Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(49,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([14, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.u (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 349.4 | ||
Character | \(\chi\) | \(=\) | 675.349 |
Dual form | 675.2.u.b.499.4 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{5}{9}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.36514 | + | 0.417037i | 1.67240 | + | 0.294890i | 0.927928 | − | 0.372760i | \(-0.121589\pi\) |
0.744475 | + | 0.667650i | \(0.232700\pi\) | |||||||
\(3\) | 1.71926 | − | 0.210069i | 0.992618 | − | 0.121284i | ||||
\(4\) | 3.54056 | + | 1.28866i | 1.77028 | + | 0.644329i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.15390 | + | 0.220155i | 1.69582 | + | 0.0898778i | ||||
\(7\) | −0.198324 | − | 0.544891i | −0.0749595 | − | 0.205950i | 0.896554 | − | 0.442935i | \(-0.146063\pi\) |
−0.971513 | + | 0.236986i | \(0.923841\pi\) | |||||||
\(8\) | 3.67675 | + | 2.12277i | 1.29993 | + | 0.750514i | ||||
\(9\) | 2.91174 | − | 0.722330i | 0.970581 | − | 0.240777i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.36944 | − | 1.98820i | −0.714413 | − | 0.599464i | 0.211421 | − | 0.977395i | \(-0.432191\pi\) |
−0.925834 | + | 0.377932i | \(0.876635\pi\) | |||||||
\(12\) | 6.35787 | + | 1.47178i | 1.83536 | + | 0.424867i | ||||
\(13\) | −4.13790 | + | 0.729623i | −1.14765 | + | 0.202361i | −0.714948 | − | 0.699178i | \(-0.753550\pi\) |
−0.432699 | + | 0.901539i | \(0.642439\pi\) | |||||||
\(14\) | −0.241824 | − | 1.37145i | −0.0646301 | − | 0.366536i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.03816 | + | 1.71022i | 0.509540 | + | 0.427555i | ||||
\(17\) | 1.72424 | − | 0.995493i | 0.418191 | − | 0.241443i | −0.276112 | − | 0.961125i | \(-0.589046\pi\) |
0.694303 | + | 0.719683i | \(0.255713\pi\) | |||||||
\(18\) | 7.18790 | − | 0.494102i | 1.69420 | − | 0.116461i | ||||
\(19\) | −1.92271 | + | 3.33023i | −0.441100 | + | 0.764008i | −0.997771 | − | 0.0667249i | \(-0.978745\pi\) |
0.556671 | + | 0.830733i | \(0.312078\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.455437 | − | 0.895151i | −0.0993845 | − | 0.195338i | ||||
\(22\) | −4.77489 | − | 5.69050i | −1.01801 | − | 1.21322i | ||||
\(23\) | −1.52295 | + | 4.18428i | −0.317558 | + | 0.872482i | 0.673517 | + | 0.739172i | \(0.264783\pi\) |
−0.991074 | + | 0.133310i | \(0.957439\pi\) | |||||||
\(24\) | 6.76724 | + | 2.87724i | 1.38136 | + | 0.587314i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −10.0910 | −1.97900 | ||||||||
\(27\) | 4.85432 | − | 1.85354i | 0.934213 | − | 0.356715i | ||||
\(28\) | − | 2.18479i | − | 0.412887i | ||||||
\(29\) | −1.11126 | + | 6.30229i | −0.206356 | + | 1.17031i | 0.688935 | + | 0.724823i | \(0.258079\pi\) |
−0.895291 | + | 0.445482i | \(0.853032\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.55754 | − | 0.566898i | −0.279743 | − | 0.101818i | 0.198339 | − | 0.980134i | \(-0.436445\pi\) |
−0.478081 | + | 0.878316i | \(0.658668\pi\) | |||||||
\(32\) | −1.35067 | − | 1.60967i | −0.238767 | − | 0.284552i | ||||
\(33\) | −4.49135 | − | 2.92049i | −0.781844 | − | 0.508392i | ||||
\(34\) | 4.49323 | − | 1.63540i | 0.770582 | − | 0.280469i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 11.2400 | + | 1.19479i | 1.87334 | + | 0.199132i | ||||
\(37\) | −3.49016 | + | 2.01505i | −0.573779 | + | 0.331272i | −0.758657 | − | 0.651490i | \(-0.774144\pi\) |
0.184878 | + | 0.982761i | \(0.440811\pi\) | |||||||
\(38\) | −5.93630 | + | 7.07461i | −0.962996 | + | 1.14765i | ||||
\(39\) | −6.96087 | + | 2.12366i | −1.11463 | + | 0.340058i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.190345 | − | 1.07950i | −0.0297270 | − | 0.168590i | 0.966330 | − | 0.257306i | \(-0.0828348\pi\) |
−0.996057 | + | 0.0887159i | \(0.971724\pi\) | |||||||
\(42\) | −0.703859 | − | 2.30709i | −0.108608 | − | 0.355991i | ||||
\(43\) | 4.43596 | − | 5.28657i | 0.676477 | − | 0.806194i | −0.313173 | − | 0.949696i | \(-0.601392\pi\) |
0.989650 | + | 0.143502i | \(0.0458364\pi\) | |||||||
\(44\) | −5.82704 | − | 10.0927i | −0.878459 | − | 1.52154i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.34699 | + | 9.26126i | −0.788370 | + | 1.36550i | ||||
\(47\) | 1.22894 | + | 3.37650i | 0.179260 | + | 0.492513i | 0.996482 | − | 0.0838106i | \(-0.0267091\pi\) |
−0.817222 | + | 0.576323i | \(0.804487\pi\) | |||||||
\(48\) | 3.86340 | + | 2.51217i | 0.557634 | + | 0.362600i | ||||
\(49\) | 5.10474 | − | 4.28338i | 0.729248 | − | 0.611912i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.75531 | − | 2.07373i | 0.385821 | − | 0.290380i | ||||
\(52\) | −15.5907 | − | 2.74906i | −2.16204 | − | 0.381226i | ||||
\(53\) | 5.40034i | 0.741793i | 0.928674 | + | 0.370897i | \(0.120950\pi\) | ||||
−0.928674 | + | 0.370897i | \(0.879050\pi\) | |||||||
\(54\) | 12.2541 | − | 2.35945i | 1.66757 | − | 0.321081i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.427492 | − | 2.42443i | 0.0571260 | − | 0.323978i | ||||
\(57\) | −2.60607 | + | 6.12946i | −0.345182 | + | 0.811866i | ||||
\(58\) | −5.25657 | + | 14.4423i | −0.690222 | + | 1.89637i | ||||
\(59\) | 7.87850 | − | 6.61085i | 1.02569 | − | 0.860659i | 0.0353615 | − | 0.999375i | \(-0.488742\pi\) |
0.990332 | + | 0.138715i | \(0.0442973\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.4005 | − | 4.51341i | 1.58772 | − | 0.577883i | 0.610855 | − | 0.791742i | \(-0.290826\pi\) |
0.976864 | + | 0.213860i | \(0.0686036\pi\) | |||||||
\(62\) | −3.44738 | − | 1.99034i | −0.437817 | − | 0.252774i | ||||
\(63\) | −0.971060 | − | 1.44333i | −0.122342 | − | 0.181842i | ||||
\(64\) | −5.18386 | − | 8.97871i | −0.647982 | − | 1.12234i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.40470 | − | 8.78041i | −1.15764 | − | 1.08079i | ||||
\(67\) | −8.70304 | + | 1.53458i | −1.06324 | + | 0.187479i | −0.677796 | − | 0.735250i | \(-0.737065\pi\) |
−0.385449 | + | 0.922729i | \(0.625954\pi\) | |||||||
\(68\) | 7.38764 | − | 1.30264i | 0.895883 | − | 0.157968i | ||||
\(69\) | −1.73937 | + | 7.51381i | −0.209396 | + | 0.904556i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.572473 | − | 0.991553i | −0.0679401 | − | 0.117676i | 0.830054 | − | 0.557683i | \(-0.188309\pi\) |
−0.897994 | + | 0.440007i | \(0.854976\pi\) | |||||||
\(72\) | 12.2391 | + | 3.52514i | 1.44239 | + | 0.415442i | ||||
\(73\) | −0.169284 | − | 0.0977361i | −0.0198132 | − | 0.0114391i | 0.490061 | − | 0.871688i | \(-0.336975\pi\) |
−0.509874 | + | 0.860249i | \(0.670308\pi\) | |||||||
\(74\) | −9.09506 | + | 3.31033i | −1.05728 | + | 0.384818i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.0990 | + | 9.31317i | −1.27314 | + | 1.06829i | ||||
\(77\) | −0.613433 | + | 1.68539i | −0.0699072 | + | 0.192069i | ||||
\(78\) | −17.3491 | + | 2.11980i | −1.96439 | + | 0.240020i | ||||
\(79\) | 1.25166 | − | 7.09849i | 0.140822 | − | 0.798642i | −0.829805 | − | 0.558054i | \(-0.811548\pi\) |
0.970627 | − | 0.240589i | \(-0.0773405\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.95648 | − | 4.20647i | 0.884053 | − | 0.467386i | ||||
\(82\) | − | 2.63255i | − | 0.290717i | ||||||
\(83\) | −14.6741 | − | 2.58744i | −1.61069 | − | 0.284008i | −0.705402 | − | 0.708808i | \(-0.749233\pi\) |
−0.905287 | + | 0.424800i | \(0.860344\pi\) | |||||||
\(84\) | −0.458958 | − | 3.75624i | −0.0500764 | − | 0.409839i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12.6963 | − | 10.6535i | 1.36908 | − | 1.14879i | ||||
\(87\) | −0.586638 | + | 11.0687i | −0.0628942 | + | 1.18669i | ||||
\(88\) | −4.49135 | − | 12.3399i | −0.478780 | − | 1.31544i | ||||
\(89\) | −0.776563 | + | 1.34505i | −0.0823155 | + | 0.142575i | −0.904244 | − | 0.427016i | \(-0.859565\pi\) |
0.821929 | + | 0.569590i | \(0.192898\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.21821 | + | 2.11000i | 0.127703 | + | 0.221189i | ||||
\(92\) | −10.7842 | + | 12.8521i | −1.12433 | + | 1.33993i | ||||
\(93\) | −2.79691 | − | 0.647457i | −0.290026 | − | 0.0671381i | ||||
\(94\) | 1.49850 | + | 8.49839i | 0.154558 | + | 0.876542i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.66030 | − | 2.48371i | −0.271516 | − | 0.253492i | ||||
\(97\) | 3.40390 | − | 4.05661i | 0.345614 | − | 0.411887i | −0.565035 | − | 0.825067i | \(-0.691137\pi\) |
0.910649 | + | 0.413180i | \(0.135582\pi\) | |||||||
\(98\) | 13.8597 | − | 8.00191i | 1.40004 | − | 0.808315i | ||||
\(99\) | −8.33533 | − | 4.07760i | −0.837732 | − | 0.409814i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.83061 | − | 2.48614i | 0.679671 | − | 0.247380i | 0.0209647 | − | 0.999780i | \(-0.493326\pi\) |
0.658706 | + | 0.752400i | \(0.271104\pi\) | |||||||
\(102\) | 7.38150 | − | 3.75558i | 0.730878 | − | 0.371858i | ||||
\(103\) | 4.11472 | + | 4.90374i | 0.405436 | + | 0.483179i | 0.929669 | − | 0.368395i | \(-0.120093\pi\) |
−0.524234 | + | 0.851574i | \(0.675648\pi\) | |||||||
\(104\) | −16.7629 | − | 6.10118i | −1.64373 | − | 0.598270i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.25214 | + | 12.7725i | −0.218747 | + | 1.24058i | ||||
\(107\) | 5.54365i | 0.535925i | 0.963429 | + | 0.267963i | \(0.0863504\pi\) | ||||
−0.963429 | + | 0.267963i | \(0.913650\pi\) | |||||||
\(108\) | 19.5756 | − | 0.307026i | 1.88366 | − | 0.0295436i | ||||
\(109\) | 6.23137 | 0.596857 | 0.298428 | − | 0.954432i | \(-0.403538\pi\) | ||||
0.298428 | + | 0.954432i | \(0.403538\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.57722 | + | 4.19758i | −0.529366 | + | 0.398416i | ||||
\(112\) | 0.527668 | − | 1.44975i | 0.0498599 | − | 0.136989i | ||||
\(113\) | −7.61316 | − | 9.07301i | −0.716186 | − | 0.853517i | 0.278068 | − | 0.960561i | \(-0.410306\pi\) |
−0.994254 | + | 0.107044i | \(0.965861\pi\) | |||||||
\(114\) | −8.71992 | + | 13.4102i | −0.816695 | + | 1.25598i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.0560 | + | 20.8816i | −1.11937 | + | 1.93881i | ||||
\(117\) | −11.5215 | + | 5.11340i | −1.06516 | + | 0.472734i | ||||
\(118\) | 21.3907 | − | 12.3499i | 1.96917 | − | 1.13690i | ||||
\(119\) | −0.884395 | − | 0.742096i | −0.0810724 | − | 0.0680278i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.248809 | − | 1.41107i | −0.0226190 | − | 0.128279i | ||||
\(122\) | 31.2111 | − | 5.50336i | 2.82572 | − | 0.498250i | ||||
\(123\) | −0.554025 | − | 1.81597i | −0.0499547 | − | 0.163740i | ||||
\(124\) | −4.78403 | − | 4.01427i | −0.429618 | − | 0.360492i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.69477 | − | 3.81863i | −0.150982 | − | 0.340191i | ||||
\(127\) | 9.98473 | + | 5.76469i | 0.886002 | + | 0.511533i | 0.872633 | − | 0.488377i | \(-0.162411\pi\) |
0.0133693 | + | 0.999911i | \(0.495744\pi\) | |||||||
\(128\) | −7.07872 | − | 19.4486i | −0.625676 | − | 1.71903i | ||||
\(129\) | 6.51604 | − | 10.0209i | 0.573705 | − | 0.882288i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.46830 | + | 3.08221i | 0.739879 | + | 0.269294i | 0.684340 | − | 0.729163i | \(-0.260090\pi\) |
0.0555383 | + | 0.998457i | \(0.482312\pi\) | |||||||
\(132\) | −12.1384 | − | 16.1280i | −1.05651 | − | 1.40376i | ||||
\(133\) | 2.19594 | + | 0.387203i | 0.190412 | + | 0.0335747i | ||||
\(134\) | −21.2238 | −1.83346 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.45283 | 0.724824 | ||||||||
\(137\) | −11.3452 | − | 2.00047i | −0.969287 | − | 0.170911i | −0.333478 | − | 0.942758i | \(-0.608222\pi\) |
−0.635809 | + | 0.771846i | \(0.719333\pi\) | |||||||
\(138\) | −7.24738 | + | 17.0458i | −0.616938 | + | 1.45103i | ||||
\(139\) | 1.60108 | + | 0.582746i | 0.135802 | + | 0.0494279i | 0.409027 | − | 0.912522i | \(-0.365868\pi\) |
−0.273225 | + | 0.961950i | \(0.588090\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.82218 | + | 5.54693i | 0.237670 | + | 0.467136i | ||||
\(142\) | −0.940462 | − | 2.58390i | −0.0789219 | − | 0.216836i | ||||
\(143\) | 11.2551 | + | 6.49816i | 0.941202 | + | 0.543403i | ||||
\(144\) | 7.16994 | + | 3.50750i | 0.597495 | + | 0.292291i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.359620 | − | 0.301757i | −0.0297623 | − | 0.0249736i | ||||
\(147\) | 7.87659 | − | 8.43662i | 0.649650 | − | 0.695840i | ||||
\(148\) | −14.9538 | + | 2.63677i | −1.22920 | + | 0.216741i | ||||
\(149\) | 3.75996 | + | 21.3238i | 0.308028 | + | 1.74691i | 0.608897 | + | 0.793249i | \(0.291612\pi\) |
−0.300869 | + | 0.953666i | \(0.597277\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.63222 | − | 3.04779i | −0.295586 | − | 0.248026i | 0.482918 | − | 0.875665i | \(-0.339577\pi\) |
−0.778504 | + | 0.627640i | \(0.784021\pi\) | |||||||
\(152\) | −14.1387 | + | 8.16296i | −1.14680 | + | 0.662104i | ||||
\(153\) | 4.30148 | − | 4.14409i | 0.347754 | − | 0.335030i | ||||
\(154\) | −2.15373 | + | 3.73036i | −0.173552 | + | 0.300601i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −27.3821 | − | 1.45124i | −2.19232 | − | 0.116192i | ||||
\(157\) | 0.134475 | + | 0.160261i | 0.0107323 | + | 0.0127902i | 0.771384 | − | 0.636370i | \(-0.219565\pi\) |
−0.760652 | + | 0.649160i | \(0.775120\pi\) | |||||||
\(158\) | 5.92067 | − | 16.2669i | 0.471023 | − | 1.29412i | ||||
\(159\) | 1.13444 | + | 9.28461i | 0.0899673 | + | 0.736317i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.58202 | 0.203491 | ||||||||
\(162\) | 20.5724 | − | 6.63073i | 1.61632 | − | 0.520960i | ||||
\(163\) | 5.62384i | 0.440493i | 0.975444 | + | 0.220247i | \(0.0706862\pi\) | ||||
−0.975444 | + | 0.220247i | \(0.929314\pi\) | |||||||
\(164\) | 0.717181 | − | 4.06733i | 0.0560024 | − | 0.317605i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −33.6271 | − | 12.2393i | −2.60997 | − | 0.949951i | ||||
\(167\) | −10.7220 | − | 12.7780i | −0.829695 | − | 0.988791i | −0.999994 | − | 0.00339914i | \(-0.998918\pi\) |
0.170300 | − | 0.985392i | \(-0.445526\pi\) | |||||||
\(168\) | 0.225674 | − | 4.25804i | 0.0174111 | − | 0.328515i | ||||
\(169\) | 4.37386 | − | 1.59195i | 0.336451 | − | 0.122458i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.19291 | + | 11.0856i | −0.244168 | + | 0.847738i | ||||
\(172\) | 22.5183 | − | 13.0010i | 1.71701 | − | 0.991315i | ||||
\(173\) | −12.2143 | + | 14.5565i | −0.928639 | + | 1.10671i | 0.0654187 | + | 0.997858i | \(0.479162\pi\) |
−0.994058 | + | 0.108851i | \(0.965283\pi\) | |||||||
\(174\) | −6.00355 | + | 25.9344i | −0.455128 | + | 1.96608i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.42905 | − | 8.10453i | −0.107718 | − | 0.610902i | ||||
\(177\) | 12.1565 | − | 13.0208i | 0.913738 | − | 0.978706i | ||||
\(178\) | −2.39761 | + | 2.85736i | −0.179709 | + | 0.214168i | ||||
\(179\) | 8.11761 | + | 14.0601i | 0.606739 | + | 1.05090i | 0.991774 | + | 0.128001i | \(0.0408560\pi\) |
−0.385035 | + | 0.922902i | \(0.625811\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.49579 | − | 2.59078i | 0.111181 | − | 0.192571i | −0.805066 | − | 0.593186i | \(-0.797870\pi\) |
0.916247 | + | 0.400614i | \(0.131203\pi\) | |||||||
\(182\) | 2.00128 | + | 5.49848i | 0.148345 | + | 0.407575i | ||||
\(183\) | 20.3716 | − | 10.3647i | 1.50591 | − | 0.766181i | ||||
\(184\) | −14.4818 | + | 12.1517i | −1.06761 | + | 0.895833i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.34506 | − | 2.69774i | −0.465242 | − | 0.197808i | ||||
\(187\) | −6.06473 | − | 1.06938i | −0.443497 | − | 0.0782005i | ||||
\(188\) | 13.5384i | 0.987388i | ||||||||
\(189\) | −1.97271 | − | 2.27747i | −0.143493 | − | 0.165662i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.391371 | + | 2.21958i | −0.0283186 | + | 0.160603i | −0.995688 | − | 0.0927685i | \(-0.970428\pi\) |
0.967369 | + | 0.253371i | \(0.0815395\pi\) | |||||||
\(192\) | −10.7986 | − | 14.3478i | −0.779320 | − | 1.03546i | ||||
\(193\) | −0.301071 | + | 0.827186i | −0.0216716 | + | 0.0595422i | −0.950057 | − | 0.312077i | \(-0.898975\pi\) |
0.928385 | + | 0.371620i | \(0.121197\pi\) | |||||||
\(194\) | 9.74245 | − | 8.17489i | 0.699467 | − | 0.586923i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 23.5934 | − | 8.58731i | 1.68525 | − | 0.613379i | ||||
\(197\) | 17.5600 | + | 10.1383i | 1.25110 | + | 0.722322i | 0.971328 | − | 0.237744i | \(-0.0764081\pi\) |
0.279771 | + | 0.960067i | \(0.409741\pi\) | |||||||
\(198\) | −18.0137 | − | 13.1202i | −1.28018 | − | 0.932413i | ||||
\(199\) | −9.50472 | − | 16.4627i | −0.673772 | − | 1.16701i | −0.976826 | − | 0.214034i | \(-0.931340\pi\) |
0.303054 | − | 0.952973i | \(-0.401994\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.6405 | + | 4.46659i | −1.03266 | + | 0.315049i | ||||
\(202\) | 17.1921 | − | 3.03144i | 1.20963 | − | 0.213291i | ||||
\(203\) | 3.65445 | − | 0.644379i | 0.256492 | − | 0.0452265i | ||||
\(204\) | 12.4277 | − | 3.79150i | 0.870110 | − | 0.265458i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.68684 | + | 13.3140i | 0.535567 | + | 0.927630i | ||||
\(207\) | −1.41202 | + | 13.2836i | −0.0981420 | + | 0.923275i | ||||
\(208\) | −9.68152 | − | 5.58963i | −0.671293 | − | 0.387571i | ||||
\(209\) | 11.1769 | − | 4.06806i | 0.773123 | − | 0.281394i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.3977 | − | 10.4029i | 0.853494 | − | 0.716166i | −0.107062 | − | 0.994252i | \(-0.534144\pi\) |
0.960556 | + | 0.278086i | \(0.0897000\pi\) | |||||||
\(212\) | −6.95919 | + | 19.1202i | −0.477959 | + | 1.31318i | ||||
\(213\) | −1.19253 | − | 1.58448i | −0.0817107 | − | 0.108567i | ||||
\(214\) | −2.31191 | + | 13.1115i | −0.158039 | + | 0.896283i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 21.7828 | + | 3.48960i | 1.48213 | + | 0.237437i | ||||
\(217\) | 0.961120i | 0.0652451i | ||||||||
\(218\) | 14.7380 | + | 2.59871i | 0.998186 | + | 0.176007i | ||||
\(219\) | −0.311575 | − | 0.132473i | −0.0210543 | − | 0.00895168i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.40842 | + | 5.37730i | −0.431077 | + | 0.361716i | ||||
\(222\) | −14.9414 | + | 7.60193i | −1.00280 | + | 0.510208i | ||||
\(223\) | −7.33883 | − | 20.1633i | −0.491444 | − | 1.35023i | −0.899359 | − | 0.437212i | \(-0.855966\pi\) |
0.407914 | − | 0.913020i | \(-0.366256\pi\) | |||||||
\(224\) | −0.609223 | + | 1.05520i | −0.0407054 | + | 0.0705038i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.2224 | − | 24.6339i | −0.946058 | − | 1.63862i | ||||
\(227\) | −12.2864 | + | 14.6424i | −0.815477 | + | 0.971848i | −0.999940 | − | 0.0109918i | \(-0.996501\pi\) |
0.184462 | + | 0.982840i | \(0.440946\pi\) | |||||||
\(228\) | −17.1257 | + | 18.3434i | −1.13418 | + | 1.21482i | ||||
\(229\) | −3.90190 | − | 22.1288i | −0.257845 | − | 1.46231i | −0.788663 | − | 0.614826i | \(-0.789226\pi\) |
0.530818 | − | 0.847486i | \(-0.321885\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.700605 | + | 3.02650i | −0.0460964 | + | 0.199129i | ||||
\(232\) | −17.4642 | + | 20.8130i | −1.14658 | + | 1.36644i | ||||
\(233\) | −15.3126 | + | 8.84074i | −1.00316 | + | 0.579176i | −0.909182 | − | 0.416398i | \(-0.863292\pi\) |
−0.0939796 | + | 0.995574i | \(0.529959\pi\) | |||||||
\(234\) | −29.3823 | + | 7.28901i | −1.92078 | + | 0.476497i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 36.4134 | − | 13.2534i | 2.37031 | − | 0.862723i | ||||
\(237\) | 0.660752 | − | 12.4671i | 0.0429204 | − | 0.809826i | ||||
\(238\) | −1.78223 | − | 2.12398i | −0.115525 | − | 0.137677i | ||||
\(239\) | −14.4904 | − | 5.27406i | −0.937303 | − | 0.341151i | −0.172203 | − | 0.985061i | \(-0.555088\pi\) |
−0.765100 | + | 0.643911i | \(0.777311\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.28373 | − | 12.9516i | 0.147108 | − | 0.834289i | −0.818543 | − | 0.574445i | \(-0.805218\pi\) |
0.965651 | − | 0.259844i | \(-0.0836711\pi\) | |||||||
\(242\) | − | 3.44113i | − | 0.221204i | ||||||
\(243\) | 12.7956 | − | 8.90345i | 0.820841 | − | 0.571157i | ||||
\(244\) | 49.7209 | 3.18305 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.553018 | − | 4.52605i | −0.0352592 | − | 0.288571i | ||||
\(247\) | 5.52617 | − | 15.1830i | 0.351622 | − | 0.966073i | ||||
\(248\) | −4.52329 | − | 5.39065i | −0.287229 | − | 0.342307i | ||||
\(249\) | −25.7722 | − | 1.36591i | −1.63324 | − | 0.0865612i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.70830 | + | 15.0832i | −0.549663 | + | 0.952045i | 0.448634 | + | 0.893716i | \(0.351911\pi\) |
−0.998297 | + | 0.0583292i | \(0.981423\pi\) | |||||||
\(252\) | −1.57814 | − | 6.36155i | −0.0994135 | − | 0.400740i | ||||
\(253\) | 11.9277 | − | 6.88646i | 0.749889 | − | 0.432948i | ||||
\(254\) | 21.2112 | + | 17.7983i | 1.33091 | + | 1.11676i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.03066 | − | 28.5303i | −0.314416 | − | 1.78314i | ||||
\(257\) | 11.0176 | − | 1.94270i | 0.687260 | − | 0.121182i | 0.180896 | − | 0.983502i | \(-0.442100\pi\) |
0.506364 | + | 0.862320i | \(0.330989\pi\) | |||||||
\(258\) | 19.5904 | − | 20.9833i | 1.21964 | − | 1.30636i | ||||
\(259\) | 1.79017 | + | 1.50213i | 0.111236 | + | 0.0933377i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.31662 | + | 19.1533i | 0.0814965 | + | 1.18556i | ||||
\(262\) | 18.7433 | + | 10.8214i | 1.15796 | + | 0.668550i | ||||
\(263\) | 7.08354 | + | 19.4619i | 0.436790 | + | 1.20007i | 0.941569 | + | 0.336821i | \(0.109352\pi\) |
−0.504779 | + | 0.863249i | \(0.668426\pi\) | |||||||
\(264\) | −10.3141 | − | 20.2720i | −0.634786 | − | 1.24766i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.03221 | + | 1.83157i | 0.308544 | + | 0.112301i | ||||
\(267\) | −1.05256 | + | 2.47562i | −0.0644159 | + | 0.151506i | ||||
\(268\) | −32.7912 | − | 5.78197i | −2.00304 | − | 0.353190i | ||||
\(269\) | 28.2449 | 1.72212 | 0.861060 | − | 0.508504i | \(-0.169801\pi\) | ||||
0.861060 | + | 0.508504i | \(0.169801\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.2626 | 1.04863 | 0.524316 | − | 0.851524i | \(-0.324321\pi\) | ||||
0.524316 | + | 0.851524i | \(0.324321\pi\) | |||||||
\(272\) | 5.21680 | + | 0.919863i | 0.316315 | + | 0.0557749i | ||||
\(273\) | 2.53767 | + | 3.37175i | 0.153587 | + | 0.204067i | ||||
\(274\) | −25.9987 | − | 9.46275i | −1.57064 | − | 0.571666i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −15.8411 | + | 24.3616i | −0.953520 | + | 1.46640i | ||||
\(277\) | 1.76789 | + | 4.85725i | 0.106222 | + | 0.291844i | 0.981405 | − | 0.191949i | \(-0.0614809\pi\) |
−0.875182 | + | 0.483793i | \(0.839259\pi\) | |||||||
\(278\) | 3.54375 | + | 2.04598i | 0.212540 | + | 0.122710i | ||||
\(279\) | −4.94464 | − | 0.525604i | −0.296028 | − | 0.0314671i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.52522 | − | 2.11891i | −0.150642 | − | 0.126404i | 0.564352 | − | 0.825534i | \(-0.309126\pi\) |
−0.714994 | + | 0.699131i | \(0.753571\pi\) | |||||||
\(282\) | 4.36156 | + | 14.2962i | 0.259727 | + | 0.851326i | ||||
\(283\) | 8.99200 | − | 1.58553i | 0.534519 | − | 0.0942501i | 0.100128 | − | 0.994975i | \(-0.468075\pi\) |
0.434391 | + | 0.900724i | \(0.356964\pi\) | |||||||
\(284\) | −0.749103 | − | 4.24837i | −0.0444511 | − | 0.252095i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 23.9099 | + | 20.0628i | 1.41382 | + | 1.18634i | ||||
\(287\) | −0.550462 | + | 0.317809i | −0.0324927 | + | 0.0187597i | ||||
\(288\) | −5.09551 | − | 3.71130i | −0.300256 | − | 0.218691i | ||||
\(289\) | −6.51799 | + | 11.2895i | −0.383411 | + | 0.664087i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.00004 | − | 7.68945i | 0.293108 | − | 0.450764i | ||||
\(292\) | −0.473411 | − | 0.564189i | −0.0277043 | − | 0.0330167i | ||||
\(293\) | −0.966697 | + | 2.65598i | −0.0564750 | + | 0.155164i | −0.964722 | − | 0.263271i | \(-0.915199\pi\) |
0.908247 | + | 0.418434i | \(0.137421\pi\) | |||||||
\(294\) | 22.1476 | − | 16.6689i | 1.29167 | − | 0.972151i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −17.1100 | −0.994496 | ||||||||
\(297\) | −15.1872 | − | 5.25947i | −0.881251 | − | 0.305185i | ||||
\(298\) | 52.0017i | 3.01238i | ||||||||
\(299\) | 3.24888 | − | 18.4253i | 0.187887 | − | 1.06556i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.76036 | − | 1.36866i | −0.216744 | − | 0.0788882i | ||||
\(302\) | −7.31964 | − | 8.72321i | −0.421198 | − | 0.501964i | ||||
\(303\) | 11.2214 | − | 5.70923i | 0.644650 | − | 0.327987i | ||||
\(304\) | −9.61423 | + | 3.49929i | −0.551414 | + | 0.200698i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 11.9018 | − | 8.00746i | 0.680382 | − | 0.457756i | ||||
\(307\) | −5.45116 | + | 3.14723i | −0.311114 | + | 0.179622i | −0.647425 | − | 0.762129i | \(-0.724154\pi\) |
0.336311 | + | 0.941751i | \(0.390821\pi\) | |||||||
\(308\) | −4.34380 | + | 5.17673i | −0.247511 | + | 0.294972i | ||||
\(309\) | 8.10442 | + | 7.56644i | 0.461045 | + | 0.430440i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.28029 | − | 7.26088i | −0.0725985 | − | 0.411727i | −0.999350 | − | 0.0360515i | \(-0.988522\pi\) |
0.926751 | − | 0.375675i | \(-0.122589\pi\) | |||||||
\(312\) | −30.1015 | − | 6.96818i | −1.70416 | − | 0.394496i | ||||
\(313\) | 2.74519 | − | 3.27159i | 0.155167 | − | 0.184921i | −0.682860 | − | 0.730549i | \(-0.739264\pi\) |
0.838028 | + | 0.545628i | \(0.183709\pi\) | |||||||
\(314\) | 0.251217 | + | 0.435120i | 0.0141770 | + | 0.0245552i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.5791 | − | 23.5197i | 0.763883 | − | 1.32308i | ||||
\(317\) | 5.52279 | + | 15.1738i | 0.310191 | + | 0.852243i | 0.992617 | + | 0.121288i | \(0.0387026\pi\) |
−0.682426 | + | 0.730954i | \(0.739075\pi\) | |||||||
\(318\) | −1.18891 | + | 22.4325i | −0.0666708 | + | 1.25795i | ||||
\(319\) | 15.1632 | − | 12.7235i | 0.848979 | − | 0.712378i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.16455 | + | 9.53101i | 0.0649989 | + | 0.531969i | ||||
\(322\) | 6.10682 | + | 1.07680i | 0.340320 | + | 0.0600075i | ||||
\(323\) | 7.65618i | 0.426001i | ||||||||
\(324\) | 33.5911 | − | 4.64009i | 1.86617 | − | 0.257783i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.34535 | + | 13.3012i | −0.129897 | + | 0.736683i | ||||
\(327\) | 10.7134 | − | 1.30902i | 0.592451 | − | 0.0723890i | ||||
\(328\) | 1.59169 | − | 4.37313i | 0.0878862 | − | 0.241465i | ||||
\(329\) | 1.59610 | − | 1.33928i | 0.0879956 | − | 0.0738371i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.0686 | + | 6.57644i | −0.993142 | + | 0.361474i | −0.786936 | − | 0.617035i | \(-0.788334\pi\) |
−0.206206 | + | 0.978509i | \(0.566112\pi\) | |||||||
\(332\) | −48.6201 | − | 28.0708i | −2.66838 | − | 1.54059i | ||||
\(333\) | −8.70693 | + | 8.38834i | −0.477137 | + | 0.459678i | ||||
\(334\) | −20.0301 | − | 34.6932i | −1.09600 | − | 1.89833i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.602651 | − | 2.60336i | 0.0328773 | − | 0.142025i | ||||
\(337\) | −29.0152 | + | 5.11615i | −1.58056 | + | 0.278695i | −0.893893 | − | 0.448281i | \(-0.852036\pi\) |
−0.686663 | + | 0.726976i | \(0.740925\pi\) | |||||||
\(338\) | 11.0087 | − | 1.94112i | 0.598792 | − | 0.105583i | ||||
\(339\) | −14.9950 | − | 13.9996i | −0.814417 | − | 0.760355i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.56339 | + | 4.43993i | 0.138815 | + | 0.240435i | ||||
\(342\) | −12.1748 | + | 24.8874i | −0.658337 | + | 1.34576i | ||||
\(343\) | −6.86159 | − | 3.96154i | −0.370491 | − | 0.213903i | ||||
\(344\) | 27.5321 | − | 10.0209i | 1.48443 | − | 0.540289i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −34.9592 | + | 29.3342i | −1.87942 | + | 1.57702i | ||||
\(347\) | −3.89801 | + | 10.7097i | −0.209256 | + | 0.574927i | −0.999272 | − | 0.0381600i | \(-0.987850\pi\) |
0.790015 | + | 0.613087i | \(0.210073\pi\) | |||||||
\(348\) | −16.3408 | + | 38.4336i | −0.875961 | + | 2.06025i | ||||
\(349\) | −4.89021 | + | 27.7338i | −0.261767 | + | 1.48456i | 0.516318 | + | 0.856397i | \(0.327302\pi\) |
−0.778085 | + | 0.628158i | \(0.783809\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.7343 | + | 11.2116i | −0.999962 | + | 0.598431i | ||||
\(352\) | 6.49941i | 0.346419i | ||||||||
\(353\) | 28.2188 | + | 4.97573i | 1.50193 | + | 0.264831i | 0.863305 | − | 0.504683i | \(-0.168391\pi\) |
0.638629 | + | 0.769515i | \(0.279502\pi\) | |||||||
\(354\) | 34.1819 | − | 25.7263i | 1.81675 | − | 1.36734i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.48277 | + | 3.76149i | −0.237586 | + | 0.199359i | ||||
\(357\) | −1.67640 | − | 1.09007i | −0.0887245 | − | 0.0576929i | ||||
\(358\) | 13.3357 | + | 36.6394i | 0.704812 | + | 1.93645i | ||||
\(359\) | −15.5161 | + | 26.8747i | −0.818909 | + | 1.41839i | 0.0875770 | + | 0.996158i | \(0.472088\pi\) |
−0.906486 | + | 0.422235i | \(0.861246\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.10636 | + | 3.64833i | 0.110861 | + | 0.192017i | ||||
\(362\) | 4.61820 | − | 5.50376i | 0.242727 | − | 0.289271i | ||||
\(363\) | −0.724191 | − | 2.37373i | −0.0380102 | − | 0.124589i | ||||
\(364\) | 1.59408 | + | 9.04045i | 0.0835523 | + | 0.473848i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 52.5040 | − | 16.0182i | 2.74443 | − | 0.837286i | ||||
\(367\) | 15.5067 | − | 18.4802i | 0.809446 | − | 0.964660i | −0.190409 | − | 0.981705i | \(-0.560981\pi\) |
0.999855 | + | 0.0170450i | \(0.00542586\pi\) | |||||||
\(368\) | −10.2601 | + | 5.92365i | −0.534843 | + | 0.308791i | ||||
\(369\) | −1.33399 | − | 3.00574i | −0.0694449 | − | 0.156473i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.94260 | − | 1.07102i | 0.152772 | − | 0.0556045i | ||||
\(372\) | −9.06828 | − | 5.89662i | −0.470169 | − | 0.305726i | ||||
\(373\) | −8.08988 | − | 9.64114i | −0.418878 | − | 0.499199i | 0.514801 | − | 0.857309i | \(-0.327866\pi\) |
−0.933679 | + | 0.358110i | \(0.883421\pi\) | |||||||
\(374\) | −13.8979 | − | 5.05843i | −0.718645 | − | 0.261565i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.64902 | + | 15.0233i | −0.136613 | + | 0.774769i | ||||
\(377\) | − | 26.8890i | − | 1.38486i | ||||||
\(378\) | −3.71593 | − | 6.20922i | −0.191127 | − | 0.319368i | ||||
\(379\) | 7.70522 | 0.395790 | 0.197895 | − | 0.980223i | \(-0.436589\pi\) | ||||
0.197895 | + | 0.980223i | \(0.436589\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.3774 | + | 7.81354i | 0.941502 | + | 0.400300i | ||||
\(382\) | −1.85129 | + | 5.08638i | −0.0947203 | + | 0.260242i | ||||
\(383\) | −11.4812 | − | 13.6828i | −0.586664 | − | 0.699159i | 0.388297 | − | 0.921534i | \(-0.373063\pi\) |
−0.974961 | + | 0.222376i | \(0.928619\pi\) | |||||||
\(384\) | −16.2557 | − | 31.9503i | −0.829548 | − | 1.63046i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.05704 | + | 1.83085i | −0.0538020 | + | 0.0931878i | ||||
\(387\) | 9.09771 | − | 18.5973i | 0.462463 | − | 0.945356i | ||||
\(388\) | 17.2793 | − | 9.97622i | 0.877224 | − | 0.506466i | ||||
\(389\) | −20.9808 | − | 17.6050i | −1.06377 | − | 0.892607i | −0.0692941 | − | 0.997596i | \(-0.522075\pi\) |
−0.994473 | + | 0.104989i | \(0.966519\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.53948 | + | 8.73081i | 0.0778547 | + | 0.441536i | ||||
\(392\) | 27.8615 | − | 4.91274i | 1.40722 | − | 0.248131i | ||||
\(393\) | 15.2067 | + | 3.52020i | 0.767078 | + | 0.177571i | ||||
\(394\) | 37.3038 | + | 31.3016i | 1.87934 | + | 1.57695i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −24.2571 | − | 25.1784i | −1.21896 | − | 1.26526i | ||||
\(397\) | 3.65115 | + | 2.10799i | 0.183246 | + | 0.105797i | 0.588817 | − | 0.808266i | \(-0.299594\pi\) |
−0.405571 | + | 0.914064i | \(0.632927\pi\) | |||||||
\(398\) | −15.6144 | − | 42.9002i | −0.782680 | − | 2.15039i | ||||
\(399\) | 3.85673 | + | 0.204405i | 0.193078 | + | 0.0102331i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.2575 | − | 5.18930i | −0.711985 | − | 0.259141i | −0.0394656 | − | 0.999221i | \(-0.512566\pi\) |
−0.672519 | + | 0.740080i | \(0.734788\pi\) | |||||||
\(402\) | −36.4894 | + | 4.45848i | −1.81993 | + | 0.222369i | ||||
\(403\) | 6.85857 | + | 1.20935i | 0.341650 | + | 0.0602420i | ||||
\(404\) | 27.3880 | 1.36260 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.91200 | 0.442295 | ||||||||
\(407\) | 12.2760 | + | 2.16460i | 0.608501 | + | 0.107295i | ||||
\(408\) | 14.5326 | − | 1.77568i | 0.719473 | − | 0.0879093i | ||||
\(409\) | 4.42559 | + | 1.61078i | 0.218831 | + | 0.0796481i | 0.449109 | − | 0.893477i | \(-0.351741\pi\) |
−0.230278 | + | 0.973125i | \(0.573964\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.9257 | − | 1.05605i | −0.982860 | − | 0.0520912i | ||||
\(412\) | 8.24918 | + | 22.6644i | 0.406408 | + | 1.11660i | ||||
\(413\) | −5.16469 | − | 2.98184i | −0.254138 | − | 0.146727i | ||||
\(414\) | −8.87937 | + | 30.8287i | −0.436397 | + | 1.51515i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.76339 | + | 5.67516i | 0.331602 | + | 0.278248i | ||||
\(417\) | 2.87510 | + | 0.665556i | 0.140794 | + | 0.0325924i | ||||
\(418\) | 28.1314 | − | 4.96033i | 1.37595 | − | 0.242618i | ||||
\(419\) | −3.43669 | − | 19.4905i | −0.167894 | − | 0.952171i | −0.946031 | − | 0.324077i | \(-0.894946\pi\) |
0.778137 | − | 0.628094i | \(-0.216165\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.5915 | + | 18.1174i | 1.05231 | + | 0.882989i | 0.993334 | − | 0.115270i | \(-0.0367734\pi\) |
0.0589715 | + | 0.998260i | \(0.481218\pi\) | |||||||
\(422\) | 33.6607 | − | 19.4340i | 1.63858 | − | 0.946032i | ||||
\(423\) | 6.01731 | + | 8.94379i | 0.292572 | + | 0.434862i | ||||
\(424\) | −11.4637 | + | 19.8557i | −0.556726 | + | 0.964278i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.15970 | − | 4.24484i | −0.104638 | − | 0.205663i | ||||
\(427\) | −4.91863 | − | 5.86180i | −0.238029 | − | 0.283672i | ||||
\(428\) | −7.14387 | + | 19.6276i | −0.345312 | + | 0.948737i | ||||
\(429\) | 20.7156 | + | 8.80769i | 1.00016 | + | 0.425239i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.19681 | −0.250321 | −0.125161 | − | 0.992136i | \(-0.539945\pi\) | ||||
−0.125161 | + | 0.992136i | \(0.539945\pi\) | |||||||
\(432\) | 13.0638 | + | 4.52413i | 0.628534 | + | 0.217667i | ||||
\(433\) | 25.3285i | 1.21721i | 0.793473 | + | 0.608605i | \(0.208270\pi\) | ||||
−0.793473 | + | 0.608605i | \(0.791730\pi\) | |||||||
\(434\) | −0.400823 | + | 2.27318i | −0.0192401 | + | 0.109116i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 22.0625 | + | 8.03011i | 1.05660 | + | 0.384572i | ||||
\(437\) | −11.0064 | − | 13.1169i | −0.526509 | − | 0.627469i | ||||
\(438\) | −0.681671 | − | 0.443254i | −0.0325715 | − | 0.0211795i | ||||
\(439\) | −14.7167 | + | 5.35646i | −0.702392 | + | 0.255650i | −0.668432 | − | 0.743773i | \(-0.733034\pi\) |
−0.0339602 | + | 0.999423i | \(0.510812\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.7697 | − | 16.1594i | 0.560460 | − | 0.769496i | ||||
\(442\) | −17.3993 | + | 10.0455i | −0.827600 | + | 0.477815i | ||||
\(443\) | 11.7333 | − | 13.9833i | 0.557468 | − | 0.664365i | −0.411541 | − | 0.911391i | \(-0.635009\pi\) |
0.969009 | + | 0.247027i | \(0.0794536\pi\) | |||||||
\(444\) | −25.1557 | + | 7.67464i | −1.19384 | + | 0.364222i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.94849 | − | 50.7494i | −0.423723 | − | 2.40305i | ||||
\(447\) | 10.9439 | + | 35.8714i | 0.517626 | + | 1.69666i | ||||
\(448\) | −3.86434 | + | 4.60534i | −0.182573 | + | 0.217582i | ||||
\(449\) | 14.3608 | + | 24.8737i | 0.677729 | + | 1.17386i | 0.975663 | + | 0.219274i | \(0.0703690\pi\) |
−0.297934 | + | 0.954586i | \(0.596298\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.69525 | + | 2.93626i | −0.0798262 | + | 0.138263i | ||||
\(452\) | −15.2628 | − | 41.9343i | −0.717904 | − | 1.97242i | ||||
\(453\) | −6.88499 | − | 4.47694i | −0.323485 | − | 0.210345i | ||||
\(454\) | −35.1654 | + | 29.5073i | −1.65039 | + | 1.38485i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −22.5933 | + | 17.0044i | −1.05803 | + | 0.796304i | ||||
\(457\) | 34.8503 | + | 6.14505i | 1.63023 | + | 0.287453i | 0.912563 | − | 0.408936i | \(-0.134100\pi\) |
0.717665 | + | 0.696389i | \(0.245211\pi\) | |||||||
\(458\) | − | 53.9648i | − | 2.52161i | ||||||
\(459\) | 6.52484 | − | 8.02840i | 0.304553 | − | 0.374734i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.395350 | − | 2.24214i | 0.0184133 | − | 0.104427i | −0.974216 | − | 0.225617i | \(-0.927560\pi\) |
0.992629 | + | 0.121190i | \(0.0386712\pi\) | |||||||
\(462\) | −2.91919 | + | 6.86591i | −0.135813 | + | 0.319431i | ||||
\(463\) | 6.28446 | − | 17.2664i | 0.292064 | − | 0.802438i | −0.703701 | − | 0.710496i | \(-0.748470\pi\) |
0.995764 | − | 0.0919417i | \(-0.0293073\pi\) | |||||||
\(464\) | −13.0432 | + | 10.9446i | −0.605517 | + | 0.508089i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −39.9033 | + | 14.5236i | −1.84848 | + | 0.672793i | ||||
\(467\) | 4.03455 | + | 2.32935i | 0.186697 | + | 0.107789i | 0.590435 | − | 0.807085i | \(-0.298956\pi\) |
−0.403738 | + | 0.914874i | \(0.632289\pi\) | |||||||
\(468\) | −47.3819 | + | 3.25707i | −2.19023 | + | 0.150558i | ||||
\(469\) | 2.56220 | + | 4.43786i | 0.118312 | + | 0.204922i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.264864 | + | 0.247282i | 0.0122043 | + | 0.0113941i | ||||
\(472\) | 43.0007 | − | 7.58218i | 1.97927 | − | 0.348998i | ||||
\(473\) | −21.0215 | + | 3.70665i | −0.966568 | + | 0.170432i | ||||
\(474\) | 6.76202 | − | 29.2109i | 0.310590 | − | 1.34170i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.17495 | − | 3.76712i | −0.0996885 | − | 0.172666i | ||||
\(477\) | 3.90082 | + | 15.7244i | 0.178606 | + | 0.719970i | ||||
\(478\) | −32.0722 | − | 18.5169i | −1.46695 | − | 0.846942i | ||||
\(479\) | −13.3210 | + | 4.84844i | −0.608651 | + | 0.221531i | −0.627913 | − | 0.778283i | \(-0.716091\pi\) |
0.0192617 | + | 0.999814i | \(0.493868\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.9717 | − | 10.8846i | 0.591460 | − | 0.496294i | ||||
\(482\) | 10.8026 | − | 29.6800i | 0.492047 | − | 1.35189i | ||||
\(483\) | 4.43917 | − | 0.542402i | 0.201989 | − | 0.0246802i | ||||
\(484\) | 0.937459 | − | 5.31660i | 0.0426118 | − | 0.241663i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 33.9765 | − | 15.7216i | 1.54121 | − | 0.713147i | ||||
\(487\) | 21.4338i | 0.971258i | 0.874165 | + | 0.485629i | \(0.161409\pi\) | ||||
−0.874165 | + | 0.485629i | \(0.838591\pi\) | |||||||
\(488\) | 55.1745 | + | 9.72875i | 2.49763 | + | 0.440400i | ||||
\(489\) | 1.18140 | + | 9.66888i | 0.0534246 | + | 0.437242i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.7919 | + | 9.05550i | −0.487033 | + | 0.408669i | −0.852961 | − | 0.521974i | \(-0.825196\pi\) |
0.365929 | + | 0.930643i | \(0.380751\pi\) | |||||||
\(492\) | 0.378601 | − | 7.14348i | 0.0170687 | − | 0.322053i | ||||
\(493\) | 4.35779 | + | 11.9729i | 0.196265 | + | 0.539234i | ||||
\(494\) | 19.4020 | − | 33.6053i | 0.872938 | − | 1.51197i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.20500 | − | 3.81917i | −0.0990073 | − | 0.171486i | ||||
\(497\) | −0.426753 | + | 0.508585i | −0.0191425 | + | 0.0228131i | ||||
\(498\) | −60.3850 | − | 13.9785i | −2.70592 | − | 0.626392i | ||||
\(499\) | −2.58898 | − | 14.6828i | −0.115899 | − | 0.657294i | −0.986301 | − | 0.164953i | \(-0.947253\pi\) |
0.870403 | − | 0.492340i | \(-0.163858\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.1182 | − | 19.7164i | −0.943494 | − | 0.880864i | ||||
\(502\) | −26.8866 | + | 32.0422i | −1.20001 | + | 1.43011i | ||||
\(503\) | −13.7378 | + | 7.93153i | −0.612539 | + | 0.353650i | −0.773958 | − | 0.633236i | \(-0.781726\pi\) |
0.161420 | + | 0.986886i | \(0.448393\pi\) | |||||||
\(504\) | −0.506490 | − | 7.36810i | −0.0225608 | − | 0.328201i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 31.0826 | − | 11.3131i | 1.38179 | − | 0.502930i | ||||
\(507\) | 7.18540 | − | 3.65580i | 0.319115 | − | 0.162360i | ||||
\(508\) | 27.9228 | + | 33.2771i | 1.23888 | + | 1.47643i | ||||
\(509\) | 31.8807 | + | 11.6036i | 1.41309 | + | 0.514321i | 0.932034 | − | 0.362371i | \(-0.118033\pi\) |
0.481052 | + | 0.876692i | \(0.340255\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0196825 | + | 0.111625i | −0.000870700 | + | 0.00493799i | ||||
\(512\) | − | 28.1824i | − | 1.24550i | ||||||
\(513\) | −3.16072 | + | 19.7298i | −0.139549 | + | 0.871093i | ||||
\(514\) | 26.8683 | 1.18511 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 35.9839 | − | 27.0825i | 1.58410 | − | 1.19224i | ||||
\(517\) | 3.80123 | − | 10.4438i | 0.167178 | − | 0.459317i | ||||
\(518\) | 3.60754 | + | 4.29930i | 0.158506 | + | 0.188900i | ||||
\(519\) | −17.9418 | + | 27.5923i | −0.787558 | + | 1.21117i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.3899 | − | 37.0484i | 0.937108 | − | 1.62312i | 0.166277 | − | 0.986079i | \(-0.446825\pi\) |
0.770831 | − | 0.637040i | \(-0.219841\pi\) | |||||||
\(522\) | −4.87367 | + | 45.8493i | −0.213315 | + | 2.00677i | ||||
\(523\) | −2.40569 | + | 1.38893i | −0.105193 | + | 0.0607335i | −0.551674 | − | 0.834060i | \(-0.686011\pi\) |
0.446480 | + | 0.894793i | \(0.352677\pi\) | |||||||
\(524\) | 26.0106 | + | 21.8255i | 1.13628 | + | 0.953451i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.63721 | + | 48.9840i | 0.376600 | + | 2.13581i | ||||
\(527\) | −3.24992 | + | 0.573049i | −0.141569 | + | 0.0249624i | ||||
\(528\) | −4.15942 | − | 13.6336i | −0.181016 | − | 0.593327i | ||||
\(529\) | 2.43023 | + | 2.03920i | 0.105662 | + | 0.0886609i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.1650 | − | 24.9400i | 0.788292 | − | 1.08230i | ||||
\(532\) | 7.27587 | + | 4.20073i | 0.315449 | + | 0.182125i | ||||
\(533\) | 1.57526 | + | 4.32799i | 0.0682321 | + | 0.187466i | ||||
\(534\) | −3.52188 | + | 5.41622i | −0.152407 | + | 0.234383i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −35.2565 | − | 12.8323i | −1.52285 | − | 0.554271i | ||||
\(537\) | 16.9099 | + | 22.4678i | 0.729717 | + | 0.969557i | ||||
\(538\) | 66.8029 | + | 11.7792i | 2.88008 | + | 0.507835i | ||||
\(539\) | −20.6116 | −0.887803 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.59390 | −0.154514 | −0.0772570 | − | 0.997011i | \(-0.524616\pi\) | ||||
−0.0772570 | + | 0.997011i | \(0.524616\pi\) | |||||||
\(542\) | 40.8285 | + | 7.19917i | 1.75373 | + | 0.309231i | ||||
\(543\) | 2.02741 | − | 4.76846i | 0.0870047 | − | 0.204634i | ||||
\(544\) | −3.93130 | − | 1.43088i | −0.168553 | − | 0.0613483i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.59580 | + | 9.03294i | 0.196682 | + | 0.386574i | ||||
\(547\) | −13.5392 | − | 37.1985i | −0.578892 | − | 1.59049i | −0.790051 | − | 0.613042i | \(-0.789946\pi\) |
0.211158 | − | 0.977452i | \(-0.432276\pi\) | |||||||
\(548\) | −37.5905 | − | 21.7029i | −1.60579 | − | 0.927101i | ||||
\(549\) | 32.8468 | − | 22.0991i | 1.40187 | − | 0.943167i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.8514 | − | 15.8182i | −0.803099 | − | 0.673880i | ||||
\(552\) | −22.3453 | + | 23.9341i | −0.951081 | + | 1.01870i | ||||
\(553\) | −4.11614 | + | 0.725786i | −0.175036 | + | 0.0308636i | ||||
\(554\) | 2.15566 | + | 12.2253i | 0.0915850 | + | 0.519405i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.91776 | + | 4.12649i | 0.208560 | + | 0.175002i | ||||
\(557\) | 9.90267 | − | 5.71731i | 0.419590 | − | 0.242250i | −0.275312 | − | 0.961355i | \(-0.588781\pi\) |
0.694902 | + | 0.719105i | \(0.255448\pi\) | |||||||
\(558\) | −11.4756 | − | 3.30522i | −0.485799 | − | 0.139921i | ||||
\(559\) | −14.4983 | + | 25.1119i | −0.613214 | + | 1.06212i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.6515 | − | 0.564526i | −0.449707 | − | 0.0238343i | ||||
\(562\) | −5.08882 | − | 6.06462i | −0.214659 | − | 0.255821i | ||||
\(563\) | 4.96298 | − | 13.6357i | 0.209165 | − | 0.574676i | −0.790101 | − | 0.612976i | \(-0.789972\pi\) |
0.999266 | + | 0.0383005i | \(0.0121944\pi\) | |||||||
\(564\) | 2.84400 | + | 23.2761i | 0.119754 | + | 0.980099i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 21.9285 | 0.921725 | ||||||||
\(567\) | −3.87003 | − | 3.50117i | −0.162526 | − | 0.147035i | ||||
\(568\) | − | 4.86093i | − | 0.203960i | ||||||
\(569\) | 0.225601 | − | 1.27945i | 0.00945767 | − | 0.0536371i | −0.979714 | − | 0.200402i | \(-0.935775\pi\) |
0.989171 | + | 0.146765i | \(0.0468862\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.0890 | − | 5.49193i | −0.631453 | − | 0.229830i | 0.00641065 | − | 0.999979i | \(-0.497959\pi\) |
−0.637864 | + | 0.770149i | \(0.720182\pi\) | |||||||
\(572\) | 31.4756 | + | 37.5111i | 1.31606 | + | 1.56842i | ||||
\(573\) | −0.206606 | + | 3.89825i | −0.00863108 | + | 0.162852i | ||||
\(574\) | −1.43445 | + | 0.522099i | −0.0598730 | + | 0.0217920i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −21.5796 | − | 22.3992i | −0.899152 | − | 0.933301i | ||||
\(577\) | 7.32686 | − | 4.23017i | 0.305021 | − | 0.176104i | −0.339675 | − | 0.940543i | \(-0.610317\pi\) |
0.644696 | + | 0.764439i | \(0.276984\pi\) | |||||||
\(578\) | −20.1241 | + | 23.9829i | −0.837050 | + | 0.997558i | ||||
\(579\) | −0.343854 | + | 1.48540i | −0.0142901 | + | 0.0617310i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.50035 | + | 8.50893i | 0.0622452 | + | 0.353010i | ||||
\(582\) | 15.0326 | − | 16.1014i | 0.623120 | − | 0.667424i | ||||
\(583\) | 10.7369 | − | 12.7958i | 0.444678 | − | 0.529947i | ||||
\(584\) | −0.414943 | − | 0.718703i | −0.0171705 | − | 0.0297401i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.39401 | + | 5.87860i | −0.140205 | + | 0.242843i | ||||
\(587\) | −6.28811 | − | 17.2764i | −0.259538 | − | 0.713075i | −0.999196 | − | 0.0400919i | \(-0.987235\pi\) |
0.739658 | − | 0.672983i | \(-0.234987\pi\) | |||||||
\(588\) | 38.7594 | − | 19.7201i | 1.59841 | − | 0.813244i | ||||
\(589\) | 4.88260 | − | 4.09699i | 0.201184 | − | 0.168814i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 32.3200 | + | 13.7416i | 1.32947 | + | 0.565252i | ||||
\(592\) | −10.5597 | − | 1.86196i | −0.434001 | − | 0.0765260i | ||||
\(593\) | 13.5128i | 0.554905i | 0.960739 | + | 0.277452i | \(0.0894901\pi\) | ||||
−0.960739 | + | 0.277452i | \(0.910510\pi\) | |||||||
\(594\) | −33.7264 | − | 18.7730i | −1.38381 | − | 0.770265i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −14.1667 | + | 80.3435i | −0.580292 | + | 3.29100i | ||||
\(597\) | −19.7994 | − | 26.3070i | −0.810337 | − | 1.07667i | ||||
\(598\) | 15.3681 | − | 42.2234i | 0.628447 | − | 1.72664i | ||||
\(599\) | −8.44772 | + | 7.08848i | −0.345165 | + | 0.289627i | −0.798845 | − | 0.601537i | \(-0.794555\pi\) |
0.453680 | + | 0.891164i | \(0.350111\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.2421 | + | 8.82341i | −0.988856 | + | 0.359914i | −0.785277 | − | 0.619144i | \(-0.787480\pi\) |
−0.203579 | + | 0.979058i | \(0.565257\pi\) | |||||||
\(602\) | −8.32298 | − | 4.80528i | −0.339219 | − | 0.195848i | ||||
\(603\) | −24.2325 | + | 10.7548i | −0.986824 | + | 0.437968i | ||||
\(604\) | −8.93252 | − | 15.4716i | −0.363459 | − | 0.629529i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 28.9210 | − | 8.82338i | 1.17484 | − | 0.358425i | ||||
\(607\) | −14.5652 | + | 2.56823i | −0.591182 | + | 0.104241i | −0.461233 | − | 0.887279i | \(-0.652593\pi\) |
−0.129950 | + | 0.991521i | \(0.541482\pi\) | |||||||
\(608\) | 7.95752 | − | 1.40312i | 0.322720 | − | 0.0569042i | ||||
\(609\) | 6.14761 | − | 1.87555i | 0.249114 | − | 0.0760009i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.54882 | − | 13.0749i | −0.305393 | − | 0.528956i | ||||
\(612\) | 20.5700 | − | 9.12926i | 0.831492 | − | 0.369029i | ||||
\(613\) | −31.4141 | − | 18.1370i | −1.26880 | − | 0.732545i | −0.294043 | − | 0.955792i | \(-0.595001\pi\) |
−0.974762 | + | 0.223248i | \(0.928334\pi\) | |||||||
\(614\) | −14.2053 | + | 5.17029i | −0.573277 | + | 0.208656i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.83316 | + | 4.89460i | −0.235025 | + | 0.197209i | ||||
\(617\) | 13.8086 | − | 37.9387i | 0.555912 | − | 1.52736i | −0.269601 | − | 0.962972i | \(-0.586892\pi\) |
0.825513 | − | 0.564383i | \(-0.190886\pi\) | |||||||
\(618\) | 16.0126 | + | 21.2755i | 0.644120 | + | 0.855826i | ||||
\(619\) | 1.19701 | − | 6.78858i | 0.0481119 | − | 0.272856i | −0.951256 | − | 0.308402i | \(-0.900206\pi\) |
0.999368 | + | 0.0355458i | \(0.0113170\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.362848 | + | 23.1347i | 0.0145606 | + | 0.928362i | ||||
\(622\) | − | 17.7069i | − | 0.709981i | ||||||
\(623\) | 0.886916 | + | 0.156387i | 0.0355335 | + | 0.00626552i | ||||
\(624\) | −17.8193 | − | 7.57626i | −0.713343 | − | 0.303293i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.85711 | − | 6.59290i | 0.314033 | − | 0.263505i | ||||
\(627\) | 18.3615 | − | 9.34200i | 0.733287 | − | 0.373083i | ||||
\(628\) | 0.269595 | + | 0.740705i | 0.0107580 | + | 0.0295574i | ||||
\(629\) | −4.01193 | + | 6.94887i | −0.159966 | + | 0.277070i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.9095 | − | 25.8241i | −0.593539 | − | 1.02804i | −0.993751 | − | 0.111617i | \(-0.964397\pi\) |
0.400212 | − | 0.916423i | \(-0.368936\pi\) | |||||||
\(632\) | 19.6705 | − | 23.4424i | 0.782451 | − | 0.932489i | ||||
\(633\) | 19.1296 | − | 20.4897i | 0.760334 | − | 0.814394i | ||||
\(634\) | 6.73414 | + | 38.1912i | 0.267447 | + | 1.51677i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.94811 | + | 34.3346i | −0.315163 | + | 1.36146i | ||||
\(637\) | −17.9976 | + | 21.4487i | −0.713092 | + | 0.849830i | ||||
\(638\) | 41.1693 | − | 23.7691i | 1.62991 | − | 0.941028i | ||||
\(639\) | −2.38312 | − | 2.47363i | −0.0942749 | − | 0.0978554i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.2947 | + | 14.6661i | −1.59155 | + | 0.579275i | −0.977673 | − | 0.210131i | \(-0.932611\pi\) |
−0.613872 | + | 0.789406i | \(0.710389\pi\) | |||||||
\(642\) | −1.22046 | + | 23.0278i | −0.0481678 | + | 0.908834i | ||||
\(643\) | −17.6209 | − | 20.9998i | −0.694901 | − | 0.828150i | 0.297038 | − | 0.954866i | \(-0.404001\pi\) |
−0.991939 | + | 0.126715i | \(0.959557\pi\) | |||||||
\(644\) | 9.14178 | + | 3.32734i | 0.360237 | + | 0.131115i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.19291 | + | 18.1079i | −0.125623 | + | 0.712446i | ||||
\(647\) | 16.1623i | 0.635407i | 0.948190 | + | 0.317703i | \(0.102912\pi\) | ||||
−0.948190 | + | 0.317703i | \(0.897088\pi\) | |||||||
\(648\) | 38.1834 | + | 1.42365i | 1.49999 | + | 0.0559261i | ||||
\(649\) | −31.8113 | −1.24870 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.201902 | + | 1.65242i | 0.00791316 | + | 0.0647634i | ||||
\(652\) | −7.24721 | + | 19.9116i | −0.283823 | + | 0.779797i | ||||
\(653\) | 20.7275 | + | 24.7021i | 0.811130 | + | 0.966668i | 0.999882 | − | 0.0153573i | \(-0.00488856\pi\) |
−0.188752 | + | 0.982025i | \(0.560444\pi\) | |||||||
\(654\) | 25.8845 | + | 1.37187i | 1.01216 | + | 0.0536442i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.45823 | − | 2.52573i | 0.0569344 | − | 0.0986133i | ||||
\(657\) | −0.563508 | − | 0.162303i | −0.0219846 | − | 0.00633206i | ||||
\(658\) | 4.33351 | − | 2.50195i | 0.168938 | − | 0.0975363i | ||||
\(659\) | −21.3103 | − | 17.8814i | −0.830130 | − | 0.696562i | 0.125191 | − | 0.992133i | \(-0.460046\pi\) |
−0.955321 | + | 0.295571i | \(0.904490\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.34639 | + | 30.3209i | 0.207950 | + | 1.17934i | 0.892729 | + | 0.450594i | \(0.148788\pi\) |
−0.684779 | + | 0.728751i | \(0.740101\pi\) | |||||||
\(662\) | −45.4774 | + | 8.01889i | −1.76753 | + | 0.311663i | ||||
\(663\) | −9.88816 | + | 10.5912i | −0.384024 | + | 0.411329i | ||||
\(664\) | −48.4604 | − | 40.6631i | −1.88063 | − | 1.57803i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −24.0913 | + | 16.2085i | −0.933519 | + | 0.628065i | ||||
\(667\) | −24.6781 | − | 14.2479i | −0.955540 | − | 0.551682i | ||||
\(668\) | −21.4955 | − | 59.0583i | −0.831684 | − | 2.28503i | ||||
\(669\) | −16.8531 | − | 33.1243i | −0.651577 | − | 1.28066i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38.3557 | − | 13.9603i | −1.48071 | − | 0.538933i | ||||
\(672\) | −0.825749 | + | 1.94216i | −0.0318540 | + | 0.0749203i | ||||
\(673\) | −25.7336 | − | 4.53753i | −0.991959 | − | 0.174909i | −0.345961 | − | 0.938249i | \(-0.612447\pi\) |
−0.645997 | + | 0.763340i | \(0.723558\pi\) | |||||||
\(674\) | −70.7584 | −2.72551 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.5374 | 0.674515 | ||||||||
\(677\) | −17.9181 | − | 3.15944i | −0.688648 | − | 0.121427i | −0.181635 | − | 0.983366i | \(-0.558139\pi\) |
−0.507012 | + | 0.861939i | \(0.669250\pi\) | |||||||
\(678\) | −29.6269 | − | 39.3645i | −1.13781 | − | 1.51178i | ||||
\(679\) | −2.88549 | − | 1.05023i | −0.110735 | − | 0.0403042i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.0477 | + | 27.7551i | −0.691588 | + | 1.06358i | ||||
\(682\) | 4.21116 | + | 11.5701i | 0.161253 | + | 0.443040i | ||||
\(683\) | −20.3491 | − | 11.7486i | −0.778636 | − | 0.449546i | 0.0573104 | − | 0.998356i | \(-0.481748\pi\) |
−0.835947 | + | 0.548811i | \(0.815081\pi\) | |||||||
\(684\) | −25.5903 | + | 35.1347i | −0.978468 | + | 1.34341i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −14.5765 | − | 12.2311i | −0.556533 | − | 0.466987i | ||||
\(687\) | −11.3570 | − | 37.2256i | −0.433296 | − | 1.42024i | ||||
\(688\) | 18.0824 | − | 3.18841i | 0.689384 | − | 0.121557i | ||||
\(689\) | −3.94021 | − | 22.3460i | −0.150110 | − | 0.851317i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.1180 | − | 28.6284i | −1.29791 | − | 1.08908i | −0.990502 | − | 0.137499i | \(-0.956094\pi\) |
−0.307409 | − | 0.951577i | \(-0.599462\pi\) | |||||||
\(692\) | −62.0039 | + | 35.7980i | −2.35704 | + | 1.36084i | ||||
\(693\) | −0.568750 | + | 5.35054i | −0.0216050 | + | 0.203250i | ||||
\(694\) | −13.6857 | + | 23.7043i | −0.519501 | + | 0.899802i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −25.6534 | + | 39.4517i | −0.972388 | + | 1.49541i | ||||
\(697\) | −1.40284 | − | 1.67184i | −0.0531363 | − | 0.0633254i | ||||
\(698\) | −23.1320 | + | 63.5547i | −0.875560 | + | 2.40558i | ||||
\(699\) | −24.4692 | + | 18.4163i | −0.925512 | + | 0.696567i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.2567 | −0.953934 | −0.476967 | − | 0.878921i | \(-0.658264\pi\) | ||||
−0.476967 | + | 0.878921i | \(0.658264\pi\) | |||||||
\(702\) | −48.9848 | + | 18.7041i | −1.84881 | + | 0.705939i | ||||
\(703\) | − | 15.4974i | − | 0.584496i | ||||||
\(704\) | −5.56859 | + | 31.5810i | −0.209874 | + | 1.19025i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 64.6662 | + | 23.5366i | 2.43374 | + | 0.885810i | ||||
\(707\) | −2.70935 | − | 3.22888i | −0.101896 | − | 0.121434i | ||||
\(708\) | 59.8202 | − | 30.4355i | 2.24818 | − | 1.14383i | ||||
\(709\) | −14.7382 | + | 5.36425i | −0.553503 | + | 0.201459i | −0.603602 | − | 0.797286i | \(-0.706269\pi\) |
0.0500991 | + | 0.998744i | \(0.484046\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.48295 | − | 21.5731i | −0.0556150 | − | 0.809053i | ||||
\(712\) | −5.71046 | + | 3.29694i | −0.214009 | + | 0.123558i | ||||
\(713\) | 4.74412 | − | 5.65382i | 0.177669 | − | 0.211737i | ||||
\(714\) | −3.51031 | − | 3.27730i | −0.131370 | − | 0.122650i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.6222 | + | 60.2415i | 0.396970 | + | 2.25133i | ||||
\(717\) | −26.0207 | − | 6.02352i | −0.971760 | − | 0.224953i | ||||
\(718\) | −47.9055 | + | 57.0915i | −1.78782 | + | 2.13064i | ||||
\(719\) | −26.5804 | − | 46.0385i | −0.991280 | − | 1.71695i | −0.609757 | − | 0.792588i | \(-0.708733\pi\) |
−0.381523 | − | 0.924359i | \(-0.624600\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.85595 | − | 3.21461i | 0.0691194 | − | 0.119718i | ||||
\(722\) | 3.46034 | + | 9.50721i | 0.128781 | + | 0.353822i | ||||
\(723\) | 1.20558 | − | 22.7471i | 0.0448361 | − | 0.845972i | ||||
\(724\) | 8.63457 | − | 7.24526i | 0.320901 | − | 0.269268i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.722875 | − | 5.91621i | −0.0268284 | − | 0.219571i | ||||
\(727\) | −0.462044 | − | 0.0814709i | −0.0171363 | − | 0.00302159i | 0.165073 | − | 0.986281i | \(-0.447214\pi\) |
−0.182210 | + | 0.983260i | \(0.558325\pi\) | |||||||
\(728\) | 10.3440i | 0.383372i | ||||||||
\(729\) | 20.1288 | − | 17.9954i | 0.745509 | − | 0.666495i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.38593 | − | 13.5313i | 0.0882469 | − | 0.500473i | ||||
\(732\) | 85.4834 | − | 10.4448i | 3.15956 | − | 0.386052i | ||||
\(733\) | −15.8719 | + | 43.6076i | −0.586241 | + | 1.61068i | 0.191075 | + | 0.981575i | \(0.438803\pi\) |
−0.777317 | + | 0.629109i | \(0.783420\pi\) | |||||||
\(734\) | 44.3825 | − | 37.2413i | 1.63819 | − | 1.37460i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.79230 | − | 3.20014i | 0.324088 | − | 0.117959i | ||||
\(737\) | 23.6724 | + | 13.6672i | 0.871983 | + | 0.503439i | ||||
\(738\) | −1.90157 | − | 7.66531i | −0.0699977 | − | 0.282164i | ||||
\(739\) | 12.9047 | + | 22.3515i | 0.474706 | + | 0.822214i | 0.999580 | − | 0.0289653i | \(-0.00922124\pi\) |
−0.524875 | + | 0.851179i | \(0.675888\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.31146 | − | 27.2645i | 0.231857 | − | 1.00159i | ||||
\(742\) | 7.40629 | − | 1.30593i | 0.271894 | − | 0.0479422i | ||||
\(743\) | −34.1823 | + | 6.02726i | −1.25403 | + | 0.221119i | −0.760918 | − | 0.648848i | \(-0.775251\pi\) |
−0.493110 | + | 0.869967i | \(0.664140\pi\) | |||||||
\(744\) | −8.90915 | − | 8.31775i | −0.326625 | − | 0.304944i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.1129 | − | 26.1764i | −0.553324 | − | 0.958385i | ||||
\(747\) | −44.5961 | + | 3.06557i | −1.63169 | + | 0.112163i | ||||
\(748\) | −20.0945 | − | 11.6015i | −0.734727 | − | 0.424195i | ||||
\(749\) | 3.02069 | − | 1.09944i | 0.110374 | − | 0.0401727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.3742 | − | 15.4178i | 0.670485 | − | 0.562604i | −0.242724 | − | 0.970095i | \(-0.578041\pi\) |
0.913209 | + | 0.407492i | \(0.133596\pi\) | |||||||
\(752\) | −3.26977 | + | 8.98361i | −0.119236 | + | 0.327599i | ||||
\(753\) | −11.8034 | + | 27.7614i | −0.430138 | + | 1.01168i | ||||
\(754\) | 11.2137 | − | 63.5962i | 0.408380 | − | 2.31604i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.04961 | − | 10.6057i | −0.147283 | − | 0.385725i | ||||
\(757\) | 8.78780i | 0.319398i | 0.987166 | + | 0.159699i | \(0.0510524\pi\) | ||||
−0.987166 | + | 0.159699i | \(0.948948\pi\) | |||||||
\(758\) | 18.2239 | + | 3.21336i | 0.661921 | + | 0.116715i | ||||
\(759\) | 19.0603 | − | 14.3453i | 0.691843 | − | 0.520701i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.5361 | − | 8.84082i | 0.381933 | − | 0.320479i | −0.431528 | − | 0.902100i | \(-0.642025\pi\) |
0.813461 | + | 0.581620i | \(0.197581\pi\) | |||||||
\(762\) | 40.2065 | + | 26.1441i | 1.45653 | + | 0.947102i | ||||
\(763\) | −1.23583 | − | 3.39542i | −0.0447401 | − | 0.122922i | ||||
\(764\) | −4.24595 | + | 7.35420i | −0.153613 | + | 0.266066i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.4484 | − | 37.1498i | −0.774963 | − | 1.34228i | ||||
\(767\) | −27.7770 | + | 33.1034i | −1.00297 | + | 1.19529i | ||||
\(768\) | −14.6424 | − | 47.9943i | −0.528361 | − | 1.73185i | ||||
\(769\) | 5.44525 | + | 30.8815i | 0.196361 | + | 1.11362i | 0.910468 | + | 0.413580i | \(0.135722\pi\) |
−0.714107 | + | 0.700036i | \(0.753167\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.5341 | − | 5.65448i | 0.667489 | − | 0.203641i | ||||
\(772\) | −2.13192 | + | 2.54072i | −0.0767295 | + | 0.0914426i | ||||
\(773\) | 24.3539 | − | 14.0607i | 0.875948 | − | 0.505729i | 0.00662776 | − | 0.999978i | \(-0.497890\pi\) |
0.869320 | + | 0.494249i | \(0.164557\pi\) | |||||||
\(774\) | 29.2731 | − | 40.1911i | 1.05220 | − | 1.44464i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 21.1266 | − | 7.68945i | 0.758400 | − | 0.276035i | ||||
\(777\) | 3.39332 | + | 2.20650i | 0.121735 | + | 0.0791576i | ||||
\(778\) | −42.2804 | − | 50.3879i | −1.51583 | − | 1.80649i | ||||
\(779\) | 3.96098 | + | 1.44168i | 0.141917 | + | 0.0516535i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.614960 | + | 3.48761i | −0.0220050 | + | 0.124797i | ||||
\(782\) | 21.2916i | 0.761385i | ||||||||
\(783\) | 6.28714 | + | 32.6531i | 0.224684 | + | 1.16693i | ||||
\(784\) | 17.7298 | 0.633207 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 34.4979 | + | 14.6675i | 1.23050 | + | 0.523173i | ||||
\(787\) | 12.3812 | − | 34.0170i | 0.441342 | − | 1.21258i | −0.497269 | − | 0.867597i | \(-0.665664\pi\) |
0.938610 | − | 0.344979i | \(-0.112114\pi\) | |||||||
\(788\) | 49.1075 | + | 58.5240i | 1.74938 | + | 2.08483i | ||||
\(789\) | 16.2668 | + | 31.9721i | 0.579114 | + | 1.13824i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.43393 | + | 5.94775i | −0.122097 | + | 0.211478i | ||||
\(792\) | −21.9911 | − | 32.6863i | −0.781421 | − | 1.16146i | ||||
\(793\) | −48.0189 | + | 27.7237i | −1.70520 | + | 0.984498i | ||||
\(794\) | 7.75636 | + | 6.50836i | 0.275263 | + | 0.230973i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.4373 | − | 70.5354i | −0.440828 | − | 2.50006i | ||||
\(797\) | −29.1504 | + | 5.14000i | −1.03256 | + | 0.182068i | −0.664153 | − | 0.747596i | \(-0.731208\pi\) |
−0.368407 | + | 0.929665i | \(0.620097\pi\) | |||||||
\(798\) | 9.03645 | + | 2.09185i | 0.319887 | + | 0.0740506i | ||||
\(799\) | 5.48028 | + | 4.59850i | 0.193878 | + | 0.162683i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.28958 | + | 4.47736i | −0.0455652 | + | 0.158200i | ||||
\(802\) | −31.5568 | − | 18.2193i | −1.11431 | − | 0.643346i | ||||
\(803\) | 0.206789 | + | 0.568149i | 0.00729744 | + | 0.0200495i | ||||
\(804\) | −57.5913 | − | 3.05231i | −2.03109 | − | 0.107647i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 15.7171 | + | 5.72055i | 0.553611 | + | 0.201498i | ||||
\(807\) | 48.5604 | − | 5.93338i | 1.70941 | − | 0.208865i | ||||
\(808\) | 30.3920 | + | 5.35892i | 1.06919 | + | 0.188526i | ||||
\(809\) | 5.75943 | 0.202491 | 0.101245 | − | 0.994861i | \(-0.467717\pi\) | ||||
0.101245 | + | 0.994861i | \(0.467717\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.4896 | 0.438569 | 0.219284 | − | 0.975661i | \(-0.429628\pi\) | ||||
0.219284 | + | 0.975661i | \(0.429628\pi\) | |||||||
\(812\) | 13.7692 | + | 2.42788i | 0.483204 | + | 0.0852019i | ||||
\(813\) | 29.6791 | − | 3.62635i | 1.04089 | − | 0.127182i | ||||
\(814\) | 28.1318 | + | 10.2391i | 0.986018 | + | 0.358881i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 9.16230 | + | 0.485598i | 0.320744 | + | 0.0169993i | ||||
\(817\) | 9.07644 | + | 24.9373i | 0.317544 | + | 0.872446i | ||||
\(818\) | 9.79536 | + | 5.65535i | 0.342487 | + | 0.197735i | ||||
\(819\) | 5.07123 | + | 5.26384i | 0.177203 | + | 0.183933i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.9911 | + | 27.6828i | 1.15140 | + | 0.966136i | 0.999751 | − | 0.0222995i | \(-0.00709873\pi\) |
0.151644 | + | 0.988435i | \(0.451543\pi\) | |||||||
\(822\) | −46.6865 | − | 10.8074i | −1.62838 | − | 0.376953i | ||||
\(823\) | −10.1279 | + | 1.78581i | −0.353035 | + | 0.0622496i | −0.347353 | − | 0.937734i | \(-0.612920\pi\) |
−0.00568141 | + | 0.999984i | \(0.501808\pi\) | |||||||
\(824\) | 4.71930 | + | 26.7645i | 0.164404 | + | 0.932384i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.9717 | − | 9.20632i | −0.381753 | − | 0.320329i | ||||
\(827\) | −5.27810 | + | 3.04731i | −0.183538 | + | 0.105965i | −0.588954 | − | 0.808167i | \(-0.700460\pi\) |
0.405416 | + | 0.914132i | \(0.367127\pi\) | |||||||
\(828\) | −22.1174 | + | 45.2118i | −0.768632 | + | 1.57122i | ||||
\(829\) | −16.8489 | + | 29.1832i | −0.585188 | + | 1.01358i | 0.409664 | + | 0.912236i | \(0.365646\pi\) |
−0.994852 | + | 0.101339i | \(0.967687\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.05984 | + | 7.97952i | 0.140834 | + | 0.276806i | ||||
\(832\) | 28.0014 | + | 33.3707i | 0.970772 | + | 1.15692i | ||||
\(833\) | 4.53774 | − | 12.4673i | 0.157223 | − | 0.431967i | ||||
\(834\) | 6.52244 | + | 2.77315i | 0.225853 | + | 0.0960264i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 44.8148 | 1.54995 | ||||||||
\(837\) | −8.61156 | + | 0.135065i | −0.297659 | + | 0.00466853i | ||||
\(838\) | − | 47.5308i | − | 1.64192i | ||||||
\(839\) | 7.33250 | − | 41.5847i | 0.253146 | − | 1.43566i | −0.547641 | − | 0.836714i | \(-0.684474\pi\) |
0.800787 | − | 0.598950i | \(-0.204415\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.2328 | − | 4.08841i | −0.387339 | − | 0.140980i | ||||
\(842\) | 43.5112 | + | 51.8546i | 1.49949 | + | 1.78703i | ||||
\(843\) | −4.78664 | − | 3.11250i | −0.164861 | − | 0.107200i | ||||
\(844\) | 57.3007 | − | 20.8557i | 1.97237 | − | 0.717884i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.5019 | + | 23.6627i | 0.361062 | + | 0.813541i | ||||
\(847\) | −0.719533 | + | 0.415423i | −0.0247235 | + | 0.0142741i | ||||
\(848\) | −9.23576 | + | 11.0068i | −0.317157 | + | 0.377973i | ||||
\(849\) | 15.1266 | − | 4.61489i | 0.519142 | − | 0.158383i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.11616 | − | 17.6726i | −0.106821 | − | 0.605810i | ||||
\(852\) | −2.18036 | − | 7.14672i | −0.0746979 | − | 0.244842i | ||||
\(853\) | 22.9665 | − | 27.3705i | 0.786359 | − | 0.937147i | −0.212843 | − | 0.977086i | \(-0.568272\pi\) |
0.999202 | + | 0.0399399i | \(0.0127166\pi\) | |||||||
\(854\) | −9.18865 | − | 15.9152i | −0.314429 | − | 0.544607i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.7679 | + | 20.3826i | −0.402219 | + | 0.696664i | ||||
\(857\) | 2.70492 | + | 7.43170i | 0.0923983 | + | 0.253862i | 0.977280 | − | 0.211954i | \(-0.0679829\pi\) |
−0.884881 | + | 0.465817i | \(0.845761\pi\) | |||||||
\(858\) | 45.3221 | + | 29.4706i | 1.54727 | + | 1.00611i | ||||
\(859\) | 34.2569 | − | 28.7449i | 1.16883 | − | 0.980764i | 0.168841 | − | 0.985643i | \(-0.445998\pi\) |
0.999988 | + | 0.00487963i | \(0.00155324\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.879627 | + | 0.662033i | −0.0299776 | + | 0.0225620i | ||||
\(862\) | −12.2911 | − | 2.16726i | −0.418638 | − | 0.0738172i | ||||
\(863\) | − | 22.9170i | − | 0.780103i | −0.920793 | − | 0.390052i | \(-0.872457\pi\) | ||
0.920793 | − | 0.390052i | \(-0.127543\pi\) | |||||||
\(864\) | −9.54017 | − | 5.31030i | −0.324563 | − | 0.180660i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −10.5629 | + | 59.9053i | −0.358943 | + | 2.03567i | ||||
\(867\) | −8.83457 | + | 20.7788i | −0.300038 | + | 0.705686i | ||||
\(868\) | −1.23856 | + | 3.40290i | −0.0420393 | + | 0.115502i | ||||
\(869\) | −17.0789 | + | 14.3309i | −0.579362 | + | 0.486143i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.8926 | − | 12.6999i | 1.18229 | − | 0.430319i | ||||
\(872\) | 22.9112 | + | 13.2278i | 0.775871 | + | 0.447950i | ||||
\(873\) | 6.98108 | − | 14.2706i | 0.236274 | − | 0.482985i | ||||
\(874\) | −20.5614 | − | 35.6134i | −0.695501 | − | 1.20464i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.932438 | − | 0.870542i | −0.0315041 | − | 0.0294129i | ||||
\(877\) | −21.8013 | + | 3.84416i | −0.736178 | + | 0.129808i | −0.529152 | − | 0.848527i | \(-0.677490\pi\) |
−0.207026 | + | 0.978335i | \(0.566379\pi\) | |||||||
\(878\) | −37.0409 | + | 6.53132i | −1.25007 | + | 0.220421i | ||||
\(879\) | −1.10407 | + | 4.76940i | −0.0372393 | + | 0.160868i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.93202 | − | 8.54251i | −0.166164 | − | 0.287804i | 0.770904 | − | 0.636951i | \(-0.219805\pi\) |
−0.937068 | + | 0.349147i | \(0.886471\pi\) | |||||||
\(882\) | 34.5759 | − | 33.3108i | 1.16423 | − | 1.12163i | ||||
\(883\) | −41.1995 | − | 23.7865i | −1.38647 | − | 0.800481i | −0.393558 | − | 0.919300i | \(-0.628756\pi\) |
−0.992916 | + | 0.118819i | \(0.962089\pi\) | |||||||
\(884\) | −29.6189 | + | 10.7804i | −0.996191 | + | 0.362584i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 33.5825 | − | 28.1791i | 1.12823 | − | 0.946694i | ||||
\(887\) | −4.56846 | + | 12.5517i | −0.153394 | + | 0.421446i | −0.992458 | − | 0.122587i | \(-0.960881\pi\) |
0.839064 | + | 0.544033i | \(0.183103\pi\) | |||||||
\(888\) | −29.4165 | + | 3.59428i | −0.987155 | + | 0.120616i | ||||
\(889\) | 1.16091 | − | 6.58387i | 0.0389358 | − | 0.220816i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.2157 | − | 5.85205i | −0.911760 | − | 0.196051i | ||||
\(892\) | − | 80.8465i | − | 2.70694i | ||||||
\(893\) | −13.6074 | − | 2.39936i | −0.455355 | − | 0.0802914i | ||||
\(894\) | 10.9240 | + | 89.4048i | 0.365352 | + | 2.99014i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9.19350 | + | 7.71427i | −0.307133 | + | 0.257716i | ||||
\(897\) | 1.71509 | − | 32.3605i | 0.0572652 | − | 1.08048i | ||||
\(898\) | 23.5920 | + | 64.8186i | 0.787276 | + | 2.16302i | ||||
\(899\) | 5.30359 | − | 9.18609i | 0.176885 | − | 0.306373i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.37600 | + | 9.31150i | 0.179100 | + | 0.310211i | ||||
\(902\) | −5.23403 | + | 6.23767i | −0.174274 | + | 0.207692i | ||||
\(903\) | −6.75257 | − | 1.56315i | −0.224712 | − | 0.0520184i | ||||
\(904\) | −8.73176 | − | 49.5203i | −0.290414 | − | 1.64702i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −14.4169 | − | 13.4599i | −0.478969 | − | 0.447174i | ||||
\(907\) | 23.7578 | − | 28.3135i | 0.788866 | − | 0.940134i | −0.210431 | − | 0.977609i | \(-0.567487\pi\) |
0.999298 | + | 0.0374746i | \(0.0119313\pi\) | |||||||
\(908\) | −62.3697 | + | 36.0092i | −2.06981 | + | 1.19501i | ||||
\(909\) | 18.0932 | − | 12.1729i | 0.600112 | − | 0.403751i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.4916 | − | 16.5576i | 1.50720 | − | 0.548577i | 0.549288 | − | 0.835633i | \(-0.314899\pi\) |
0.957914 | + | 0.287056i | \(0.0926766\pi\) | |||||||
\(912\) | −15.7943 | + | 8.03587i | −0.523002 | + | 0.266094i | ||||
\(913\) | 29.6250 | + | 35.3057i | 0.980445 | + | 1.16845i | ||||
\(914\) | 79.8629 | + | 29.0677i | 2.64163 | + | 0.961475i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.7015 | − | 83.3765i | 0.485752 | − | 2.75484i | ||||
\(917\) | − | 5.22558i | − | 0.172564i | ||||||
\(918\) | 18.7803 | − | 16.2671i | 0.619841 | − | 0.536896i | ||||
\(919\) | −8.93459 | −0.294725 | −0.147363 | − | 0.989083i | \(-0.547078\pi\) | ||||
−0.147363 | + | 0.989083i | \(0.547078\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.71086 | + | 6.55604i | −0.287032 | + | 0.216029i | ||||
\(922\) | 1.87011 | − | 5.13809i | 0.0615889 | − | 0.169214i | ||||
\(923\) | 3.09230 | + | 3.68526i | 0.101784 | + | 0.121302i | ||||
\(924\) | −6.38066 | + | 9.81267i | −0.209908 | + | 0.322813i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 22.0643 | − | 38.2165i | 0.725079 | − | 1.25587i | ||||
\(927\) | 15.5231 | + | 11.3062i | 0.509846 | + | 0.371345i | ||||
\(928\) | 11.6455 | − | 6.72355i | 0.382283 | − | 0.220711i | ||||
\(929\) | 4.78330 | + | 4.01366i | 0.156935 | + | 0.131684i | 0.717874 | − | 0.696173i | \(-0.245115\pi\) |
−0.560939 | + | 0.827857i | \(0.689560\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.44973 | + | 25.2357i | 0.145834 | + | 0.827066i | ||||
\(932\) | −65.6079 | + | 11.5684i | −2.14906 | + | 0.378937i | ||||
\(933\) | −3.72644 | − | 12.2144i | −0.121998 | − | 0.399882i | ||||
\(934\) | 8.57084 | + | 7.19179i | 0.280446 | + | 0.235322i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −53.2162 | − | 5.65676i | −1.73943 | − | 0.184897i | ||||
\(937\) | 39.7006 | + | 22.9212i | 1.29696 | + | 0.748802i | 0.979878 | − | 0.199595i | \(-0.0639626\pi\) |
0.317085 | + | 0.948397i | \(0.397296\pi\) | |||||||
\(938\) | 4.20920 | + | 11.5647i | 0.137435 | + | 0.377600i | ||||
\(939\) | 4.03244 | − | 6.20140i | 0.131594 | − | 0.202375i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.09014 | + | 1.48869i | 0.133335 | + | 0.0485298i | 0.407826 | − | 0.913060i | \(-0.366287\pi\) |
−0.274491 | + | 0.961590i | \(0.588509\pi\) | |||||||
\(942\) | 0.523313 | + | 0.695313i | 0.0170505 | + | 0.0226545i | ||||
\(943\) | 4.80683 | + | 0.847573i | 0.156532 | + | 0.0276008i | ||||
\(944\) | 27.3637 | 0.890612 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −51.2644 | −1.66675 | ||||||||
\(947\) | −1.98610 | − | 0.350202i | −0.0645395 | − | 0.0113800i | 0.141285 | − | 0.989969i | \(-0.454877\pi\) |
−0.205825 | + | 0.978589i | \(0.565988\pi\) | |||||||
\(948\) | 18.4053 | − | 43.2891i | 0.597776 | − | 1.40596i | ||||
\(949\) | 0.771790 | + | 0.280909i | 0.0250534 | + | 0.00911868i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.6827 | + | 24.9275i | 0.411264 | + | 0.808331i | ||||
\(952\) | −1.67640 | − | 4.60587i | −0.0543325 | − | 0.149277i | ||||
\(953\) | 30.9420 | + | 17.8644i | 1.00231 | + | 0.578684i | 0.908931 | − | 0.416947i | \(-0.136900\pi\) |
0.0933786 | + | 0.995631i | \(0.470233\pi\) | |||||||
\(954\) | 2.66832 | + | 38.8171i | 0.0863900 | + | 1.25675i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −44.5075 | − | 37.3462i | −1.43948 | − | 1.20786i | ||||
\(957\) | 23.3968 | − | 25.0604i | 0.756312 | − | 0.810086i | ||||
\(958\) | −33.5279 | + | 5.91188i | −1.08324 | + | 0.191004i | ||||
\(959\) | 1.15999 | + | 6.57865i | 0.0374581 | + | 0.212436i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.6428 | − | 18.1605i | −0.698155 | − | 0.585822i | ||||
\(962\) | 35.2191 | − | 20.3338i | 1.13551 | − | 0.655587i | ||||
\(963\) | 4.00434 | + | 16.1417i | 0.129038 | + | 0.520159i | ||||
\(964\) | 24.7759 | − | 42.9131i | 0.797978 | − | 1.38214i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 10.7254 | + | 0.568443i | 0.345085 | + | 0.0182894i | ||||
\(967\) | 0.445656 | + | 0.531112i | 0.0143313 | + | 0.0170794i | 0.773163 | − | 0.634208i | \(-0.218674\pi\) |
−0.758831 | + | 0.651287i | \(0.774229\pi\) | |||||||
\(968\) | 2.08057 | − | 5.71631i | 0.0668719 | − | 0.183729i | ||||
\(969\) | 1.60833 | + | 13.1630i | 0.0516670 | + | 0.422857i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.4942 | 1.52416 | 0.762081 | − | 0.647482i | \(-0.224178\pi\) | ||||
0.762081 | + | 0.647482i | \(0.224178\pi\) | |||||||
\(972\) | 56.7772 | − | 15.0340i | 1.82113 | − | 0.482216i | ||||
\(973\) | − | 0.987988i | − | 0.0316734i | ||||||
\(974\) | −8.93869 | + | 50.6938i | −0.286414 | + | 1.62434i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.9931 | + | 12.0085i | 1.05608 | + | 0.384383i | ||||
\(977\) | 8.10126 | + | 9.65470i | 0.259182 | + | 0.308881i | 0.879906 | − | 0.475148i | \(-0.157606\pi\) |
−0.620724 | + | 0.784029i | \(0.713161\pi\) | |||||||
\(978\) | −1.23812 | + | 23.3609i | −0.0395906 | + | 0.746999i | ||||
\(979\) | 4.51423 | − | 1.64305i | 0.144276 | − | 0.0525120i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.1441 | − | 4.50110i | 0.579298 | − | 0.143709i | ||||
\(982\) | −29.3008 | + | 16.9168i | −0.935027 | + | 0.539838i | ||||
\(983\) | −7.42100 | + | 8.84400i | −0.236693 | + | 0.282080i | −0.871295 | − | 0.490759i | \(-0.836720\pi\) |
0.634602 | + | 0.772839i | \(0.281164\pi\) | |||||||
\(984\) | 1.81787 | − | 7.85292i | 0.0579517 | − | 0.250342i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.31361 | + | 30.1350i | 0.169220 | + | 0.959693i | ||||
\(987\) | 2.46277 | − | 2.63787i | 0.0783908 | − | 0.0839644i | ||||
\(988\) | 39.1315 | − | 46.6351i | 1.24494 | − | 1.48366i | ||||
\(989\) | 15.3647 | + | 26.6125i | 0.488569 | + | 0.846227i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.34676 | + | 16.1891i | −0.296910 | + | 0.514263i | −0.975427 | − | 0.220322i | \(-0.929289\pi\) |
0.678518 | + | 0.734584i | \(0.262623\pi\) | |||||||
\(992\) | 1.19121 | + | 3.27281i | 0.0378209 | + | 0.103912i | ||||
\(993\) | −29.6832 | + | 15.1023i | −0.941969 | + | 0.479257i | ||||
\(994\) | −1.22143 | + | 1.02490i | −0.0387413 | + | 0.0325079i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −89.4877 | − | 38.0476i | −2.83553 | − | 1.20558i | ||||
\(997\) | −3.30778 | − | 0.583250i | −0.104758 | − | 0.0184717i | 0.121023 | − | 0.992650i | \(-0.461382\pi\) |
−0.225782 | + | 0.974178i | \(0.572494\pi\) | |||||||
\(998\) | − | 35.8066i | − | 1.13344i | ||||||
\(999\) | −13.2074 | + | 16.2508i | −0.417863 | + | 0.514154i |
(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 | 675.2.u.b.349.4 | 24 | ||
5.2 | odd | 4 | 27.2.e.a.25.1 | yes | 12 | ||
5.3 | odd | 4 | 675.2.l.c.376.2 | 12 | |||
5.4 | even | 2 | inner | 675.2.u.b.349.1 | 24 | ||
15.2 | even | 4 | 81.2.e.a.73.2 | 12 | |||
20.7 | even | 4 | 432.2.u.c.241.1 | 12 | |||
27.13 | even | 9 | inner | 675.2.u.b.499.1 | 24 | ||
45.2 | even | 12 | 243.2.e.a.55.1 | 12 | |||
45.7 | odd | 12 | 243.2.e.d.55.2 | 12 | |||
45.22 | odd | 12 | 243.2.e.c.136.1 | 12 | |||
45.32 | even | 12 | 243.2.e.b.136.2 | 12 | |||
135.2 | even | 36 | 729.2.c.b.487.1 | 12 | |||
135.7 | odd | 36 | 729.2.c.e.244.6 | 12 | |||
135.13 | odd | 36 | 675.2.l.c.526.2 | 12 | |||
135.22 | odd | 36 | 243.2.e.d.190.2 | 12 | |||
135.32 | even | 36 | 243.2.e.a.190.1 | 12 | |||
135.47 | even | 36 | 729.2.c.b.244.1 | 12 | |||
135.52 | odd | 36 | 729.2.c.e.487.6 | 12 | |||
135.67 | odd | 36 | 27.2.e.a.13.1 | ✓ | 12 | ||
135.77 | even | 36 | 243.2.e.b.109.2 | 12 | |||
135.92 | even | 36 | 729.2.a.d.1.6 | 6 | |||
135.94 | even | 18 | inner | 675.2.u.b.499.4 | 24 | ||
135.97 | odd | 36 | 729.2.a.a.1.1 | 6 | |||
135.112 | odd | 36 | 243.2.e.c.109.1 | 12 | |||
135.122 | even | 36 | 81.2.e.a.10.2 | 12 | |||
540.67 | even | 36 | 432.2.u.c.337.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.2.e.a.13.1 | ✓ | 12 | 135.67 | odd | 36 | ||
27.2.e.a.25.1 | yes | 12 | 5.2 | odd | 4 | ||
81.2.e.a.10.2 | 12 | 135.122 | even | 36 | |||
81.2.e.a.73.2 | 12 | 15.2 | even | 4 | |||
243.2.e.a.55.1 | 12 | 45.2 | even | 12 | |||
243.2.e.a.190.1 | 12 | 135.32 | even | 36 | |||
243.2.e.b.109.2 | 12 | 135.77 | even | 36 | |||
243.2.e.b.136.2 | 12 | 45.32 | even | 12 | |||
243.2.e.c.109.1 | 12 | 135.112 | odd | 36 | |||
243.2.e.c.136.1 | 12 | 45.22 | odd | 12 | |||
243.2.e.d.55.2 | 12 | 45.7 | odd | 12 | |||
243.2.e.d.190.2 | 12 | 135.22 | odd | 36 | |||
432.2.u.c.241.1 | 12 | 20.7 | even | 4 | |||
432.2.u.c.337.1 | 12 | 540.67 | even | 36 | |||
675.2.l.c.376.2 | 12 | 5.3 | odd | 4 | |||
675.2.l.c.526.2 | 12 | 135.13 | odd | 36 | |||
675.2.u.b.349.1 | 24 | 5.4 | even | 2 | inner | ||
675.2.u.b.349.4 | 24 | 1.1 | even | 1 | trivial | ||
675.2.u.b.499.1 | 24 | 27.13 | even | 9 | inner | ||
675.2.u.b.499.4 | 24 | 135.94 | even | 18 | inner | ||
729.2.a.a.1.1 | 6 | 135.97 | odd | 36 | |||
729.2.a.d.1.6 | 6 | 135.92 | even | 36 | |||
729.2.c.b.244.1 | 12 | 135.47 | even | 36 | |||
729.2.c.b.487.1 | 12 | 135.2 | even | 36 | |||
729.2.c.e.244.6 | 12 | 135.7 | odd | 36 | |||
729.2.c.e.487.6 | 12 | 135.52 | odd | 36 |