Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [171,2,Mod(106,171)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(171, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("171.106");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 171 = 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 171.g (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.36544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 106.13 | ||
Character | \(\chi\) | \(=\) | 171.106 |
Dual form | 171.2.g.c.121.13 |
$q$-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 \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).
\(n\) | \(20\) | \(154\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.01016 | + | 1.74964i | 0.714288 | + | 1.23718i | 0.963233 | + | 0.268666i | \(0.0865828\pi\) |
−0.248945 | + | 0.968518i | \(0.580084\pi\) | |||||||
\(3\) | −1.70377 | + | 0.311691i | −0.983675 | + | 0.179955i | ||||
\(4\) | −1.04083 | + | 1.80277i | −0.520415 | + | 0.901386i | ||||
\(5\) | −4.18739 | −1.87266 | −0.936328 | − | 0.351127i | \(-0.885799\pi\) | ||||
−0.936328 | + | 0.351127i | \(0.885799\pi\) | |||||||
\(6\) | −2.26643 | − | 2.66614i | −0.925265 | − | 1.08845i | ||||
\(7\) | −0.976107 | + | 1.69067i | −0.368934 | + | 0.639012i | −0.989399 | − | 0.145222i | \(-0.953610\pi\) |
0.620465 | + | 0.784234i | \(0.286944\pi\) | |||||||
\(8\) | −0.164982 | −0.0583299 | ||||||||
\(9\) | 2.80570 | − | 1.06210i | 0.935232 | − | 0.354034i | ||||
\(10\) | −4.22991 | − | 7.32643i | −1.33762 | − | 2.31682i | ||||
\(11\) | −0.669450 | + | 1.15952i | −0.201847 | + | 0.349609i | −0.949124 | − | 0.314904i | \(-0.898028\pi\) |
0.747277 | + | 0.664513i | \(0.231361\pi\) | |||||||
\(12\) | 1.21143 | − | 3.39593i | 0.349711 | − | 0.980322i | ||||
\(13\) | −0.975550 | + | 1.68970i | −0.270569 | + | 0.468639i | −0.969008 | − | 0.247031i | \(-0.920545\pi\) |
0.698439 | + | 0.715670i | \(0.253878\pi\) | |||||||
\(14\) | −3.94408 | −1.05410 | ||||||||
\(15\) | 7.13436 | − | 1.30517i | 1.84208 | − | 0.336994i | ||||
\(16\) | 1.91500 | + | 3.31688i | 0.478751 | + | 0.829221i | ||||
\(17\) | −3.34047 | + | 5.78587i | −0.810184 | + | 1.40328i | 0.102552 | + | 0.994728i | \(0.467299\pi\) |
−0.912735 | + | 0.408551i | \(0.866034\pi\) | |||||||
\(18\) | 4.69249 | + | 3.83607i | 1.10603 | + | 0.904172i | ||||
\(19\) | 4.11317 | − | 1.44285i | 0.943626 | − | 0.331012i | ||||
\(20\) | 4.35836 | − | 7.54890i | 0.974559 | − | 1.68799i | ||||
\(21\) | 1.13610 | − | 3.18476i | 0.247917 | − | 0.694972i | ||||
\(22\) | −2.70500 | −0.576707 | ||||||||
\(23\) | 0.986266 | − | 1.70826i | 0.205651 | − | 0.356197i | −0.744689 | − | 0.667411i | \(-0.767402\pi\) |
0.950340 | + | 0.311214i | \(0.100736\pi\) | |||||||
\(24\) | 0.281092 | − | 0.0514234i | 0.0573777 | − | 0.0104968i | ||||
\(25\) | 12.5342 | 2.50684 | ||||||||
\(26\) | −3.94183 | −0.773056 | ||||||||
\(27\) | −4.44923 | + | 2.68410i | −0.856254 | + | 0.516554i | ||||
\(28\) | −2.03192 | − | 3.51940i | −0.383998 | − | 0.665103i | ||||
\(29\) | −5.90062 | −1.09572 | −0.547859 | − | 0.836571i | \(-0.684557\pi\) | ||||
−0.547859 | + | 0.836571i | \(0.684557\pi\) | |||||||
\(30\) | 9.49040 | + | 11.1642i | 1.73270 | + | 2.03829i | ||||
\(31\) | −0.385886 | − | 0.668373i | −0.0693071 | − | 0.120043i | 0.829289 | − | 0.558819i | \(-0.188746\pi\) |
−0.898596 | + | 0.438776i | \(0.855412\pi\) | |||||||
\(32\) | −4.03389 | + | 6.98690i | −0.713097 | + | 1.23512i | ||||
\(33\) | 0.779180 | − | 2.18423i | 0.135638 | − | 0.380225i | ||||
\(34\) | −13.4976 | −2.31482 | ||||||||
\(35\) | 4.08734 | − | 7.07948i | 0.690886 | − | 1.19665i | ||||
\(36\) | −1.00553 | + | 6.16350i | −0.167588 | + | 1.02725i | ||||
\(37\) | 2.26011 | 0.371560 | 0.185780 | − | 0.982591i | \(-0.440519\pi\) | ||||
0.185780 | + | 0.982591i | \(0.440519\pi\) | |||||||
\(38\) | 6.67941 | + | 5.73908i | 1.08354 | + | 0.931001i | ||||
\(39\) | 1.13545 | − | 3.18294i | 0.181818 | − | 0.509679i | ||||
\(40\) | 0.690843 | 0.109232 | ||||||||
\(41\) | 7.59691 | 1.18644 | 0.593219 | − | 0.805041i | \(-0.297857\pi\) | ||||
0.593219 | + | 0.805041i | \(0.297857\pi\) | |||||||
\(42\) | 6.71983 | − | 1.22934i | 1.03689 | − | 0.189691i | ||||
\(43\) | −3.97802 | − | 6.89012i | −0.606642 | − | 1.05073i | −0.991790 | − | 0.127879i | \(-0.959183\pi\) |
0.385148 | − | 0.922855i | \(-0.374150\pi\) | |||||||
\(44\) | −1.39357 | − | 2.41373i | −0.210088 | − | 0.363884i | ||||
\(45\) | −11.7485 | + | 4.44744i | −1.75137 | + | 0.662985i | ||||
\(46\) | 3.98513 | 0.587576 | ||||||||
\(47\) | −1.10774 | −0.161580 | −0.0807902 | − | 0.996731i | \(-0.525744\pi\) | ||||
−0.0807902 | + | 0.996731i | \(0.525744\pi\) | |||||||
\(48\) | −4.29658 | − | 5.05433i | −0.620158 | − | 0.729530i | ||||
\(49\) | 1.59443 | + | 2.76163i | 0.227776 | + | 0.394519i | ||||
\(50\) | 12.6615 | + | 21.9304i | 1.79061 | + | 3.10142i | ||||
\(51\) | 3.88801 | − | 10.8990i | 0.544430 | − | 1.52617i | ||||
\(52\) | −2.03076 | − | 3.51739i | −0.281616 | − | 0.487774i | ||||
\(53\) | 3.75226 | + | 6.49910i | 0.515412 | + | 0.892721i | 0.999840 | + | 0.0178892i | \(0.00569461\pi\) |
−0.484427 | + | 0.874831i | \(0.660972\pi\) | |||||||
\(54\) | −9.19062 | − | 5.07320i | −1.25069 | − | 0.690375i | ||||
\(55\) | 2.80325 | − | 4.85537i | 0.377990 | − | 0.654697i | ||||
\(56\) | 0.161040 | − | 0.278929i | 0.0215199 | − | 0.0372735i | ||||
\(57\) | −6.55820 | + | 3.74033i | −0.868654 | + | 0.495419i | ||||
\(58\) | −5.96055 | − | 10.3240i | −0.782658 | − | 1.35560i | ||||
\(59\) | 1.01399 | 0.132011 | 0.0660053 | − | 0.997819i | \(-0.478975\pi\) | ||||
0.0660053 | + | 0.997819i | \(0.478975\pi\) | |||||||
\(60\) | −5.07274 | + | 14.2201i | −0.654888 | + | 1.83581i | ||||
\(61\) | 0.332081 | 0.0425186 | 0.0212593 | − | 0.999774i | \(-0.493232\pi\) | ||||
0.0212593 | + | 0.999774i | \(0.493232\pi\) | |||||||
\(62\) | 0.779609 | − | 1.35032i | 0.0990105 | − | 0.171491i | ||||
\(63\) | −0.942998 | + | 5.78023i | −0.118807 | + | 0.728240i | ||||
\(64\) | −8.63941 | −1.07993 | ||||||||
\(65\) | 4.08500 | − | 7.07543i | 0.506682 | − | 0.877599i | ||||
\(66\) | 4.60871 | − | 0.843124i | 0.567293 | − | 0.103781i | ||||
\(67\) | −6.45447 | + | 11.1795i | −0.788539 | + | 1.36579i | 0.138322 | + | 0.990387i | \(0.455829\pi\) |
−0.926862 | + | 0.375403i | \(0.877504\pi\) | |||||||
\(68\) | −6.95373 | − | 12.0442i | −0.843264 | − | 1.46058i | ||||
\(69\) | −1.14792 | + | 3.21791i | −0.138194 | + | 0.387390i | ||||
\(70\) | 16.5154 | 1.97397 | ||||||||
\(71\) | 1.81291 | − | 3.14004i | 0.215152 | − | 0.372655i | −0.738167 | − | 0.674618i | \(-0.764309\pi\) |
0.953320 | + | 0.301963i | \(0.0976419\pi\) | |||||||
\(72\) | −0.462889 | + | 0.175228i | −0.0545520 | + | 0.0206508i | ||||
\(73\) | −2.48182 | + | 4.29864i | −0.290475 | + | 0.503118i | −0.973922 | − | 0.226882i | \(-0.927147\pi\) |
0.683447 | + | 0.730000i | \(0.260480\pi\) | |||||||
\(74\) | 2.28306 | + | 3.95438i | 0.265401 | + | 0.459688i | ||||
\(75\) | −21.3555 | + | 3.90680i | −2.46592 | + | 0.451118i | ||||
\(76\) | −1.67999 | + | 8.91687i | −0.192708 | + | 1.02284i | ||||
\(77\) | −1.30691 | − | 2.26363i | −0.148936 | − | 0.257965i | ||||
\(78\) | 6.71599 | − | 1.22863i | 0.760436 | − | 0.139115i | ||||
\(79\) | −2.58841 | − | 4.48326i | −0.291219 | − | 0.504406i | 0.682879 | − | 0.730531i | \(-0.260728\pi\) |
−0.974098 | + | 0.226125i | \(0.927394\pi\) | |||||||
\(80\) | −8.01886 | − | 13.8891i | −0.896536 | − | 1.55285i | ||||
\(81\) | 6.74387 | − | 5.95988i | 0.749319 | − | 0.662209i | ||||
\(82\) | 7.67406 | + | 13.2919i | 0.847458 | + | 1.46784i | ||||
\(83\) | 6.30706 | − | 10.9242i | 0.692290 | − | 1.19908i | −0.278796 | − | 0.960350i | \(-0.589935\pi\) |
0.971086 | − | 0.238731i | \(-0.0767315\pi\) | |||||||
\(84\) | 4.55891 | + | 5.36293i | 0.497417 | + | 0.585143i | ||||
\(85\) | 13.9878 | − | 24.2277i | 1.51720 | − | 2.62786i | ||||
\(86\) | 8.03683 | − | 13.9202i | 0.866634 | − | 1.50105i | ||||
\(87\) | 10.0533 | − | 1.83917i | 1.07783 | − | 0.197180i | ||||
\(88\) | 0.110447 | − | 0.191300i | 0.0117737 | − | 0.0203927i | ||||
\(89\) | 0.569098 | + | 0.985707i | 0.0603243 | + | 0.104485i | 0.894610 | − | 0.446847i | \(-0.147453\pi\) |
−0.834286 | + | 0.551332i | \(0.814120\pi\) | |||||||
\(90\) | −19.6493 | − | 16.0631i | −2.07122 | − | 1.69320i | ||||
\(91\) | −1.90448 | − | 3.29866i | −0.199644 | − | 0.345793i | ||||
\(92\) | 2.05307 | + | 3.55603i | 0.214048 | + | 0.370741i | ||||
\(93\) | 0.865788 | + | 1.01848i | 0.0897781 | + | 0.105612i | ||||
\(94\) | −1.11899 | − | 1.93815i | −0.115415 | − | 0.199904i | ||||
\(95\) | −17.2234 | + | 6.04176i | −1.76709 | + | 0.619872i | ||||
\(96\) | 4.69508 | − | 13.1614i | 0.479190 | − | 1.34328i | ||||
\(97\) | 1.87936 | + | 3.25515i | 0.190821 | + | 0.330511i | 0.945522 | − | 0.325557i | \(-0.105552\pi\) |
−0.754702 | + | 0.656068i | \(0.772218\pi\) | |||||||
\(98\) | −3.22125 | + | 5.57936i | −0.325395 | + | 0.563601i | ||||
\(99\) | −0.646743 | + | 3.96429i | −0.0650001 | + | 0.398426i | ||||
\(100\) | −13.0460 | + | 22.5963i | −1.30460 | + | 2.25963i | ||||
\(101\) | −8.28686 | −0.824574 | −0.412287 | − | 0.911054i | \(-0.635270\pi\) | ||||
−0.412287 | + | 0.911054i | \(0.635270\pi\) | |||||||
\(102\) | 22.9969 | − | 4.20708i | 2.27703 | − | 0.416563i | ||||
\(103\) | 1.96614 | + | 3.40546i | 0.193730 | + | 0.335550i | 0.946483 | − | 0.322752i | \(-0.104608\pi\) |
−0.752754 | + | 0.658302i | \(0.771275\pi\) | |||||||
\(104\) | 0.160948 | − | 0.278770i | 0.0157823 | − | 0.0273357i | ||||
\(105\) | −4.75729 | + | 13.3358i | −0.464264 | + | 1.30144i | ||||
\(106\) | −7.58074 | + | 13.1302i | −0.736306 | + | 1.27532i | ||||
\(107\) | −0.188538 | −0.0182266 | −0.00911332 | − | 0.999958i | \(-0.502901\pi\) | ||||
−0.00911332 | + | 0.999958i | \(0.502901\pi\) | |||||||
\(108\) | −0.207919 | − | 10.8146i | −0.0200070 | − | 1.04064i | ||||
\(109\) | −1.08750 | + | 1.88361i | −0.104164 | + | 0.180417i | −0.913396 | − | 0.407072i | \(-0.866550\pi\) |
0.809233 | + | 0.587488i | \(0.199883\pi\) | |||||||
\(110\) | 11.3269 | 1.07997 | ||||||||
\(111\) | −3.85072 | + | 0.704456i | −0.365494 | + | 0.0668640i | ||||
\(112\) | −7.47700 | −0.706510 | ||||||||
\(113\) | 6.33171 | + | 10.9669i | 0.595638 | + | 1.03167i | 0.993457 | + | 0.114211i | \(0.0364339\pi\) |
−0.397819 | + | 0.917464i | \(0.630233\pi\) | |||||||
\(114\) | −13.1690 | − | 7.69618i | −1.23339 | − | 0.720813i | ||||
\(115\) | −4.12988 | + | 7.15316i | −0.385113 | + | 0.667035i | ||||
\(116\) | 6.14155 | − | 10.6375i | 0.570228 | − | 0.987665i | ||||
\(117\) | −0.942460 | + | 5.77693i | −0.0871304 | + | 0.534077i | ||||
\(118\) | 1.02429 | + | 1.77412i | 0.0942936 | + | 0.163321i | ||||
\(119\) | −6.52132 | − | 11.2953i | −0.597808 | − | 1.03543i | ||||
\(120\) | −1.17704 | + | 0.215330i | −0.107449 | + | 0.0196568i | ||||
\(121\) | 4.60367 | + | 7.97379i | 0.418516 | + | 0.724890i | ||||
\(122\) | 0.335454 | + | 0.581023i | 0.0303706 | + | 0.0526033i | ||||
\(123\) | −12.9434 | + | 2.36789i | −1.16707 | + | 0.213505i | ||||
\(124\) | 1.60657 | 0.144274 | ||||||||
\(125\) | −31.5486 | −2.82179 | ||||||||
\(126\) | −11.0659 | + | 4.18902i | −0.985829 | + | 0.373188i | ||||
\(127\) | −2.35619 | − | 4.08103i | −0.209078 | − | 0.362133i | 0.742347 | − | 0.670016i | \(-0.233713\pi\) |
−0.951424 | + | 0.307883i | \(0.900379\pi\) | |||||||
\(128\) | −0.659378 | − | 1.14208i | −0.0582813 | − | 0.100946i | ||||
\(129\) | 8.92523 | + | 10.4993i | 0.785823 | + | 0.924413i | ||||
\(130\) | 16.5060 | 1.44767 | ||||||||
\(131\) | 18.9020 | 1.65148 | 0.825740 | − | 0.564051i | \(-0.190758\pi\) | ||||
0.825740 | + | 0.564051i | \(0.190758\pi\) | |||||||
\(132\) | 3.12667 | + | 3.67809i | 0.272141 | + | 0.320137i | ||||
\(133\) | −1.57552 | + | 8.36238i | −0.136615 | + | 0.725110i | ||||
\(134\) | −26.0801 | −2.25298 | ||||||||
\(135\) | 18.6306 | − | 11.2393i | 1.60347 | − | 0.967329i | ||||
\(136\) | 0.551117 | − | 0.954564i | 0.0472579 | − | 0.0818531i | ||||
\(137\) | 5.66962 | 0.484388 | 0.242194 | − | 0.970228i | \(-0.422133\pi\) | ||||
0.242194 | + | 0.970228i | \(0.422133\pi\) | |||||||
\(138\) | −6.78977 | + | 1.24213i | −0.577983 | + | 0.105737i | ||||
\(139\) | 3.58154 | − | 6.20340i | 0.303782 | − | 0.526166i | −0.673207 | − | 0.739454i | \(-0.735084\pi\) |
0.976989 | + | 0.213288i | \(0.0684172\pi\) | |||||||
\(140\) | 8.50845 | + | 14.7371i | 0.719095 | + | 1.24551i | ||||
\(141\) | 1.88734 | − | 0.345272i | 0.158942 | − | 0.0290772i | ||||
\(142\) | 7.32527 | 0.614723 | ||||||||
\(143\) | −1.30616 | − | 2.26234i | −0.109227 | − | 0.189187i | ||||
\(144\) | 8.89580 | + | 7.27224i | 0.741316 | + | 0.606020i | ||||
\(145\) | 24.7082 | 2.05190 | ||||||||
\(146\) | −10.0281 | −0.829932 | ||||||||
\(147\) | −3.57733 | − | 4.20823i | −0.295053 | − | 0.347089i | ||||
\(148\) | −2.35239 | + | 4.07446i | −0.193365 | + | 0.334919i | ||||
\(149\) | −18.0309 | −1.47715 | −0.738576 | − | 0.674171i | \(-0.764501\pi\) | ||||
−0.738576 | + | 0.674171i | \(0.764501\pi\) | |||||||
\(150\) | −28.4078 | − | 33.4179i | −2.31949 | − | 2.72856i | ||||
\(151\) | −3.24064 | + | 5.61296i | −0.263720 | + | 0.456776i | −0.967227 | − | 0.253911i | \(-0.918283\pi\) |
0.703508 | + | 0.710688i | \(0.251616\pi\) | |||||||
\(152\) | −0.678599 | + | 0.238044i | −0.0550416 | + | 0.0193079i | ||||
\(153\) | −3.22717 | + | 19.7813i | −0.260901 | + | 1.59922i | ||||
\(154\) | 2.64037 | − | 4.57325i | 0.212767 | − | 0.368523i | ||||
\(155\) | 1.61585 | + | 2.79874i | 0.129788 | + | 0.224800i | ||||
\(156\) | 4.55630 | + | 5.35986i | 0.364796 | + | 0.429133i | ||||
\(157\) | −0.273786 | −0.0218505 | −0.0109252 | − | 0.999940i | \(-0.503478\pi\) | ||||
−0.0109252 | + | 0.999940i | \(0.503478\pi\) | |||||||
\(158\) | 5.22940 | − | 9.05759i | 0.416029 | − | 0.720583i | ||||
\(159\) | −8.41872 | − | 9.90346i | −0.667648 | − | 0.785396i | ||||
\(160\) | 16.8914 | − | 29.2568i | 1.33539 | − | 2.31296i | ||||
\(161\) | 1.92540 | + | 3.33490i | 0.151743 | + | 0.262827i | ||||
\(162\) | 17.2400 | + | 5.77895i | 1.35450 | + | 0.454037i | ||||
\(163\) | −8.01750 | −0.627979 | −0.313989 | − | 0.949426i | \(-0.601666\pi\) | ||||
−0.313989 | + | 0.949426i | \(0.601666\pi\) | |||||||
\(164\) | −7.90709 | + | 13.6955i | −0.617440 | + | 1.06944i | ||||
\(165\) | −3.26273 | + | 9.14620i | −0.254003 | + | 0.712030i | ||||
\(166\) | 25.4845 | 1.97798 | ||||||||
\(167\) | 10.3735 | − | 17.9674i | 0.802724 | − | 1.39036i | −0.115094 | − | 0.993355i | \(-0.536717\pi\) |
0.917817 | − | 0.397003i | \(-0.129950\pi\) | |||||||
\(168\) | −0.187436 | + | 0.525428i | −0.0144610 | + | 0.0405376i | ||||
\(169\) | 4.59661 | + | 7.96155i | 0.353585 | + | 0.612427i | ||||
\(170\) | 56.5196 | 4.33486 | ||||||||
\(171\) | 10.0079 | − | 8.41681i | 0.765320 | − | 0.643650i | ||||
\(172\) | 16.5618 | 1.26282 | ||||||||
\(173\) | 8.94526 | + | 15.4936i | 0.680095 | + | 1.17796i | 0.974951 | + | 0.222418i | \(0.0713949\pi\) |
−0.294856 | + | 0.955542i | \(0.595272\pi\) | |||||||
\(174\) | 13.3733 | + | 15.7319i | 1.01383 | + | 1.19263i | ||||
\(175\) | −12.2347 | + | 21.1912i | −0.924858 | + | 1.60190i | ||||
\(176\) | −5.12800 | −0.386538 | ||||||||
\(177\) | −1.72761 | + | 0.316053i | −0.129855 | + | 0.0237560i | ||||
\(178\) | −1.14976 | + | 1.99144i | −0.0861778 | + | 0.149264i | ||||
\(179\) | 0.212492 | 0.0158824 | 0.00794121 | − | 0.999968i | \(-0.497472\pi\) | ||||
0.00794121 | + | 0.999968i | \(0.497472\pi\) | |||||||
\(180\) | 4.21053 | − | 25.8090i | 0.313834 | − | 1.92369i | ||||
\(181\) | 7.99132 | + | 13.8414i | 0.593990 | + | 1.02882i | 0.993689 | + | 0.112174i | \(0.0357815\pi\) |
−0.399698 | + | 0.916647i | \(0.630885\pi\) | |||||||
\(182\) | 3.84765 | − | 6.66432i | 0.285207 | − | 0.493992i | ||||
\(183\) | −0.565791 | + | 0.103507i | −0.0418245 | + | 0.00765144i | ||||
\(184\) | −0.162716 | + | 0.281833i | −0.0119956 | + | 0.0207770i | ||||
\(185\) | −9.46395 | −0.695803 | ||||||||
\(186\) | −0.907395 | + | 2.54364i | −0.0665334 | + | 0.186509i | ||||
\(187\) | −4.47256 | − | 7.74670i | −0.327066 | − | 0.566495i | ||||
\(188\) | 1.15297 | − | 1.99700i | 0.0840889 | − | 0.145646i | ||||
\(189\) | −0.194989 | − | 10.1421i | −0.0141834 | − | 0.737731i | ||||
\(190\) | −27.9693 | − | 24.0317i | −2.02911 | − | 1.74344i | ||||
\(191\) | 6.86947 | − | 11.8983i | 0.497057 | − | 0.860928i | −0.502937 | − | 0.864323i | \(-0.667747\pi\) |
0.999994 | + | 0.00339491i | \(0.00108063\pi\) | |||||||
\(192\) | 14.7196 | − | 2.69283i | 1.06230 | − | 0.194338i | ||||
\(193\) | −14.4859 | −1.04272 | −0.521359 | − | 0.853337i | \(-0.674575\pi\) | ||||
−0.521359 | + | 0.853337i | \(0.674575\pi\) | |||||||
\(194\) | −3.79690 | + | 6.57643i | −0.272602 | + | 0.472160i | ||||
\(195\) | −4.75458 | + | 13.3282i | −0.340482 | + | 0.954453i | ||||
\(196\) | −6.63813 | −0.474152 | ||||||||
\(197\) | 16.6680 | 1.18755 | 0.593774 | − | 0.804632i | \(-0.297637\pi\) | ||||
0.593774 | + | 0.804632i | \(0.297637\pi\) | |||||||
\(198\) | −7.58940 | + | 2.87299i | −0.539355 | + | 0.204174i | ||||
\(199\) | −4.99765 | − | 8.65619i | −0.354274 | − | 0.613621i | 0.632719 | − | 0.774381i | \(-0.281939\pi\) |
−0.986993 | + | 0.160760i | \(0.948605\pi\) | |||||||
\(200\) | −2.06792 | −0.146224 | ||||||||
\(201\) | 7.51242 | − | 21.0591i | 0.529885 | − | 1.48539i | ||||
\(202\) | −8.37102 | − | 14.4990i | −0.588983 | − | 1.02015i | ||||
\(203\) | 5.75964 | − | 9.97599i | 0.404247 | − | 0.700177i | ||||
\(204\) | 15.6017 | + | 18.3532i | 1.09234 | + | 1.28498i | ||||
\(205\) | −31.8112 | −2.22179 | ||||||||
\(206\) | −3.97222 | + | 6.88009i | −0.276758 | + | 0.479359i | ||||
\(207\) | 0.952813 | − | 5.84039i | 0.0662250 | − | 0.405935i | ||||
\(208\) | −7.47273 | −0.518140 | ||||||||
\(209\) | −1.08055 | + | 5.73523i | −0.0747432 | + | 0.396714i | ||||
\(210\) | −28.1385 | + | 5.14770i | −1.94174 | + | 0.355225i | ||||
\(211\) | 2.04396 | 0.140712 | 0.0703559 | − | 0.997522i | \(-0.477586\pi\) | ||||
0.0703559 | + | 0.997522i | \(0.477586\pi\) | |||||||
\(212\) | −15.6219 | −1.07291 | ||||||||
\(213\) | −2.11006 | + | 5.91499i | −0.144579 | + | 0.405289i | ||||
\(214\) | −0.190453 | − | 0.329874i | −0.0130191 | − | 0.0225497i | ||||
\(215\) | 16.6575 | + | 28.8516i | 1.13603 | + | 1.96766i | ||||
\(216\) | 0.734042 | − | 0.442827i | 0.0499452 | − | 0.0301306i | ||||
\(217\) | 1.50666 | 0.102279 | ||||||||
\(218\) | −4.39418 | −0.297611 | ||||||||
\(219\) | 2.88862 | − | 8.09748i | 0.195195 | − | 0.547177i | ||||
\(220\) | 5.83541 | + | 10.1072i | 0.393423 | + | 0.681429i | ||||
\(221\) | −6.51759 | − | 11.2888i | −0.438421 | − | 0.759367i | ||||
\(222\) | −5.12237 | − | 6.02576i | −0.343791 | − | 0.404423i | ||||
\(223\) | 13.1253 | + | 22.7337i | 0.878937 | + | 1.52236i | 0.852509 | + | 0.522712i | \(0.175080\pi\) |
0.0264273 | + | 0.999651i | \(0.491587\pi\) | |||||||
\(224\) | −7.87501 | − | 13.6399i | −0.526171 | − | 0.911356i | ||||
\(225\) | 35.1672 | − | 13.3126i | 2.34448 | − | 0.887508i | ||||
\(226\) | −12.7920 | + | 22.1565i | −0.850914 | + | 1.47383i | ||||
\(227\) | −12.4225 | + | 21.5163i | −0.824508 | + | 1.42809i | 0.0777867 | + | 0.996970i | \(0.475215\pi\) |
−0.902295 | + | 0.431120i | \(0.858119\pi\) | |||||||
\(228\) | 0.0830138 | − | 15.7160i | 0.00549773 | − | 1.04082i | ||||
\(229\) | −13.6496 | − | 23.6419i | −0.901993 | − | 1.56230i | −0.824903 | − | 0.565274i | \(-0.808771\pi\) |
−0.0770898 | − | 0.997024i | \(-0.524563\pi\) | |||||||
\(230\) | −16.6873 | −1.10033 | ||||||||
\(231\) | 2.93224 | + | 3.44937i | 0.192927 | + | 0.226952i | ||||
\(232\) | 0.973496 | 0.0639131 | ||||||||
\(233\) | 8.88155 | − | 15.3833i | 0.581850 | − | 1.00779i | −0.413411 | − | 0.910545i | \(-0.635663\pi\) |
0.995260 | − | 0.0972483i | \(-0.0310041\pi\) | |||||||
\(234\) | −11.0596 | + | 4.18663i | −0.722987 | + | 0.273689i | ||||
\(235\) | 4.63853 | 0.302584 | ||||||||
\(236\) | −1.05539 | + | 1.82800i | −0.0687003 | + | 0.118992i | ||||
\(237\) | 5.80746 | + | 6.83168i | 0.377235 | + | 0.443765i | ||||
\(238\) | 13.1751 | − | 22.8199i | 0.854015 | − | 1.47920i | ||||
\(239\) | 5.94744 | + | 10.3013i | 0.384708 | + | 0.666334i | 0.991729 | − | 0.128352i | \(-0.0409688\pi\) |
−0.607021 | + | 0.794686i | \(0.707635\pi\) | |||||||
\(240\) | 17.9914 | + | 21.1644i | 1.16134 | + | 1.36616i | ||||
\(241\) | −1.93933 | −0.124923 | −0.0624616 | − | 0.998047i | \(-0.519895\pi\) | ||||
−0.0624616 | + | 0.998047i | \(0.519895\pi\) | |||||||
\(242\) | −9.30086 | + | 16.1096i | −0.597882 | + | 1.03556i | ||||
\(243\) | −9.63240 | + | 12.2563i | −0.617919 | + | 0.786242i | ||||
\(244\) | −0.345640 | + | 0.598666i | −0.0221273 | + | 0.0383257i | ||||
\(245\) | −6.67649 | − | 11.5640i | −0.426546 | − | 0.738799i | ||||
\(246\) | −17.2178 | − | 20.2544i | −1.09777 | − | 1.29137i | ||||
\(247\) | −1.57462 | + | 8.35760i | −0.100191 | + | 0.531782i | ||||
\(248\) | 0.0636641 | + | 0.110270i | 0.00404268 | + | 0.00700212i | ||||
\(249\) | −7.34085 | + | 20.5782i | −0.465208 | + | 1.30409i | ||||
\(250\) | −31.8690 | − | 55.1988i | −2.01557 | − | 3.49108i | ||||
\(251\) | −8.69809 | − | 15.0655i | −0.549019 | − | 0.950928i | −0.998342 | − | 0.0575591i | \(-0.981668\pi\) |
0.449323 | − | 0.893369i | \(-0.351665\pi\) | |||||||
\(252\) | −9.43893 | − | 7.71625i | −0.594597 | − | 0.486078i | ||||
\(253\) | 1.32051 | + | 2.28719i | 0.0830199 | + | 0.143795i | ||||
\(254\) | 4.76023 | − | 8.24496i | 0.298684 | − | 0.517335i | ||||
\(255\) | −16.2806 | + | 45.6384i | −1.01953 | + | 2.85799i | ||||
\(256\) | −7.30726 | + | 12.6565i | −0.456704 | + | 0.791034i | ||||
\(257\) | 14.0906 | − | 24.4056i | 0.878946 | − | 1.52238i | 0.0264478 | − | 0.999650i | \(-0.491580\pi\) |
0.852499 | − | 0.522730i | \(-0.175086\pi\) | |||||||
\(258\) | −9.35415 | + | 26.2219i | −0.582364 | + | 1.63250i | ||||
\(259\) | −2.20611 | + | 3.82109i | −0.137081 | + | 0.237431i | ||||
\(260\) | 8.50359 | + | 14.7287i | 0.527371 | + | 0.913433i | ||||
\(261\) | −16.5554 | + | 6.26707i | −1.02475 | + | 0.387922i | ||||
\(262\) | 19.0940 | + | 33.0718i | 1.17963 | + | 2.04318i | ||||
\(263\) | 0.599297 | + | 1.03801i | 0.0369542 | + | 0.0640066i | 0.883911 | − | 0.467655i | \(-0.154901\pi\) |
−0.846957 | + | 0.531662i | \(0.821568\pi\) | |||||||
\(264\) | −0.128551 | + | 0.360358i | −0.00791174 | + | 0.0221785i | ||||
\(265\) | −15.7122 | − | 27.2143i | −0.965190 | − | 1.67176i | ||||
\(266\) | −16.2227 | + | 5.69071i | −0.994677 | + | 0.348920i | ||||
\(267\) | −1.27685 | − | 1.50204i | −0.0781420 | − | 0.0919233i | ||||
\(268\) | −13.4360 | − | 23.2719i | −0.820736 | − | 1.42156i | ||||
\(269\) | 3.49711 | − | 6.05717i | 0.213222 | − | 0.369312i | −0.739499 | − | 0.673158i | \(-0.764937\pi\) |
0.952721 | + | 0.303846i | \(0.0982708\pi\) | |||||||
\(270\) | 38.4847 | + | 21.2434i | 2.34210 | + | 1.29283i | ||||
\(271\) | 6.19864 | − | 10.7364i | 0.376541 | − | 0.652188i | −0.614016 | − | 0.789294i | \(-0.710447\pi\) |
0.990556 | + | 0.137106i | \(0.0437801\pi\) | |||||||
\(272\) | −25.5881 | −1.55150 | ||||||||
\(273\) | 4.27297 | + | 5.02656i | 0.258612 | + | 0.304221i | ||||
\(274\) | 5.72720 | + | 9.91980i | 0.345993 | + | 0.599277i | ||||
\(275\) | −8.39103 | + | 14.5337i | −0.505998 | + | 0.876414i | ||||
\(276\) | −4.60636 | − | 5.41874i | −0.277270 | − | 0.326170i | ||||
\(277\) | 9.75455 | − | 16.8954i | 0.586094 | − | 1.01514i | −0.408644 | − | 0.912694i | \(-0.633998\pi\) |
0.994738 | − | 0.102451i | \(-0.0326684\pi\) | |||||||
\(278\) | 14.4716 | 0.867952 | ||||||||
\(279\) | −1.79256 | − | 1.46540i | −0.107318 | − | 0.0877314i | ||||
\(280\) | −0.674337 | + | 1.16799i | −0.0402993 | + | 0.0698005i | ||||
\(281\) | −24.1496 | −1.44064 | −0.720321 | − | 0.693641i | \(-0.756006\pi\) | ||||
−0.720321 | + | 0.693641i | \(0.756006\pi\) | |||||||
\(282\) | 2.51061 | + | 2.95339i | 0.149505 | + | 0.175872i | ||||
\(283\) | 21.2081 | 1.26069 | 0.630344 | − | 0.776316i | \(-0.282914\pi\) | ||||
0.630344 | + | 0.776316i | \(0.282914\pi\) | |||||||
\(284\) | 3.77386 | + | 6.53651i | 0.223937 | + | 0.387870i | ||||
\(285\) | 27.4617 | − | 15.6622i | 1.62669 | − | 0.927749i | ||||
\(286\) | 2.63886 | − | 4.57064i | 0.156039 | − | 0.270268i | ||||
\(287\) | −7.41539 | + | 12.8438i | −0.437717 | + | 0.758148i | ||||
\(288\) | −3.89706 | + | 23.8875i | −0.229636 | + | 1.40759i | ||||
\(289\) | −13.8175 | − | 23.9326i | −0.812795 | − | 1.40780i | ||||
\(290\) | 24.9591 | + | 43.2305i | 1.46565 | + | 2.53858i | ||||
\(291\) | −4.21662 | − | 4.96027i | −0.247182 | − | 0.290776i | ||||
\(292\) | −5.16631 | − | 8.94832i | −0.302336 | − | 0.523661i | ||||
\(293\) | 7.84223 | + | 13.5831i | 0.458148 | + | 0.793535i | 0.998863 | − | 0.0476705i | \(-0.0151797\pi\) |
−0.540715 | + | 0.841206i | \(0.681846\pi\) | |||||||
\(294\) | 3.74924 | − | 10.5100i | 0.218660 | − | 0.612956i | ||||
\(295\) | −4.24598 | −0.247210 | ||||||||
\(296\) | −0.372877 | −0.0216730 | ||||||||
\(297\) | −0.133731 | − | 6.95585i | −0.00775986 | − | 0.403619i | ||||
\(298\) | −18.2141 | − | 31.5477i | −1.05511 | − | 1.82751i | ||||
\(299\) | 1.92430 | + | 3.33299i | 0.111285 | + | 0.192752i | ||||
\(300\) | 15.1843 | − | 42.5653i | 0.876669 | − | 2.45751i | ||||
\(301\) | 15.5319 | 0.895242 | ||||||||
\(302\) | −13.0942 | −0.753488 | ||||||||
\(303\) | 14.1189 | − | 2.58294i | 0.811112 | − | 0.148386i | ||||
\(304\) | 12.6625 | + | 10.8799i | 0.726244 | + | 0.624003i | ||||
\(305\) | −1.39055 | −0.0796228 | ||||||||
\(306\) | −37.8702 | + | 14.3358i | −2.16489 | + | 0.819525i | ||||
\(307\) | 8.67805 | − | 15.0308i | 0.495283 | − | 0.857855i | −0.504703 | − | 0.863293i | \(-0.668398\pi\) |
0.999985 | + | 0.00543863i | \(0.00173118\pi\) | |||||||
\(308\) | 5.44109 | 0.310035 | ||||||||
\(309\) | −4.41132 | − | 5.18931i | −0.250951 | − | 0.295209i | ||||
\(310\) | −3.26453 | + | 5.65432i | −0.185413 | + | 0.321144i | ||||
\(311\) | −9.13185 | − | 15.8168i | −0.517820 | − | 0.896890i | −0.999786 | − | 0.0207003i | \(-0.993410\pi\) |
0.481966 | − | 0.876190i | \(-0.339923\pi\) | |||||||
\(312\) | −0.187329 | + | 0.525128i | −0.0106054 | + | 0.0297295i | ||||
\(313\) | −9.81792 | −0.554942 | −0.277471 | − | 0.960734i | \(-0.589496\pi\) | ||||
−0.277471 | + | 0.960734i | \(0.589496\pi\) | |||||||
\(314\) | −0.276566 | − | 0.479027i | −0.0156075 | − | 0.0270330i | ||||
\(315\) | 3.94870 | − | 24.2040i | 0.222484 | − | 1.36374i | ||||
\(316\) | 10.7764 | 0.606220 | ||||||||
\(317\) | −11.3538 | −0.637691 | −0.318846 | − | 0.947807i | \(-0.603295\pi\) | ||||
−0.318846 | + | 0.947807i | \(0.603295\pi\) | |||||||
\(318\) | 8.82329 | − | 24.7338i | 0.494786 | − | 1.38700i | ||||
\(319\) | 3.95017 | − | 6.84190i | 0.221167 | − | 0.383073i | ||||
\(320\) | 36.1765 | 2.02233 | ||||||||
\(321\) | 0.321226 | − | 0.0587656i | 0.0179291 | − | 0.00327997i | ||||
\(322\) | −3.88991 | + | 6.73753i | −0.216776 | + | 0.375468i | ||||
\(323\) | −5.39181 | + | 28.6181i | −0.300008 | + | 1.59235i | ||||
\(324\) | 3.72507 | + | 18.3609i | 0.206948 | + | 1.02005i | ||||
\(325\) | −12.2277 | + | 21.1791i | −0.678273 | + | 1.17480i | ||||
\(326\) | −8.09892 | − | 14.0277i | −0.448558 | − | 0.776925i | ||||
\(327\) | 1.26575 | − | 3.54820i | 0.0699962 | − | 0.196216i | ||||
\(328\) | −1.25335 | −0.0692048 | ||||||||
\(329\) | 1.08127 | − | 1.87282i | 0.0596124 | − | 0.103252i | ||||
\(330\) | −19.2984 | + | 3.53048i | −1.06234 | + | 0.194347i | ||||
\(331\) | 2.31414 | − | 4.00820i | 0.127196 | − | 0.220311i | −0.795393 | − | 0.606094i | \(-0.792735\pi\) |
0.922589 | + | 0.385783i | \(0.126069\pi\) | |||||||
\(332\) | 13.1292 | + | 22.7404i | 0.720557 | + | 1.24804i | ||||
\(333\) | 6.34118 | − | 2.40047i | 0.347495 | − | 0.131545i | ||||
\(334\) | 41.9153 | 2.29350 | ||||||||
\(335\) | 27.0274 | − | 46.8128i | 1.47666 | − | 2.55765i | ||||
\(336\) | 12.7391 | − | 2.33051i | 0.694976 | − | 0.127140i | ||||
\(337\) | −14.6645 | −0.798829 | −0.399414 | − | 0.916771i | \(-0.630787\pi\) | ||||
−0.399414 | + | 0.916771i | \(0.630787\pi\) | |||||||
\(338\) | −9.28658 | + | 16.0848i | −0.505123 | + | 0.874899i | ||||
\(339\) | −14.2061 | − | 16.7115i | −0.771569 | − | 0.907644i | ||||
\(340\) | 29.1180 | + | 50.4338i | 1.57914 | + | 2.73516i | ||||
\(341\) | 1.03332 | 0.0559577 | ||||||||
\(342\) | 24.8359 | + | 9.00788i | 1.34297 | + | 0.487090i | ||||
\(343\) | −19.8908 | −1.07400 | ||||||||
\(344\) | 0.656301 | + | 1.13675i | 0.0353854 | + | 0.0612892i | ||||
\(345\) | 4.80680 | − | 13.4746i | 0.258790 | − | 0.725449i | ||||
\(346\) | −18.0722 | + | 31.3020i | −0.971568 | + | 1.68281i | ||||
\(347\) | 30.1189 | 1.61687 | 0.808434 | − | 0.588587i | \(-0.200316\pi\) | ||||
0.808434 | + | 0.588587i | \(0.200316\pi\) | |||||||
\(348\) | −7.14821 | + | 20.0381i | −0.383184 | + | 1.07416i | ||||
\(349\) | 1.39279 | − | 2.41239i | 0.0745545 | − | 0.129132i | −0.826338 | − | 0.563175i | \(-0.809580\pi\) |
0.900892 | + | 0.434042i | \(0.142913\pi\) | |||||||
\(350\) | −49.4359 | −2.64246 | ||||||||
\(351\) | −0.194878 | − | 10.1363i | −0.0104018 | − | 0.541038i | ||||
\(352\) | −5.40098 | − | 9.35476i | −0.287873 | − | 0.498611i | ||||
\(353\) | 5.04882 | − | 8.74482i | 0.268722 | − | 0.465440i | −0.699810 | − | 0.714329i | \(-0.746732\pi\) |
0.968532 | + | 0.248889i | \(0.0800655\pi\) | |||||||
\(354\) | −2.29814 | − | 2.70344i | −0.122145 | − | 0.143686i | ||||
\(355\) | −7.59133 | + | 13.1486i | −0.402906 | + | 0.697854i | ||||
\(356\) | −2.36934 | −0.125575 | ||||||||
\(357\) | 14.6315 | + | 17.2119i | 0.774380 | + | 0.910952i | ||||
\(358\) | 0.214650 | + | 0.371785i | 0.0113446 | + | 0.0196495i | ||||
\(359\) | −3.12391 | + | 5.41076i | −0.164873 | + | 0.285569i | −0.936610 | − | 0.350373i | \(-0.886055\pi\) |
0.771737 | + | 0.635942i | \(0.219388\pi\) | |||||||
\(360\) | 1.93830 | − | 0.733746i | 0.102157 | − | 0.0386718i | ||||
\(361\) | 14.8364 | − | 11.8694i | 0.780862 | − | 0.624704i | ||||
\(362\) | −16.1450 | + | 27.9639i | −0.848560 | + | 1.46975i | ||||
\(363\) | −10.3290 | − | 12.1506i | −0.542131 | − | 0.637743i | ||||
\(364\) | 7.92897 | 0.415591 | ||||||||
\(365\) | 10.3923 | − | 18.0001i | 0.543960 | − | 0.942167i | ||||
\(366\) | −0.752637 | − | 0.885374i | −0.0393410 | − | 0.0462792i | ||||
\(367\) | 2.89031 | 0.150873 | 0.0754366 | − | 0.997151i | \(-0.475965\pi\) | ||||
0.0754366 | + | 0.997151i | \(0.475965\pi\) | |||||||
\(368\) | 7.55482 | 0.393822 | ||||||||
\(369\) | 21.3146 | − | 8.06870i | 1.10959 | − | 0.420040i | ||||
\(370\) | −9.56007 | − | 16.5585i | −0.497004 | − | 0.860837i | ||||
\(371\) | −14.6504 | −0.760612 | ||||||||
\(372\) | −2.73723 | + | 0.500753i | −0.141919 | + | 0.0259628i | ||||
\(373\) | −7.36377 | − | 12.7544i | −0.381282 | − | 0.660399i | 0.609964 | − | 0.792429i | \(-0.291184\pi\) |
−0.991246 | + | 0.132030i | \(0.957851\pi\) | |||||||
\(374\) | 9.03597 | − | 15.6508i | 0.467239 | − | 0.809281i | ||||
\(375\) | 53.7517 | − | 9.83342i | 2.77573 | − | 0.507796i | ||||
\(376\) | 0.182757 | 0.00942496 | ||||||||
\(377\) | 5.75635 | − | 9.97029i | 0.296467 | − | 0.513496i | ||||
\(378\) | 17.5481 | − | 10.5863i | 0.902578 | − | 0.544500i | ||||
\(379\) | 11.7601 | 0.604077 | 0.302038 | − | 0.953296i | \(-0.402333\pi\) | ||||
0.302038 | + | 0.953296i | \(0.402333\pi\) | |||||||
\(380\) | 7.03477 | − | 37.3384i | 0.360876 | − | 1.91542i | ||||
\(381\) | 5.28643 | + | 6.21876i | 0.270832 | + | 0.318597i | ||||
\(382\) | 27.7569 | 1.42017 | ||||||||
\(383\) | −30.9063 | −1.57924 | −0.789619 | − | 0.613597i | \(-0.789722\pi\) | ||||
−0.789619 | + | 0.613597i | \(0.789722\pi\) | |||||||
\(384\) | 1.47941 | + | 1.74032i | 0.0754956 | + | 0.0888102i | ||||
\(385\) | 5.47254 | + | 9.47871i | 0.278906 | + | 0.483080i | ||||
\(386\) | −14.6330 | − | 25.3451i | −0.744801 | − | 1.29003i | ||||
\(387\) | −18.4791 | − | 15.1065i | −0.939347 | − | 0.767909i | ||||
\(388\) | −7.82440 | −0.397224 | ||||||||
\(389\) | 14.1775 | 0.718828 | 0.359414 | − | 0.933178i | \(-0.382977\pi\) | ||||
0.359414 | + | 0.933178i | \(0.382977\pi\) | |||||||
\(390\) | −28.1224 | + | 5.14476i | −1.42404 | + | 0.260515i | ||||
\(391\) | 6.58919 | + | 11.4128i | 0.333230 | + | 0.577171i | ||||
\(392\) | −0.263052 | − | 0.455620i | −0.0132861 | − | 0.0230123i | ||||
\(393\) | −32.2048 | + | 5.89160i | −1.62452 | + | 0.297192i | ||||
\(394\) | 16.8373 | + | 29.1631i | 0.848252 | + | 1.46922i | ||||
\(395\) | 10.8387 | + | 18.7731i | 0.545353 | + | 0.944579i | ||||
\(396\) | −6.47357 | − | 5.29209i | −0.325309 | − | 0.265937i | ||||
\(397\) | −3.48803 | + | 6.04144i | −0.175059 | + | 0.303211i | −0.940182 | − | 0.340673i | \(-0.889345\pi\) |
0.765123 | + | 0.643885i | \(0.222678\pi\) | |||||||
\(398\) | 10.0968 | − | 17.4882i | 0.506108 | − | 0.876604i | ||||
\(399\) | 0.0778516 | − | 14.7387i | 0.00389746 | − | 0.737857i | ||||
\(400\) | 24.0030 | + | 41.5745i | 1.20015 | + | 2.07872i | ||||
\(401\) | 16.7884 | 0.838371 | 0.419186 | − | 0.907901i | \(-0.362316\pi\) | ||||
0.419186 | + | 0.907901i | \(0.362316\pi\) | |||||||
\(402\) | 44.4346 | − | 8.12894i | 2.21620 | − | 0.405435i | ||||
\(403\) | 1.50580 | 0.0750094 | ||||||||
\(404\) | 8.62522 | − | 14.9393i | 0.429121 | − | 0.743259i | ||||
\(405\) | −28.2392 | + | 24.9563i | −1.40322 | + | 1.24009i | ||||
\(406\) | 23.2725 | 1.15500 | ||||||||
\(407\) | −1.51303 | + | 2.62065i | −0.0749982 | + | 0.129901i | ||||
\(408\) | −0.641451 | + | 1.79814i | −0.0317566 | + | 0.0890212i | ||||
\(409\) | −6.70008 | + | 11.6049i | −0.331298 | + | 0.573824i | −0.982767 | − | 0.184851i | \(-0.940820\pi\) |
0.651469 | + | 0.758675i | \(0.274153\pi\) | |||||||
\(410\) | −32.1343 | − | 55.6582i | −1.58700 | − | 2.74876i | ||||
\(411\) | −9.65975 | + | 1.76717i | −0.476480 | + | 0.0871681i | ||||
\(412\) | −8.18569 | −0.403280 | ||||||||
\(413\) | −0.989765 | + | 1.71432i | −0.0487032 | + | 0.0843563i | ||||
\(414\) | 11.1811 | − | 4.23262i | 0.549520 | − | 0.208022i | ||||
\(415\) | −26.4101 | + | 45.7436i | −1.29642 | + | 2.24547i | ||||
\(416\) | −7.87052 | − | 13.6321i | −0.385884 | − | 0.668370i | ||||
\(417\) | −4.16859 | + | 11.6855i | −0.204137 | + | 0.572243i | ||||
\(418\) | −11.1261 | + | 3.90290i | −0.544196 | + | 0.190897i | ||||
\(419\) | 5.28778 | + | 9.15870i | 0.258325 | + | 0.447432i | 0.965793 | − | 0.259313i | \(-0.0834962\pi\) |
−0.707468 | + | 0.706745i | \(0.750163\pi\) | |||||||
\(420\) | −19.0899 | − | 22.4566i | −0.931492 | − | 1.09577i | ||||
\(421\) | 9.63348 | + | 16.6857i | 0.469507 | + | 0.813210i | 0.999392 | − | 0.0348593i | \(-0.0110983\pi\) |
−0.529885 | + | 0.848069i | \(0.677765\pi\) | |||||||
\(422\) | 2.06472 | + | 3.57619i | 0.100509 | + | 0.174086i | ||||
\(423\) | −3.10798 | + | 1.17653i | −0.151115 | + | 0.0572050i | ||||
\(424\) | −0.619055 | − | 1.07223i | −0.0300640 | − | 0.0520723i | ||||
\(425\) | −41.8702 | + | 72.5212i | −2.03100 | + | 3.51780i | ||||
\(426\) | −12.4806 | + | 2.28322i | −0.604687 | + | 0.110622i | ||||
\(427\) | −0.324147 | + | 0.561438i | −0.0156866 | + | 0.0271699i | ||||
\(428\) | 0.196236 | − | 0.339891i | 0.00948542 | − | 0.0164292i | ||||
\(429\) | 2.93056 | + | 3.44740i | 0.141489 | + | 0.166442i | ||||
\(430\) | −33.6533 | + | 58.2893i | −1.62291 | + | 2.81096i | ||||
\(431\) | 13.7684 | + | 23.8476i | 0.663203 | + | 1.14870i | 0.979769 | + | 0.200130i | \(0.0641366\pi\) |
−0.316567 | + | 0.948570i | \(0.602530\pi\) | |||||||
\(432\) | −17.4231 | − | 9.61752i | −0.838271 | − | 0.462723i | ||||
\(433\) | −10.9652 | − | 18.9923i | −0.526954 | − | 0.912711i | −0.999507 | − | 0.0314088i | \(-0.990001\pi\) |
0.472552 | − | 0.881303i | \(-0.343333\pi\) | |||||||
\(434\) | 1.52196 | + | 2.63612i | 0.0730566 | + | 0.126538i | ||||
\(435\) | −42.0972 | + | 7.70132i | −2.01841 | + | 0.369250i | ||||
\(436\) | −2.26381 | − | 3.92103i | −0.108417 | − | 0.187783i | ||||
\(437\) | 1.59192 | − | 8.44941i | 0.0761518 | − | 0.404190i | ||||
\(438\) | 17.0856 | − | 3.12567i | 0.816383 | − | 0.149350i | ||||
\(439\) | 7.11143 | + | 12.3174i | 0.339410 | + | 0.587876i | 0.984322 | − | 0.176381i | \(-0.0564392\pi\) |
−0.644912 | + | 0.764257i | \(0.723106\pi\) | |||||||
\(440\) | −0.462485 | + | 0.801047i | −0.0220481 | + | 0.0381884i | ||||
\(441\) | 7.40663 | + | 6.05486i | 0.352697 | + | 0.288327i | ||||
\(442\) | 13.1676 | − | 22.8069i | 0.626318 | − | 1.08481i | ||||
\(443\) | 14.2332 | 0.676240 | 0.338120 | − | 0.941103i | \(-0.390209\pi\) | ||||
0.338120 | + | 0.941103i | \(0.390209\pi\) | |||||||
\(444\) | 2.73797 | − | 7.67518i | 0.129938 | − | 0.364248i | ||||
\(445\) | −2.38303 | − | 4.12753i | −0.112967 | − | 0.195664i | ||||
\(446\) | −26.5172 | + | 45.9292i | −1.25563 | + | 2.17481i | ||||
\(447\) | 30.7206 | − | 5.62008i | 1.45304 | − | 0.265821i | ||||
\(448\) | 8.43299 | − | 14.6064i | 0.398421 | − | 0.690086i | ||||
\(449\) | 3.11473 | 0.146993 | 0.0734966 | − | 0.997295i | \(-0.476584\pi\) | ||||
0.0734966 | + | 0.997295i | \(0.476584\pi\) | |||||||
\(450\) | 58.8166 | + | 48.0821i | 2.77264 | + | 2.26661i | ||||
\(451\) | −5.08575 | + | 8.80878i | −0.239479 | + | 0.414789i | ||||
\(452\) | −26.3610 | −1.23992 | ||||||||
\(453\) | 3.77182 | − | 10.5733i | 0.177215 | − | 0.496777i | ||||
\(454\) | −50.1945 | −2.35575 | ||||||||
\(455\) | 7.97480 | + | 13.8128i | 0.373864 | + | 0.647552i | ||||
\(456\) | 1.08198 | − | 0.617087i | 0.0506685 | − | 0.0288977i | ||||
\(457\) | 5.77896 | − | 10.0095i | 0.270329 | − | 0.468223i | −0.698617 | − | 0.715495i | \(-0.746201\pi\) |
0.968946 | + | 0.247273i | \(0.0795344\pi\) | |||||||
\(458\) | 27.5765 | − | 47.7639i | 1.28857 | − | 2.23186i | ||||
\(459\) | −0.667301 | − | 34.7088i | −0.0311469 | − | 1.62007i | ||||
\(460\) | −8.59701 | − | 14.8905i | −0.400838 | − | 0.694271i | ||||
\(461\) | 2.76252 | + | 4.78482i | 0.128663 | + | 0.222851i | 0.923159 | − | 0.384419i | \(-0.125598\pi\) |
−0.794496 | + | 0.607270i | \(0.792265\pi\) | |||||||
\(462\) | −3.07315 | + | 8.61477i | −0.142976 | + | 0.400795i | ||||
\(463\) | −6.11457 | − | 10.5907i | −0.284168 | − | 0.492193i | 0.688239 | − | 0.725484i | \(-0.258384\pi\) |
−0.972407 | + | 0.233291i | \(0.925051\pi\) | |||||||
\(464\) | −11.2997 | − | 19.5717i | −0.524576 | − | 0.908592i | ||||
\(465\) | −3.62539 | − | 4.26477i | −0.168123 | − | 0.197774i | ||||
\(466\) | 35.8870 | 1.66243 | ||||||||
\(467\) | 2.22377 | 0.102904 | 0.0514518 | − | 0.998675i | \(-0.483615\pi\) | ||||
0.0514518 | + | 0.998675i | \(0.483615\pi\) | |||||||
\(468\) | −9.43354 | − | 7.71184i | −0.436065 | − | 0.356480i | ||||
\(469\) | −12.6005 | − | 21.8247i | −0.581838 | − | 1.00777i | ||||
\(470\) | 4.68564 | + | 8.11577i | 0.216132 | + | 0.374352i | ||||
\(471\) | 0.466469 | − | 0.0853365i | 0.0214938 | − | 0.00393210i | ||||
\(472\) | −0.167290 | −0.00770016 | ||||||||
\(473\) | 10.6523 | 0.489795 | ||||||||
\(474\) | −6.08655 | + | 17.0620i | −0.279565 | + | 0.783686i | ||||
\(475\) | 51.5553 | − | 18.0850i | 2.36552 | − | 0.829795i | ||||
\(476\) | 27.1504 | 1.24443 | ||||||||
\(477\) | 17.4304 | + | 14.2492i | 0.798084 | + | 0.652427i | ||||
\(478\) | −12.0157 | + | 20.8118i | −0.549585 | + | 0.951909i | ||||
\(479\) | 13.9176 | 0.635913 | 0.317957 | − | 0.948105i | \(-0.397003\pi\) | ||||
0.317957 | + | 0.948105i | \(0.397003\pi\) | |||||||
\(480\) | −19.6601 | + | 55.1120i | −0.897358 | + | 2.51551i | ||||
\(481\) | −2.20485 | + | 3.81891i | −0.100532 | + | 0.174127i | ||||
\(482\) | −1.95903 | − | 3.39313i | −0.0892312 | − | 0.154553i | ||||
\(483\) | −4.31991 | − | 5.08178i | −0.196563 | − | 0.231229i | ||||
\(484\) | −19.1666 | −0.871208 | ||||||||
\(485\) | −7.86962 | − | 13.6306i | −0.357341 | − | 0.618933i | ||||
\(486\) | −31.1744 | − | 4.47247i | −1.41410 | − | 0.202875i | ||||
\(487\) | −24.5312 | −1.11161 | −0.555807 | − | 0.831312i | \(-0.687590\pi\) | ||||
−0.555807 | + | 0.831312i | \(0.687590\pi\) | |||||||
\(488\) | −0.0547874 | −0.00248011 | ||||||||
\(489\) | 13.6600 | − | 2.49898i | 0.617727 | − | 0.113008i | ||||
\(490\) | 13.4886 | − | 23.3629i | 0.609353 | − | 1.05543i | ||||
\(491\) | 17.4039 | 0.785425 | 0.392712 | − | 0.919661i | \(-0.371537\pi\) | ||||
0.392712 | + | 0.919661i | \(0.371537\pi\) | |||||||
\(492\) | 9.20314 | − | 25.7986i | 0.414910 | − | 1.16309i | ||||
\(493\) | 19.7109 | − | 34.1402i | 0.887733 | − | 1.53760i | ||||
\(494\) | −16.2134 | + | 5.68746i | −0.729477 | + | 0.255891i | ||||
\(495\) | 2.70816 | − | 16.6000i | 0.121723 | − | 0.746116i | ||||
\(496\) | 1.47795 | − | 2.55988i | 0.0663617 | − | 0.114942i | ||||
\(497\) | 3.53918 | + | 6.13004i | 0.158754 | + | 0.274970i | ||||
\(498\) | −43.4198 | + | 7.94329i | −1.94569 | + | 0.355947i | ||||
\(499\) | −38.4075 | −1.71936 | −0.859678 | − | 0.510836i | \(-0.829336\pi\) | ||||
−0.859678 | + | 0.510836i | \(0.829336\pi\) | |||||||
\(500\) | 32.8368 | − | 56.8749i | 1.46850 | − | 2.54353i | ||||
\(501\) | −12.0738 | + | 33.8457i | −0.539417 | + | 1.51211i | ||||
\(502\) | 17.5729 | − | 30.4371i | 0.784315 | − | 1.35847i | ||||
\(503\) | −0.757962 | − | 1.31283i | −0.0337958 | − | 0.0585361i | 0.848633 | − | 0.528982i | \(-0.177426\pi\) |
−0.882429 | + | 0.470446i | \(0.844093\pi\) | |||||||
\(504\) | 0.155578 | − | 0.953633i | 0.00692998 | − | 0.0424782i | ||||
\(505\) | 34.7003 | 1.54414 | ||||||||
\(506\) | −2.66785 | + | 4.62085i | −0.118600 | + | 0.205422i | ||||
\(507\) | −10.3131 | − | 12.1320i | −0.458022 | − | 0.538800i | ||||
\(508\) | 9.80956 | 0.435229 | ||||||||
\(509\) | −0.607618 | + | 1.05243i | −0.0269322 | + | 0.0466480i | −0.879177 | − | 0.476495i | \(-0.841907\pi\) |
0.852245 | + | 0.523143i | \(0.175240\pi\) | |||||||
\(510\) | −96.2967 | + | 17.6167i | −4.26409 | + | 0.780079i | ||||
\(511\) | −4.84505 | − | 8.39187i | −0.214332 | − | 0.371234i | ||||
\(512\) | −32.1634 | −1.42144 | ||||||||
\(513\) | −14.4277 | + | 17.4597i | −0.636998 | + | 0.770865i | ||||
\(514\) | 56.9348 | 2.51128 | ||||||||
\(515\) | −8.23300 | − | 14.2600i | −0.362789 | − | 0.628370i | ||||
\(516\) | −28.2175 | + | 5.16216i | −1.24221 | + | 0.227251i | ||||
\(517\) | 0.741576 | − | 1.28445i | 0.0326145 | − | 0.0564899i | ||||
\(518\) | −8.91406 | −0.391661 | ||||||||
\(519\) | −20.0699 | − | 23.6095i | −0.880972 | − | 1.03634i | ||||
\(520\) | −0.673952 | + | 1.16732i | −0.0295547 | + | 0.0511903i | ||||
\(521\) | −11.3543 | −0.497443 | −0.248721 | − | 0.968575i | \(-0.580010\pi\) | ||||
−0.248721 | + | 0.968575i | \(0.580010\pi\) | |||||||
\(522\) | −27.6886 | − | 22.6352i | −1.21190 | − | 0.990717i | ||||
\(523\) | −2.83152 | − | 4.90434i | −0.123814 | − | 0.214452i | 0.797455 | − | 0.603379i | \(-0.206179\pi\) |
−0.921269 | + | 0.388927i | \(0.872846\pi\) | |||||||
\(524\) | −19.6738 | + | 34.0761i | −0.859455 | + | 1.48862i | ||||
\(525\) | 14.2401 | − | 39.9184i | 0.621490 | − | 1.74218i | ||||
\(526\) | −1.21077 | + | 2.09711i | −0.0527919 | + | 0.0914383i | ||||
\(527\) | 5.15616 | 0.224606 | ||||||||
\(528\) | 8.73696 | − | 1.59835i | 0.380227 | − | 0.0695594i | ||||
\(529\) | 9.55456 | + | 16.5490i | 0.415416 | + | 0.719521i | ||||
\(530\) | 31.7435 | − | 54.9813i | 1.37885 | − | 2.38824i | ||||
\(531\) | 2.84496 | − | 1.07696i | 0.123461 | − | 0.0467363i | ||||
\(532\) | −13.4356 | − | 11.5441i | −0.582508 | − | 0.500501i | ||||
\(533\) | −7.41116 | + | 12.8365i | −0.321013 | + | 0.556011i | ||||
\(534\) | 1.33821 | − | 3.75133i | 0.0579101 | − | 0.162336i | ||||
\(535\) | 0.789481 | 0.0341322 | ||||||||
\(536\) | 1.06487 | − | 1.84441i | 0.0459954 | − | 0.0796664i | ||||
\(537\) | −0.362039 | + | 0.0662320i | −0.0156231 | + | 0.00285812i | ||||
\(538\) | 14.1305 | 0.609209 | ||||||||
\(539\) | −4.26957 | −0.183903 | ||||||||
\(540\) | 0.870636 | + | 45.2850i | 0.0374662 | + | 1.94876i | ||||
\(541\) | 21.0798 | + | 36.5114i | 0.906293 | + | 1.56975i | 0.819172 | + | 0.573549i | \(0.194434\pi\) |
0.0871219 | + | 0.996198i | \(0.472233\pi\) | |||||||
\(542\) | 25.0464 | 1.07583 | ||||||||
\(543\) | −17.9296 | − | 21.0918i | −0.769435 | − | 0.905134i | ||||
\(544\) | −26.9502 | − | 46.6791i | −1.15548 | − | 2.00135i | ||||
\(545\) | 4.55378 | − | 7.88738i | 0.195063 | − | 0.337858i | ||||
\(546\) | −4.47832 | + | 12.5538i | −0.191654 | + | 0.537252i | ||||
\(547\) | 10.4784 | 0.448023 | 0.224011 | − | 0.974587i | \(-0.428085\pi\) | ||||
0.224011 | + | 0.974587i | \(0.428085\pi\) | |||||||
\(548\) | −5.90111 | + | 10.2210i | −0.252083 | + | 0.436621i | ||||
\(549\) | 0.931719 | − | 0.352704i | 0.0397648 | − | 0.0150531i | ||||
\(550\) | −33.9050 | −1.44571 | ||||||||
\(551\) | −24.2703 | + | 8.51370i | −1.03395 | + | 0.362696i | ||||
\(552\) | 0.189387 | − | 0.530896i | 0.00806084 | − | 0.0225964i | ||||
\(553\) | 10.1063 | 0.429762 | ||||||||
\(554\) | 39.4145 | 1.67456 | ||||||||
\(555\) | 16.1244 | − | 2.94983i | 0.684444 | − | 0.125213i | ||||
\(556\) | 7.45555 | + | 12.9134i | 0.316186 | + | 0.547650i | ||||
\(557\) | −18.3181 | − | 31.7279i | −0.776164 | − | 1.34436i | −0.934138 | − | 0.356913i | \(-0.883829\pi\) |
0.157973 | − | 0.987443i | \(-0.449504\pi\) | |||||||
\(558\) | 0.753165 | − | 4.61662i | 0.0318840 | − | 0.195437i | ||||
\(559\) | 15.5230 | 0.656553 | ||||||||
\(560\) | 31.3091 | 1.32305 | ||||||||
\(561\) | 10.0348 | + | 11.8046i | 0.423670 | + | 0.498390i | ||||
\(562\) | −24.3948 | − | 42.2531i | −1.02903 | − | 1.78234i | ||||
\(563\) | 4.29307 | + | 7.43582i | 0.180931 | + | 0.313382i | 0.942198 | − | 0.335057i | \(-0.108755\pi\) |
−0.761267 | + | 0.648439i | \(0.775422\pi\) | |||||||
\(564\) | −1.34195 | + | 3.76181i | −0.0565063 | + | 0.158401i | ||||
\(565\) | −26.5133 | − | 45.9224i | −1.11542 | − | 1.93197i | ||||
\(566\) | 21.4235 | + | 37.1065i | 0.900495 | + | 1.55970i | ||||
\(567\) | 3.49343 | + | 17.2191i | 0.146710 | + | 0.723135i | ||||
\(568\) | −0.299097 | + | 0.518050i | −0.0125498 | + | 0.0217369i | ||||
\(569\) | −2.90516 | + | 5.03189i | −0.121791 | + | 0.210948i | −0.920474 | − | 0.390804i | \(-0.872197\pi\) |
0.798683 | + | 0.601752i | \(0.205530\pi\) | |||||||
\(570\) | 55.1438 | + | 32.2269i | 2.30972 | + | 1.34984i | ||||
\(571\) | 4.11198 | + | 7.12216i | 0.172081 | + | 0.298053i | 0.939147 | − | 0.343515i | \(-0.111618\pi\) |
−0.767066 | + | 0.641568i | \(0.778284\pi\) | |||||||
\(572\) | 5.43798 | 0.227373 | ||||||||
\(573\) | −7.99544 | + | 22.4131i | −0.334014 | + | 0.936321i | ||||
\(574\) | −29.9628 | −1.25062 | ||||||||
\(575\) | 12.3621 | − | 21.4117i | 0.515534 | − | 0.892930i | ||||
\(576\) | −24.2396 | + | 9.17595i | −1.00998 | + | 0.382331i | ||||
\(577\) | −24.3169 | −1.01232 | −0.506162 | − | 0.862438i | \(-0.668936\pi\) | ||||
−0.506162 | + | 0.862438i | \(0.668936\pi\) | |||||||
\(578\) | 27.9157 | − | 48.3514i | 1.16114 | − | 2.01115i | ||||
\(579\) | 24.6807 | − | 4.51513i | 1.02570 | − | 0.187642i | ||||
\(580\) | −25.7170 | + | 44.5432i | −1.06784 | + | 1.84956i | ||||
\(581\) | 12.3127 | + | 21.3263i | 0.510818 | + | 0.884763i | ||||
\(582\) | 4.41925 | − | 12.3882i | 0.183184 | − | 0.513508i | ||||
\(583\) | −10.0478 | −0.416138 | ||||||||
\(584\) | 0.409456 | − | 0.709198i | 0.0169434 | − | 0.0293468i | ||||
\(585\) | 3.94644 | − | 24.1902i | 0.163165 | − | 1.00014i | ||||
\(586\) | −15.8437 | + | 27.4422i | −0.654499 | + | 1.13363i | ||||
\(587\) | 0.607944 | + | 1.05299i | 0.0250925 | + | 0.0434615i | 0.878299 | − | 0.478112i | \(-0.158679\pi\) |
−0.853206 | + | 0.521573i | \(0.825345\pi\) | |||||||
\(588\) | 11.3099 | − | 2.06905i | 0.466411 | − | 0.0853260i | ||||
\(589\) | −2.55158 | − | 2.19236i | −0.105136 | − | 0.0903347i | ||||
\(590\) | −4.28910 | − | 7.42894i | −0.176579 | − | 0.305845i | ||||
\(591\) | −28.3986 | + | 5.19528i | −1.16816 | + | 0.213705i | ||||
\(592\) | 4.32812 | + | 7.49652i | 0.177885 | + | 0.308105i | ||||
\(593\) | 5.40934 | + | 9.36925i | 0.222135 | + | 0.384749i | 0.955456 | − | 0.295134i | \(-0.0953641\pi\) |
−0.733321 | + | 0.679882i | \(0.762031\pi\) | |||||||
\(594\) | 12.0351 | − | 7.26047i | 0.493808 | − | 0.297901i | ||||
\(595\) | 27.3073 | + | 47.2976i | 1.11949 | + | 1.93901i | ||||
\(596\) | 18.7671 | − | 32.5056i | 0.768732 | − | 1.33148i | ||||
\(597\) | 11.2129 | + | 13.1905i | 0.458915 | + | 0.539850i | ||||
\(598\) | −3.88769 | + | 6.73368i | −0.158980 | + | 0.275361i | ||||
\(599\) | −22.9328 | + | 39.7207i | −0.937007 | + | 1.62294i | −0.165992 | + | 0.986127i | \(0.553083\pi\) |
−0.771015 | + | 0.636817i | \(0.780251\pi\) | |||||||
\(600\) | 3.52326 | − | 0.644551i | 0.143837 | − | 0.0263137i | ||||
\(601\) | −14.2594 | + | 24.6980i | −0.581652 | + | 1.00745i | 0.413632 | + | 0.910444i | \(0.364260\pi\) |
−0.995284 | + | 0.0970064i | \(0.969073\pi\) | |||||||
\(602\) | 15.6896 | + | 27.1752i | 0.639461 | + | 1.10758i | ||||
\(603\) | −6.23554 | + | 38.2215i | −0.253931 | + | 1.55650i | ||||
\(604\) | −6.74593 | − | 11.6843i | −0.274488 | − | 0.475427i | ||||
\(605\) | −19.2774 | − | 33.3894i | −0.783736 | − | 1.35747i | ||||
\(606\) | 18.7816 | + | 22.0939i | 0.762949 | + | 0.897504i | ||||
\(607\) | 14.8706 | + | 25.7567i | 0.603580 | + | 1.04543i | 0.992274 | + | 0.124065i | \(0.0395931\pi\) |
−0.388694 | + | 0.921367i | \(0.627074\pi\) | |||||||
\(608\) | −6.51104 | + | 34.5586i | −0.264058 | + | 1.40154i | ||||
\(609\) | −6.70370 | + | 18.7921i | −0.271648 | + | 0.761493i | ||||
\(610\) | −1.40467 | − | 2.43297i | −0.0568736 | − | 0.0985080i | ||||
\(611\) | 1.08065 | − | 1.87175i | 0.0437186 | − | 0.0757228i | ||||
\(612\) | −32.3023 | − | 26.4068i | −1.30574 | − | 1.06743i | ||||
\(613\) | −15.9215 | + | 27.5769i | −0.643065 | + | 1.11382i | 0.341680 | + | 0.939816i | \(0.389004\pi\) |
−0.984745 | + | 0.174005i | \(0.944329\pi\) | |||||||
\(614\) | 35.0648 | 1.41510 | ||||||||
\(615\) | 54.1991 | − | 9.91526i | 2.18552 | − | 0.399822i | ||||
\(616\) | 0.215617 | + | 0.373459i | 0.00868744 | + | 0.0150471i | ||||
\(617\) | −16.9134 | + | 29.2948i | −0.680907 | + | 1.17937i | 0.293797 | + | 0.955868i | \(0.405081\pi\) |
−0.974704 | + | 0.223498i | \(0.928252\pi\) | |||||||
\(618\) | 4.62331 | − | 12.9602i | 0.185977 | − | 0.521337i | ||||
\(619\) | −2.12694 | + | 3.68397i | −0.0854890 | + | 0.148071i | −0.905599 | − | 0.424134i | \(-0.860579\pi\) |
0.820111 | + | 0.572205i | \(0.193912\pi\) | |||||||
\(620\) | −6.72731 | −0.270175 | ||||||||
\(621\) | 0.197019 | + | 10.2477i | 0.00790609 | + | 0.411225i | ||||
\(622\) | 18.4492 | − | 31.9549i | 0.739745 | − | 1.28128i | ||||
\(623\) | −2.22200 | −0.0890227 | ||||||||
\(624\) | 12.7318 | − | 2.32918i | 0.509682 | − | 0.0932419i | ||||
\(625\) | 69.4352 | 2.77741 | ||||||||
\(626\) | −9.91764 | − | 17.1778i | −0.396388 | − | 0.686565i | ||||
\(627\) | 0.0533935 | − | 10.1083i | 0.00213233 | − | 0.403688i | ||||
\(628\) | 0.284964 | − | 0.493573i | 0.0113713 | − | 0.0196957i | ||||
\(629\) | −7.54983 | + | 13.0767i | −0.301032 | + | 0.521402i | ||||
\(630\) | 46.3372 | − | 17.5411i | 1.84612 | − | 0.698852i | ||||
\(631\) | −14.9006 | − | 25.8087i | −0.593185 | − | 1.02743i | −0.993800 | − | 0.111180i | \(-0.964537\pi\) |
0.400615 | − | 0.916246i | \(-0.368796\pi\) | |||||||
\(632\) | 0.427041 | + | 0.739657i | 0.0169868 | + | 0.0294220i | ||||
\(633\) | −3.48244 | + | 0.637084i | −0.138415 | + | 0.0253218i | ||||
\(634\) | −11.4691 | − | 19.8650i | −0.455496 | − | 0.788941i | ||||
\(635\) | 9.86626 | + | 17.0889i | 0.391531 | + | 0.678151i | ||||
\(636\) | 26.6161 | − | 4.86920i | 1.05540 | − | 0.193076i | ||||
\(637\) | −6.22178 | −0.246516 | ||||||||
\(638\) | 15.9612 | 0.631909 | ||||||||
\(639\) | 1.75141 | − | 10.7355i | 0.0692848 | − | 0.424690i | ||||
\(640\) | 2.76107 | + | 4.78231i | 0.109141 | + | 0.189037i | ||||
\(641\) | −7.37662 | − | 12.7767i | −0.291359 | − | 0.504649i | 0.682772 | − | 0.730631i | \(-0.260774\pi\) |
−0.974131 | + | 0.225983i | \(0.927441\pi\) | |||||||
\(642\) | 0.427307 | + | 0.502668i | 0.0168645 | + | 0.0198387i | ||||
\(643\) | 28.8099 | 1.13615 | 0.568076 | − | 0.822976i | \(-0.307688\pi\) | ||||
0.568076 | + | 0.822976i | \(0.307688\pi\) | |||||||
\(644\) | −8.01607 | −0.315878 | ||||||||
\(645\) | −37.3734 | − | 43.9647i | −1.47158 | − | 1.73111i | ||||
\(646\) | −55.5179 | + | 19.4750i | −2.18432 | + | 0.766233i | ||||
\(647\) | 6.79304 | 0.267062 | 0.133531 | − | 0.991045i | \(-0.457368\pi\) | ||||
0.133531 | + | 0.991045i | \(0.457368\pi\) | |||||||
\(648\) | −1.11262 | + | 0.983272i | −0.0437077 | + | 0.0386266i | ||||
\(649\) | −0.678817 | + | 1.17575i | −0.0266459 | + | 0.0461521i | ||||
\(650\) | −49.4077 | −1.93793 | ||||||||
\(651\) | −2.56701 | + | 0.469613i | −0.100609 | + | 0.0184056i | ||||
\(652\) | 8.34486 | − | 14.4537i | 0.326810 | − | 0.566051i | ||||
\(653\) | 1.09463 | + | 1.89596i | 0.0428363 | + | 0.0741946i | 0.886649 | − | 0.462444i | \(-0.153027\pi\) |
−0.843812 | + | 0.536638i | \(0.819694\pi\) | |||||||
\(654\) | 7.48669 | − | 1.36963i | 0.292753 | − | 0.0535566i | ||||
\(655\) | −79.1502 | −3.09265 | ||||||||
\(656\) | 14.5481 | + | 25.1981i | 0.568008 | + | 0.983819i | ||||
\(657\) | −2.39764 | + | 14.6966i | −0.0935408 | + | 0.573370i | ||||
\(658\) | 4.36901 | 0.170322 | ||||||||
\(659\) | 27.2122 | 1.06004 | 0.530019 | − | 0.847986i | \(-0.322185\pi\) | ||||
0.530019 | + | 0.847986i | \(0.322185\pi\) | |||||||
\(660\) | −13.0926 | − | 15.4016i | −0.509627 | − | 0.599506i | ||||
\(661\) | 1.30114 | − | 2.25364i | 0.0506086 | − | 0.0876566i | −0.839611 | − | 0.543188i | \(-0.817217\pi\) |
0.890220 | + | 0.455531i | \(0.150551\pi\) | |||||||
\(662\) | 9.35056 | 0.363420 | ||||||||
\(663\) | 14.6231 | + | 17.2021i | 0.567915 | + | 0.668074i | ||||
\(664\) | −1.04055 | + | 1.80229i | −0.0403812 | + | 0.0699423i | ||||
\(665\) | 6.59731 | − | 35.0165i | 0.255833 | − | 1.35788i | ||||
\(666\) | 10.6055 | + | 8.66995i | 0.410957 | + | 0.335954i | ||||
\(667\) | −5.81958 | + | 10.0798i | −0.225335 | + | 0.390292i | ||||
\(668\) | 21.5941 | + | 37.4020i | 0.835499 | + | 1.44713i | ||||
\(669\) | −29.4485 | − | 34.6421i | −1.13854 | − | 1.33934i | ||||
\(670\) | 109.207 | 4.21905 | ||||||||
\(671\) | −0.222312 | + | 0.385055i | −0.00858225 | + | 0.0148649i | ||||
\(672\) | 17.6687 | + | 20.7848i | 0.681585 | + | 0.801790i | ||||
\(673\) | 15.2685 | − | 26.4458i | 0.588558 | − | 1.01941i | −0.405863 | − | 0.913934i | \(-0.633029\pi\) |
0.994422 | − | 0.105479i | \(-0.0336375\pi\) | |||||||
\(674\) | −14.8135 | − | 25.6577i | −0.570594 | − | 0.988298i | ||||
\(675\) | −55.7675 | + | 33.6430i | −2.14649 | + | 1.29492i | ||||
\(676\) | −19.1372 | −0.736044 | ||||||||
\(677\) | −8.89435 | + | 15.4055i | −0.341838 | + | 0.592080i | −0.984774 | − | 0.173839i | \(-0.944383\pi\) |
0.642936 | + | 0.765920i | \(0.277716\pi\) | |||||||
\(678\) | 14.8888 | − | 41.7368i | 0.571800 | − | 1.60289i | ||||
\(679\) | −7.33784 | −0.281601 | ||||||||
\(680\) | −2.30774 | + | 3.99713i | −0.0884979 | + | 0.153283i | ||||
\(681\) | 14.4586 | − | 40.5310i | 0.554056 | − | 1.55315i | ||||
\(682\) | 1.04382 | + | 1.80795i | 0.0399699 | + | 0.0692299i | ||||
\(683\) | −35.2754 | −1.34978 | −0.674888 | − | 0.737920i | \(-0.735808\pi\) | ||||
−0.674888 | + | 0.737920i | \(0.735808\pi\) | |||||||
\(684\) | 4.75710 | + | 26.8024i | 0.181892 | + | 1.02481i | ||||
\(685\) | −23.7409 | −0.907092 | ||||||||
\(686\) | −20.0929 | − | 34.8018i | −0.767149 | − | 1.32874i | ||||
\(687\) | 30.6249 | + | 36.0259i | 1.16841 | + | 1.37448i | ||||
\(688\) | 15.2358 | − | 26.3892i | 0.580861 | − | 1.00608i | ||||
\(689\) | −14.6421 | −0.557818 | ||||||||
\(690\) | 28.4314 | − | 5.20128i | 1.08236 | − | 0.198009i | ||||
\(691\) | 1.14295 | − | 1.97964i | 0.0434797 | − | 0.0753090i | −0.843467 | − | 0.537182i | \(-0.819489\pi\) |
0.886946 | + | 0.461873i | \(0.152822\pi\) | |||||||
\(692\) | −37.2420 | −1.41573 | ||||||||
\(693\) | −6.07101 | − | 4.96300i | −0.230619 | − | 0.188529i | ||||
\(694\) | 30.4248 | + | 52.6973i | 1.15491 | + | 2.00036i | ||||
\(695\) | −14.9973 | + | 25.9761i | −0.568879 | + | 0.985328i | ||||
\(696\) | −1.65862 | + | 0.303430i | −0.0628697 | + | 0.0115015i | ||||
\(697\) | −25.3773 | + | 43.9547i | −0.961232 | + | 1.66490i | ||||
\(698\) | 5.62775 | 0.213013 | ||||||||
\(699\) | −10.3373 | + | 28.9780i | −0.390993 | + | 1.09605i | ||||
\(700\) | −25.4686 | − | 44.1128i | −0.962621 | − | 1.66731i | ||||
\(701\) | −1.58169 | + | 2.73956i | −0.0597395 | + | 0.103472i | −0.894348 | − | 0.447371i | \(-0.852360\pi\) |
0.834609 | + | 0.550843i | \(0.185694\pi\) | |||||||
\(702\) | 17.5381 | − | 10.5802i | 0.661933 | − | 0.399326i | ||||
\(703\) | 9.29622 | − | 3.26100i | 0.350614 | − | 0.122991i | ||||
\(704\) | 5.78366 | − | 10.0176i | 0.217980 | − | 0.377552i | ||||
\(705\) | −7.90301 | + | 1.44579i | −0.297645 | + | 0.0544516i | ||||
\(706\) | 20.4004 | 0.767779 | ||||||||
\(707\) | 8.08886 | − | 14.0103i | 0.304213 | − | 0.526912i | ||||
\(708\) | 1.22838 | − | 3.44345i | 0.0461655 | − | 0.129413i | ||||
\(709\) | −13.5961 | −0.510612 | −0.255306 | − | 0.966860i | \(-0.582176\pi\) | ||||
−0.255306 | + | 0.966860i | \(0.582176\pi\) | |||||||
\(710\) | −30.6737 | −1.15116 | ||||||||
\(711\) | −12.0240 | − | 9.82951i | −0.450935 | − | 0.368635i | ||||
\(712\) | −0.0938909 | − | 0.162624i | −0.00351871 | − | 0.00609458i | ||||
\(713\) | −1.52234 | −0.0570122 | ||||||||
\(714\) | −15.3346 | + | 42.9866i | −0.573884 | + | 1.60873i | ||||
\(715\) | 5.46941 | + | 9.47330i | 0.204544 | + | 0.354281i | ||||
\(716\) | −0.221169 | + | 0.383075i | −0.00826546 | + | 0.0143162i | ||||
\(717\) | −13.3439 | − | 15.6973i | −0.498338 | − | 0.586226i | ||||
\(718\) | −12.6225 | −0.471069 | ||||||||
\(719\) | −19.2497 | + | 33.3414i | −0.717891 | + | 1.24342i | 0.243943 | + | 0.969790i | \(0.421559\pi\) |
−0.961834 | + | 0.273634i | \(0.911774\pi\) | |||||||
\(720\) | −37.2501 | − | 30.4517i | −1.38823 | − | 1.13487i | ||||
\(721\) | −7.67666 | −0.285894 | ||||||||
\(722\) | 35.7542 | + | 13.9684i | 1.33063 | + | 0.519851i | ||||
\(723\) | 3.30418 | − | 0.604472i | 0.122884 | − | 0.0224806i | ||||
\(724\) | −33.2704 | −1.23649 | ||||||||
\(725\) | −73.9596 | −2.74679 | ||||||||
\(726\) | 10.8254 | − | 30.3461i | 0.401767 | − | 1.12625i | ||||
\(727\) | −25.9243 | − | 44.9022i | −0.961478 | − | 1.66533i | −0.718794 | − | 0.695224i | \(-0.755305\pi\) |
−0.242685 | − | 0.970105i | \(-0.578028\pi\) | |||||||
\(728\) | 0.314205 | + | 0.544219i | 0.0116452 | + | 0.0201701i | ||||
\(729\) | 12.5913 | − | 23.8843i | 0.466343 | − | 0.884604i | ||||
\(730\) | 41.9916 | 1.55418 | ||||||||
\(731\) | 53.1538 | 1.96596 | ||||||||
\(732\) | 0.402294 | − | 1.12773i | 0.0148692 | − | 0.0416819i | ||||
\(733\) | 12.1069 | + | 20.9698i | 0.447179 | + | 0.774536i | 0.998201 | − | 0.0599543i | \(-0.0190955\pi\) |
−0.551023 | + | 0.834490i | \(0.685762\pi\) | |||||||
\(734\) | 2.91967 | + | 5.05701i | 0.107767 | + | 0.186658i | ||||
\(735\) | 14.9796 | + | 17.6215i | 0.552533 | + | 0.649979i | ||||
\(736\) | 7.95698 | + | 13.7819i | 0.293298 | + | 0.508007i | ||||
\(737\) | −8.64190 | − | 14.9682i | −0.318328 | − | 0.551361i | ||||
\(738\) | 35.6484 | + | 29.1423i | 1.31224 | + | 1.07274i | ||||
\(739\) | −5.83272 | + | 10.1026i | −0.214560 | + | 0.371629i | −0.953136 | − | 0.302541i | \(-0.902165\pi\) |
0.738576 | + | 0.674170i | \(0.235498\pi\) | |||||||
\(740\) | 9.85037 | − | 17.0613i | 0.362107 | − | 0.627187i | ||||
\(741\) | 0.0778072 | − | 14.7303i | 0.00285832 | − | 0.541130i | ||||
\(742\) | −14.7992 | − | 25.6330i | −0.543296 | − | 0.941017i | ||||
\(743\) | −16.0857 | −0.590127 | −0.295063 | − | 0.955478i | \(-0.595341\pi\) | ||||
−0.295063 | + | 0.955478i | \(0.595341\pi\) | |||||||
\(744\) | −0.142839 | − | 0.168031i | −0.00523675 | − | 0.00616031i | ||||
\(745\) | 75.5025 | 2.76620 | ||||||||
\(746\) | 14.8771 | − | 25.7679i | 0.544690 | − | 0.943431i | ||||
\(747\) | 6.09313 | − | 37.3486i | 0.222936 | − | 1.36651i | ||||
\(748\) | 18.6207 | 0.680841 | ||||||||
\(749\) | 0.184033 | − | 0.318755i | 0.00672442 | − | 0.0116470i | ||||
\(750\) | 71.5026 | + | 84.1130i | 2.61091 | + | 3.07137i | ||||
\(751\) | 11.5670 | − | 20.0346i | 0.422084 | − | 0.731071i | −0.574059 | − | 0.818814i | \(-0.694632\pi\) |
0.996143 | + | 0.0877427i | \(0.0279653\pi\) | |||||||
\(752\) | −2.12132 | − | 3.67424i | −0.0773567 | − | 0.133986i | ||||
\(753\) | 19.5154 | + | 22.9572i | 0.711180 | + | 0.836606i | ||||
\(754\) | 23.2592 | 0.847052 | ||||||||
\(755\) | 13.5698 | − | 23.5036i | 0.493857 | − | 0.855385i | ||||
\(756\) | 18.4869 | + | 10.2047i | 0.672362 | + | 0.371142i | ||||
\(757\) | 3.49346 | − | 6.05085i | 0.126972 | − | 0.219922i | −0.795530 | − | 0.605914i | \(-0.792807\pi\) |
0.922502 | + | 0.385992i | \(0.126141\pi\) | |||||||
\(758\) | 11.8796 | + | 20.5760i | 0.431485 | + | 0.747354i | ||||
\(759\) | −2.96275 | − | 3.48527i | −0.107541 | − | 0.126507i | ||||
\(760\) | 2.84156 | − | 0.996782i | 0.103074 | − | 0.0361571i | ||||
\(761\) | −6.33130 | − | 10.9661i | −0.229510 | − | 0.397522i | 0.728153 | − | 0.685414i | \(-0.240379\pi\) |
−0.957663 | + | 0.287892i | \(0.907046\pi\) | |||||||
\(762\) | −5.54048 | + | 15.5313i | −0.200710 | + | 0.562639i | ||||
\(763\) | −2.12303 | − | 3.67720i | −0.0768589 | − | 0.133124i | ||||
\(764\) | 14.2999 | + | 24.7682i | 0.517352 | + | 0.896080i | ||||
\(765\) | 13.5134 | − | 82.8320i | 0.488578 | − | 2.99480i | ||||
\(766\) | −31.2202 | − | 54.0749i | −1.12803 | − | 1.95381i | ||||
\(767\) | −0.989200 | + | 1.71334i | −0.0357179 | + | 0.0618653i | ||||
\(768\) | 8.50499 | − | 23.8415i | 0.306898 | − | 0.860307i | ||||
\(769\) | 14.6931 | − | 25.4492i | 0.529847 | − | 0.917722i | −0.469547 | − | 0.882908i | \(-0.655583\pi\) |
0.999394 | − | 0.0348142i | \(-0.0110839\pi\) | |||||||
\(770\) | −11.0562 | + | 19.1500i | −0.398439 | + | 0.690117i | ||||
\(771\) | −16.4002 | + | 45.9736i | −0.590638 | + | 1.65570i | ||||
\(772\) | 15.0774 | − | 26.1148i | 0.542647 | − | 0.939892i | ||||
\(773\) | 15.3004 | + | 26.5010i | 0.550316 | + | 0.953176i | 0.998252 | + | 0.0591096i | \(0.0188261\pi\) |
−0.447935 | + | 0.894066i | \(0.647841\pi\) | |||||||
\(774\) | 7.76423 | − | 47.5918i | 0.279079 | − | 1.71065i | ||||
\(775\) | −4.83677 | − | 8.37753i | −0.173742 | − | 0.300930i | ||||
\(776\) | −0.310061 | − | 0.537042i | −0.0111305 | − | 0.0192787i | ||||
\(777\) | 2.56771 | − | 7.19791i | 0.0921161 | − | 0.258223i | ||||
\(778\) | 14.3215 | + | 24.8056i | 0.513451 | + | 0.889322i | ||||
\(779\) | 31.2474 | − | 10.9612i | 1.11955 | − | 0.392725i | ||||
\(780\) | −19.0790 | − | 22.4438i | −0.683138 | − | 0.803618i | ||||
\(781\) | 2.42730 | + | 4.20421i | 0.0868556 | + | 0.150438i | ||||
\(782\) | −13.3122 | + | 23.0574i | −0.476044 | + | 0.824533i | ||||
\(783\) | 26.2532 | − | 15.8378i | 0.938213 | − | 0.565998i | ||||
\(784\) | −6.10668 | + | 10.5771i | −0.218096 | + | 0.377753i | ||||
\(785\) | 1.14645 | 0.0409184 | ||||||||
\(786\) | −42.8401 | − | 50.3955i | −1.52806 | − | 1.79755i | ||||
\(787\) | 1.32618 | + | 2.29700i | 0.0472731 | + | 0.0818794i | 0.888694 | − | 0.458501i | \(-0.151614\pi\) |
−0.841421 | + | 0.540381i | \(0.818280\pi\) | |||||||
\(788\) | −17.3486 | + | 30.0487i | −0.618019 | + | 1.07044i | ||||
\(789\) | −1.34461 | − | 1.58174i | −0.0478693 | − | 0.0563116i | ||||
\(790\) | −21.8975 | + | 37.9276i | −0.779079 | + | 1.34940i | ||||
\(791\) | −24.7217 | −0.879003 | ||||||||
\(792\) | 0.106701 | − | 0.654037i | 0.00379145 | − | 0.0232402i | ||||
\(793\) | −0.323962 | + | 0.561118i | −0.0115042 | + | 0.0199259i | ||||
\(794\) | −14.0938 | −0.500170 | ||||||||
\(795\) | 35.2524 | + | 41.4696i | 1.25027 | + | 1.47078i | ||||
\(796\) | 20.8068 | 0.737479 | ||||||||
\(797\) | 4.98622 | + | 8.63638i | 0.176621 | + | 0.305916i | 0.940721 | − | 0.339181i | \(-0.110150\pi\) |
−0.764100 | + | 0.645098i | \(0.776817\pi\) | |||||||
\(798\) | 25.8661 | − | 14.7522i | 0.915649 | − | 0.522221i | ||||
\(799\) | 3.70037 | − | 6.40923i | 0.130910 | − | 0.226742i | ||||
\(800\) | −50.5616 | + | 87.5752i | −1.78762 | + | 3.09625i | ||||
\(801\) | 2.64364 | + | 2.16115i | 0.0934084 | + | 0.0763606i | ||||
\(802\) | 16.9589 | + | 29.3736i | 0.598839 | + | 1.03722i | ||||
\(803\) | −3.32291 | − | 5.75545i | −0.117263 | − | 0.203106i | ||||
\(804\) | 30.1456 | + | 35.4622i | 1.06315 | + | 1.25065i | ||||
\(805\) | −8.06240 | − | 13.9645i | −0.284162 | − | 0.492184i | ||||
\(806\) | 1.52110 | + | 2.63461i | 0.0535783 | + | 0.0928003i | ||||
\(807\) | −4.07032 | + | 11.4101i | −0.143282 | + | 0.401653i | ||||
\(808\) | 1.36718 | 0.0480973 | ||||||||
\(809\) | 35.7179 | 1.25578 | 0.627888 | − | 0.778304i | \(-0.283920\pi\) | ||||
0.627888 | + | 0.778304i | \(0.283920\pi\) | |||||||
\(810\) | −72.1906 | − | 24.1987i | −2.53652 | − | 0.850256i | ||||
\(811\) | 0.139604 | + | 0.241802i | 0.00490217 | + | 0.00849080i | 0.868466 | − | 0.495749i | \(-0.165106\pi\) |
−0.863564 | + | 0.504239i | \(0.831773\pi\) | |||||||
\(812\) | 11.9896 | + | 20.7666i | 0.420753 | + | 0.728766i | ||||
\(813\) | −7.21466 | + | 20.2244i | −0.253029 | + | 0.709301i | ||||
\(814\) | −6.11359 | −0.214281 | ||||||||
\(815\) | 33.5724 | 1.17599 | ||||||||
\(816\) | 43.5963 | − | 7.97558i | 1.52618 | − | 0.279201i | ||||
\(817\) | −26.3037 | − | 22.6006i | −0.920249 | − | 0.790695i | ||||
\(818\) | −27.0725 | −0.946568 | ||||||||
\(819\) | −8.84692 | − | 7.23228i | −0.309136 | − | 0.252716i | ||||
\(820\) | 33.1101 | − | 57.3483i | 1.15625 | − | 2.00269i | ||||
\(821\) | 39.8386 | 1.39038 | 0.695188 | − | 0.718828i | \(-0.255321\pi\) | ||||
0.695188 | + | 0.718828i | \(0.255321\pi\) | |||||||
\(822\) | −12.8498 | − | 15.1160i | −0.448187 | − | 0.527231i | ||||
\(823\) | 17.6480 | − | 30.5672i | 0.615171 | − | 1.06551i | −0.375184 | − | 0.926950i | \(-0.622420\pi\) |
0.990355 | − | 0.138557i | \(-0.0442463\pi\) | |||||||
\(824\) | −0.324378 | − | 0.561839i | −0.0113002 | − | 0.0195726i | ||||
\(825\) | 9.76640 | − | 27.3775i | 0.340022 | − | 0.953163i | ||||
\(826\) | −3.99927 | −0.139152 | ||||||||
\(827\) | −3.59739 | − | 6.23087i | −0.125094 | − | 0.216669i | 0.796676 | − | 0.604407i | \(-0.206590\pi\) |
−0.921770 | + | 0.387738i | \(0.873256\pi\) | |||||||
\(828\) | 9.53717 | + | 7.79656i | 0.331439 | + | 0.270949i | ||||
\(829\) | 23.9258 | 0.830976 | 0.415488 | − | 0.909599i | \(-0.363611\pi\) | ||||
0.415488 | + | 0.909599i | \(0.363611\pi\) | |||||||
\(830\) | −106.713 | −3.70407 | ||||||||
\(831\) | −11.3534 | + | 31.8263i | −0.393846 | + | 1.10404i | ||||
\(832\) | 8.42817 | − | 14.5980i | 0.292194 | − | 0.506096i | ||||
\(833\) | −21.3046 | −0.738161 | ||||||||
\(834\) | −24.6564 | + | 4.51069i | −0.853782 | + | 0.156192i | ||||
\(835\) | −43.4377 | + | 75.2364i | −1.50323 | + | 2.60366i | ||||
\(836\) | −9.21464 | − | 7.91739i | −0.318695 | − | 0.273829i | ||||
\(837\) | 3.51087 | + | 1.93799i | 0.121353 | + | 0.0669868i | ||||
\(838\) | −10.6830 | + | 18.5034i | −0.369037 | + | 0.639190i | ||||
\(839\) | −5.33632 | − | 9.24278i | −0.184230 | − | 0.319096i | 0.759087 | − | 0.650990i | \(-0.225646\pi\) |
−0.943317 | + | 0.331893i | \(0.892313\pi\) | |||||||
\(840\) | 0.784867 | − | 2.20017i | 0.0270805 | − | 0.0759130i | ||||
\(841\) | 5.81733 | 0.200598 | ||||||||
\(842\) | −19.4626 | + | 33.7103i | −0.670727 | + | 1.16173i | ||||
\(843\) | 41.1454 | − | 7.52721i | 1.41712 | − | 0.259251i | ||||
\(844\) | −2.12741 | + | 3.68479i | −0.0732286 | + | 0.126836i | ||||
\(845\) | −19.2478 | − | 33.3381i | −0.662143 | − | 1.14687i | ||||
\(846\) | −5.19806 | − | 4.24937i | −0.178713 | − | 0.146096i | ||||
\(847\) | −17.9747 | −0.617618 | ||||||||
\(848\) | −14.3712 | + | 24.8916i | −0.493509 | + | 0.854782i | ||||
\(849\) | −36.1338 | + | 6.61037i | −1.24011 | + | 0.226867i | ||||
\(850\) | −169.182 | −5.80288 | ||||||||
\(851\) | 2.22907 | − | 3.86086i | 0.0764115 | − | 0.132349i | ||||
\(852\) | −8.46717 | − | 9.96046i | −0.290081 | − | 0.341240i | ||||
\(853\) | −16.1031 | − | 27.8914i | −0.551359 | − | 0.954982i | −0.998177 | − | 0.0603572i | \(-0.980776\pi\) |
0.446818 | − | 0.894625i | \(-0.352557\pi\) | |||||||
\(854\) | −1.30975 | −0.0448189 | ||||||||
\(855\) | −41.9068 | + | 35.2444i | −1.43318 | + | 1.20533i | ||||
\(856\) | 0.0311053 | 0.00106316 | ||||||||
\(857\) | −10.8449 | − | 18.7838i | −0.370453 | − | 0.641644i | 0.619182 | − | 0.785247i | \(-0.287464\pi\) |
−0.989635 | + | 0.143604i | \(0.954131\pi\) | |||||||
\(858\) | −3.07139 | + | 8.60985i | −0.104856 | + | 0.293935i | ||||
\(859\) | −10.7990 | + | 18.7044i | −0.368457 | + | 0.638186i | −0.989324 | − | 0.145729i | \(-0.953447\pi\) |
0.620868 | + | 0.783915i | \(0.286780\pi\) | |||||||
\(860\) | −69.3505 | −2.36483 | ||||||||
\(861\) | 8.63085 | − | 24.1943i | 0.294139 | − | 0.824540i | ||||
\(862\) | −27.8166 | + | 48.1797i | −0.947436 | + | 1.64101i | ||||
\(863\) | −38.7369 | −1.31862 | −0.659309 | − | 0.751872i | \(-0.729151\pi\) | ||||
−0.659309 | + | 0.751872i | \(0.729151\pi\) | |||||||
\(864\) | −0.805819 | − | 41.9136i | −0.0274145 | − | 1.42593i | ||||
\(865\) | −37.4572 | − | 64.8778i | −1.27358 | − | 2.20591i | ||||
\(866\) | 22.1531 | − | 38.3704i | 0.752794 | − | 1.30388i | ||||
\(867\) | 31.0015 | + | 36.4690i | 1.05287 | + | 1.23855i | ||||
\(868\) | −1.56818 | + | 2.71617i | −0.0532275 | + | 0.0921928i | ||||
\(869\) | 6.93125 | 0.235127 | ||||||||
\(870\) | −55.9993 | − | 65.8754i | −1.89855 | − | 2.23339i | ||||
\(871\) | −12.5933 | − | 21.8123i | −0.426708 | − | 0.739080i | ||||
\(872\) | 0.179418 | − | 0.310761i | 0.00607585 | − | 0.0105237i | ||||
\(873\) | 8.73024 | + | 7.13690i | 0.295474 | + | 0.241547i | ||||
\(874\) | 16.3915 | − | 5.74994i | 0.554452 | − | 0.194495i | ||||
\(875\) | 30.7948 | − | 53.3382i | 1.04106 | − | 1.80316i | ||||
\(876\) | 11.5913 | + | 13.6356i | 0.391635 | + | 0.460705i | ||||
\(877\) | 48.4496 | 1.63603 | 0.818014 | − | 0.575198i | \(-0.195075\pi\) | ||||
0.818014 | + | 0.575198i | \(0.195075\pi\) | |||||||
\(878\) | −14.3673 | + | 24.8849i | −0.484873 | + | 0.839825i | ||||
\(879\) | −17.5951 | − | 20.6982i | −0.593469 | − | 0.698135i | ||||
\(880\) | 21.4729 | 0.723852 | ||||||||
\(881\) | 40.7710 | 1.37361 | 0.686804 | − | 0.726842i | \(-0.259013\pi\) | ||||
0.686804 | + | 0.726842i | \(0.259013\pi\) | |||||||
\(882\) | −3.11198 | + | 19.0753i | −0.104786 | + | 0.642299i | ||||
\(883\) | 13.5637 | + | 23.4930i | 0.456455 | + | 0.790604i | 0.998771 | − | 0.0495713i | \(-0.0157855\pi\) |
−0.542315 | + | 0.840175i | \(0.682452\pi\) | |||||||
\(884\) | 27.1348 | 0.912644 | ||||||||
\(885\) | 7.23419 | − | 1.32343i | 0.243175 | − | 0.0444867i | ||||
\(886\) | 14.3778 | + | 24.9030i | 0.483030 | + | 0.836633i | ||||
\(887\) | 20.7932 | − | 36.0149i | 0.698169 | − | 1.20926i | −0.270932 | − | 0.962598i | \(-0.587332\pi\) |
0.969101 | − | 0.246665i | \(-0.0793348\pi\) | |||||||
\(888\) | 0.635299 | − | 0.116223i | 0.0213192 | − | 0.00390017i | ||||
\(889\) | 9.19956 | 0.308543 | ||||||||
\(890\) | 4.81447 | − | 8.33891i | 0.161381 | − | 0.279521i | ||||
\(891\) | 2.39592 | + | 11.8095i | 0.0802665 | + | 0.395634i | ||||
\(892\) | −54.6450 | −1.82965 | ||||||||
\(893\) | −4.55632 | + | 1.59830i | −0.152471 | + | 0.0534850i | ||||
\(894\) | 40.8658 | + | 48.0730i | 1.36676 | + | 1.60780i | ||||
\(895\) | −0.889787 | −0.0297423 | ||||||||
\(896\) | 2.57449 | 0.0860077 | ||||||||
\(897\) | −4.31744 | − | 5.07888i | −0.144155 | − | 0.169579i | ||||
\(898\) | 3.14636 | + | 5.44966i | 0.104995 | + | 0.181857i | ||||
\(899\) | 2.27696 | + | 3.94382i | 0.0759410 | + | 0.131534i | ||||
\(900\) | −12.6035 | + | 77.2546i | −0.420116 | + | 2.57515i | ||||
\(901\) | −50.1373 | −1.67031 | ||||||||
\(902\) | −20.5496 | −0.684227 | ||||||||
\(903\) | −26.4628 | + | 4.84115i | −0.880627 | + | 0.161103i | ||||
\(904\) | −1.04462 | − | 1.80933i | −0.0347435 | − | 0.0601775i | ||||
\(905\) | −33.4627 | − | 57.9592i | −1.11234 | − | 1.92663i | ||||
\(906\) | 22.3096 | − | 4.08136i | 0.741187 | − | 0.135594i | ||||
\(907\) | 9.34320 | + | 16.1829i | 0.310236 | + | 0.537344i | 0.978413 | − | 0.206658i | \(-0.0662586\pi\) |
−0.668177 | + | 0.744002i | \(0.732925\pi\) | |||||||
\(908\) | −25.8594 | − | 44.7897i | −0.858173 | − | 1.48640i | ||||
\(909\) | −23.2504 | + | 8.80150i | −0.771168 | + | 0.291927i | ||||
\(910\) | −16.1116 | + | 27.9061i | −0.534094 | + | 0.925078i | ||||
\(911\) | −1.65127 | + | 2.86008i | −0.0547090 | + | 0.0947587i | −0.892083 | − | 0.451872i | \(-0.850756\pi\) |
0.837374 | + | 0.546631i | \(0.184090\pi\) | |||||||
\(912\) | −24.9652 | − | 14.5900i | −0.826681 | − | 0.483124i | ||||
\(913\) | 8.44453 | + | 14.6264i | 0.279473 | + | 0.484062i | ||||
\(914\) | 23.3506 | 0.772370 | ||||||||
\(915\) | 2.36919 | − | 0.433423i | 0.0783229 | − | 0.0143285i | ||||
\(916\) | 56.8278 | 1.87764 | ||||||||
\(917\) | −18.4504 | + | 31.9571i | −0.609287 | + | 1.05532i | ||||
\(918\) | 60.0539 | − | 36.2288i | 1.98207 | − | 1.19573i | ||||
\(919\) | 11.0557 | 0.364695 | 0.182348 | − | 0.983234i | \(-0.441630\pi\) | ||||
0.182348 | + | 0.983234i | \(0.441630\pi\) | |||||||
\(920\) | 0.681355 | − | 1.18014i | 0.0224636 | − | 0.0389081i | ||||
\(921\) | −10.1005 | + | 28.3140i | −0.332822 | + | 0.932979i | ||||
\(922\) | −5.58115 | + | 9.66683i | −0.183805 | + | 0.318360i | ||||
\(923\) | 3.53716 | + | 6.12654i | 0.116427 | + | 0.201657i | ||||
\(924\) | −9.27039 | + | 1.69594i | −0.304973 | + | 0.0557923i | ||||
\(925\) | 28.3287 | 0.931441 | ||||||||
\(926\) | 12.3533 | − | 21.3966i | 0.405956 | − | 0.703136i | ||||
\(927\) | 9.13335 | + | 7.46644i | 0.299979 | + | 0.245230i | ||||
\(928\) | 23.8024 | − | 41.2270i | 0.781354 | − | 1.35334i | ||||
\(929\) | 13.2406 | + | 22.9334i | 0.434411 | + | 0.752422i | 0.997247 | − | 0.0741463i | \(-0.0236232\pi\) |
−0.562836 | + | 0.826568i | \(0.690290\pi\) | |||||||
\(930\) | 3.79961 | − | 10.6512i | 0.124594 | − | 0.349267i | ||||
\(931\) | 10.5428 | + | 9.05856i | 0.345526 | + | 0.296882i | ||||
\(932\) | 18.4884 | + | 32.0228i | 0.605607 | + | 1.04894i | ||||
\(933\) | 20.4886 | + | 24.1020i | 0.670766 | + | 0.789064i | ||||
\(934\) | 2.24635 | + | 3.89080i | 0.0735029 | + | 0.127311i | ||||
\(935\) | 18.7283 | + | 32.4384i | 0.612482 | + | 1.06085i | ||||
\(936\) | 0.155489 | − | 0.953088i | 0.00508231 | − | 0.0311527i | ||||
\(937\) | −2.52504 | − | 4.37349i | −0.0824894 | − | 0.142876i | 0.821829 | − | 0.569734i | \(-0.192954\pi\) |
−0.904319 | + | 0.426858i | \(0.859620\pi\) | |||||||
\(938\) | 25.4570 | − | 44.0928i | 0.831199 | − | 1.43968i | ||||
\(939\) | 16.7275 | − | 3.06016i | 0.545882 | − | 0.0998646i | ||||
\(940\) | −4.82792 | + | 8.36221i | −0.157470 | + | 0.272745i | ||||
\(941\) | −2.94492 | + | 5.10075i | −0.0960016 | + | 0.166280i | −0.910026 | − | 0.414551i | \(-0.863939\pi\) |
0.814025 | + | 0.580830i | \(0.197272\pi\) | |||||||
\(942\) | 0.620515 | + | 0.729950i | 0.0202175 | + | 0.0237831i | ||||
\(943\) | 7.49257 | − | 12.9775i | 0.243992 | − | 0.422606i | ||||
\(944\) | 1.94180 | + | 3.36330i | 0.0632002 | + | 0.109466i | ||||
\(945\) | 0.816496 | + | 42.4690i | 0.0265606 | + | 1.38152i | ||||
\(946\) | 10.7605 | + | 18.6378i | 0.349855 | + | 0.605966i | ||||
\(947\) | −22.9230 | − | 39.7039i | −0.744899 | − | 1.29020i | −0.950242 | − | 0.311513i | \(-0.899164\pi\) |
0.205343 | − | 0.978690i | \(-0.434169\pi\) | |||||||
\(948\) | −18.3606 | + | 3.35891i | −0.596323 | + | 0.109092i | ||||
\(949\) | −4.84228 | − | 8.38708i | −0.157187 | − | 0.272256i | ||||
\(950\) | 83.7211 | + | 71.9347i | 2.71627 | + | 2.33387i | ||||
\(951\) | 19.3443 | − | 3.53887i | 0.627281 | − | 0.114756i | ||||
\(952\) | 1.07590 | + | 1.86351i | 0.0348701 | + | 0.0603968i | ||||
\(953\) | −10.9280 | + | 18.9279i | −0.353993 | + | 0.613134i | −0.986945 | − | 0.161057i | \(-0.948510\pi\) |
0.632952 | + | 0.774191i | \(0.281843\pi\) | |||||||
\(954\) | −7.32360 | + | 44.8909i | −0.237110 | + | 1.45340i | ||||
\(955\) | −28.7651 | + | 49.8226i | −0.930817 | + | 1.61222i | ||||
\(956\) | −24.7611 | −0.800832 | ||||||||
\(957\) | −4.59764 | + | 12.8883i | −0.148621 | + | 0.416619i | ||||
\(958\) | 14.0590 | + | 24.3509i | 0.454225 | + | 0.786741i | ||||
\(959\) | −5.53415 | + | 9.58544i | −0.178707 | + | 0.309530i | ||||
\(960\) | −61.6367 | + | 11.2759i | −1.98932 | + | 0.363928i | ||||
\(961\) | 15.2022 | − | 26.3310i | 0.490393 | − | 0.849386i | ||||
\(962\) | −8.90897 | −0.287237 | ||||||||
\(963\) | −0.528980 | + | 0.200247i | −0.0170461 | + | 0.00645286i | ||||
\(964\) | 2.01852 | − | 3.49617i | 0.0650120 | − | 0.112604i | ||||
\(965\) | 60.6581 | 1.95265 | ||||||||
\(966\) | 4.52751 | − | 12.6917i | 0.145670 | − | 0.408348i | ||||
\(967\) | −32.8276 | −1.05567 | −0.527833 | − | 0.849348i | \(-0.676995\pi\) | ||||
−0.527833 | + | 0.849348i | \(0.676995\pi\) | |||||||
\(968\) | −0.759523 | − | 1.31553i | −0.0244120 | − | 0.0422828i | ||||
\(969\) | 0.266427 | − | 50.4393i | 0.00855887 | − | 1.62034i | ||||
\(970\) | 15.8991 | − | 27.5380i | 0.510489 | − | 0.884193i | ||||
\(971\) | 10.5807 | − | 18.3264i | 0.339552 | − | 0.588121i | −0.644797 | − | 0.764354i | \(-0.723058\pi\) |
0.984348 | + | 0.176233i | \(0.0563913\pi\) | |||||||
\(972\) | −12.0696 | − | 30.1218i | −0.387133 | − | 0.966156i | ||||
\(973\) | 6.99193 | + | 12.1104i | 0.224151 | + | 0.388241i | ||||
\(974\) | −24.7803 | − | 42.9207i | −0.794012 | − | 1.37527i | ||||
\(975\) | 14.2320 | − | 39.8956i | 0.455788 | − | 1.27768i | ||||
\(976\) | 0.635937 | + | 1.10147i | 0.0203558 | + | 0.0352573i | ||||
\(977\) | −25.9506 | − | 44.9478i | −0.830234 | − | 1.43801i | −0.897853 | − | 0.440296i | \(-0.854874\pi\) |
0.0676189 | − | 0.997711i | \(-0.478460\pi\) | |||||||
\(978\) | 18.1711 | + | 21.3758i | 0.581047 | + | 0.683522i | ||||
\(979\) | −1.52393 | −0.0487051 | ||||||||
\(980\) | 27.7964 | 0.887924 | ||||||||
\(981\) | −1.05061 | + | 6.43986i | −0.0335435 | + | 0.205609i | ||||
\(982\) | 17.5806 | + | 30.4505i | 0.561020 | + | 0.971715i | ||||
\(983\) | 0.305071 | + | 0.528398i | 0.00973025 | + | 0.0168533i | 0.870850 | − | 0.491550i | \(-0.163569\pi\) |
−0.861119 | + | 0.508403i | \(0.830236\pi\) | |||||||
\(984\) | 2.13543 | − | 0.390659i | 0.0680750 | − | 0.0124537i | ||||
\(985\) | −69.7955 | −2.22387 | ||||||||
\(986\) | 79.6442 | 2.53639 | ||||||||
\(987\) | −1.25850 | + | 3.52788i | −0.0400586 | + | 0.112294i | ||||
\(988\) | −13.4279 | − | 11.5375i | −0.427200 | − | 0.367058i | ||||
\(989\) | −15.6935 | −0.499025 | ||||||||
\(990\) | 31.7798 | − | 12.0303i | 1.01003 | − | 0.382348i | ||||
\(991\) | 25.6460 | − | 44.4202i | 0.814673 | − | 1.41106i | −0.0948888 | − | 0.995488i | \(-0.530250\pi\) |
0.909562 | − | 0.415568i | \(-0.136417\pi\) | |||||||
\(992\) | 6.22648 | 0.197691 | ||||||||
\(993\) | −2.69345 | + | 7.55037i | −0.0854739 | + | 0.239604i | ||||
\(994\) | −7.15025 | + | 12.3846i | −0.226792 | + | 0.392815i | ||||
\(995\) | 20.9271 | + | 36.2468i | 0.663434 | + | 1.14910i | ||||
\(996\) | −29.4571 | − | 34.6523i | −0.933385 | − | 1.09800i | ||||
\(997\) | −4.42088 | −0.140011 | −0.0700054 | − | 0.997547i | \(-0.522302\pi\) | ||||
−0.0700054 | + | 0.997547i | \(0.522302\pi\) | |||||||
\(998\) | −38.7976 | − | 67.1994i | −1.22812 | − | 2.12716i | ||||
\(999\) | −10.0557 | + | 6.06635i | −0.318150 | + | 0.191931i |
(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 | 171.2.g.c.106.13 | ✓ | 32 | |
3.2 | odd | 2 | 513.2.g.c.505.4 | 32 | |||
9.4 | even | 3 | 171.2.h.c.49.4 | yes | 32 | ||
9.5 | odd | 6 | 513.2.h.c.334.13 | 32 | |||
19.7 | even | 3 | 171.2.h.c.7.4 | yes | 32 | ||
57.26 | odd | 6 | 513.2.h.c.235.13 | 32 | |||
171.121 | even | 3 | inner | 171.2.g.c.121.13 | yes | 32 | |
171.140 | odd | 6 | 513.2.g.c.64.4 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.2.g.c.106.13 | ✓ | 32 | 1.1 | even | 1 | trivial | |
171.2.g.c.121.13 | yes | 32 | 171.121 | even | 3 | inner | |
171.2.h.c.7.4 | yes | 32 | 19.7 | even | 3 | ||
171.2.h.c.49.4 | yes | 32 | 9.4 | even | 3 | ||
513.2.g.c.64.4 | 32 | 171.140 | odd | 6 | |||
513.2.g.c.505.4 | 32 | 3.2 | odd | 2 | |||
513.2.h.c.235.13 | 32 | 57.26 | odd | 6 | |||
513.2.h.c.334.13 | 32 | 9.5 | odd | 6 |