Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(47,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.i (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 323.4 | ||
Character | \(\chi\) | \(=\) | 690.323 |
Dual form | 690.2.i.f.47.4 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | −0.144577 | + | 1.72601i | −0.0834716 | + | 0.996510i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 1.25275 | − | 1.85219i | 0.560247 | − | 0.828325i | ||||
\(6\) | 1.32270 | − | 1.11824i | 0.539991 | − | 0.456519i | ||||
\(7\) | −2.31531 | + | 2.31531i | −0.875106 | + | 0.875106i | −0.993023 | − | 0.117918i | \(-0.962378\pi\) |
0.117918 | + | 0.993023i | \(0.462378\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | −2.95819 | − | 0.499082i | −0.986065 | − | 0.166361i | ||||
\(10\) | −2.19553 | + | 0.423868i | −0.694286 | + | 0.134039i | ||||
\(11\) | 0.0826422i | 0.0249176i | 0.999922 | + | 0.0124588i | \(0.00396585\pi\) | ||||
−0.999922 | + | 0.0124588i | \(0.996034\pi\) | |||||||
\(12\) | −1.72601 | − | 0.144577i | −0.498255 | − | 0.0417358i | ||||
\(13\) | −2.92164 | − | 2.92164i | −0.810317 | − | 0.810317i | 0.174364 | − | 0.984681i | \(-0.444213\pi\) |
−0.984681 | + | 0.174364i | \(0.944213\pi\) | |||||||
\(14\) | 3.27434 | 0.875106 | ||||||||
\(15\) | 3.01578 | + | 2.43004i | 0.778670 | + | 0.627434i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −5.30247 | − | 5.30247i | −1.28604 | − | 1.28604i | −0.937172 | − | 0.348866i | \(-0.886567\pi\) |
−0.348866 | − | 0.937172i | \(-0.613433\pi\) | |||||||
\(18\) | 1.73886 | + | 2.44466i | 0.409852 | + | 0.576213i | ||||
\(19\) | 6.47652i | 1.48582i | 0.669393 | + | 0.742908i | \(0.266554\pi\) | ||||
−0.669393 | + | 0.742908i | \(0.733446\pi\) | |||||||
\(20\) | 1.85219 | + | 1.25275i | 0.414163 | + | 0.280124i | ||||
\(21\) | −3.66150 | − | 4.33098i | −0.799005 | − | 0.945098i | ||||
\(22\) | 0.0584368 | − | 0.0584368i | 0.0124588 | − | 0.0124588i | ||||
\(23\) | −0.707107 | + | 0.707107i | −0.147442 | + | 0.147442i | ||||
\(24\) | 1.11824 | + | 1.32270i | 0.228260 | + | 0.269995i | ||||
\(25\) | −1.86123 | − | 4.64067i | −0.372246 | − | 0.928134i | ||||
\(26\) | 4.13182i | 0.810317i | ||||||||
\(27\) | 1.28911 | − | 5.03371i | 0.248088 | − | 0.968737i | ||||
\(28\) | −2.31531 | − | 2.31531i | −0.437553 | − | 0.437553i | ||||
\(29\) | 1.98555 | 0.368708 | 0.184354 | − | 0.982860i | \(-0.440981\pi\) | ||||
0.184354 | + | 0.982860i | \(0.440981\pi\) | |||||||
\(30\) | −0.414176 | − | 3.85077i | −0.0756179 | − | 0.703052i | ||||
\(31\) | −4.16017 | −0.747188 | −0.373594 | − | 0.927592i | \(-0.621875\pi\) | ||||
−0.373594 | + | 0.927592i | \(0.621875\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −0.142641 | − | 0.0119482i | −0.0248306 | − | 0.00207991i | ||||
\(34\) | 7.49883i | 1.28604i | ||||||||
\(35\) | 1.38789 | + | 7.18891i | 0.234596 | + | 1.21515i | ||||
\(36\) | 0.499082 | − | 2.95819i | 0.0831803 | − | 0.493032i | ||||
\(37\) | 4.80467 | − | 4.80467i | 0.789883 | − | 0.789883i | −0.191591 | − | 0.981475i | \(-0.561365\pi\) |
0.981475 | + | 0.191591i | \(0.0613649\pi\) | |||||||
\(38\) | 4.57959 | − | 4.57959i | 0.742908 | − | 0.742908i | ||||
\(39\) | 5.46517 | − | 4.62037i | 0.875128 | − | 0.739851i | ||||
\(40\) | −0.423868 | − | 2.19553i | −0.0670194 | − | 0.347143i | ||||
\(41\) | 0.882958i | 0.137895i | 0.997620 | + | 0.0689474i | \(0.0219641\pi\) | ||||
−0.997620 | + | 0.0689474i | \(0.978036\pi\) | |||||||
\(42\) | −0.473395 | + | 5.65154i | −0.0730465 | + | 0.872052i | ||||
\(43\) | −1.69981 | − | 1.69981i | −0.259219 | − | 0.259219i | 0.565518 | − | 0.824736i | \(-0.308676\pi\) |
−0.824736 | + | 0.565518i | \(0.808676\pi\) | |||||||
\(44\) | −0.0826422 | −0.0124588 | ||||||||
\(45\) | −4.63028 | + | 4.85392i | −0.690241 | + | 0.723579i | ||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −7.63231 | − | 7.63231i | −1.11329 | − | 1.11329i | −0.992703 | − | 0.120584i | \(-0.961523\pi\) |
−0.120584 | − | 0.992703i | \(-0.538477\pi\) | |||||||
\(48\) | 0.144577 | − | 1.72601i | 0.0208679 | − | 0.249128i | ||||
\(49\) | − | 3.72133i | − | 0.531619i | ||||||
\(50\) | −1.96536 | + | 4.59754i | −0.277944 | + | 0.650190i | ||||
\(51\) | 9.91872 | − | 8.38549i | 1.38890 | − | 1.17420i | ||||
\(52\) | 2.92164 | − | 2.92164i | 0.405159 | − | 0.405159i | ||||
\(53\) | −7.26221 | + | 7.26221i | −0.997541 | + | 0.997541i | −0.999997 | − | 0.00245571i | \(-0.999218\pi\) |
0.00245571 | + | 0.999997i | \(0.499218\pi\) | |||||||
\(54\) | −4.47090 | + | 2.64783i | −0.608413 | + | 0.360324i | ||||
\(55\) | 0.153069 | + | 0.103530i | 0.0206398 | + | 0.0139600i | ||||
\(56\) | 3.27434i | 0.437553i | ||||||||
\(57\) | −11.1785 | − | 0.936357i | −1.48063 | − | 0.124023i | ||||
\(58\) | −1.40400 | − | 1.40400i | −0.184354 | − | 0.184354i | ||||
\(59\) | −10.0777 | −1.31201 | −0.656003 | − | 0.754759i | \(-0.727754\pi\) | ||||
−0.656003 | + | 0.754759i | \(0.727754\pi\) | |||||||
\(60\) | −2.43004 | + | 3.01578i | −0.313717 | + | 0.389335i | ||||
\(61\) | −0.876183 | −0.112184 | −0.0560919 | − | 0.998426i | \(-0.517864\pi\) | ||||
−0.0560919 | + | 0.998426i | \(0.517864\pi\) | |||||||
\(62\) | 2.94168 | + | 2.94168i | 0.373594 | + | 0.373594i | ||||
\(63\) | 8.00467 | − | 5.69361i | 1.00849 | − | 0.717328i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −9.07153 | + | 1.75135i | −1.12518 | + | 0.217228i | ||||
\(66\) | 0.0924137 | + | 0.109311i | 0.0113753 | + | 0.0134553i | ||||
\(67\) | 0.768241 | − | 0.768241i | 0.0938556 | − | 0.0938556i | −0.658620 | − | 0.752476i | \(-0.728860\pi\) |
0.752476 | + | 0.658620i | \(0.228860\pi\) | |||||||
\(68\) | 5.30247 | − | 5.30247i | 0.643019 | − | 0.643019i | ||||
\(69\) | −1.11824 | − | 1.32270i | −0.134620 | − | 0.159235i | ||||
\(70\) | 4.10194 | − | 6.06471i | 0.490276 | − | 0.724872i | ||||
\(71\) | − | 1.70346i | − | 0.202163i | −0.994878 | − | 0.101082i | \(-0.967770\pi\) | ||
0.994878 | − | 0.101082i | \(-0.0322303\pi\) | |||||||
\(72\) | −2.44466 | + | 1.73886i | −0.288106 | + | 0.204926i | ||||
\(73\) | −0.265720 | − | 0.265720i | −0.0311002 | − | 0.0311002i | 0.691386 | − | 0.722486i | \(-0.257001\pi\) |
−0.722486 | + | 0.691386i | \(0.757001\pi\) | |||||||
\(74\) | −6.79483 | −0.789883 | ||||||||
\(75\) | 8.27892 | − | 2.54156i | 0.955967 | − | 0.293474i | ||||
\(76\) | −6.47652 | −0.742908 | ||||||||
\(77\) | −0.191342 | − | 0.191342i | −0.0218055 | − | 0.0218055i | ||||
\(78\) | −7.13155 | − | 0.597367i | −0.807490 | − | 0.0676385i | ||||
\(79\) | − | 16.8063i | − | 1.89085i | −0.325834 | − | 0.945427i | \(-0.605645\pi\) | ||
0.325834 | − | 0.945427i | \(-0.394355\pi\) | |||||||
\(80\) | −1.25275 | + | 1.85219i | −0.140062 | + | 0.207081i | ||||
\(81\) | 8.50183 | + | 2.95276i | 0.944648 | + | 0.328085i | ||||
\(82\) | 0.624346 | − | 0.624346i | 0.0689474 | − | 0.0689474i | ||||
\(83\) | −8.84618 | + | 8.84618i | −0.970994 | + | 0.970994i | −0.999591 | − | 0.0285970i | \(-0.990896\pi\) |
0.0285970 | + | 0.999591i | \(0.490896\pi\) | |||||||
\(84\) | 4.33098 | − | 3.66150i | 0.472549 | − | 0.399503i | ||||
\(85\) | −16.4639 | + | 3.17852i | −1.78576 | + | 0.344758i | ||||
\(86\) | 2.40390i | 0.259219i | ||||||||
\(87\) | −0.287065 | + | 3.42708i | −0.0307766 | + | 0.367421i | ||||
\(88\) | 0.0584368 | + | 0.0584368i | 0.00622939 | + | 0.00622939i | ||||
\(89\) | 5.65142 | 0.599049 | 0.299525 | − | 0.954089i | \(-0.403172\pi\) | ||||
0.299525 | + | 0.954089i | \(0.403172\pi\) | |||||||
\(90\) | 6.70634 | − | 0.158137i | 0.706910 | − | 0.0166691i | ||||
\(91\) | 13.5290 | 1.41823 | ||||||||
\(92\) | −0.707107 | − | 0.707107i | −0.0737210 | − | 0.0737210i | ||||
\(93\) | 0.601465 | − | 7.18048i | 0.0623690 | − | 0.744581i | ||||
\(94\) | 10.7937i | 1.11329i | ||||||||
\(95\) | 11.9958 | + | 8.11347i | 1.23074 | + | 0.832425i | ||||
\(96\) | −1.32270 | + | 1.11824i | −0.134998 | + | 0.114130i | ||||
\(97\) | −7.30890 | + | 7.30890i | −0.742107 | + | 0.742107i | −0.972983 | − | 0.230876i | \(-0.925841\pi\) |
0.230876 | + | 0.972983i | \(0.425841\pi\) | |||||||
\(98\) | −2.63138 | + | 2.63138i | −0.265810 | + | 0.265810i | ||||
\(99\) | 0.0412452 | − | 0.244472i | 0.00414530 | − | 0.0245703i | ||||
\(100\) | 4.64067 | − | 1.86123i | 0.464067 | − | 0.186123i | ||||
\(101\) | 2.99650i | 0.298163i | 0.988825 | + | 0.149082i | \(0.0476317\pi\) | ||||
−0.988825 | + | 0.149082i | \(0.952368\pi\) | |||||||
\(102\) | −12.9430 | − | 1.08416i | −1.28155 | − | 0.107348i | ||||
\(103\) | 7.92493 | + | 7.92493i | 0.780866 | + | 0.780866i | 0.979977 | − | 0.199111i | \(-0.0638053\pi\) |
−0.199111 | + | 0.979977i | \(0.563805\pi\) | |||||||
\(104\) | −4.13182 | −0.405159 | ||||||||
\(105\) | −12.6088 | + | 1.35616i | −1.23049 | + | 0.132347i | ||||
\(106\) | 10.2703 | 0.997541 | ||||||||
\(107\) | −5.54562 | − | 5.54562i | −0.536115 | − | 0.536115i | 0.386270 | − | 0.922386i | \(-0.373763\pi\) |
−0.922386 | + | 0.386270i | \(0.873763\pi\) | |||||||
\(108\) | 5.03371 | + | 1.28911i | 0.484369 | + | 0.124044i | ||||
\(109\) | 14.3159i | 1.37121i | 0.727974 | + | 0.685605i | \(0.240462\pi\) | ||||
−0.727974 | + | 0.685605i | \(0.759538\pi\) | |||||||
\(110\) | −0.0350294 | − | 0.181443i | −0.00333992 | − | 0.0172999i | ||||
\(111\) | 7.59825 | + | 8.98754i | 0.721194 | + | 0.853060i | ||||
\(112\) | 2.31531 | − | 2.31531i | 0.218776 | − | 0.218776i | ||||
\(113\) | 1.54977 | − | 1.54977i | 0.145791 | − | 0.145791i | −0.630444 | − | 0.776235i | \(-0.717127\pi\) |
0.776235 | + | 0.630444i | \(0.217127\pi\) | |||||||
\(114\) | 7.24230 | + | 8.56651i | 0.678304 | + | 0.802327i | ||||
\(115\) | 0.423868 | + | 2.19553i | 0.0395259 | + | 0.204734i | ||||
\(116\) | 1.98555i | 0.184354i | ||||||||
\(117\) | 7.18465 | + | 10.1009i | 0.664221 | + | 0.933831i | ||||
\(118\) | 7.12601 | + | 7.12601i | 0.656003 | + | 0.656003i | ||||
\(119\) | 24.5538 | 2.25084 | ||||||||
\(120\) | 3.85077 | − | 0.414176i | 0.351526 | − | 0.0378090i | ||||
\(121\) | 10.9932 | 0.999379 | ||||||||
\(122\) | 0.619555 | + | 0.619555i | 0.0560919 | + | 0.0560919i | ||||
\(123\) | −1.52399 | − | 0.127655i | −0.137414 | − | 0.0115103i | ||||
\(124\) | − | 4.16017i | − | 0.373594i | ||||||
\(125\) | −10.9271 | − | 2.36626i | −0.977347 | − | 0.211645i | ||||
\(126\) | −9.68615 | − | 1.63417i | −0.862911 | − | 0.145583i | ||||
\(127\) | −2.65907 | + | 2.65907i | −0.235954 | + | 0.235954i | −0.815172 | − | 0.579218i | \(-0.803358\pi\) |
0.579218 | + | 0.815172i | \(0.303358\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 3.17964 | − | 2.68813i | 0.279952 | − | 0.236677i | ||||
\(130\) | 7.65293 | + | 5.17615i | 0.671206 | + | 0.453978i | ||||
\(131\) | 12.0048i | 1.04887i | 0.851452 | + | 0.524433i | \(0.175723\pi\) | ||||
−0.851452 | + | 0.524433i | \(0.824277\pi\) | |||||||
\(132\) | 0.0119482 | − | 0.142641i | 0.00103995 | − | 0.0124153i | ||||
\(133\) | −14.9952 | − | 14.9952i | −1.30025 | − | 1.30025i | ||||
\(134\) | −1.08646 | −0.0938556 | ||||||||
\(135\) | −7.70846 | − | 8.69365i | −0.663439 | − | 0.748231i | ||||
\(136\) | −7.49883 | −0.643019 | ||||||||
\(137\) | 4.13246 | + | 4.13246i | 0.353060 | + | 0.353060i | 0.861247 | − | 0.508187i | \(-0.169684\pi\) |
−0.508187 | + | 0.861247i | \(0.669684\pi\) | |||||||
\(138\) | −0.144577 | + | 1.72601i | −0.0123072 | + | 0.146927i | ||||
\(139\) | − | 0.433456i | − | 0.0367652i | −0.999831 | − | 0.0183826i | \(-0.994148\pi\) | ||
0.999831 | − | 0.0183826i | \(-0.00585170\pi\) | |||||||
\(140\) | −7.18891 | + | 1.38789i | −0.607574 | + | 0.117298i | ||||
\(141\) | 14.2769 | − | 12.0700i | 1.20233 | − | 1.01647i | ||||
\(142\) | −1.20453 | + | 1.20453i | −0.101082 | + | 0.101082i | ||||
\(143\) | 0.241451 | − | 0.241451i | 0.0201911 | − | 0.0201911i | ||||
\(144\) | 2.95819 | + | 0.499082i | 0.246516 | + | 0.0415902i | ||||
\(145\) | 2.48740 | − | 3.67762i | 0.206568 | − | 0.305410i | ||||
\(146\) | 0.375785i | 0.0311002i | ||||||||
\(147\) | 6.42305 | + | 0.538020i | 0.529764 | + | 0.0443751i | ||||
\(148\) | 4.80467 | + | 4.80467i | 0.394942 | + | 0.394942i | ||||
\(149\) | 20.0239 | 1.64042 | 0.820212 | − | 0.572059i | \(-0.193855\pi\) | ||||
0.820212 | + | 0.572059i | \(0.193855\pi\) | |||||||
\(150\) | −7.65123 | − | 4.05693i | −0.624720 | − | 0.331247i | ||||
\(151\) | −17.1989 | −1.39963 | −0.699814 | − | 0.714325i | \(-0.746734\pi\) | ||||
−0.699814 | + | 0.714325i | \(0.746734\pi\) | |||||||
\(152\) | 4.57959 | + | 4.57959i | 0.371454 | + | 0.371454i | ||||
\(153\) | 13.0394 | + | 18.3321i | 1.05417 | + | 1.48206i | ||||
\(154\) | 0.270599i | 0.0218055i | ||||||||
\(155\) | −5.21166 | + | 7.70543i | −0.418610 | + | 0.618915i | ||||
\(156\) | 4.62037 | + | 5.46517i | 0.369926 | + | 0.437564i | ||||
\(157\) | 16.4821 | − | 16.4821i | 1.31542 | − | 1.31542i | 0.398054 | − | 0.917362i | \(-0.369686\pi\) |
0.917362 | − | 0.398054i | \(-0.130314\pi\) | |||||||
\(158\) | −11.8838 | + | 11.8838i | −0.945427 | + | 0.945427i | ||||
\(159\) | −11.4847 | − | 13.5846i | −0.910794 | − | 1.07733i | ||||
\(160\) | 2.19553 | − | 0.423868i | 0.173572 | − | 0.0335097i | ||||
\(161\) | − | 3.27434i | − | 0.258055i | ||||||
\(162\) | −3.92379 | − | 8.09962i | −0.308282 | − | 0.636367i | ||||
\(163\) | 7.21629 | + | 7.21629i | 0.565224 | + | 0.565224i | 0.930787 | − | 0.365563i | \(-0.119124\pi\) |
−0.365563 | + | 0.930787i | \(0.619124\pi\) | |||||||
\(164\) | −0.882958 | −0.0689474 | ||||||||
\(165\) | −0.200824 | + | 0.249230i | −0.0156341 | + | 0.0194025i | ||||
\(166\) | 12.5104 | 0.970994 | ||||||||
\(167\) | 11.3314 | + | 11.3314i | 0.876846 | + | 0.876846i | 0.993207 | − | 0.116361i | \(-0.0371228\pi\) |
−0.116361 | + | 0.993207i | \(0.537123\pi\) | |||||||
\(168\) | −5.65154 | − | 0.473395i | −0.436026 | − | 0.0365232i | ||||
\(169\) | 4.07197i | 0.313229i | ||||||||
\(170\) | 13.8893 | + | 9.39417i | 1.06526 | + | 0.720500i | ||||
\(171\) | 3.23232 | − | 19.1588i | 0.247181 | − | 1.46511i | ||||
\(172\) | 1.69981 | − | 1.69981i | 0.129609 | − | 0.129609i | ||||
\(173\) | −6.03766 | + | 6.03766i | −0.459035 | + | 0.459035i | −0.898339 | − | 0.439304i | \(-0.855225\pi\) |
0.439304 | + | 0.898339i | \(0.355225\pi\) | |||||||
\(174\) | 2.62629 | − | 2.22032i | 0.199099 | − | 0.168322i | ||||
\(175\) | 15.0539 | + | 6.43528i | 1.13797 | + | 0.486461i | ||||
\(176\) | − | 0.0826422i | − | 0.00622939i | ||||||
\(177\) | 1.45700 | − | 17.3942i | 0.109515 | − | 1.30743i | ||||
\(178\) | −3.99616 | − | 3.99616i | −0.299525 | − | 0.299525i | ||||
\(179\) | 10.2241 | 0.764188 | 0.382094 | − | 0.924123i | \(-0.375203\pi\) | ||||
0.382094 | + | 0.924123i | \(0.375203\pi\) | |||||||
\(180\) | −4.85392 | − | 4.63028i | −0.361790 | − | 0.345121i | ||||
\(181\) | −7.86650 | −0.584712 | −0.292356 | − | 0.956310i | \(-0.594439\pi\) | ||||
−0.292356 | + | 0.956310i | \(0.594439\pi\) | |||||||
\(182\) | −9.56646 | − | 9.56646i | −0.709113 | − | 0.709113i | ||||
\(183\) | 0.126676 | − | 1.51230i | 0.00936416 | − | 0.111792i | ||||
\(184\) | 1.00000i | 0.0737210i | ||||||||
\(185\) | −2.88011 | − | 14.9182i | −0.211750 | − | 1.09681i | ||||
\(186\) | −5.50266 | + | 4.65206i | −0.403475 | + | 0.341106i | ||||
\(187\) | 0.438208 | − | 0.438208i | 0.0320449 | − | 0.0320449i | ||||
\(188\) | 7.63231 | − | 7.63231i | 0.556644 | − | 0.556644i | ||||
\(189\) | 8.66992 | + | 14.6393i | 0.630644 | + | 1.06485i | ||||
\(190\) | −2.74519 | − | 14.2194i | −0.199157 | − | 1.03158i | ||||
\(191\) | − | 23.2816i | − | 1.68460i | −0.539009 | − | 0.842300i | \(-0.681201\pi\) | ||
0.539009 | − | 0.842300i | \(-0.318799\pi\) | |||||||
\(192\) | 1.72601 | + | 0.144577i | 0.124564 | + | 0.0104340i | ||||
\(193\) | −13.3531 | − | 13.3531i | −0.961176 | − | 0.961176i | 0.0380984 | − | 0.999274i | \(-0.487870\pi\) |
−0.999274 | + | 0.0380984i | \(0.987870\pi\) | |||||||
\(194\) | 10.3363 | 0.742107 | ||||||||
\(195\) | −1.71130 | − | 15.9107i | −0.122549 | − | 1.13939i | ||||
\(196\) | 3.72133 | 0.265810 | ||||||||
\(197\) | 3.92746 | + | 3.92746i | 0.279820 | + | 0.279820i | 0.833037 | − | 0.553217i | \(-0.186600\pi\) |
−0.553217 | + | 0.833037i | \(0.686600\pi\) | |||||||
\(198\) | −0.202032 | + | 0.143703i | −0.0143578 | + | 0.0102125i | ||||
\(199\) | 14.6406i | 1.03784i | 0.854822 | + | 0.518921i | \(0.173666\pi\) | ||||
−0.854822 | + | 0.518921i | \(0.826334\pi\) | |||||||
\(200\) | −4.59754 | − | 1.96536i | −0.325095 | − | 0.138972i | ||||
\(201\) | 1.21492 | + | 1.43706i | 0.0856937 | + | 0.101362i | ||||
\(202\) | 2.11885 | − | 2.11885i | 0.149082 | − | 0.149082i | ||||
\(203\) | −4.59717 | + | 4.59717i | −0.322658 | + | 0.322658i | ||||
\(204\) | 8.38549 | + | 9.91872i | 0.587102 | + | 0.694449i | ||||
\(205\) | 1.63541 | + | 1.10613i | 0.114222 | + | 0.0772553i | ||||
\(206\) | − | 11.2075i | − | 0.780866i | ||||||
\(207\) | 2.44466 | − | 1.73886i | 0.169916 | − | 0.120859i | ||||
\(208\) | 2.92164 | + | 2.92164i | 0.202579 | + | 0.202579i | ||||
\(209\) | −0.535234 | −0.0370229 | ||||||||
\(210\) | 9.87469 | + | 7.95679i | 0.681418 | + | 0.549071i | ||||
\(211\) | 1.39261 | 0.0958715 | 0.0479357 | − | 0.998850i | \(-0.484736\pi\) | ||||
0.0479357 | + | 0.998850i | \(0.484736\pi\) | |||||||
\(212\) | −7.26221 | − | 7.26221i | −0.498771 | − | 0.498771i | ||||
\(213\) | 2.94018 | + | 0.246281i | 0.201458 | + | 0.0168749i | ||||
\(214\) | 7.84269i | 0.536115i | ||||||||
\(215\) | −5.27782 | + | 1.01894i | −0.359944 | + | 0.0694908i | ||||
\(216\) | −2.64783 | − | 4.47090i | −0.180162 | − | 0.304206i | ||||
\(217\) | 9.63209 | − | 9.63209i | 0.653869 | − | 0.653869i | ||||
\(218\) | 10.1228 | − | 10.1228i | 0.685605 | − | 0.685605i | ||||
\(219\) | 0.497052 | − | 0.420218i | 0.0335876 | − | 0.0283957i | ||||
\(220\) | −0.103530 | + | 0.153069i | −0.00698000 | + | 0.0103199i | ||||
\(221\) | 30.9839i | 2.08420i | ||||||||
\(222\) | 0.982377 | − | 11.7279i | 0.0659328 | − | 0.787127i | ||||
\(223\) | 16.9943 | + | 16.9943i | 1.13802 | + | 1.13802i | 0.988805 | + | 0.149216i | \(0.0476749\pi\) |
0.149216 | + | 0.988805i | \(0.452325\pi\) | |||||||
\(224\) | −3.27434 | −0.218776 | ||||||||
\(225\) | 3.18980 | + | 14.6569i | 0.212653 | + | 0.977128i | ||||
\(226\) | −2.19171 | −0.145791 | ||||||||
\(227\) | −6.77558 | − | 6.77558i | −0.449711 | − | 0.449711i | 0.445547 | − | 0.895258i | \(-0.353009\pi\) |
−0.895258 | + | 0.445547i | \(0.853009\pi\) | |||||||
\(228\) | 0.936357 | − | 11.1785i | 0.0620117 | − | 0.740316i | ||||
\(229\) | − | 11.6200i | − | 0.767870i | −0.923360 | − | 0.383935i | \(-0.874569\pi\) | ||
0.923360 | − | 0.383935i | \(-0.125431\pi\) | |||||||
\(230\) | 1.25275 | − | 1.85219i | 0.0826040 | − | 0.122130i | ||||
\(231\) | 0.357922 | − | 0.302594i | 0.0235495 | − | 0.0199093i | ||||
\(232\) | 1.40400 | − | 1.40400i | 0.0921770 | − | 0.0921770i | ||||
\(233\) | −12.9668 | + | 12.9668i | −0.849484 | + | 0.849484i | −0.990069 | − | 0.140585i | \(-0.955102\pi\) |
0.140585 | + | 0.990069i | \(0.455102\pi\) | |||||||
\(234\) | 2.06212 | − | 12.2227i | 0.134805 | − | 0.799026i | ||||
\(235\) | −23.6979 | + | 4.57512i | −1.54588 | + | 0.298448i | ||||
\(236\) | − | 10.0777i | − | 0.656003i | ||||||
\(237\) | 29.0077 | + | 2.42980i | 1.88426 | + | 0.157833i | ||||
\(238\) | −17.3621 | − | 17.3621i | −1.12542 | − | 1.12542i | ||||
\(239\) | −6.05401 | −0.391602 | −0.195801 | − | 0.980644i | \(-0.562731\pi\) | ||||
−0.195801 | + | 0.980644i | \(0.562731\pi\) | |||||||
\(240\) | −3.01578 | − | 2.43004i | −0.194667 | − | 0.156858i | ||||
\(241\) | −17.7288 | −1.14201 | −0.571007 | − | 0.820945i | \(-0.693447\pi\) | ||||
−0.571007 | + | 0.820945i | \(0.693447\pi\) | |||||||
\(242\) | −7.77335 | − | 7.77335i | −0.499690 | − | 0.499690i | ||||
\(243\) | −6.32566 | + | 14.2473i | −0.405791 | + | 0.913966i | ||||
\(244\) | − | 0.876183i | − | 0.0560919i | ||||||
\(245\) | −6.89263 | − | 4.66191i | −0.440354 | − | 0.297838i | ||||
\(246\) | 0.987358 | + | 1.16789i | 0.0629517 | + | 0.0744620i | ||||
\(247\) | 18.9221 | − | 18.9221i | 1.20398 | − | 1.20398i | ||||
\(248\) | −2.94168 | + | 2.94168i | −0.186797 | + | 0.186797i | ||||
\(249\) | −13.9896 | − | 16.5475i | −0.886555 | − | 1.04866i | ||||
\(250\) | 6.05341 | + | 9.39980i | 0.382851 | + | 0.594496i | ||||
\(251\) | − | 22.3292i | − | 1.40941i | −0.709501 | − | 0.704705i | \(-0.751079\pi\) | ||
0.709501 | − | 0.704705i | \(-0.248921\pi\) | |||||||
\(252\) | 5.69361 | + | 8.00467i | 0.358664 | + | 0.504247i | ||||
\(253\) | −0.0584368 | − | 0.0584368i | −0.00367389 | − | 0.00367389i | ||||
\(254\) | 3.76049 | 0.235954 | ||||||||
\(255\) | −3.10584 | − | 28.8763i | −0.194495 | − | 1.80830i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.75966 | + | 3.75966i | 0.234521 | + | 0.234521i | 0.814577 | − | 0.580056i | \(-0.196969\pi\) |
−0.580056 | + | 0.814577i | \(0.696969\pi\) | |||||||
\(258\) | −4.14914 | − | 0.347548i | −0.258314 | − | 0.0216374i | ||||
\(259\) | 22.2486i | 1.38246i | ||||||||
\(260\) | −1.75135 | − | 9.07153i | −0.108614 | − | 0.562592i | ||||
\(261\) | −5.87365 | − | 0.990953i | −0.363570 | − | 0.0613385i | ||||
\(262\) | 8.48869 | − | 8.48869i | 0.524433 | − | 0.524433i | ||||
\(263\) | −9.73597 | + | 9.73597i | −0.600346 | + | 0.600346i | −0.940404 | − | 0.340058i | \(-0.889553\pi\) |
0.340058 | + | 0.940404i | \(0.389553\pi\) | |||||||
\(264\) | −0.109311 | + | 0.0924137i | −0.00672763 | + | 0.00568767i | ||||
\(265\) | 4.35326 | + | 22.5487i | 0.267419 | + | 1.38516i | ||||
\(266\) | 21.2064i | 1.30025i | ||||||||
\(267\) | −0.817066 | + | 9.75439i | −0.0500036 | + | 0.596959i | ||||
\(268\) | 0.768241 | + | 0.768241i | 0.0469278 | + | 0.0469278i | ||||
\(269\) | −1.99991 | −0.121937 | −0.0609684 | − | 0.998140i | \(-0.519419\pi\) | ||||
−0.0609684 | + | 0.998140i | \(0.519419\pi\) | |||||||
\(270\) | −0.696637 | + | 11.5980i | −0.0423960 | + | 0.705835i | ||||
\(271\) | −7.75320 | −0.470973 | −0.235487 | − | 0.971878i | \(-0.575668\pi\) | ||||
−0.235487 | + | 0.971878i | \(0.575668\pi\) | |||||||
\(272\) | 5.30247 | + | 5.30247i | 0.321510 | + | 0.321510i | ||||
\(273\) | −1.95599 | + | 23.3512i | −0.118382 | + | 1.41328i | ||||
\(274\) | − | 5.84419i | − | 0.353060i | ||||||
\(275\) | 0.383515 | − | 0.153816i | 0.0231268 | − | 0.00927545i | ||||
\(276\) | 1.32270 | − | 1.11824i | 0.0796173 | − | 0.0673101i | ||||
\(277\) | −8.36272 | + | 8.36272i | −0.502467 | + | 0.502467i | −0.912204 | − | 0.409737i | \(-0.865621\pi\) |
0.409737 | + | 0.912204i | \(0.365621\pi\) | |||||||
\(278\) | −0.306500 | + | 0.306500i | −0.0183826 | + | 0.0183826i | ||||
\(279\) | 12.3066 | + | 2.07627i | 0.736776 | + | 0.124303i | ||||
\(280\) | 6.06471 | + | 4.10194i | 0.362436 | + | 0.245138i | ||||
\(281\) | 10.4388i | 0.622729i | 0.950291 | + | 0.311365i | \(0.100786\pi\) | ||||
−0.950291 | + | 0.311365i | \(0.899214\pi\) | |||||||
\(282\) | −18.6300 | − | 1.56052i | −1.10940 | − | 0.0929279i | ||||
\(283\) | 9.18213 | + | 9.18213i | 0.545821 | + | 0.545821i | 0.925229 | − | 0.379408i | \(-0.123872\pi\) |
−0.379408 | + | 0.925229i | \(0.623872\pi\) | |||||||
\(284\) | 1.70346 | 0.101082 | ||||||||
\(285\) | −15.7382 | + | 19.5317i | −0.932252 | + | 1.15696i | ||||
\(286\) | −0.341463 | −0.0201911 | ||||||||
\(287\) | −2.04432 | − | 2.04432i | −0.120673 | − | 0.120673i | ||||
\(288\) | −1.73886 | − | 2.44466i | −0.102463 | − | 0.144053i | ||||
\(289\) | 39.2325i | 2.30779i | ||||||||
\(290\) | −4.35933 | + | 0.841612i | −0.255989 | + | 0.0494212i | ||||
\(291\) | −11.5585 | − | 13.6719i | −0.677572 | − | 0.801462i | ||||
\(292\) | 0.265720 | − | 0.265720i | 0.0155501 | − | 0.0155501i | ||||
\(293\) | 12.9233 | − | 12.9233i | 0.754988 | − | 0.754988i | −0.220418 | − | 0.975406i | \(-0.570742\pi\) |
0.975406 | + | 0.220418i | \(0.0707421\pi\) | |||||||
\(294\) | −4.16134 | − | 4.92222i | −0.242694 | − | 0.287070i | ||||
\(295\) | −12.6249 | + | 18.6658i | −0.735048 | + | 1.08677i | ||||
\(296\) | − | 6.79483i | − | 0.394942i | ||||||
\(297\) | 0.415997 | + | 0.106534i | 0.0241386 | + | 0.00618176i | ||||
\(298\) | −14.1591 | − | 14.1591i | −0.820212 | − | 0.820212i | ||||
\(299\) | 4.13182 | 0.238950 | ||||||||
\(300\) | 2.54156 | + | 8.27892i | 0.146737 | + | 0.477984i | ||||
\(301\) | 7.87119 | 0.453688 | ||||||||
\(302\) | 12.1615 | + | 12.1615i | 0.699814 | + | 0.699814i | ||||
\(303\) | −5.17198 | − | 0.433226i | −0.297123 | − | 0.0248882i | ||||
\(304\) | − | 6.47652i | − | 0.371454i | ||||||
\(305\) | −1.09764 | + | 1.62286i | −0.0628507 | + | 0.0929246i | ||||
\(306\) | 3.74253 | − | 22.1830i | 0.213946 | − | 1.26812i | ||||
\(307\) | −9.27023 | + | 9.27023i | −0.529080 | + | 0.529080i | −0.920298 | − | 0.391218i | \(-0.872054\pi\) |
0.391218 | + | 0.920298i | \(0.372054\pi\) | |||||||
\(308\) | 0.191342 | − | 0.191342i | 0.0109027 | − | 0.0109027i | ||||
\(309\) | −14.8242 | + | 12.5327i | −0.843321 | + | 0.712961i | ||||
\(310\) | 9.13376 | − | 1.76336i | 0.518763 | − | 0.100152i | ||||
\(311\) | 34.1062i | 1.93399i | 0.254804 | + | 0.966993i | \(0.417989\pi\) | ||||
−0.254804 | + | 0.966993i | \(0.582011\pi\) | |||||||
\(312\) | 0.597367 | − | 7.13155i | 0.0338193 | − | 0.403745i | ||||
\(313\) | −21.0097 | − | 21.0097i | −1.18754 | − | 1.18754i | −0.977745 | − | 0.209795i | \(-0.932720\pi\) |
−0.209795 | − | 0.977745i | \(-0.567280\pi\) | |||||||
\(314\) | −23.3092 | −1.31542 | ||||||||
\(315\) | −0.517796 | − | 21.9589i | −0.0291745 | − | 1.23724i | ||||
\(316\) | 16.8063 | 0.945427 | ||||||||
\(317\) | 1.88900 | + | 1.88900i | 0.106097 | + | 0.106097i | 0.758163 | − | 0.652066i | \(-0.226097\pi\) |
−0.652066 | + | 0.758163i | \(0.726097\pi\) | |||||||
\(318\) | −1.48485 | + | 17.7266i | −0.0832664 | + | 0.994060i | ||||
\(319\) | 0.164090i | 0.00918730i | ||||||||
\(320\) | −1.85219 | − | 1.25275i | −0.103541 | − | 0.0700309i | ||||
\(321\) | 10.3735 | − | 8.77000i | 0.578995 | − | 0.489494i | ||||
\(322\) | −2.31531 | + | 2.31531i | −0.129027 | + | 0.129027i | ||||
\(323\) | 34.3416 | − | 34.3416i | 1.91082 | − | 1.91082i | ||||
\(324\) | −2.95276 | + | 8.50183i | −0.164042 | + | 0.472324i | ||||
\(325\) | −8.12054 | + | 18.9962i | −0.450446 | + | 1.05372i | ||||
\(326\) | − | 10.2054i | − | 0.565224i | ||||||
\(327\) | −24.7092 | − | 2.06974i | −1.36642 | − | 0.114457i | ||||
\(328\) | 0.624346 | + | 0.624346i | 0.0344737 | + | 0.0344737i | ||||
\(329\) | 35.3424 | 1.94849 | ||||||||
\(330\) | 0.318236 | − | 0.0342284i | 0.0175183 | − | 0.00188421i | ||||
\(331\) | −18.4120 | −1.01202 | −0.506008 | − | 0.862529i | \(-0.668879\pi\) | ||||
−0.506008 | + | 0.862529i | \(0.668879\pi\) | |||||||
\(332\) | −8.84618 | − | 8.84618i | −0.485497 | − | 0.485497i | ||||
\(333\) | −16.6111 | + | 11.8152i | −0.910282 | + | 0.647471i | ||||
\(334\) | − | 16.0250i | − | 0.876846i | ||||||
\(335\) | −0.460514 | − | 2.38534i | −0.0251606 | − | 0.130325i | ||||
\(336\) | 3.66150 | + | 4.33098i | 0.199751 | + | 0.236274i | ||||
\(337\) | −4.80586 | + | 4.80586i | −0.261792 | + | 0.261792i | −0.825782 | − | 0.563990i | \(-0.809266\pi\) |
0.563990 | + | 0.825782i | \(0.309266\pi\) | |||||||
\(338\) | 2.87932 | − | 2.87932i | 0.156614 | − | 0.156614i | ||||
\(339\) | 2.45086 | + | 2.89898i | 0.133112 | + | 0.157451i | ||||
\(340\) | −3.17852 | − | 16.4639i | −0.172379 | − | 0.892879i | ||||
\(341\) | − | 0.343805i | − | 0.0186181i | ||||||
\(342\) | −15.8329 | + | 11.2617i | −0.856146 | + | 0.608965i | ||||
\(343\) | −7.59113 | − | 7.59113i | −0.409883 | − | 0.409883i | ||||
\(344\) | −2.40390 | −0.129609 | ||||||||
\(345\) | −3.85077 | + | 0.414176i | −0.207319 | + | 0.0222985i | ||||
\(346\) | 8.53854 | 0.459035 | ||||||||
\(347\) | −17.1222 | − | 17.1222i | −0.919167 | − | 0.919167i | 0.0778017 | − | 0.996969i | \(-0.475210\pi\) |
−0.996969 | + | 0.0778017i | \(0.975210\pi\) | |||||||
\(348\) | −3.42708 | − | 0.287065i | −0.183711 | − | 0.0153883i | ||||
\(349\) | − | 2.01226i | − | 0.107714i | −0.998549 | − | 0.0538569i | \(-0.982849\pi\) | ||
0.998549 | − | 0.0538569i | \(-0.0171515\pi\) | |||||||
\(350\) | −6.09430 | − | 15.1952i | −0.325754 | − | 0.812215i | ||||
\(351\) | −18.4730 | + | 10.9404i | −0.986015 | + | 0.583954i | ||||
\(352\) | −0.0584368 | + | 0.0584368i | −0.00311469 | + | 0.00311469i | ||||
\(353\) | −23.0099 | + | 23.0099i | −1.22469 | + | 1.22469i | −0.258749 | + | 0.965945i | \(0.583310\pi\) |
−0.965945 | + | 0.258749i | \(0.916690\pi\) | |||||||
\(354\) | −13.3298 | + | 11.2693i | −0.708471 | + | 0.598956i | ||||
\(355\) | −3.15513 | − | 2.13401i | −0.167457 | − | 0.113261i | ||||
\(356\) | 5.65142i | 0.299525i | ||||||||
\(357\) | −3.54991 | + | 42.3799i | −0.187881 | + | 2.24298i | ||||
\(358\) | −7.22956 | − | 7.22956i | −0.382094 | − | 0.382094i | ||||
\(359\) | 19.5535 | 1.03199 | 0.515996 | − | 0.856591i | \(-0.327422\pi\) | ||||
0.515996 | + | 0.856591i | \(0.327422\pi\) | |||||||
\(360\) | 0.158137 | + | 6.70634i | 0.00833457 | + | 0.353455i | ||||
\(361\) | −22.9454 | −1.20765 | ||||||||
\(362\) | 5.56245 | + | 5.56245i | 0.292356 | + | 0.292356i | ||||
\(363\) | −1.58936 | + | 18.9743i | −0.0834198 | + | 0.995891i | ||||
\(364\) | 13.5290i | 0.709113i | ||||||||
\(365\) | −0.825046 | + | 0.159283i | −0.0431849 | + | 0.00833727i | ||||
\(366\) | −1.15893 | + | 0.979782i | −0.0605782 | + | 0.0512140i | ||||
\(367\) | 6.00838 | − | 6.00838i | 0.313635 | − | 0.313635i | −0.532681 | − | 0.846316i | \(-0.678815\pi\) |
0.846316 | + | 0.532681i | \(0.178815\pi\) | |||||||
\(368\) | 0.707107 | − | 0.707107i | 0.0368605 | − | 0.0368605i | ||||
\(369\) | 0.440668 | − | 2.61196i | 0.0229403 | − | 0.135973i | ||||
\(370\) | −8.51224 | + | 12.5853i | −0.442530 | + | 0.654280i | ||||
\(371\) | − | 33.6286i | − | 1.74591i | ||||||
\(372\) | 7.18048 | + | 0.601465i | 0.372290 | + | 0.0311845i | ||||
\(373\) | −18.4696 | − | 18.4696i | −0.956318 | − | 0.956318i | 0.0427675 | − | 0.999085i | \(-0.486383\pi\) |
−0.999085 | + | 0.0427675i | \(0.986383\pi\) | |||||||
\(374\) | −0.619720 | −0.0320449 | ||||||||
\(375\) | 5.66398 | − | 18.5181i | 0.292487 | − | 0.956270i | ||||
\(376\) | −10.7937 | −0.556644 | ||||||||
\(377\) | −5.80107 | − | 5.80107i | −0.298770 | − | 0.298770i | ||||
\(378\) | 4.22098 | − | 16.4821i | 0.217104 | − | 0.847747i | ||||
\(379\) | 2.21381i | 0.113716i | 0.998382 | + | 0.0568579i | \(0.0181082\pi\) | ||||
−0.998382 | + | 0.0568579i | \(0.981892\pi\) | |||||||
\(380\) | −8.11347 | + | 11.9958i | −0.416212 | + | 0.615370i | ||||
\(381\) | −4.20513 | − | 4.97401i | −0.215435 | − | 0.254826i | ||||
\(382\) | −16.4626 | + | 16.4626i | −0.842300 | + | 0.842300i | ||||
\(383\) | 24.0015 | − | 24.0015i | 1.22642 | − | 1.22642i | 0.261112 | − | 0.965308i | \(-0.415911\pi\) |
0.965308 | − | 0.261112i | \(-0.0840893\pi\) | |||||||
\(384\) | −1.11824 | − | 1.32270i | −0.0570649 | − | 0.0674989i | ||||
\(385\) | −0.594107 | + | 0.114698i | −0.0302785 | + | 0.00584557i | ||||
\(386\) | 18.8841i | 0.961176i | ||||||||
\(387\) | 4.18003 | + | 5.87672i | 0.212483 | + | 0.298730i | ||||
\(388\) | −7.30890 | − | 7.30890i | −0.371053 | − | 0.371053i | ||||
\(389\) | 8.89237 | 0.450861 | 0.225431 | − | 0.974259i | \(-0.427621\pi\) | ||||
0.225431 | + | 0.974259i | \(0.427621\pi\) | |||||||
\(390\) | −10.0405 | + | 12.4607i | −0.508421 | + | 0.630970i | ||||
\(391\) | 7.49883 | 0.379232 | ||||||||
\(392\) | −2.63138 | − | 2.63138i | −0.132905 | − | 0.132905i | ||||
\(393\) | −20.7204 | − | 1.73562i | −1.04521 | − | 0.0875505i | ||||
\(394\) | − | 5.55427i | − | 0.279820i | ||||||
\(395\) | −31.1284 | − | 21.0541i | −1.56624 | − | 1.05935i | ||||
\(396\) | 0.244472 | + | 0.0412452i | 0.0122852 | + | 0.00207265i | ||||
\(397\) | 21.4168 | − | 21.4168i | 1.07488 | − | 1.07488i | 0.0779195 | − | 0.996960i | \(-0.475172\pi\) |
0.996960 | − | 0.0779195i | \(-0.0248277\pi\) | |||||||
\(398\) | 10.3524 | − | 10.3524i | 0.518921 | − | 0.518921i | ||||
\(399\) | 28.0497 | − | 23.7138i | 1.40424 | − | 1.18717i | ||||
\(400\) | 1.86123 | + | 4.64067i | 0.0930614 | + | 0.232034i | ||||
\(401\) | − | 32.8935i | − | 1.64262i | −0.570480 | − | 0.821312i | \(-0.693243\pi\) | ||
0.570480 | − | 0.821312i | \(-0.306757\pi\) | |||||||
\(402\) | 0.157077 | − | 1.87523i | 0.00783428 | − | 0.0935280i | ||||
\(403\) | 12.1545 | + | 12.1545i | 0.605460 | + | 0.605460i | ||||
\(404\) | −2.99650 | −0.149082 | ||||||||
\(405\) | 16.1198 | − | 12.0479i | 0.800998 | − | 0.598667i | ||||
\(406\) | 6.50138 | 0.322658 | ||||||||
\(407\) | 0.397069 | + | 0.397069i | 0.0196820 | + | 0.0196820i | ||||
\(408\) | 1.08416 | − | 12.9430i | 0.0536739 | − | 0.640775i | ||||
\(409\) | − | 29.4036i | − | 1.45392i | −0.686682 | − | 0.726958i | \(-0.740934\pi\) | ||
0.686682 | − | 0.726958i | \(-0.259066\pi\) | |||||||
\(410\) | −0.374258 | − | 1.93856i | −0.0184833 | − | 0.0957385i | ||||
\(411\) | −7.73012 | + | 6.53520i | −0.381299 | + | 0.322358i | ||||
\(412\) | −7.92493 | + | 7.92493i | −0.390433 | + | 0.390433i | ||||
\(413\) | 23.3330 | − | 23.3330i | 1.14814 | − | 1.14814i | ||||
\(414\) | −2.95819 | − | 0.499082i | −0.145387 | − | 0.0245285i | ||||
\(415\) | 5.30275 | + | 27.4669i | 0.260302 | + | 1.34830i | ||||
\(416\) | − | 4.13182i | − | 0.202579i | ||||||
\(417\) | 0.748148 | + | 0.0626678i | 0.0366369 | + | 0.00306885i | ||||
\(418\) | 0.378468 | + | 0.378468i | 0.0185115 | + | 0.0185115i | ||||
\(419\) | 4.84269 | 0.236581 | 0.118290 | − | 0.992979i | \(-0.462259\pi\) | ||||
0.118290 | + | 0.992979i | \(0.462259\pi\) | |||||||
\(420\) | −1.35616 | − | 12.6088i | −0.0661736 | − | 0.615245i | ||||
\(421\) | 19.4455 | 0.947714 | 0.473857 | − | 0.880602i | \(-0.342861\pi\) | ||||
0.473857 | + | 0.880602i | \(0.342861\pi\) | |||||||
\(422\) | −0.984727 | − | 0.984727i | −0.0479357 | − | 0.0479357i | ||||
\(423\) | 18.7687 | + | 26.3870i | 0.912567 | + | 1.28298i | ||||
\(424\) | 10.2703i | 0.498771i | ||||||||
\(425\) | −14.7379 | + | 34.4762i | −0.714895 | + | 1.67234i | ||||
\(426\) | −1.90487 | − | 2.25317i | −0.0922913 | − | 0.109166i | ||||
\(427\) | 2.02864 | − | 2.02864i | 0.0981726 | − | 0.0981726i | ||||
\(428\) | 5.54562 | − | 5.54562i | 0.268058 | − | 0.268058i | ||||
\(429\) | 0.381837 | + | 0.451654i | 0.0184353 | + | 0.0218061i | ||||
\(430\) | 4.45248 | + | 3.01148i | 0.214717 | + | 0.145227i | ||||
\(431\) | − | 23.4150i | − | 1.12786i | −0.825822 | − | 0.563932i | \(-0.809288\pi\) | ||
0.825822 | − | 0.563932i | \(-0.190712\pi\) | |||||||
\(432\) | −1.28911 | + | 5.03371i | −0.0620221 | + | 0.242184i | ||||
\(433\) | −18.6129 | − | 18.6129i | −0.894478 | − | 0.894478i | 0.100463 | − | 0.994941i | \(-0.467968\pi\) |
−0.994941 | + | 0.100463i | \(0.967968\pi\) | |||||||
\(434\) | −13.6218 | −0.653869 | ||||||||
\(435\) | 5.98798 | + | 4.82497i | 0.287102 | + | 0.231340i | ||||
\(436\) | −14.3159 | −0.685605 | ||||||||
\(437\) | −4.57959 | − | 4.57959i | −0.219072 | − | 0.219072i | ||||
\(438\) | −0.648607 | − | 0.0543299i | −0.0309917 | − | 0.00259598i | ||||
\(439\) | − | 2.74419i | − | 0.130973i | −0.997853 | − | 0.0654864i | \(-0.979140\pi\) | ||
0.997853 | − | 0.0654864i | \(-0.0208599\pi\) | |||||||
\(440\) | 0.181443 | − | 0.0350294i | 0.00864996 | − | 0.00166996i | ||||
\(441\) | −1.85725 | + | 11.0084i | −0.0884405 | + | 0.524211i | ||||
\(442\) | 21.9089 | − | 21.9089i | 1.04210 | − | 1.04210i | ||||
\(443\) | −5.24175 | + | 5.24175i | −0.249043 | + | 0.249043i | −0.820578 | − | 0.571535i | \(-0.806348\pi\) |
0.571535 | + | 0.820578i | \(0.306348\pi\) | |||||||
\(444\) | −8.98754 | + | 7.59825i | −0.426530 | + | 0.360597i | ||||
\(445\) | 7.07983 | − | 10.4675i | 0.335616 | − | 0.496208i | ||||
\(446\) | − | 24.0335i | − | 1.13802i | ||||||
\(447\) | −2.89500 | + | 34.5614i | −0.136929 | + | 1.63470i | ||||
\(448\) | 2.31531 | + | 2.31531i | 0.109388 | + | 0.109388i | ||||
\(449\) | −4.17586 | −0.197071 | −0.0985356 | − | 0.995134i | \(-0.531416\pi\) | ||||
−0.0985356 | + | 0.995134i | \(0.531416\pi\) | |||||||
\(450\) | 8.10848 | − | 12.6195i | 0.382237 | − | 0.594890i | ||||
\(451\) | −0.0729696 | −0.00343600 | ||||||||
\(452\) | 1.54977 | + | 1.54977i | 0.0728953 | + | 0.0728953i | ||||
\(453\) | 2.48657 | − | 29.6854i | 0.116829 | − | 1.39474i | ||||
\(454\) | 9.58212i | 0.449711i | ||||||||
\(455\) | 16.9485 | − | 25.0583i | 0.794558 | − | 1.17475i | ||||
\(456\) | −8.56651 | + | 7.24230i | −0.401164 | + | 0.339152i | ||||
\(457\) | 3.72841 | − | 3.72841i | 0.174408 | − | 0.174408i | −0.614505 | − | 0.788913i | \(-0.710644\pi\) |
0.788913 | + | 0.614505i | \(0.210644\pi\) | |||||||
\(458\) | −8.21656 | + | 8.21656i | −0.383935 | + | 0.383935i | ||||
\(459\) | −33.5266 | + | 19.8557i | −1.56489 | + | 0.926783i | ||||
\(460\) | −2.19553 | + | 0.423868i | −0.102367 | + | 0.0197630i | ||||
\(461\) | − | 11.3512i | − | 0.528680i | −0.964430 | − | 0.264340i | \(-0.914846\pi\) | ||
0.964430 | − | 0.264340i | \(-0.0851541\pi\) | |||||||
\(462\) | −0.467056 | − | 0.0391224i | −0.0217294 | − | 0.00182014i | ||||
\(463\) | 15.3561 | + | 15.3561i | 0.713657 | + | 0.713657i | 0.967298 | − | 0.253641i | \(-0.0816282\pi\) |
−0.253641 | + | 0.967298i | \(0.581628\pi\) | |||||||
\(464\) | −1.98555 | −0.0921770 | ||||||||
\(465\) | −12.5461 | − | 10.1094i | −0.581813 | − | 0.468811i | ||||
\(466\) | 18.3378 | 0.849484 | ||||||||
\(467\) | 5.99931 | + | 5.99931i | 0.277615 | + | 0.277615i | 0.832156 | − | 0.554541i | \(-0.187106\pi\) |
−0.554541 | + | 0.832156i | \(0.687106\pi\) | |||||||
\(468\) | −10.1009 | + | 7.18465i | −0.466915 | + | 0.332110i | ||||
\(469\) | 3.55743i | 0.164267i | ||||||||
\(470\) | 19.9920 | + | 13.5219i | 0.922164 | + | 0.623717i | ||||
\(471\) | 26.0653 | + | 30.8312i | 1.20103 | + | 1.42063i | ||||
\(472\) | −7.12601 | + | 7.12601i | −0.328001 | + | 0.328001i | ||||
\(473\) | 0.140476 | − | 0.140476i | 0.00645910 | − | 0.00645910i | ||||
\(474\) | −18.7934 | − | 22.2297i | −0.863211 | − | 1.02104i | ||||
\(475\) | 30.0554 | − | 12.0543i | 1.37904 | − | 0.553088i | ||||
\(476\) | 24.5538i | 1.12542i | ||||||||
\(477\) | 25.1075 | − | 17.8586i | 1.14959 | − | 0.817689i | ||||
\(478\) | 4.28083 | + | 4.28083i | 0.195801 | + | 0.195801i | ||||
\(479\) | −31.7615 | −1.45122 | −0.725611 | − | 0.688105i | \(-0.758443\pi\) | ||||
−0.725611 | + | 0.688105i | \(0.758443\pi\) | |||||||
\(480\) | 0.414176 | + | 3.85077i | 0.0189045 | + | 0.175763i | ||||
\(481\) | −28.0751 | −1.28011 | ||||||||
\(482\) | 12.5362 | + | 12.5362i | 0.571007 | + | 0.571007i | ||||
\(483\) | 5.65154 | + | 0.473395i | 0.257154 | + | 0.0215402i | ||||
\(484\) | 10.9932i | 0.499690i | ||||||||
\(485\) | 4.38125 | + | 22.6937i | 0.198942 | + | 1.03047i | ||||
\(486\) | 14.5473 | − | 5.60146i | 0.659878 | − | 0.254087i | ||||
\(487\) | 8.53395 | − | 8.53395i | 0.386710 | − | 0.386710i | −0.486802 | − | 0.873512i | \(-0.661837\pi\) |
0.873512 | + | 0.486802i | \(0.161837\pi\) | |||||||
\(488\) | −0.619555 | + | 0.619555i | −0.0280459 | + | 0.0280459i | ||||
\(489\) | −13.4987 | + | 11.4121i | −0.610431 | + | 0.516071i | ||||
\(490\) | 1.57736 | + | 8.17029i | 0.0712577 | + | 0.369096i | ||||
\(491\) | − | 15.5734i | − | 0.702820i | −0.936222 | − | 0.351410i | \(-0.885702\pi\) | ||
0.936222 | − | 0.351410i | \(-0.114298\pi\) | |||||||
\(492\) | 0.127655 | − | 1.52399i | 0.00575515 | − | 0.0687068i | ||||
\(493\) | −10.5283 | − | 10.5283i | −0.474173 | − | 0.474173i | ||||
\(494\) | −26.7599 | −1.20398 | ||||||||
\(495\) | −0.401138 | − | 0.382656i | −0.0180298 | − | 0.0171991i | ||||
\(496\) | 4.16017 | 0.186797 | ||||||||
\(497\) | 3.94403 | + | 3.94403i | 0.176914 | + | 0.176914i | ||||
\(498\) | −1.80871 | + | 21.5930i | −0.0810504 | + | 0.967605i | ||||
\(499\) | − | 29.9183i | − | 1.33933i | −0.742664 | − | 0.669664i | \(-0.766438\pi\) | ||
0.742664 | − | 0.669664i | \(-0.233562\pi\) | |||||||
\(500\) | 2.36626 | − | 10.9271i | 0.105822 | − | 0.488673i | ||||
\(501\) | −21.1962 | + | 17.9197i | −0.946978 | + | 0.800595i | ||||
\(502\) | −15.7892 | + | 15.7892i | −0.704705 | + | 0.704705i | ||||
\(503\) | −3.60669 | + | 3.60669i | −0.160814 | + | 0.160814i | −0.782927 | − | 0.622113i | \(-0.786274\pi\) |
0.622113 | + | 0.782927i | \(0.286274\pi\) | |||||||
\(504\) | 1.63417 | − | 9.68615i | 0.0727915 | − | 0.431455i | ||||
\(505\) | 5.55010 | + | 3.75387i | 0.246976 | + | 0.167045i | ||||
\(506\) | 0.0826422i | 0.00367389i | ||||||||
\(507\) | −7.02825 | − | 0.588714i | −0.312136 | − | 0.0261457i | ||||
\(508\) | −2.65907 | − | 2.65907i | −0.117977 | − | 0.117977i | ||||
\(509\) | −28.7783 | −1.27558 | −0.637789 | − | 0.770211i | \(-0.720151\pi\) | ||||
−0.637789 | + | 0.770211i | \(0.720151\pi\) | |||||||
\(510\) | −18.2225 | + | 22.6148i | −0.806904 | + | 1.00140i | ||||
\(511\) | 1.23045 | 0.0544319 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 32.6009 | + | 8.34892i | 1.43937 | + | 0.368614i | ||||
\(514\) | − | 5.31696i | − | 0.234521i | ||||||
\(515\) | 24.6065 | − | 4.75052i | 1.08429 | − | 0.209333i | ||||
\(516\) | 2.68813 | + | 3.17964i | 0.118338 | + | 0.139976i | ||||
\(517\) | 0.630751 | − | 0.630751i | 0.0277404 | − | 0.0277404i | ||||
\(518\) | 15.7322 | − | 15.7322i | 0.691231 | − | 0.691231i | ||||
\(519\) | −9.54813 | − | 11.2939i | −0.419116 | − | 0.495749i | ||||
\(520\) | −5.17615 | + | 7.65293i | −0.226989 | + | 0.335603i | ||||
\(521\) | − | 10.8265i | − | 0.474319i | −0.971471 | − | 0.237159i | \(-0.923784\pi\) | ||
0.971471 | − | 0.237159i | \(-0.0762164\pi\) | |||||||
\(522\) | 3.45259 | + | 4.85401i | 0.151116 | + | 0.212454i | ||||
\(523\) | 0.723443 | + | 0.723443i | 0.0316339 | + | 0.0316339i | 0.722747 | − | 0.691113i | \(-0.242879\pi\) |
−0.691113 | + | 0.722747i | \(0.742879\pi\) | |||||||
\(524\) | −12.0048 | −0.524433 | ||||||||
\(525\) | −13.2838 | + | 25.0528i | −0.579752 | + | 1.09339i | ||||
\(526\) | 13.7687 | 0.600346 | ||||||||
\(527\) | 22.0592 | + | 22.0592i | 0.960913 | + | 0.960913i | ||||
\(528\) | 0.142641 | + | 0.0119482i | 0.00620765 | + | 0.000519977i | ||||
\(529\) | − | 1.00000i | − | 0.0434783i | ||||||
\(530\) | 12.8662 | − | 19.0226i | 0.558870 | − | 0.826289i | ||||
\(531\) | 29.8118 | + | 5.02960i | 1.29372 | + | 0.218266i | ||||
\(532\) | 14.9952 | − | 14.9952i | 0.650123 | − | 0.650123i | ||||
\(533\) | 2.57969 | − | 2.57969i | 0.111739 | − | 0.111739i | ||||
\(534\) | 7.47515 | − | 6.31964i | 0.323481 | − | 0.273478i | ||||
\(535\) | −17.2188 | + | 3.32427i | −0.744435 | + | 0.143721i | ||||
\(536\) | − | 1.08646i | − | 0.0469278i | ||||||
\(537\) | −1.47818 | + | 17.6469i | −0.0637880 | + | 0.761521i | ||||
\(538\) | 1.41415 | + | 1.41415i | 0.0609684 | + | 0.0609684i | ||||
\(539\) | 0.307539 | 0.0132467 | ||||||||
\(540\) | 8.69365 | − | 7.70846i | 0.374115 | − | 0.331719i | ||||
\(541\) | −1.29260 | −0.0555732 | −0.0277866 | − | 0.999614i | \(-0.508846\pi\) | ||||
−0.0277866 | + | 0.999614i | \(0.508846\pi\) | |||||||
\(542\) | 5.48234 | + | 5.48234i | 0.235487 | + | 0.235487i | ||||
\(543\) | 1.13732 | − | 13.5776i | 0.0488069 | − | 0.582672i | ||||
\(544\) | − | 7.49883i | − | 0.321510i | ||||||
\(545\) | 26.5157 | + | 17.9342i | 1.13581 | + | 0.768217i | ||||
\(546\) | 17.8949 | − | 15.1287i | 0.765829 | − | 0.647448i | ||||
\(547\) | 2.94655 | − | 2.94655i | 0.125985 | − | 0.125985i | −0.641303 | − | 0.767288i | \(-0.721606\pi\) |
0.767288 | + | 0.641303i | \(0.221606\pi\) | |||||||
\(548\) | −4.13246 | + | 4.13246i | −0.176530 | + | 0.176530i | ||||
\(549\) | 2.59192 | + | 0.437287i | 0.110620 | + | 0.0186630i | ||||
\(550\) | −0.379950 | − | 0.162422i | −0.0162011 | − | 0.00692570i | ||||
\(551\) | 12.8595i | 0.547832i | ||||||||
\(552\) | −1.72601 | − | 0.144577i | −0.0734637 | − | 0.00615361i | ||||
\(553\) | 38.9118 | + | 38.9118i | 1.65470 | + | 1.65470i | ||||
\(554\) | 11.8267 | 0.502467 | ||||||||
\(555\) | 26.1654 | − | 2.81426i | 1.11066 | − | 0.119459i | ||||
\(556\) | 0.433456 | 0.0183826 | ||||||||
\(557\) | 1.34754 | + | 1.34754i | 0.0570969 | + | 0.0570969i | 0.735079 | − | 0.677982i | \(-0.237145\pi\) |
−0.677982 | + | 0.735079i | \(0.737145\pi\) | |||||||
\(558\) | −7.23393 | − | 10.1702i | −0.306237 | − | 0.430540i | ||||
\(559\) | 9.93248i | 0.420099i | ||||||||
\(560\) | −1.38789 | − | 7.18891i | −0.0586491 | − | 0.303787i | ||||
\(561\) | 0.692995 | + | 0.819705i | 0.0292583 | + | 0.0346080i | ||||
\(562\) | 7.38138 | − | 7.38138i | 0.311365 | − | 0.311365i | ||||
\(563\) | 6.51282 | − | 6.51282i | 0.274483 | − | 0.274483i | −0.556419 | − | 0.830902i | \(-0.687825\pi\) |
0.830902 | + | 0.556419i | \(0.187825\pi\) | |||||||
\(564\) | 12.0700 | + | 14.2769i | 0.508237 | + | 0.601165i | ||||
\(565\) | −0.928997 | − | 4.81196i | −0.0390832 | − | 0.202441i | ||||
\(566\) | − | 12.9855i | − | 0.545821i | ||||||
\(567\) | −26.5210 | + | 12.8478i | −1.11378 | + | 0.539558i | ||||
\(568\) | −1.20453 | − | 1.20453i | −0.0505408 | − | 0.0505408i | ||||
\(569\) | −11.6625 | −0.488917 | −0.244458 | − | 0.969660i | \(-0.578610\pi\) | ||||
−0.244458 | + | 0.969660i | \(0.578610\pi\) | |||||||
\(570\) | 24.9396 | − | 2.68242i | 1.04461 | − | 0.112354i | ||||
\(571\) | −30.0173 | −1.25619 | −0.628093 | − | 0.778138i | \(-0.716164\pi\) | ||||
−0.628093 | + | 0.778138i | \(0.716164\pi\) | |||||||
\(572\) | 0.241451 | + | 0.241451i | 0.0100956 | + | 0.0100956i | ||||
\(573\) | 40.1842 | + | 3.36599i | 1.67872 | + | 0.140616i | ||||
\(574\) | 2.89111i | 0.120673i | ||||||||
\(575\) | 4.59754 | + | 1.96536i | 0.191731 | + | 0.0819613i | ||||
\(576\) | −0.499082 | + | 2.95819i | −0.0207951 | + | 0.123258i | ||||
\(577\) | 30.9222 | − | 30.9222i | 1.28731 | − | 1.28731i | 0.350894 | − | 0.936415i | \(-0.385878\pi\) |
0.936415 | − | 0.350894i | \(-0.114122\pi\) | |||||||
\(578\) | 27.7415 | − | 27.7415i | 1.15390 | − | 1.15390i | ||||
\(579\) | 24.9780 | − | 21.1169i | 1.03805 | − | 0.877590i | ||||
\(580\) | 3.67762 | + | 2.48740i | 0.152705 | + | 0.103284i | ||||
\(581\) | − | 40.9633i | − | 1.69944i | ||||||
\(582\) | −1.49440 | + | 17.8406i | −0.0619448 | + | 0.739517i | ||||
\(583\) | −0.600165 | − | 0.600165i | −0.0248563 | − | 0.0248563i | ||||
\(584\) | −0.375785 | −0.0155501 | ||||||||
\(585\) | 27.7094 | − | 0.653396i | 1.14564 | − | 0.0270146i | ||||
\(586\) | −18.2763 | −0.754988 | ||||||||
\(587\) | −22.4198 | − | 22.4198i | −0.925363 | − | 0.925363i | 0.0720385 | − | 0.997402i | \(-0.477050\pi\) |
−0.997402 | + | 0.0720385i | \(0.977050\pi\) | |||||||
\(588\) | −0.538020 | + | 6.42305i | −0.0221876 | + | 0.264882i | ||||
\(589\) | − | 26.9434i | − | 1.11018i | ||||||
\(590\) | 22.1259 | − | 4.27162i | 0.910907 | − | 0.175860i | ||||
\(591\) | −7.34664 | + | 6.21100i | −0.302201 | + | 0.255486i | ||||
\(592\) | −4.80467 | + | 4.80467i | −0.197471 | + | 0.197471i | ||||
\(593\) | −1.81620 | + | 1.81620i | −0.0745825 | + | 0.0745825i | −0.743414 | − | 0.668831i | \(-0.766795\pi\) |
0.668831 | + | 0.743414i | \(0.266795\pi\) | |||||||
\(594\) | −0.218823 | − | 0.369485i | −0.00897840 | − | 0.0151602i | ||||
\(595\) | 30.7598 | − | 45.4783i | 1.26103 | − | 1.86443i | ||||
\(596\) | 20.0239i | 0.820212i | ||||||||
\(597\) | −25.2697 | − | 2.11669i | −1.03422 | − | 0.0866304i | ||||
\(598\) | −2.92164 | − | 2.92164i | −0.119475 | − | 0.119475i | ||||
\(599\) | 8.91093 | 0.364091 | 0.182045 | − | 0.983290i | \(-0.441728\pi\) | ||||
0.182045 | + | 0.983290i | \(0.441728\pi\) | |||||||
\(600\) | 4.05693 | − | 7.65123i | 0.165623 | − | 0.312360i | ||||
\(601\) | −45.6488 | −1.86205 | −0.931027 | − | 0.364951i | \(-0.881086\pi\) | ||||
−0.931027 | + | 0.364951i | \(0.881086\pi\) | |||||||
\(602\) | −5.56577 | − | 5.56577i | −0.226844 | − | 0.226844i | ||||
\(603\) | −2.65602 | + | 1.88919i | −0.108162 | + | 0.0769338i | ||||
\(604\) | − | 17.1989i | − | 0.699814i | ||||||
\(605\) | 13.7717 | − | 20.3615i | 0.559900 | − | 0.827811i | ||||
\(606\) | 3.35081 | + | 3.96348i | 0.136117 | + | 0.161005i | ||||
\(607\) | −14.6214 | + | 14.6214i | −0.593463 | + | 0.593463i | −0.938565 | − | 0.345102i | \(-0.887844\pi\) |
0.345102 | + | 0.938565i | \(0.387844\pi\) | |||||||
\(608\) | −4.57959 | + | 4.57959i | −0.185727 | + | 0.185727i | ||||
\(609\) | −7.27010 | − | 8.59939i | −0.294599 | − | 0.348465i | ||||
\(610\) | 1.92368 | − | 0.371386i | 0.0778877 | − | 0.0150370i | ||||
\(611\) | 44.5978i | 1.80423i | ||||||||
\(612\) | −18.3321 | + | 13.0394i | −0.741032 | + | 0.527086i | ||||
\(613\) | 25.3682 | + | 25.3682i | 1.02461 | + | 1.02461i | 0.999689 | + | 0.0249223i | \(0.00793383\pi\) |
0.0249223 | + | 0.999689i | \(0.492066\pi\) | |||||||
\(614\) | 13.1101 | 0.529080 | ||||||||
\(615\) | −2.14562 | + | 2.66280i | −0.0865199 | + | 0.107375i | ||||
\(616\) | −0.270599 | −0.0109027 | ||||||||
\(617\) | 15.8956 | + | 15.8956i | 0.639931 | + | 0.639931i | 0.950538 | − | 0.310607i | \(-0.100532\pi\) |
−0.310607 | + | 0.950538i | \(0.600532\pi\) | |||||||
\(618\) | 19.3443 | + | 1.62035i | 0.778141 | + | 0.0651802i | ||||
\(619\) | − | 40.8815i | − | 1.64317i | −0.570088 | − | 0.821584i | \(-0.693091\pi\) | ||
0.570088 | − | 0.821584i | \(-0.306909\pi\) | |||||||
\(620\) | −7.70543 | − | 5.21166i | −0.309458 | − | 0.209305i | ||||
\(621\) | 2.64783 | + | 4.47090i | 0.106254 | + | 0.179411i | ||||
\(622\) | 24.1167 | − | 24.1167i | 0.966993 | − | 0.966993i | ||||
\(623\) | −13.0848 | + | 13.0848i | −0.524231 | + | 0.524231i | ||||
\(624\) | −5.46517 | + | 4.62037i | −0.218782 | + | 0.184963i | ||||
\(625\) | −18.0717 | + | 17.2747i | −0.722867 | + | 0.690988i | ||||
\(626\) | 29.7123i | 1.18754i | ||||||||
\(627\) | 0.0773826 | − | 0.923817i | 0.00309036 | − | 0.0368937i | ||||
\(628\) | 16.4821 | + | 16.4821i | 0.657708 | + | 0.657708i | ||||
\(629\) | −50.9533 | −2.03164 | ||||||||
\(630\) | −15.1611 | + | 15.8934i | −0.604034 | + | 0.633208i | ||||
\(631\) | −0.512624 | −0.0204072 | −0.0102036 | − | 0.999948i | \(-0.503248\pi\) | ||||
−0.0102036 | + | 0.999948i | \(0.503248\pi\) | |||||||
\(632\) | −11.8838 | − | 11.8838i | −0.472714 | − | 0.472714i | ||||
\(633\) | −0.201340 | + | 2.40366i | −0.00800255 | + | 0.0955369i | ||||
\(634\) | − | 2.67145i | − | 0.106097i | ||||||
\(635\) | 1.59395 | + | 8.25625i | 0.0632540 | + | 0.327639i | ||||
\(636\) | 13.5846 | − | 11.4847i | 0.538663 | − | 0.455397i | ||||
\(637\) | −10.8724 | + | 10.8724i | −0.430780 | + | 0.430780i | ||||
\(638\) | 0.116029 | − | 0.116029i | 0.00459365 | − | 0.00459365i | ||||
\(639\) | −0.850164 | + | 5.03916i | −0.0336320 | + | 0.199346i | ||||
\(640\) | 0.423868 | + | 2.19553i | 0.0167549 | + | 0.0867858i | ||||
\(641\) | 41.0820i | 1.62264i | 0.584600 | + | 0.811322i | \(0.301251\pi\) | ||||
−0.584600 | + | 0.811322i | \(0.698749\pi\) | |||||||
\(642\) | −13.5365 | − | 1.13387i | −0.534244 | − | 0.0447504i | ||||
\(643\) | −11.1338 | − | 11.1338i | −0.439076 | − | 0.439076i | 0.452625 | − | 0.891701i | \(-0.350488\pi\) |
−0.891701 | + | 0.452625i | \(0.850488\pi\) | |||||||
\(644\) | 3.27434 | 0.129027 | ||||||||
\(645\) | −0.995637 | − | 9.25686i | −0.0392032 | − | 0.364489i | ||||
\(646\) | −48.5664 | −1.91082 | ||||||||
\(647\) | −19.7653 | − | 19.7653i | −0.777052 | − | 0.777052i | 0.202276 | − | 0.979329i | \(-0.435166\pi\) |
−0.979329 | + | 0.202276i | \(0.935166\pi\) | |||||||
\(648\) | 8.09962 | − | 3.92379i | 0.318183 | − | 0.154141i | ||||
\(649\) | − | 0.832843i | − | 0.0326920i | ||||||
\(650\) | 19.1744 | − | 7.69027i | 0.752083 | − | 0.301637i | ||||
\(651\) | 15.2325 | + | 18.0176i | 0.597007 | + | 0.706166i | ||||
\(652\) | −7.21629 | + | 7.21629i | −0.282612 | + | 0.282612i | ||||
\(653\) | 1.85033 | − | 1.85033i | 0.0724089 | − | 0.0724089i | −0.669975 | − | 0.742384i | \(-0.733695\pi\) |
0.742384 | + | 0.669975i | \(0.233695\pi\) | |||||||
\(654\) | 16.0085 | + | 18.9356i | 0.625984 | + | 0.740441i | ||||
\(655\) | 22.2352 | + | 15.0391i | 0.868802 | + | 0.587624i | ||||
\(656\) | − | 0.882958i | − | 0.0344737i | ||||||
\(657\) | 0.653436 | + | 0.918668i | 0.0254930 | + | 0.0358406i | ||||
\(658\) | −24.9908 | − | 24.9908i | −0.974244 | − | 0.974244i | ||||
\(659\) | −28.7705 | −1.12074 | −0.560370 | − | 0.828243i | \(-0.689341\pi\) | ||||
−0.560370 | + | 0.828243i | \(0.689341\pi\) | |||||||
\(660\) | −0.249230 | − | 0.200824i | −0.00970127 | − | 0.00781706i | ||||
\(661\) | −10.2697 | −0.399445 | −0.199722 | − | 0.979853i | \(-0.564004\pi\) | ||||
−0.199722 | + | 0.979853i | \(0.564004\pi\) | |||||||
\(662\) | 13.0193 | + | 13.0193i | 0.506008 | + | 0.506008i | ||||
\(663\) | −53.4783 | − | 4.47956i | −2.07693 | − | 0.173972i | ||||
\(664\) | 12.5104i | 0.485497i | ||||||||
\(665\) | −46.5591 | + | 8.98871i | −1.80549 | + | 0.348567i | ||||
\(666\) | 20.1004 | + | 3.39118i | 0.778876 | + | 0.131405i | ||||
\(667\) | −1.40400 | + | 1.40400i | −0.0543630 | + | 0.0543630i | ||||
\(668\) | −11.3314 | + | 11.3314i | −0.438423 | + | 0.438423i | ||||
\(669\) | −31.7892 | + | 26.8752i | −1.22904 | + | 1.03906i | ||||
\(670\) | −1.36106 | + | 2.01233i | −0.0525823 | + | 0.0777429i | ||||
\(671\) | − | 0.0724097i | − | 0.00279535i | ||||||
\(672\) | 0.473395 | − | 5.65154i | 0.0182616 | − | 0.218013i | ||||
\(673\) | 6.49107 | + | 6.49107i | 0.250212 | + | 0.250212i | 0.821058 | − | 0.570845i | \(-0.193384\pi\) |
−0.570845 | + | 0.821058i | \(0.693384\pi\) | |||||||
\(674\) | 6.79651 | 0.261792 | ||||||||
\(675\) | −25.7591 | + | 3.38656i | −0.991468 | + | 0.130349i | ||||
\(676\) | −4.07197 | −0.156614 | ||||||||
\(677\) | 11.6214 | + | 11.6214i | 0.446646 | + | 0.446646i | 0.894238 | − | 0.447592i | \(-0.147718\pi\) |
−0.447592 | + | 0.894238i | \(0.647718\pi\) | |||||||
\(678\) | 0.316871 | − | 3.78291i | 0.0121694 | − | 0.145282i | ||||
\(679\) | − | 33.8448i | − | 1.29884i | ||||||
\(680\) | −9.39417 | + | 13.8893i | −0.360250 | + | 0.532629i | ||||
\(681\) | 12.6743 | − | 10.7151i | 0.485680 | − | 0.410604i | ||||
\(682\) | −0.243107 | + | 0.243107i | −0.00930906 | + | 0.00930906i | ||||
\(683\) | −13.1189 | + | 13.1189i | −0.501983 | + | 0.501983i | −0.912054 | − | 0.410071i | \(-0.865504\pi\) |
0.410071 | + | 0.912054i | \(0.365504\pi\) | |||||||
\(684\) | 19.1588 | + | 3.23232i | 0.732556 | + | 0.123591i | ||||
\(685\) | 12.8311 | − | 2.47716i | 0.490250 | − | 0.0946476i | ||||
\(686\) | 10.7355i | 0.409883i | ||||||||
\(687\) | 20.0561 | + | 1.67998i | 0.765190 | + | 0.0640953i | ||||
\(688\) | 1.69981 | + | 1.69981i | 0.0648047 | + | 0.0648047i | ||||
\(689\) | 42.4351 | 1.61665 | ||||||||
\(690\) | 3.01578 | + | 2.43004i | 0.114809 | + | 0.0925101i | ||||
\(691\) | 26.0545 | 0.991159 | 0.495580 | − | 0.868563i | \(-0.334956\pi\) | ||||
0.495580 | + | 0.868563i | \(0.334956\pi\) | |||||||
\(692\) | −6.03766 | − | 6.03766i | −0.229517 | − | 0.229517i | ||||
\(693\) | 0.470533 | + | 0.661524i | 0.0178741 | + | 0.0251292i | ||||
\(694\) | 24.2144i | 0.919167i | ||||||||
\(695\) | −0.802843 | − | 0.543012i | −0.0304536 | − | 0.0205976i | ||||
\(696\) | 2.22032 | + | 2.62629i | 0.0841611 | + | 0.0995494i | ||||
\(697\) | 4.68186 | − | 4.68186i | 0.177338 | − | 0.177338i | ||||
\(698\) | −1.42288 | + | 1.42288i | −0.0538569 | + | 0.0538569i | ||||
\(699\) | −20.5061 | − | 24.2555i | −0.775611 | − | 0.917427i | ||||
\(700\) | −6.43528 | + | 15.0539i | −0.243231 | + | 0.568985i | ||||
\(701\) | − | 39.5869i | − | 1.49518i | −0.664162 | − | 0.747588i | \(-0.731212\pi\) | ||
0.664162 | − | 0.747588i | \(-0.268788\pi\) | |||||||
\(702\) | 20.7984 | + | 5.32636i | 0.784985 | + | 0.201030i | ||||
\(703\) | 31.1176 | + | 31.1176i | 1.17362 | + | 1.17362i | ||||
\(704\) | 0.0826422 | 0.00311469 | ||||||||
\(705\) | −4.47050 | − | 41.5642i | −0.168369 | − | 1.56540i | ||||
\(706\) | 32.5409 | 1.22469 | ||||||||
\(707\) | −6.93784 | − | 6.93784i | −0.260924 | − | 0.260924i | ||||
\(708\) | 17.3942 | + | 1.45700i | 0.653713 | + | 0.0547576i | ||||
\(709\) | − | 0.0916175i | − | 0.00344077i | −0.999999 | − | 0.00172038i | \(-0.999452\pi\) | ||
0.999999 | − | 0.00172038i | \(-0.000547616\pi\) | |||||||
\(710\) | 0.722041 | + | 3.73998i | 0.0270977 | + | 0.140359i | ||||
\(711\) | −8.38771 | + | 49.7162i | −0.314564 | + | 1.86450i | ||||
\(712\) | 3.99616 | − | 3.99616i | 0.149762 | − | 0.149762i | ||||
\(713\) | 2.94168 | − | 2.94168i | 0.110167 | − | 0.110167i | ||||
\(714\) | 32.4773 | − | 27.4570i | 1.21543 | − | 1.02755i | ||||
\(715\) | −0.144735 | − | 0.749691i | −0.00541279 | − | 0.0280369i | ||||
\(716\) | 10.2241i | 0.382094i | ||||||||
\(717\) | 0.875272 | − | 10.4493i | 0.0326876 | − | 0.390235i | ||||
\(718\) | −13.8264 | − | 13.8264i | −0.515996 | − | 0.515996i | ||||
\(719\) | 9.47790 | 0.353466 | 0.176733 | − | 0.984259i | \(-0.443447\pi\) | ||||
0.176733 | + | 0.984259i | \(0.443447\pi\) | |||||||
\(720\) | 4.63028 | − | 4.85392i | 0.172560 | − | 0.180895i | ||||
\(721\) | −36.6974 | −1.36668 | ||||||||
\(722\) | 16.2248 | + | 16.2248i | 0.603825 | + | 0.603825i | ||||
\(723\) | 2.56318 | − | 30.6001i | 0.0953258 | − | 1.13803i | ||||
\(724\) | − | 7.86650i | − | 0.292356i | ||||||
\(725\) | −3.69556 | − | 9.21430i | −0.137250 | − | 0.342210i | ||||
\(726\) | 14.5407 | − | 12.2930i | 0.539656 | − | 0.456236i | ||||
\(727\) | −16.4918 | + | 16.4918i | −0.611648 | + | 0.611648i | −0.943375 | − | 0.331727i | \(-0.892369\pi\) |
0.331727 | + | 0.943375i | \(0.392369\pi\) | |||||||
\(728\) | 9.56646 | − | 9.56646i | 0.354557 | − | 0.354557i | ||||
\(729\) | −23.6764 | − | 12.9780i | −0.876904 | − | 0.480665i | ||||
\(730\) | 0.696026 | + | 0.470765i | 0.0257611 | + | 0.0174238i | ||||
\(731\) | 18.0264i | 0.666731i | ||||||||
\(732\) | 1.51230 | + | 0.126676i | 0.0558961 | + | 0.00468208i | ||||
\(733\) | 14.5823 | + | 14.5823i | 0.538610 | + | 0.538610i | 0.923121 | − | 0.384510i | \(-0.125630\pi\) |
−0.384510 | + | 0.923121i | \(0.625630\pi\) | |||||||
\(734\) | −8.49714 | −0.313635 | ||||||||
\(735\) | 9.04300 | − | 11.2227i | 0.333556 | − | 0.413956i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 0.0634891 | + | 0.0634891i | 0.00233865 | + | 0.00233865i | ||||
\(738\) | −2.15854 | + | 1.53534i | −0.0794568 | + | 0.0565165i | ||||
\(739\) | − | 8.04723i | − | 0.296022i | −0.988986 | − | 0.148011i | \(-0.952713\pi\) | ||
0.988986 | − | 0.148011i | \(-0.0472871\pi\) | |||||||
\(740\) | 14.9182 | − | 2.88011i | 0.548405 | − | 0.105875i | ||||
\(741\) | 29.9239 | + | 35.3953i | 1.09928 | + | 1.30028i | ||||
\(742\) | −23.7790 | + | 23.7790i | −0.872954 | + | 0.872954i | ||||
\(743\) | −3.40804 | + | 3.40804i | −0.125029 | + | 0.125029i | −0.766852 | − | 0.641823i | \(-0.778178\pi\) |
0.641823 | + | 0.766852i | \(0.278178\pi\) | |||||||
\(744\) | −4.65206 | − | 5.50266i | −0.170553 | − | 0.201737i | ||||
\(745\) | 25.0850 | − | 37.0882i | 0.919044 | − | 1.35881i | ||||
\(746\) | 26.1199i | 0.956318i | ||||||||
\(747\) | 30.5837 | − | 21.7537i | 1.11900 | − | 0.795928i | ||||
\(748\) | 0.438208 | + | 0.438208i | 0.0160225 | + | 0.0160225i | ||||
\(749\) | 25.6797 | 0.938315 | ||||||||
\(750\) | −17.0993 | + | 9.08922i | −0.624378 | + | 0.331891i | ||||
\(751\) | 40.5910 | 1.48119 | 0.740594 | − | 0.671953i | \(-0.234544\pi\) | ||||
0.740594 | + | 0.671953i | \(0.234544\pi\) | |||||||
\(752\) | 7.63231 | + | 7.63231i | 0.278322 | + | 0.278322i | ||||
\(753\) | 38.5404 | + | 3.22830i | 1.40449 | + | 0.117646i | ||||
\(754\) | 8.20395i | 0.298770i | ||||||||
\(755\) | −21.5460 | + | 31.8557i | −0.784138 | + | 1.15935i | ||||
\(756\) | −14.6393 | + | 8.66992i | −0.532426 | + | 0.315322i | ||||
\(757\) | 34.6920 | − | 34.6920i | 1.26090 | − | 1.26090i | 0.310243 | − | 0.950657i | \(-0.399589\pi\) |
0.950657 | − | 0.310243i | \(-0.100411\pi\) | |||||||
\(758\) | 1.56540 | − | 1.56540i | 0.0568579 | − | 0.0568579i | ||||
\(759\) | 0.109311 | − | 0.0924137i | 0.00396774 | − | 0.00335441i | ||||
\(760\) | 14.2194 | − | 2.74519i | 0.515791 | − | 0.0995786i | ||||
\(761\) | 50.5466i | 1.83231i | 0.400823 | + | 0.916156i | \(0.368724\pi\) | ||||
−0.400823 | + | 0.916156i | \(0.631276\pi\) | |||||||
\(762\) | −0.543680 | + | 6.49063i | −0.0196955 | + | 0.235131i | ||||
\(763\) | −33.1457 | − | 33.1457i | −1.19995 | − | 1.19995i | ||||
\(764\) | 23.2816 | 0.842300 | ||||||||
\(765\) | 50.2897 | − | 1.18585i | 1.81823 | − | 0.0428743i | ||||
\(766\) | −33.9433 | −1.22642 | ||||||||
\(767\) | 29.4434 | + | 29.4434i | 1.06314 | + | 1.06314i | ||||
\(768\) | −0.144577 | + | 1.72601i | −0.00521698 | + | 0.0622819i | ||||
\(769\) | 52.5084i | 1.89350i | 0.321969 | + | 0.946750i | \(0.395655\pi\) | ||||
−0.321969 | + | 0.946750i | \(0.604345\pi\) | |||||||
\(770\) | 0.501201 | + | 0.338993i | 0.0180620 | + | 0.0122165i | ||||
\(771\) | −7.03275 | + | 5.94563i | −0.253278 | + | 0.214127i | ||||
\(772\) | 13.3531 | − | 13.3531i | 0.480588 | − | 0.480588i | ||||
\(773\) | −20.1139 | + | 20.1139i | −0.723445 | + | 0.723445i | −0.969305 | − | 0.245860i | \(-0.920930\pi\) |
0.245860 | + | 0.969305i | \(0.420930\pi\) | |||||||
\(774\) | 1.19974 | − | 7.11119i | 0.0431238 | − | 0.255607i | ||||
\(775\) | 7.74302 | + | 19.3060i | 0.278138 | + | 0.693491i | ||||
\(776\) | 10.3363i | 0.371053i | ||||||||
\(777\) | −38.4013 | − | 3.21664i | −1.37764 | − | 0.115396i | ||||
\(778\) | −6.28786 | − | 6.28786i | −0.225431 | − | 0.225431i | ||||
\(779\) | −5.71850 | −0.204886 | ||||||||
\(780\) | 15.9107 | − | 1.71130i | 0.569695 | − | 0.0612745i | ||||
\(781\) | 0.140777 | 0.00503741 | ||||||||
\(782\) | −5.30247 | − | 5.30247i | −0.189616 | − | 0.189616i | ||||
\(783\) | 2.55959 | − | 9.99469i | 0.0914722 | − | 0.357181i | ||||
\(784\) | 3.72133i | 0.132905i | ||||||||
\(785\) | −9.88004 | − | 51.1760i | −0.352634 | − | 1.82655i | ||||
\(786\) | 13.4243 | + | 15.8788i | 0.478827 | + | 0.566378i | ||||
\(787\) | −7.69708 | + | 7.69708i | −0.274371 | + | 0.274371i | −0.830857 | − | 0.556486i | \(-0.812149\pi\) |
0.556486 | + | 0.830857i | \(0.312149\pi\) | |||||||
\(788\) | −3.92746 | + | 3.92746i | −0.139910 | + | 0.139910i | ||||
\(789\) | −15.3968 | − | 18.2120i | −0.548139 | − | 0.648363i | ||||
\(790\) | 7.12365 | + | 36.8986i | 0.253448 | + | 1.31279i | ||||
\(791\) | 7.17642i | 0.255164i | ||||||||
\(792\) | −0.143703 | − | 0.202032i | −0.00510626 | − | 0.00717891i | ||||
\(793\) | 2.55989 | + | 2.55989i | 0.0909045 | + | 0.0909045i | ||||
\(794\) | −30.2880 | −1.07488 | ||||||||
\(795\) | −39.5487 | + | 4.25372i | −1.40265 | + | 0.150864i | ||||
\(796\) | −14.6406 | −0.518921 | ||||||||
\(797\) | 1.30291 | + | 1.30291i | 0.0461515 | + | 0.0461515i | 0.729806 | − | 0.683654i | \(-0.239610\pi\) |
−0.683654 | + | 0.729806i | \(0.739610\pi\) | |||||||
\(798\) | −36.6023 | − | 3.06596i | −1.29571 | − | 0.108534i | ||||
\(799\) | 80.9403i | 2.86346i | ||||||||
\(800\) | 1.96536 | − | 4.59754i | 0.0694861 | − | 0.162547i | ||||
\(801\) | −16.7180 | − | 2.82052i | −0.590702 | − | 0.0996582i | ||||
\(802\) | −23.2592 | + | 23.2592i | −0.821312 | + | 0.821312i | ||||
\(803\) | 0.0219597 | − | 0.0219597i | 0.000774941 | − | 0.000774941i | ||||
\(804\) | −1.43706 | + | 1.21492i | −0.0506811 | + | 0.0428469i | ||||
\(805\) | −6.06471 | − | 4.10194i | −0.213753 | − | 0.144574i | ||||
\(806\) | − | 17.1891i | − | 0.605460i | ||||||
\(807\) | 0.289141 | − | 3.45186i | 0.0101783 | − | 0.121511i | ||||
\(808\) | 2.11885 | + | 2.11885i | 0.0745408 | + | 0.0745408i | ||||
\(809\) | 8.03171 | 0.282380 | 0.141190 | − | 0.989983i | \(-0.454907\pi\) | ||||
0.141190 | + | 0.989983i | \(0.454907\pi\) | |||||||
\(810\) | −19.9176 | − | 2.87921i | −0.699833 | − | 0.101165i | ||||
\(811\) | 24.6723 | 0.866363 | 0.433181 | − | 0.901307i | \(-0.357391\pi\) | ||||
0.433181 | + | 0.901307i | \(0.357391\pi\) | |||||||
\(812\) | −4.59717 | − | 4.59717i | −0.161329 | − | 0.161329i | ||||
\(813\) | 1.12093 | − | 13.3821i | 0.0393129 | − | 0.469329i | ||||
\(814\) | − | 0.561540i | − | 0.0196820i | ||||||
\(815\) | 22.4062 | − | 4.32573i | 0.784854 | − | 0.151524i | ||||
\(816\) | −9.91872 | + | 8.38549i | −0.347225 | + | 0.293551i | ||||
\(817\) | 11.0089 | − | 11.0089i | 0.385152 | − | 0.385152i | ||||
\(818\) | −20.7915 | + | 20.7915i | −0.726958 | + | 0.726958i | ||||
\(819\) | −40.0215 | − | 6.75209i | −1.39846 | − | 0.235937i | ||||
\(820\) | −1.10613 | + | 1.63541i | −0.0386276 | + | 0.0571109i | ||||
\(821\) | − | 27.9798i | − | 0.976501i | −0.872704 | − | 0.488250i | \(-0.837635\pi\) | ||
0.872704 | − | 0.488250i | \(-0.162365\pi\) | |||||||
\(822\) | 10.0871 | + | 0.844935i | 0.351828 | + | 0.0294705i | ||||
\(823\) | −6.77408 | − | 6.77408i | −0.236130 | − | 0.236130i | 0.579116 | − | 0.815245i | \(-0.303398\pi\) |
−0.815245 | + | 0.579116i | \(0.803398\pi\) | |||||||
\(824\) | 11.2075 | 0.390433 | ||||||||
\(825\) | 0.210040 | + | 0.684188i | 0.00731264 | + | 0.0238204i | ||||
\(826\) | −32.9979 | −1.14814 | ||||||||
\(827\) | 1.39537 | + | 1.39537i | 0.0485217 | + | 0.0485217i | 0.730951 | − | 0.682430i | \(-0.239077\pi\) |
−0.682430 | + | 0.730951i | \(0.739077\pi\) | |||||||
\(828\) | 1.73886 | + | 2.44466i | 0.0604294 | + | 0.0849579i | ||||
\(829\) | − | 32.2465i | − | 1.11997i | −0.828504 | − | 0.559984i | \(-0.810807\pi\) | ||
0.828504 | − | 0.559984i | \(-0.189193\pi\) | |||||||
\(830\) | 15.6724 | − | 23.1716i | 0.543997 | − | 0.804299i | ||||
\(831\) | −13.2251 | − | 15.6432i | −0.458772 | − | 0.542655i | ||||
\(832\) | −2.92164 | + | 2.92164i | −0.101290 | + | 0.101290i | ||||
\(833\) | −19.7323 | + | 19.7323i | −0.683683 | + | 0.683683i | ||||
\(834\) | −0.484707 | − | 0.573333i | −0.0167840 | − | 0.0198529i | ||||
\(835\) | 35.1832 | − | 6.79247i | 1.21757 | − | 0.235063i | ||||
\(836\) | − | 0.535234i | − | 0.0185115i | ||||||
\(837\) | −5.36290 | + | 20.9411i | −0.185369 | + | 0.723829i | ||||
\(838\) | −3.42430 | − | 3.42430i | −0.118290 | − | 0.118290i | ||||
\(839\) | 8.38491 | 0.289479 | 0.144740 | − | 0.989470i | \(-0.453766\pi\) | ||||
0.144740 | + | 0.989470i | \(0.453766\pi\) | |||||||
\(840\) | −7.95679 | + | 9.87469i | −0.274535 | + | 0.340709i | ||||
\(841\) | −25.0576 | −0.864055 | ||||||||
\(842\) | −13.7500 | − | 13.7500i | −0.473857 | − | 0.473857i | ||||
\(843\) | −18.0175 | − | 1.50922i | −0.620556 | − | 0.0519802i | ||||
\(844\) | 1.39261i | 0.0479357i | ||||||||
\(845\) | 7.54208 | + | 5.10117i | 0.259455 | + | 0.175486i | ||||
\(846\) | 5.38695 | − | 31.9299i | 0.185207 | − | 1.09777i | ||||
\(847\) | −25.4526 | + | 25.4526i | −0.874562 | + | 0.874562i | ||||
\(848\) | 7.26221 | − | 7.26221i | 0.249385 | − | 0.249385i | ||||
\(849\) | −17.1759 | + | 14.5209i | −0.589477 | + | 0.498356i | ||||
\(850\) | 34.7996 | − | 13.9570i | 1.19362 | − | 0.478722i | ||||
\(851\) | 6.79483i | 0.232924i | ||||||||
\(852\) | −0.246281 | + | 2.94018i | −0.00843744 | + | 0.100729i | ||||
\(853\) | −2.47888 | − | 2.47888i | −0.0848752 | − | 0.0848752i | 0.663395 | − | 0.748270i | \(-0.269115\pi\) |
−0.748270 | + | 0.663395i | \(0.769115\pi\) | |||||||
\(854\) | −2.86893 | −0.0981726 | ||||||||
\(855\) | −31.4365 | − | 29.9881i | −1.07511 | − | 1.02557i | ||||
\(856\) | −7.84269 | −0.268058 | ||||||||
\(857\) | −13.4091 | − | 13.4091i | −0.458047 | − | 0.458047i | 0.439967 | − | 0.898014i | \(-0.354990\pi\) |
−0.898014 | + | 0.439967i | \(0.854990\pi\) | |||||||
\(858\) | 0.0493677 | − | 0.589367i | 0.00168539 | − | 0.0201207i | ||||
\(859\) | − | 40.6567i | − | 1.38719i | −0.720366 | − | 0.693594i | \(-0.756026\pi\) | ||
0.720366 | − | 0.693594i | \(-0.243974\pi\) | |||||||
\(860\) | −1.01894 | − | 5.27782i | −0.0347454 | − | 0.179972i | ||||
\(861\) | 3.82408 | − | 3.23295i | 0.130324 | − | 0.110179i | ||||
\(862\) | −16.5569 | + | 16.5569i | −0.563932 | + | 0.563932i | ||||
\(863\) | −14.4645 | + | 14.4645i | −0.492376 | + | 0.492376i | −0.909054 | − | 0.416678i | \(-0.863194\pi\) |
0.416678 | + | 0.909054i | \(0.363194\pi\) | |||||||
\(864\) | 4.47090 | − | 2.64783i | 0.152103 | − | 0.0900811i | ||||
\(865\) | 3.61921 | + | 18.7466i | 0.123057 | + | 0.637403i | ||||
\(866\) | 26.3226i | 0.894478i | ||||||||
\(867\) | −67.7155 | − | 5.67212i | −2.29974 | − | 0.192635i | ||||
\(868\) | 9.63209 | + | 9.63209i | 0.326934 | + | 0.326934i | ||||
\(869\) | 1.38891 | 0.0471155 | ||||||||
\(870\) | −0.822369 | − | 7.64591i | −0.0278809 | − | 0.259221i | ||||
\(871\) | −4.48905 | −0.152106 | ||||||||
\(872\) | 10.1228 | + | 10.1228i | 0.342802 | + | 0.342802i | ||||
\(873\) | 25.2689 | − | 17.9734i | 0.855223 | − | 0.608308i | ||||
\(874\) | 6.47652i | 0.219072i | ||||||||
\(875\) | 30.7782 | − | 19.8209i | 1.04049 | − | 0.670070i | ||||
\(876\) | 0.420218 | + | 0.497052i | 0.0141978 | + | 0.0167938i | ||||
\(877\) | 28.2774 | − | 28.2774i | 0.954860 | − | 0.954860i | −0.0441640 | − | 0.999024i | \(-0.514062\pi\) |
0.999024 | + | 0.0441640i | \(0.0140624\pi\) | |||||||
\(878\) | −1.94043 | + | 1.94043i | −0.0654864 | + | 0.0654864i | ||||
\(879\) | 20.4373 | + | 24.1741i | 0.689333 | + | 0.815373i | ||||
\(880\) | −0.153069 | − | 0.103530i | −0.00515996 | − | 0.00349000i | ||||
\(881\) | − | 16.0524i | − | 0.540818i | −0.962746 | − | 0.270409i | \(-0.912841\pi\) | ||
0.962746 | − | 0.270409i | \(-0.0871589\pi\) | |||||||
\(882\) | 9.09741 | − | 6.47086i | 0.306326 | − | 0.217885i | ||||
\(883\) | −39.6316 | − | 39.6316i | −1.33371 | − | 1.33371i | −0.902024 | − | 0.431687i | \(-0.857919\pi\) |
−0.431687 | − | 0.902024i | \(-0.642081\pi\) | |||||||
\(884\) | −30.9839 | −1.04210 | ||||||||
\(885\) | −30.3921 | − | 24.4892i | −1.02162 | − | 0.823197i | ||||
\(886\) | 7.41295 | 0.249043 | ||||||||
\(887\) | 25.8440 | + | 25.8440i | 0.867756 | + | 0.867756i | 0.992224 | − | 0.124467i | \(-0.0397222\pi\) |
−0.124467 | + | 0.992224i | \(0.539722\pi\) | |||||||
\(888\) | 11.7279 | + | 0.982377i | 0.393563 | + | 0.0329664i | ||||
\(889\) | − | 12.3131i | − | 0.412969i | ||||||
\(890\) | −12.4078 | + | 2.39546i | −0.415912 | + | 0.0802959i | ||||
\(891\) | −0.244023 | + | 0.702610i | −0.00817507 | + | 0.0235383i | ||||
\(892\) | −16.9943 | + | 16.9943i | −0.569010 | + | 0.569010i | ||||
\(893\) | 49.4309 | − | 49.4309i | 1.65414 | − | 1.65414i | ||||
\(894\) | 26.4857 | − | 22.3915i | 0.885814 | − | 0.748885i | ||||
\(895\) | 12.8083 | − | 18.9371i | 0.428134 | − | 0.632996i | ||||
\(896\) | − | 3.27434i | − | 0.109388i | ||||||
\(897\) | −0.597367 | + | 7.13155i | −0.0199455 | + | 0.238116i | ||||
\(898\) | 2.95278 | + | 2.95278i | 0.0985356 | + | 0.0985356i | ||||
\(899\) | −8.26023 | −0.275494 | ||||||||
\(900\) | −14.6569 | + | 3.18980i | −0.488564 | + | 0.106327i | ||||
\(901\) | 77.0154 | 2.56575 | ||||||||
\(902\) | 0.0515973 | + | 0.0515973i | 0.00171800 | + | 0.00171800i | ||||
\(903\) | −1.13799 | + | 13.5857i | −0.0378700 | + | 0.452104i | ||||
\(904\) | − | 2.19171i | − | 0.0728953i | ||||||
\(905\) | −9.85477 | + | 14.5703i | −0.327583 | + | 0.484332i | ||||
\(906\) | −22.7490 | + | 19.2325i | −0.755786 | + | 0.638957i | ||||
\(907\) | 26.9227 | − | 26.9227i | 0.893953 | − | 0.893953i | −0.100939 | − | 0.994893i | \(-0.532185\pi\) |
0.994893 | + | 0.100939i | \(0.0321848\pi\) | |||||||
\(908\) | 6.77558 | − | 6.77558i | 0.224856 | − | 0.224856i | ||||
\(909\) | 1.49550 | − | 8.86424i | 0.0496026 | − | 0.294008i | ||||
\(910\) | −29.7033 | + | 5.73452i | −0.984655 | + | 0.190098i | ||||
\(911\) | − | 3.29887i | − | 0.109296i | −0.998506 | − | 0.0546482i | \(-0.982596\pi\) | ||
0.998506 | − | 0.0546482i | \(-0.0174037\pi\) | |||||||
\(912\) | 11.1785 | + | 0.936357i | 0.370158 | + | 0.0310059i | ||||
\(913\) | −0.731067 | − | 0.731067i | −0.0241948 | − | 0.0241948i | ||||
\(914\) | −5.27277 | −0.174408 | ||||||||
\(915\) | −2.64237 | − | 2.12916i | −0.0873541 | − | 0.0703879i | ||||
\(916\) | 11.6200 | 0.383935 | ||||||||
\(917\) | −27.7949 | − | 27.7949i | −0.917868 | − | 0.917868i | ||||
\(918\) | 37.7469 | + | 9.66678i | 1.24583 | + | 0.319051i | ||||
\(919\) | − | 26.6450i | − | 0.878936i | −0.898258 | − | 0.439468i | \(-0.855167\pi\) | ||
0.898258 | − | 0.439468i | \(-0.144833\pi\) | |||||||
\(920\) | 1.85219 | + | 1.25275i | 0.0610649 | + | 0.0413020i | ||||
\(921\) | −14.6602 | − | 17.3407i | −0.483070 | − | 0.571396i | ||||
\(922\) | −8.02653 | + | 8.02653i | −0.264340 | + | 0.264340i | ||||
\(923\) | −4.97689 | + | 4.97689i | −0.163816 | + | 0.163816i | ||||
\(924\) | 0.302594 | + | 0.357922i | 0.00995463 | + | 0.0117748i | ||||
\(925\) | −31.2395 | − | 13.3543i | −1.02715 | − | 0.439087i | ||||
\(926\) | − | 21.7168i | − | 0.713657i | ||||||
\(927\) | −19.4883 | − | 27.3987i | −0.640080 | − | 0.899890i | ||||
\(928\) | 1.40400 | + | 1.40400i | 0.0460885 | + | 0.0460885i | ||||
\(929\) | −7.77474 | −0.255081 | −0.127541 | − | 0.991833i | \(-0.540708\pi\) | ||||
−0.127541 | + | 0.991833i | \(0.540708\pi\) | |||||||
\(930\) | 1.72304 | + | 16.0199i | 0.0565008 | + | 0.525312i | ||||
\(931\) | 24.1013 | 0.789889 | ||||||||
\(932\) | −12.9668 | − | 12.9668i | −0.424742 | − | 0.424742i | ||||
\(933\) | −58.8675 | − | 4.93098i | −1.92724 | − | 0.161433i | ||||
\(934\) | − | 8.48431i | − | 0.277615i | ||||||
\(935\) | −0.262679 | − | 1.36061i | −0.00859054 | − | 0.0444967i | ||||
\(936\) | 12.2227 | + | 2.06212i | 0.399513 | + | 0.0674025i | ||||
\(937\) | 8.36629 | − | 8.36629i | 0.273315 | − | 0.273315i | −0.557118 | − | 0.830433i | \(-0.688093\pi\) |
0.830433 | + | 0.557118i | \(0.188093\pi\) | |||||||
\(938\) | 2.51549 | − | 2.51549i | 0.0821335 | − | 0.0821335i | ||||
\(939\) | 39.3005 | − | 33.2254i | 1.28252 | − | 1.08427i | ||||
\(940\) | −4.57512 | − | 23.6979i | −0.149224 | − | 0.772940i | ||||
\(941\) | 35.8516i | 1.16873i | 0.811491 | + | 0.584364i | \(0.198656\pi\) | ||||
−0.811491 | + | 0.584364i | \(0.801344\pi\) | |||||||
\(942\) | 3.36998 | − | 40.2319i | 0.109800 | − | 1.31083i | ||||
\(943\) | −0.624346 | − | 0.624346i | −0.0203315 | − | 0.0203315i | ||||
\(944\) | 10.0777 | 0.328001 | ||||||||
\(945\) | 37.9760 | + | 2.28103i | 1.23536 | + | 0.0742019i | ||||
\(946\) | −0.198663 | −0.00645910 | ||||||||
\(947\) | 3.74296 | + | 3.74296i | 0.121630 | + | 0.121630i | 0.765302 | − | 0.643672i | \(-0.222590\pi\) |
−0.643672 | + | 0.765302i | \(0.722590\pi\) | |||||||
\(948\) | −2.42980 | + | 29.0077i | −0.0789163 | + | 0.942128i | ||||
\(949\) | 1.55268i | 0.0504020i | ||||||||
\(950\) | −29.7761 | − | 12.7287i | −0.966063 | − | 0.412974i | ||||
\(951\) | −3.53353 | + | 2.98732i | −0.114583 | + | 0.0968705i | ||||
\(952\) | 17.3621 | − | 17.3621i | 0.562710 | − | 0.562710i | ||||
\(953\) | 15.5762 | − | 15.5762i | 0.504563 | − | 0.504563i | −0.408290 | − | 0.912852i | \(-0.633875\pi\) |
0.912852 | + | 0.408290i | \(0.133875\pi\) | |||||||
\(954\) | −30.3816 | − | 5.12573i | −0.983641 | − | 0.165952i | ||||
\(955\) | −43.1220 | − | 29.1661i | −1.39540 | − | 0.943793i | ||||
\(956\) | − | 6.05401i | − | 0.195801i | ||||||
\(957\) | −0.283221 | − | 0.0237237i | −0.00915524 | − | 0.000766879i | ||||
\(958\) | 22.4588 | + | 22.4588i | 0.725611 | + | 0.725611i | ||||
\(959\) | −19.1359 | −0.617930 | ||||||||
\(960\) | 2.43004 | − | 3.01578i | 0.0784292 | − | 0.0973337i | ||||
\(961\) | −13.6930 | −0.441709 | ||||||||
\(962\) | 19.8521 | + | 19.8521i | 0.640056 | + | 0.640056i | ||||
\(963\) | 13.6373 | + | 19.1727i | 0.439456 | + | 0.617833i | ||||
\(964\) | − | 17.7288i | − | 0.571007i | ||||||
\(965\) | −41.4605 | + | 8.00437i | −1.33466 | + | 0.257670i | ||||
\(966\) | −3.66150 | − | 4.33098i | −0.117807 | − | 0.139347i | ||||
\(967\) | −34.8919 | + | 34.8919i | −1.12205 | + | 1.12205i | −0.130614 | + | 0.991433i | \(0.541695\pi\) |
−0.991433 | + | 0.130614i | \(0.958305\pi\) | |||||||
\(968\) | 7.77335 | − | 7.77335i | 0.249845 | − | 0.249845i | ||||
\(969\) | 54.3088 | + | 64.2388i | 1.74465 | + | 2.06365i | ||||
\(970\) | 12.9489 | − | 19.1449i | 0.415763 | − | 0.614706i | ||||
\(971\) | − | 9.46212i | − | 0.303654i | −0.988407 | − | 0.151827i | \(-0.951484\pi\) | ||
0.988407 | − | 0.151827i | \(-0.0485156\pi\) | |||||||
\(972\) | −14.2473 | − | 6.32566i | −0.456983 | − | 0.202896i | ||||
\(973\) | 1.00359 | + | 1.00359i | 0.0321735 | + | 0.0321735i | ||||
\(974\) | −12.0688 | −0.386710 | ||||||||
\(975\) | −31.6135 | − | 16.7625i | −1.01244 | − | 0.536830i | ||||
\(976\) | 0.876183 | 0.0280459 | ||||||||
\(977\) | 39.3682 | + | 39.3682i | 1.25950 | + | 1.25950i | 0.951331 | + | 0.308170i | \(0.0997166\pi\) |
0.308170 | + | 0.951331i | \(0.400283\pi\) | |||||||
\(978\) | 17.6145 | + | 1.47546i | 0.563251 | + | 0.0471801i | ||||
\(979\) | 0.467046i | 0.0149268i | ||||||||
\(980\) | 4.66191 | − | 6.89263i | 0.148919 | − | 0.220177i | ||||
\(981\) | 7.14478 | − | 42.3491i | 0.228115 | − | 1.35210i | ||||
\(982\) | −11.0121 | + | 11.0121i | −0.351410 | + | 0.351410i | ||||
\(983\) | 5.98476 | − | 5.98476i | 0.190884 | − | 0.190884i | −0.605194 | − | 0.796078i | \(-0.706904\pi\) |
0.796078 | + | 0.605194i | \(0.206904\pi\) | |||||||
\(984\) | −1.16789 | + | 0.987358i | −0.0372310 | + | 0.0314758i | ||||
\(985\) | 12.1945 | − | 2.35428i | 0.388551 | − | 0.0750135i | ||||
\(986\) | 14.8893i | 0.474173i | ||||||||
\(987\) | −5.10970 | + | 61.0012i | −0.162643 | + | 1.94169i | ||||
\(988\) | 18.9221 | + | 18.9221i | 0.601991 | + | 0.601991i | ||||
\(989\) | 2.40390 | 0.0764395 | ||||||||
\(990\) | 0.0130688 | + | 0.554227i | 0.000415354 | + | 0.0176145i | ||||
\(991\) | 15.7047 | 0.498876 | 0.249438 | − | 0.968391i | \(-0.419754\pi\) | ||||
0.249438 | + | 0.968391i | \(0.419754\pi\) | |||||||
\(992\) | −2.94168 | − | 2.94168i | −0.0933986 | − | 0.0933986i | ||||
\(993\) | 2.66195 | − | 31.7792i | 0.0844746 | − | 1.00848i | ||||
\(994\) | − | 5.57770i | − | 0.176914i | ||||||
\(995\) | 27.1171 | + | 18.3410i | 0.859671 | + | 0.581449i | ||||
\(996\) | 16.5475 | − | 13.9896i | 0.524328 | − | 0.443277i | ||||
\(997\) | −36.2178 | + | 36.2178i | −1.14703 | + | 1.14703i | −0.159894 | + | 0.987134i | \(0.551115\pi\) |
−0.987134 | + | 0.159894i | \(0.948885\pi\) | |||||||
\(998\) | −21.1555 | + | 21.1555i | −0.669664 | + | 0.669664i | ||||
\(999\) | −17.9916 | − | 30.3790i | −0.569228 | − | 0.961150i |
(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 | 690.2.i.f.323.4 | yes | 32 | |
3.2 | odd | 2 | inner | 690.2.i.f.323.15 | yes | 32 | |
5.2 | odd | 4 | inner | 690.2.i.f.47.15 | yes | 32 | |
15.2 | even | 4 | inner | 690.2.i.f.47.4 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.i.f.47.4 | ✓ | 32 | 15.2 | even | 4 | inner | |
690.2.i.f.47.15 | yes | 32 | 5.2 | odd | 4 | inner | |
690.2.i.f.323.4 | yes | 32 | 1.1 | even | 1 | trivial | |
690.2.i.f.323.15 | yes | 32 | 3.2 | odd | 2 | inner |