Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), degree \(4\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 165.2 | ||
Character | \(\chi\) | \(=\) | 784.165 |
Dual form | 784.2.x.l.765.2 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.29835 | + | 0.560616i | −0.918071 | + | 0.396416i | ||||
\(3\) | −0.752181 | − | 2.80718i | −0.434272 | − | 1.62072i | −0.742803 | − | 0.669510i | \(-0.766504\pi\) |
0.308531 | − | 0.951214i | \(-0.400163\pi\) | |||||||
\(4\) | 1.37142 | − | 1.45575i | 0.685709 | − | 0.727876i | ||||
\(5\) | 0.998394 | − | 3.72606i | 0.446495 | − | 1.66634i | −0.265462 | − | 0.964121i | \(-0.585525\pi\) |
0.711958 | − | 0.702222i | \(-0.247809\pi\) | |||||||
\(6\) | 2.55034 | + | 3.22301i | 1.04117 | + | 1.31579i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.964462 | + | 2.65891i | −0.340989 | + | 0.940067i | ||||
\(9\) | −4.71639 | + | 2.72301i | −1.57213 | + | 0.907670i | ||||
\(10\) | 0.792625 | + | 5.39744i | 0.250650 | + | 1.70682i | ||||
\(11\) | −1.25622 | + | 0.336603i | −0.378764 | + | 0.101490i | −0.443178 | − | 0.896434i | \(-0.646149\pi\) |
0.0644137 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(12\) | −5.11811 | − | 2.75483i | −1.47747 | − | 0.795250i | ||||
\(13\) | −1.12607 | + | 1.12607i | −0.312316 | + | 0.312316i | −0.845806 | − | 0.533490i | \(-0.820880\pi\) |
0.533490 | + | 0.845806i | \(0.320880\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −11.2107 | −2.89458 | ||||||||
\(16\) | −0.238422 | − | 3.99289i | −0.0596056 | − | 0.998222i | ||||
\(17\) | 0.754426 | − | 1.30670i | 0.182975 | − | 0.316922i | −0.759917 | − | 0.650020i | \(-0.774761\pi\) |
0.942892 | + | 0.333098i | \(0.108094\pi\) | |||||||
\(18\) | 4.59696 | − | 6.17950i | 1.08351 | − | 1.45652i | ||||
\(19\) | −1.99810 | − | 0.535390i | −0.458396 | − | 0.122827i | 0.0222291 | − | 0.999753i | \(-0.492924\pi\) |
−0.480625 | + | 0.876926i | \(0.659590\pi\) | |||||||
\(20\) | −4.05500 | − | 6.56340i | −0.906725 | − | 1.46762i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.44230 | − | 1.14128i | 0.307500 | − | 0.243323i | ||||
\(23\) | −4.13121 | + | 2.38515i | −0.861416 | + | 0.497339i | −0.864486 | − | 0.502657i | \(-0.832356\pi\) |
0.00307023 | + | 0.999995i | \(0.499023\pi\) | |||||||
\(24\) | 8.18949 | + | 0.707432i | 1.67167 | + | 0.144404i | ||||
\(25\) | −8.55659 | − | 4.94015i | −1.71132 | − | 0.988030i | ||||
\(26\) | 0.830740 | − | 2.09333i | 0.162922 | − | 0.410536i | ||||
\(27\) | 5.02656 | + | 5.02656i | 0.967362 | + | 0.967362i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.10069 | − | 4.10069i | 0.761478 | − | 0.761478i | −0.215111 | − | 0.976590i | \(-0.569011\pi\) |
0.976590 | + | 0.215111i | \(0.0690115\pi\) | |||||||
\(30\) | 14.5554 | − | 6.28489i | 2.65743 | − | 1.14746i | ||||
\(31\) | −2.05500 | + | 3.55936i | −0.369088 | + | 0.639280i | −0.989423 | − | 0.145057i | \(-0.953663\pi\) |
0.620335 | + | 0.784337i | \(0.286997\pi\) | |||||||
\(32\) | 2.54803 | + | 5.05050i | 0.450433 | + | 0.892810i | ||||
\(33\) | 1.88981 | + | 3.27324i | 0.328973 | + | 0.569798i | ||||
\(34\) | −0.246948 | + | 2.11950i | −0.0423513 | + | 0.363491i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.50412 | + | 10.6003i | −0.417354 | + | 1.76671i | ||||
\(37\) | −0.605650 | + | 2.26031i | −0.0995682 | + | 0.371593i | −0.997672 | − | 0.0681892i | \(-0.978278\pi\) |
0.898104 | + | 0.439783i | \(0.144945\pi\) | |||||||
\(38\) | 2.89438 | − | 0.425046i | 0.469531 | − | 0.0689516i | ||||
\(39\) | 4.00810 | + | 2.31408i | 0.641809 | + | 0.370549i | ||||
\(40\) | 8.94435 | + | 6.24828i | 1.41423 | + | 0.987940i | ||||
\(41\) | − | 7.45533i | − | 1.16433i | −0.813072 | − | 0.582163i | \(-0.802206\pi\) | ||
0.813072 | − | 0.582163i | \(-0.197794\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.68992 | + | 5.68992i | 0.867705 | + | 0.867705i | 0.992218 | − | 0.124513i | \(-0.0397369\pi\) |
−0.124513 | + | 0.992218i | \(0.539737\pi\) | |||||||
\(44\) | −1.23279 | + | 2.29036i | −0.185850 | + | 0.345285i | ||||
\(45\) | 5.43727 | + | 20.2922i | 0.810541 | + | 3.02498i | ||||
\(46\) | 4.02659 | − | 5.41278i | 0.593688 | − | 0.798071i | ||||
\(47\) | −1.79874 | − | 3.11551i | −0.262373 | − | 0.454444i | 0.704499 | − | 0.709705i | \(-0.251172\pi\) |
−0.966872 | + | 0.255261i | \(0.917838\pi\) | |||||||
\(48\) | −11.0294 | + | 3.67267i | −1.59196 | + | 0.530104i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 13.8790 | + | 1.61707i | 1.96278 | + | 0.228689i | ||||
\(51\) | −4.23561 | − | 1.13493i | −0.593105 | − | 0.158922i | ||||
\(52\) | 0.0949645 | + | 3.18360i | 0.0131692 | + | 0.441486i | ||||
\(53\) | 0.923043 | − | 0.247329i | 0.126790 | − | 0.0339732i | −0.194866 | − | 0.980830i | \(-0.562427\pi\) |
0.321656 | + | 0.946857i | \(0.395761\pi\) | |||||||
\(54\) | −9.34420 | − | 3.70826i | −1.27158 | − | 0.504630i | ||||
\(55\) | 5.01680i | 0.676466i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.01174i | 0.796275i | ||||||||
\(58\) | −3.02521 | + | 7.62303i | −0.397229 | + | 1.00095i | ||||
\(59\) | −1.55512 | + | 0.416693i | −0.202459 | + | 0.0542489i | −0.358624 | − | 0.933482i | \(-0.616754\pi\) |
0.156164 | + | 0.987731i | \(0.450087\pi\) | |||||||
\(60\) | −15.3745 | + | 16.3200i | −1.98484 | + | 2.10690i | ||||
\(61\) | 4.39698 | + | 1.17817i | 0.562975 | + | 0.150849i | 0.529073 | − | 0.848576i | \(-0.322540\pi\) |
0.0339025 | + | 0.999425i | \(0.489206\pi\) | |||||||
\(62\) | 0.672667 | − | 5.77335i | 0.0854288 | − | 0.733216i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.13963 | − | 5.12884i | −0.767453 | − | 0.641105i | ||||
\(65\) | 3.07155 | + | 5.32008i | 0.380979 | + | 0.659875i | ||||
\(66\) | −4.28866 | − | 3.19035i | −0.527898 | − | 0.392705i | ||||
\(67\) | −0.558703 | − | 2.08511i | −0.0682564 | − | 0.254736i | 0.923363 | − | 0.383927i | \(-0.125429\pi\) |
−0.991620 | + | 0.129191i | \(0.958762\pi\) | |||||||
\(68\) | −0.867602 | − | 2.89029i | −0.105212 | − | 0.350500i | ||||
\(69\) | 9.80296 | + | 9.80296i | 1.18014 | + | 1.18014i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.8202i | − | 1.64016i | −0.572251 | − | 0.820079i | \(-0.693930\pi\) | ||
0.572251 | − | 0.820079i | \(-0.306070\pi\) | |||||||
\(72\) | −2.69147 | − | 15.1667i | −0.317192 | − | 1.78741i | ||||
\(73\) | −12.5356 | − | 7.23744i | −1.46718 | − | 0.847078i | −0.467857 | − | 0.883804i | \(-0.654974\pi\) |
−0.999325 | + | 0.0367258i | \(0.988307\pi\) | |||||||
\(74\) | −0.480825 | − | 3.27421i | −0.0558948 | − | 0.380620i | ||||
\(75\) | −7.43177 | + | 27.7357i | −0.858147 | + | 3.20265i | ||||
\(76\) | −3.51963 | + | 2.17450i | −0.403729 | + | 0.249432i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.50122 | − | 0.757473i | −0.736118 | − | 0.0857669i | ||||
\(79\) | 0.889807 | + | 1.54119i | 0.100111 | + | 0.173397i | 0.911730 | − | 0.410789i | \(-0.134747\pi\) |
−0.811619 | + | 0.584187i | \(0.801414\pi\) | |||||||
\(80\) | −15.1158 | − | 3.09810i | −1.68999 | − | 0.346378i | ||||
\(81\) | 2.16054 | − | 3.74216i | 0.240060 | − | 0.415795i | ||||
\(82\) | 4.17958 | + | 9.67961i | 0.461557 | + | 1.06893i | ||||
\(83\) | −7.16133 | + | 7.16133i | −0.786058 | + | 0.786058i | −0.980845 | − | 0.194787i | \(-0.937598\pi\) |
0.194787 | + | 0.980845i | \(0.437598\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.11564 | − | 4.11564i | −0.446404 | − | 0.446404i | ||||
\(86\) | −10.5774 | − | 4.19764i | −1.14059 | − | 0.452643i | ||||
\(87\) | −14.5958 | − | 8.42689i | −1.56483 | − | 0.903458i | ||||
\(88\) | 0.316577 | − | 3.66481i | 0.0337473 | − | 0.390671i | ||||
\(89\) | 7.32570 | − | 4.22949i | 0.776522 | − | 0.448325i | −0.0586740 | − | 0.998277i | \(-0.518687\pi\) |
0.835196 | + | 0.549952i | \(0.185354\pi\) | |||||||
\(90\) | −18.4356 | − | 23.2981i | −1.94328 | − | 2.45584i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.19342 | + | 9.28505i | −0.228680 | + | 0.968033i | ||||
\(93\) | 11.5375 | + | 3.09146i | 1.19638 | + | 0.320569i | ||||
\(94\) | 4.08200 | + | 3.03661i | 0.421026 | + | 0.313203i | ||||
\(95\) | −3.98979 | + | 6.91052i | −0.409344 | + | 0.709004i | ||||
\(96\) | 12.2611 | − | 10.9517i | 1.25139 | − | 1.11775i | ||||
\(97\) | 16.2227 | 1.64717 | 0.823585 | − | 0.567194i | \(-0.191971\pi\) | ||||
0.823585 | + | 0.567194i | \(0.191971\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.00824 | − | 5.00824i | 0.503348 | − | 0.503348i | ||||
\(100\) | −18.9263 | + | 5.68125i | −1.89263 | + | 0.568125i | ||||
\(101\) | 15.8001 | − | 4.23361i | 1.57216 | − | 0.421260i | 0.635675 | − | 0.771957i | \(-0.280722\pi\) |
0.936489 | + | 0.350696i | \(0.114055\pi\) | |||||||
\(102\) | 6.13556 | − | 0.901021i | 0.607511 | − | 0.0892143i | ||||
\(103\) | −14.8848 | + | 8.59375i | −1.46664 | + | 0.846768i | −0.999304 | − | 0.0373093i | \(-0.988121\pi\) |
−0.467341 | + | 0.884077i | \(0.654788\pi\) | |||||||
\(104\) | −1.90808 | − | 4.08018i | −0.187102 | − | 0.400095i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.05977 | + | 0.838591i | −0.102934 | + | 0.0814512i | ||||
\(107\) | 1.50123 | − | 5.60266i | 0.145129 | − | 0.541630i | −0.854620 | − | 0.519253i | \(-0.826210\pi\) |
0.999750 | − | 0.0223764i | \(-0.00712323\pi\) | |||||||
\(108\) | 14.2109 | − | 0.423902i | 1.36745 | − | 0.0407900i | ||||
\(109\) | −1.19819 | − | 4.47170i | −0.114766 | − | 0.428311i | 0.884504 | − | 0.466533i | \(-0.154497\pi\) |
−0.999269 | + | 0.0382223i | \(0.987831\pi\) | |||||||
\(110\) | −2.81250 | − | 6.51356i | −0.268162 | − | 0.621044i | ||||
\(111\) | 6.80066 | 0.645490 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.17193 | −0.862822 | −0.431411 | − | 0.902155i | \(-0.641984\pi\) | ||||
−0.431411 | + | 0.902155i | \(0.641984\pi\) | |||||||
\(114\) | −3.37028 | − | 7.80534i | −0.315656 | − | 0.731037i | ||||
\(115\) | 4.76265 | + | 17.7744i | 0.444119 | + | 1.65747i | ||||
\(116\) | −0.345821 | − | 11.5933i | −0.0321087 | − | 1.07641i | ||||
\(117\) | 2.24469 | − | 8.37731i | 0.207522 | − | 0.774483i | ||||
\(118\) | 1.78548 | − | 1.41284i | 0.164367 | − | 0.130062i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 10.8123 | − | 29.8082i | 0.987021 | − | 2.72110i | ||||
\(121\) | −8.06150 | + | 4.65431i | −0.732863 | + | 0.423119i | ||||
\(122\) | −6.36931 | + | 0.935347i | −0.576650 | + | 0.0846823i | ||||
\(123\) | −20.9284 | + | 5.60775i | −1.88705 | + | 0.505634i | ||||
\(124\) | 2.36328 | + | 7.87293i | 0.212229 | + | 0.707010i | ||||
\(125\) | −13.3118 | + | 13.3118i | −1.19064 | + | 1.19064i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9787 | −1.15167 | −0.575835 | − | 0.817566i | \(-0.695323\pi\) | ||||
−0.575835 | + | 0.817566i | \(0.695323\pi\) | |||||||
\(128\) | 10.8467 | + | 3.21704i | 0.958721 | + | 0.284349i | ||||
\(129\) | 11.6928 | − | 20.2525i | 1.02949 | − | 1.78313i | ||||
\(130\) | −6.97046 | − | 5.18536i | −0.611350 | − | 0.454786i | ||||
\(131\) | 9.31582 | + | 2.49617i | 0.813927 | + | 0.218091i | 0.641690 | − | 0.766964i | \(-0.278234\pi\) |
0.172237 | + | 0.985055i | \(0.444900\pi\) | |||||||
\(132\) | 7.35674 | + | 1.73790i | 0.640322 | + | 0.151264i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.89434 | + | 2.39398i | 0.163646 | + | 0.206808i | ||||
\(135\) | 23.7477 | − | 13.7108i | 2.04388 | − | 1.18004i | ||||
\(136\) | 2.74680 | + | 3.26622i | 0.235536 | + | 0.280076i | ||||
\(137\) | 19.6192 | + | 11.3271i | 1.67618 | + | 0.967742i | 0.964061 | + | 0.265682i | \(0.0855973\pi\) |
0.712118 | + | 0.702060i | \(0.247736\pi\) | |||||||
\(138\) | −18.2234 | − | 7.23196i | −1.55128 | − | 0.615625i | ||||
\(139\) | −6.64728 | − | 6.64728i | −0.563815 | − | 0.563815i | 0.366574 | − | 0.930389i | \(-0.380531\pi\) |
−0.930389 | + | 0.366574i | \(0.880531\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.39281 | + | 7.39281i | −0.622587 | + | 0.622587i | ||||
\(142\) | 7.74784 | + | 17.9435i | 0.650184 | + | 1.50578i | ||||
\(143\) | 1.03555 | − | 1.79363i | 0.0865974 | − | 0.149991i | ||||
\(144\) | 11.9972 | + | 18.1828i | 0.999764 | + | 1.51523i | ||||
\(145\) | −11.1853 | − | 19.3735i | −0.928888 | − | 1.60888i | ||||
\(146\) | 20.3330 | + | 2.36905i | 1.68277 | + | 0.196064i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.45986 | + | 3.98151i | 0.202199 | + | 0.327278i | ||||
\(149\) | 2.84413 | − | 10.6144i | 0.233000 | − | 0.869568i | −0.746040 | − | 0.665901i | \(-0.768047\pi\) |
0.979040 | − | 0.203667i | \(-0.0652861\pi\) | |||||||
\(150\) | −5.90008 | − | 40.1770i | −0.481740 | − | 3.28044i | ||||
\(151\) | −4.73568 | − | 2.73415i | −0.385384 | − | 0.222502i | 0.294774 | − | 0.955567i | \(-0.404756\pi\) |
−0.680158 | + | 0.733065i | \(0.738089\pi\) | |||||||
\(152\) | 3.35065 | − | 4.79642i | 0.271774 | − | 0.389041i | ||||
\(153\) | 8.21724i | 0.664324i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.2107 | + | 11.2107i | 0.900463 | + | 0.900463i | ||||
\(156\) | 8.86550 | − | 2.66122i | 0.709808 | − | 0.213069i | ||||
\(157\) | −2.05605 | − | 7.67327i | −0.164090 | − | 0.612393i | −0.998154 | − | 0.0607259i | \(-0.980658\pi\) |
0.834064 | − | 0.551667i | \(-0.186008\pi\) | |||||||
\(158\) | −2.01930 | − | 1.50216i | −0.160647 | − | 0.119506i | ||||
\(159\) | −1.38859 | − | 2.40511i | −0.110122 | − | 0.190737i | ||||
\(160\) | 21.3624 | − | 4.45173i | 1.68885 | − | 0.351940i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.707214 | + | 6.06986i | −0.0555640 | + | 0.476893i | ||||
\(163\) | 8.62997 | + | 2.31239i | 0.675951 | + | 0.181121i | 0.580434 | − | 0.814307i | \(-0.302883\pi\) |
0.0955171 | + | 0.995428i | \(0.469550\pi\) | |||||||
\(164\) | −10.8531 | − | 10.2244i | −0.847485 | − | 0.798390i | ||||
\(165\) | 14.0831 | − | 3.77354i | 1.09636 | − | 0.293770i | ||||
\(166\) | 5.28314 | − | 13.3127i | 0.410051 | − | 1.03326i | ||||
\(167\) | − | 11.8175i | − | 0.914463i | −0.889348 | − | 0.457231i | \(-0.848841\pi\) | ||
0.889348 | − | 0.457231i | \(-0.151159\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4639i | 0.804917i | ||||||||
\(170\) | 7.65083 | + | 3.03624i | 0.586792 | + | 0.232869i | ||||
\(171\) | 10.8817 | − | 2.91575i | 0.832145 | − | 0.222973i | ||||
\(172\) | 16.0864 | − | 0.479845i | 1.22657 | − | 0.0365879i | ||||
\(173\) | −7.70245 | − | 2.06387i | −0.585606 | − | 0.156913i | −0.0461620 | − | 0.998934i | \(-0.514699\pi\) |
−0.539444 | + | 0.842021i | \(0.681366\pi\) | |||||||
\(174\) | 23.6747 | + | 2.75840i | 1.79477 | + | 0.209114i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.64353 | + | 4.93569i | 0.123886 | + | 0.372041i | ||||
\(177\) | 2.33946 | + | 4.05207i | 0.175845 | + | 0.304572i | ||||
\(178\) | −7.14019 | + | 9.59826i | −0.535180 | + | 0.719420i | ||||
\(179\) | 4.29266 | + | 16.0204i | 0.320849 | + | 1.19742i | 0.918420 | + | 0.395608i | \(0.129466\pi\) |
−0.597571 | + | 0.801816i | \(0.703867\pi\) | |||||||
\(180\) | 36.9971 | + | 19.9138i | 2.75760 | + | 1.48428i | ||||
\(181\) | −4.18574 | − | 4.18574i | −0.311124 | − | 0.311124i | 0.534221 | − | 0.845345i | \(-0.320605\pi\) |
−0.845345 | + | 0.534221i | \(0.820605\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 13.2293i | − | 0.977937i | ||||||
\(184\) | −2.35752 | − | 13.2849i | −0.173799 | − | 0.979376i | ||||
\(185\) | 7.81739 | + | 4.51337i | 0.574746 | + | 0.331830i | ||||
\(186\) | −16.7128 | + | 2.45431i | −1.22544 | + | 0.179959i | ||||
\(187\) | −0.507884 | + | 1.89545i | −0.0371401 | + | 0.138609i | ||||
\(188\) | −7.00223 | − | 1.65415i | −0.510690 | − | 0.120641i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.30599 | − | 11.2090i | 0.0947464 | − | 0.813187i | ||||
\(191\) | −6.18382 | − | 10.7107i | −0.447445 | − | 0.774998i | 0.550774 | − | 0.834655i | \(-0.314333\pi\) |
−0.998219 | + | 0.0596566i | \(0.980999\pi\) | |||||||
\(192\) | −9.77944 | + | 21.0928i | −0.705771 | + | 1.52224i | ||||
\(193\) | −11.8419 | + | 20.5107i | −0.852395 | + | 1.47639i | 0.0266452 | + | 0.999645i | \(0.491518\pi\) |
−0.879041 | + | 0.476747i | \(0.841816\pi\) | |||||||
\(194\) | −21.0628 | + | 9.09473i | −1.51222 | + | 0.652964i | ||||
\(195\) | 12.6240 | − | 12.6240i | 0.904026 | − | 0.904026i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.4195 | − | 11.4195i | −0.813606 | − | 0.813606i | 0.171566 | − | 0.985173i | \(-0.445117\pi\) |
−0.985173 | + | 0.171566i | \(0.945117\pi\) | |||||||
\(198\) | −3.69474 | + | 9.31015i | −0.262574 | + | 0.661644i | ||||
\(199\) | −4.76039 | − | 2.74841i | −0.337455 | − | 0.194830i | 0.321691 | − | 0.946845i | \(-0.395749\pi\) |
−0.659146 | + | 0.752015i | \(0.729082\pi\) | |||||||
\(200\) | 21.3879 | − | 17.9866i | 1.51235 | − | 1.27185i | ||||
\(201\) | −5.43302 | + | 3.13675i | −0.383216 | + | 0.221250i | ||||
\(202\) | −18.1406 | + | 14.3545i | −1.27636 | + | 1.00998i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.46098 | + | 4.60954i | −0.522373 | + | 0.322732i | ||||
\(205\) | −27.7790 | − | 7.44336i | −1.94017 | − | 0.519867i | ||||
\(206\) | 14.5079 | − | 19.5024i | 1.01081 | − | 1.35879i | ||||
\(207\) | 12.9896 | − | 22.4986i | 0.902839 | − | 1.56376i | ||||
\(208\) | 4.76476 | + | 4.22780i | 0.330377 | + | 0.293145i | ||||
\(209\) | 2.69027 | 0.186090 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.907874 | − | 0.907874i | 0.0625007 | − | 0.0625007i | −0.675166 | − | 0.737666i | \(-0.735928\pi\) |
0.737666 | + | 0.675166i | \(0.235928\pi\) | |||||||
\(212\) | 0.905829 | − | 1.68291i | 0.0622126 | − | 0.115583i | ||||
\(213\) | −38.7958 | + | 10.3953i | −2.65824 | + | 0.712274i | ||||
\(214\) | 1.19183 | + | 8.11582i | 0.0814715 | + | 0.554786i | ||||
\(215\) | 26.8818 | − | 15.5202i | 1.83332 | − | 1.05847i | ||||
\(216\) | −18.2131 | + | 8.51726i | −1.23925 | + | 0.579526i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.06257 | + | 5.13410i | 0.275152 | + | 0.347725i | ||||
\(219\) | −10.8877 | + | 40.6336i | −0.735724 | + | 2.74576i | ||||
\(220\) | 7.30322 | + | 6.88014i | 0.492383 | + | 0.463859i | ||||
\(221\) | 0.621906 | + | 2.32098i | 0.0418339 | + | 0.156126i | ||||
\(222\) | −8.82963 | + | 3.81256i | −0.592606 | + | 0.255882i | ||||
\(223\) | −3.20318 | −0.214501 | −0.107250 | − | 0.994232i | \(-0.534205\pi\) | ||||
−0.107250 | + | 0.994232i | \(0.534205\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 53.8083 | 3.58722 | ||||||||
\(226\) | 11.9084 | − | 5.14193i | 0.792132 | − | 0.342036i | ||||
\(227\) | −5.04862 | − | 18.8417i | −0.335089 | − | 1.25057i | −0.903773 | − | 0.428012i | \(-0.859214\pi\) |
0.568684 | − | 0.822556i | \(-0.307453\pi\) | |||||||
\(228\) | 8.75160 | + | 8.24461i | 0.579589 | + | 0.546013i | ||||
\(229\) | 2.57015 | − | 9.59192i | 0.169840 | − | 0.633852i | −0.827533 | − | 0.561417i | \(-0.810256\pi\) |
0.997373 | − | 0.0724349i | \(-0.0230769\pi\) | |||||||
\(230\) | −16.1482 | − | 20.4074i | −1.06478 | − | 1.34562i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.94841 | + | 14.8583i | 0.456185 | + | 0.975496i | ||||
\(233\) | 2.54488 | − | 1.46929i | 0.166720 | − | 0.0962561i | −0.414318 | − | 0.910132i | \(-0.635980\pi\) |
0.581039 | + | 0.813876i | \(0.302647\pi\) | |||||||
\(234\) | 1.78206 | + | 12.1351i | 0.116497 | + | 0.793295i | ||||
\(235\) | −13.4044 | + | 3.59170i | −0.874408 | + | 0.234297i | ||||
\(236\) | −1.52612 | + | 2.83533i | −0.0993419 | + | 0.184564i | ||||
\(237\) | 3.65710 | − | 3.65710i | 0.237554 | − | 0.237554i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.2109 | 1.04859 | 0.524297 | − | 0.851536i | \(-0.324328\pi\) | ||||
0.524297 | + | 0.851536i | \(0.324328\pi\) | |||||||
\(240\) | 2.67287 | + | 44.7630i | 0.172533 | + | 2.88944i | ||||
\(241\) | 7.05829 | − | 12.2253i | 0.454665 | − | 0.787502i | −0.544004 | − | 0.839082i | \(-0.683092\pi\) |
0.998669 | + | 0.0515803i | \(0.0164258\pi\) | |||||||
\(242\) | 7.85735 | − | 10.5623i | 0.505090 | − | 0.678972i | ||||
\(243\) | 8.46922 | + | 2.26932i | 0.543301 | + | 0.145577i | ||||
\(244\) | 7.74522 | − | 4.78515i | 0.495837 | − | 0.306338i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 24.0286 | − | 19.0136i | 1.53201 | − | 1.21227i | ||||
\(247\) | 2.85290 | − | 1.64712i | 0.181526 | − | 0.104804i | ||||
\(248\) | −7.48206 | − | 8.89692i | −0.475111 | − | 0.564955i | ||||
\(249\) | 25.4897 | + | 14.7165i | 1.61535 | + | 0.932621i | ||||
\(250\) | 9.82055 | − | 24.7462i | 0.621106 | − | 1.56509i | ||||
\(251\) | −14.1967 | − | 14.1967i | −0.896091 | − | 0.896091i | 0.0989969 | − | 0.995088i | \(-0.468437\pi\) |
−0.995088 | + | 0.0989969i | \(0.968437\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.38685 | − | 4.38685i | 0.275799 | − | 0.275799i | ||||
\(254\) | 16.8508 | − | 7.27605i | 1.05732 | − | 0.456540i | ||||
\(255\) | −8.45763 | + | 14.6490i | −0.529637 | + | 0.917358i | ||||
\(256\) | −15.8863 | + | 1.90399i | −0.992894 | + | 0.118999i | ||||
\(257\) | 1.61839 | + | 2.80314i | 0.100953 | + | 0.174855i | 0.912077 | − | 0.410018i | \(-0.134478\pi\) |
−0.811125 | + | 0.584873i | \(0.801144\pi\) | |||||||
\(258\) | −3.82742 | + | 32.8499i | −0.238285 | + | 2.04515i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 11.9571 | + | 2.82464i | 0.741547 | + | 0.175177i | ||||
\(261\) | −8.17423 | + | 30.5066i | −0.505972 | + | 1.88831i | ||||
\(262\) | −13.4946 | + | 1.98171i | −0.833698 | + | 0.122430i | ||||
\(263\) | −20.7985 | − | 12.0080i | −1.28249 | − | 0.740448i | −0.305190 | − | 0.952292i | \(-0.598720\pi\) |
−0.977304 | + | 0.211844i | \(0.932053\pi\) | |||||||
\(264\) | −10.5259 | + | 1.86791i | −0.647825 | + | 0.114962i | ||||
\(265\) | − | 3.68624i | − | 0.226444i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.3832 | − | 17.3832i | −1.06383 | − | 1.06383i | ||||
\(268\) | −3.80161 | − | 2.04622i | −0.232220 | − | 0.124993i | ||||
\(269\) | −0.0320287 | − | 0.119533i | −0.00195282 | − | 0.00728804i | 0.964943 | − | 0.262461i | \(-0.0845342\pi\) |
−0.966895 | + | 0.255173i | \(0.917868\pi\) | |||||||
\(270\) | −23.1464 | + | 31.1147i | −1.40864 | + | 1.89358i | ||||
\(271\) | 5.05692 | + | 8.75884i | 0.307186 | + | 0.532062i | 0.977746 | − | 0.209794i | \(-0.0672793\pi\) |
−0.670560 | + | 0.741856i | \(0.733946\pi\) | |||||||
\(272\) | −5.39739 | − | 2.70079i | −0.327265 | − | 0.163760i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −31.8227 | − | 3.70774i | −1.92248 | − | 0.223993i | ||||
\(275\) | 12.4118 | + | 3.32573i | 0.748460 | + | 0.200549i | ||||
\(276\) | 27.7146 | − | 0.826708i | 1.66822 | − | 0.0497620i | ||||
\(277\) | 15.0372 | − | 4.02921i | 0.903498 | − | 0.242092i | 0.222980 | − | 0.974823i | \(-0.428422\pi\) |
0.680518 | + | 0.732732i | \(0.261755\pi\) | |||||||
\(278\) | 12.3571 | + | 4.90391i | 0.741127 | + | 0.294117i | ||||
\(279\) | − | 22.3831i | − | 1.34004i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4.21999i | − | 0.251743i | −0.992047 | − | 0.125872i | \(-0.959827\pi\) | ||
0.992047 | − | 0.125872i | \(-0.0401727\pi\) | |||||||
\(282\) | 5.45391 | − | 13.7430i | 0.324776 | − | 0.818382i | ||||
\(283\) | 22.6533 | − | 6.06995i | 1.34660 | − | 0.360821i | 0.487722 | − | 0.872999i | \(-0.337828\pi\) |
0.858879 | + | 0.512178i | \(0.171161\pi\) | |||||||
\(284\) | −20.1188 | − | 18.9533i | −1.19383 | − | 1.12467i | ||||
\(285\) | 22.4001 | + | 6.00209i | 1.32687 | + | 0.355533i | ||||
\(286\) | −0.338971 | + | 2.90931i | −0.0200438 | + | 0.172031i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −25.7701 | − | 16.8818i | −1.51852 | − | 0.994770i | ||||
\(289\) | 7.36168 | + | 12.7508i | 0.433040 | + | 0.750048i | ||||
\(290\) | 25.3835 | + | 18.8829i | 1.49057 | + | 1.10884i | ||||
\(291\) | −12.2024 | − | 45.5401i | −0.715319 | − | 2.66961i | ||||
\(292\) | −27.7275 | + | 8.32317i | −1.62263 | + | 0.487077i | ||||
\(293\) | −13.5242 | − | 13.5242i | −0.790093 | − | 0.790093i | 0.191416 | − | 0.981509i | \(-0.438692\pi\) |
−0.981509 | + | 0.191416i | \(0.938692\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.21049i | 0.361589i | ||||||||
\(296\) | −5.42585 | − | 3.79036i | −0.315371 | − | 0.220310i | ||||
\(297\) | −8.00641 | − | 4.62250i | −0.464579 | − | 0.268225i | ||||
\(298\) | 2.25795 | + | 15.3757i | 0.130800 | + | 0.890691i | ||||
\(299\) | 1.96618 | − | 7.33790i | 0.113707 | − | 0.424361i | ||||
\(300\) | 30.1843 | + | 48.8561i | 1.74269 | + | 2.82071i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.68137 | + | 0.894976i | 0.442013 | + | 0.0515001i | ||||
\(303\) | −23.7690 | − | 41.1691i | −1.36549 | − | 2.36510i | ||||
\(304\) | −1.66136 | + | 8.10585i | −0.0952856 | + | 0.464903i | ||||
\(305\) | 8.77984 | − | 15.2071i | 0.502732 | − | 0.870757i | ||||
\(306\) | −4.60672 | − | 10.6688i | −0.263349 | − | 0.609897i | ||||
\(307\) | −8.93389 | + | 8.93389i | −0.509884 | + | 0.509884i | −0.914491 | − | 0.404607i | \(-0.867408\pi\) |
0.404607 | + | 0.914491i | \(0.367408\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 35.3203 | + | 35.3203i | 2.00930 | + | 2.00930i | ||||
\(310\) | −20.8403 | − | 8.27048i | −1.18365 | − | 0.469732i | ||||
\(311\) | −17.1245 | − | 9.88684i | −0.971042 | − | 0.560631i | −0.0714882 | − | 0.997441i | \(-0.522775\pi\) |
−0.899554 | + | 0.436810i | \(0.856108\pi\) | |||||||
\(312\) | −10.0186 | + | 8.42534i | −0.567190 | + | 0.476991i | ||||
\(313\) | 7.55817 | − | 4.36371i | 0.427213 | − | 0.246652i | −0.270945 | − | 0.962595i | \(-0.587336\pi\) |
0.698159 | + | 0.715943i | \(0.254003\pi\) | |||||||
\(314\) | 6.97122 | + | 8.80992i | 0.393409 | + | 0.497173i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.46389 | + | 0.818280i | 0.194859 | + | 0.0460319i | ||||
\(317\) | −25.9814 | − | 6.96171i | −1.45926 | − | 0.391008i | −0.560028 | − | 0.828474i | \(-0.689210\pi\) |
−0.899235 | + | 0.437465i | \(0.855876\pi\) | |||||||
\(318\) | 3.15122 | + | 2.34420i | 0.176711 | + | 0.131456i | ||||
\(319\) | −3.77105 | + | 6.53166i | −0.211138 | + | 0.365703i | ||||
\(320\) | −25.2401 | + | 17.7560i | −1.41097 | + | 0.992591i | ||||
\(321\) | −16.8569 | −0.940858 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.20702 | + | 2.20702i | −0.122802 | + | 0.122802i | ||||
\(324\) | −2.48465 | − | 8.27727i | −0.138036 | − | 0.459848i | ||||
\(325\) | 15.1983 | − | 4.07238i | 0.843051 | − | 0.225895i | ||||
\(326\) | −12.5011 | + | 1.83581i | −0.692370 | + | 0.101676i | ||||
\(327\) | −11.6516 | + | 6.72705i | −0.644335 | + | 0.372007i | ||||
\(328\) | 19.8231 | + | 7.19038i | 1.09455 | + | 0.397022i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −16.1692 | + | 12.7946i | −0.890086 | + | 0.704318i | ||||
\(331\) | 8.17436 | − | 30.5071i | 0.449303 | − | 1.67682i | −0.255014 | − | 0.966937i | \(-0.582080\pi\) |
0.704317 | − | 0.709885i | \(-0.251253\pi\) | |||||||
\(332\) | 0.603933 | + | 20.2463i | 0.0331451 | + | 1.11116i | ||||
\(333\) | −3.29838 | − | 12.3097i | −0.180750 | − | 0.674568i | ||||
\(334\) | 6.62507 | + | 15.3432i | 0.362507 | + | 0.839542i | ||||
\(335\) | −8.32703 | −0.454954 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.4825 | −1.27918 | −0.639588 | − | 0.768718i | \(-0.720895\pi\) | ||||
−0.639588 | + | 0.768718i | \(0.720895\pi\) | |||||||
\(338\) | −5.86624 | − | 13.5858i | −0.319082 | − | 0.738971i | ||||
\(339\) | 6.89895 | + | 25.7472i | 0.374699 | + | 1.39840i | ||||
\(340\) | −11.6356 | + | 0.347082i | −0.631030 | + | 0.0188232i | ||||
\(341\) | 1.38343 | − | 5.16305i | 0.0749172 | − | 0.279595i | ||||
\(342\) | −12.4936 | + | 9.88612i | −0.675579 | + | 0.534580i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −20.6167 | + | 9.64129i | −1.11158 | + | 0.519824i | ||||
\(345\) | 46.3136 | − | 26.7392i | 2.49344 | − | 1.43959i | ||||
\(346\) | 11.1575 | − | 1.63850i | 0.599831 | − | 0.0880865i | ||||
\(347\) | 8.60207 | − | 2.30492i | 0.461784 | − | 0.123735i | −0.0204242 | − | 0.999791i | \(-0.506502\pi\) |
0.482208 | + | 0.876057i | \(0.339835\pi\) | |||||||
\(348\) | −32.2844 | + | 9.69106i | −1.73063 | + | 0.519496i | ||||
\(349\) | 6.94033 | − | 6.94033i | 0.371507 | − | 0.371507i | −0.496519 | − | 0.868026i | \(-0.665389\pi\) |
0.868026 | + | 0.496519i | \(0.165389\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.3206 | −0.604246 | ||||||||
\(352\) | −4.90090 | − | 5.48685i | −0.261219 | − | 0.292450i | ||||
\(353\) | −15.0467 | + | 26.0617i | −0.800856 | + | 1.38712i | 0.118198 | + | 0.992990i | \(0.462288\pi\) |
−0.919054 | + | 0.394133i | \(0.871045\pi\) | |||||||
\(354\) | −5.30910 | − | 3.94946i | −0.282175 | − | 0.209911i | ||||
\(355\) | −51.4949 | − | 13.7980i | −2.73307 | − | 0.732323i | ||||
\(356\) | 3.88951 | − | 16.4648i | 0.206144 | − | 0.872633i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.5547 | − | 18.3936i | −0.769239 | − | 0.972131i | ||||
\(359\) | 8.98209 | − | 5.18581i | 0.474057 | − | 0.273697i | −0.243880 | − | 0.969806i | \(-0.578420\pi\) |
0.717936 | + | 0.696109i | \(0.245087\pi\) | |||||||
\(360\) | −59.1992 | − | 5.11380i | −3.12007 | − | 0.269521i | ||||
\(361\) | −12.7487 | − | 7.36047i | −0.670985 | − | 0.387393i | ||||
\(362\) | 7.78114 | + | 3.08796i | 0.408968 | + | 0.162299i | ||||
\(363\) | 19.1292 | + | 19.1292i | 1.00402 | + | 1.00402i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −39.4826 | + | 39.4826i | −2.06661 | + | 2.06661i | ||||
\(366\) | 7.41656 | + | 17.1762i | 0.387670 | + | 0.897816i | ||||
\(367\) | 4.06486 | − | 7.04055i | 0.212184 | − | 0.367514i | −0.740214 | − | 0.672372i | \(-0.765276\pi\) |
0.952398 | + | 0.304858i | \(0.0986090\pi\) | |||||||
\(368\) | 10.5086 | + | 15.9268i | 0.547800 | + | 0.830240i | ||||
\(369\) | 20.3009 | + | 35.1622i | 1.05682 | + | 1.83047i | ||||
\(370\) | −12.6800 | − | 1.47737i | −0.659200 | − | 0.0768050i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 20.3231 | − | 12.5560i | 1.05370 | − | 0.650999i | ||||
\(373\) | −1.16648 | + | 4.35336i | −0.0603980 | + | 0.225408i | −0.989527 | − | 0.144347i | \(-0.953892\pi\) |
0.929129 | + | 0.369755i | \(0.120559\pi\) | |||||||
\(374\) | −0.403209 | − | 2.74568i | −0.0208494 | − | 0.141976i | ||||
\(375\) | 47.3815 | + | 27.3557i | 2.44677 | + | 1.41264i | ||||
\(376\) | 10.0187 | − | 1.77790i | 0.516674 | − | 0.0916884i | ||||
\(377\) | 9.23534i | 0.475644i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.839080 | − | 0.839080i | −0.0431006 | − | 0.0431006i | 0.685228 | − | 0.728329i | \(-0.259703\pi\) |
−0.728329 | + | 0.685228i | \(0.759703\pi\) | |||||||
\(380\) | 4.58832 | + | 15.2854i | 0.235376 | + | 0.784122i | ||||
\(381\) | 9.76231 | + | 36.4334i | 0.500138 | + | 1.86654i | ||||
\(382\) | 14.0333 | + | 10.4395i | 0.718008 | + | 0.534129i | ||||
\(383\) | 17.1874 | + | 29.7695i | 0.878237 | + | 1.52115i | 0.853274 | + | 0.521463i | \(0.174614\pi\) |
0.0249634 | + | 0.999688i | \(0.492053\pi\) | |||||||
\(384\) | 0.872140 | − | 32.8684i | 0.0445062 | − | 1.67731i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.87623 | − | 33.2688i | 0.197295 | − | 1.69334i | ||||
\(387\) | −42.3296 | − | 11.3422i | −2.15173 | − | 0.576556i | ||||
\(388\) | 22.2482 | − | 23.6163i | 1.12948 | − | 1.19893i | ||||
\(389\) | −14.9761 | + | 4.01283i | −0.759319 | + | 0.203459i | −0.617648 | − | 0.786455i | \(-0.711914\pi\) |
−0.141671 | + | 0.989914i | \(0.545247\pi\) | |||||||
\(390\) | −9.31316 | + | 23.4677i | −0.471590 | + | 1.18833i | ||||
\(391\) | 7.19768i | 0.364003i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 28.0287i | − | 1.41386i | ||||||
\(394\) | 21.2285 | + | 8.42454i | 1.06947 | + | 0.424422i | ||||
\(395\) | 6.63094 | − | 1.77676i | 0.333639 | − | 0.0893983i | ||||
\(396\) | −0.422358 | − | 14.1592i | −0.0212243 | − | 0.711524i | ||||
\(397\) | −36.1143 | − | 9.67679i | −1.81252 | − | 0.485664i | −0.816708 | − | 0.577051i | \(-0.804203\pi\) |
−0.995815 | + | 0.0913869i | \(0.970870\pi\) | |||||||
\(398\) | 7.72146 | + | 0.899646i | 0.387042 | + | 0.0450952i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17.6854 | + | 35.3433i | −0.884269 | + | 1.76717i | ||||
\(401\) | −2.48812 | − | 4.30956i | −0.124251 | − | 0.215209i | 0.797189 | − | 0.603730i | \(-0.206319\pi\) |
−0.921440 | + | 0.388521i | \(0.872986\pi\) | |||||||
\(402\) | 5.29544 | − | 7.11844i | 0.264112 | − | 0.355036i | ||||
\(403\) | −1.69402 | − | 6.32217i | −0.0843852 | − | 0.314930i | ||||
\(404\) | 15.5054 | − | 28.8070i | 0.771423 | − | 1.43320i | ||||
\(405\) | −11.7864 | − | 11.7864i | −0.585672 | − | 0.585672i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.04331i | − | 0.150851i | ||||||
\(408\) | 7.10277 | − | 10.1675i | 0.351639 | − | 0.503368i | ||||
\(409\) | −3.51917 | − | 2.03180i | −0.174012 | − | 0.100466i | 0.410464 | − | 0.911877i | \(-0.365367\pi\) |
−0.584476 | + | 0.811411i | \(0.698700\pi\) | |||||||
\(410\) | 40.2397 | − | 5.90928i | 1.98730 | − | 0.291839i | ||||
\(411\) | 17.0401 | − | 63.5945i | 0.840526 | − | 3.13689i | ||||
\(412\) | −7.90295 | + | 33.4542i | −0.389350 | + | 1.64817i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.25192 | + | 36.4932i | −0.208970 | + | 1.79354i | ||||
\(415\) | 19.5337 | + | 33.8334i | 0.958871 | + | 1.66081i | ||||
\(416\) | −8.55650 | − | 2.81796i | −0.419517 | − | 0.138162i | ||||
\(417\) | −13.6601 | + | 23.6600i | −0.668940 | + | 1.15864i | ||||
\(418\) | −3.49291 | + | 1.50821i | −0.170844 | + | 0.0737689i | ||||
\(419\) | 0.552238 | − | 0.552238i | 0.0269786 | − | 0.0269786i | −0.693489 | − | 0.720467i | \(-0.743927\pi\) |
0.720467 | + | 0.693489i | \(0.243927\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.77763 | − | 3.77763i | −0.184110 | − | 0.184110i | 0.609034 | − | 0.793144i | \(-0.291557\pi\) |
−0.793144 | + | 0.609034i | \(0.791557\pi\) | |||||||
\(422\) | −0.669768 | + | 1.68771i | −0.0326038 | + | 0.0821563i | ||||
\(423\) | 16.9671 | + | 9.79598i | 0.824970 | + | 0.476297i | ||||
\(424\) | −0.232614 | + | 2.69283i | −0.0112968 | + | 0.130775i | ||||
\(425\) | −12.9106 | + | 7.45395i | −0.626257 | + | 0.361570i | ||||
\(426\) | 44.5427 | − | 35.2463i | 2.15810 | − | 1.70769i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.09727 | − | 9.86901i | −0.294723 | − | 0.477037i | ||||
\(429\) | −5.81397 | − | 1.55785i | −0.280701 | − | 0.0752136i | ||||
\(430\) | −26.2010 | + | 35.2210i | −1.26353 | + | 1.69851i | ||||
\(431\) | −0.590931 | + | 1.02352i | −0.0284641 | + | 0.0493013i | −0.879907 | − | 0.475147i | \(-0.842395\pi\) |
0.851442 | + | 0.524448i | \(0.175728\pi\) | |||||||
\(432\) | 18.8721 | − | 21.2689i | 0.907982 | − | 1.02330i | ||||
\(433\) | −15.2584 | −0.733273 | −0.366637 | − | 0.930364i | \(-0.619491\pi\) | ||||
−0.366637 | + | 0.930364i | \(0.619491\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −45.9715 | + | 45.9715i | −2.20416 | + | 2.20416i | ||||
\(436\) | −8.15290 | − | 4.38831i | −0.390453 | − | 0.210162i | ||||
\(437\) | 9.53156 | − | 2.55398i | 0.455957 | − | 0.122173i | ||||
\(438\) | −8.64377 | − | 58.8604i | −0.413015 | − | 2.81246i | ||||
\(439\) | 3.76290 | − | 2.17251i | 0.179593 | − | 0.103688i | −0.407508 | − | 0.913202i | \(-0.633602\pi\) |
0.587102 | + | 0.809513i | \(0.300269\pi\) | |||||||
\(440\) | −13.3392 | − | 4.83851i | −0.635923 | − | 0.230667i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.10863 | − | 2.66479i | −0.100297 | − | 0.126751i | ||||
\(443\) | −1.57901 | + | 5.89293i | −0.0750208 | + | 0.279981i | −0.993238 | − | 0.116096i | \(-0.962962\pi\) |
0.918217 | + | 0.396077i | \(0.129629\pi\) | |||||||
\(444\) | 9.32655 | − | 9.90007i | 0.442619 | − | 0.469837i | ||||
\(445\) | −8.44540 | − | 31.5187i | −0.400351 | − | 1.49413i | ||||
\(446\) | 4.15885 | − | 1.79576i | 0.196927 | − | 0.0850315i | ||||
\(447\) | −31.9359 | −1.51052 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.72499 | 0.175793 | 0.0878967 | − | 0.996130i | \(-0.471985\pi\) | ||||
0.0878967 | + | 0.996130i | \(0.471985\pi\) | |||||||
\(450\) | −69.8619 | + | 30.1658i | −3.29332 | + | 1.42203i | ||||
\(451\) | 2.50948 | + | 9.36552i | 0.118167 | + | 0.441005i | ||||
\(452\) | −12.5785 | + | 13.3520i | −0.591645 | + | 0.628027i | ||||
\(453\) | −4.11315 | + | 15.3505i | −0.193252 | + | 0.721228i | ||||
\(454\) | 17.1178 | + | 21.6328i | 0.803380 | + | 1.01528i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15.9847 | − | 5.79809i | −0.748552 | − | 0.271521i | ||||
\(457\) | 9.30556 | − | 5.37257i | 0.435296 | − | 0.251318i | −0.266304 | − | 0.963889i | \(-0.585803\pi\) |
0.701600 | + | 0.712571i | \(0.252469\pi\) | |||||||
\(458\) | 2.04044 | + | 13.8945i | 0.0953435 | + | 0.649248i | ||||
\(459\) | 10.3604 | − | 2.77606i | 0.483582 | − | 0.129575i | ||||
\(460\) | 32.4067 | + | 17.4430i | 1.51097 | + | 0.813282i | ||||
\(461\) | 7.88785 | − | 7.88785i | 0.367374 | − | 0.367374i | −0.499145 | − | 0.866519i | \(-0.666352\pi\) |
0.866519 | + | 0.499145i | \(0.166352\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.3485 | 1.27099 | 0.635496 | − | 0.772104i | \(-0.280796\pi\) | ||||
0.635496 | + | 0.772104i | \(0.280796\pi\) | |||||||
\(464\) | −17.3513 | − | 15.3959i | −0.805513 | − | 0.714736i | ||||
\(465\) | 23.0379 | − | 39.9028i | 1.06836 | − | 1.85045i | ||||
\(466\) | −2.48043 | + | 3.33434i | −0.114904 | + | 0.154461i | ||||
\(467\) | −15.5610 | − | 4.16957i | −0.720079 | − | 0.192945i | −0.119872 | − | 0.992789i | \(-0.538248\pi\) |
−0.600207 | + | 0.799845i | \(0.704915\pi\) | |||||||
\(468\) | −9.11686 | − | 14.7565i | −0.421427 | − | 0.682120i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 15.3900 | − | 12.1780i | 0.709890 | − | 0.561730i | ||||
\(471\) | −19.9937 | + | 11.5434i | −0.921261 | + | 0.531890i | ||||
\(472\) | 0.391903 | − | 4.53681i | 0.0180388 | − | 0.208824i | ||||
\(473\) | −9.06303 | − | 5.23254i | −0.416718 | − | 0.240592i | ||||
\(474\) | −2.69796 | + | 6.79842i | −0.123921 | + | 0.312262i | ||||
\(475\) | 14.4520 | + | 14.4520i | 0.663105 | + | 0.663105i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.67995 | + | 3.67995i | −0.168493 | + | 0.168493i | ||||
\(478\) | −21.0473 | + | 9.08807i | −0.962683 | + | 0.415679i | ||||
\(479\) | −5.69399 | + | 9.86229i | −0.260165 | + | 0.450619i | −0.966286 | − | 0.257472i | \(-0.917110\pi\) |
0.706120 | + | 0.708092i | \(0.250444\pi\) | |||||||
\(480\) | −28.5652 | − | 56.6195i | −1.30382 | − | 2.58431i | ||||
\(481\) | −1.86327 | − | 3.22729i | −0.0849580 | − | 0.147152i | ||||
\(482\) | −2.31041 | + | 19.8297i | −0.105236 | + | 0.903219i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.28017 | + | 18.1185i | −0.194553 | + | 0.823570i | ||||
\(485\) | 16.1967 | − | 60.4468i | 0.735453 | − | 2.74475i | ||||
\(486\) | −12.2682 | + | 1.80161i | −0.556498 | + | 0.0817229i | ||||
\(487\) | 27.1526 | + | 15.6766i | 1.23040 | + | 0.710373i | 0.967114 | − | 0.254344i | \(-0.0818597\pi\) |
0.263288 | + | 0.964717i | \(0.415193\pi\) | |||||||
\(488\) | −7.37336 | + | 10.5549i | −0.333776 | + | 0.477797i | ||||
\(489\) | − | 25.9652i | − | 1.17419i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.2775 | + | 20.2775i | 0.915112 | + | 0.915112i | 0.996669 | − | 0.0815572i | \(-0.0259893\pi\) |
−0.0815572 | + | 0.996669i | \(0.525989\pi\) | |||||||
\(492\) | −20.5381 | + | 38.1572i | −0.925931 | + | 1.72026i | ||||
\(493\) | −2.26472 | − | 8.45204i | −0.101998 | − | 0.380661i | ||||
\(494\) | −2.78065 | + | 3.73792i | −0.125108 | + | 0.168177i | ||||
\(495\) | −13.6608 | − | 23.6612i | −0.614008 | − | 1.06349i | ||||
\(496\) | 14.7021 | + | 7.35674i | 0.660143 | + | 0.330327i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −41.3449 | − | 4.81719i | −1.85271 | − | 0.215864i | ||||
\(499\) | 25.2943 | + | 6.77758i | 1.13233 | + | 0.303406i | 0.775862 | − | 0.630902i | \(-0.217315\pi\) |
0.356465 | + | 0.934309i | \(0.383982\pi\) | |||||||
\(500\) | 1.12262 | + | 37.6348i | 0.0502050 | + | 1.68308i | ||||
\(501\) | −33.1737 | + | 8.88887i | −1.48209 | + | 0.397126i | ||||
\(502\) | 26.3913 | + | 10.4734i | 1.17790 | + | 0.467451i | ||||
\(503\) | − | 31.9854i | − | 1.42616i | −0.701082 | − | 0.713080i | \(-0.747299\pi\) | ||
0.701082 | − | 0.713080i | \(-0.252701\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 63.0987i | − | 2.80786i | ||||||
\(506\) | −3.23632 | + | 8.15500i | −0.143872 | + | 0.362534i | ||||
\(507\) | 29.3741 | − | 7.87076i | 1.30455 | − | 0.349553i | ||||
\(508\) | −17.7992 | + | 18.8937i | −0.789711 | + | 0.838273i | ||||
\(509\) | −16.6168 | − | 4.45247i | −0.736529 | − | 0.197352i | −0.128994 | − | 0.991645i | \(-0.541175\pi\) |
−0.607535 | + | 0.794293i | \(0.707841\pi\) | |||||||
\(510\) | 2.76846 | − | 23.7610i | 0.122589 | − | 1.05216i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 19.5586 | − | 11.3782i | 0.864375 | − | 0.502849i | ||||
\(513\) | −7.35242 | − | 12.7348i | −0.324617 | − | 0.562254i | ||||
\(514\) | −3.67273 | − | 2.73216i | −0.161997 | − | 0.120510i | ||||
\(515\) | 17.1599 | + | 64.0417i | 0.756156 | + | 2.82201i | ||||
\(516\) | −13.4469 | − | 44.7964i | −0.591966 | − | 1.97205i | ||||
\(517\) | 3.30830 | + | 3.30830i | 0.145499 | + | 0.145499i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.1745i | 1.01725i | ||||||||
\(520\) | −17.1080 | + | 3.03597i | −0.750236 | + | 0.133136i | ||||
\(521\) | 29.8192 | + | 17.2161i | 1.30640 | + | 0.754251i | 0.981494 | − | 0.191495i | \(-0.0613336\pi\) |
0.324907 | + | 0.945746i | \(0.394667\pi\) | |||||||
\(522\) | −6.48952 | − | 44.1909i | −0.284039 | − | 1.93418i | ||||
\(523\) | −5.63792 | + | 21.0410i | −0.246529 | + | 0.920060i | 0.726079 | + | 0.687611i | \(0.241340\pi\) |
−0.972609 | + | 0.232449i | \(0.925326\pi\) | |||||||
\(524\) | 16.4097 | − | 10.1382i | 0.716861 | − | 0.442890i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 33.7357 | + | 3.93062i | 1.47094 | + | 0.171383i | ||||
\(527\) | 3.10069 | + | 5.37054i | 0.135068 | + | 0.233945i | ||||
\(528\) | 12.6191 | − | 8.32620i | 0.549176 | − | 0.362351i | ||||
\(529\) | −0.122092 | + | 0.211469i | −0.00530834 | + | 0.00919432i | ||||
\(530\) | 2.06657 | + | 4.78603i | 0.0897659 | + | 0.207892i | ||||
\(531\) | 6.19990 | − | 6.19990i | 0.269053 | − | 0.269053i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.39524 | + | 8.39524i | 0.363638 | + | 0.363638i | ||||
\(534\) | 32.3147 | + | 12.8241i | 1.39840 | + | 0.554955i | ||||
\(535\) | −19.3770 | − | 11.1873i | −0.837742 | − | 0.483670i | ||||
\(536\) | 6.08296 | + | 0.525464i | 0.262744 | + | 0.0226966i | ||||
\(537\) | 41.7433 | − | 24.1005i | 1.80136 | − | 1.04001i | ||||
\(538\) | 0.108596 | + | 0.137239i | 0.00468192 | + | 0.00591681i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 12.6086 | − | 53.3740i | 0.542589 | − | 2.29685i | ||||
\(541\) | 32.3972 | + | 8.68080i | 1.39286 | + | 0.373217i | 0.875777 | − | 0.482716i | \(-0.160350\pi\) |
0.517087 | + | 0.855933i | \(0.327016\pi\) | |||||||
\(542\) | −11.4760 | − | 8.53704i | −0.492936 | − | 0.366697i | ||||
\(543\) | −8.60168 | + | 14.8985i | −0.369133 | + | 0.639358i | ||||
\(544\) | 8.52181 | + | 0.480700i | 0.365370 | + | 0.0206099i | ||||
\(545\) | −17.8581 | −0.764956 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.8819 | − | 27.8819i | 1.19214 | − | 1.19214i | 0.215680 | − | 0.976464i | \(-0.430803\pi\) |
0.976464 | − | 0.215680i | \(-0.0691967\pi\) | |||||||
\(548\) | 43.3956 | − | 13.0264i | 1.85377 | − | 0.556460i | ||||
\(549\) | −23.9460 | + | 6.41632i | −1.02199 | + | 0.273842i | ||||
\(550\) | −17.9793 | + | 2.64030i | −0.766641 | + | 0.112583i | ||||
\(551\) | −10.3891 | + | 5.99813i | −0.442589 | + | 0.255529i | ||||
\(552\) | −35.5198 | + | 16.6106i | −1.51182 | + | 0.706995i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −17.2647 | + | 13.6614i | −0.733506 | + | 0.580418i | ||||
\(555\) | 6.78974 | − | 25.3397i | 0.288208 | − | 1.07561i | ||||
\(556\) | −18.7930 | + | 0.560582i | −0.797000 | + | 0.0237740i | ||||
\(557\) | 0.101002 | + | 0.376946i | 0.00427960 | + | 0.0159717i | 0.968033 | − | 0.250824i | \(-0.0807017\pi\) |
−0.963753 | + | 0.266796i | \(0.914035\pi\) | |||||||
\(558\) | 12.5483 | + | 29.0611i | 0.531213 | + | 1.23025i | ||||
\(559\) | −12.8145 | −0.541997 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.70288 | 0.240776 | ||||||||
\(562\) | 2.36579 | + | 5.47901i | 0.0997949 | + | 0.231118i | ||||
\(563\) | −5.08448 | − | 18.9755i | −0.214285 | − | 0.799724i | −0.986417 | − | 0.164261i | \(-0.947476\pi\) |
0.772132 | − | 0.635463i | \(-0.219191\pi\) | |||||||
\(564\) | 0.623454 | + | 20.9007i | 0.0262521 | + | 0.880079i | ||||
\(565\) | −9.15720 | + | 34.1751i | −0.385246 | + | 1.43776i | ||||
\(566\) | −26.0090 | + | 20.5807i | −1.09324 | + | 0.865073i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 36.7467 | + | 13.3291i | 1.54186 | + | 0.559275i | ||||
\(569\) | −6.99814 | + | 4.04038i | −0.293377 | + | 0.169381i | −0.639464 | − | 0.768821i | \(-0.720844\pi\) |
0.346087 | + | 0.938203i | \(0.387510\pi\) | |||||||
\(570\) | −32.4480 | + | 4.76506i | −1.35910 | + | 0.199586i | ||||
\(571\) | 10.3246 | − | 2.76648i | 0.432073 | − | 0.115774i | −0.0362262 | − | 0.999344i | \(-0.511534\pi\) |
0.468299 | + | 0.883570i | \(0.344867\pi\) | |||||||
\(572\) | −1.19090 | − | 3.96733i | −0.0497942 | − | 0.165882i | ||||
\(573\) | −25.4154 | + | 25.4154i | −1.06175 | + | 1.06175i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 47.1320 | 1.96554 | ||||||||
\(576\) | 42.9228 | + | 7.47134i | 1.78845 | + | 0.311306i | ||||
\(577\) | −0.979847 | + | 1.69714i | −0.0407915 | + | 0.0706530i | −0.885700 | − | 0.464257i | \(-0.846321\pi\) |
0.844909 | + | 0.534910i | \(0.179655\pi\) | |||||||
\(578\) | −16.7063 | − | 12.4279i | −0.694892 | − | 0.516933i | ||||
\(579\) | 66.4844 | + | 17.8144i | 2.76300 | + | 0.740343i | ||||
\(580\) | −43.5427 | − | 10.2862i | −1.80801 | − | 0.427110i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 41.3735 | + | 52.2860i | 1.71499 | + | 2.16733i | ||||
\(583\) | −1.07629 | + | 0.621397i | −0.0445754 | + | 0.0257356i | ||||
\(584\) | 31.3338 | − | 26.3509i | 1.29660 | − | 1.09041i | ||||
\(585\) | −28.9733 | − | 16.7277i | −1.19790 | − | 0.691606i | ||||
\(586\) | 25.1410 | + | 9.97725i | 1.03857 | + | 0.412156i | ||||
\(587\) | 24.6131 | + | 24.6131i | 1.01589 | + | 1.01589i | 0.999872 | + | 0.0160192i | \(0.00509930\pi\) |
0.0160192 | + | 0.999872i | \(0.494901\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.01174 | − | 6.01174i | 0.247709 | − | 0.247709i | ||||
\(590\) | −3.48170 | − | 8.06339i | −0.143340 | − | 0.331964i | ||||
\(591\) | −23.4670 | + | 40.6461i | −0.965305 | + | 1.67196i | ||||
\(592\) | 9.16958 | + | 1.87938i | 0.376868 | + | 0.0772421i | ||||
\(593\) | −8.27415 | − | 14.3313i | −0.339779 | − | 0.588514i | 0.644612 | − | 0.764510i | \(-0.277019\pi\) |
−0.984391 | + | 0.175996i | \(0.943686\pi\) | |||||||
\(594\) | 12.9866 | + | 1.51310i | 0.532845 | + | 0.0620831i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.5515 | − | 18.6972i | −0.473167 | − | 0.765866i | ||||
\(597\) | −4.13461 | + | 15.4306i | −0.169218 | + | 0.631531i | ||||
\(598\) | 1.56095 | + | 10.6294i | 0.0638321 | + | 0.434669i | ||||
\(599\) | −8.88965 | − | 5.13244i | −0.363221 | − | 0.209706i | 0.307272 | − | 0.951622i | \(-0.400584\pi\) |
−0.670493 | + | 0.741916i | \(0.733917\pi\) | |||||||
\(600\) | −66.5793 | − | 46.5105i | −2.71809 | − | 1.89878i | ||||
\(601\) | 35.6586i | 1.45455i | 0.686348 | + | 0.727273i | \(0.259213\pi\) | ||||
−0.686348 | + | 0.727273i | \(0.740787\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.31283 | + | 8.31283i | 0.338524 | + | 0.338524i | ||||
\(604\) | −10.4748 | + | 3.14431i | −0.426215 | + | 0.127940i | ||||
\(605\) | 9.29367 | + | 34.6844i | 0.377841 | + | 1.41012i | ||||
\(606\) | 53.9405 | + | 40.1266i | 2.19118 | + | 1.63003i | ||||
\(607\) | −11.5556 | − | 20.0148i | −0.469026 | − | 0.812377i | 0.530347 | − | 0.847780i | \(-0.322062\pi\) |
−0.999373 | + | 0.0354040i | \(0.988728\pi\) | |||||||
\(608\) | −2.38725 | − | 11.4556i | −0.0968157 | − | 0.464586i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.87393 | + | 24.6663i | −0.116362 | + | 0.998708i | ||||
\(611\) | 5.53381 | + | 1.48278i | 0.223874 | + | 0.0599868i | ||||
\(612\) | 11.9623 | + | 11.2693i | 0.483545 | + | 0.455533i | ||||
\(613\) | 36.7734 | − | 9.85340i | 1.48526 | − | 0.397975i | 0.577129 | − | 0.816653i | \(-0.304173\pi\) |
0.908135 | + | 0.418678i | \(0.137507\pi\) | |||||||
\(614\) | 6.59082 | − | 16.6078i | 0.265984 | − | 0.670236i | ||||
\(615\) | 83.5793i | 3.37024i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.9337i | 1.92974i | 0.262732 | + | 0.964869i | \(0.415377\pi\) | ||||
−0.262732 | + | 0.964869i | \(0.584623\pi\) | |||||||
\(618\) | −65.6591 | − | 26.0569i | −2.64120 | − | 1.04816i | ||||
\(619\) | −5.53313 | + | 1.48260i | −0.222395 | + | 0.0595906i | −0.368296 | − | 0.929709i | \(-0.620059\pi\) |
0.145901 | + | 0.989299i | \(0.453392\pi\) | |||||||
\(620\) | 31.6945 | − | 0.945424i | 1.27288 | − | 0.0379692i | ||||
\(621\) | −32.7549 | − | 8.77664i | −1.31441 | − | 0.352195i | ||||
\(622\) | 27.7763 | + | 3.23629i | 1.11373 | + | 0.129763i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.28423 | − | 16.5556i | 0.331634 | − | 0.662755i | ||||
\(625\) | 11.6094 | + | 20.1081i | 0.464376 | + | 0.804323i | ||||
\(626\) | −7.36678 | + | 9.90286i | −0.294436 | + | 0.395798i | ||||
\(627\) | −2.02357 | − | 7.55206i | −0.0808135 | − | 0.301600i | ||||
\(628\) | −13.9901 | − | 7.53017i | −0.558264 | − | 0.300486i | ||||
\(629\) | 2.49664 | + | 2.49664i | 0.0995477 | + | 0.0995477i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.35784i | 0.0938640i | 0.998898 | + | 0.0469320i | \(0.0149444\pi\) | ||||
−0.998898 | + | 0.0469320i | \(0.985056\pi\) | |||||||
\(632\) | −4.95607 | + | 0.879499i | −0.197142 | + | 0.0349846i | ||||
\(633\) | −3.23145 | − | 1.86568i | −0.128439 | − | 0.0741541i | ||||
\(634\) | 37.6358 | − | 5.52690i | 1.49471 | − | 0.219501i | ||||
\(635\) | −12.9578 | + | 48.3593i | −0.514216 | + | 1.91908i | ||||
\(636\) | −5.40558 | − | 1.27697i | −0.214345 | − | 0.0506351i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.23439 | − | 10.5945i | 0.0488699 | − | 0.419440i | ||||
\(639\) | 37.6326 | + | 65.1815i | 1.48872 | + | 2.57854i | ||||
\(640\) | 22.8162 | − | 37.2035i | 0.901888 | − | 1.47060i | ||||
\(641\) | 24.9208 | − | 43.1640i | 0.984311 | − | 1.70488i | 0.339354 | − | 0.940659i | \(-0.389791\pi\) |
0.644957 | − | 0.764219i | \(-0.276875\pi\) | |||||||
\(642\) | 21.8861 | − | 9.45023i | 0.863775 | − | 0.372971i | ||||
\(643\) | −6.07975 | + | 6.07975i | −0.239762 | + | 0.239762i | −0.816751 | − | 0.576990i | \(-0.804227\pi\) |
0.576990 | + | 0.816751i | \(0.304227\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −63.7879 | − | 63.7879i | −2.51165 | − | 2.51165i | ||||
\(646\) | 1.62819 | − | 4.10277i | 0.0640602 | − | 0.161421i | ||||
\(647\) | 0.401199 | + | 0.231632i | 0.0157727 | + | 0.00910640i | 0.507866 | − | 0.861436i | \(-0.330435\pi\) |
−0.492093 | + | 0.870543i | \(0.663768\pi\) | |||||||
\(648\) | 7.86632 | + | 9.35384i | 0.309018 | + | 0.367454i | ||||
\(649\) | 1.81331 | − | 1.04692i | 0.0711787 | − | 0.0410950i | ||||
\(650\) | −17.4497 | + | 13.8078i | −0.684432 | + | 0.541586i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.2016 | − | 9.39183i | 0.595339 | − | 0.367812i | ||||
\(653\) | −9.06587 | − | 2.42919i | −0.354775 | − | 0.0950617i | 0.0770297 | − | 0.997029i | \(-0.475456\pi\) |
−0.431805 | + | 0.901967i | \(0.642123\pi\) | |||||||
\(654\) | 11.3565 | − | 15.2661i | 0.444076 | − | 0.596953i | ||||
\(655\) | 18.6017 | − | 32.2191i | 0.726829 | − | 1.25891i | ||||
\(656\) | −29.7683 | + | 1.77752i | −1.16226 | + | 0.0694003i | ||||
\(657\) | 78.8305 | 3.07547 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.62922 | + | 4.62922i | −0.180329 | + | 0.180329i | −0.791499 | − | 0.611170i | \(-0.790699\pi\) |
0.611170 | + | 0.791499i | \(0.290699\pi\) | |||||||
\(660\) | 13.8204 | − | 25.6765i | 0.537959 | − | 0.999458i | ||||
\(661\) | 3.08328 | − | 0.826161i | 0.119926 | − | 0.0321339i | −0.198357 | − | 0.980130i | \(-0.563561\pi\) |
0.318283 | + | 0.947996i | \(0.396894\pi\) | |||||||
\(662\) | 6.48962 | + | 44.1916i | 0.252226 | + | 1.71755i | ||||
\(663\) | 6.04763 | − | 3.49160i | 0.234870 | − | 0.135602i | ||||
\(664\) | −12.1345 | − | 25.9482i | −0.470911 | − | 1.00698i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.1835 | + | 14.1332i | 0.433351 | + | 0.547650i | ||||
\(667\) | −7.16001 | + | 26.7215i | −0.277237 | + | 1.03466i | ||||
\(668\) | −17.2033 | − | 16.2067i | −0.665615 | − | 0.627056i | ||||
\(669\) | 2.40937 | + | 8.99190i | 0.0931517 | + | 0.347647i | ||||
\(670\) | 10.8114 | − | 4.66827i | 0.417681 | − | 0.180351i | ||||
\(671\) | −5.92014 | −0.228544 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.82222 | 0.262977 | 0.131489 | − | 0.991318i | \(-0.458024\pi\) | ||||
0.131489 | + | 0.991318i | \(0.458024\pi\) | |||||||
\(674\) | 30.4885 | − | 13.1647i | 1.17437 | − | 0.507085i | ||||
\(675\) | −18.1783 | − | 67.8422i | −0.699682 | − | 2.61125i | ||||
\(676\) | 15.2329 | + | 14.3504i | 0.585879 | + | 0.551939i | ||||
\(677\) | 1.74903 | − | 6.52747i | 0.0672207 | − | 0.250871i | −0.924136 | − | 0.382063i | \(-0.875214\pi\) |
0.991357 | + | 0.131192i | \(0.0418804\pi\) | |||||||
\(678\) | −23.3916 | − | 29.5612i | −0.898347 | − | 1.13529i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 14.9125 | − | 6.97375i | 0.571868 | − | 0.267431i | ||||
\(681\) | −49.0946 | + | 28.3448i | −1.88131 | + | 1.08617i | ||||
\(682\) | 1.09831 | + | 7.47901i | 0.0420564 | + | 0.286386i | ||||
\(683\) | 39.9884 | − | 10.7149i | 1.53012 | − | 0.409993i | 0.607059 | − | 0.794657i | \(-0.292349\pi\) |
0.923057 | + | 0.384664i | \(0.125683\pi\) | |||||||
\(684\) | 10.6788 | − | 19.8398i | 0.408313 | − | 0.758593i | ||||
\(685\) | 61.7932 | − | 61.7932i | 2.36100 | − | 2.36100i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.8594 | −1.10106 | ||||||||
\(688\) | 21.3626 | − | 24.0758i | 0.814442 | − | 0.917882i | ||||
\(689\) | −0.760903 | + | 1.31792i | −0.0289881 | + | 0.0502089i | ||||
\(690\) | −45.1408 | + | 60.6810i | −1.71848 | + | 2.31008i | ||||
\(691\) | 6.35289 | + | 1.70225i | 0.241675 | + | 0.0647567i | 0.377624 | − | 0.925959i | \(-0.376741\pi\) |
−0.135948 | + | 0.990716i | \(0.543408\pi\) | |||||||
\(692\) | −13.5678 | + | 8.38243i | −0.515769 | + | 0.318652i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.87632 | + | 7.81505i | −0.374900 | + | 0.296655i | ||||
\(695\) | −31.4048 | + | 18.1315i | −1.19125 | + | 0.687769i | ||||
\(696\) | 36.4835 | − | 30.6816i | 1.38290 | − | 1.16298i | ||||
\(697\) | −9.74191 | − | 5.62449i | −0.369001 | − | 0.213043i | ||||
\(698\) | −5.12011 | + | 12.9018i | −0.193799 | + | 0.488341i | ||||
\(699\) | −6.03875 | − | 6.03875i | −0.228407 | − | 0.228407i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.01206 | + | 4.01206i | −0.151533 | + | 0.151533i | −0.778802 | − | 0.627269i | \(-0.784173\pi\) |
0.627269 | + | 0.778802i | \(0.284173\pi\) | |||||||
\(702\) | 14.6980 | − | 6.34649i | 0.554741 | − | 0.239533i | ||||
\(703\) | 2.42030 | − | 4.19208i | 0.0912834 | − | 0.158107i | ||||
\(704\) | 9.43909 | + | 4.37632i | 0.355749 | + | 0.164939i | ||||
\(705\) | 20.1651 | + | 34.9270i | 0.759462 | + | 1.31543i | ||||
\(706\) | 4.92528 | − | 42.2726i | 0.185365 | − | 1.59095i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 9.10719 | + | 2.15141i | 0.342269 | + | 0.0808549i | ||||
\(709\) | 13.1812 | − | 49.1929i | 0.495030 | − | 1.84748i | −0.0348304 | − | 0.999393i | \(-0.511089\pi\) |
0.529861 | − | 0.848085i | \(-0.322244\pi\) | |||||||
\(710\) | 74.5938 | − | 10.9543i | 2.79945 | − | 0.411106i | ||||
\(711\) | −8.39335 | − | 4.84590i | −0.314775 | − | 0.181736i | ||||
\(712\) | 4.18050 | + | 23.5576i | 0.156671 | + | 0.882857i | ||||
\(713\) | − | 19.6059i | − | 0.734248i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.64929 | − | 5.64929i | −0.211271 | − | 0.211271i | ||||
\(716\) | 29.2088 | + | 15.7217i | 1.09158 | + | 0.587547i | ||||
\(717\) | −12.1935 | − | 45.5068i | −0.455375 | − | 1.69948i | ||||
\(718\) | −8.75464 | + | 11.7685i | −0.326720 | + | 0.439197i | ||||
\(719\) | −3.81125 | − | 6.60127i | −0.142135 | − | 0.246186i | 0.786165 | − | 0.618017i | \(-0.212064\pi\) |
−0.928301 | + | 0.371831i | \(0.878730\pi\) | |||||||
\(720\) | 79.7281 | − | 26.5485i | 2.97129 | − | 0.989406i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 20.6787 | + | 2.40932i | 0.769580 | + | 0.0896657i | ||||
\(723\) | −39.6278 | − | 10.6182i | −1.47377 | − | 0.394896i | ||||
\(724\) | −11.8338 | + | 0.352994i | −0.439800 | + | 0.0131189i | ||||
\(725\) | −55.3459 | + | 14.8299i | −2.05549 | + | 0.550768i | ||||
\(726\) | −35.5605 | − | 14.1122i | −1.31977 | − | 0.523753i | ||||
\(727\) | − | 25.4856i | − | 0.945207i | −0.881275 | − | 0.472604i | \(-0.843314\pi\) | ||
0.881275 | − | 0.472604i | \(-0.156686\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 38.4448i | − | 1.42388i | ||||||
\(730\) | 29.1276 | − | 73.3968i | 1.07806 | − | 2.71654i | ||||
\(731\) | 11.7277 | − | 3.14242i | 0.433763 | − | 0.116227i | ||||
\(732\) | −19.2586 | − | 18.1429i | −0.711817 | − | 0.670581i | ||||
\(733\) | 20.4559 | + | 5.48115i | 0.755557 | + | 0.202451i | 0.615982 | − | 0.787761i | \(-0.288760\pi\) |
0.139575 | + | 0.990211i | \(0.455426\pi\) | |||||||
\(734\) | −1.33056 | + | 11.4199i | −0.0491120 | + | 0.421517i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −22.5727 | − | 14.7872i | −0.832039 | − | 0.545063i | ||||
\(737\) | 1.40371 | + | 2.43129i | 0.0517061 | + | 0.0895577i | ||||
\(738\) | −46.0702 | − | 34.2718i | −1.69587 | − | 1.26156i | ||||
\(739\) | −4.51737 | − | 16.8591i | −0.166174 | − | 0.620170i | −0.997888 | − | 0.0649652i | \(-0.979306\pi\) |
0.831713 | − | 0.555205i | \(-0.187360\pi\) | |||||||
\(740\) | 17.2913 | − | 5.19045i | 0.635639 | − | 0.190805i | ||||
\(741\) | −6.76966 | − | 6.76966i | −0.248690 | − | 0.248690i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.6724i | 0.391531i | 0.980651 | + | 0.195766i | \(0.0627192\pi\) | ||||
−0.980651 | + | 0.195766i | \(0.937281\pi\) | |||||||
\(744\) | −19.3474 | + | 27.6955i | −0.709309 | + | 1.01537i | ||||
\(745\) | −36.7104 | − | 21.1948i | −1.34497 | − | 0.776517i | ||||
\(746\) | −0.926068 | − | 6.30613i | −0.0339058 | − | 0.230884i | ||||
\(747\) | 14.2753 | − | 53.2760i | 0.522305 | − | 1.94927i | ||||
\(748\) | 2.06278 | + | 3.33880i | 0.0754226 | + | 0.122079i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −76.8538 | − | 8.95442i | −2.80630 | − | 0.326969i | ||||
\(751\) | 1.41476 | + | 2.45044i | 0.0516254 | + | 0.0894178i | 0.890683 | − | 0.454624i | \(-0.150226\pi\) |
−0.839058 | + | 0.544042i | \(0.816893\pi\) | |||||||
\(752\) | −12.0110 | + | 7.92498i | −0.437997 | + | 0.288994i | ||||
\(753\) | −29.1743 | + | 50.5313i | −1.06317 | + | 1.84146i | ||||
\(754\) | −5.17748 | − | 11.9907i | −0.188553 | − | 0.436675i | ||||
\(755\) | −14.9157 | + | 14.9157i | −0.542837 | + | 0.542837i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.6590 | + | 15.6590i | 0.569136 | + | 0.569136i | 0.931886 | − | 0.362750i | \(-0.118162\pi\) |
−0.362750 | + | 0.931886i | \(0.618162\pi\) | |||||||
\(758\) | 1.55982 | + | 0.619016i | 0.0566552 | + | 0.0224837i | ||||
\(759\) | −15.6144 | − | 9.01496i | −0.566765 | − | 0.327222i | ||||
\(760\) | −14.5265 | − | 17.2734i | −0.526930 | − | 0.626573i | ||||
\(761\) | 4.15144 | − | 2.39683i | 0.150490 | − | 0.0868852i | −0.422864 | − | 0.906193i | \(-0.638975\pi\) |
0.573354 | + | 0.819308i | \(0.305642\pi\) | |||||||
\(762\) | −33.1001 | − | 41.8304i | −1.19909 | − | 1.51535i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −24.0727 | − | 5.68674i | −0.870920 | − | 0.205739i | ||||
\(765\) | 30.6179 | + | 8.20404i | 1.10699 | + | 0.296618i | ||||
\(766\) | −39.0046 | − | 29.0157i | −1.40929 | − | 1.04838i | ||||
\(767\) | 1.28195 | − | 2.22041i | 0.0462886 | − | 0.0801742i | ||||
\(768\) | 17.2942 | + | 43.1635i | 0.624051 | + | 1.55753i | ||||
\(769\) | 13.5489 | 0.488585 | 0.244293 | − | 0.969702i | \(-0.421444\pi\) | ||||
0.244293 | + | 0.969702i | \(0.421444\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.65159 | − | 6.65159i | 0.239551 | − | 0.239551i | ||||
\(772\) | 13.6183 | + | 45.3675i | 0.490134 | + | 1.63281i | ||||
\(773\) | −25.6544 | + | 6.87406i | −0.922723 | + | 0.247243i | −0.688749 | − | 0.725000i | \(-0.741840\pi\) |
−0.233974 | + | 0.972243i | \(0.575173\pi\) | |||||||
\(774\) | 61.3172 | − | 9.00456i | 2.20400 | − | 0.323662i | ||||
\(775\) | 35.1675 | − | 20.3040i | 1.26325 | − | 0.729340i | ||||
\(776\) | −15.6462 | + | 43.1348i | −0.561666 | + | 1.54845i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.1945 | − | 13.6059i | 0.616454 | − | 0.487795i | ||||
\(779\) | −3.99151 | + | 14.8965i | −0.143011 | + | 0.533723i | ||||
\(780\) | −1.06462 | − | 35.6903i | −0.0381194 | − | 1.27792i | ||||
\(781\) | 4.65192 | + | 17.3612i | 0.166459 | + | 0.621233i | ||||
\(782\) | −4.03514 | − | 9.34510i | −0.144296 | − | 0.334180i | ||||
\(783\) | 41.2247 | 1.47325 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.6438 | −1.09372 | ||||||||
\(786\) | 15.7134 | + | 36.3911i | 0.560477 | + | 1.29803i | ||||
\(787\) | 8.96168 | + | 33.4454i | 0.319449 | + | 1.19220i | 0.919775 | + | 0.392446i | \(0.128371\pi\) |
−0.600326 | + | 0.799756i | \(0.704962\pi\) | |||||||
\(788\) | −32.2849 | + | 0.963035i | −1.15010 | + | 0.0343067i | ||||
\(789\) | −18.0644 | + | 67.4174i | −0.643111 | + | 2.40012i | ||||
\(790\) | −7.61320 | + | 6.02426i | −0.270865 | + | 0.214334i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 8.48622 | + | 18.1467i | 0.301545 | + | 0.644816i | ||||
\(793\) | −6.27802 | + | 3.62462i | −0.222939 | + | 0.128714i | ||||
\(794\) | 52.3139 | − | 7.68241i | 1.85655 | − | 0.272638i | ||||
\(795\) | −10.3479 | + | 2.77272i | −0.367003 | + | 0.0983383i | ||||
\(796\) | −10.5295 | + | 3.16072i | −0.373208 | + | 0.112029i | ||||
\(797\) | −17.6690 | + | 17.6690i | −0.625870 | + | 0.625870i | −0.947026 | − | 0.321157i | \(-0.895928\pi\) |
0.321157 | + | 0.947026i | \(0.395928\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.42807 | −0.192031 | ||||||||
\(800\) | 3.14773 | − | 55.8027i | 0.111289 | − | 1.97292i | ||||
\(801\) | −23.0339 | + | 39.8959i | −0.813863 | + | 1.40965i | ||||
\(802\) | 5.64646 | + | 4.20042i | 0.199383 | + | 0.148322i | ||||
\(803\) | 18.1836 | + | 4.87228i | 0.641686 | + | 0.171939i | ||||
\(804\) | −2.88461 | + | 12.2109i | −0.101732 | + | 0.430646i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.74374 | + | 7.25869i | 0.202315 | + | 0.255676i | ||||
\(807\) | −0.311458 | + | 0.179820i | −0.0109638 | + | 0.00632998i | ||||
\(808\) | −3.98174 | + | 46.0941i | −0.140077 | + | 1.62159i | ||||
\(809\) | 2.59269 | + | 1.49689i | 0.0911540 | + | 0.0526278i | 0.544884 | − | 0.838511i | \(-0.316574\pi\) |
−0.453730 | + | 0.891139i | \(0.649907\pi\) | |||||||
\(810\) | 21.9106 | + | 8.69523i | 0.769859 | + | 0.305519i | ||||
\(811\) | −2.28628 | − | 2.28628i | −0.0802820 | − | 0.0802820i | 0.665825 | − | 0.746108i | \(-0.268080\pi\) |
−0.746108 | + | 0.665825i | \(0.768080\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.7839 | − | 20.7839i | 0.728923 | − | 0.728923i | ||||
\(814\) | 1.70613 | + | 3.95128i | 0.0597998 | + | 0.138492i | ||||
\(815\) | 17.2322 | − | 29.8471i | 0.603618 | − | 1.04550i | ||||
\(816\) | −3.52178 | + | 17.1829i | −0.123287 | + | 0.601523i | ||||
\(817\) | −8.32272 | − | 14.4154i | −0.291175 | − | 0.504330i | ||||
\(818\) | 5.70817 | + | 0.665073i | 0.199582 | + | 0.0232537i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −48.9323 | + | 30.2313i | −1.70879 | + | 1.05572i | ||||
\(821\) | −10.4808 | + | 39.1150i | −0.365783 | + | 1.36512i | 0.500572 | + | 0.865695i | \(0.333123\pi\) |
−0.866356 | + | 0.499428i | \(0.833544\pi\) | |||||||
\(822\) | 13.5281 | + | 92.1208i | 0.471848 | + | 3.21308i | ||||
\(823\) | −35.5496 | − | 20.5246i | −1.23918 | − | 0.715442i | −0.270255 | − | 0.962789i | \(-0.587108\pi\) |
−0.968927 | + | 0.247347i | \(0.920441\pi\) | |||||||
\(824\) | −8.49420 | − | 47.8658i | −0.295910 | − | 1.66748i | ||||
\(825\) | − | 37.3437i | − | 1.30014i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.3987 | − | 20.3987i | −0.709331 | − | 0.709331i | 0.257064 | − | 0.966394i | \(-0.417245\pi\) |
−0.966394 | + | 0.257064i | \(0.917245\pi\) | |||||||
\(828\) | −14.9382 | − | 49.7646i | −0.519140 | − | 1.72944i | ||||
\(829\) | −6.76750 | − | 25.2567i | −0.235045 | − | 0.877200i | −0.978129 | − | 0.208001i | \(-0.933304\pi\) |
0.743083 | − | 0.669199i | \(-0.233363\pi\) | |||||||
\(830\) | −44.3291 | − | 32.9766i | −1.53868 | − | 1.14463i | ||||
\(831\) | −22.6214 | − | 39.1814i | −0.784727 | − | 1.35919i | ||||
\(832\) | 12.6891 | − | 1.13822i | 0.439916 | − | 0.0394608i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.47141 | − | 38.3771i | 0.154832 | − | 1.32889i | ||||
\(835\) | −44.0326 | − | 11.7985i | −1.52381 | − | 0.408304i | ||||
\(836\) | 3.68948 | − | 3.91636i | 0.127603 | − | 0.135450i | ||||
\(837\) | −28.2209 | + | 7.56177i | −0.975457 | + | 0.261373i | ||||
\(838\) | −0.407404 | + | 1.02659i | −0.0140735 | + | 0.0354630i | ||||
\(839\) | − | 41.9862i | − | 1.44953i | −0.688999 | − | 0.724763i | \(-0.741949\pi\) | ||
0.688999 | − | 0.724763i | \(-0.258051\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 4.63123i | − | 0.159698i | ||||||
\(842\) | 7.02247 | + | 2.78688i | 0.242010 | + | 0.0960421i | ||||
\(843\) | −11.8462 | + | 3.17419i | −0.408006 | + | 0.109325i | ||||
\(844\) | −0.0765633 | − | 2.56672i | −0.00263542 | − | 0.0883500i | ||||
\(845\) | 38.9892 | + | 10.4471i | 1.34127 | + | 0.359392i | ||||
\(846\) | −27.5210 | − | 3.20654i | −0.946193 | − | 0.110243i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.20763 | − | 3.62664i | −0.0414701 | − | 0.124539i | ||||
\(849\) | −34.0788 | − | 59.0263i | −1.16958 | − | 2.02578i | ||||
\(850\) | 12.5837 | − | 16.9157i | 0.431617 | − | 0.580205i | ||||
\(851\) | −2.88913 | − | 10.7824i | −0.0990382 | − | 0.369616i | ||||
\(852\) | −38.0723 | + | 70.7333i | −1.30434 | + | 2.42328i | ||||
\(853\) | 10.9845 | + | 10.9845i | 0.376104 | + | 0.376104i | 0.869694 | − | 0.493591i | \(-0.164316\pi\) |
−0.493591 | + | 0.869694i | \(0.664316\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 43.4570i | − | 1.48620i | ||||||
\(856\) | 13.4491 | + | 9.39519i | 0.459681 | + | 0.321121i | ||||
\(857\) | −40.9817 | − | 23.6608i | −1.39991 | − | 0.808237i | −0.405524 | − | 0.914084i | \(-0.632911\pi\) |
−0.994382 | + | 0.105848i | \(0.966244\pi\) | |||||||
\(858\) | 8.42191 | − | 1.23678i | 0.287519 | − | 0.0422228i | ||||
\(859\) | 1.87086 | − | 6.98214i | 0.0638329 | − | 0.238228i | −0.926637 | − | 0.375957i | \(-0.877314\pi\) |
0.990470 | + | 0.137730i | \(0.0439806\pi\) | |||||||
\(860\) | 14.2726 | − | 60.4178i | 0.486692 | − | 2.06023i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.193431 | − | 1.66017i | 0.00658828 | − | 0.0565458i | ||||
\(863\) | −5.05527 | − | 8.75599i | −0.172084 | − | 0.298057i | 0.767065 | − | 0.641570i | \(-0.221717\pi\) |
−0.939148 | + | 0.343512i | \(0.888383\pi\) | |||||||
\(864\) | −12.5788 | + | 38.1945i | −0.427939 | + | 1.29940i | ||||
\(865\) | −15.3802 | + | 26.6392i | −0.522941 | + | 0.905761i | ||||
\(866\) | 19.8108 | − | 8.55412i | 0.673197 | − | 0.290681i | ||||
\(867\) | 30.2565 | − | 30.2565i | 1.02756 | − | 1.02756i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.63656 | − | 1.63656i | −0.0555165 | − | 0.0555165i | ||||
\(870\) | 33.9146 | − | 85.4593i | 1.14981 | − | 2.89734i | ||||
\(871\) | 2.97712 | + | 1.71884i | 0.100876 | + | 0.0582408i | ||||
\(872\) | 13.0455 | + | 1.12690i | 0.441775 | + | 0.0381618i | ||||
\(873\) | −76.5128 | + | 44.1747i | −2.58956 | + | 1.49509i | ||||
\(874\) | −10.9435 | + | 8.65950i | −0.370169 | + | 0.292912i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 44.2207 | + | 71.5754i | 1.49408 | + | 2.41831i | ||||
\(877\) | 51.9964 | + | 13.9324i | 1.75579 | + | 0.470463i | 0.985847 | − | 0.167646i | \(-0.0536165\pi\) |
0.769946 | + | 0.638109i | \(0.220283\pi\) | |||||||
\(878\) | −3.66761 | + | 4.93022i | −0.123776 | + | 0.166387i | ||||
\(879\) | −27.7922 | + | 48.1375i | −0.937408 | + | 1.62364i | ||||
\(880\) | 20.0315 | − | 1.19612i | 0.675263 | − | 0.0403211i | ||||
\(881\) | −21.5769 | −0.726946 | −0.363473 | − | 0.931605i | \(-0.618409\pi\) | ||||
−0.363473 | + | 0.931605i | \(0.618409\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.5700 | − | 21.5700i | 0.725888 | − | 0.725888i | −0.243910 | − | 0.969798i | \(-0.578430\pi\) |
0.969798 | + | 0.243910i | \(0.0784300\pi\) | |||||||
\(884\) | 4.23167 | + | 2.27770i | 0.142326 | + | 0.0766073i | ||||
\(885\) | 17.4340 | − | 4.67141i | 0.586036 | − | 0.157028i | ||||
\(886\) | −1.25357 | − | 8.53629i | −0.0421146 | − | 0.286782i | ||||
\(887\) | 29.1946 | − | 16.8555i | 0.980260 | − | 0.565953i | 0.0779110 | − | 0.996960i | \(-0.475175\pi\) |
0.902348 | + | 0.431007i | \(0.141842\pi\) | |||||||
\(888\) | −6.55898 | + | 18.0824i | −0.220105 | + | 0.606804i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 28.6350 | + | 36.1876i | 0.959846 | + | 1.21301i | ||||
\(891\) | −1.45448 | + | 5.42821i | −0.0487271 | + | 0.181852i | ||||
\(892\) | −4.39290 | + | 4.66303i | −0.147085 | + | 0.156130i | ||||
\(893\) | 1.92606 | + | 7.18814i | 0.0644530 | + | 0.240542i | ||||
\(894\) | 41.4639 | − | 17.9038i | 1.38676 | − | 0.598792i | ||||
\(895\) | 63.9788 | 2.13858 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.0777 | −0.737153 | ||||||||
\(898\) | −4.83634 | + | 2.08829i | −0.161391 | + | 0.0696872i | ||||
\(899\) | 6.16891 | + | 23.0227i | 0.205745 | + | 0.767850i | ||||
\(900\) | 73.7937 | − | 78.3315i | 2.45979 | − | 2.61105i | ||||
\(901\) | 0.373182 | − | 1.39273i | 0.0124325 | − | 0.0463987i | ||||
\(902\) | −8.50865 | − | 10.7529i | −0.283307 | − | 0.358031i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.84597 | − | 24.3873i | 0.294213 | − | 0.811111i | ||||
\(905\) | −19.7753 | + | 11.4173i | −0.657354 | + | 0.379524i | ||||
\(906\) | −3.26543 | − | 22.2362i | −0.108487 | − | 0.738747i | ||||
\(907\) | −1.26216 | + | 0.338194i | −0.0419092 | + | 0.0112295i | −0.279713 | − | 0.960084i | \(-0.590239\pi\) |
0.237804 | + | 0.971313i | \(0.423573\pi\) | |||||||
\(908\) | −34.3526 | − | 18.4903i | −1.14003 | − | 0.613624i | ||||
\(909\) | −62.9911 | + | 62.9911i | −2.08928 | + | 2.08928i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.9873 | −0.993522 | −0.496761 | − | 0.867887i | \(-0.665477\pi\) | ||||
−0.496761 | + | 0.867887i | \(0.665477\pi\) | |||||||
\(912\) | 24.0042 | − | 1.43333i | 0.794859 | − | 0.0474624i | ||||
\(913\) | 6.58567 | − | 11.4067i | 0.217954 | − | 0.377507i | ||||
\(914\) | −9.06991 | + | 12.1923i | −0.300006 | + | 0.403286i | ||||
\(915\) | −49.2931 | − | 13.2080i | −1.62958 | − | 0.436645i | ||||
\(916\) | −10.4387 | − | 16.8960i | −0.344904 | − | 0.558261i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −11.8951 | + | 9.41250i | −0.392597 | + | 0.310659i | ||||
\(919\) | 11.3211 | − | 6.53623i | 0.373448 | − | 0.215610i | −0.301516 | − | 0.953461i | \(-0.597493\pi\) |
0.674964 | + | 0.737851i | \(0.264159\pi\) | |||||||
\(920\) | −51.8541 | − | 4.47930i | −1.70958 | − | 0.147678i | ||||
\(921\) | 31.7989 | + | 18.3591i | 1.04781 | + | 0.604953i | ||||
\(922\) | −5.81912 | + | 14.6632i | −0.191643 | + | 0.482908i | ||||
\(923\) | 15.5626 | + | 15.5626i | 0.512248 | + | 0.512248i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.3486 | − | 16.3486i | 0.537538 | − | 0.537538i | ||||
\(926\) | −35.5079 | + | 15.3320i | −1.16686 | + | 0.503841i | ||||
\(927\) | 46.8018 | − | 81.0630i | 1.53717 | − | 2.66246i | ||||
\(928\) | 31.1592 | + | 10.2618i | 1.02285 | + | 0.336861i | ||||
\(929\) | 10.3529 | + | 17.9317i | 0.339667 | + | 0.588320i | 0.984370 | − | 0.176113i | \(-0.0563524\pi\) |
−0.644703 | + | 0.764433i | \(0.723019\pi\) | |||||||
\(930\) | −7.54106 | + | 64.7232i | −0.247281 | + | 2.12236i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.35118 | − | 5.71971i | 0.0442593 | − | 0.187355i | ||||
\(933\) | −14.8734 | + | 55.5082i | −0.486933 | + | 1.81726i | ||||
\(934\) | 22.5412 | − | 3.31022i | 0.737570 | − | 0.108314i | ||||
\(935\) | 6.55548 | + | 3.78481i | 0.214387 | + | 0.123776i | ||||
\(936\) | 20.1096 | + | 14.0480i | 0.657303 | + | 0.459174i | ||||
\(937\) | 5.93799i | 0.193986i | 0.995285 | + | 0.0969929i | \(0.0309224\pi\) | ||||
−0.995285 | + | 0.0969929i | \(0.969078\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.9348 | − | 17.9348i | −0.585281 | − | 0.585281i | ||||
\(940\) | −13.1544 | + | 24.4392i | −0.429051 | + | 0.797120i | ||||
\(941\) | −5.12272 | − | 19.1182i | −0.166996 | − | 0.623237i | −0.997777 | − | 0.0666382i | \(-0.978773\pi\) |
0.830781 | − | 0.556599i | \(-0.187894\pi\) | |||||||
\(942\) | 19.4874 | − | 26.1961i | 0.634934 | − | 0.853516i | ||||
\(943\) | 17.7821 | + | 30.7995i | 0.579065 | + | 1.00297i | ||||
\(944\) | 2.03459 | + | 6.11007i | 0.0662201 | + | 0.198866i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.7004 | + | 1.71278i | 0.477952 | + | 0.0556873i | ||||
\(947\) | 41.3482 | + | 11.0792i | 1.34364 | + | 0.360027i | 0.857782 | − | 0.514013i | \(-0.171842\pi\) |
0.485855 | + | 0.874039i | \(0.338508\pi\) | |||||||
\(948\) | −0.308412 | − | 10.3392i | −0.0100168 | − | 0.335803i | ||||
\(949\) | 22.2659 | − | 5.96613i | 0.722782 | − | 0.193669i | ||||
\(950\) | −26.8658 | − | 10.6617i | −0.871643 | − | 0.345913i | ||||
\(951\) | 78.1710i | 2.53487i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 0.689500i | − | 0.0223351i | −0.999938 | − | 0.0111675i | \(-0.996445\pi\) | ||
0.999938 | − | 0.0111675i | \(-0.00355481\pi\) | |||||||
\(954\) | 2.71482 | − | 6.84090i | 0.0878955 | − | 0.221482i | ||||
\(955\) | −46.0825 | + | 12.3478i | −1.49120 | + | 0.399565i | ||||
\(956\) | 22.2319 | − | 23.5990i | 0.719030 | − | 0.763245i | ||||
\(957\) | 21.1720 | + | 5.67303i | 0.684395 | + | 0.183383i | ||||
\(958\) | 1.86383 | − | 15.9968i | 0.0602176 | − | 0.516834i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 68.8294 | + | 57.4977i | 2.22146 | + | 1.85573i | ||||
\(961\) | 7.05398 | + | 12.2179i | 0.227548 | + | 0.394124i | ||||
\(962\) | 4.22845 | + | 3.14556i | 0.136331 | + | 0.101417i | ||||
\(963\) | 8.17572 | + | 30.5122i | 0.263459 | + | 0.983242i | ||||
\(964\) | −8.11715 | − | 27.0411i | −0.261436 | − | 0.870937i | ||||
\(965\) | 64.6012 | + | 64.6012i | 2.07959 | + | 2.07959i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.1022i | 0.453497i | 0.973953 | + | 0.226749i | \(0.0728096\pi\) | ||||
−0.973953 | + | 0.226749i | \(0.927190\pi\) | |||||||
\(968\) | −4.60039 | − | 25.9237i | −0.147862 | − | 0.833220i | ||||
\(969\) | 7.85557 | + | 4.53541i | 0.252357 | + | 0.145698i | ||||
\(970\) | 12.8585 | + | 87.5612i | 0.412863 | + | 2.81142i | ||||
\(971\) | −0.0934205 | + | 0.348650i | −0.00299801 | + | 0.0111887i | −0.967409 | − | 0.253220i | \(-0.918510\pi\) |
0.964411 | + | 0.264409i | \(0.0851769\pi\) | |||||||
\(972\) | 14.9184 | − | 9.21689i | 0.478508 | − | 0.295632i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −44.0421 | − | 5.13145i | −1.41120 | − | 0.164422i | ||||
\(975\) | −22.8638 | − | 39.6012i | −0.732226 | − | 1.26825i | ||||
\(976\) | 3.65595 | − | 17.8375i | 0.117024 | − | 0.570966i | ||||
\(977\) | 4.91955 | − | 8.52091i | 0.157390 | − | 0.272608i | −0.776536 | − | 0.630072i | \(-0.783025\pi\) |
0.933927 | + | 0.357464i | \(0.116359\pi\) | |||||||
\(978\) | 14.5565 | + | 33.7119i | 0.465466 | + | 1.07799i | ||||
\(979\) | −7.77902 | + | 7.77902i | −0.248618 | + | 0.248618i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.8276 | + | 17.8276i | 0.569191 | + | 0.569191i | ||||
\(982\) | −37.6952 | − | 14.9594i | −1.20290 | − | 0.477373i | ||||
\(983\) | 23.0786 | + | 13.3244i | 0.736094 | + | 0.424984i | 0.820647 | − | 0.571435i | \(-0.193613\pi\) |
−0.0845537 | + | 0.996419i | \(0.526946\pi\) | |||||||
\(984\) | 5.27414 | − | 61.0553i | 0.168133 | − | 1.94637i | ||||
\(985\) | −53.9509 | + | 31.1486i | −1.71902 | + | 0.992476i | ||||
\(986\) | 7.67875 | + | 9.70406i | 0.244541 | + | 0.309040i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.51472 | − | 6.41201i | 0.0481896 | − | 0.203993i | ||||
\(989\) | −37.0776 | − | 9.93490i | −1.17900 | − | 0.315912i | ||||
\(990\) | 31.0014 | + | 23.0620i | 0.985288 | + | 0.732959i | ||||
\(991\) | −8.41437 | + | 14.5741i | −0.267291 | + | 0.462962i | −0.968161 | − | 0.250327i | \(-0.919462\pi\) |
0.700870 | + | 0.713289i | \(0.252795\pi\) | |||||||
\(992\) | −23.2127 | − | 1.30939i | −0.737005 | − | 0.0415732i | ||||
\(993\) | −91.7875 | −2.91279 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.9935 | + | 14.9935i | −0.475326 | + | 0.475326i | ||||
\(996\) | 56.3807 | − | 16.9242i | 1.78649 | − | 0.536264i | ||||
\(997\) | 35.2183 | − | 9.43672i | 1.11538 | − | 0.298864i | 0.346365 | − | 0.938100i | \(-0.387416\pi\) |
0.769011 | + | 0.639236i | \(0.220749\pi\) | |||||||
\(998\) | −36.6404 | + | 5.38072i | −1.15983 | + | 0.170324i | ||||
\(999\) | −14.4059 | + | 8.31728i | −0.455784 | + | 0.263147i |
(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 | 784.2.x.l.165.2 | 24 | ||
7.2 | even | 3 | inner | 784.2.x.l.373.5 | 24 | ||
7.3 | odd | 6 | 784.2.m.h.197.3 | 12 | |||
7.4 | even | 3 | 112.2.m.d.85.3 | yes | 12 | ||
7.5 | odd | 6 | 784.2.x.m.373.5 | 24 | |||
7.6 | odd | 2 | 784.2.x.m.165.2 | 24 | |||
16.13 | even | 4 | inner | 784.2.x.l.557.5 | 24 | ||
28.11 | odd | 6 | 448.2.m.d.113.6 | 12 | |||
56.11 | odd | 6 | 896.2.m.h.225.1 | 12 | |||
56.53 | even | 6 | 896.2.m.g.225.6 | 12 | |||
112.11 | odd | 12 | 896.2.m.h.673.1 | 12 | |||
112.13 | odd | 4 | 784.2.x.m.557.5 | 24 | |||
112.45 | odd | 12 | 784.2.m.h.589.3 | 12 | |||
112.53 | even | 12 | 896.2.m.g.673.6 | 12 | |||
112.61 | odd | 12 | 784.2.x.m.765.2 | 24 | |||
112.67 | odd | 12 | 448.2.m.d.337.6 | 12 | |||
112.93 | even | 12 | inner | 784.2.x.l.765.2 | 24 | ||
112.109 | even | 12 | 112.2.m.d.29.3 | ✓ | 12 | ||
224.67 | odd | 24 | 7168.2.a.bi.1.11 | 12 | |||
224.109 | even | 24 | 7168.2.a.bj.1.11 | 12 | |||
224.179 | odd | 24 | 7168.2.a.bi.1.2 | 12 | |||
224.221 | even | 24 | 7168.2.a.bj.1.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.d.29.3 | ✓ | 12 | 112.109 | even | 12 | ||
112.2.m.d.85.3 | yes | 12 | 7.4 | even | 3 | ||
448.2.m.d.113.6 | 12 | 28.11 | odd | 6 | |||
448.2.m.d.337.6 | 12 | 112.67 | odd | 12 | |||
784.2.m.h.197.3 | 12 | 7.3 | odd | 6 | |||
784.2.m.h.589.3 | 12 | 112.45 | odd | 12 | |||
784.2.x.l.165.2 | 24 | 1.1 | even | 1 | trivial | ||
784.2.x.l.373.5 | 24 | 7.2 | even | 3 | inner | ||
784.2.x.l.557.5 | 24 | 16.13 | even | 4 | inner | ||
784.2.x.l.765.2 | 24 | 112.93 | even | 12 | inner | ||
784.2.x.m.165.2 | 24 | 7.6 | odd | 2 | |||
784.2.x.m.373.5 | 24 | 7.5 | odd | 6 | |||
784.2.x.m.557.5 | 24 | 112.13 | odd | 4 | |||
784.2.x.m.765.2 | 24 | 112.61 | odd | 12 | |||
896.2.m.g.225.6 | 12 | 56.53 | even | 6 | |||
896.2.m.g.673.6 | 12 | 112.53 | even | 12 | |||
896.2.m.h.225.1 | 12 | 56.11 | odd | 6 | |||
896.2.m.h.673.1 | 12 | 112.11 | odd | 12 | |||
7168.2.a.bi.1.2 | 12 | 224.179 | odd | 24 | |||
7168.2.a.bi.1.11 | 12 | 224.67 | odd | 24 | |||
7168.2.a.bj.1.2 | 12 | 224.221 | even | 24 | |||
7168.2.a.bj.1.11 | 12 | 224.109 | even | 24 |