Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [471,2,Mod(169,471)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(471, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("471.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 471 = 3 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 471.e (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: | \(3.76095393520\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 301.8 | ||
Character | \(\chi\) | \(=\) | 471.301 |
Dual form | 471.2.e.b.169.8 |
$q$-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 \(\left(\mathbb{Z}/471\mathbb{Z}\right)^\times\).
\(n\) | \(158\) | \(319\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.32447 | 0.936544 | 0.468272 | − | 0.883584i | \(-0.344877\pi\) | ||||
0.468272 | + | 0.883584i | \(0.344877\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.245772 | −0.122886 | ||||||||
\(5\) | −2.05322 | + | 3.55628i | −0.918229 | + | 1.59042i | −0.116124 | + | 0.993235i | \(0.537047\pi\) |
−0.802104 | + | 0.597184i | \(0.796286\pi\) | |||||||
\(6\) | 0.662236 | − | 1.14703i | 0.270357 | − | 0.468272i | ||||
\(7\) | −3.69381 | −1.39613 | −0.698064 | − | 0.716035i | \(-0.745955\pi\) | ||||
−0.698064 | + | 0.716035i | \(0.745955\pi\) | |||||||
\(8\) | −2.97446 | −1.05163 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −2.71944 | + | 4.71020i | −0.859961 | + | 1.48950i | ||||
\(11\) | 0.214620 | − | 0.371733i | 0.0647105 | − | 0.112082i | −0.831855 | − | 0.554993i | \(-0.812721\pi\) |
0.896566 | + | 0.442911i | \(0.146054\pi\) | |||||||
\(12\) | −0.122886 | + | 0.212845i | −0.0354741 | + | 0.0614430i | ||||
\(13\) | 1.17636 | + | 2.03752i | 0.326265 | + | 0.565107i | 0.981768 | − | 0.190086i | \(-0.0608765\pi\) |
−0.655503 | + | 0.755193i | \(0.727543\pi\) | |||||||
\(14\) | −4.89235 | −1.30753 | ||||||||
\(15\) | 2.05322 | + | 3.55628i | 0.530139 | + | 0.918229i | ||||
\(16\) | −3.44805 | −0.862013 | ||||||||
\(17\) | 0.765484 | − | 1.32586i | 0.185657 | − | 0.321568i | −0.758141 | − | 0.652091i | \(-0.773892\pi\) |
0.943798 | + | 0.330523i | \(0.107225\pi\) | |||||||
\(18\) | −0.662236 | − | 1.14703i | −0.156091 | − | 0.270357i | ||||
\(19\) | −3.35849 | + | 5.81708i | −0.770492 | + | 1.33453i | 0.166802 | + | 0.985990i | \(0.446656\pi\) |
−0.937294 | + | 0.348540i | \(0.886677\pi\) | |||||||
\(20\) | 0.504625 | − | 0.874035i | 0.112837 | − | 0.195440i | ||||
\(21\) | −1.84690 | + | 3.19893i | −0.403027 | + | 0.698064i | ||||
\(22\) | 0.284259 | − | 0.492351i | 0.0606042 | − | 0.104970i | ||||
\(23\) | 1.95301 | 0.407230 | 0.203615 | − | 0.979051i | \(-0.434731\pi\) | ||||
0.203615 | + | 0.979051i | \(0.434731\pi\) | |||||||
\(24\) | −1.48723 | + | 2.57596i | −0.303580 | + | 0.525816i | ||||
\(25\) | −5.93144 | − | 10.2735i | −1.18629 | − | 2.05471i | ||||
\(26\) | 1.55806 | + | 2.69864i | 0.305561 | + | 0.529248i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.907835 | 0.171565 | ||||||||
\(29\) | 6.08537 | 1.13003 | 0.565013 | − | 0.825082i | \(-0.308871\pi\) | ||||
0.565013 | + | 0.825082i | \(0.308871\pi\) | |||||||
\(30\) | 2.71944 | + | 4.71020i | 0.496499 | + | 0.859961i | ||||
\(31\) | −2.68966 | − | 4.65864i | −0.483078 | − | 0.836716i | 0.516733 | − | 0.856147i | \(-0.327148\pi\) |
−0.999811 | + | 0.0194308i | \(0.993815\pi\) | |||||||
\(32\) | 1.38208 | 0.244319 | ||||||||
\(33\) | −0.214620 | − | 0.371733i | −0.0373606 | − | 0.0647105i | ||||
\(34\) | 1.01386 | − | 1.75606i | 0.173876 | − | 0.301162i | ||||
\(35\) | 7.58420 | − | 13.1362i | 1.28196 | − | 2.22043i | ||||
\(36\) | 0.122886 | + | 0.212845i | 0.0204810 | + | 0.0354741i | ||||
\(37\) | 4.23513 | + | 7.33547i | 0.696252 | + | 1.20594i | 0.969757 | + | 0.244073i | \(0.0784837\pi\) |
−0.273505 | + | 0.961871i | \(0.588183\pi\) | |||||||
\(38\) | −4.44823 | + | 7.70457i | −0.721599 | + | 1.24985i | ||||
\(39\) | 2.35273 | 0.376738 | ||||||||
\(40\) | 6.10723 | − | 10.5780i | 0.965638 | − | 1.67253i | ||||
\(41\) | −9.93710 | −1.55191 | −0.775957 | − | 0.630785i | \(-0.782733\pi\) | ||||
−0.775957 | + | 0.630785i | \(0.782733\pi\) | |||||||
\(42\) | −2.44617 | + | 4.23690i | −0.377453 | + | 0.653767i | ||||
\(43\) | 4.73108 | + | 8.19447i | 0.721483 | + | 1.24964i | 0.960405 | + | 0.278606i | \(0.0898724\pi\) |
−0.238923 | + | 0.971039i | \(0.576794\pi\) | |||||||
\(44\) | −0.0527477 | + | 0.0913617i | −0.00795202 | + | 0.0137733i | ||||
\(45\) | 4.10644 | 0.612152 | ||||||||
\(46\) | 2.58671 | 0.381389 | ||||||||
\(47\) | −3.29832 | − | 5.71285i | −0.481109 | − | 0.833305i | 0.518656 | − | 0.854983i | \(-0.326433\pi\) |
−0.999765 | + | 0.0216776i | \(0.993099\pi\) | |||||||
\(48\) | −1.72403 | + | 2.98610i | −0.248842 | + | 0.431006i | ||||
\(49\) | 6.64421 | 0.949173 | ||||||||
\(50\) | −7.85603 | − | 13.6070i | −1.11101 | − | 1.92433i | ||||
\(51\) | −0.765484 | − | 1.32586i | −0.107189 | − | 0.185657i | ||||
\(52\) | −0.289118 | − | 0.500766i | −0.0400934 | − | 0.0694438i | ||||
\(53\) | 4.67219 | + | 8.09247i | 0.641774 | + | 1.11159i | 0.985036 | + | 0.172346i | \(0.0551348\pi\) |
−0.343262 | + | 0.939240i | \(0.611532\pi\) | |||||||
\(54\) | −1.32447 | −0.180238 | ||||||||
\(55\) | 0.881327 | + | 1.52650i | 0.118838 | + | 0.205834i | ||||
\(56\) | 10.9871 | 1.46821 | ||||||||
\(57\) | 3.35849 | + | 5.81708i | 0.444844 | + | 0.770492i | ||||
\(58\) | 8.05991 | 1.05832 | ||||||||
\(59\) | −3.06926 | −0.399584 | −0.199792 | − | 0.979838i | \(-0.564027\pi\) | ||||
−0.199792 | + | 0.979838i | \(0.564027\pi\) | |||||||
\(60\) | −0.504625 | − | 0.874035i | −0.0651467 | − | 0.112837i | ||||
\(61\) | −4.87315 | + | 8.44054i | −0.623943 | + | 1.08070i | 0.364801 | + | 0.931085i | \(0.381137\pi\) |
−0.988744 | + | 0.149616i | \(0.952196\pi\) | |||||||
\(62\) | −3.56239 | − | 6.17024i | −0.452424 | − | 0.783621i | ||||
\(63\) | 1.84690 | + | 3.19893i | 0.232688 | + | 0.403027i | ||||
\(64\) | 8.72663 | 1.09083 | ||||||||
\(65\) | −9.66135 | −1.19834 | ||||||||
\(66\) | −0.284259 | − | 0.492351i | −0.0349899 | − | 0.0606042i | ||||
\(67\) | −13.8840 | −1.69621 | −0.848103 | − | 0.529832i | \(-0.822255\pi\) | ||||
−0.848103 | + | 0.529832i | \(0.822255\pi\) | |||||||
\(68\) | −0.188135 | + | 0.325859i | −0.0228147 | + | 0.0395162i | ||||
\(69\) | 0.976504 | − | 1.69135i | 0.117557 | − | 0.203615i | ||||
\(70\) | 10.0451 | − | 17.3986i | 1.20062 | − | 2.07953i | ||||
\(71\) | 0.536628 | + | 0.929468i | 0.0636861 | + | 0.110308i | 0.896110 | − | 0.443831i | \(-0.146381\pi\) |
−0.832424 | + | 0.554139i | \(0.813048\pi\) | |||||||
\(72\) | 1.48723 | + | 2.57596i | 0.175272 | + | 0.303580i | ||||
\(73\) | 2.85438 | − | 4.94393i | 0.334080 | − | 0.578643i | −0.649228 | − | 0.760594i | \(-0.724908\pi\) |
0.983308 | + | 0.181951i | \(0.0582412\pi\) | |||||||
\(74\) | 5.60932 | + | 9.71563i | 0.652070 | + | 1.12942i | ||||
\(75\) | −11.8629 | −1.36981 | ||||||||
\(76\) | 0.825424 | − | 1.42968i | 0.0946827 | − | 0.163995i | ||||
\(77\) | −0.792767 | + | 1.37311i | −0.0903441 | + | 0.156481i | ||||
\(78\) | 3.11613 | 0.352832 | ||||||||
\(79\) | 7.18928 | 0.808858 | 0.404429 | − | 0.914569i | \(-0.367470\pi\) | ||||
0.404429 | + | 0.914569i | \(0.367470\pi\) | |||||||
\(80\) | 7.07961 | − | 12.2623i | 0.791525 | − | 1.37096i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −13.1614 | −1.45344 | ||||||||
\(83\) | −5.58924 | − | 9.68086i | −0.613499 | − | 1.06261i | −0.990646 | − | 0.136458i | \(-0.956428\pi\) |
0.377147 | − | 0.926154i | \(-0.376905\pi\) | |||||||
\(84\) | 0.453917 | − | 0.786208i | 0.0495264 | − | 0.0857823i | ||||
\(85\) | 3.14342 | + | 5.44456i | 0.340951 | + | 0.590545i | ||||
\(86\) | 6.26618 | + | 10.8533i | 0.675700 | + | 1.17035i | ||||
\(87\) | 3.04269 | − | 5.27009i | 0.326210 | − | 0.565013i | ||||
\(88\) | −0.638381 | + | 1.10571i | −0.0680516 | + | 0.117869i | ||||
\(89\) | 0.330579 | − | 0.572580i | 0.0350413 | − | 0.0606934i | −0.847973 | − | 0.530040i | \(-0.822177\pi\) |
0.883014 | + | 0.469346i | \(0.155510\pi\) | |||||||
\(90\) | 5.43887 | 0.573307 | ||||||||
\(91\) | −4.34526 | − | 7.52622i | −0.455507 | − | 0.788962i | ||||
\(92\) | −0.479995 | −0.0500429 | ||||||||
\(93\) | −5.37933 | −0.557810 | ||||||||
\(94\) | −4.36853 | − | 7.56652i | −0.450580 | − | 0.780427i | ||||
\(95\) | −13.7915 | − | 23.8875i | −1.41497 | − | 2.45081i | ||||
\(96\) | 0.691038 | − | 1.19691i | 0.0705288 | − | 0.122160i | ||||
\(97\) | 1.13737 | + | 1.96997i | 0.115482 | + | 0.200021i | 0.917972 | − | 0.396645i | \(-0.129825\pi\) |
−0.802490 | + | 0.596665i | \(0.796492\pi\) | |||||||
\(98\) | 8.80008 | 0.888942 | ||||||||
\(99\) | −0.429241 | −0.0431403 | ||||||||
\(100\) | 1.45778 | + | 2.52495i | 0.145778 | + | 0.252495i | ||||
\(101\) | 1.31245 | 0.130593 | 0.0652966 | − | 0.997866i | \(-0.479201\pi\) | ||||
0.0652966 | + | 0.997866i | \(0.479201\pi\) | |||||||
\(102\) | −1.01386 | − | 1.75606i | −0.100387 | − | 0.173876i | ||||
\(103\) | −5.53994 | −0.545866 | −0.272933 | − | 0.962033i | \(-0.587994\pi\) | ||||
−0.272933 | + | 0.962033i | \(0.587994\pi\) | |||||||
\(104\) | −3.49905 | − | 6.06054i | −0.343110 | − | 0.594285i | ||||
\(105\) | −7.58420 | − | 13.1362i | −0.740143 | − | 1.28196i | ||||
\(106\) | 6.18819 | + | 10.7183i | 0.601050 | + | 1.04105i | ||||
\(107\) | −1.28393 | − | 2.22382i | −0.124122 | − | 0.214985i | 0.797268 | − | 0.603626i | \(-0.206278\pi\) |
−0.921389 | + | 0.388641i | \(0.872945\pi\) | |||||||
\(108\) | 0.245772 | 0.0236494 | ||||||||
\(109\) | −5.71543 | + | 9.89942i | −0.547439 | + | 0.948192i | 0.451010 | + | 0.892519i | \(0.351064\pi\) |
−0.998449 | + | 0.0556732i | \(0.982270\pi\) | |||||||
\(110\) | 1.16729 | + | 2.02181i | 0.111297 | + | 0.192772i | ||||
\(111\) | 8.47027 | 0.803962 | ||||||||
\(112\) | 12.7364 | 1.20348 | ||||||||
\(113\) | −5.37142 | + | 9.30356i | −0.505300 | + | 0.875206i | 0.494681 | + | 0.869075i | \(0.335285\pi\) |
−0.999981 | + | 0.00613105i | \(0.998048\pi\) | |||||||
\(114\) | 4.44823 | + | 7.70457i | 0.416615 | + | 0.721599i | ||||
\(115\) | −4.00996 | + | 6.94545i | −0.373931 | + | 0.647667i | ||||
\(116\) | −1.49561 | −0.138864 | ||||||||
\(117\) | 1.17636 | − | 2.03752i | 0.108755 | − | 0.188369i | ||||
\(118\) | −4.06515 | −0.374228 | ||||||||
\(119\) | −2.82755 | + | 4.89746i | −0.259201 | + | 0.448950i | ||||
\(120\) | −6.10723 | − | 10.5780i | −0.557512 | − | 0.965638i | ||||
\(121\) | 5.40788 | + | 9.36672i | 0.491625 | + | 0.851520i | ||||
\(122\) | −6.45436 | + | 11.1793i | −0.584350 | + | 1.01212i | ||||
\(123\) | −4.96855 | + | 8.60578i | −0.447999 | + | 0.775957i | ||||
\(124\) | 0.661045 | + | 1.14496i | 0.0593635 | + | 0.102821i | ||||
\(125\) | 28.1820 | 2.52067 | ||||||||
\(126\) | 2.44617 | + | 4.23690i | 0.217922 | + | 0.377453i | ||||
\(127\) | −4.21390 | − | 7.29869i | −0.373923 | − | 0.647654i | 0.616242 | − | 0.787557i | \(-0.288654\pi\) |
−0.990165 | + | 0.139903i | \(0.955321\pi\) | |||||||
\(128\) | 8.79403 | 0.777289 | ||||||||
\(129\) | 9.46216 | 0.833096 | ||||||||
\(130\) | −12.7962 | −1.12230 | ||||||||
\(131\) | −3.40489 | − | 5.89744i | −0.297487 | − | 0.515262i | 0.678074 | − | 0.734994i | \(-0.262815\pi\) |
−0.975560 | + | 0.219732i | \(0.929482\pi\) | |||||||
\(132\) | 0.0527477 | + | 0.0913617i | 0.00459110 | + | 0.00795202i | ||||
\(133\) | 12.4056 | − | 21.4872i | 1.07570 | − | 1.86318i | ||||
\(134\) | −18.3890 | −1.58857 | ||||||||
\(135\) | 2.05322 | − | 3.55628i | 0.176713 | − | 0.306076i | ||||
\(136\) | −2.27690 | + | 3.94371i | −0.195243 | + | 0.338171i | ||||
\(137\) | 0.794852 | − | 1.37672i | 0.0679088 | − | 0.117621i | −0.830072 | − | 0.557656i | \(-0.811701\pi\) |
0.897981 | + | 0.440035i | \(0.145034\pi\) | |||||||
\(138\) | 1.29335 | − | 2.24015i | 0.110098 | − | 0.190695i | ||||
\(139\) | 11.4414 | + | 19.8170i | 0.970443 | + | 1.68086i | 0.694219 | + | 0.719764i | \(0.255750\pi\) |
0.276224 | + | 0.961093i | \(0.410917\pi\) | |||||||
\(140\) | −1.86399 | + | 3.22852i | −0.157536 | + | 0.272860i | ||||
\(141\) | −6.59664 | −0.555537 | ||||||||
\(142\) | 0.710750 | + | 1.23105i | 0.0596448 | + | 0.103308i | ||||
\(143\) | 1.00989 | 0.0844510 | ||||||||
\(144\) | 1.72403 | + | 2.98610i | 0.143669 | + | 0.248842i | ||||
\(145\) | −12.4946 | + | 21.6413i | −1.03762 | + | 1.79721i | ||||
\(146\) | 3.78055 | − | 6.54810i | 0.312880 | − | 0.541924i | ||||
\(147\) | 3.32211 | − | 5.75406i | 0.274003 | − | 0.474587i | ||||
\(148\) | −1.04088 | − | 1.80285i | −0.0855596 | − | 0.148194i | ||||
\(149\) | 18.7365 | 1.53496 | 0.767478 | − | 0.641075i | \(-0.221511\pi\) | ||||
0.767478 | + | 0.641075i | \(0.221511\pi\) | |||||||
\(150\) | −15.7121 | −1.28288 | ||||||||
\(151\) | −6.10258 | + | 10.5700i | −0.496621 | + | 0.860173i | −0.999992 | − | 0.00389698i | \(-0.998760\pi\) |
0.503371 | + | 0.864070i | \(0.332093\pi\) | |||||||
\(152\) | 9.98972 | − | 17.3027i | 0.810273 | − | 1.40343i | ||||
\(153\) | −1.53097 | −0.123771 | ||||||||
\(154\) | −1.05000 | + | 1.81865i | −0.0846112 | + | 0.146551i | ||||
\(155\) | 22.0899 | 1.77430 | ||||||||
\(156\) | −0.578235 | −0.0462959 | ||||||||
\(157\) | 1.42338 | + | 12.4489i | 0.113598 | + | 0.993527i | ||||
\(158\) | 9.52201 | 0.757531 | ||||||||
\(159\) | 9.34438 | 0.741057 | ||||||||
\(160\) | −2.83771 | + | 4.91506i | −0.224341 | + | 0.388569i | ||||
\(161\) | −7.21404 | −0.568546 | ||||||||
\(162\) | −0.662236 | + | 1.14703i | −0.0520302 | + | 0.0901190i | ||||
\(163\) | 1.53395 | − | 2.65688i | 0.120148 | − | 0.208103i | −0.799678 | − | 0.600429i | \(-0.794996\pi\) |
0.919826 | + | 0.392327i | \(0.128330\pi\) | |||||||
\(164\) | 2.44226 | 0.190709 | ||||||||
\(165\) | 1.76265 | 0.137222 | ||||||||
\(166\) | −7.40280 | − | 12.8220i | −0.574569 | − | 0.995182i | ||||
\(167\) | −0.0125513 | + | 0.0217395i | −0.000971250 | + | 0.00168225i | −0.866511 | − | 0.499159i | \(-0.833642\pi\) |
0.865539 | + | 0.500841i | \(0.166976\pi\) | |||||||
\(168\) | 5.49355 | − | 9.51510i | 0.423836 | − | 0.734106i | ||||
\(169\) | 3.73233 | − | 6.46459i | 0.287102 | − | 0.497276i | ||||
\(170\) | 4.16337 | + | 7.21117i | 0.319316 | + | 0.553071i | ||||
\(171\) | 6.71699 | 0.513661 | ||||||||
\(172\) | −1.16277 | − | 2.01397i | −0.0886602 | − | 0.153564i | ||||
\(173\) | −19.3577 | −1.47174 | −0.735868 | − | 0.677125i | \(-0.763225\pi\) | ||||
−0.735868 | + | 0.677125i | \(0.763225\pi\) | |||||||
\(174\) | 4.02995 | − | 6.98009i | 0.305510 | − | 0.529159i | ||||
\(175\) | 21.9096 | + | 37.9485i | 1.65621 | + | 2.86864i | ||||
\(176\) | −0.740022 | + | 1.28176i | −0.0557813 | + | 0.0966160i | ||||
\(177\) | −1.53463 | + | 2.65806i | −0.115350 | + | 0.199792i | ||||
\(178\) | 0.437843 | − | 0.758367i | 0.0328177 | − | 0.0568420i | ||||
\(179\) | 6.55306 | − | 11.3502i | 0.489799 | − | 0.848357i | −0.510132 | − | 0.860096i | \(-0.670404\pi\) |
0.999931 | + | 0.0117394i | \(0.00373686\pi\) | |||||||
\(180\) | −1.00925 | −0.0752250 | ||||||||
\(181\) | −6.86093 | + | 11.8835i | −0.509969 | + | 0.883292i | 0.489964 | + | 0.871743i | \(0.337010\pi\) |
−0.999933 | + | 0.0115498i | \(0.996324\pi\) | |||||||
\(182\) | −5.75518 | − | 9.96827i | −0.426603 | − | 0.738897i | ||||
\(183\) | 4.87315 | + | 8.44054i | 0.360234 | + | 0.623943i | ||||
\(184\) | −5.80915 | −0.428256 | ||||||||
\(185\) | −34.7827 | −2.55727 | ||||||||
\(186\) | −7.12478 | −0.522414 | ||||||||
\(187\) | −0.328577 | − | 0.569112i | −0.0240279 | − | 0.0416176i | ||||
\(188\) | 0.810635 | + | 1.40406i | 0.0591216 | + | 0.102402i | ||||
\(189\) | 3.69381 | 0.268685 | ||||||||
\(190\) | −18.2664 | − | 31.6384i | −1.32519 | − | 2.29529i | ||||
\(191\) | 11.4553 | − | 19.8411i | 0.828874 | − | 1.43565i | −0.0700488 | − | 0.997544i | \(-0.522315\pi\) |
0.898922 | − | 0.438108i | \(-0.144351\pi\) | |||||||
\(192\) | 4.36331 | − | 7.55748i | 0.314895 | − | 0.545414i | ||||
\(193\) | −9.78696 | − | 16.9515i | −0.704481 | − | 1.22020i | −0.966879 | − | 0.255237i | \(-0.917847\pi\) |
0.262398 | − | 0.964960i | \(-0.415487\pi\) | |||||||
\(194\) | 1.50641 | + | 2.60918i | 0.108154 | + | 0.187328i | ||||
\(195\) | −4.83067 | + | 8.36697i | −0.345932 | + | 0.599171i | ||||
\(196\) | −1.63296 | −0.116640 | ||||||||
\(197\) | 3.49793 | − | 6.05859i | 0.249217 | − | 0.431657i | −0.714092 | − | 0.700052i | \(-0.753160\pi\) |
0.963309 | + | 0.268395i | \(0.0864934\pi\) | |||||||
\(198\) | −0.568518 | −0.0404028 | ||||||||
\(199\) | 3.22382 | − | 5.58381i | 0.228530 | − | 0.395826i | −0.728842 | − | 0.684681i | \(-0.759941\pi\) |
0.957373 | + | 0.288855i | \(0.0932747\pi\) | |||||||
\(200\) | 17.6428 | + | 30.5583i | 1.24754 | + | 2.16080i | ||||
\(201\) | −6.94202 | + | 12.0239i | −0.489652 | + | 0.848103i | ||||
\(202\) | 1.73830 | 0.122306 | ||||||||
\(203\) | −22.4782 | −1.57766 | ||||||||
\(204\) | 0.188135 | + | 0.325859i | 0.0131721 | + | 0.0228147i | ||||
\(205\) | 20.4031 | − | 35.3392i | 1.42501 | − | 2.46819i | ||||
\(206\) | −7.33750 | −0.511228 | ||||||||
\(207\) | −0.976504 | − | 1.69135i | −0.0678717 | − | 0.117557i | ||||
\(208\) | −4.05617 | − | 7.02549i | −0.281245 | − | 0.487130i | ||||
\(209\) | 1.44160 | + | 2.49693i | 0.0997178 | + | 0.172716i | ||||
\(210\) | −10.0451 | − | 17.3986i | −0.693176 | − | 1.20062i | ||||
\(211\) | 1.17153 | 0.0806518 | 0.0403259 | − | 0.999187i | \(-0.487160\pi\) | ||||
0.0403259 | + | 0.999187i | \(0.487160\pi\) | |||||||
\(212\) | −1.14829 | − | 1.98890i | −0.0788651 | − | 0.136598i | ||||
\(213\) | 1.07326 | 0.0735383 | ||||||||
\(214\) | −1.70052 | − | 2.94539i | −0.116245 | − | 0.201343i | ||||
\(215\) | −38.8558 | −2.64994 | ||||||||
\(216\) | 2.97446 | 0.202387 | ||||||||
\(217\) | 9.93510 | + | 17.2081i | 0.674439 | + | 1.16816i | ||||
\(218\) | −7.56993 | + | 13.1115i | −0.512700 | + | 0.888023i | ||||
\(219\) | −2.85438 | − | 4.94393i | −0.192881 | − | 0.334080i | ||||
\(220\) | −0.216605 | − | 0.375172i | −0.0146035 | − | 0.0252941i | ||||
\(221\) | 3.60195 | 0.242294 | ||||||||
\(222\) | 11.2186 | 0.752946 | ||||||||
\(223\) | 12.0052 | + | 20.7935i | 0.803925 | + | 1.39244i | 0.917014 | + | 0.398854i | \(0.130592\pi\) |
−0.113089 | + | 0.993585i | \(0.536075\pi\) | |||||||
\(224\) | −5.10513 | −0.341101 | ||||||||
\(225\) | −5.93144 | + | 10.2735i | −0.395429 | + | 0.684903i | ||||
\(226\) | −7.11429 | + | 12.3223i | −0.473236 | + | 0.819668i | ||||
\(227\) | −7.40268 | + | 12.8218i | −0.491333 | + | 0.851014i | −0.999950 | − | 0.00997867i | \(-0.996824\pi\) |
0.508617 | + | 0.860993i | \(0.330157\pi\) | |||||||
\(228\) | −0.825424 | − | 1.42968i | −0.0546651 | − | 0.0946827i | ||||
\(229\) | −8.46544 | − | 14.6626i | −0.559412 | − | 0.968930i | −0.997546 | − | 0.0700202i | \(-0.977694\pi\) |
0.438134 | − | 0.898910i | \(-0.355640\pi\) | |||||||
\(230\) | −5.31108 | + | 9.19906i | −0.350202 | + | 0.606568i | ||||
\(231\) | 0.792767 | + | 1.37311i | 0.0521602 | + | 0.0903441i | ||||
\(232\) | −18.1007 | −1.18837 | ||||||||
\(233\) | −8.30278 | + | 14.3808i | −0.543933 | + | 0.942120i | 0.454740 | + | 0.890624i | \(0.349732\pi\) |
−0.998673 | + | 0.0514960i | \(0.983601\pi\) | |||||||
\(234\) | 1.55806 | − | 2.69864i | 0.101854 | − | 0.176416i | ||||
\(235\) | 27.0887 | 1.76707 | ||||||||
\(236\) | 0.754338 | 0.0491033 | ||||||||
\(237\) | 3.59464 | − | 6.22610i | 0.233497 | − | 0.404429i | ||||
\(238\) | −3.74501 | + | 6.48655i | −0.242753 | + | 0.420461i | ||||
\(239\) | 19.4025 | 1.25504 | 0.627522 | − | 0.778599i | \(-0.284069\pi\) | ||||
0.627522 | + | 0.778599i | \(0.284069\pi\) | |||||||
\(240\) | −7.07961 | − | 12.2623i | −0.456987 | − | 0.791525i | ||||
\(241\) | 8.95415 | − | 15.5090i | 0.576787 | − | 0.999025i | −0.419058 | − | 0.907960i | \(-0.637639\pi\) |
0.995845 | − | 0.0910652i | \(-0.0290272\pi\) | |||||||
\(242\) | 7.16258 | + | 12.4060i | 0.460428 | + | 0.797485i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 1.19768 | − | 2.07445i | 0.0766739 | − | 0.132803i | ||||
\(245\) | −13.6420 | + | 23.6287i | −0.871558 | + | 1.50958i | ||||
\(246\) | −6.58071 | + | 11.3981i | −0.419571 | + | 0.726718i | ||||
\(247\) | −15.8033 | −1.00554 | ||||||||
\(248\) | 8.00031 | + | 13.8569i | 0.508020 | + | 0.879917i | ||||
\(249\) | −11.1785 | −0.708408 | ||||||||
\(250\) | 37.3263 | 2.36072 | ||||||||
\(251\) | 0.0947791 | + | 0.164162i | 0.00598240 | + | 0.0103618i | 0.869001 | − | 0.494810i | \(-0.164762\pi\) |
−0.863019 | + | 0.505172i | \(0.831429\pi\) | |||||||
\(252\) | −0.453917 | − | 0.786208i | −0.0285941 | − | 0.0495264i | ||||
\(253\) | 0.419156 | − | 0.725999i | 0.0263521 | − | 0.0456431i | ||||
\(254\) | −5.58119 | − | 9.66691i | −0.350195 | − | 0.606556i | ||||
\(255\) | 6.28683 | 0.393697 | ||||||||
\(256\) | −5.80581 | −0.362863 | ||||||||
\(257\) | −4.07555 | − | 7.05906i | −0.254226 | − | 0.440332i | 0.710459 | − | 0.703739i | \(-0.248487\pi\) |
−0.964685 | + | 0.263406i | \(0.915154\pi\) | |||||||
\(258\) | 12.5324 | 0.780231 | ||||||||
\(259\) | −15.6438 | − | 27.0958i | −0.972057 | − | 1.68365i | ||||
\(260\) | 2.37449 | 0.147260 | ||||||||
\(261\) | −3.04269 | − | 5.27009i | −0.188338 | − | 0.326210i | ||||
\(262\) | −4.50969 | − | 7.81100i | −0.278609 | − | 0.482565i | ||||
\(263\) | 0.830323 | + | 1.43816i | 0.0511999 | + | 0.0886808i | 0.890489 | − | 0.455004i | \(-0.150362\pi\) |
−0.839290 | + | 0.543685i | \(0.817029\pi\) | |||||||
\(264\) | 0.638381 | + | 1.10571i | 0.0392896 | + | 0.0680516i | ||||
\(265\) | −38.3721 | −2.35718 | ||||||||
\(266\) | 16.4309 | − | 28.4592i | 1.00744 | − | 1.74494i | ||||
\(267\) | −0.330579 | − | 0.572580i | −0.0202311 | − | 0.0350413i | ||||
\(268\) | 3.41231 | 0.208440 | ||||||||
\(269\) | 26.1622 | 1.59514 | 0.797569 | − | 0.603228i | \(-0.206119\pi\) | ||||
0.797569 | + | 0.603228i | \(0.206119\pi\) | |||||||
\(270\) | 2.71944 | − | 4.71020i | 0.165500 | − | 0.286654i | ||||
\(271\) | −2.77646 | − | 4.80898i | −0.168658 | − | 0.292125i | 0.769290 | − | 0.638900i | \(-0.220610\pi\) |
−0.937948 | + | 0.346775i | \(0.887277\pi\) | |||||||
\(272\) | −2.63943 | + | 4.57163i | −0.160039 | + | 0.277195i | ||||
\(273\) | −8.69053 | −0.525975 | ||||||||
\(274\) | 1.05276 | − | 1.82343i | 0.0635995 | − | 0.110158i | ||||
\(275\) | −5.09203 | −0.307061 | ||||||||
\(276\) | −0.239997 | + | 0.415688i | −0.0144462 | + | 0.0250215i | ||||
\(277\) | 11.8128 | + | 20.4604i | 0.709765 | + | 1.22935i | 0.964944 | + | 0.262455i | \(0.0845321\pi\) |
−0.255179 | + | 0.966894i | \(0.582135\pi\) | |||||||
\(278\) | 15.1538 | + | 26.2471i | 0.908862 | + | 1.57420i | ||||
\(279\) | −2.68966 | + | 4.65864i | −0.161026 | + | 0.278905i | ||||
\(280\) | −22.5589 | + | 39.0732i | −1.34815 | + | 2.33507i | ||||
\(281\) | 9.96368 | + | 17.2576i | 0.594383 | + | 1.02950i | 0.993634 | + | 0.112660i | \(0.0359371\pi\) |
−0.399250 | + | 0.916842i | \(0.630730\pi\) | |||||||
\(282\) | −8.73706 | −0.520285 | ||||||||
\(283\) | −0.645127 | − | 1.11739i | −0.0383488 | − | 0.0664221i | 0.846214 | − | 0.532843i | \(-0.178876\pi\) |
−0.884563 | + | 0.466421i | \(0.845543\pi\) | |||||||
\(284\) | −0.131888 | − | 0.228437i | −0.00782613 | − | 0.0135553i | ||||
\(285\) | −27.5829 | −1.63387 | ||||||||
\(286\) | 1.33757 | 0.0790921 | ||||||||
\(287\) | 36.7057 | 2.16667 | ||||||||
\(288\) | −0.691038 | − | 1.19691i | −0.0407198 | − | 0.0705288i | ||||
\(289\) | 7.32807 | + | 12.6926i | 0.431063 | + | 0.746623i | ||||
\(290\) | −16.5488 | + | 28.6633i | −0.971778 | + | 1.68317i | ||||
\(291\) | 2.27473 | 0.133347 | ||||||||
\(292\) | −0.701526 | + | 1.21508i | −0.0410537 | + | 0.0711071i | ||||
\(293\) | −9.31375 | + | 16.1319i | −0.544115 | + | 0.942435i | 0.454547 | + | 0.890723i | \(0.349801\pi\) |
−0.998662 | + | 0.0517122i | \(0.983532\pi\) | |||||||
\(294\) | 4.40004 | − | 7.62109i | 0.256615 | − | 0.444471i | ||||
\(295\) | 6.30187 | − | 10.9152i | 0.366909 | − | 0.635505i | ||||
\(296\) | −12.5973 | − | 21.8191i | −0.732201 | − | 1.26821i | ||||
\(297\) | −0.214620 | + | 0.371733i | −0.0124535 | + | 0.0215702i | ||||
\(298\) | 24.8160 | 1.43755 | ||||||||
\(299\) | 2.29745 | + | 3.97930i | 0.132865 | + | 0.230129i | ||||
\(300\) | 2.91556 | 0.168330 | ||||||||
\(301\) | −17.4757 | − | 30.2688i | −1.00728 | − | 1.74466i | ||||
\(302\) | −8.08271 | + | 13.9997i | −0.465108 | + | 0.805590i | ||||
\(303\) | 0.656223 | − | 1.13661i | 0.0376990 | − | 0.0652966i | ||||
\(304\) | 11.5803 | − | 20.0576i | 0.664174 | − | 1.15038i | ||||
\(305\) | −20.0113 | − | 34.6606i | −1.14584 | − | 1.98466i | ||||
\(306\) | −2.02773 | −0.115917 | ||||||||
\(307\) | −23.1941 | −1.32376 | −0.661879 | − | 0.749611i | \(-0.730241\pi\) | ||||
−0.661879 | + | 0.749611i | \(0.730241\pi\) | |||||||
\(308\) | 0.194840 | − | 0.337473i | 0.0111020 | − | 0.0192293i | ||||
\(309\) | −2.76997 | + | 4.79773i | −0.157578 | + | 0.272933i | ||||
\(310\) | 29.2575 | 1.66171 | ||||||||
\(311\) | −2.05469 | + | 3.55882i | −0.116511 | + | 0.201802i | −0.918383 | − | 0.395694i | \(-0.870504\pi\) |
0.801872 | + | 0.597496i | \(0.203838\pi\) | |||||||
\(312\) | −6.99811 | −0.396190 | ||||||||
\(313\) | 23.1132 | 1.30644 | 0.653218 | − | 0.757170i | \(-0.273418\pi\) | ||||
0.653218 | + | 0.757170i | \(0.273418\pi\) | |||||||
\(314\) | 1.88523 | + | 16.4882i | 0.106390 | + | 0.930481i | ||||
\(315\) | −15.1684 | −0.854643 | ||||||||
\(316\) | −1.76693 | −0.0993973 | ||||||||
\(317\) | 6.55839 | − | 11.3595i | 0.368356 | − | 0.638012i | −0.620953 | − | 0.783848i | \(-0.713254\pi\) |
0.989309 | + | 0.145837i | \(0.0465874\pi\) | |||||||
\(318\) | 12.3764 | 0.694032 | ||||||||
\(319\) | 1.30605 | − | 2.26214i | 0.0731245 | − | 0.126655i | ||||
\(320\) | −17.9177 | + | 31.0344i | −1.00163 | + | 1.73487i | ||||
\(321\) | −2.56785 | −0.143323 | ||||||||
\(322\) | −9.55479 | −0.532468 | ||||||||
\(323\) | 5.14175 | + | 8.90577i | 0.286095 | + | 0.495530i | ||||
\(324\) | 0.122886 | − | 0.212845i | 0.00682700 | − | 0.0118247i | ||||
\(325\) | 13.9551 | − | 24.1709i | 0.774088 | − | 1.34076i | ||||
\(326\) | 2.03167 | − | 3.51896i | 0.112524 | − | 0.194897i | ||||
\(327\) | 5.71543 | + | 9.89942i | 0.316064 | + | 0.547439i | ||||
\(328\) | 29.5576 | 1.63204 | ||||||||
\(329\) | 12.1834 | + | 21.1022i | 0.671690 | + | 1.16340i | ||||
\(330\) | 2.33459 | 0.128515 | ||||||||
\(331\) | −11.5903 | + | 20.0749i | −0.637058 | + | 1.10342i | 0.349017 | + | 0.937116i | \(0.386515\pi\) |
−0.986075 | + | 0.166300i | \(0.946818\pi\) | |||||||
\(332\) | 1.37368 | + | 2.37928i | 0.0753905 | + | 0.130580i | ||||
\(333\) | 4.23513 | − | 7.33547i | 0.232084 | − | 0.401981i | ||||
\(334\) | −0.0166239 | + | 0.0287934i | −0.000909618 | + | 0.00157550i | ||||
\(335\) | 28.5070 | − | 49.3756i | 1.55750 | − | 2.69768i | ||||
\(336\) | 6.36822 | − | 11.0301i | 0.347415 | − | 0.601740i | ||||
\(337\) | −10.0712 | −0.548615 | −0.274307 | − | 0.961642i | \(-0.588449\pi\) | ||||
−0.274307 | + | 0.961642i | \(0.588449\pi\) | |||||||
\(338\) | 4.94337 | − | 8.56217i | 0.268884 | − | 0.465721i | ||||
\(339\) | 5.37142 | + | 9.30356i | 0.291735 | + | 0.505300i | ||||
\(340\) | −0.772564 | − | 1.33812i | −0.0418982 | − | 0.0725698i | ||||
\(341\) | −2.30903 | −0.125041 | ||||||||
\(342\) | 8.89647 | 0.481066 | ||||||||
\(343\) | 1.31421 | 0.0709607 | ||||||||
\(344\) | −14.0724 | − | 24.3741i | −0.758734 | − | 1.31417i | ||||
\(345\) | 4.00996 | + | 6.94545i | 0.215889 | + | 0.373931i | ||||
\(346\) | −25.6387 | −1.37834 | ||||||||
\(347\) | 6.63666 | + | 11.4950i | 0.356275 | + | 0.617086i | 0.987335 | − | 0.158648i | \(-0.0507134\pi\) |
−0.631060 | + | 0.775734i | \(0.717380\pi\) | |||||||
\(348\) | −0.747807 | + | 1.29524i | −0.0400867 | + | 0.0694322i | ||||
\(349\) | −8.13102 | + | 14.0833i | −0.435244 | + | 0.753864i | −0.997315 | − | 0.0732244i | \(-0.976671\pi\) |
0.562072 | + | 0.827088i | \(0.310004\pi\) | |||||||
\(350\) | 29.0186 | + | 50.2618i | 1.55111 | + | 2.68660i | ||||
\(351\) | −1.17636 | − | 2.03752i | −0.0627897 | − | 0.108755i | ||||
\(352\) | 0.296622 | − | 0.513764i | 0.0158100 | − | 0.0273837i | ||||
\(353\) | −18.3823 | −0.978390 | −0.489195 | − | 0.872174i | \(-0.662709\pi\) | ||||
−0.489195 | + | 0.872174i | \(0.662709\pi\) | |||||||
\(354\) | −2.03258 | + | 3.52052i | −0.108030 | + | 0.187114i | ||||
\(355\) | −4.40727 | −0.233913 | ||||||||
\(356\) | −0.0812471 | + | 0.140724i | −0.00430609 | + | 0.00745837i | ||||
\(357\) | 2.82755 | + | 4.89746i | 0.149650 | + | 0.259201i | ||||
\(358\) | 8.67935 | − | 15.0331i | 0.458718 | − | 0.794523i | ||||
\(359\) | −0.310445 | −0.0163847 | −0.00819234 | − | 0.999966i | \(-0.502608\pi\) | ||||
−0.00819234 | + | 0.999966i | \(0.502608\pi\) | |||||||
\(360\) | −12.2145 | −0.643759 | ||||||||
\(361\) | −13.0590 | − | 22.6188i | −0.687314 | − | 1.19046i | ||||
\(362\) | −9.08712 | + | 15.7393i | −0.477608 | + | 0.827242i | ||||
\(363\) | 10.8158 | 0.567680 | ||||||||
\(364\) | 1.06794 | + | 1.84973i | 0.0559755 | + | 0.0969524i | ||||
\(365\) | 11.7213 | + | 20.3020i | 0.613523 | + | 1.06265i | ||||
\(366\) | 6.45436 | + | 11.1793i | 0.337375 | + | 0.584350i | ||||
\(367\) | −11.9759 | − | 20.7429i | −0.625137 | − | 1.08277i | −0.988514 | − | 0.151127i | \(-0.951710\pi\) |
0.363378 | − | 0.931642i | \(-0.381623\pi\) | |||||||
\(368\) | −6.73407 | −0.351038 | ||||||||
\(369\) | 4.96855 | + | 8.60578i | 0.258652 | + | 0.447999i | ||||
\(370\) | −46.0687 | −2.39500 | ||||||||
\(371\) | −17.2582 | − | 29.8920i | −0.895999 | − | 1.55192i | ||||
\(372\) | 1.32209 | 0.0685471 | ||||||||
\(373\) | −16.6412 | −0.861651 | −0.430826 | − | 0.902435i | \(-0.641778\pi\) | ||||
−0.430826 | + | 0.902435i | \(0.641778\pi\) | |||||||
\(374\) | −0.435191 | − | 0.753774i | −0.0225032 | − | 0.0389767i | ||||
\(375\) | 14.0910 | − | 24.4063i | 0.727656 | − | 1.26034i | ||||
\(376\) | 9.81073 | + | 16.9927i | 0.505950 | + | 0.876331i | ||||
\(377\) | 7.15862 | + | 12.3991i | 0.368687 | + | 0.638585i | ||||
\(378\) | 4.89235 | 0.251635 | ||||||||
\(379\) | −19.0309 | −0.977553 | −0.488777 | − | 0.872409i | \(-0.662557\pi\) | ||||
−0.488777 | + | 0.872409i | \(0.662557\pi\) | |||||||
\(380\) | 3.38956 | + | 5.87089i | 0.173881 | + | 0.301170i | ||||
\(381\) | −8.42780 | −0.431769 | ||||||||
\(382\) | 15.1722 | − | 26.2790i | 0.776276 | − | 1.34455i | ||||
\(383\) | −1.75435 | + | 3.03863i | −0.0896432 | + | 0.155267i | −0.907360 | − | 0.420354i | \(-0.861906\pi\) |
0.817717 | + | 0.575620i | \(0.195239\pi\) | |||||||
\(384\) | 4.39701 | − | 7.61585i | 0.224384 | − | 0.388645i | ||||
\(385\) | −3.25545 | − | 5.63861i | −0.165913 | − | 0.287370i | ||||
\(386\) | −12.9626 | − | 22.4518i | −0.659777 | − | 1.14277i | ||||
\(387\) | 4.73108 | − | 8.19447i | 0.240494 | − | 0.416548i | ||||
\(388\) | −0.279533 | − | 0.484165i | −0.0141911 | − | 0.0245797i | ||||
\(389\) | −25.1623 | −1.27578 | −0.637888 | − | 0.770129i | \(-0.720192\pi\) | ||||
−0.637888 | + | 0.770129i | \(0.720192\pi\) | |||||||
\(390\) | −6.39810 | + | 11.0818i | −0.323980 | + | 0.561150i | ||||
\(391\) | 1.49500 | − | 2.58941i | 0.0756052 | − | 0.130952i | ||||
\(392\) | −19.7630 | −0.998181 | ||||||||
\(393\) | −6.80978 | −0.343508 | ||||||||
\(394\) | 4.63291 | − | 8.02444i | 0.233403 | − | 0.404265i | ||||
\(395\) | −14.7612 | + | 25.5671i | −0.742716 | + | 1.28642i | ||||
\(396\) | 0.105495 | 0.00530134 | ||||||||
\(397\) | −2.29616 | − | 3.97706i | −0.115241 | − | 0.199603i | 0.802635 | − | 0.596470i | \(-0.203431\pi\) |
−0.917876 | + | 0.396867i | \(0.870097\pi\) | |||||||
\(398\) | 4.26986 | − | 7.39561i | 0.214029 | − | 0.370708i | ||||
\(399\) | −12.4056 | − | 21.4872i | −0.621058 | − | 1.07570i | ||||
\(400\) | 20.4519 | + | 35.4237i | 1.02260 | + | 1.77119i | ||||
\(401\) | −12.5987 | + | 21.8216i | −0.629150 | + | 1.08972i | 0.358573 | + | 0.933502i | \(0.383264\pi\) |
−0.987723 | + | 0.156218i | \(0.950070\pi\) | |||||||
\(402\) | −9.19451 | + | 15.9254i | −0.458581 | + | 0.794285i | ||||
\(403\) | 6.32805 | − | 10.9605i | 0.315223 | − | 0.545982i | ||||
\(404\) | −0.322562 | −0.0160481 | ||||||||
\(405\) | −2.05322 | − | 3.55628i | −0.102025 | − | 0.176713i | ||||
\(406\) | −29.7717 | −1.47755 | ||||||||
\(407\) | 3.63579 | 0.180219 | ||||||||
\(408\) | 2.27690 | + | 3.94371i | 0.112724 | + | 0.195243i | ||||
\(409\) | 4.52293 | + | 7.83395i | 0.223645 | + | 0.387364i | 0.955912 | − | 0.293653i | \(-0.0948711\pi\) |
−0.732267 | + | 0.681017i | \(0.761538\pi\) | |||||||
\(410\) | 27.0233 | − | 46.8058i | 1.33459 | − | 2.31157i | ||||
\(411\) | −0.794852 | − | 1.37672i | −0.0392071 | − | 0.0679088i | ||||
\(412\) | 1.36156 | 0.0670793 | ||||||||
\(413\) | 11.3373 | 0.557870 | ||||||||
\(414\) | −1.29335 | − | 2.24015i | −0.0635648 | − | 0.110098i | ||||
\(415\) | 45.9038 | 2.25333 | ||||||||
\(416\) | 1.62583 | + | 2.81601i | 0.0797127 | + | 0.138066i | ||||
\(417\) | 22.8827 | 1.12057 | ||||||||
\(418\) | 1.90936 | + | 3.30712i | 0.0933901 | + | 0.161756i | ||||
\(419\) | 11.5864 | + | 20.0683i | 0.566035 | + | 0.980401i | 0.996953 | + | 0.0780099i | \(0.0248566\pi\) |
−0.430918 | + | 0.902391i | \(0.641810\pi\) | |||||||
\(420\) | 1.86399 | + | 3.22852i | 0.0909532 | + | 0.157536i | ||||
\(421\) | −7.27810 | − | 12.6060i | −0.354713 | − | 0.614381i | 0.632356 | − | 0.774678i | \(-0.282088\pi\) |
−0.987069 | + | 0.160297i | \(0.948755\pi\) | |||||||
\(422\) | 1.55167 | 0.0755339 | ||||||||
\(423\) | −3.29832 | + | 5.71285i | −0.160370 | + | 0.277768i | ||||
\(424\) | −13.8973 | − | 24.0708i | −0.674910 | − | 1.16898i | ||||
\(425\) | −18.1617 | −0.880971 | ||||||||
\(426\) | 1.42150 | 0.0688719 | ||||||||
\(427\) | 18.0005 | − | 31.1777i | 0.871104 | − | 1.50880i | ||||
\(428\) | 0.315553 | + | 0.546554i | 0.0152528 | + | 0.0264187i | ||||
\(429\) | 0.504944 | − | 0.874588i | 0.0243789 | − | 0.0422255i | ||||
\(430\) | −51.4635 | −2.48179 | ||||||||
\(431\) | 14.4568 | − | 25.0400i | 0.696362 | − | 1.20613i | −0.273358 | − | 0.961912i | \(-0.588134\pi\) |
0.969719 | − | 0.244221i | \(-0.0785324\pi\) | |||||||
\(432\) | 3.44805 | 0.165894 | ||||||||
\(433\) | 4.24578 | − | 7.35390i | 0.204039 | − | 0.353406i | −0.745787 | − | 0.666184i | \(-0.767926\pi\) |
0.949826 | + | 0.312778i | \(0.101260\pi\) | |||||||
\(434\) | 13.1588 | + | 22.7917i | 0.631641 | + | 1.09403i | ||||
\(435\) | 12.4946 | + | 21.6413i | 0.599071 | + | 1.03762i | ||||
\(436\) | 1.40469 | − | 2.43300i | 0.0672726 | − | 0.116520i | ||||
\(437\) | −6.55917 | + | 11.3608i | −0.313768 | + | 0.543461i | ||||
\(438\) | −3.78055 | − | 6.54810i | −0.180641 | − | 0.312880i | ||||
\(439\) | 28.3381 | 1.35251 | 0.676253 | − | 0.736670i | \(-0.263603\pi\) | ||||
0.676253 | + | 0.736670i | \(0.263603\pi\) | |||||||
\(440\) | −2.62147 | − | 4.54053i | −0.124974 | − | 0.216461i | ||||
\(441\) | −3.32211 | − | 5.75406i | −0.158196 | − | 0.274003i | ||||
\(442\) | 4.77069 | 0.226919 | ||||||||
\(443\) | 16.0616 | 0.763110 | 0.381555 | − | 0.924346i | \(-0.375389\pi\) | ||||
0.381555 | + | 0.924346i | \(0.375389\pi\) | |||||||
\(444\) | −2.08176 | −0.0987958 | ||||||||
\(445\) | 1.35750 | + | 2.35127i | 0.0643519 | + | 0.111461i | ||||
\(446\) | 15.9005 | + | 27.5405i | 0.752911 | + | 1.30408i | ||||
\(447\) | 9.36827 | − | 16.2263i | 0.443104 | − | 0.767478i | ||||
\(448\) | −32.2345 | −1.52294 | ||||||||
\(449\) | 14.6417 | − | 25.3602i | 0.690986 | − | 1.19682i | −0.280529 | − | 0.959845i | \(-0.590510\pi\) |
0.971515 | − | 0.236977i | \(-0.0761566\pi\) | |||||||
\(450\) | −7.85603 | + | 13.6070i | −0.370337 | + | 0.641442i | ||||
\(451\) | −2.13271 | + | 3.69395i | −0.100425 | + | 0.173941i | ||||
\(452\) | 1.32014 | − | 2.28656i | 0.0620943 | − | 0.107551i | ||||
\(453\) | 6.10258 | + | 10.5700i | 0.286724 | + | 0.496621i | ||||
\(454\) | −9.80465 | + | 16.9822i | −0.460155 | + | 0.797012i | ||||
\(455\) | 35.6872 | 1.67304 | ||||||||
\(456\) | −9.98972 | − | 17.3027i | −0.467812 | − | 0.810273i | ||||
\(457\) | −10.0387 | −0.469593 | −0.234796 | − | 0.972045i | \(-0.575442\pi\) | ||||
−0.234796 | + | 0.972045i | \(0.575442\pi\) | |||||||
\(458\) | −11.2122 | − | 19.4202i | −0.523914 | − | 0.907445i | ||||
\(459\) | −0.765484 | + | 1.32586i | −0.0357297 | + | 0.0618857i | ||||
\(460\) | 0.985536 | − | 1.70700i | 0.0459508 | − | 0.0795892i | ||||
\(461\) | 14.7359 | − | 25.5233i | 0.686319 | − | 1.18874i | −0.286702 | − | 0.958020i | \(-0.592559\pi\) |
0.973020 | − | 0.230719i | \(-0.0741077\pi\) | |||||||
\(462\) | 1.05000 | + | 1.81865i | 0.0488503 | + | 0.0846112i | ||||
\(463\) | −24.6185 | −1.14412 | −0.572059 | − | 0.820213i | \(-0.693855\pi\) | ||||
−0.572059 | + | 0.820213i | \(0.693855\pi\) | |||||||
\(464\) | −20.9827 | −0.974096 | ||||||||
\(465\) | 11.0450 | − | 19.1304i | 0.512198 | − | 0.887152i | ||||
\(466\) | −10.9968 | + | 19.0470i | −0.509417 | + | 0.882337i | ||||
\(467\) | −7.63755 | −0.353424 | −0.176712 | − | 0.984263i | \(-0.556546\pi\) | ||||
−0.176712 | + | 0.984263i | \(0.556546\pi\) | |||||||
\(468\) | −0.289118 | + | 0.500766i | −0.0133645 | + | 0.0231479i | ||||
\(469\) | 51.2850 | 2.36812 | ||||||||
\(470\) | 35.8783 | 1.65494 | ||||||||
\(471\) | 11.4927 | + | 4.99174i | 0.529556 | + | 0.230007i | ||||
\(472\) | 9.12940 | 0.420215 | ||||||||
\(473\) | 4.06154 | 0.186750 | ||||||||
\(474\) | 4.76101 | − | 8.24630i | 0.218680 | − | 0.378765i | ||||
\(475\) | 79.6828 | 3.65610 | ||||||||
\(476\) | 0.694933 | − | 1.20366i | 0.0318522 | − | 0.0551696i | ||||
\(477\) | 4.67219 | − | 8.09247i | 0.213925 | − | 0.370529i | ||||
\(478\) | 25.6981 | 1.17540 | ||||||||
\(479\) | 26.9637 | 1.23200 | 0.616001 | − | 0.787745i | \(-0.288752\pi\) | ||||
0.616001 | + | 0.787745i | \(0.288752\pi\) | |||||||
\(480\) | 2.83771 | + | 4.91506i | 0.129523 | + | 0.224341i | ||||
\(481\) | −9.96413 | + | 17.2584i | −0.454325 | + | 0.786914i | ||||
\(482\) | 11.8595 | − | 20.5413i | 0.540186 | − | 0.935630i | ||||
\(483\) | −3.60702 | + | 6.24754i | −0.164125 | + | 0.284273i | ||||
\(484\) | −1.32910 | − | 2.30208i | −0.0604139 | − | 0.104640i | ||||
\(485\) | −9.34105 | −0.424155 | ||||||||
\(486\) | 0.662236 | + | 1.14703i | 0.0300397 | + | 0.0520302i | ||||
\(487\) | −2.26360 | −0.102574 | −0.0512868 | − | 0.998684i | \(-0.516332\pi\) | ||||
−0.0512868 | + | 0.998684i | \(0.516332\pi\) | |||||||
\(488\) | 14.4950 | − | 25.1061i | 0.656158 | − | 1.13650i | ||||
\(489\) | −1.53395 | − | 2.65688i | −0.0693675 | − | 0.120148i | ||||
\(490\) | −18.0685 | + | 31.2956i | −0.816252 | + | 1.41379i | ||||
\(491\) | 10.4739 | − | 18.1413i | 0.472680 | − | 0.818706i | −0.526831 | − | 0.849970i | \(-0.676620\pi\) |
0.999511 | + | 0.0312643i | \(0.00995335\pi\) | |||||||
\(492\) | 1.22113 | − | 2.11506i | 0.0550528 | − | 0.0953543i | ||||
\(493\) | 4.65826 | − | 8.06833i | 0.209797 | − | 0.363380i | ||||
\(494\) | −20.9310 | −0.941730 | ||||||||
\(495\) | 0.881327 | − | 1.52650i | 0.0396127 | − | 0.0686112i | ||||
\(496\) | 9.27410 | + | 16.0632i | 0.416420 | + | 0.721260i | ||||
\(497\) | −1.98220 | − | 3.43327i | −0.0889139 | − | 0.154003i | ||||
\(498\) | −14.8056 | −0.663455 | ||||||||
\(499\) | 16.3218 | 0.730664 | 0.365332 | − | 0.930877i | \(-0.380955\pi\) | ||||
0.365332 | + | 0.930877i | \(0.380955\pi\) | |||||||
\(500\) | −6.92635 | −0.309756 | ||||||||
\(501\) | 0.0125513 | + | 0.0217395i | 0.000560751 | + | 0.000971250i | ||||
\(502\) | 0.125532 | + | 0.217428i | 0.00560278 | + | 0.00970430i | ||||
\(503\) | 44.6201 | 1.98951 | 0.994756 | − | 0.102273i | \(-0.0326116\pi\) | ||||
0.994756 | + | 0.102273i | \(0.0326116\pi\) | |||||||
\(504\) | −5.49355 | − | 9.51510i | −0.244702 | − | 0.423836i | ||||
\(505\) | −2.69474 | + | 4.66743i | −0.119914 | + | 0.207698i | ||||
\(506\) | 0.555160 | − | 0.961565i | 0.0246799 | − | 0.0427468i | ||||
\(507\) | −3.73233 | − | 6.46459i | −0.165759 | − | 0.287102i | ||||
\(508\) | 1.03566 | + | 1.79381i | 0.0459499 | + | 0.0795876i | ||||
\(509\) | −8.28770 | + | 14.3547i | −0.367346 | + | 0.636262i | −0.989150 | − | 0.146911i | \(-0.953067\pi\) |
0.621804 | + | 0.783173i | \(0.286400\pi\) | |||||||
\(510\) | 8.32674 | 0.368714 | ||||||||
\(511\) | −10.5435 | + | 18.2619i | −0.466418 | + | 0.807860i | ||||
\(512\) | −25.2777 | −1.11713 | ||||||||
\(513\) | 3.35849 | − | 5.81708i | 0.148281 | − | 0.256831i | ||||
\(514\) | −5.39796 | − | 9.34954i | −0.238094 | − | 0.412390i | ||||
\(515\) | 11.3747 | − | 19.7016i | 0.501230 | − | 0.868156i | ||||
\(516\) | −2.32553 | −0.102376 | ||||||||
\(517\) | −2.83155 | −0.124531 | ||||||||
\(518\) | −20.7197 | − | 35.8877i | −0.910373 | − | 1.57681i | ||||
\(519\) | −9.67883 | + | 16.7642i | −0.424853 | + | 0.735868i | ||||
\(520\) | 28.7373 | 1.26022 | ||||||||
\(521\) | −14.2912 | − | 24.7531i | −0.626110 | − | 1.08445i | −0.988325 | − | 0.152360i | \(-0.951313\pi\) |
0.362215 | − | 0.932095i | \(-0.382021\pi\) | |||||||
\(522\) | −4.02995 | − | 6.98009i | −0.176386 | − | 0.305510i | ||||
\(523\) | −7.63600 | − | 13.2259i | −0.333899 | − | 0.578330i | 0.649374 | − | 0.760469i | \(-0.275031\pi\) |
−0.983273 | + | 0.182140i | \(0.941698\pi\) | |||||||
\(524\) | 0.836827 | + | 1.44943i | 0.0365570 | + | 0.0633185i | ||||
\(525\) | 43.8192 | 1.91243 | ||||||||
\(526\) | 1.09974 | + | 1.90480i | 0.0479509 | + | 0.0830534i | ||||
\(527\) | −8.23558 | −0.358748 | ||||||||
\(528\) | 0.740022 | + | 1.28176i | 0.0322053 | + | 0.0557813i | ||||
\(529\) | −19.1858 | −0.834163 | ||||||||
\(530\) | −50.8229 | −2.20760 | ||||||||
\(531\) | 1.53463 | + | 2.65806i | 0.0665973 | + | 0.115350i | ||||
\(532\) | −3.04896 | + | 5.28095i | −0.132189 | + | 0.228958i | ||||
\(533\) | −11.6897 | − | 20.2471i | −0.506335 | − | 0.876998i | ||||
\(534\) | −0.437843 | − | 0.758367i | −0.0189473 | − | 0.0328177i | ||||
\(535\) | 10.5447 | 0.455889 | ||||||||
\(536\) | 41.2976 | 1.78378 | ||||||||
\(537\) | −6.55306 | − | 11.3502i | −0.282786 | − | 0.489799i | ||||
\(538\) | 34.6511 | 1.49392 | ||||||||
\(539\) | 1.42598 | − | 2.46988i | 0.0614215 | − | 0.106385i | ||||
\(540\) | −0.504625 | + | 0.874035i | −0.0217156 | + | 0.0376125i | ||||
\(541\) | −7.19393 | + | 12.4602i | −0.309291 | + | 0.535708i | −0.978207 | − | 0.207630i | \(-0.933425\pi\) |
0.668916 | + | 0.743338i | \(0.266758\pi\) | |||||||
\(542\) | −3.67735 | − | 6.36936i | −0.157956 | − | 0.273587i | ||||
\(543\) | 6.86093 | + | 11.8835i | 0.294431 | + | 0.509969i | ||||
\(544\) | 1.05796 | − | 1.83244i | 0.0453596 | − | 0.0785651i | ||||
\(545\) | −23.4701 | − | 40.6514i | −1.00535 | − | 1.74131i | ||||
\(546\) | −11.5104 | −0.492598 | ||||||||
\(547\) | 6.98784 | − | 12.1033i | 0.298778 | − | 0.517499i | −0.677078 | − | 0.735911i | \(-0.736754\pi\) |
0.975857 | + | 0.218412i | \(0.0700875\pi\) | |||||||
\(548\) | −0.195352 | + | 0.338360i | −0.00834504 | + | 0.0144540i | ||||
\(549\) | 9.74630 | 0.415962 | ||||||||
\(550\) | −6.74425 | −0.287576 | ||||||||
\(551\) | −20.4377 | + | 35.3991i | −0.870675 | + | 1.50805i | ||||
\(552\) | −2.90458 | + | 5.03087i | −0.123627 | + | 0.214128i | ||||
\(553\) | −26.5558 | −1.12927 | ||||||||
\(554\) | 15.6458 | + | 27.0993i | 0.664726 | + | 1.15134i | ||||
\(555\) | −17.3913 | + | 30.1227i | −0.738221 | + | 1.27864i | ||||
\(556\) | −2.81197 | − | 4.87047i | −0.119254 | − | 0.206554i | ||||
\(557\) | 9.34061 | + | 16.1784i | 0.395774 | + | 0.685501i | 0.993200 | − | 0.116423i | \(-0.0371429\pi\) |
−0.597425 | + | 0.801924i | \(0.703810\pi\) | |||||||
\(558\) | −3.56239 | + | 6.17024i | −0.150808 | + | 0.261207i | ||||
\(559\) | −11.1309 | + | 19.2794i | −0.470789 | + | 0.815430i | ||||
\(560\) | −26.1507 | + | 45.2944i | −1.10507 | + | 1.91404i | ||||
\(561\) | −0.657154 | −0.0277451 | ||||||||
\(562\) | 13.1966 | + | 22.8572i | 0.556666 | + | 0.964174i | ||||
\(563\) | −29.5188 | −1.24407 | −0.622034 | − | 0.782990i | \(-0.713693\pi\) | ||||
−0.622034 | + | 0.782990i | \(0.713693\pi\) | |||||||
\(564\) | 1.62127 | 0.0682677 | ||||||||
\(565\) | −22.0574 | − | 38.2046i | −0.927962 | − | 1.60728i | ||||
\(566\) | −0.854453 | − | 1.47996i | −0.0359154 | − | 0.0622072i | ||||
\(567\) | 1.84690 | − | 3.19893i | 0.0775627 | − | 0.134342i | ||||
\(568\) | −1.59618 | − | 2.76467i | −0.0669743 | − | 0.116003i | ||||
\(569\) | 29.3278 | 1.22948 | 0.614742 | − | 0.788728i | \(-0.289260\pi\) | ||||
0.614742 | + | 0.788728i | \(0.289260\pi\) | |||||||
\(570\) | −36.5328 | −1.53019 | ||||||||
\(571\) | −20.6703 | − | 35.8021i | −0.865026 | − | 1.49827i | −0.867021 | − | 0.498272i | \(-0.833968\pi\) |
0.00199457 | − | 0.999998i | \(-0.499365\pi\) | |||||||
\(572\) | −0.248202 | −0.0103779 | ||||||||
\(573\) | −11.4553 | − | 19.8411i | −0.478550 | − | 0.828874i | ||||
\(574\) | 48.6158 | 2.02918 | ||||||||
\(575\) | −11.5841 | − | 20.0643i | −0.483092 | − | 0.836740i | ||||
\(576\) | −4.36331 | − | 7.55748i | −0.181805 | − | 0.314895i | ||||
\(577\) | 6.00504 | + | 10.4010i | 0.249993 | + | 0.433001i | 0.963524 | − | 0.267623i | \(-0.0862383\pi\) |
−0.713530 | + | 0.700624i | \(0.752905\pi\) | |||||||
\(578\) | 9.70583 | + | 16.8110i | 0.403709 | + | 0.699245i | ||||
\(579\) | −19.5739 | −0.813464 | ||||||||
\(580\) | 3.07083 | − | 5.31883i | 0.127509 | − | 0.220852i | ||||
\(581\) | 20.6456 | + | 35.7592i | 0.856523 | + | 1.48354i | ||||
\(582\) | 3.01282 | 0.124885 | ||||||||
\(583\) | 4.01099 | 0.166118 | ||||||||
\(584\) | −8.49024 | + | 14.7055i | −0.351329 | + | 0.608519i | ||||
\(585\) | 4.83067 | + | 8.36697i | 0.199724 | + | 0.345932i | ||||
\(586\) | −12.3358 | + | 21.3662i | −0.509587 | + | 0.882631i | ||||
\(587\) | −8.96665 | −0.370093 | −0.185047 | − | 0.982730i | \(-0.559244\pi\) | ||||
−0.185047 | + | 0.982730i | \(0.559244\pi\) | |||||||
\(588\) | −0.816481 | + | 1.41419i | −0.0336711 | + | 0.0583201i | ||||
\(589\) | 36.1329 | 1.48883 | ||||||||
\(590\) | 8.34666 | − | 14.4568i | 0.343626 | − | 0.595178i | ||||
\(591\) | −3.49793 | − | 6.05859i | −0.143886 | − | 0.249217i | ||||
\(592\) | −14.6030 | − | 25.2931i | −0.600178 | − | 1.03954i | ||||
\(593\) | 17.6972 | − | 30.6525i | 0.726738 | − | 1.25875i | −0.231517 | − | 0.972831i | \(-0.574369\pi\) |
0.958255 | − | 0.285916i | \(-0.0922978\pi\) | |||||||
\(594\) | −0.284259 | + | 0.492351i | −0.0116633 | + | 0.0202014i | ||||
\(595\) | −11.6112 | − | 20.1111i | −0.476012 | − | 0.824477i | ||||
\(596\) | −4.60492 | −0.188625 | ||||||||
\(597\) | −3.22382 | − | 5.58381i | −0.131942 | − | 0.228530i | ||||
\(598\) | 3.04291 | + | 5.27047i | 0.124434 | + | 0.215526i | ||||
\(599\) | 17.3550 | 0.709106 | 0.354553 | − | 0.935036i | \(-0.384633\pi\) | ||||
0.354553 | + | 0.935036i | \(0.384633\pi\) | |||||||
\(600\) | 35.2857 | 1.44053 | ||||||||
\(601\) | −19.8373 | −0.809179 | −0.404590 | − | 0.914498i | \(-0.632586\pi\) | ||||
−0.404590 | + | 0.914498i | \(0.632586\pi\) | |||||||
\(602\) | −23.1461 | − | 40.0902i | −0.943364 | − | 1.63395i | ||||
\(603\) | 6.94202 | + | 12.0239i | 0.282701 | + | 0.489652i | ||||
\(604\) | 1.49984 | − | 2.59781i | 0.0610278 | − | 0.105703i | ||||
\(605\) | −44.4143 | −1.80570 | ||||||||
\(606\) | 0.869149 | − | 1.50541i | 0.0353068 | − | 0.0611531i | ||||
\(607\) | −15.9725 | + | 27.6652i | −0.648303 | + | 1.12289i | 0.335225 | + | 0.942138i | \(0.391188\pi\) |
−0.983528 | + | 0.180756i | \(0.942146\pi\) | |||||||
\(608\) | −4.64170 | + | 8.03966i | −0.188246 | + | 0.326051i | ||||
\(609\) | −11.2391 | + | 19.4667i | −0.455431 | + | 0.788830i | ||||
\(610\) | −26.5044 | − | 45.9070i | −1.07313 | − | 1.85872i | ||||
\(611\) | 7.76005 | − | 13.4408i | 0.313938 | − | 0.543757i | ||||
\(612\) | 0.376269 | 0.0152098 | ||||||||
\(613\) | 7.95929 | + | 13.7859i | 0.321473 | + | 0.556807i | 0.980792 | − | 0.195056i | \(-0.0624888\pi\) |
−0.659319 | + | 0.751863i | \(0.729155\pi\) | |||||||
\(614\) | −30.7200 | −1.23976 | ||||||||
\(615\) | −20.4031 | − | 35.3392i | −0.822731 | − | 1.42501i | ||||
\(616\) | 2.35806 | − | 4.08427i | 0.0950088 | − | 0.164560i | ||||
\(617\) | −14.4686 | + | 25.0603i | −0.582484 | + | 1.00889i | 0.412700 | + | 0.910867i | \(0.364586\pi\) |
−0.995184 | + | 0.0980244i | \(0.968748\pi\) | |||||||
\(618\) | −3.66875 | + | 6.35446i | −0.147579 | + | 0.255614i | ||||
\(619\) | −8.27505 | − | 14.3328i | −0.332602 | − | 0.576084i | 0.650419 | − | 0.759576i | \(-0.274593\pi\) |
−0.983021 | + | 0.183492i | \(0.941260\pi\) | |||||||
\(620\) | −5.42908 | −0.218037 | ||||||||
\(621\) | −1.95301 | −0.0783715 | ||||||||
\(622\) | −2.72138 | + | 4.71356i | −0.109117 | + | 0.188997i | ||||
\(623\) | −1.22110 | + | 2.11500i | −0.0489222 | + | 0.0847357i | ||||
\(624\) | −8.11233 | −0.324753 | ||||||||
\(625\) | −28.2067 | + | 48.8554i | −1.12827 | + | 1.95422i | ||||
\(626\) | 30.6128 | 1.22353 | ||||||||
\(627\) | 2.88321 | 0.115144 | ||||||||
\(628\) | −0.349828 | − | 3.05958i | −0.0139596 | − | 0.122091i | ||||
\(629\) | 12.9677 | 0.517057 | ||||||||
\(630\) | −20.0901 | −0.800410 | ||||||||
\(631\) | 1.10751 | − | 1.91827i | 0.0440894 | − | 0.0763650i | −0.843139 | − | 0.537696i | \(-0.819295\pi\) |
0.887228 | + | 0.461331i | \(0.152628\pi\) | |||||||
\(632\) | −21.3843 | −0.850620 | ||||||||
\(633\) | 0.585767 | − | 1.01458i | 0.0232822 | − | 0.0403259i | ||||
\(634\) | 8.68641 | − | 15.0453i | 0.344982 | − | 0.597526i | ||||
\(635\) | 34.6083 | 1.37339 | ||||||||
\(636\) | −2.29659 | −0.0910656 | ||||||||
\(637\) | 7.81602 | + | 13.5377i | 0.309682 | + | 0.536385i | ||||
\(638\) | 1.72982 | − | 2.99614i | 0.0684843 | − | 0.118618i | ||||
\(639\) | 0.536628 | − | 0.929468i | 0.0212287 | − | 0.0367692i | ||||
\(640\) | −18.0561 | + | 31.2741i | −0.713729 | + | 1.23622i | ||||
\(641\) | 8.58773 | + | 14.8744i | 0.339195 | + | 0.587503i | 0.984282 | − | 0.176607i | \(-0.0565121\pi\) |
−0.645087 | + | 0.764109i | \(0.723179\pi\) | |||||||
\(642\) | −3.40105 | −0.134229 | ||||||||
\(643\) | 5.76022 | + | 9.97699i | 0.227161 | + | 0.393454i | 0.956966 | − | 0.290202i | \(-0.0937224\pi\) |
−0.729805 | + | 0.683656i | \(0.760389\pi\) | |||||||
\(644\) | 1.77301 | 0.0698663 | ||||||||
\(645\) | −19.4279 | + | 33.6501i | −0.764973 | + | 1.32497i | ||||
\(646\) | 6.81011 | + | 11.7954i | 0.267940 | + | 0.464086i | ||||
\(647\) | −0.476192 | + | 0.824788i | −0.0187210 | + | 0.0324258i | −0.875234 | − | 0.483699i | \(-0.839293\pi\) |
0.856513 | + | 0.516125i | \(0.172626\pi\) | |||||||
\(648\) | 1.48723 | − | 2.57596i | 0.0584240 | − | 0.101193i | ||||
\(649\) | −0.658726 | + | 1.14095i | −0.0258573 | + | 0.0447861i | ||||
\(650\) | 18.4831 | − | 32.0137i | 0.724967 | − | 1.25568i | ||||
\(651\) | 19.8702 | 0.778775 | ||||||||
\(652\) | −0.377002 | + | 0.652986i | −0.0147645 | + | 0.0255729i | ||||
\(653\) | 7.59087 | + | 13.1478i | 0.297054 | + | 0.514512i | 0.975461 | − | 0.220174i | \(-0.0706626\pi\) |
−0.678407 | + | 0.734687i | \(0.737329\pi\) | |||||||
\(654\) | 7.56993 | + | 13.1115i | 0.296008 | + | 0.512700i | ||||
\(655\) | 27.9640 | 1.09264 | ||||||||
\(656\) | 34.2636 | 1.33777 | ||||||||
\(657\) | −5.70876 | −0.222720 | ||||||||
\(658\) | 16.1365 | + | 27.9493i | 0.629067 | + | 1.08958i | ||||
\(659\) | −6.33771 | − | 10.9772i | −0.246882 | − | 0.427612i | 0.715777 | − | 0.698329i | \(-0.246073\pi\) |
−0.962659 | + | 0.270717i | \(0.912739\pi\) | |||||||
\(660\) | −0.433211 | −0.0168627 | ||||||||
\(661\) | 11.8957 | + | 20.6040i | 0.462689 | + | 0.801401i | 0.999094 | − | 0.0425595i | \(-0.0135512\pi\) |
−0.536405 | + | 0.843961i | \(0.680218\pi\) | |||||||
\(662\) | −15.3510 | + | 26.5887i | −0.596632 | + | 1.03340i | ||||
\(663\) | 1.80098 | − | 3.11938i | 0.0699441 | − | 0.121147i | ||||
\(664\) | 16.6250 | + | 28.7954i | 0.645175 | + | 1.11748i | ||||
\(665\) | 50.9430 | + | 88.2359i | 1.97549 | + | 3.42164i | ||||
\(666\) | 5.60932 | − | 9.71563i | 0.217357 | − | 0.376473i | ||||
\(667\) | 11.8848 | 0.460181 | ||||||||
\(668\) | 0.00308476 | − | 0.00534296i | 0.000119353 | − | 0.000206725i | ||||
\(669\) | 24.0103 | 0.928293 | ||||||||
\(670\) | 37.7567 | − | 65.3966i | 1.45867 | − | 2.52649i | ||||
\(671\) | 2.09176 | + | 3.62303i | 0.0807513 | + | 0.139865i | ||||
\(672\) | −2.55256 | + | 4.42117i | −0.0984673 | + | 0.170550i | ||||
\(673\) | 31.2291 | 1.20379 | 0.601897 | − | 0.798574i | \(-0.294412\pi\) | ||||
0.601897 | + | 0.798574i | \(0.294412\pi\) | |||||||
\(674\) | −13.3391 | −0.513802 | ||||||||
\(675\) | 5.93144 | + | 10.2735i | 0.228301 | + | 0.395429i | ||||
\(676\) | −0.917303 | + | 1.58882i | −0.0352809 | + | 0.0611083i | ||||
\(677\) | −43.9667 | −1.68978 | −0.844889 | − | 0.534942i | \(-0.820333\pi\) | ||||
−0.844889 | + | 0.534942i | \(0.820333\pi\) | |||||||
\(678\) | 7.11429 | + | 12.3223i | 0.273223 | + | 0.473236i | ||||
\(679\) | −4.20121 | − | 7.27670i | −0.161228 | − | 0.279254i | ||||
\(680\) | −9.34998 | − | 16.1946i | −0.358555 | − | 0.621036i | ||||
\(681\) | 7.40268 | + | 12.8218i | 0.283671 | + | 0.491333i | ||||
\(682\) | −3.05824 | −0.117106 | ||||||||
\(683\) | −13.6091 | − | 23.5716i | −0.520737 | − | 0.901943i | −0.999709 | − | 0.0241132i | \(-0.992324\pi\) |
0.478972 | − | 0.877830i | \(-0.341010\pi\) | |||||||
\(684\) | −1.65085 | −0.0631218 | ||||||||
\(685\) | 3.26401 | + | 5.65344i | 0.124712 | + | 0.216007i | ||||
\(686\) | 1.74064 | 0.0664578 | ||||||||
\(687\) | −16.9309 | −0.645953 | ||||||||
\(688\) | −16.3130 | − | 28.2550i | −0.621927 | − | 1.07721i | ||||
\(689\) | −10.9924 | + | 19.0394i | −0.418777 | + | 0.725343i | ||||
\(690\) | 5.31108 | + | 9.19906i | 0.202189 | + | 0.350202i | ||||
\(691\) | 23.3655 | + | 40.4702i | 0.888866 | + | 1.53956i | 0.841218 | + | 0.540696i | \(0.181839\pi\) |
0.0476480 | + | 0.998864i | \(0.484827\pi\) | |||||||
\(692\) | 4.75757 | 0.180856 | ||||||||
\(693\) | 1.58553 | 0.0602294 | ||||||||
\(694\) | 8.79008 | + | 15.2249i | 0.333667 | + | 0.577928i | ||||
\(695\) | −93.9666 | −3.56435 | ||||||||
\(696\) | −9.05036 | + | 15.6757i | −0.343053 | + | 0.594185i | ||||
\(697\) | −7.60669 | + | 13.1752i | −0.288124 | + | 0.499046i | ||||
\(698\) | −10.7693 | + | 18.6530i | −0.407625 | + | 0.706026i | ||||
\(699\) | 8.30278 | + | 14.3808i | 0.314040 | + | 0.543933i | ||||
\(700\) | −5.38476 | − | 9.32668i | −0.203525 | − | 0.352516i | ||||
\(701\) | 9.20063 | − | 15.9360i | 0.347503 | − | 0.601893i | −0.638302 | − | 0.769786i | \(-0.720363\pi\) |
0.985805 | + | 0.167893i | \(0.0536963\pi\) | |||||||
\(702\) | −1.55806 | − | 2.69864i | −0.0588053 | − | 0.101854i | ||||
\(703\) | −56.8947 | −2.14582 | ||||||||
\(704\) | 1.87291 | − | 3.24398i | 0.0705880 | − | 0.122262i | ||||
\(705\) | 13.5444 | − | 23.4595i | 0.510110 | − | 0.883536i | ||||
\(706\) | −24.3468 | −0.916305 | ||||||||
\(707\) | −4.84792 | −0.182325 | ||||||||
\(708\) | 0.377169 | − | 0.653276i | 0.0141749 | − | 0.0245516i | ||||
\(709\) | −5.71706 | + | 9.90224i | −0.214709 | + | 0.371887i | −0.953182 | − | 0.302396i | \(-0.902214\pi\) |
0.738474 | + | 0.674282i | \(0.235547\pi\) | |||||||
\(710\) | −5.83731 | −0.219070 | ||||||||
\(711\) | −3.59464 | − | 6.22610i | −0.134810 | − | 0.233497i | ||||
\(712\) | −0.983296 | + | 1.70312i | −0.0368506 | + | 0.0638271i | ||||
\(713\) | −5.25294 | − | 9.09836i | −0.196724 | − | 0.340736i | ||||
\(714\) | 3.74501 | + | 6.48655i | 0.140154 | + | 0.242753i | ||||
\(715\) | −2.07352 | + | 3.59145i | −0.0775454 | + | 0.134312i | ||||
\(716\) | −1.61056 | + | 2.78957i | −0.0601894 | + | 0.104251i | ||||
\(717\) | 9.70125 | − | 16.8031i | 0.362300 | − | 0.627522i | ||||
\(718\) | −0.411176 | −0.0153450 | ||||||||
\(719\) | 21.9655 | + | 38.0453i | 0.819174 | + | 1.41885i | 0.906291 | + | 0.422654i | \(0.138901\pi\) |
−0.0871169 | + | 0.996198i | \(0.527765\pi\) | |||||||
\(720\) | −14.1592 | −0.527683 | ||||||||
\(721\) | 20.4635 | 0.762099 | ||||||||
\(722\) | −17.2963 | − | 29.9580i | −0.643700 | − | 1.11492i | ||||
\(723\) | −8.95415 | − | 15.5090i | −0.333008 | − | 0.576787i | ||||
\(724\) | 1.68623 | − | 2.92063i | 0.0626681 | − | 0.108544i | ||||
\(725\) | −36.0950 | − | 62.5184i | −1.34053 | − | 2.32187i | ||||
\(726\) | 14.3252 | 0.531657 | ||||||||
\(727\) | −36.5297 | −1.35481 | −0.677405 | − | 0.735610i | \(-0.736896\pi\) | ||||
−0.677405 | + | 0.735610i | \(0.736896\pi\) | |||||||
\(728\) | 12.9248 | + | 22.3865i | 0.479026 | + | 0.829698i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 15.5246 | + | 26.8894i | 0.574591 | + | 0.995221i | ||||
\(731\) | 14.4863 | 0.535794 | ||||||||
\(732\) | −1.19768 | − | 2.07445i | −0.0442677 | − | 0.0766739i | ||||
\(733\) | −2.94043 | − | 5.09298i | −0.108607 | − | 0.188113i | 0.806599 | − | 0.591099i | \(-0.201306\pi\) |
−0.915206 | + | 0.402986i | \(0.867972\pi\) | |||||||
\(734\) | −15.8617 | − | 27.4734i | −0.585468 | − | 1.01406i | ||||
\(735\) | 13.6420 | + | 23.6287i | 0.503194 | + | 0.871558i | ||||
\(736\) | 2.69921 | 0.0994941 | ||||||||
\(737\) | −2.97980 | + | 5.16116i | −0.109762 | + | 0.190114i | ||||
\(738\) | 6.58071 | + | 11.3981i | 0.242239 | + | 0.419571i | ||||
\(739\) | 29.7338 | 1.09377 | 0.546887 | − | 0.837206i | \(-0.315813\pi\) | ||||
0.546887 | + | 0.837206i | \(0.315813\pi\) | |||||||
\(740\) | 8.54861 | 0.314253 | ||||||||
\(741\) | −7.90163 | + | 13.6860i | −0.290274 | + | 0.502769i | ||||
\(742\) | −22.8580 | − | 39.5912i | −0.839142 | − | 1.45344i | ||||
\(743\) | −8.50203 | + | 14.7260i | −0.311909 | + | 0.540243i | −0.978776 | − | 0.204935i | \(-0.934302\pi\) |
0.666866 | + | 0.745177i | \(0.267635\pi\) | |||||||
\(744\) | 16.0006 | 0.586611 | ||||||||
\(745\) | −38.4703 | + | 66.6324i | −1.40944 | + | 2.44122i | ||||
\(746\) | −22.0409 | −0.806974 | ||||||||
\(747\) | −5.58924 | + | 9.68086i | −0.204500 | + | 0.354204i | ||||
\(748\) | 0.0807551 | + | 0.139872i | 0.00295270 | + | 0.00511422i | ||||
\(749\) | 4.74257 | + | 8.21438i | 0.173290 | + | 0.300147i | ||||
\(750\) | 18.6631 | − | 32.3255i | 0.681482 | − | 1.18036i | ||||
\(751\) | 6.79611 | − | 11.7712i | 0.247994 | − | 0.429537i | −0.714975 | − | 0.699150i | \(-0.753562\pi\) |
0.962969 | + | 0.269612i | \(0.0868955\pi\) | |||||||
\(752\) | 11.3728 | + | 19.6982i | 0.414722 | + | 0.718320i | ||||
\(753\) | 0.189558 | 0.00690788 | ||||||||
\(754\) | 9.48139 | + | 16.4223i | 0.345292 | + | 0.598063i | ||||
\(755\) | −25.0599 | − | 43.4050i | −0.912024 | − | 1.57967i | ||||
\(756\) | −0.907835 | −0.0330176 | ||||||||
\(757\) | −1.51356 | −0.0550112 | −0.0275056 | − | 0.999622i | \(-0.508756\pi\) | ||||
−0.0275056 | + | 0.999622i | \(0.508756\pi\) | |||||||
\(758\) | −25.2060 | −0.915521 | ||||||||
\(759\) | −0.419156 | − | 0.725999i | −0.0152144 | − | 0.0263521i | ||||
\(760\) | 41.0222 | + | 71.0526i | 1.48803 | + | 2.57735i | ||||
\(761\) | 15.8443 | − | 27.4432i | 0.574356 | − | 0.994814i | −0.421755 | − | 0.906710i | \(-0.638586\pi\) |
0.996111 | − | 0.0881043i | \(-0.0280809\pi\) | |||||||
\(762\) | −11.1624 | −0.404371 | ||||||||
\(763\) | 21.1117 | − | 36.5665i | 0.764295 | − | 1.32380i | ||||
\(764\) | −2.81538 | + | 4.87639i | −0.101857 | + | 0.176422i | ||||
\(765\) | 3.14342 | − | 5.44456i | 0.113650 | − | 0.196848i | ||||
\(766\) | −2.32359 | + | 4.02458i | −0.0839548 | + | 0.145414i | ||||
\(767\) | −3.61057 | − | 6.25369i | −0.130370 | − | 0.225808i | ||||
\(768\) | −2.90290 | + | 5.02798i | −0.104750 | + | 0.181431i | ||||
\(769\) | −33.1361 | −1.19492 | −0.597459 | − | 0.801900i | \(-0.703823\pi\) | ||||
−0.597459 | + | 0.801900i | \(0.703823\pi\) | |||||||
\(770\) | −4.31176 | − | 7.46818i | −0.155385 | − | 0.269134i | ||||
\(771\) | −8.15110 | −0.293555 | ||||||||
\(772\) | 2.40536 | + | 4.16621i | 0.0865708 | + | 0.149945i | ||||
\(773\) | −4.62049 | + | 8.00292i | −0.166187 | + | 0.287845i | −0.937076 | − | 0.349125i | \(-0.886479\pi\) |
0.770889 | + | 0.636970i | \(0.219812\pi\) | |||||||
\(774\) | 6.26618 | − | 10.8533i | 0.225233 | − | 0.390116i | ||||
\(775\) | −31.9072 | + | 55.2648i | −1.14614 | + | 1.98517i | ||||
\(776\) | −3.38305 | − | 5.85962i | −0.121444 | − | 0.210348i | ||||
\(777\) | −31.2875 | −1.12243 | ||||||||
\(778\) | −33.3267 | −1.19482 | ||||||||
\(779\) | 33.3737 | − | 57.8050i | 1.19574 | − | 2.07108i | ||||
\(780\) | 1.18724 | − | 2.05637i | 0.0425102 | − | 0.0736298i | ||||
\(781\) | 0.460686 | 0.0164846 | ||||||||
\(782\) | 1.98008 | − | 3.42960i | 0.0708076 | − | 0.122642i | ||||
\(783\) | −6.08537 | −0.217473 | ||||||||
\(784\) | −22.9096 | −0.818200 | ||||||||
\(785\) | −47.1942 | − | 20.4983i | −1.68443 | − | 0.731616i | ||||
\(786\) | −9.01937 | −0.321710 | ||||||||
\(787\) | 37.1471 | 1.32415 | 0.662075 | − | 0.749438i | \(-0.269676\pi\) | ||||
0.662075 | + | 0.749438i | \(0.269676\pi\) | |||||||
\(788\) | −0.859693 | + | 1.48903i | −0.0306253 | + | 0.0530446i | ||||
\(789\) | 1.66065 | 0.0591205 | ||||||||
\(790\) | −19.5508 | + | 33.8630i | −0.695586 | + | 1.20479i | ||||
\(791\) | 19.8410 | − | 34.3656i | 0.705464 | − | 1.22190i | ||||
\(792\) | 1.27676 | 0.0453677 | ||||||||
\(793\) | −22.9304 | −0.814283 | ||||||||
\(794\) | −3.04120 | − | 5.26751i | −0.107928 | − | 0.186937i | ||||
\(795\) | −19.1861 | + | 33.2313i | −0.680460 | + | 1.17859i | ||||
\(796\) | −0.792324 | + | 1.37235i | −0.0280832 | + | 0.0486415i | ||||
\(797\) | 15.8021 | − | 27.3701i | 0.559739 | − | 0.969497i | −0.437778 | − | 0.899083i | \(-0.644235\pi\) |
0.997518 | − | 0.0704143i | \(-0.0224321\pi\) | |||||||
\(798\) | −16.4309 | − | 28.4592i | −0.581648 | − | 1.00744i | ||||
\(799\) | −10.0992 | −0.357285 | ||||||||
\(800\) | −8.19770 | − | 14.1988i | −0.289833 | − | 0.502005i | ||||
\(801\) | −0.661158 | −0.0233609 | ||||||||
\(802\) | −16.6867 | + | 28.9021i | −0.589226 | + | 1.02057i | ||||
\(803\) | −1.22522 | − | 2.12214i | −0.0432369 | − | 0.0748885i | ||||
\(804\) | 1.70615 | − | 2.95515i | 0.0601714 | − | 0.104220i | ||||
\(805\) | 14.8120 | − | 25.6552i | 0.522055 | − | 0.904226i | ||||
\(806\) | 8.38133 | − | 14.5169i | 0.295220 | − | 0.511336i | ||||
\(807\) | 13.0811 | − | 22.6571i | 0.460477 | − | 0.797569i | ||||
\(808\) | −3.90382 | −0.137336 | ||||||||
\(809\) | −4.36683 | + | 7.56358i | −0.153530 | + | 0.265921i | −0.932523 | − | 0.361111i | \(-0.882397\pi\) |
0.778993 | + | 0.627033i | \(0.215731\pi\) | |||||||
\(810\) | −2.71944 | − | 4.71020i | −0.0955512 | − | 0.165500i | ||||
\(811\) | 1.70727 | + | 2.95707i | 0.0599502 | + | 0.103837i | 0.894443 | − | 0.447182i | \(-0.147572\pi\) |
−0.834493 | + | 0.551019i | \(0.814239\pi\) | |||||||
\(812\) | 5.52451 | 0.193872 | ||||||||
\(813\) | −5.55293 | −0.194750 | ||||||||
\(814\) | 4.81550 | 0.168783 | ||||||||
\(815\) | 6.29907 | + | 10.9103i | 0.220647 | + | 0.382172i | ||||
\(816\) | 2.63943 | + | 4.57163i | 0.0923985 | + | 0.160039i | ||||
\(817\) | −63.5572 | −2.22359 | ||||||||
\(818\) | 5.99050 | + | 10.3759i | 0.209453 | + | 0.362783i | ||||
\(819\) | −4.34526 | + | 7.52622i | −0.151836 | + | 0.262987i | ||||
\(820\) | −5.01451 | + | 8.68538i | −0.175114 | + | 0.303307i | ||||
\(821\) | −0.331118 | − | 0.573514i | −0.0115561 | − | 0.0200158i | 0.860190 | − | 0.509974i | \(-0.170345\pi\) |
−0.871746 | + | 0.489959i | \(0.837012\pi\) | |||||||
\(822\) | −1.05276 | − | 1.82343i | −0.0367192 | − | 0.0635995i | ||||
\(823\) | −15.1637 | + | 26.2643i | −0.528574 | + | 0.915516i | 0.470871 | + | 0.882202i | \(0.343940\pi\) |
−0.999445 | + | 0.0333144i | \(0.989394\pi\) | |||||||
\(824\) | 16.4783 | 0.574050 | ||||||||
\(825\) | −2.54601 | + | 4.40983i | −0.0886409 | + | 0.153530i | ||||
\(826\) | 15.0159 | 0.522469 | ||||||||
\(827\) | −17.5350 | + | 30.3714i | −0.609750 | + | 1.05612i | 0.381531 | + | 0.924356i | \(0.375397\pi\) |
−0.991281 | + | 0.131762i | \(0.957936\pi\) | |||||||
\(828\) | 0.239997 | + | 0.415688i | 0.00834049 | + | 0.0144462i | ||||
\(829\) | −22.5841 | + | 39.1169i | −0.784380 | + | 1.35859i | 0.144989 | + | 0.989433i | \(0.453685\pi\) |
−0.929369 | + | 0.369152i | \(0.879648\pi\) | |||||||
\(830\) | 60.7984 | 2.11034 | ||||||||
\(831\) | 23.6257 | 0.819566 | ||||||||
\(832\) | 10.2657 | + | 17.7807i | 0.355899 | + | 0.616435i | ||||
\(833\) | 5.08604 | − | 8.80928i | 0.176221 | − | 0.305223i | ||||
\(834\) | 30.3075 | 1.04946 | ||||||||
\(835\) | −0.0515412 | − | 0.0892721i | −0.00178366 | − | 0.00308939i | ||||
\(836\) | −0.354306 | − | 0.613676i | −0.0122539 | − | 0.0212244i | ||||
\(837\) | 2.68966 | + | 4.65864i | 0.0929684 | + | 0.161026i | ||||
\(838\) | 15.3459 | + | 26.5799i | 0.530116 | + | 0.918188i | ||||
\(839\) | −30.7730 | −1.06240 | −0.531201 | − | 0.847246i | \(-0.678259\pi\) | ||||
−0.531201 | + | 0.847246i | \(0.678259\pi\) | |||||||
\(840\) | 22.5589 | + | 39.0732i | 0.778357 | + | 1.34815i | ||||
\(841\) | 8.03175 | 0.276957 | ||||||||
\(842\) | −9.63965 | − | 16.6964i | −0.332204 | − | 0.575394i | ||||
\(843\) | 19.9274 | 0.686335 | ||||||||
\(844\) | −0.287931 | −0.00991098 | ||||||||
\(845\) | 15.3266 | + | 26.5465i | 0.527251 | + | 0.913226i | ||||
\(846\) | −4.36853 | + | 7.56652i | −0.150193 | + | 0.260142i | ||||
\(847\) | −19.9757 | − | 34.5988i | −0.686372 | − | 1.18883i | ||||
\(848\) | −16.1099 | − | 27.9032i | −0.553218 | − | 0.958201i | ||||
\(849\) | −1.29025 | −0.0442814 | ||||||||
\(850\) | −24.0547 | −0.825068 | ||||||||
\(851\) | 8.27125 | + | 14.3262i | 0.283535 | + | 0.491097i | ||||
\(852\) | −0.263777 | −0.00903684 | ||||||||
\(853\) | −0.742393 | + | 1.28586i | −0.0254191 | + | 0.0440271i | −0.878455 | − | 0.477825i | \(-0.841425\pi\) |
0.853036 | + | 0.521852i | \(0.174759\pi\) | |||||||
\(854\) | 23.8411 | − | 41.2941i | 0.815827 | − | 1.41305i | ||||
\(855\) | −13.7915 | + | 23.8875i | −0.471658 | + | 0.816936i | ||||
\(856\) | 3.81899 | + | 6.61468i | 0.130530 | + | 0.226085i | ||||
\(857\) | 17.5817 | + | 30.4523i | 0.600578 | + | 1.04023i | 0.992734 | + | 0.120332i | \(0.0383960\pi\) |
−0.392156 | + | 0.919899i | \(0.628271\pi\) | |||||||
\(858\) | 0.668784 | − | 1.15837i | 0.0228319 | − | 0.0395460i | ||||
\(859\) | −4.00596 | − | 6.93853i | −0.136682 | − | 0.236740i | 0.789557 | − | 0.613677i | \(-0.210310\pi\) |
−0.926239 | + | 0.376938i | \(0.876977\pi\) | |||||||
\(860\) | 9.54967 | 0.325641 | ||||||||
\(861\) | 18.3529 | − | 31.7881i | 0.625464 | − | 1.08334i | ||||
\(862\) | 19.1477 | − | 33.1648i | 0.652173 | − | 1.12960i | ||||
\(863\) | −17.5909 | −0.598801 | −0.299401 | − | 0.954127i | \(-0.596787\pi\) | ||||
−0.299401 | + | 0.954127i | \(0.596787\pi\) | |||||||
\(864\) | −1.38208 | −0.0470192 | ||||||||
\(865\) | 39.7456 | − | 68.8413i | 1.35139 | − | 2.34067i | ||||
\(866\) | 5.62342 | − | 9.74004i | 0.191091 | − | 0.330980i | ||||
\(867\) | 14.6561 | 0.497748 | ||||||||
\(868\) | −2.44177 | − | 4.22927i | −0.0828791 | − | 0.143551i | ||||
\(869\) | 1.54297 | − | 2.67250i | 0.0523416 | − | 0.0906583i | ||||
\(870\) | 16.5488 | + | 28.6633i | 0.561056 | + | 0.971778i | ||||
\(871\) | −16.3327 | − | 28.2891i | −0.553412 | − | 0.958538i | ||||
\(872\) | 17.0003 | − | 29.4455i | 0.575704 | − | 0.997149i | ||||
\(873\) | 1.13737 | − | 1.96997i | 0.0384940 | − | 0.0666735i | ||||
\(874\) | −8.68744 | + | 15.0471i | −0.293857 | + | 0.508975i | ||||
\(875\) | −104.099 | −3.51918 | ||||||||
\(876\) | 0.701526 | + | 1.21508i | 0.0237024 | + | 0.0410537i | ||||
\(877\) | −25.0843 | −0.847035 | −0.423518 | − | 0.905888i | \(-0.639205\pi\) | ||||
−0.423518 | + | 0.905888i | \(0.639205\pi\) | |||||||
\(878\) | 37.5331 | 1.26668 | ||||||||
\(879\) | 9.31375 | + | 16.1319i | 0.314145 | + | 0.544115i | ||||
\(880\) | −3.03886 | − | 5.26346i | −0.102440 | − | 0.177431i | ||||
\(881\) | 22.9002 | − | 39.6644i | 0.771529 | − | 1.33633i | −0.165196 | − | 0.986261i | \(-0.552826\pi\) |
0.936725 | − | 0.350067i | \(-0.113841\pi\) | |||||||
\(882\) | −4.40004 | − | 7.62109i | −0.148157 | − | 0.256615i | ||||
\(883\) | −11.5593 | −0.389001 | −0.194501 | − | 0.980902i | \(-0.562309\pi\) | ||||
−0.194501 | + | 0.980902i | \(0.562309\pi\) | |||||||
\(884\) | −0.885260 | −0.0297745 | ||||||||
\(885\) | −6.30187 | − | 10.9152i | −0.211835 | − | 0.366909i | ||||
\(886\) | 21.2732 | 0.714686 | ||||||||
\(887\) | −3.06528 | − | 5.30922i | −0.102922 | − | 0.178266i | 0.809965 | − | 0.586478i | \(-0.199486\pi\) |
−0.912887 | + | 0.408212i | \(0.866153\pi\) | |||||||
\(888\) | −25.1945 | −0.845472 | ||||||||
\(889\) | 15.5653 | + | 26.9599i | 0.522044 | + | 0.904207i | ||||
\(890\) | 1.79798 | + | 3.11419i | 0.0602684 | + | 0.104388i | ||||
\(891\) | 0.214620 | + | 0.371733i | 0.00719005 | + | 0.0124535i | ||||
\(892\) | −2.95053 | − | 5.11047i | −0.0987912 | − | 0.171111i | ||||
\(893\) | 44.3095 | 1.48276 | ||||||||
\(894\) | 12.4080 | − | 21.4913i | 0.414986 | − | 0.718777i | ||||
\(895\) | 26.9098 | + | 46.6091i | 0.899495 | + | 1.55797i | ||||
\(896\) | −32.4834 | −1.08520 | ||||||||
\(897\) | 4.59490 | 0.153419 | ||||||||
\(898\) | 19.3926 | − | 33.5889i | 0.647138 | − | 1.12088i | ||||
\(899\) | −16.3676 | − | 28.3495i | −0.545890 | − | 0.945510i | ||||
\(900\) | 1.45778 | − | 2.52495i | 0.0485927 | − | 0.0841651i | ||||
\(901\) | 14.3059 | 0.476600 | ||||||||
\(902\) | −2.82471 | + | 4.89254i | −0.0940526 | + | 0.162904i | ||||
\(903\) | −34.9514 | −1.16311 | ||||||||
\(904\) | 15.9771 | − | 27.6731i | 0.531390 | − | 0.920394i | ||||
\(905\) | −28.1740 | − | 48.7988i | −0.936536 | − | 1.62213i | ||||
\(906\) | 8.08271 | + | 13.9997i | 0.268530 | + | 0.465108i | ||||
\(907\) | 0.703869 | − | 1.21914i | 0.0233716 | − | 0.0404808i | −0.854103 | − | 0.520104i | \(-0.825893\pi\) |
0.877475 | + | 0.479623i | \(0.159227\pi\) | |||||||
\(908\) | 1.81937 | − | 3.15125i | 0.0603780 | − | 0.104578i | ||||
\(909\) | −0.656223 | − | 1.13661i | −0.0217655 | − | 0.0376990i | ||||
\(910\) | 47.2667 | 1.56687 | ||||||||
\(911\) | 17.4290 | + | 30.1879i | 0.577448 | + | 1.00017i | 0.995771 | + | 0.0918711i | \(0.0292848\pi\) |
−0.418323 | + | 0.908298i | \(0.637382\pi\) | |||||||
\(912\) | −11.5803 | − | 20.0576i | −0.383461 | − | 0.664174i | ||||
\(913\) | −4.79826 | −0.158799 | ||||||||
\(914\) | −13.2960 | −0.439794 | ||||||||
\(915\) | −40.0226 | −1.32311 | ||||||||
\(916\) | 2.08057 | + | 3.60365i | 0.0687439 | + | 0.119068i | ||||
\(917\) | 12.5770 | + | 21.7840i | 0.415330 | + | 0.719372i | ||||
\(918\) | −1.01386 | + | 1.75606i | −0.0334625 | + | 0.0579587i | ||||
\(919\) | −45.7684 | −1.50976 | −0.754879 | − | 0.655864i | \(-0.772305\pi\) | ||||
−0.754879 | + | 0.655864i | \(0.772305\pi\) | |||||||
\(920\) | 11.9275 | − | 20.6590i | 0.393237 | − | 0.681107i | ||||
\(921\) | −11.5971 | + | 20.0867i | −0.382136 | + | 0.661879i | ||||
\(922\) | 19.5173 | − | 33.8049i | 0.642767 | − | 1.11331i | ||||
\(923\) | −1.26254 | + | 2.18679i | −0.0415571 | + | 0.0719789i | ||||
\(924\) | −0.194840 | − | 0.337473i | −0.00640976 | − | 0.0111020i | ||||
\(925\) | 50.2409 | − | 87.0197i | 1.65191 | − | 2.86119i | ||||
\(926\) | −32.6065 | −1.07152 | ||||||||
\(927\) | 2.76997 | + | 4.79773i | 0.0909777 | + | 0.157578i | ||||
\(928\) | 8.41045 | 0.276087 | ||||||||
\(929\) | 17.8929 | + | 30.9914i | 0.587047 | + | 1.01680i | 0.994617 | + | 0.103622i | \(0.0330432\pi\) |
−0.407569 | + | 0.913174i | \(0.633624\pi\) | |||||||
\(930\) | 14.6287 | − | 25.3377i | 0.479695 | − | 0.830857i | ||||
\(931\) | −22.3146 | + | 38.6499i | −0.731330 | + | 1.26670i | ||||
\(932\) | 2.04059 | − | 3.53441i | 0.0668418 | − | 0.115773i | ||||
\(933\) | 2.05469 | + | 3.55882i | 0.0672674 | + | 0.116511i | ||||
\(934\) | −10.1157 | −0.330997 | ||||||||
\(935\) | 2.69857 | 0.0882525 | ||||||||
\(936\) | −3.49905 | + | 6.06054i | −0.114370 | + | 0.198095i | ||||
\(937\) | 6.44187 | − | 11.1576i | 0.210447 | − | 0.364504i | −0.741408 | − | 0.671055i | \(-0.765842\pi\) |
0.951854 | + | 0.306551i | \(0.0991749\pi\) | |||||||
\(938\) | 67.9255 | 2.21785 | ||||||||
\(939\) | 11.5566 | − | 20.0166i | 0.377136 | − | 0.653218i | ||||
\(940\) | −6.65765 | −0.217149 | ||||||||
\(941\) | 56.2699 | 1.83435 | 0.917174 | − | 0.398487i | \(-0.130465\pi\) | ||||
0.917174 | + | 0.398487i | \(0.130465\pi\) | |||||||
\(942\) | 15.2218 | + | 6.61143i | 0.495953 | + | 0.215412i | ||||
\(943\) | −19.4072 | −0.631987 | ||||||||
\(944\) | 10.5830 | 0.344446 | ||||||||
\(945\) | −7.58420 | + | 13.1362i | −0.246714 | + | 0.427322i | ||||
\(946\) | 5.37940 | 0.174900 | ||||||||
\(947\) | −15.6433 | + | 27.0949i | −0.508338 | + | 0.880467i | 0.491615 | + | 0.870812i | \(0.336407\pi\) |
−0.999953 | + | 0.00965487i | \(0.996927\pi\) | |||||||
\(948\) | −0.883463 | + | 1.53020i | −0.0286935 | + | 0.0496987i | ||||
\(949\) | 13.4312 | 0.435994 | ||||||||
\(950\) | 105.538 | 3.42409 | ||||||||
\(951\) | −6.55839 | − | 11.3595i | −0.212671 | − | 0.368356i | ||||
\(952\) | 8.41045 | − | 14.5673i | 0.272584 | − | 0.472130i | ||||
\(953\) | −2.55116 | + | 4.41874i | −0.0826402 | + | 0.143137i | −0.904383 | − | 0.426721i | \(-0.859669\pi\) |
0.821743 | + | 0.569858i | \(0.193002\pi\) | |||||||
\(954\) | 6.18819 | − | 10.7183i | 0.200350 | − | 0.347016i | ||||
\(955\) | 47.0404 | + | 81.4763i | 1.52219 | + | 2.63651i | ||||
\(956\) | −4.76859 | −0.154227 | ||||||||
\(957\) | −1.30605 | − | 2.26214i | −0.0422184 | − | 0.0731245i | ||||
\(958\) | 35.7127 | 1.15382 | ||||||||
\(959\) | −2.93603 | + | 5.08535i | −0.0948093 | + | 0.164215i | ||||
\(960\) | 17.9177 | + | 31.0344i | 0.578291 | + | 1.00163i | ||||
\(961\) | 1.03141 | − | 1.78645i | 0.0332712 | − | 0.0576274i | ||||
\(962\) | −13.1972 | + | 22.8582i | −0.425495 | + | 0.736979i | ||||
\(963\) | −1.28393 | + | 2.22382i | −0.0413739 | + | 0.0716617i | ||||
\(964\) | −2.20068 | + | 3.81169i | −0.0708791 | + | 0.122766i | ||||
\(965\) | 80.3792 | 2.58750 | ||||||||
\(966\) | −4.77740 | + | 8.27469i | −0.153710 | + | 0.266234i | ||||
\(967\) | −2.40548 | − | 4.16641i | −0.0773549 | − | 0.133983i | 0.824753 | − | 0.565493i | \(-0.191314\pi\) |
−0.902108 | + | 0.431510i | \(0.857981\pi\) | |||||||
\(968\) | −16.0855 | − | 27.8610i | −0.517009 | − | 0.895485i | ||||
\(969\) | 10.2835 | 0.330354 | ||||||||
\(970\) | −12.3720 | −0.397240 | ||||||||
\(971\) | −38.1458 | −1.22416 | −0.612079 | − | 0.790797i | \(-0.709666\pi\) | ||||
−0.612079 | + | 0.790797i | \(0.709666\pi\) | |||||||
\(972\) | −0.122886 | − | 0.212845i | −0.00394157 | − | 0.00682700i | ||||
\(973\) | −42.2622 | − | 73.2002i | −1.35486 | − | 2.34669i | ||||
\(974\) | −2.99808 | −0.0960646 | ||||||||
\(975\) | −13.9551 | − | 24.1709i | −0.446920 | − | 0.774088i | ||||
\(976\) | 16.8029 | − | 29.1034i | 0.537847 | − | 0.931578i | ||||
\(977\) | 4.95186 | − | 8.57688i | 0.158424 | − | 0.274399i | −0.775876 | − | 0.630885i | \(-0.782692\pi\) |
0.934301 | + | 0.356486i | \(0.116025\pi\) | |||||||
\(978\) | −2.03167 | − | 3.51896i | −0.0649657 | − | 0.112524i | ||||
\(979\) | −0.141898 | − | 0.245775i | −0.00453508 | − | 0.00785500i | ||||
\(980\) | 3.35283 | − | 5.80728i | 0.107102 | − | 0.185507i | ||||
\(981\) | 11.4309 | 0.364959 | ||||||||
\(982\) | 13.8724 | − | 24.0277i | 0.442685 | − | 0.766754i | ||||
\(983\) | 46.4859 | 1.48267 | 0.741335 | − | 0.671135i | \(-0.234193\pi\) | ||||
0.741335 | + | 0.671135i | \(0.234193\pi\) | |||||||
\(984\) | 14.7788 | − | 25.5976i | 0.471130 | − | 0.816021i | ||||
\(985\) | 14.3640 | + | 24.8793i | 0.457677 | + | 0.792719i | ||||
\(986\) | 6.16973 | − | 10.6863i | 0.196484 | − | 0.340321i | ||||
\(987\) | 24.3667 | 0.775601 | ||||||||
\(988\) | 3.88400 | 0.123566 | ||||||||
\(989\) | 9.23984 | + | 16.0039i | 0.293810 | + | 0.508893i | ||||
\(990\) | 1.16729 | − | 2.02181i | 0.0370990 | − | 0.0642574i | ||||
\(991\) | −13.7158 | −0.435698 | −0.217849 | − | 0.975982i | \(-0.569904\pi\) | ||||
−0.217849 | + | 0.975982i | \(0.569904\pi\) | |||||||
\(992\) | −3.71732 | − | 6.43859i | −0.118025 | − | 0.204426i | ||||
\(993\) | 11.5903 | + | 20.0749i | 0.367805 | + | 0.637058i | ||||
\(994\) | −2.62537 | − | 4.54728i | −0.0832718 | − | 0.144231i | ||||
\(995\) | 13.2384 | + | 22.9296i | 0.419686 | + | 0.726918i | ||||
\(996\) | 2.74736 | 0.0870534 | ||||||||
\(997\) | −19.0529 | − | 33.0006i | −0.603412 | − | 1.04514i | −0.992300 | − | 0.123855i | \(-0.960474\pi\) |
0.388888 | − | 0.921285i | \(-0.372859\pi\) | |||||||
\(998\) | 21.6178 | 0.684299 | ||||||||
\(999\) | −4.23513 | − | 7.33547i | −0.133994 | − | 0.232084i |
(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 | 471.2.e.b.301.8 | yes | 22 | |
157.12 | even | 3 | inner | 471.2.e.b.169.8 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
471.2.e.b.169.8 | ✓ | 22 | 157.12 | even | 3 | inner | |
471.2.e.b.301.8 | yes | 22 | 1.1 | even | 1 | trivial |