Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [243,2,Mod(28,243)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(243, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("243.28");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 243 = 3^{5} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 243.e (of order \(9\), 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: | \(1.94036476912\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | 12.0.1952986685049.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 190.2 | ||
Root | \(0.500000 - 1.00210i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 243.190 |
Dual form | 243.2.e.d.55.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.25679 | + | 0.821403i | 1.59579 | + | 0.580820i | 0.978560 | − | 0.205964i | \(-0.0660330\pi\) |
0.617229 | + | 0.786784i | \(0.288255\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.88629 | + | 2.42189i | 1.44315 | + | 1.21094i | ||||
\(5\) | 0.0161638 | − | 0.0916693i | 0.00722866 | − | 0.0409957i | −0.980980 | − | 0.194108i | \(-0.937819\pi\) |
0.988209 | + | 0.153113i | \(0.0489297\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.444200 | + | 0.372728i | −0.167892 | + | 0.140878i | −0.722862 | − | 0.690992i | \(-0.757174\pi\) |
0.554971 | + | 0.831870i | \(0.312729\pi\) | |||||||
\(8\) | 2.12277 | + | 3.67675i | 0.750514 | + | 1.29993i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.111776 | − | 0.193601i | 0.0353465 | − | 0.0612220i | ||||
\(11\) | −0.537108 | − | 3.04609i | −0.161944 | − | 0.918431i | −0.952159 | − | 0.305602i | \(-0.901142\pi\) |
0.790215 | − | 0.612830i | \(-0.209969\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.94834 | + | 1.43708i | −1.09507 | + | 0.398574i | −0.825497 | − | 0.564406i | \(-0.809105\pi\) |
−0.269574 | + | 0.962980i | \(0.586883\pi\) | |||||||
\(14\) | −1.30862 | + | 0.476300i | −0.349744 | + | 0.127296i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.462014 | + | 2.62021i | 0.115503 | + | 0.655052i | ||||
\(17\) | 0.995493 | − | 1.72424i | 0.241443 | − | 0.418191i | −0.719683 | − | 0.694303i | \(-0.755713\pi\) |
0.961125 | + | 0.276112i | \(0.0890461\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.92271 | + | 3.33023i | 0.441100 | + | 0.764008i | 0.997771 | − | 0.0667249i | \(-0.0212550\pi\) |
−0.556671 | + | 0.830733i | \(0.687922\pi\) | |||||||
\(20\) | 0.268666 | − | 0.225437i | 0.0600755 | − | 0.0504093i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.28993 | − | 7.31556i | 0.275014 | − | 1.55968i | ||||
\(23\) | −3.41105 | − | 2.86221i | −0.711254 | − | 0.596813i | 0.213697 | − | 0.976900i | \(-0.431450\pi\) |
−0.924951 | + | 0.380087i | \(0.875894\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.69032 | + | 1.70714i | 0.938064 | + | 0.341427i | ||||
\(26\) | −10.0910 | −1.97900 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.18479 | −0.412887 | ||||||||
\(29\) | −6.01357 | − | 2.18876i | −1.11669 | − | 0.406443i | −0.283248 | − | 0.959047i | \(-0.591412\pi\) |
−0.833444 | + | 0.552604i | \(0.813634\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.26972 | + | 1.06542i | 0.228048 | + | 0.191355i | 0.749651 | − | 0.661833i | \(-0.230221\pi\) |
−0.521603 | + | 0.853188i | \(0.674666\pi\) | |||||||
\(32\) | 0.364882 | − | 2.06935i | 0.0645026 | − | 0.365812i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.66291 | − | 3.07355i | 0.628185 | − | 0.527109i | ||||
\(35\) | 0.0269877 | + | 0.0467441i | 0.00456176 | + | 0.00790120i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.01505 | + | 3.49016i | −0.331272 | + | 0.573779i | −0.982761 | − | 0.184878i | \(-0.940811\pi\) |
0.651490 | + | 0.758657i | \(0.274144\pi\) | |||||||
\(38\) | 1.60368 | + | 9.09494i | 0.260152 | + | 1.47539i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.371357 | − | 0.135163i | 0.0587167 | − | 0.0213711i | ||||
\(41\) | 1.03005 | − | 0.374907i | 0.160867 | − | 0.0585507i | −0.260332 | − | 0.965519i | \(-0.583832\pi\) |
0.421198 | + | 0.906969i | \(0.361610\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.19837 | − | 6.79628i | −0.182749 | − | 1.03642i | −0.928813 | − | 0.370548i | \(-0.879170\pi\) |
0.746064 | − | 0.665874i | \(-0.231941\pi\) | |||||||
\(44\) | 5.82704 | − | 10.0927i | 0.878459 | − | 1.52154i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.34699 | − | 9.26126i | −0.788370 | − | 1.36550i | ||||
\(47\) | 2.75255 | − | 2.30966i | 0.401500 | − | 0.336899i | −0.419573 | − | 0.907722i | \(-0.637820\pi\) |
0.821073 | + | 0.570823i | \(0.193376\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.15715 | + | 6.56252i | −0.165307 | + | 0.937503i | ||||
\(50\) | 9.18280 | + | 7.70529i | 1.29864 | + | 1.08969i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −14.8765 | − | 5.41460i | −2.06300 | − | 0.750870i | ||||
\(53\) | 5.40034 | 0.741793 | 0.370897 | − | 0.928674i | \(-0.379050\pi\) | ||||
0.370897 | + | 0.928674i | \(0.379050\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.287915 | −0.0388224 | ||||||||
\(56\) | −2.31336 | − | 0.841995i | −0.309136 | − | 0.112516i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −11.7735 | − | 9.87913i | −1.54593 | − | 1.29719i | ||||
\(59\) | −1.78591 | + | 10.1284i | −0.232506 | + | 1.31861i | 0.615297 | + | 0.788295i | \(0.289036\pi\) |
−0.847803 | + | 0.530311i | \(0.822075\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.1090 | + | 8.48243i | −1.29432 | + | 1.08606i | −0.303224 | + | 0.952919i | \(0.598063\pi\) |
−0.991097 | + | 0.133145i | \(0.957492\pi\) | |||||||
\(62\) | 1.99034 | + | 3.44738i | 0.252774 | + | 0.437817i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.18386 | − | 8.97871i | 0.647982 | − | 1.12234i | ||||
\(65\) | 0.0679158 | + | 0.385170i | 0.00842392 | + | 0.0477744i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.30434 | − | 3.02253i | 1.01454 | − | 0.369261i | 0.219363 | − | 0.975643i | \(-0.429602\pi\) |
0.795173 | + | 0.606382i | \(0.207380\pi\) | |||||||
\(68\) | 7.04920 | − | 2.56570i | 0.854842 | − | 0.311137i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0225098 | + | 0.127659i | 0.00269043 | + | 0.0152582i | ||||
\(71\) | −0.572473 | + | 0.991553i | −0.0679401 | + | 0.117676i | −0.897994 | − | 0.440007i | \(-0.854976\pi\) |
0.830054 | + | 0.557683i | \(0.188309\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.0977361 | − | 0.169284i | −0.0114391 | − | 0.0198132i | 0.860249 | − | 0.509874i | \(-0.170308\pi\) |
−0.871688 | + | 0.490061i | \(0.836975\pi\) | |||||||
\(74\) | −7.41436 | + | 6.22139i | −0.861902 | + | 0.723221i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.51594 | + | 14.2686i | −0.288598 | + | 1.63672i | ||||
\(77\) | 1.37395 | + | 1.15288i | 0.156576 | + | 0.131383i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.77330 | + | 2.46528i | 0.762056 | + | 0.277366i | 0.693670 | − | 0.720293i | \(-0.255993\pi\) |
0.0683861 | + | 0.997659i | \(0.478215\pi\) | |||||||
\(80\) | 0.247661 | 0.0276893 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.63255 | 0.290717 | ||||||||
\(83\) | 14.0018 | + | 5.09625i | 1.53690 | + | 0.559386i | 0.965300 | − | 0.261145i | \(-0.0841000\pi\) |
0.571602 | + | 0.820531i | \(0.306322\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.141969 | − | 0.119126i | −0.0153987 | − | 0.0129211i | ||||
\(86\) | 2.87802 | − | 16.3221i | 0.310345 | − | 1.76006i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.0596 | − | 8.44098i | 1.07235 | − | 0.899812i | ||||
\(89\) | 0.776563 | + | 1.34505i | 0.0823155 | + | 0.142575i | 0.904244 | − | 0.427016i | \(-0.140435\pi\) |
−0.821929 | + | 0.569590i | \(0.807102\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.21821 | − | 2.11000i | 0.127703 | − | 0.221189i | ||||
\(92\) | −2.91334 | − | 16.5224i | −0.303737 | − | 1.72258i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.10907 | − | 2.95146i | 0.836387 | − | 0.304420i | ||||
\(95\) | 0.336358 | − | 0.122424i | 0.0345096 | − | 0.0125605i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.919560 | + | 5.21508i | 0.0933672 | + | 0.529511i | 0.995235 | + | 0.0975004i | \(0.0310847\pi\) |
−0.901868 | + | 0.432011i | \(0.857804\pi\) | |||||||
\(98\) | −8.00191 | + | 13.8597i | −0.808315 | + | 1.40004i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.40314 | + | 16.2867i | 0.940314 | + | 1.62867i | ||||
\(101\) | −5.56836 | + | 4.67241i | −0.554073 | + | 0.464922i | −0.876317 | − | 0.481734i | \(-0.840007\pi\) |
0.322245 | + | 0.946656i | \(0.395563\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.11159 | − | 6.30412i | 0.109528 | − | 0.621164i | −0.879787 | − | 0.475368i | \(-0.842315\pi\) |
0.989315 | − | 0.145795i | \(-0.0465741\pi\) | |||||||
\(104\) | −13.6652 | − | 11.4665i | −1.33998 | − | 1.12438i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.1874 | + | 4.43585i | 1.18374 | + | 0.430848i | ||||
\(107\) | −5.54365 | −0.535925 | −0.267963 | − | 0.963429i | \(-0.586350\pi\) | ||||
−0.267963 | + | 0.963429i | \(0.586350\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.23137 | −0.596857 | −0.298428 | − | 0.954432i | \(-0.596462\pi\) | ||||
−0.298428 | + | 0.954432i | \(0.596462\pi\) | |||||||
\(110\) | −0.649762 | − | 0.236494i | −0.0619524 | − | 0.0225488i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.18185 | − | 0.991691i | −0.111674 | − | 0.0937060i | ||||
\(113\) | −2.05669 | + | 11.6640i | −0.193477 | + | 1.09726i | 0.721095 | + | 0.692836i | \(0.243639\pi\) |
−0.914571 | + | 0.404424i | \(0.867472\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.317513 | + | 0.266425i | −0.0296082 | + | 0.0248442i | ||||
\(116\) | −12.0560 | − | 20.8816i | −1.11937 | − | 1.93881i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.3499 | + | 21.3907i | −1.13690 | + | 1.96917i | ||||
\(119\) | 0.200476 | + | 1.13696i | 0.0183776 | + | 0.104225i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.34642 | − | 0.490058i | 0.122402 | − | 0.0445508i | ||||
\(122\) | −29.7813 | + | 10.8395i | −2.69627 | + | 0.981362i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.08445 | + | 6.15022i | 0.0973865 | + | 0.552306i | ||||
\(125\) | 0.465014 | − | 0.805428i | 0.0415921 | − | 0.0720396i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.76469 | − | 9.98473i | −0.511533 | − | 0.886002i | −0.999911 | − | 0.0133693i | \(-0.995744\pi\) |
0.488377 | − | 0.872633i | \(-0.337589\pi\) | |||||||
\(128\) | 15.8547 | − | 13.3036i | 1.40137 | − | 1.17589i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.163108 | + | 0.925032i | −0.0143055 | + | 0.0811307i | ||||
\(131\) | −6.90342 | − | 5.79266i | −0.603155 | − | 0.506107i | 0.289303 | − | 0.957237i | \(-0.406576\pi\) |
−0.892458 | + | 0.451131i | \(0.851021\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.09534 | − | 0.762641i | −0.181689 | − | 0.0661293i | ||||
\(134\) | 21.2238 | 1.83346 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.45283 | 0.724824 | ||||||||
\(137\) | −10.8255 | − | 3.94015i | −0.924883 | − | 0.336630i | −0.164703 | − | 0.986343i | \(-0.552667\pi\) |
−0.760179 | + | 0.649713i | \(0.774889\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.30521 | + | 1.09520i | 0.110707 | + | 0.0928940i | 0.696461 | − | 0.717595i | \(-0.254757\pi\) |
−0.585754 | + | 0.810489i | \(0.699202\pi\) | |||||||
\(140\) | −0.0353145 | + | 0.200278i | −0.00298462 | + | 0.0169266i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.10641 | + | 1.76749i | −0.176766 | + | 0.148325i | ||||
\(143\) | 6.49816 | + | 11.2551i | 0.543403 | + | 0.941202i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.297844 | + | 0.515881i | −0.0247346 | + | 0.0428416i | ||||
\(146\) | −0.0815191 | − | 0.462318i | −0.00674657 | − | 0.0382617i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −14.2688 | + | 5.19341i | −1.17289 | + | 0.426896i | ||||
\(149\) | 20.3469 | − | 7.40568i | 1.66689 | − | 0.606697i | 0.675464 | − | 0.737393i | \(-0.263943\pi\) |
0.991423 | + | 0.130696i | \(0.0417211\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.823357 | − | 4.66949i | −0.0670038 | − | 0.379998i | −0.999808 | − | 0.0196130i | \(-0.993757\pi\) |
0.932804 | − | 0.360385i | \(-0.117355\pi\) | |||||||
\(152\) | −8.16296 | + | 14.1387i | −0.662104 | + | 1.14680i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.15373 | + | 3.73036i | 0.173552 | + | 0.300601i | ||||
\(155\) | 0.118190 | − | 0.0991730i | 0.00949323 | − | 0.00796576i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.0363282 | + | 0.206027i | −0.00289931 | + | 0.0164428i | −0.986223 | − | 0.165421i | \(-0.947102\pi\) |
0.983324 | + | 0.181864i | \(0.0582129\pi\) | |||||||
\(158\) | 13.2609 | + | 11.1272i | 1.05498 | + | 0.885234i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.183798 | − | 0.0668969i | −0.0145305 | − | 0.00528866i | ||||
\(161\) | 2.58202 | 0.203491 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.62384 | 0.440493 | 0.220247 | − | 0.975444i | \(-0.429314\pi\) | ||||
0.220247 | + | 0.975444i | \(0.429314\pi\) | |||||||
\(164\) | 3.88100 | + | 1.41257i | 0.303056 | + | 0.110303i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 27.4131 | + | 23.0023i | 2.12767 | + | 1.78532i | ||||
\(167\) | 2.89654 | − | 16.4271i | 0.224141 | − | 1.27117i | −0.640180 | − | 0.768225i | \(-0.721140\pi\) |
0.864321 | − | 0.502941i | \(-0.167749\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.56560 | − | 2.99189i | 0.274277 | − | 0.230146i | ||||
\(170\) | −0.222544 | − | 0.385457i | −0.0170683 | − | 0.0295632i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.0010 | − | 22.5183i | 0.991315 | − | 1.71701i | ||||
\(173\) | 3.29969 | + | 18.7135i | 0.250871 | + | 1.42276i | 0.806454 | + | 0.591297i | \(0.201384\pi\) |
−0.555583 | + | 0.831461i | \(0.687505\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.71974 | + | 0.989903i | −0.205593 | + | 0.0748296i | ||||
\(176\) | 7.73325 | − | 2.81467i | 0.582916 | − | 0.212164i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.647711 | + | 3.67335i | 0.0485480 | + | 0.275329i | ||||
\(179\) | −8.11761 | + | 14.0601i | −0.606739 | + | 1.05090i | 0.385035 | + | 0.922902i | \(0.374189\pi\) |
−0.991774 | + | 0.128001i | \(0.959144\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.49579 | + | 2.59078i | 0.111181 | + | 0.192571i | 0.916247 | − | 0.400614i | \(-0.131203\pi\) |
−0.805066 | + | 0.593186i | \(0.797870\pi\) | |||||||
\(182\) | 4.48241 | − | 3.76118i | 0.332258 | − | 0.278798i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.28276 | − | 18.6174i | 0.242008 | − | 1.37250i | ||||
\(185\) | 0.287370 | + | 0.241132i | 0.0211279 | + | 0.0177284i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.78690 | − | 2.10626i | −0.423180 | − | 0.154025i | ||||
\(188\) | 13.5384 | 0.987388 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.859649 | 0.0623655 | ||||||||
\(191\) | 2.11790 | + | 0.770851i | 0.153246 | + | 0.0557768i | 0.417504 | − | 0.908675i | \(-0.362905\pi\) |
−0.264258 | + | 0.964452i | \(0.585127\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.674328 | − | 0.565829i | −0.0485392 | − | 0.0407292i | 0.618195 | − | 0.786025i | \(-0.287864\pi\) |
−0.666735 | + | 0.745295i | \(0.732309\pi\) | |||||||
\(194\) | −2.20843 | + | 12.5247i | −0.158556 | + | 0.899218i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −19.2335 | + | 16.1389i | −1.37382 | + | 1.15278i | ||||
\(197\) | −10.1383 | − | 17.5600i | −0.722322 | − | 1.25110i | −0.960067 | − | 0.279771i | \(-0.909741\pi\) |
0.237744 | − | 0.971328i | \(-0.423592\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.50472 | − | 16.4627i | 0.673772 | − | 1.16701i | −0.303054 | − | 0.952973i | \(-0.598006\pi\) |
0.976826 | − | 0.214034i | \(-0.0686603\pi\) | |||||||
\(200\) | 3.67977 | + | 20.8690i | 0.260199 | + | 1.47566i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −16.4045 | + | 5.97076i | −1.15422 | + | 0.420101i | ||||
\(203\) | 3.48704 | − | 1.26918i | 0.244742 | − | 0.0890788i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0177180 | − | 0.100484i | −0.00123748 | − | 0.00701809i | ||||
\(206\) | 7.68684 | − | 13.3140i | 0.535567 | − | 0.927630i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.58963 | − | 9.68152i | −0.387571 | − | 0.671293i | ||||
\(209\) | 9.11150 | − | 7.64545i | 0.630255 | − | 0.528847i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.81033 | − | 15.9382i | 0.193471 | − | 1.09723i | −0.721108 | − | 0.692823i | \(-0.756367\pi\) |
0.914579 | − | 0.404408i | \(-0.132522\pi\) | |||||||
\(212\) | 15.5869 | + | 13.0790i | 1.07052 | + | 0.898269i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.5108 | − | 4.55357i | −0.855223 | − | 0.311276i | ||||
\(215\) | −0.642380 | −0.0438100 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.961120 | −0.0652451 | ||||||||
\(218\) | −14.0629 | − | 5.11846i | −0.952458 | − | 0.346666i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.831006 | − | 0.697297i | −0.0560264 | − | 0.0470117i | ||||
\(221\) | −1.45267 | + | 8.23850i | −0.0977171 | + | 0.554181i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.4372 | − | 13.7925i | 1.10072 | − | 0.923613i | 0.103246 | − | 0.994656i | \(-0.467077\pi\) |
0.997473 | + | 0.0710428i | \(0.0226327\pi\) | |||||||
\(224\) | 0.609223 | + | 1.05520i | 0.0407054 | + | 0.0705038i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.2224 | + | 24.6339i | −0.946058 | + | 1.63862i | ||||
\(227\) | −3.31915 | − | 18.8239i | −0.220300 | − | 1.24938i | −0.871469 | − | 0.490451i | \(-0.836832\pi\) |
0.651169 | − | 0.758933i | \(-0.274279\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.1150 | + | 7.68525i | −1.39532 | + | 0.507855i | −0.926786 | − | 0.375589i | \(-0.877440\pi\) |
−0.468535 | + | 0.883445i | \(0.655218\pi\) | |||||||
\(230\) | −0.935400 | + | 0.340458i | −0.0616784 | + | 0.0224491i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.71792 | − | 26.7567i | −0.309747 | − | 1.75666i | ||||
\(233\) | 8.84074 | − | 15.3126i | 0.579176 | − | 1.00316i | −0.416398 | − | 0.909182i | \(-0.636708\pi\) |
0.995574 | − | 0.0939796i | \(-0.0299589\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.167233 | − | 0.289657i | −0.0109091 | − | 0.0188951i | ||||
\(236\) | −29.6845 | + | 24.9083i | −1.93230 | + | 1.62139i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.481468 | + | 2.73054i | −0.0312089 | + | 0.176995i | ||||
\(239\) | −11.8126 | − | 9.91199i | −0.764097 | − | 0.641153i | 0.175093 | − | 0.984552i | \(-0.443977\pi\) |
−0.939190 | + | 0.343399i | \(0.888422\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.3583 | − | 4.49806i | −0.796069 | − | 0.289746i | −0.0882127 | − | 0.996102i | \(-0.528116\pi\) |
−0.707857 | + | 0.706356i | \(0.750338\pi\) | |||||||
\(242\) | 3.44113 | 0.221204 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −49.7209 | −3.18305 | ||||||||
\(245\) | 0.582878 | + | 0.212150i | 0.0372387 | + | 0.0135538i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.3773 | − | 10.3858i | −0.787550 | − | 0.660833i | ||||
\(248\) | −1.22196 | + | 6.93009i | −0.0775946 | + | 0.440061i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.71102 | − | 1.43571i | 0.108214 | − | 0.0908025i | ||||
\(251\) | −8.70830 | − | 15.0832i | −0.549663 | − | 0.952045i | −0.998297 | − | 0.0583292i | \(-0.981423\pi\) |
0.448634 | − | 0.893716i | \(-0.351911\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.88646 | + | 11.9277i | −0.432948 | + | 0.749889i | ||||
\(254\) | −4.80818 | − | 27.2685i | −0.301692 | − | 1.71098i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 27.2233 | − | 9.90846i | 1.70145 | − | 0.619279i | ||||
\(257\) | −10.5129 | + | 3.82638i | −0.655776 | + | 0.238683i | −0.648412 | − | 0.761290i | \(-0.724566\pi\) |
−0.00736433 | + | 0.999973i | \(0.502344\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.405798 | − | 2.30139i | −0.0252150 | − | 0.143002i | ||||
\(260\) | −0.736812 | + | 1.27620i | −0.0456952 | + | 0.0791463i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.8214 | − | 18.7433i | −0.668550 | − | 1.15796i | ||||
\(263\) | −15.8655 | + | 13.3127i | −0.978306 | + | 0.820896i | −0.983833 | − | 0.179088i | \(-0.942685\pi\) |
0.00552693 | + | 0.999985i | \(0.498241\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.0872898 | − | 0.495045i | 0.00536217 | − | 0.0304104i | ||||
\(266\) | −4.10229 | − | 3.44223i | −0.251528 | − | 0.211057i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 31.2890 | + | 11.3883i | 1.91128 | + | 0.695648i | ||||
\(269\) | −28.2449 | −1.72212 | −0.861060 | − | 0.508504i | \(-0.830199\pi\) | ||||
−0.861060 | + | 0.508504i | \(0.830199\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.2626 | 1.04863 | 0.524316 | − | 0.851524i | \(-0.324321\pi\) | ||||
0.524316 | + | 0.851524i | \(0.324321\pi\) | |||||||
\(272\) | 4.97781 | + | 1.81178i | 0.301824 | + | 0.109855i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −21.1943 | − | 17.7842i | −1.28040 | − | 1.07438i | ||||
\(275\) | 2.68089 | − | 15.2041i | 0.161664 | − | 0.916840i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.95967 | − | 3.32256i | 0.237913 | − | 0.199633i | −0.516034 | − | 0.856568i | \(-0.672592\pi\) |
0.753947 | + | 0.656935i | \(0.228148\pi\) | |||||||
\(278\) | 2.04598 | + | 3.54375i | 0.122710 | + | 0.212540i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.114578 | + | 0.198454i | −0.00684733 | + | 0.0118599i | ||||
\(281\) | −0.572421 | − | 3.24636i | −0.0341478 | − | 0.193662i | 0.962962 | − | 0.269638i | \(-0.0869039\pi\) |
−0.997110 | + | 0.0759760i | \(0.975793\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.58007 | − | 3.12289i | 0.510032 | − | 0.185637i | −0.0741686 | − | 0.997246i | \(-0.523630\pi\) |
0.584201 | + | 0.811609i | \(0.301408\pi\) | |||||||
\(284\) | −4.05375 | + | 1.47544i | −0.240546 | + | 0.0875516i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.41994 | + | 30.7380i | 0.320488 | + | 1.81758i | ||||
\(287\) | −0.317809 | + | 0.550462i | −0.0187597 | + | 0.0324927i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.51799 | + | 11.2895i | 0.383411 | + | 0.664087i | ||||
\(290\) | −1.09592 | + | 0.919583i | −0.0643544 | + | 0.0539998i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.127891 | − | 0.725308i | 0.00748427 | − | 0.0424454i | ||||
\(293\) | −2.16517 | − | 1.81680i | −0.126491 | − | 0.106138i | 0.577348 | − | 0.816498i | \(-0.304088\pi\) |
−0.703839 | + | 0.710360i | \(0.748532\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.899597 | + | 0.327426i | 0.0523766 | + | 0.0190635i | ||||
\(296\) | −17.1100 | −0.994496 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 52.0017 | 3.01238 | ||||||||
\(299\) | 17.5812 | + | 6.39904i | 1.01675 | + | 0.370066i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.06548 | + | 2.57224i | 0.176691 | + | 0.148261i | ||||
\(302\) | 1.97739 | − | 11.2143i | 0.113786 | − | 0.645313i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.83759 | + | 6.57652i | −0.449517 | + | 0.377189i | ||||
\(305\) | 0.614179 | + | 1.06379i | 0.0351678 | + | 0.0609124i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.14723 | + | 5.45116i | −0.179622 | + | 0.311114i | −0.941751 | − | 0.336311i | \(-0.890821\pi\) |
0.762129 | + | 0.647425i | \(0.224154\pi\) | |||||||
\(308\) | 1.17347 | + | 6.65508i | 0.0668647 | + | 0.379208i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.348190 | − | 0.126731i | 0.0197759 | − | 0.00719782i | ||||
\(311\) | 6.92825 | − | 2.52168i | 0.392865 | − | 0.142991i | −0.138031 | − | 0.990428i | \(-0.544078\pi\) |
0.530896 | + | 0.847437i | \(0.321855\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.741608 | − | 4.20587i | −0.0419182 | − | 0.237730i | 0.956649 | − | 0.291244i | \(-0.0940690\pi\) |
−0.998567 | + | 0.0535138i | \(0.982958\pi\) | |||||||
\(314\) | −0.251217 | + | 0.435120i | −0.0141770 | + | 0.0245552i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.5791 | + | 23.5197i | 0.763883 | + | 1.32308i | ||||
\(317\) | 12.3698 | − | 10.3795i | 0.694755 | − | 0.582968i | −0.225521 | − | 0.974238i | \(-0.572409\pi\) |
0.920276 | + | 0.391270i | \(0.127964\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.43723 | + | 19.4935i | −0.192448 | + | 1.09143i | ||||
\(320\) | −0.739281 | − | 0.620330i | −0.0413271 | − | 0.0346775i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.82706 | + | 2.12087i | 0.324729 | + | 0.118192i | ||||
\(323\) | 7.65618 | 0.426001 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.9723 | −1.16333 | ||||||||
\(326\) | 12.6918 | + | 4.61944i | 0.702934 | + | 0.255847i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.56500 | + | 2.99139i | 0.196844 | + | 0.165172i | ||||
\(329\) | −0.361805 | + | 2.05190i | −0.0199470 | + | 0.113125i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.7297 | − | 12.3597i | 0.809616 | − | 0.679349i | −0.140900 | − | 0.990024i | \(-0.545000\pi\) |
0.950516 | + | 0.310675i | \(0.100555\pi\) | |||||||
\(332\) | 28.0708 | + | 48.6201i | 1.54059 | + | 2.66838i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.0301 | − | 34.6932i | 1.09600 | − | 1.89833i | ||||
\(335\) | −0.142844 | − | 0.810108i | −0.00780440 | − | 0.0442609i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.6859 | − | 10.0769i | 1.50815 | − | 0.548921i | 0.549993 | − | 0.835169i | \(-0.314630\pi\) |
0.958156 | + | 0.286248i | \(0.0924080\pi\) | |||||||
\(338\) | 10.5043 | − | 3.82327i | 0.571361 | − | 0.207958i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.121254 | − | 0.687667i | −0.00657593 | − | 0.0372940i | ||||
\(341\) | 2.56339 | − | 4.43993i | 0.138815 | − | 0.240435i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.96154 | − | 6.86159i | −0.213903 | − | 0.370491i | ||||
\(344\) | 22.4444 | − | 18.8331i | 1.21012 | − | 1.01541i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.92460 | + | 44.9426i | −0.426029 | + | 2.41613i | ||||
\(347\) | 8.73063 | + | 7.32587i | 0.468685 | + | 0.393273i | 0.846315 | − | 0.532683i | \(-0.178816\pi\) |
−0.377630 | + | 0.925957i | \(0.623261\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.4633 | − | 9.63184i | −1.41655 | − | 0.515581i | −0.483502 | − | 0.875343i | \(-0.660635\pi\) |
−0.933044 | + | 0.359763i | \(0.882858\pi\) | |||||||
\(350\) | −6.95097 | −0.371545 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.49941 | −0.346419 | ||||||||
\(353\) | −26.9260 | − | 9.80028i | −1.43313 | − | 0.521616i | −0.495302 | − | 0.868721i | \(-0.664943\pi\) |
−0.937826 | + | 0.347104i | \(0.887165\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.0816416 | + | 0.0685054i | 0.00433309 | + | 0.00363589i | ||||
\(356\) | −1.01616 | + | 5.76294i | −0.0538565 | + | 0.305435i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −29.8687 | + | 25.0628i | −1.57861 | + | 1.32461i | ||||
\(359\) | 15.5161 | + | 26.8747i | 0.818909 | + | 1.41839i | 0.906486 | + | 0.422235i | \(0.138754\pi\) |
−0.0875770 | + | 0.996158i | \(0.527912\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.10636 | − | 3.64833i | 0.110861 | − | 0.192017i | ||||
\(362\) | 1.24760 | + | 7.07549i | 0.0655724 | + | 0.371880i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.62630 | − | 3.13972i | 0.452141 | − | 0.164566i | ||||
\(365\) | −0.0170979 | + | 0.00622313i | −0.000894945 | + | 0.000325733i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.18913 | + | 23.7577i | 0.218671 | + | 1.24014i | 0.874422 | + | 0.485166i | \(0.161241\pi\) |
−0.655751 | + | 0.754977i | \(0.727648\pi\) | |||||||
\(368\) | 5.92365 | − | 10.2601i | 0.308791 | − | 0.534843i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.450466 | + | 0.780230i | 0.0234186 | + | 0.0405622i | ||||
\(371\) | −2.39883 | + | 2.01285i | −0.124541 | + | 0.104502i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.18547 | + | 12.3944i | −0.113159 | + | 0.641758i | 0.874486 | + | 0.485051i | \(0.161199\pi\) |
−0.987645 | + | 0.156707i | \(0.949912\pi\) | |||||||
\(374\) | −11.3297 | − | 9.50675i | −0.585845 | − | 0.491582i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14.3351 | + | 5.21754i | 0.739276 | + | 0.269074i | ||||
\(377\) | 26.8890 | 1.38486 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.70522 | −0.395790 | −0.197895 | − | 0.980223i | \(-0.563411\pi\) | ||||
−0.197895 | + | 0.980223i | \(0.563411\pi\) | |||||||
\(380\) | 1.26733 | + | 0.461269i | 0.0650124 | + | 0.0236626i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.14646 | + | 3.47929i | 0.212151 | + | 0.178016i | ||||
\(383\) | −3.10164 | + | 17.5903i | −0.158486 | + | 0.898821i | 0.797042 | + | 0.603923i | \(0.206397\pi\) |
−0.955529 | + | 0.294898i | \(0.904714\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.127892 | − | 0.107314i | 0.00651796 | − | 0.00546922i | ||||
\(386\) | −1.05704 | − | 1.83085i | −0.0538020 | − | 0.0931878i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.97622 | + | 17.2793i | −0.506466 | + | 0.877224i | ||||
\(389\) | 4.75596 | + | 26.9724i | 0.241137 | + | 1.36755i | 0.829297 | + | 0.558809i | \(0.188741\pi\) |
−0.588160 | + | 0.808744i | \(0.700148\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.33084 | + | 3.03218i | −0.421309 | + | 0.153344i | ||||
\(392\) | −26.5851 | + | 9.67620i | −1.34275 | + | 0.488722i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.45608 | − | 47.9568i | −0.426011 | − | 2.41603i | ||||
\(395\) | 0.335472 | − | 0.581055i | 0.0168794 | − | 0.0292361i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.10799 | − | 3.65115i | −0.105797 | − | 0.183246i | 0.808266 | − | 0.588817i | \(-0.200406\pi\) |
−0.914064 | + | 0.405571i | \(0.867073\pi\) | |||||||
\(398\) | 34.9726 | − | 29.3455i | 1.75302 | − | 1.47096i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.30606 | + | 13.0783i | −0.115303 | + | 0.653917i | ||||
\(401\) | 11.6228 | + | 9.75269i | 0.580415 | + | 0.487026i | 0.885084 | − | 0.465432i | \(-0.154101\pi\) |
−0.304668 | + | 0.952459i | \(0.598546\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.54437 | − | 2.38196i | −0.325998 | − | 0.118654i | ||||
\(404\) | −27.3880 | −1.36260 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.91200 | 0.442295 | ||||||||
\(407\) | 11.7137 | + | 4.26342i | 0.580625 | + | 0.211330i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.60777 | + | 3.02728i | 0.178393 | + | 0.149689i | 0.727612 | − | 0.685989i | \(-0.240630\pi\) |
−0.549219 | + | 0.835679i | \(0.685075\pi\) | |||||||
\(410\) | 0.0425519 | − | 0.241324i | 0.00210149 | − | 0.0119181i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 18.4762 | − | 15.5034i | 0.910258 | − | 0.763797i | ||||
\(413\) | −2.98184 | − | 5.16469i | −0.146727 | − | 0.254138i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.693492 | − | 1.20116i | 0.0340422 | − | 0.0589628i | ||||
\(416\) | 1.53314 | + | 8.69485i | 0.0751682 | + | 0.426300i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 26.8427 | − | 9.76994i | 1.31292 | − | 0.477863i | ||||
\(419\) | −18.5976 | + | 6.76897i | −0.908551 | + | 0.330686i | −0.753674 | − | 0.657248i | \(-0.771720\pi\) |
−0.154877 | + | 0.987934i | \(0.549498\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.89440 | + | 27.7575i | 0.238538 | + | 1.35282i | 0.835032 | + | 0.550201i | \(0.185449\pi\) |
−0.596494 | + | 0.802617i | \(0.703440\pi\) | |||||||
\(422\) | 19.4340 | − | 33.6607i | 0.946032 | − | 1.63858i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.4637 | + | 19.8557i | 0.556726 | + | 0.964278i | ||||
\(425\) | 7.61270 | − | 6.38782i | 0.369270 | − | 0.309855i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.32876 | − | 7.53578i | 0.0643033 | − | 0.364682i | ||||
\(428\) | −16.0006 | − | 13.4261i | −0.773418 | − | 0.648975i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.44971 | − | 0.527653i | −0.0699114 | − | 0.0254457i | ||||
\(431\) | −5.19681 | −0.250321 | −0.125161 | − | 0.992136i | \(-0.539945\pi\) | ||||
−0.125161 | + | 0.992136i | \(0.539945\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.3285 | 1.21721 | 0.608605 | − | 0.793473i | \(-0.291730\pi\) | ||||
0.608605 | + | 0.793473i | \(0.291730\pi\) | |||||||
\(434\) | −2.16904 | − | 0.789467i | −0.104117 | − | 0.0378956i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.9855 | − | 15.0917i | −0.861351 | − | 0.722760i | ||||
\(437\) | 2.97337 | − | 16.8628i | 0.142236 | − | 0.806658i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.9972 | + | 10.0668i | −0.572595 | + | 0.480464i | −0.882506 | − | 0.470301i | \(-0.844145\pi\) |
0.309911 | + | 0.950766i | \(0.399701\pi\) | |||||||
\(440\) | −0.611178 | − | 1.05859i | −0.0291368 | − | 0.0504664i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.0455 | + | 17.3993i | −0.477815 | + | 0.827600i | ||||
\(443\) | −3.16975 | − | 17.9765i | −0.150599 | − | 0.854091i | −0.962700 | − | 0.270573i | \(-0.912787\pi\) |
0.812100 | − | 0.583518i | \(-0.198324\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.135852 | − | 0.0494459i | 0.00643998 | − | 0.00234396i | ||||
\(446\) | 48.4245 | − | 17.6251i | 2.29297 | − | 0.834572i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.04394 | + | 5.92050i | 0.0493218 | + | 0.279718i | ||||
\(449\) | −14.3608 | + | 24.8737i | −0.677729 | + | 1.17386i | 0.297934 | + | 0.954586i | \(0.403702\pi\) |
−0.975663 | + | 0.219274i | \(0.929631\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.69525 | − | 2.93626i | −0.0798262 | − | 0.138263i | ||||
\(452\) | −34.1852 | + | 28.6848i | −1.60793 | + | 1.34922i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.97135 | − | 45.2078i | 0.374114 | − | 2.12171i | ||||
\(455\) | −0.173732 | − | 0.145778i | −0.00814466 | − | 0.00683419i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.2538 | + | 12.1034i | 1.55555 | + | 0.566172i | 0.969710 | − | 0.244258i | \(-0.0785444\pi\) |
0.585835 | + | 0.810430i | \(0.300767\pi\) | |||||||
\(458\) | −53.9648 | −2.52161 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.56168 | −0.0728139 | ||||||||
\(461\) | −2.13943 | − | 0.778687i | −0.0996430 | − | 0.0362671i | 0.291718 | − | 0.956504i | \(-0.405773\pi\) |
−0.391361 | + | 0.920237i | \(0.627995\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0757 | + | 11.8109i | 0.654154 | + | 0.548900i | 0.908328 | − | 0.418258i | \(-0.137359\pi\) |
−0.254175 | + | 0.967158i | \(0.581804\pi\) | |||||||
\(464\) | 2.95666 | − | 16.7681i | 0.137260 | − | 0.778437i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 32.5295 | − | 27.2955i | 1.50690 | − | 1.26444i | ||||
\(467\) | −2.32935 | − | 4.03455i | −0.107789 | − | 0.186697i | 0.807085 | − | 0.590435i | \(-0.201044\pi\) |
−0.914874 | + | 0.403738i | \(0.867711\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.56220 | + | 4.43786i | −0.118312 | + | 0.204922i | ||||
\(470\) | −0.139485 | − | 0.791059i | −0.00643397 | − | 0.0364888i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −41.0307 | + | 14.9340i | −1.88859 | + | 0.687392i | ||||
\(473\) | −20.0584 | + | 7.30068i | −0.922288 | + | 0.335685i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.33297 | + | 18.9022i | 0.152927 | + | 0.867292i | ||||
\(476\) | −2.17495 | + | 3.76712i | −0.0996885 | + | 0.172666i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18.5169 | − | 32.0722i | −0.846942 | − | 1.46695i | ||||
\(479\) | −10.8594 | + | 9.11209i | −0.496177 | + | 0.416342i | −0.856234 | − | 0.516588i | \(-0.827202\pi\) |
0.360057 | + | 0.932930i | \(0.382757\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.94045 | − | 16.6761i | 0.134073 | − | 0.760366i | ||||
\(482\) | −24.1954 | − | 20.3023i | −1.10207 | − | 0.924745i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.07304 | + | 1.84643i | 0.230593 | + | 0.0839288i | ||||
\(485\) | 0.492926 | 0.0223826 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.4338 | −0.971258 | −0.485629 | − | 0.874165i | \(-0.661409\pi\) | ||||
−0.485629 | + | 0.874165i | \(0.661409\pi\) | |||||||
\(488\) | −52.6469 | − | 19.1619i | −2.38321 | − | 0.867418i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.14117 | + | 0.957555i | 0.0515528 | + | 0.0432579i | ||||
\(491\) | −2.44633 | + | 13.8738i | −0.110401 | + | 0.626117i | 0.878523 | + | 0.477699i | \(0.158529\pi\) |
−0.988925 | + | 0.148418i | \(0.952582\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.76043 | + | 8.18997i | −0.439588 | + | 0.368858i | ||||
\(494\) | −19.4020 | − | 33.6053i | −0.872938 | − | 1.51197i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.20500 | + | 3.81917i | −0.0990073 | + | 0.171486i | ||||
\(497\) | −0.115287 | − | 0.653824i | −0.00517132 | − | 0.0293280i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0102 | + | 5.09929i | −0.627182 | + | 0.228276i | −0.636004 | − | 0.771685i | \(-0.719414\pi\) |
0.00882219 | + | 0.999961i | \(0.497192\pi\) | |||||||
\(500\) | 3.29282 | − | 1.19849i | 0.147259 | − | 0.0535980i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.26337 | − | 41.1926i | −0.324180 | − | 1.83852i | ||||
\(503\) | 7.93153 | − | 13.7378i | 0.353650 | − | 0.612539i | −0.633236 | − | 0.773958i | \(-0.718274\pi\) |
0.986886 | + | 0.161420i | \(0.0516072\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.338311 | + | 0.585972i | 0.0150546 | + | 0.0260754i | ||||
\(506\) | −25.3387 | + | 21.2617i | −1.12644 | + | 0.945199i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.54331 | − | 42.7803i | 0.334680 | − | 1.89807i | ||||
\(509\) | 25.9894 | + | 21.8077i | 1.15196 | + | 0.966608i | 0.999764 | − | 0.0217430i | \(-0.00692156\pi\) |
0.152194 | + | 0.988351i | \(0.451366\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.106511 | + | 0.0387669i | 0.00471177 | + | 0.00171495i | ||||
\(512\) | 28.1824 | 1.24550 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.8683 | −1.18511 | ||||||||
\(515\) | −0.559927 | − | 0.203797i | −0.0246733 | − | 0.00898036i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.51386 | − | 7.14397i | −0.374439 | − | 0.314192i | ||||
\(518\) | 0.974572 | − | 5.52707i | 0.0428203 | − | 0.242846i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.27200 | + | 1.06734i | −0.0557811 | + | 0.0468059i | ||||
\(521\) | 21.3899 | + | 37.0484i | 0.937108 | + | 1.62312i | 0.770831 | + | 0.637040i | \(0.219841\pi\) |
0.166277 | + | 0.986079i | \(0.446825\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.38893 | − | 2.40569i | 0.0607335 | − | 0.105193i | −0.834060 | − | 0.551674i | \(-0.813989\pi\) |
0.894793 | + | 0.446480i | \(0.147323\pi\) | |||||||
\(524\) | −5.89612 | − | 33.4386i | −0.257573 | − | 1.46077i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −46.7400 | + | 17.0120i | −2.03796 | + | 0.741758i | ||||
\(527\) | 3.10104 | − | 1.12869i | 0.135083 | − | 0.0491664i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.550887 | − | 3.12424i | −0.0239516 | − | 0.135836i | ||||
\(530\) | 0.603626 | − | 1.04551i | 0.0262198 | − | 0.0454141i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.20073 | − | 7.27587i | −0.182125 | − | 0.315449i | ||||
\(533\) | −3.52821 | + | 2.96052i | −0.152824 | + | 0.128234i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.0896063 | + | 0.508183i | −0.00387402 | + | 0.0219707i | ||||
\(536\) | 28.7413 | + | 24.1168i | 1.24144 | + | 1.04169i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −63.7426 | − | 23.2004i | −2.74814 | − | 1.00024i | ||||
\(539\) | 20.6116 | 0.887803 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.59390 | −0.154514 | −0.0772570 | − | 0.997011i | \(-0.524616\pi\) | ||||
−0.0772570 | + | 0.997011i | \(0.524616\pi\) | |||||||
\(542\) | 38.9581 | + | 14.1796i | 1.67339 | + | 0.609065i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.20482 | − | 2.68917i | −0.137406 | − | 0.115297i | ||||
\(545\) | −0.100722 | + | 0.571225i | −0.00431447 | + | 0.0244686i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.3245 | + | 25.4453i | −1.29658 | + | 1.08796i | −0.305858 | + | 0.952077i | \(0.598943\pi\) |
−0.990725 | + | 0.135884i | \(0.956612\pi\) | |||||||
\(548\) | −21.7029 | − | 37.5905i | −0.927101 | − | 1.60579i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 18.5389 | − | 32.1102i | 0.790499 | − | 1.36919i | ||||
\(551\) | −4.27328 | − | 24.2350i | −0.182048 | − | 1.03244i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.92757 | + | 1.42952i | −0.167017 | + | 0.0607894i | ||||
\(554\) | 11.6653 | − | 4.24581i | 0.495610 | − | 0.180387i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.11477 | + | 6.32215i | 0.0472766 | + | 0.268119i | ||||
\(557\) | 5.71731 | − | 9.90267i | 0.242250 | − | 0.419590i | −0.719105 | − | 0.694902i | \(-0.755448\pi\) |
0.961355 | + | 0.275312i | \(0.0887812\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.4983 | + | 25.1119i | 0.613214 | + | 1.06212i | ||||
\(560\) | −0.110011 | + | 0.0923099i | −0.00464880 | + | 0.00390081i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.37474 | − | 7.79653i | 0.0579898 | − | 0.328877i | ||||
\(563\) | 11.1159 | + | 9.32736i | 0.468480 | + | 0.393101i | 0.846240 | − | 0.532802i | \(-0.178861\pi\) |
−0.377760 | + | 0.925904i | \(0.623306\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.03599 | + | 0.377070i | 0.0435844 | + | 0.0158634i | ||||
\(566\) | 21.9285 | 0.921725 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.86093 | −0.203960 | ||||||||
\(569\) | 1.22083 | + | 0.444347i | 0.0511800 | + | 0.0186280i | 0.367483 | − | 0.930030i | \(-0.380220\pi\) |
−0.316303 | + | 0.948658i | \(0.602442\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.3006 | + | 10.3214i | 0.514765 | + | 0.431939i | 0.862802 | − | 0.505542i | \(-0.168707\pi\) |
−0.348037 | + | 0.937481i | \(0.613152\pi\) | |||||||
\(572\) | −8.50308 | + | 48.2234i | −0.355532 | + | 2.01632i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.16938 | + | 0.981225i | −0.0488089 | + | 0.0409555i | ||||
\(575\) | −11.1127 | − | 19.2478i | −0.463434 | − | 0.802691i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.23017 | − | 7.32686i | 0.176104 | − | 0.305021i | −0.764439 | − | 0.644696i | \(-0.776984\pi\) |
0.940543 | + | 0.339675i | \(0.110317\pi\) | |||||||
\(578\) | 5.43649 | + | 30.8318i | 0.226128 | + | 1.28244i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.10907 | + | 0.767638i | −0.0875743 | + | 0.0318745i | ||||
\(581\) | −8.11913 | + | 2.95512i | −0.336838 | + | 0.122599i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.90057 | − | 16.4499i | −0.120129 | − | 0.681286i | ||||
\(584\) | 0.414943 | − | 0.718703i | 0.0171705 | − | 0.0297401i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.39401 | − | 5.87860i | −0.140205 | − | 0.242843i | ||||
\(587\) | −14.0839 | + | 11.8178i | −0.581304 | + | 0.487772i | −0.885375 | − | 0.464877i | \(-0.846098\pi\) |
0.304071 | + | 0.952649i | \(0.401654\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.10680 | + | 6.27696i | −0.0456048 | + | 0.258637i | ||||
\(590\) | 1.76125 | + | 1.47786i | 0.0725094 | + | 0.0608426i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.0759 | − | 3.66734i | −0.414119 | − | 0.150727i | ||||
\(593\) | 13.5128 | 0.554905 | 0.277452 | − | 0.960739i | \(-0.410510\pi\) | ||||
0.277452 | + | 0.960739i | \(0.410510\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.107464 | 0.00440561 | ||||||||
\(596\) | 76.6629 | + | 27.9030i | 3.14023 | + | 1.14295i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 34.4209 | + | 28.8825i | 1.40757 | + | 1.18109i | ||||
\(599\) | 1.91494 | − | 10.8602i | 0.0782425 | − | 0.443735i | −0.920369 | − | 0.391051i | \(-0.872111\pi\) |
0.998611 | − | 0.0526835i | \(-0.0167775\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.7624 | − | 16.5826i | 0.806123 | − | 0.676418i | −0.143556 | − | 0.989642i | \(-0.545854\pi\) |
0.949679 | + | 0.313225i | \(0.101409\pi\) | |||||||
\(602\) | 4.80528 | + | 8.32298i | 0.195848 | + | 0.339219i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.93252 | − | 15.4716i | 0.363459 | − | 0.629529i | ||||
\(605\) | −0.0231600 | − | 0.131347i | −0.000941588 | − | 0.00534001i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.8979 | − | 5.05843i | 0.564100 | − | 0.205316i | −0.0442003 | − | 0.999023i | \(-0.514074\pi\) |
0.608300 | + | 0.793707i | \(0.291852\pi\) | |||||||
\(608\) | 7.59297 | − | 2.76362i | 0.307936 | − | 0.112079i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.512271 | + | 2.90523i | 0.0207413 | + | 0.117629i | ||||
\(611\) | −7.54882 | + | 13.0749i | −0.305393 | + | 0.528956i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.1370 | − | 31.4141i | −0.732545 | − | 1.26880i | −0.955792 | − | 0.294043i | \(-0.904999\pi\) |
0.223248 | − | 0.974762i | \(-0.428334\pi\) | |||||||
\(614\) | −11.5802 | + | 9.71696i | −0.467340 | + | 0.392145i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.32227 | + | 7.49896i | −0.0532757 | + | 0.302142i | ||||
\(617\) | −30.9279 | − | 25.9516i | −1.24511 | − | 1.04477i | −0.997107 | − | 0.0760138i | \(-0.975781\pi\) |
−0.248005 | − | 0.968759i | \(-0.579775\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.47759 | + | 2.35765i | 0.260356 | + | 0.0947619i | 0.468900 | − | 0.883251i | \(-0.344650\pi\) |
−0.208544 | + | 0.978013i | \(0.566873\pi\) | |||||||
\(620\) | 0.581315 | 0.0233462 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.7069 | 0.709981 | ||||||||
\(623\) | −0.846285 | − | 0.308023i | −0.0339057 | − | 0.0123407i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.0516 | + | 15.9862i | 0.762064 | + | 0.639448i | ||||
\(626\) | 1.78106 | − | 10.1009i | 0.0711856 | − | 0.403713i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.603829 | + | 0.506672i | −0.0240954 | + | 0.0202184i | ||||
\(629\) | 4.01193 | + | 6.94887i | 0.159966 | + | 0.277070i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.9095 | + | 25.8241i | −0.593539 | + | 1.02804i | 0.400212 | + | 0.916423i | \(0.368936\pi\) |
−0.993751 | + | 0.111617i | \(0.964397\pi\) | |||||||
\(632\) | 5.31396 | + | 30.1370i | 0.211378 | + | 1.19878i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 36.4416 | − | 13.2637i | 1.44728 | − | 0.526767i | ||||
\(635\) | −1.00847 | + | 0.367054i | −0.0400200 | + | 0.0145661i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.86204 | − | 27.5740i | −0.192641 | − | 1.09252i | ||||
\(638\) | −23.7691 | + | 41.1693i | −0.941028 | + | 1.62991i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.963264 | − | 1.66842i | −0.0380763 | − | 0.0659502i | ||||
\(641\) | 32.8485 | − | 27.5632i | 1.29744 | − | 1.08868i | 0.306858 | − | 0.951755i | \(-0.400722\pi\) |
0.990581 | − | 0.136926i | \(-0.0437222\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.76026 | + | 26.9968i | −0.187726 | + | 1.06465i | 0.734676 | + | 0.678419i | \(0.237334\pi\) |
−0.922402 | + | 0.386231i | \(0.873777\pi\) | |||||||
\(644\) | 7.45245 | + | 6.25335i | 0.293668 | + | 0.246416i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.2784 | + | 6.28881i | 0.679808 | + | 0.247430i | ||||
\(647\) | −16.1623 | −0.635407 | −0.317703 | − | 0.948190i | \(-0.602912\pi\) | ||||
−0.317703 | + | 0.948190i | \(0.602912\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.8113 | 1.24870 | ||||||||
\(650\) | −47.3299 | − | 17.2267i | −1.85643 | − | 0.675686i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.2320 | + | 13.6203i | 0.635696 | + | 0.533412i | ||||
\(653\) | 5.59951 | − | 31.7564i | 0.219126 | − | 1.24272i | −0.654476 | − | 0.756083i | \(-0.727111\pi\) |
0.873602 | − | 0.486641i | \(-0.161778\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.642594 | + | 0.539200i | −0.0251082 | + | 0.0210683i | ||||
\(656\) | 1.45823 | + | 2.52573i | 0.0569344 | + | 0.0986133i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.50195 | + | 4.33351i | −0.0975363 | + | 0.168938i | ||||
\(659\) | 4.83065 | + | 27.3960i | 0.188175 | + | 1.06719i | 0.921807 | + | 0.387648i | \(0.126712\pi\) |
−0.733632 | + | 0.679547i | \(0.762176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.9318 | + | 10.5303i | −1.12532 | + | 0.409582i | −0.836590 | − | 0.547829i | \(-0.815454\pi\) |
−0.288728 | + | 0.957411i | \(0.593232\pi\) | |||||||
\(662\) | 43.3940 | − | 15.7941i | 1.68656 | − | 0.613856i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.9851 | + | 62.2995i | 0.426304 | + | 2.41769i | ||||
\(665\) | −0.103779 | + | 0.179751i | −0.00402439 | + | 0.00697044i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.2479 | + | 24.6781i | 0.551682 | + | 0.955540i | ||||
\(668\) | 48.1448 | − | 40.3982i | 1.86278 | − | 1.56306i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.343057 | − | 1.94557i | 0.0132534 | − | 0.0751640i | ||||
\(671\) | 31.2679 | + | 26.2369i | 1.20708 | + | 1.01286i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.5547 | + | 8.93720i | 0.946516 | + | 0.344504i | 0.768736 | − | 0.639567i | \(-0.220886\pi\) |
0.177780 | + | 0.984070i | \(0.443108\pi\) | |||||||
\(674\) | 70.7584 | 2.72551 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.5374 | 0.674515 | ||||||||
\(677\) | −17.0972 | − | 6.22288i | −0.657100 | − | 0.239165i | −0.00811624 | − | 0.999967i | \(-0.502584\pi\) |
−0.648984 | + | 0.760802i | \(0.724806\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.35227 | − | 1.97379i | −0.0902720 | − | 0.0757472i | ||||
\(680\) | 0.136630 | − | 0.774865i | 0.00523950 | − | 0.0297147i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.43200 | − | 7.91438i | 0.361170 | − | 0.303057i | ||||
\(683\) | −11.7486 | − | 20.3491i | −0.449546 | − | 0.778636i | 0.548811 | − | 0.835947i | \(-0.315081\pi\) |
−0.998356 | + | 0.0573104i | \(0.981748\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.536171 | + | 0.928676i | −0.0204860 | + | 0.0354829i | ||||
\(686\) | −3.30422 | − | 18.7392i | −0.126156 | − | 0.715465i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 17.2540 | − | 6.27995i | 0.657803 | − | 0.239421i | ||||
\(689\) | −21.3223 | + | 7.76070i | −0.812317 | + | 0.295659i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.73393 | − | 43.8613i | −0.294213 | − | 1.66856i | −0.670386 | − | 0.742013i | \(-0.733871\pi\) |
0.376173 | − | 0.926549i | \(-0.377240\pi\) | |||||||
\(692\) | −35.7980 | + | 62.0039i | −1.36084 | + | 2.35704i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.6857 | + | 23.7043i | 0.519501 | + | 0.899802i | ||||
\(695\) | 0.121494 | − | 0.101945i | 0.00460852 | − | 0.00386701i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.378975 | − | 2.14928i | 0.0143547 | − | 0.0814096i | ||||
\(698\) | −51.8103 | − | 43.4740i | −1.96105 | − | 1.64552i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −10.2474 | − | 3.72974i | −0.387315 | − | 0.140971i | ||||
\(701\) | −25.2567 | −0.953934 | −0.476967 | − | 0.878921i | \(-0.658264\pi\) | ||||
−0.476967 | + | 0.878921i | \(0.658264\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.4974 | −0.584496 | ||||||||
\(704\) | −30.1343 | − | 10.9680i | −1.13573 | − | 0.413371i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −52.7163 | − | 44.2343i | −1.98401 | − | 1.66478i | ||||
\(707\) | 0.731927 | − | 4.15097i | 0.0275270 | − | 0.156113i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.0147 | + | 10.0815i | −0.451220 | + | 0.378618i | −0.839888 | − | 0.542759i | \(-0.817380\pi\) |
0.388668 | + | 0.921378i | \(0.372935\pi\) | |||||||
\(710\) | 0.127977 | + | 0.221663i | 0.00480289 | + | 0.00831886i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.29694 | + | 5.71046i | −0.123558 | + | 0.214009i | ||||
\(713\) | −1.28162 | − | 7.26841i | −0.0479970 | − | 0.272204i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.13678 | − | 0.413756i | 0.0425133 | − | 0.0154736i | ||||
\(716\) | −57.4818 | + | 20.9217i | −2.14820 | + | 0.781879i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.9416 | + | 73.3954i | 0.482976 | + | 2.73909i | ||||
\(719\) | 26.5804 | − | 46.0385i | 0.991280 | − | 1.71695i | 0.381523 | − | 0.924359i | \(-0.375400\pi\) |
0.609757 | − | 0.792588i | \(-0.291267\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.85595 | + | 3.21461i | 0.0691194 | + | 0.119718i | ||||
\(722\) | 7.75035 | − | 6.50332i | 0.288438 | − | 0.242028i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.95730 | + | 11.1004i | −0.0727424 | + | 0.412543i | ||||
\(725\) | −24.4691 | − | 20.5320i | −0.908758 | − | 0.762539i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.440878 | − | 0.160466i | −0.0163512 | − | 0.00595137i | 0.333832 | − | 0.942633i | \(-0.391658\pi\) |
−0.350183 | + | 0.936681i | \(0.613881\pi\) | |||||||
\(728\) | 10.3440 | 0.383372 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.0436980 | −0.00161734 | ||||||||
\(731\) | −12.9114 | − | 4.69937i | −0.477546 | − | 0.173812i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.5493 | − | 29.8294i | −1.31304 | − | 1.10177i | −0.987731 | − | 0.156166i | \(-0.950086\pi\) |
−0.325312 | − | 0.945607i | \(-0.605469\pi\) | |||||||
\(734\) | −10.0607 | + | 57.0570i | −0.371347 | + | 2.10601i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.16755 | + | 6.01429i | −0.264199 | + | 0.221690i | ||||
\(737\) | −13.6672 | − | 23.6724i | −0.503439 | − | 0.871983i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.9047 | + | 22.3515i | −0.474706 | + | 0.822214i | −0.999580 | − | 0.0289653i | \(-0.990779\pi\) |
0.524875 | + | 0.851179i | \(0.324112\pi\) | |||||||
\(740\) | 0.245439 | + | 1.39195i | 0.00902252 | + | 0.0511693i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.06700 | + | 2.57218i | −0.259438 | + | 0.0944276i | ||||
\(743\) | −32.6164 | + | 11.8714i | −1.19658 | + | 0.435519i | −0.862029 | − | 0.506859i | \(-0.830807\pi\) |
−0.334550 | + | 0.942378i | \(0.608584\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.349990 | − | 1.98489i | −0.0128226 | − | 0.0727209i | ||||
\(746\) | −15.1129 | + | 26.1764i | −0.553324 | + | 0.958385i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11.6015 | − | 20.0945i | −0.424195 | − | 0.734727i | ||||
\(749\) | 2.46249 | − | 2.06627i | 0.0899774 | − | 0.0755000i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.16510 | − | 23.6214i | 0.151987 | − | 0.861959i | −0.809503 | − | 0.587116i | \(-0.800263\pi\) |
0.961489 | − | 0.274843i | \(-0.0886257\pi\) | |||||||
\(752\) | 7.32351 | + | 6.14515i | 0.267061 | + | 0.224091i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 60.6828 | + | 22.0867i | 2.20994 | + | 0.804351i | ||||
\(755\) | −0.441357 | −0.0160626 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.78780 | −0.319398 | −0.159699 | − | 0.987166i | \(-0.551052\pi\) | ||||
−0.159699 | + | 0.987166i | \(0.551052\pi\) | |||||||
\(758\) | −17.3890 | − | 6.32909i | −0.631598 | − | 0.229883i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.16414 | + | 0.976827i | 0.0422277 | + | 0.0354332i | ||||
\(761\) | 2.38833 | − | 13.5449i | 0.0865771 | − | 0.491003i | −0.910428 | − | 0.413667i | \(-0.864248\pi\) |
0.997005 | − | 0.0773355i | \(-0.0246413\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.76797 | − | 2.32260i | 0.100207 | − | 0.0840839i | ||||
\(764\) | 4.24595 | + | 7.35420i | 0.153613 | + | 0.266066i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.4484 | + | 37.1498i | −0.774963 | + | 1.34228i | ||||
\(767\) | −7.50392 | − | 42.5569i | −0.270951 | − | 1.53664i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.4668 | − | 10.7250i | 1.06260 | − | 0.386755i | 0.249196 | − | 0.968453i | \(-0.419834\pi\) |
0.813405 | + | 0.581698i | \(0.197611\pi\) | |||||||
\(770\) | 0.376772 | − | 0.137134i | 0.0135779 | − | 0.00494196i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.575935 | − | 3.26629i | −0.0207284 | − | 0.117556i | ||||
\(773\) | −14.0607 | + | 24.3539i | −0.505729 | + | 0.875948i | 0.494249 | + | 0.869320i | \(0.335443\pi\) |
−0.999978 | + | 0.00662776i | \(0.997890\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.13657 | + | 7.16475i | 0.148590 | + | 0.257365i | ||||
\(776\) | −17.2226 | + | 14.4514i | −0.618254 | + | 0.518776i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.4220 | + | 64.7774i | −0.409499 | + | 2.32238i | ||||
\(779\) | 3.22902 | + | 2.70947i | 0.115692 | + | 0.0970767i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.32784 | + | 1.21124i | 0.119080 | + | 0.0433414i | ||||
\(782\) | −21.2916 | −0.761385 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −17.7298 | −0.633207 | ||||||||
\(785\) | 0.0182992 | + | 0.00666036i | 0.000653126 | + | 0.000237718i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.7309 | − | 23.2690i | −0.988501 | − | 0.829451i | −0.00315089 | − | 0.999995i | \(-0.501003\pi\) |
−0.985350 | + | 0.170544i | \(0.945447\pi\) | |||||||
\(788\) | 13.2663 | − | 75.2370i | 0.472593 | − | 2.68021i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.23437 | − | 1.03576i | 0.0439169 | − | 0.0368507i | ||||
\(791\) | −3.43393 | − | 5.94775i | −0.122097 | − | 0.211478i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.7237 | − | 48.0189i | 0.984498 | − | 1.70520i | ||||
\(794\) | −1.75822 | − | 9.97138i | −0.0623970 | − | 0.353871i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 67.3041 | − | 24.4967i | 2.38553 | − | 0.868262i | ||||
\(797\) | 27.8150 | − | 10.1238i | 0.985258 | − | 0.358604i | 0.201376 | − | 0.979514i | \(-0.435459\pi\) |
0.783882 | + | 0.620910i | \(0.213237\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.24228 | − | 7.04531i | −0.0439487 | − | 0.249245i | ||||
\(800\) | 5.24407 | − | 9.08300i | 0.185406 | − | 0.321133i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.2193 | + | 31.5568i | 0.643346 | + | 1.11431i | ||||
\(803\) | −0.463159 | + | 0.388637i | −0.0163445 | + | 0.0137147i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0417351 | − | 0.236691i | 0.00147097 | − | 0.00834228i | ||||
\(806\) | −12.8127 | − | 10.7511i | −0.451308 | − | 0.378692i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −28.9997 | − | 10.5550i | −1.02021 | − | 0.371324i | ||||
\(809\) | −5.75943 | −0.202491 | −0.101245 | − | 0.994861i | \(-0.532283\pi\) | ||||
−0.101245 | + | 0.994861i | \(0.532283\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.4896 | 0.438569 | 0.219284 | − | 0.975661i | \(-0.429628\pi\) | ||||
0.219284 | + | 0.975661i | \(0.429628\pi\) | |||||||
\(812\) | 13.1384 | + | 4.78199i | 0.461068 | + | 0.167815i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22.9332 | + | 19.2433i | 0.803809 | + | 0.674476i | ||||
\(815\) | 0.0909025 | − | 0.515534i | 0.00318418 | − | 0.0180584i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.3291 | − | 17.0581i | 0.711225 | − | 0.596788i | ||||
\(818\) | 5.65535 | + | 9.79536i | 0.197735 | + | 0.342487i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.192221 | − | 0.332936i | 0.00671265 | − | 0.0116266i | ||||
\(821\) | 7.47846 | + | 42.4125i | 0.261000 | + | 1.48021i | 0.780188 | + | 0.625545i | \(0.215123\pi\) |
−0.519188 | + | 0.854660i | \(0.673765\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.66389 | + | 3.51737i | −0.336862 | + | 0.122608i | −0.504912 | − | 0.863171i | \(-0.668475\pi\) |
0.168050 | + | 0.985778i | \(0.446253\pi\) | |||||||
\(824\) | 25.5383 | − | 9.29520i | 0.889670 | − | 0.323814i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.48707 | − | 14.1049i | −0.0865364 | − | 0.490772i | ||||
\(827\) | −3.04731 | + | 5.27810i | −0.105965 | + | 0.183538i | −0.914132 | − | 0.405416i | \(-0.867127\pi\) |
0.808167 | + | 0.588954i | \(0.200460\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.8489 | + | 29.1832i | 0.585188 | + | 1.01358i | 0.994852 | + | 0.101339i | \(0.0323126\pi\) |
−0.409664 | + | 0.912236i | \(0.634354\pi\) | |||||||
\(830\) | 2.55170 | − | 2.14113i | 0.0885709 | − | 0.0743198i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.56453 | + | 42.9006i | −0.262253 | + | 1.48731i | ||||
\(833\) | 10.1635 | + | 8.52816i | 0.352143 | + | 0.295483i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.45904 | − | 0.531047i | −0.0504922 | − | 0.0183776i | ||||
\(836\) | 44.8148 | 1.54995 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −47.5308 | −1.64192 | ||||||||
\(839\) | 39.6797 | + | 14.4422i | 1.36989 | + | 0.498601i | 0.919099 | − | 0.394027i | \(-0.128918\pi\) |
0.450795 | + | 0.892628i | \(0.351141\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.15708 | + | 7.68370i | 0.315761 | + | 0.264955i | ||||
\(842\) | −11.7545 | + | 66.6630i | −0.405086 | + | 2.29736i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 46.7119 | − | 39.1960i | 1.60789 | − | 1.34918i | ||||
\(845\) | −0.216631 | − | 0.375216i | −0.00745234 | − | 0.0129078i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.415423 | + | 0.719533i | −0.0142741 | + | 0.0247235i | ||||
\(848\) | 2.49503 | + | 14.1500i | 0.0856796 | + | 0.485913i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 22.4272 | − | 8.16284i | 0.769247 | − | 0.279983i | ||||
\(851\) | 16.8630 | − | 6.13764i | 0.578057 | − | 0.210396i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.20438 | − | 35.1868i | −0.212434 | − | 1.20477i | −0.885304 | − | 0.465012i | \(-0.846050\pi\) |
0.672870 | − | 0.739760i | \(-0.265061\pi\) | |||||||
\(854\) | 9.18865 | − | 15.9152i | 0.314429 | − | 0.544607i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.7679 | − | 20.3826i | −0.402219 | − | 0.696664i | ||||
\(857\) | 6.05838 | − | 5.08358i | 0.206950 | − | 0.173652i | −0.533421 | − | 0.845850i | \(-0.679094\pi\) |
0.740372 | + | 0.672198i | \(0.234650\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.76540 | + | 44.0398i | −0.264952 | + | 1.50262i | 0.504220 | + | 0.863575i | \(0.331780\pi\) |
−0.769172 | + | 0.639042i | \(0.779331\pi\) | |||||||
\(860\) | −1.85410 | − | 1.55577i | −0.0632241 | − | 0.0530513i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.7281 | − | 4.26867i | −0.399460 | − | 0.145391i | ||||
\(863\) | −22.9170 | −0.780103 | −0.390052 | − | 0.920793i | \(-0.627543\pi\) | ||||
−0.390052 | + | 0.920793i | \(0.627543\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.76878 | 0.0601405 | ||||||||
\(866\) | 57.1610 | + | 20.8049i | 1.94241 | + | 0.706979i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.77407 | − | 2.32772i | −0.0941581 | − | 0.0790080i | ||||
\(869\) | 3.87147 | − | 21.9562i | 0.131331 | − | 0.744814i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.4447 | + | 23.8680i | −0.963813 | + | 0.808735i | ||||
\(872\) | −13.2278 | − | 22.9112i | −0.447950 | − | 0.775871i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 20.5614 | − | 35.6134i | 0.695501 | − | 1.20464i | ||||
\(875\) | 0.0936462 | + | 0.531094i | 0.00316582 | + | 0.0179543i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.8026 | − | 7.57152i | 0.702453 | − | 0.255672i | 0.0339951 | − | 0.999422i | \(-0.489177\pi\) |
0.668458 | + | 0.743750i | \(0.266955\pi\) | |||||||
\(878\) | −35.3441 | + | 12.8642i | −1.19280 | + | 0.434145i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.133021 | − | 0.754397i | −0.00448412 | − | 0.0254307i | ||||
\(881\) | −4.93202 | + | 8.54251i | −0.166164 | + | 0.287804i | −0.937068 | − | 0.349147i | \(-0.886471\pi\) |
0.770904 | + | 0.636951i | \(0.219805\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.7865 | − | 41.1995i | −0.800481 | − | 1.38647i | −0.919300 | − | 0.393558i | \(-0.871244\pi\) |
0.118819 | − | 0.992916i | \(-0.462089\pi\) | |||||||
\(884\) | −24.1455 | + | 20.2605i | −0.812102 | + | 0.681434i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.61253 | − | 43.1728i | 0.255748 | − | 1.45042i | ||||
\(887\) | 10.2323 | + | 8.58590i | 0.343566 | + | 0.288286i | 0.798200 | − | 0.602392i | \(-0.205786\pi\) |
−0.454634 | + | 0.890678i | \(0.650230\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.28226 | + | 2.28656i | 0.210700 | + | 0.0766886i | ||||
\(890\) | 0.347203 | 0.0116383 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 80.8465 | 2.70694 | ||||||||
\(893\) | 12.9841 | + | 4.72581i | 0.434495 | + | 0.158143i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.15767 | + | 0.971400i | 0.0386966 | + | 0.0324703i | ||||
\(896\) | −2.08400 | + | 11.8189i | −0.0696215 | + | 0.394843i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −52.8406 | + | 44.3385i | −1.76331 | + | 1.47960i | ||||
\(899\) | −5.30359 | − | 9.18609i | −0.176885 | − | 0.306373i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.37600 | − | 9.31150i | 0.179100 | − | 0.310211i | ||||
\(902\) | −1.41397 | − | 8.01899i | −0.0470799 | − | 0.267003i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −47.2517 | + | 17.1982i | −1.57157 | + | 0.572004i | ||||
\(905\) | 0.261673 | − | 0.0952412i | 0.00869830 | − | 0.00316592i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.41815 | + | 36.3991i | 0.213111 | + | 1.20861i | 0.884154 | + | 0.467195i | \(0.154735\pi\) |
−0.671043 | + | 0.741418i | \(0.734154\pi\) | |||||||
\(908\) | 36.0092 | − | 62.3697i | 1.19501 | − | 2.06981i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.272332 | − | 0.471694i | −0.00902773 | − | 0.0156365i | ||||
\(911\) | −37.0851 | + | 31.1181i | −1.22868 | + | 1.03099i | −0.230359 | + | 0.973106i | \(0.573990\pi\) |
−0.998323 | + | 0.0578814i | \(0.981565\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.00315 | − | 45.3881i | 0.264866 | − | 1.50213i | ||||
\(914\) | 65.1049 | + | 54.6295i | 2.15348 | + | 1.80698i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −79.5569 | − | 28.9564i | −2.62863 | − | 0.956745i | ||||
\(917\) | 5.22558 | 0.172564 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.93459 | 0.294725 | 0.147363 | − | 0.989083i | \(-0.452922\pi\) | ||||
0.147363 | + | 0.989083i | \(0.452922\pi\) | |||||||
\(920\) | −1.65359 | − | 0.601856i | −0.0545171 | − | 0.0198426i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.18861 | − | 3.51466i | −0.137945 | − | 0.115749i | ||||
\(923\) | 0.835380 | − | 4.73767i | 0.0274969 | − | 0.155942i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.4094 | + | 12.9300i | −0.506658 | + | 0.425137i | ||||
\(926\) | 22.0643 | + | 38.2165i | 0.725079 | + | 1.25587i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.72355 | + | 11.6455i | −0.220711 | + | 0.382283i | ||||
\(929\) | −1.08429 | − | 6.14929i | −0.0355742 | − | 0.201752i | 0.961841 | − | 0.273611i | \(-0.0882179\pi\) |
−0.997415 | + | 0.0718590i | \(0.977107\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.0796 | + | 8.76426i | −0.789177 | + | 0.287237i | ||||
\(932\) | 62.6023 | − | 22.7854i | 2.05061 | − | 0.746360i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.94285 | − | 11.0185i | −0.0635720 | − | 0.360535i | ||||
\(935\) | −0.286617 | + | 0.496435i | −0.00937338 | + | 0.0162352i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.9212 | − | 39.7006i | −0.748802 | − | 1.29696i | −0.948397 | − | 0.317085i | \(-0.897296\pi\) |
0.199595 | − | 0.979878i | \(-0.436037\pi\) | |||||||
\(938\) | −9.42762 | + | 7.91071i | −0.307823 | + | 0.258294i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.218831 | − | 1.24105i | 0.00713749 | − | 0.0404787i | ||||
\(941\) | −3.33431 | − | 2.79782i | −0.108695 | − | 0.0912063i | 0.586820 | − | 0.809717i | \(-0.300380\pi\) |
−0.695516 | + | 0.718511i | \(0.744824\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.58662 | − | 1.66939i | −0.149361 | − | 0.0543629i | ||||
\(944\) | −27.3637 | −0.890612 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −51.2644 | −1.66675 | ||||||||
\(947\) | −1.89511 | − | 0.689764i | −0.0615828 | − | 0.0224143i | 0.311045 | − | 0.950395i | \(-0.399321\pi\) |
−0.372628 | + | 0.927981i | \(0.621543\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.629169 | + | 0.527935i | 0.0204237 | + | 0.0171375i | ||||
\(950\) | −8.00453 | + | 45.3959i | −0.259701 | + | 1.47284i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.75474 | + | 3.15060i | −0.121692 | + | 0.102112i | ||||
\(953\) | 17.8644 | + | 30.9420i | 0.578684 | + | 1.00231i | 0.995631 | + | 0.0933786i | \(0.0297667\pi\) |
−0.416947 | + | 0.908931i | \(0.636900\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.104896 | − | 0.181686i | 0.00339437 | − | 0.00587922i | ||||
\(956\) | −10.0890 | − | 57.2178i | −0.326303 | − | 1.85055i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −31.9920 | + | 11.6441i | −1.03361 | + | 0.376205i | ||||
\(959\) | 6.27727 | − | 2.28474i | 0.202704 | − | 0.0737781i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.90603 | − | 27.8235i | −0.158259 | − | 0.897531i | ||||
\(962\) | 20.3338 | − | 35.2191i | 0.655587 | − | 1.13551i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −24.7759 | − | 42.9131i | −0.797978 | − | 1.38214i | ||||
\(965\) | −0.0627688 | + | 0.0526693i | −0.00202060 | + | 0.00169548i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.120393 | + | 0.682784i | −0.00387159 | + | 0.0219569i | −0.986682 | − | 0.162659i | \(-0.947993\pi\) |
0.982811 | + | 0.184616i | \(0.0591041\pi\) | |||||||
\(968\) | 4.65998 | + | 3.91019i | 0.149777 | + | 0.125678i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.11243 | + | 0.404891i | 0.0357180 | + | 0.0130003i | ||||
\(971\) | 47.4942 | 1.52416 | 0.762081 | − | 0.647482i | \(-0.224178\pi\) | ||||
0.762081 | + | 0.647482i | \(0.224178\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.987988 | −0.0316734 | ||||||||
\(974\) | −48.3715 | − | 17.6058i | −1.54992 | − | 0.564126i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.8962 | − | 22.5686i | −0.860927 | − | 0.722404i | ||||
\(977\) | −2.18854 | + | 12.4118i | −0.0700177 | + | 0.397090i | 0.929577 | + | 0.368628i | \(0.120172\pi\) |
−0.999595 | + | 0.0284625i | \(0.990939\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.68004 | − | 3.08792i | 0.117615 | − | 0.0986903i | ||||
\(980\) | 1.16855 | + | 2.02399i | 0.0373280 | + | 0.0646540i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −16.9168 | + | 29.3008i | −0.539838 | + | 0.935027i | ||||
\(983\) | 2.00477 | + | 11.3696i | 0.0639423 | + | 0.362635i | 0.999943 | + | 0.0106378i | \(0.00338618\pi\) |
−0.936001 | + | 0.351997i | \(0.885503\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.77359 | + | 0.645533i | −0.0565111 | + | 0.0205684i | ||||
\(986\) | −28.7545 | + | 10.4658i | −0.915729 | + | 0.333298i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.5713 | − | 59.9529i | −0.336318 | − | 1.90736i | ||||
\(989\) | −15.3647 | + | 26.6125i | −0.488569 | + | 0.846227i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.34676 | − | 16.1891i | −0.296910 | − | 0.514263i | 0.678518 | − | 0.734584i | \(-0.262623\pi\) |
−0.975427 | + | 0.220322i | \(0.929289\pi\) | |||||||
\(992\) | 2.66802 | − | 2.23874i | 0.0847098 | − | 0.0710800i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.276875 | − | 1.57024i | 0.00878195 | − | 0.0498049i | ||||
\(995\) | −1.35549 | − | 1.13739i | −0.0429719 | − | 0.0360577i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.15624 | − | 1.14878i | −0.0999593 | − | 0.0363822i | 0.291556 | − | 0.956554i | \(-0.405827\pi\) |
−0.391516 | + | 0.920171i | \(0.628049\pi\) | |||||||
\(998\) | −35.8066 | −1.13344 | ||||||||
\(999\) | 0 | 0 |
(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 | 243.2.e.d.190.2 | 12 | ||
3.2 | odd | 2 | 243.2.e.a.190.1 | 12 | |||
9.2 | odd | 6 | 81.2.e.a.10.2 | 12 | |||
9.4 | even | 3 | 243.2.e.c.109.1 | 12 | |||
9.5 | odd | 6 | 243.2.e.b.109.2 | 12 | |||
9.7 | even | 3 | 27.2.e.a.13.1 | ✓ | 12 | ||
27.2 | odd | 18 | 243.2.e.b.136.2 | 12 | |||
27.4 | even | 9 | 729.2.c.e.244.6 | 12 | |||
27.5 | odd | 18 | 729.2.c.b.487.1 | 12 | |||
27.7 | even | 9 | inner | 243.2.e.d.55.2 | 12 | ||
27.11 | odd | 18 | 81.2.e.a.73.2 | 12 | |||
27.13 | even | 9 | 729.2.a.a.1.1 | 6 | |||
27.14 | odd | 18 | 729.2.a.d.1.6 | 6 | |||
27.16 | even | 9 | 27.2.e.a.25.1 | yes | 12 | ||
27.20 | odd | 18 | 243.2.e.a.55.1 | 12 | |||
27.22 | even | 9 | 729.2.c.e.487.6 | 12 | |||
27.23 | odd | 18 | 729.2.c.b.244.1 | 12 | |||
27.25 | even | 9 | 243.2.e.c.136.1 | 12 | |||
36.7 | odd | 6 | 432.2.u.c.337.1 | 12 | |||
45.7 | odd | 12 | 675.2.u.b.499.4 | 24 | |||
45.34 | even | 6 | 675.2.l.c.526.2 | 12 | |||
45.43 | odd | 12 | 675.2.u.b.499.1 | 24 | |||
108.43 | odd | 18 | 432.2.u.c.241.1 | 12 | |||
135.43 | odd | 36 | 675.2.u.b.349.4 | 24 | |||
135.97 | odd | 36 | 675.2.u.b.349.1 | 24 | |||
135.124 | even | 18 | 675.2.l.c.376.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.2.e.a.13.1 | ✓ | 12 | 9.7 | even | 3 | ||
27.2.e.a.25.1 | yes | 12 | 27.16 | even | 9 | ||
81.2.e.a.10.2 | 12 | 9.2 | odd | 6 | |||
81.2.e.a.73.2 | 12 | 27.11 | odd | 18 | |||
243.2.e.a.55.1 | 12 | 27.20 | odd | 18 | |||
243.2.e.a.190.1 | 12 | 3.2 | odd | 2 | |||
243.2.e.b.109.2 | 12 | 9.5 | odd | 6 | |||
243.2.e.b.136.2 | 12 | 27.2 | odd | 18 | |||
243.2.e.c.109.1 | 12 | 9.4 | even | 3 | |||
243.2.e.c.136.1 | 12 | 27.25 | even | 9 | |||
243.2.e.d.55.2 | 12 | 27.7 | even | 9 | inner | ||
243.2.e.d.190.2 | 12 | 1.1 | even | 1 | trivial | ||
432.2.u.c.241.1 | 12 | 108.43 | odd | 18 | |||
432.2.u.c.337.1 | 12 | 36.7 | odd | 6 | |||
675.2.l.c.376.2 | 12 | 135.124 | even | 18 | |||
675.2.l.c.526.2 | 12 | 45.34 | even | 6 | |||
675.2.u.b.349.1 | 24 | 135.97 | odd | 36 | |||
675.2.u.b.349.4 | 24 | 135.43 | odd | 36 | |||
675.2.u.b.499.1 | 24 | 45.43 | odd | 12 | |||
675.2.u.b.499.4 | 24 | 45.7 | odd | 12 | |||
729.2.a.a.1.1 | 6 | 27.13 | even | 9 | |||
729.2.a.d.1.6 | 6 | 27.14 | odd | 18 | |||
729.2.c.b.244.1 | 12 | 27.23 | odd | 18 | |||
729.2.c.b.487.1 | 12 | 27.5 | odd | 18 | |||
729.2.c.e.244.6 | 12 | 27.4 | even | 9 | |||
729.2.c.e.487.6 | 12 | 27.22 | even | 9 |