||||
\(698\) | −13.0167 | −0.492688 | ||||||||
\(699\) | −14.9789 | + | 25.9442i | −0.566553 | + | 0.981299i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.4083 | −0.393117 | −0.196559 | − | 0.980492i | \(-0.562977\pi\) | ||||
−0.196559 | + | 0.980492i | \(0.562977\pi\) | |||||||
\(702\) | 19.1833 | + | 6.92820i | 0.724028 | + | 0.261488i | ||||
\(703\) | 9.61076 | + | 16.6463i | 0.362477 | + | 0.627828i | ||||
\(704\) | 40.5708 | 1.52907 | ||||||||
\(705\) | −5.36812 | − | 9.29785i | −0.202175 | − | 0.350177i | ||||
\(706\) | −7.56162 | − | 13.0971i | −0.284585 | − | 0.492916i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.795832 | + | 1.37842i | 0.0299092 | + | 0.0518042i | ||||
\(709\) | −18.7958 | −0.705892 | −0.352946 | − | 0.935644i | \(-0.614820\pi\) | ||||
−0.352946 | + | 0.935644i | \(0.614820\pi\) | |||||||
\(710\) | −8.05217 | − | 13.9468i | −0.302193 | − | 0.523413i | ||||
\(711\) | −5.89792 | + | 10.2155i | −0.221189 | + | 0.383111i | ||||
\(712\) | −18.2257 | − | 31.5678i | −0.683036 | − | 1.18305i | ||||
\(713\) | −1.26984 | + | 2.19944i | −0.0475561 | + | 0.0823695i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.87707 | − | 55.2127i | −0.369382 | − | 2.06484i | ||||
\(716\) | −0.204168 | + | 0.353630i | −0.00763013 | + | 0.0132158i | ||||
\(717\) | 27.9955 | 1.04551 | ||||||||
\(718\) | −4.00000 | −0.149279 | ||||||||
\(719\) | −29.1210 | −1.08603 | −0.543015 | − | 0.839723i | \(-0.682717\pi\) | ||||
−0.543015 | + | 0.839723i | \(0.682717\pi\) | |||||||
\(720\) | 2.68406 | 0.100029 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.50000 | + | 9.52628i | 0.204689 | + | 0.354531i | ||||
\(723\) | −3.10208 | + | 5.37297i | −0.115368 | + | 0.199823i | ||||
\(724\) | 8.26873 | − | 14.3219i | 0.307305 | − | 0.532268i | ||||
\(725\) | −19.3875 | −0.720033 | ||||||||
\(726\) | 15.9747 | + | 27.6690i | 0.592877 | + | 1.02689i | ||||
\(727\) | 35.3259 | 1.31016 | 0.655082 | − | 0.755558i | \(-0.272634\pi\) | ||||
0.655082 | + | 0.755558i | \(0.272634\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | −7.78541 | − | 13.4847i | −0.288151 | − | 0.499092i | ||||
\(731\) | 9.89949 | 0.366146 | ||||||||
\(732\) | 1.10208 | − | 1.90887i | 0.0407342 | − | 0.0705537i | ||||
\(733\) | 0.346184 | − | 0.599609i | 0.0127866 | − | 0.0221471i | −0.859561 | − | 0.511033i | \(-0.829263\pi\) |
0.872348 | + | 0.488886i | \(0.162596\pi\) | |||||||
\(734\) | 10.6066 | + | 18.3712i | 0.391497 | + | 0.678092i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.97916 | 0.330976 | ||||||||
\(737\) | 33.5917 | 1.23736 | ||||||||
\(738\) | 9.75513 | 0.359091 | ||||||||
\(739\) | 15.1833 | 0.558528 | 0.279264 | − | 0.960214i | \(-0.409910\pi\) | ||||
0.279264 | + | 0.960214i | \(0.409910\pi\) | |||||||
\(740\) | −9.12020 | + | 15.7967i | −0.335265 | + | 0.580697i | ||||
\(741\) | 11.0250 | − | 9.29785i | 0.405012 | − | 0.341565i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.59166 | + | 7.95299i | −0.168452 | + | 0.291767i | −0.937876 | − | 0.346971i | \(-0.887210\pi\) |
0.769424 | + | 0.638738i | \(0.220543\pi\) | |||||||
\(744\) | −3.00000 | − | 5.19615i | −0.109985 | − | 0.190500i | ||||
\(745\) | −6.16215 | + | 10.6731i | −0.225764 | + | 0.391034i | ||||
\(746\) | 6.29583 | + | 10.9047i | 0.230507 | + | 0.399249i | ||||
\(747\) | −9.89949 | −0.362204 | ||||||||
\(748\) | −15.9747 | − | 27.6690i | −0.584094 | − | 1.01168i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −5.30625 | − | 9.19070i | −0.193757 | − | 0.335597i | ||||
\(751\) | −0.897916 | − | 1.55524i | −0.0327654 | − | 0.0567514i | 0.849178 | − | 0.528107i | \(-0.177098\pi\) |
−0.881943 | + | 0.471356i | \(0.843765\pi\) | |||||||
\(752\) | 2.82843 | 0.103142 | ||||||||
\(753\) | 2.20417 | + | 3.81773i | 0.0803244 | + | 0.139126i | ||||
\(754\) | 24.2434 | − | 20.4456i | 0.882894 | − | 0.744584i | ||||
\(755\) | −47.2170 | −1.71840 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.5917 | − | 21.8094i | 0.457652 | − | 0.792676i | −0.541185 | − | 0.840904i | \(-0.682024\pi\) |
0.998836 | + | 0.0482277i | \(0.0153573\pi\) | |||||||
\(758\) | −3.38749 | −0.123039 | ||||||||
\(759\) | 7.35981 | + | 12.7476i | 0.267144 | + | 0.462707i | ||||
\(760\) | 11.3875 | − | 19.7237i | 0.413068 | − | 0.715454i | ||||
\(761\) | −9.32202 | −0.337923 | −0.168961 | − | 0.985623i | \(-0.554041\pi\) | ||||
−0.168961 | + | 0.985623i | \(0.554041\pi\) | |||||||
\(762\) | −10.7362 | −0.388933 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12.8979 | + | 22.3398i | −0.466630 | + | 0.808227i | ||||
\(765\) | −7.39792 | − | 12.8136i | −0.267472 | − | 0.463275i | ||||
\(766\) | −7.48944 | − | 12.9721i | −0.270604 | − | 0.468700i | ||||
\(767\) | 0.714590 | + | 3.99455i | 0.0258023 | + | 0.144235i | ||||
\(768\) | −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 | ||||||||
\(771\) | −10.8979 | − | 18.8757i | −0.392479 | − | 0.679793i | ||||
\(772\) | 1.70417 | − | 2.95171i | 0.0613344 | − | 0.106234i | ||||
\(773\) | 3.82427 | − | 6.62383i | 0.137549 | − | 0.238243i | −0.789019 | − | 0.614369i | \(-0.789411\pi\) |
0.926568 | + | 0.376126i | \(0.122744\pi\) | |||||||
\(774\) | −0.897916 | + | 1.55524i | −0.0322749 | + | 0.0559018i | ||||
\(775\) | −1.55858 | + | 2.69954i | −0.0559859 | + | 0.0969705i | ||||
\(776\) | 6.36396 | + | 11.0227i | 0.228453 | + | 0.395692i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.1937 | + | 24.5843i | −0.508870 | + | 0.881390i | ||||
\(779\) | 13.7958 | − | 23.8951i | 0.494287 | − | 0.856130i | ||||
\(780\) | 12.8723 | + | 4.64893i | 0.460902 | + | 0.166458i | ||||
\(781\) | −17.3875 | − | 30.1160i | −0.622173 | − | 1.07764i | ||||
\(782\) | 4.94975 | + | 8.57321i | 0.177003 | + | 0.306578i | ||||
\(783\) | 24.8784 | − | 43.0906i | 0.889080 | − | 1.53993i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.5917 | 0.663565 | ||||||||
\(786\) | −11.5917 | −0.413461 | ||||||||
\(787\) | 12.7132 | − | 22.0199i | 0.453176 | − | 0.784924i | −0.545405 | − | 0.838173i | \(-0.683624\pi\) |
0.998581 | + | 0.0532485i | \(0.0169575\pi\) | |||||||
\(788\) | −4.00000 | − | 6.92820i | −0.142494 | − | 0.246807i | ||||
\(789\) | 35.9033 | 1.27819 | ||||||||
\(790\) | 15.8303 | − | 27.4190i | 0.563219 | − | 0.975523i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 17.3875 | 0.617838 | ||||||||
\(793\) | 4.29583 | − | 3.62287i | 0.152549 | − | 0.128652i | ||||
\(794\) | 3.53553 | + | 6.12372i | 0.125471 | + | 0.217323i | ||||
\(795\) | −25.0208 | −0.887398 | ||||||||
\(796\) | 11.0250 | + | 19.0958i | 0.390770 | + | 0.676833i | ||||
\(797\) | −13.1463 | − | 22.7700i | −0.465666 | − | 0.806556i | 0.533566 | − | 0.845759i | \(-0.320852\pi\) |
−0.999231 | + | 0.0392022i | \(0.987518\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.79583 | − | 13.5028i | −0.275797 | − | 0.477694i | ||||
\(800\) | 11.0208 | 0.389646 | ||||||||
\(801\) | −6.07522 | − | 10.5226i | −0.214657 | − | 0.371798i | ||||
\(802\) | −12.1937 | + | 21.1202i | −0.430576 | + | 0.745780i | ||||
\(803\) | −16.8115 | − | 29.1183i | −0.593263 | − | 1.02756i | ||||
\(804\) | −4.09827 | + | 7.09841i | −0.144535 | + | 0.250342i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.897916 | − | 5.01934i | −0.0316277 | − | 0.176799i | ||||
\(807\) | 0.795832 | − | 1.37842i | 0.0280146 | − | 0.0485227i | ||||
\(808\) | −8.91839 | −0.313748 | ||||||||
\(809\) | 39.3667 | 1.38406 | 0.692029 | − | 0.721870i | \(-0.256717\pi\) | ||||
0.692029 | + | 0.721870i | \(0.256717\pi\) | |||||||
\(810\) | −13.4203 | −0.471541 | ||||||||
\(811\) | 38.4725 | 1.35095 | 0.675476 | − | 0.737382i | \(-0.263938\pi\) | ||||
0.675476 | + | 0.737382i | \(0.263938\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.3875 | + | 28.3840i | 0.574735 | + | 0.995469i | ||||
\(814\) | 19.6937 | − | 34.1106i | 0.690265 | − | 1.19557i | ||||
\(815\) | 17.9664 | − | 31.1187i | 0.629336 | − | 1.09004i | ||||
\(816\) | −7.79583 | −0.272909 | ||||||||
\(817\) | 2.53969 | + | 4.39887i | 0.0888525 | + | 0.153897i | ||||
\(818\) | 28.6879 | 1.00305 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 26.1833 | 0.914361 | ||||||||
\(821\) | 20.1833 | + | 34.9585i | 0.704403 | + | 1.22006i | 0.966907 | + | 0.255131i | \(0.0821185\pi\) |
−0.262504 | + | 0.964931i | \(0.584548\pi\) | |||||||
\(822\) | 13.0167 | 0.454008 | ||||||||
\(823\) | −18.3875 | + | 31.8481i | −0.640948 | + | 1.11015i | 0.344274 | + | 0.938869i | \(0.388125\pi\) |
−0.985222 | + | 0.171285i | \(0.945208\pi\) | |||||||
\(824\) | 12.2948 | − | 21.2952i | 0.428310 | − | 0.741855i | ||||
\(825\) | 9.03328 | + | 15.6461i | 0.314498 | + | 0.544727i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.9792 | 0.938157 | 0.469079 | − | 0.883156i | \(-0.344586\pi\) | ||||
0.469079 | + | 0.883156i | \(0.344586\pi\) | |||||||
\(828\) | 1.79583 | 0.0624095 | ||||||||
\(829\) | −20.2026 | −0.701666 | −0.350833 | − | 0.936438i | \(-0.614102\pi\) | ||||
−0.350833 | + | 0.936438i | \(0.614102\pi\) | |||||||
\(830\) | 26.5708 | 0.922287 | ||||||||
\(831\) | −4.37227 | + | 7.57300i | −0.151672 | + | 0.262704i | ||||
\(832\) | −19.2937 | + | 16.2712i | −0.668889 | + | 0.564104i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.7958 | − | 18.6989i | 0.373829 | − | 0.647491i | ||||
\(835\) | 20.4896 | + | 35.4890i | 0.709071 | + | 1.22815i | ||||
\(836\) | 8.19654 | − | 14.1968i | 0.283483 | − | 0.491008i | ||||
\(837\) | −4.00000 | − | 6.92820i | −0.138260 | − | 0.239474i | ||||
\(838\) | −28.5435 | −0.986020 | ||||||||
\(839\) | 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 | ||||||||
\(841\) | −24.1833 | − | 41.8867i | −0.833908 | − | 1.44437i | ||||
\(842\) | 3.29583 | + | 5.70855i | 0.113582 | + | 0.196730i | ||||
\(843\) | −21.5019 | −0.740566 | ||||||||
\(844\) | −0.897916 | − | 1.55524i | −0.0309075 | − | 0.0535334i | ||||
\(845\) | 26.8406 | + | 22.2955i | 0.923344 | + | 0.766987i | ||||
\(846\) | 2.82843 | 0.0972433 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.29583 | − | 5.70855i | 0.113179 | − | 0.196032i | ||||
\(849\) | −41.5917 | −1.42742 | ||||||||
\(850\) | 6.07522 | + | 10.5226i | 0.208378 | + | 0.360922i | ||||
\(851\) | 6.10208 | − | 10.5691i | 0.209177 | − | 0.362305i | ||||
\(852\) | 8.48528 | 0.290701 | ||||||||
\(853\) | 13.1610 | 0.450625 | 0.225313 | − | 0.974287i | \(-0.427660\pi\) | ||||
0.225313 | + | 0.974287i | \(0.427660\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.79583 | − | 6.57457i | 0.129815 | − | 0.224846i | ||||
\(856\) | −9.00000 | − | 15.5885i | −0.307614 | − | 0.532803i | ||||
\(857\) | −18.8753 | − | 32.6930i | −0.644769 | − | 1.11677i | −0.984355 | − | 0.176198i | \(-0.943620\pi\) |
0.339586 | − | 0.940575i | \(-0.389713\pi\) | |||||||
\(858\) | −27.7958 | − | 10.0387i | −0.948934 | − | 0.342715i | ||||
\(859\) | 11.8764 | − | 20.5706i | 0.405219 | − | 0.701860i | −0.589128 | − | 0.808040i | \(-0.700529\pi\) |
0.994347 | + | 0.106180i | \(0.0338619\pi\) | |||||||
\(860\) | −2.41006 | + | 4.17434i | −0.0821823 | + | 0.142344i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.59166 | + | 4.48889i | 0.0882724 | + | 0.152892i | ||||
\(863\) | −8.89792 | + | 15.4116i | −0.302889 | + | 0.524618i | −0.976789 | − | 0.214204i | \(-0.931284\pi\) |
0.673900 | + | 0.738822i | \(0.264618\pi\) | |||||||
\(864\) | −14.1421 | + | 24.4949i | −0.481125 | + | 0.833333i | ||||
\(865\) | 12.5104 | − | 21.6687i | 0.425367 | − | 0.736757i | ||||
\(866\) | 6.71015 | − | 11.6223i | 0.228020 | − | 0.394942i | ||||
\(867\) | 9.46639 | + | 16.3963i | 0.321495 | + | 0.556846i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.1833 | − | 59.2073i | 1.15959 | − | 2.00847i | ||||
\(870\) | −16.6937 | + | 28.9144i | −0.565971 | + | 0.980291i | ||||
\(871\) | −15.9747 | + | 13.4722i | −0.541283 | + | 0.456488i | ||||
\(872\) | −26.3875 | − | 45.7045i | −0.893593 | − | 1.54775i | ||||
\(873\) | 2.12132 | + | 3.67423i | 0.0717958 | + | 0.124354i | ||||
\(874\) | −2.53969 | + | 4.39887i | −0.0859063 | + | 0.148794i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.20417 | 0.277193 | ||||||||
\(877\) | −4.79583 | −0.161944 | −0.0809719 | − | 0.996716i | \(-0.525802\pi\) | ||||
−0.0809719 | + | 0.996716i | \(0.525802\pi\) | |||||||
\(878\) | 17.1002 | − | 29.6184i | 0.577104 | − | 0.999573i | ||||
\(879\) | 6.89792 | + | 11.9475i | 0.232661 | + | 0.402981i | ||||
\(880\) | −15.5563 | −0.524404 | ||||||||
\(881\) | −11.6599 | + | 20.1955i | −0.392832 | + | 0.680405i | −0.992822 | − | 0.119603i | \(-0.961838\pi\) |
0.599990 | + | 0.800007i | \(0.295171\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.6125 | −0.559055 | −0.279528 | − | 0.960138i | \(-0.590178\pi\) | ||||
−0.279528 | + | 0.960138i | \(0.590178\pi\) | |||||||
\(884\) | 18.6937 | + | 6.75139i | 0.628739 | + | 0.227074i | ||||
\(885\) | −2.13606 | − | 3.69976i | −0.0718028 | − | 0.124366i | ||||
\(886\) | 10.0000 | 0.335957 | ||||||||
\(887\) | −14.2865 | − | 24.7450i | −0.479694 | − | 0.830854i | 0.520035 | − | 0.854145i | \(-0.325919\pi\) |
−0.999729 | + | 0.0232909i | \(0.992586\pi\) | |||||||
\(888\) | 14.4161 | + | 24.9695i | 0.483774 | + | 0.837921i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16.3063 | + | 28.2433i | 0.546587 | + | 0.946716i | ||||
\(891\) | −28.9792 | −0.970838 | ||||||||
\(892\) | 2.82843 | + | 4.89898i | 0.0947027 | + | 0.164030i | ||||
\(893\) | 4.00000 | − | 6.92820i | 0.133855 | − | 0.231843i | ||||
\(894\) | 3.24680 | + | 5.62362i | 0.108589 | + | 0.188082i | ||||
\(895\) | 0.548000 | − | 0.949164i | 0.0183176 | − | 0.0317271i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.61251 | − | 3.11047i | −0.287563 | − | 0.103856i | ||||
\(898\) | −2.20417 | + | 3.81773i | −0.0735541 | + | 0.127399i | ||||
\(899\) | −12.4392 | −0.414870 | ||||||||
\(900\) | 2.20417 | 0.0734723 | ||||||||
\(901\) | −36.3364 | −1.21054 | ||||||||
\(902\) | −56.5391 | −1.88255 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −24.8875 | − | 43.1064i | −0.827746 | − | 1.43370i | ||||
\(905\) | −22.1937 | + | 38.4407i | −0.737745 | + | 1.27781i | ||||
\(906\) | −12.4392 | + | 21.5453i | −0.413264 | + | 0.715795i | ||||
\(907\) | 49.3875 | 1.63988 | 0.819942 | − | 0.572446i | \(-0.194005\pi\) | ||||
0.819942 | + | 0.572446i | \(0.194005\pi\) | |||||||
\(908\) | −10.4622 | − | 18.1211i | −0.347201 | − | 0.601370i | ||||
\(909\) | −2.97280 | −0.0986014 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.1833 | −1.43073 | −0.715364 | − | 0.698752i | \(-0.753739\pi\) | ||||
−0.715364 | + | 0.698752i | \(0.753739\pi\) | |||||||
\(912\) | −2.00000 | − | 3.46410i | −0.0662266 | − | 0.114708i | ||||
\(913\) | 57.3758 | 1.89886 | ||||||||
\(914\) | 7.29583 | − | 12.6368i | 0.241325 | − | 0.417987i | ||||
\(915\) | −2.95806 | + | 5.12351i | −0.0977904 | + | 0.169378i | ||||
\(916\) | −6.36396 | − | 11.0227i | −0.210271 | − | 0.364200i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −31.1833 | −1.02920 | ||||||||
\(919\) | 10.0000 | 0.329870 | 0.164935 | − | 0.986304i | \(-0.447259\pi\) | ||||
0.164935 | + | 0.986304i | \(0.447259\pi\) | |||||||
\(920\) | −14.4603 | −0.476744 | ||||||||
\(921\) | 48.3667 | 1.59374 | ||||||||
\(922\) | 15.4842 | − | 26.8194i | 0.509944 | − | 0.883249i | ||||
\(923\) | 20.3470 | + | 7.34847i | 0.669729 | + | 0.241878i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.48958 | − | 12.9723i | 0.246256 | − | 0.426528i | ||||
\(926\) | −5.69375 | − | 9.86186i | −0.187108 | − | 0.324081i | ||||
\(927\) | 4.09827 | − | 7.09841i | 0.134605 | − | 0.233143i | ||||
\(928\) | 21.9896 | + | 38.0871i | 0.721843 | + | 1.25027i | ||||
\(929\) | 28.1399 | 0.923240 | 0.461620 | − | 0.887078i | \(-0.347268\pi\) | ||||
0.461620 | + | 0.887078i | \(0.347268\pi\) | |||||||
\(930\) | 2.68406 | + | 4.64893i | 0.0880137 | + | 0.152444i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.5917 | − | 18.3453i | −0.346941 | − | 0.600920i | ||||
\(933\) | −8.38749 | − | 14.5276i | −0.274594 | − | 0.475611i | ||||
\(934\) | 4.82012 | 0.157719 | ||||||||
\(935\) | 42.8771 | + | 74.2653i | 1.40223 | + | 2.42873i | ||||
\(936\) | −8.26873 | + | 6.97339i | −0.270272 | + | 0.227932i | ||||
\(937\) | −6.63796 | −0.216853 | −0.108426 | − | 0.994104i | \(-0.534581\pi\) | ||||
−0.108426 | + | 0.994104i | \(0.534581\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.20417 | + | 2.08568i | −0.0392966 | + | 0.0680636i | ||||
\(940\) | 7.59166 | 0.247613 | ||||||||
\(941\) | −11.7321 | − | 20.3206i | −0.382455 | − | 0.662431i | 0.608958 | − | 0.793203i | \(-0.291588\pi\) |
−0.991413 | + | 0.130772i | \(0.958255\pi\) | |||||||
\(942\) | 4.89792 | − | 8.48344i | 0.159583 | − | 0.276405i | ||||
\(943\) | −17.5186 | −0.570483 | ||||||||
\(944\) | 1.12548 | 0.0366311 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.20417 | − | 9.01388i | 0.169202 | − | 0.293067i | ||||
\(947\) | −14.1021 | − | 24.4255i | −0.458256 | − | 0.793723i | 0.540613 | − | 0.841272i | \(-0.318192\pi\) |
−0.998869 | + | 0.0475486i | \(0.984859\pi\) | |||||||
\(948\) | 8.34091 | + | 14.4469i | 0.270900 | + | 0.469213i | ||||
\(949\) | 19.6729 | + | 7.10502i | 0.638610 | + | 0.230639i | ||||
\(950\) | −3.11716 | + | 5.39909i | −0.101134 | + | 0.175170i | ||||
\(951\) | −8.90365 | + | 15.4216i | −0.288721 | + | 0.500079i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.40834 | + | 4.17136i | 0.0780137 | + | 0.135124i | 0.902393 | − | 0.430914i | \(-0.141809\pi\) |
−0.824379 | + | 0.566038i | \(0.808476\pi\) | |||||||
\(954\) | 3.29583 | − | 5.70855i | 0.106706 | − | 0.184821i | ||||
\(955\) | 34.6188 | − | 59.9614i | 1.12024 | − | 1.94031i | ||||
\(956\) | −9.89792 | + | 17.1437i | −0.320121 | + | 0.554467i | ||||
\(957\) | −36.0477 | + | 62.4365i | −1.16526 | + | 2.01828i | ||||
\(958\) | −3.67990 | − | 6.37378i | −0.118892 | − | 0.205927i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 13.2854 | − | 23.0110i | 0.428785 | − | 0.742677i | ||||
\(961\) | 14.5000 | − | 25.1147i | 0.467742 | − | 0.810153i | ||||
\(962\) | 4.31483 | + | 24.1198i | 0.139116 | + | 0.777654i | ||||
\(963\) | −3.00000 | − | 5.19615i | −0.0966736 | − | 0.167444i | ||||
\(964\) | −2.19350 | − | 3.79926i | −0.0706480 | − | 0.122366i | ||||
\(965\) | −4.57409 | + | 7.92255i | −0.147245 | + | 0.255036i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.3875 | 0.366197 | 0.183099 | − | 0.983095i | \(-0.441387\pi\) | ||||
0.183099 | + | 0.983095i | \(0.441387\pi\) | |||||||
\(968\) | −67.7750 | −2.17837 | ||||||||
\(969\) | −11.0250 | + | 19.0958i | −0.354173 | + | 0.613446i | ||||
\(970\) | −5.69375 | − | 9.86186i | −0.182815 | − | 0.316645i | ||||
\(971\) | 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 | ||||||||
\(974\) | 19.5917 | 0.627757 | ||||||||
\(975\) | −10.5708 | − | 3.81773i | −0.338537 | − | 0.122265i | ||||
\(976\) | −0.779291 | − | 1.34977i | −0.0249445 | − | 0.0432051i | ||||
\(977\) | 0.387495 | 0.0123970 | 0.00619852 | − | 0.999981i | \(-0.498027\pi\) | ||||
0.00619852 | + | 0.999981i | \(0.498027\pi\) | |||||||
\(978\) | −9.46639 | − | 16.3963i | −0.302702 | − | 0.524295i | ||||
\(979\) | 35.2110 | + | 60.9872i | 1.12535 | + | 1.94916i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.79583 | − | 15.2348i | −0.280829 | − | 0.486411i | ||||
\(982\) | −9.59166 | −0.306082 | ||||||||
\(983\) | 20.7801 | + | 35.9922i | 0.662782 | + | 1.14797i | 0.979882 | + | 0.199580i | \(0.0639578\pi\) |
−0.317099 | + | 0.948392i | \(0.602709\pi\) | |||||||
\(984\) | 20.6937 | − | 35.8426i | 0.659693 | − | 1.14262i | ||||
\(985\) | 10.7362 | + | 18.5957i | 0.342085 | + | 0.592508i | ||||
\(986\) | −24.2434 | + | 41.9909i | −0.772069 | + | 1.33726i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.79583 | + | 10.0387i | 0.0571330 | + | 0.319373i | ||||
\(989\) | 1.61251 | − | 2.79294i | 0.0512747 | − | 0.0888104i | ||||
\(990\) | −15.5563 | −0.494413 | ||||||||
\(991\) | 18.2042 | 0.578274 | 0.289137 | − | 0.957288i | \(-0.406632\pi\) | ||||
0.289137 | + | 0.957288i | \(0.406632\pi\) | |||||||
\(992\) | 7.07107 | 0.224507 | ||||||||
\(993\) | −0.866213 | −0.0274885 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.5917 | − | 51.2543i | −0.938119 | − | 1.62487i | ||||
\(996\) | −7.00000 | + | 12.1244i | −0.221803 | + | 0.384175i | ||||
\(997\) | −2.75624 | + | 4.77395i | −0.0872911 | + | 0.151193i | −0.906365 | − | 0.422495i | \(-0.861154\pi\) |
0.819074 | + | 0.573688i | \(0.194488\pi\) | |||||||
\(998\) | 16.2042 | 0.512934 | ||||||||
\(999\) | 19.2215 | + | 33.2926i | 0.608142 | + | 1.05333i |
(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.373.1 | 8 | ||
7.2 | even | 3 | 637.2.f.g.295.4 | yes | 8 | ||
7.3 | odd | 6 | 637.2.h.k.165.2 | 8 | |||
7.4 | even | 3 | 637.2.h.k.165.3 | 8 | |||
7.5 | odd | 6 | 637.2.f.g.295.1 | ✓ | 8 | ||
7.6 | odd | 2 | inner | 637.2.g.h.373.4 | 8 | ||
13.3 | even | 3 | 637.2.h.k.471.3 | 8 | |||
91.3 | odd | 6 | inner | 637.2.g.h.263.4 | 8 | ||
91.9 | even | 3 | 8281.2.a.bv.1.2 | 4 | |||
91.16 | even | 3 | 637.2.f.g.393.4 | yes | 8 | ||
91.30 | even | 6 | 8281.2.a.bn.1.1 | 4 | |||
91.55 | odd | 6 | 637.2.h.k.471.2 | 8 | |||
91.61 | odd | 6 | 8281.2.a.bv.1.3 | 4 | |||
91.68 | odd | 6 | 637.2.f.g.393.1 | yes | 8 | ||
91.81 | even | 3 | inner | 637.2.g.h.263.1 | 8 | ||
91.82 | odd | 6 | 8281.2.a.bn.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.f.g.295.1 | ✓ | 8 | 7.5 | odd | 6 | ||
637.2.f.g.295.4 | yes | 8 | 7.2 | even | 3 | ||
637.2.f.g.393.1 | yes | 8 | 91.68 | odd | 6 | ||
637.2.f.g.393.4 | yes | 8 | 91.16 | even | 3 | ||
637.2.g.h.263.1 | 8 | 91.81 | even | 3 | inner | ||
637.2.g.h.263.4 | 8 | 91.3 | odd | 6 | inner | ||
637.2.g.h.373.1 | 8 | 1.1 | even | 1 | trivial | ||
637.2.g.h.373.4 | 8 | 7.6 | odd | 2 | inner | ||
637.2.h.k.165.2 | 8 | 7.3 | odd | 6 | |||
637.2.h.k.165.3 | 8 | 7.4 | even | 3 | |||
637.2.h.k.471.2 | 8 | 91.55 | odd | 6 | |||
637.2.h.k.471.3 | 8 | 13.3 | even | 3 | |||
8281.2.a.bn.1.1 | 4 | 91.30 | even | 6 | |||
8281.2.a.bn.1.4 | 4 | 91.82 | odd | 6 | |||
8281.2.a.bv.1.2 | 4 | 91.9 | even | 3 | |||
8281.2.a.bv.1.3 | 4 | 91.61 | odd | 6 |