Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [241,2,Mod(15,241)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(241, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("241.15");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 241.c (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: | \(1.92439468871\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Relative dimension: | \(19\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 15.15 | ||
Character | \(\chi\) | \(=\) | 241.15 |
Dual form | 241.2.c.a.225.15 |
$q$-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 \(\left(\mathbb{Z}/241\mathbb{Z}\right)^\times\).
\(n\) | \(7\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.820137 | + | 1.42052i | 0.579925 | + | 1.00446i | 0.995487 | + | 0.0948944i | \(0.0302513\pi\) |
−0.415563 | + | 0.909565i | \(0.636415\pi\) | |||||||
\(3\) | −1.19817 | + | 2.07530i | −0.691767 | + | 1.19817i | 0.279492 | + | 0.960148i | \(0.409834\pi\) |
−0.971259 | + | 0.238027i | \(0.923499\pi\) | |||||||
\(4\) | −0.345250 | + | 0.597991i | −0.172625 | + | 0.298995i | ||||
\(5\) | −4.29952 | −1.92280 | −0.961402 | − | 0.275149i | \(-0.911273\pi\) | ||||
−0.961402 | + | 0.275149i | \(0.911273\pi\) | |||||||
\(6\) | −3.93067 | −1.60469 | ||||||||
\(7\) | −0.578431 | − | 1.00187i | −0.218626 | − | 0.378672i | 0.735762 | − | 0.677240i | \(-0.236824\pi\) |
−0.954388 | + | 0.298568i | \(0.903491\pi\) | |||||||
\(8\) | 2.14794 | 0.759411 | ||||||||
\(9\) | −1.37125 | − | 2.37507i | −0.457082 | − | 0.791689i | ||||
\(10\) | −3.52620 | − | 6.10755i | −1.11508 | − | 1.93138i | ||||
\(11\) | −0.0451539 | − | 0.0782089i | −0.0136144 | − | 0.0235809i | 0.859138 | − | 0.511744i | \(-0.171000\pi\) |
−0.872752 | + | 0.488163i | \(0.837667\pi\) | |||||||
\(12\) | −0.827340 | − | 1.43300i | −0.238833 | − | 0.413670i | ||||
\(13\) | −2.65056 | + | 4.59090i | −0.735132 | + | 1.27329i | 0.219533 | + | 0.975605i | \(0.429547\pi\) |
−0.954665 | + | 0.297682i | \(0.903787\pi\) | |||||||
\(14\) | 0.948786 | − | 1.64335i | 0.253574 | − | 0.439203i | ||||
\(15\) | 5.15157 | − | 8.92279i | 1.33013 | − | 2.30385i | ||||
\(16\) | 2.45211 | + | 4.24717i | 0.613026 | + | 1.06179i | ||||
\(17\) | −1.64306 | −0.398500 | −0.199250 | − | 0.979949i | \(-0.563851\pi\) | ||||
−0.199250 | + | 0.979949i | \(0.563851\pi\) | |||||||
\(18\) | 2.24922 | − | 3.89576i | 0.530146 | − | 0.918240i | ||||
\(19\) | 1.20168 | + | 2.08136i | 0.275683 | + | 0.477497i | 0.970307 | − | 0.241876i | \(-0.0777626\pi\) |
−0.694624 | + | 0.719373i | \(0.744429\pi\) | |||||||
\(20\) | 1.48441 | − | 2.57107i | 0.331924 | − | 0.574909i | ||||
\(21\) | 2.77225 | 0.604954 | ||||||||
\(22\) | 0.0740648 | − | 0.128284i | 0.0157907 | − | 0.0273503i | ||||
\(23\) | −7.62049 | −1.58898 | −0.794491 | − | 0.607276i | \(-0.792262\pi\) | ||||
−0.794491 | + | 0.607276i | \(0.792262\pi\) | |||||||
\(24\) | −2.57361 | + | 4.45762i | −0.525335 | + | 0.909907i | ||||
\(25\) | 13.4859 | 2.69717 | ||||||||
\(26\) | −8.69528 | −1.70529 | ||||||||
\(27\) | −0.617081 | −0.118757 | ||||||||
\(28\) | 0.798814 | 0.150962 | ||||||||
\(29\) | 3.30454 | + | 5.72364i | 0.613638 | + | 1.06285i | 0.990622 | + | 0.136633i | \(0.0436280\pi\) |
−0.376984 | + | 0.926220i | \(0.623039\pi\) | |||||||
\(30\) | 16.9000 | 3.08550 | ||||||||
\(31\) | 2.44152 | + | 4.22884i | 0.438510 | + | 0.759522i | 0.997575 | − | 0.0696019i | \(-0.0221729\pi\) |
−0.559064 | + | 0.829124i | \(0.688840\pi\) | |||||||
\(32\) | −1.87419 | + | 3.24619i | −0.331312 | + | 0.573850i | ||||
\(33\) | 0.216409 | 0.0376720 | ||||||||
\(34\) | −1.34753 | − | 2.33399i | −0.231100 | − | 0.400277i | ||||
\(35\) | 2.48698 | + | 4.30757i | 0.420376 | + | 0.728112i | ||||
\(36\) | 1.89369 | 0.315615 | ||||||||
\(37\) | −3.76545 | − | 6.52195i | −0.619036 | − | 1.07220i | −0.989662 | − | 0.143420i | \(-0.954190\pi\) |
0.370626 | − | 0.928782i | \(-0.379143\pi\) | |||||||
\(38\) | −1.97108 | + | 3.41401i | −0.319751 | + | 0.553825i | ||||
\(39\) | −6.35166 | − | 11.0014i | −1.01708 | − | 1.76163i | ||||
\(40\) | −9.23510 | −1.46020 | ||||||||
\(41\) | −0.316578 | −0.0494412 | −0.0247206 | − | 0.999694i | \(-0.507870\pi\) | ||||
−0.0247206 | + | 0.999694i | \(0.507870\pi\) | |||||||
\(42\) | 2.27362 | + | 3.93803i | 0.350828 | + | 0.607651i | ||||
\(43\) | 4.02686 | 0.614090 | 0.307045 | − | 0.951695i | \(-0.400660\pi\) | ||||
0.307045 | + | 0.951695i | \(0.400660\pi\) | |||||||
\(44\) | 0.0623576 | 0.00940076 | ||||||||
\(45\) | 5.89570 | + | 10.2116i | 0.878878 | + | 1.52226i | ||||
\(46\) | −6.24985 | − | 10.8251i | −0.921490 | − | 1.59607i | ||||
\(47\) | −1.08055 | −0.157614 | −0.0788069 | − | 0.996890i | \(-0.525111\pi\) | ||||
−0.0788069 | + | 0.996890i | \(0.525111\pi\) | |||||||
\(48\) | −11.7522 | −1.69628 | ||||||||
\(49\) | 2.83083 | − | 4.90315i | 0.404405 | − | 0.700450i | ||||
\(50\) | 11.0603 | + | 19.1569i | 1.56416 | + | 2.70920i | ||||
\(51\) | 1.96867 | − | 3.40984i | 0.275669 | − | 0.477472i | ||||
\(52\) | −1.83021 | − | 3.17002i | −0.253805 | − | 0.439603i | ||||
\(53\) | −4.62703 | + | 8.01425i | −0.635572 | + | 1.10084i | 0.350822 | + | 0.936442i | \(0.385902\pi\) |
−0.986394 | + | 0.164400i | \(0.947431\pi\) | |||||||
\(54\) | −0.506091 | − | 0.876576i | −0.0688703 | − | 0.119287i | ||||
\(55\) | 0.194140 | + | 0.336261i | 0.0261779 | + | 0.0453414i | ||||
\(56\) | −1.24243 | − | 2.15196i | −0.166027 | − | 0.287568i | ||||
\(57\) | −5.75927 | −0.762834 | ||||||||
\(58\) | −5.42036 | + | 9.38833i | −0.711728 | + | 1.23275i | ||||
\(59\) | 2.07761 | + | 3.59852i | 0.270481 | + | 0.468488i | 0.968985 | − | 0.247119i | \(-0.0794838\pi\) |
−0.698504 | + | 0.715606i | \(0.746150\pi\) | |||||||
\(60\) | 3.55716 | + | 6.16119i | 0.459228 | + | 0.795406i | ||||
\(61\) | 10.5427 | 1.34986 | 0.674930 | − | 0.737882i | \(-0.264174\pi\) | ||||
0.674930 | + | 0.737882i | \(0.264174\pi\) | |||||||
\(62\) | −4.00477 | + | 6.93646i | −0.508606 | + | 0.880931i | ||||
\(63\) | −1.58634 | + | 2.74763i | −0.199860 | + | 0.346168i | ||||
\(64\) | 3.66006 | 0.457507 | ||||||||
\(65\) | 11.3961 | − | 19.7387i | 1.41352 | − | 2.44828i | ||||
\(66\) | 0.177485 | + | 0.307413i | 0.0218469 | + | 0.0378400i | ||||
\(67\) | 3.71258 | + | 6.43038i | 0.453564 | + | 0.785596i | 0.998604 | − | 0.0528135i | \(-0.0168189\pi\) |
−0.545040 | + | 0.838410i | \(0.683486\pi\) | |||||||
\(68\) | 0.567266 | − | 0.982533i | 0.0687911 | − | 0.119150i | ||||
\(69\) | 9.13068 | − | 15.8148i | 1.09920 | − | 1.90388i | ||||
\(70\) | −4.07932 | + | 7.06559i | −0.487572 | + | 0.844500i | ||||
\(71\) | 7.25388 | + | 12.5641i | 0.860878 | + | 1.49108i | 0.871083 | + | 0.491136i | \(0.163418\pi\) |
−0.0102052 | + | 0.999948i | \(0.503248\pi\) | |||||||
\(72\) | −2.94535 | − | 5.10150i | −0.347113 | − | 0.601217i | ||||
\(73\) | 9.21934 | 1.07904 | 0.539521 | − | 0.841972i | \(-0.318605\pi\) | ||||
0.539521 | + | 0.841972i | \(0.318605\pi\) | |||||||
\(74\) | 6.17637 | − | 10.6978i | 0.717989 | − | 1.24359i | ||||
\(75\) | −16.1584 | + | 27.9872i | −1.86581 | + | 3.23168i | ||||
\(76\) | −1.65951 | −0.190359 | ||||||||
\(77\) | −0.0522369 | + | 0.0904769i | −0.00595295 | + | 0.0103108i | ||||
\(78\) | 10.4185 | − | 18.0453i | 1.17966 | − | 2.04323i | ||||
\(79\) | −9.74235 | −1.09610 | −0.548050 | − | 0.836446i | \(-0.684630\pi\) | ||||
−0.548050 | + | 0.836446i | \(0.684630\pi\) | |||||||
\(80\) | −10.5429 | − | 18.2608i | −1.17873 | − | 2.04162i | ||||
\(81\) | 4.85311 | − | 8.40583i | 0.539234 | − | 0.933981i | ||||
\(82\) | −0.259637 | − | 0.449705i | −0.0286721 | − | 0.0496616i | ||||
\(83\) | −3.84438 | − | 6.65867i | −0.421976 | − | 0.730884i | 0.574157 | − | 0.818745i | \(-0.305330\pi\) |
−0.996133 | + | 0.0878615i | \(0.971997\pi\) | |||||||
\(84\) | −0.957119 | + | 1.65778i | −0.104430 | + | 0.180878i | ||||
\(85\) | 7.06435 | 0.766237 | ||||||||
\(86\) | 3.30258 | + | 5.72023i | 0.356126 | + | 0.616828i | ||||
\(87\) | −15.8377 | −1.69798 | ||||||||
\(88\) | −0.0969879 | − | 0.167988i | −0.0103389 | − | 0.0179076i | ||||
\(89\) | −2.61828 | − | 4.53499i | −0.277537 | − | 0.480708i | 0.693235 | − | 0.720711i | \(-0.256185\pi\) |
−0.970772 | + | 0.240004i | \(0.922851\pi\) | |||||||
\(90\) | −9.67056 | + | 16.7499i | −1.01937 | + | 1.76559i | ||||
\(91\) | 6.13266 | 0.642878 | ||||||||
\(92\) | 2.63098 | − | 4.55698i | 0.274298 | − | 0.475098i | ||||
\(93\) | −11.7015 | −1.21339 | ||||||||
\(94\) | −0.886195 | − | 1.53494i | −0.0914041 | − | 0.158317i | ||||
\(95\) | −5.16662 | − | 8.94886i | −0.530085 | − | 0.918133i | ||||
\(96\) | −4.49121 | − | 7.77900i | −0.458382 | − | 0.793941i | ||||
\(97\) | −1.12438 | + | 1.94749i | −0.114164 | + | 0.197738i | −0.917445 | − | 0.397862i | \(-0.869752\pi\) |
0.803281 | + | 0.595600i | \(0.203086\pi\) | |||||||
\(98\) | 9.28669 | 0.938098 | ||||||||
\(99\) | −0.123834 | + | 0.214487i | −0.0124458 | + | 0.0215568i | ||||
\(100\) | −4.65600 | + | 8.06442i | −0.465600 | + | 0.806442i | ||||
\(101\) | 5.68725 | 0.565902 | 0.282951 | − | 0.959134i | \(-0.408687\pi\) | ||||
0.282951 | + | 0.959134i | \(0.408687\pi\) | |||||||
\(102\) | 6.45832 | 0.639469 | ||||||||
\(103\) | 3.27870 | 0.323060 | 0.161530 | − | 0.986868i | \(-0.448357\pi\) | ||||
0.161530 | + | 0.986868i | \(0.448357\pi\) | |||||||
\(104\) | −5.69324 | + | 9.86097i | −0.558268 | + | 0.966948i | ||||
\(105\) | −11.9193 | −1.16321 | ||||||||
\(106\) | −15.1792 | −1.47433 | ||||||||
\(107\) | −1.79273 | + | 3.10510i | −0.173310 | + | 0.300181i | −0.939575 | − | 0.342343i | \(-0.888780\pi\) |
0.766265 | + | 0.642524i | \(0.222113\pi\) | |||||||
\(108\) | 0.213047 | − | 0.369009i | 0.0205005 | − | 0.0355079i | ||||
\(109\) | −3.39723 | + | 5.88418i | −0.325396 | + | 0.563602i | −0.981592 | − | 0.190988i | \(-0.938831\pi\) |
0.656196 | + | 0.754590i | \(0.272164\pi\) | |||||||
\(110\) | −0.318443 | + | 0.551560i | −0.0303624 | + | 0.0525892i | ||||
\(111\) | 18.0467 | 1.71291 | ||||||||
\(112\) | 2.83675 | − | 4.91339i | 0.268047 | − | 0.464272i | ||||
\(113\) | −10.3195 | − | 17.8738i | −0.970774 | − | 1.68143i | −0.693229 | − | 0.720718i | \(-0.743812\pi\) |
−0.277545 | − | 0.960713i | \(-0.589521\pi\) | |||||||
\(114\) | −4.72339 | − | 8.18115i | −0.442386 | − | 0.766235i | ||||
\(115\) | 32.7644 | 3.05530 | ||||||||
\(116\) | −4.56358 | −0.423717 | ||||||||
\(117\) | 14.5383 | 1.34406 | ||||||||
\(118\) | −3.40785 | + | 5.90256i | −0.313718 | + | 0.543375i | ||||
\(119\) | 0.950395 | + | 1.64613i | 0.0871226 | + | 0.150901i | ||||
\(120\) | 11.0653 | − | 19.1656i | 1.01012 | − | 1.74957i | ||||
\(121\) | 5.49592 | − | 9.51922i | 0.499629 | − | 0.865383i | ||||
\(122\) | 8.64649 | + | 14.9762i | 0.782817 | + | 1.35588i | ||||
\(123\) | 0.379316 | − | 0.656994i | 0.0342017 | − | 0.0592391i | ||||
\(124\) | −3.37174 | −0.302792 | ||||||||
\(125\) | −36.4851 | −3.26333 | ||||||||
\(126\) | −5.20407 | −0.463616 | ||||||||
\(127\) | −7.10717 | − | 12.3100i | −0.630659 | − | 1.09233i | −0.987417 | − | 0.158137i | \(-0.949451\pi\) |
0.356758 | − | 0.934197i | \(-0.383882\pi\) | |||||||
\(128\) | 6.75012 | + | 11.6916i | 0.596632 | + | 1.03340i | ||||
\(129\) | −4.82488 | + | 8.35694i | −0.424807 | + | 0.735787i | ||||
\(130\) | 37.3855 | 3.27893 | ||||||||
\(131\) | 0.856334 | − | 1.48321i | 0.0748182 | − | 0.129589i | −0.826189 | − | 0.563393i | \(-0.809496\pi\) |
0.901007 | + | 0.433804i | \(0.142829\pi\) | |||||||
\(132\) | −0.0747153 | + | 0.129411i | −0.00650313 | + | 0.0112638i | ||||
\(133\) | 1.39017 | − | 2.40785i | 0.120543 | − | 0.208787i | ||||
\(134\) | −6.08966 | + | 10.5476i | −0.526066 | + | 0.911173i | ||||
\(135\) | 2.65315 | 0.228347 | ||||||||
\(136\) | −3.52919 | −0.302625 | ||||||||
\(137\) | −5.55249 | + | 9.61719i | −0.474381 | + | 0.821652i | −0.999570 | − | 0.0293338i | \(-0.990661\pi\) |
0.525189 | + | 0.850986i | \(0.323995\pi\) | |||||||
\(138\) | 29.9536 | 2.54982 | ||||||||
\(139\) | −18.9875 | −1.61050 | −0.805248 | − | 0.592938i | \(-0.797968\pi\) | ||||
−0.805248 | + | 0.592938i | \(0.797968\pi\) | |||||||
\(140\) | −3.43452 | −0.290270 | ||||||||
\(141\) | 1.29468 | − | 2.24246i | 0.109032 | − | 0.188849i | ||||
\(142\) | −11.8984 | + | 20.6086i | −0.998488 | + | 1.72943i | ||||
\(143\) | 0.478732 | 0.0400336 | ||||||||
\(144\) | 6.72488 | − | 11.6478i | 0.560406 | − | 0.970652i | ||||
\(145\) | −14.2079 | − | 24.6089i | −1.17991 | − | 2.04366i | ||||
\(146\) | 7.56112 | + | 13.0962i | 0.625763 | + | 1.08385i | ||||
\(147\) | 6.78367 | + | 11.7497i | 0.559508 | + | 0.969096i | ||||
\(148\) | 5.20009 | 0.427445 | ||||||||
\(149\) | 1.61547 | − | 2.79808i | 0.132344 | − | 0.229227i | −0.792235 | − | 0.610216i | \(-0.791083\pi\) |
0.924580 | + | 0.380988i | \(0.124416\pi\) | |||||||
\(150\) | −53.0085 | −4.32812 | ||||||||
\(151\) | −9.81435 | + | 16.9990i | −0.798680 | + | 1.38335i | 0.121795 | + | 0.992555i | \(0.461135\pi\) |
−0.920476 | + | 0.390800i | \(0.872198\pi\) | |||||||
\(152\) | 2.58112 | + | 4.47064i | 0.209357 | + | 0.362617i | ||||
\(153\) | 2.25303 | + | 3.90237i | 0.182147 | + | 0.315488i | ||||
\(154\) | −0.171366 | −0.0138090 | ||||||||
\(155\) | −10.4974 | − | 18.1820i | −0.843169 | − | 1.46041i | ||||
\(156\) | 8.77165 | 0.702294 | ||||||||
\(157\) | −2.59744 | + | 4.49890i | −0.207298 | + | 0.359051i | −0.950863 | − | 0.309613i | \(-0.899800\pi\) |
0.743564 | + | 0.668664i | \(0.233134\pi\) | |||||||
\(158\) | −7.99007 | − | 13.8392i | −0.635655 | − | 1.10099i | ||||
\(159\) | −11.0880 | − | 19.2049i | −0.879334 | − | 1.52305i | ||||
\(160\) | 8.05810 | − | 13.9570i | 0.637049 | − | 1.10340i | ||||
\(161\) | 4.40793 | + | 7.63476i | 0.347393 | + | 0.601703i | ||||
\(162\) | 15.9209 | 1.25086 | ||||||||
\(163\) | −9.24647 | + | 16.0153i | −0.724239 | + | 1.25442i | 0.235047 | + | 0.971984i | \(0.424476\pi\) |
−0.959286 | + | 0.282435i | \(0.908858\pi\) | |||||||
\(164\) | 0.109299 | − | 0.189311i | 0.00853478 | − | 0.0147827i | ||||
\(165\) | −0.930455 | −0.0724359 | ||||||||
\(166\) | 6.30585 | − | 10.9220i | 0.489429 | − | 0.847715i | ||||
\(167\) | 5.26704 | − | 9.12278i | 0.407576 | − | 0.705942i | −0.587042 | − | 0.809557i | \(-0.699708\pi\) |
0.994618 | + | 0.103615i | \(0.0330409\pi\) | |||||||
\(168\) | 5.95462 | 0.459409 | ||||||||
\(169\) | −7.55091 | − | 13.0786i | −0.580840 | − | 1.00604i | ||||
\(170\) | 5.79374 | + | 10.0351i | 0.444360 | + | 0.769653i | ||||
\(171\) | 3.29558 | − | 5.70812i | 0.252020 | − | 0.436511i | ||||
\(172\) | −1.39027 | + | 2.40802i | −0.106007 | + | 0.183610i | ||||
\(173\) | 2.55325 | − | 4.42236i | 0.194120 | − | 0.336225i | −0.752492 | − | 0.658602i | \(-0.771148\pi\) |
0.946612 | + | 0.322376i | \(0.104482\pi\) | |||||||
\(174\) | −12.9891 | − | 22.4977i | −0.984699 | − | 1.70555i | ||||
\(175\) | −7.80064 | − | 13.5111i | −0.589673 | − | 1.02134i | ||||
\(176\) | 0.221444 | − | 0.383553i | 0.0166920 | − | 0.0289114i | ||||
\(177\) | −9.95735 | −0.748440 | ||||||||
\(178\) | 4.29469 | − | 7.43863i | 0.321901 | − | 0.557549i | ||||
\(179\) | 1.84215 | − | 3.19069i | 0.137688 | − | 0.238483i | −0.788933 | − | 0.614479i | \(-0.789366\pi\) |
0.926621 | + | 0.375996i | \(0.122699\pi\) | |||||||
\(180\) | −8.14196 | −0.606866 | ||||||||
\(181\) | 1.37596 | + | 2.38323i | 0.102274 | + | 0.177144i | 0.912621 | − | 0.408806i | \(-0.134055\pi\) |
−0.810347 | + | 0.585950i | \(0.800721\pi\) | |||||||
\(182\) | 5.02962 | + | 8.71156i | 0.372821 | + | 0.645744i | ||||
\(183\) | −12.6320 | + | 21.8793i | −0.933788 | + | 1.61737i | ||||
\(184\) | −16.3683 | −1.20669 | ||||||||
\(185\) | 16.1896 | + | 28.0413i | 1.19028 | + | 2.06163i | ||||
\(186\) | −9.59682 | − | 16.6222i | −0.703673 | − | 1.21880i | ||||
\(187\) | 0.0741905 | + | 0.128502i | 0.00542535 | + | 0.00939697i | ||||
\(188\) | 0.373058 | − | 0.646156i | 0.0272081 | − | 0.0471258i | ||||
\(189\) | 0.356939 | + | 0.618237i | 0.0259635 | + | 0.0449701i | ||||
\(190\) | 8.47468 | − | 14.6786i | 0.614818 | − | 1.06490i | ||||
\(191\) | 4.44997 | + | 7.70758i | 0.321989 | + | 0.557701i | 0.980898 | − | 0.194521i | \(-0.0623153\pi\) |
−0.658909 | + | 0.752222i | \(0.728982\pi\) | |||||||
\(192\) | −4.38539 | + | 7.59572i | −0.316488 | + | 0.548174i | ||||
\(193\) | 20.1406 | 1.44975 | 0.724877 | − | 0.688878i | \(-0.241897\pi\) | ||||
0.724877 | + | 0.688878i | \(0.241897\pi\) | |||||||
\(194\) | −3.68860 | −0.264826 | ||||||||
\(195\) | 27.3091 | + | 47.3007i | 1.95564 | + | 3.38728i | ||||
\(196\) | 1.95469 | + | 3.38563i | 0.139621 | + | 0.241830i | ||||
\(197\) | 12.5193 | 0.891962 | 0.445981 | − | 0.895042i | \(-0.352855\pi\) | ||||
0.445981 | + | 0.895042i | \(0.352855\pi\) | |||||||
\(198\) | −0.406244 | −0.0288705 | ||||||||
\(199\) | −0.407338 | − | 0.705530i | −0.0288754 | − | 0.0500137i | 0.851227 | − | 0.524798i | \(-0.175859\pi\) |
−0.880102 | + | 0.474785i | \(0.842526\pi\) | |||||||
\(200\) | 28.9668 | 2.04826 | ||||||||
\(201\) | −17.7933 | −1.25504 | ||||||||
\(202\) | 4.66432 | + | 8.07884i | 0.328181 | + | 0.568425i | ||||
\(203\) | 3.82290 | − | 6.62146i | 0.268315 | − | 0.464735i | ||||
\(204\) | 1.35937 | + | 2.35449i | 0.0951747 | + | 0.164847i | ||||
\(205\) | 1.36113 | 0.0950656 | ||||||||
\(206\) | 2.68899 | + | 4.65746i | 0.187351 | + | 0.324501i | ||||
\(207\) | 10.4496 | + | 18.0992i | 0.726295 | + | 1.25798i | ||||
\(208\) | −25.9978 | −1.80262 | ||||||||
\(209\) | 0.108521 | − | 0.187963i | 0.00750654 | − | 0.0130017i | ||||
\(210\) | −9.77548 | − | 16.9316i | −0.674572 | − | 1.16839i | ||||
\(211\) | 10.4425 | 0.718892 | 0.359446 | − | 0.933166i | \(-0.382966\pi\) | ||||
0.359446 | + | 0.933166i | \(0.382966\pi\) | |||||||
\(212\) | −3.19497 | − | 5.53384i | −0.219431 | − | 0.380066i | ||||
\(213\) | −34.7657 | −2.38211 | ||||||||
\(214\) | −5.88114 | −0.402027 | ||||||||
\(215\) | −17.3136 | −1.18077 | ||||||||
\(216\) | −1.32545 | −0.0901856 | ||||||||
\(217\) | 2.82451 | − | 4.89219i | 0.191740 | − | 0.332103i | ||||
\(218\) | −11.1448 | −0.754821 | ||||||||
\(219\) | −11.0464 | + | 19.1329i | −0.746445 | + | 1.29288i | ||||
\(220\) | −0.268108 | −0.0180758 | ||||||||
\(221\) | 4.35502 | − | 7.54311i | 0.292950 | − | 0.507405i | ||||
\(222\) | 14.8007 | + | 25.6356i | 0.993361 | + | 1.72055i | ||||
\(223\) | −2.21892 | + | 3.84328i | −0.148590 | + | 0.257365i | −0.930706 | − | 0.365767i | \(-0.880807\pi\) |
0.782117 | + | 0.623132i | \(0.214140\pi\) | |||||||
\(224\) | 4.33635 | 0.289735 | ||||||||
\(225\) | −18.4924 | − | 32.0298i | −1.23283 | − | 2.13532i | ||||
\(226\) | 16.9268 | − | 29.3180i | 1.12595 | − | 1.95021i | ||||
\(227\) | 8.35490 | − | 14.4711i | 0.554534 | − | 0.960481i | −0.443405 | − | 0.896321i | \(-0.646230\pi\) |
0.997940 | − | 0.0641603i | \(-0.0204369\pi\) | |||||||
\(228\) | 1.98839 | − | 3.44399i | 0.131684 | − | 0.228084i | ||||
\(229\) | −8.72600 | − | 15.1139i | −0.576631 | − | 0.998753i | −0.995862 | − | 0.0908742i | \(-0.971034\pi\) |
0.419232 | − | 0.907879i | \(-0.362299\pi\) | |||||||
\(230\) | 26.8713 | + | 46.5425i | 1.77184 | + | 3.06892i | ||||
\(231\) | −0.125178 | − | 0.216814i | −0.00823610 | − | 0.0142653i | ||||
\(232\) | 7.09796 | + | 12.2940i | 0.466004 | + | 0.807142i | ||||
\(233\) | 4.72806 | 0.309745 | 0.154873 | − | 0.987934i | \(-0.450503\pi\) | ||||
0.154873 | + | 0.987934i | \(0.450503\pi\) | |||||||
\(234\) | 11.9234 | + | 20.6519i | 0.779455 | + | 1.35006i | ||||
\(235\) | 4.64582 | 0.303060 | ||||||||
\(236\) | −2.86918 | −0.186768 | ||||||||
\(237\) | 11.6730 | − | 20.2183i | 0.758245 | − | 1.31332i | ||||
\(238\) | −1.55891 | + | 2.70011i | −0.101049 | + | 0.175022i | ||||
\(239\) | 4.96075 | + | 8.59227i | 0.320884 | + | 0.555787i | 0.980671 | − | 0.195666i | \(-0.0626867\pi\) |
−0.659787 | + | 0.751453i | \(0.729353\pi\) | |||||||
\(240\) | 50.5288 | 3.26162 | ||||||||
\(241\) | 11.1596 | + | 10.7918i | 0.718855 | + | 0.695160i | ||||
\(242\) | 18.0296 | 1.15899 | ||||||||
\(243\) | 10.7041 | + | 18.5401i | 0.686670 | + | 1.18935i | ||||
\(244\) | −3.63988 | + | 6.30446i | −0.233020 | + | 0.403602i | ||||
\(245\) | −12.1712 | + | 21.0812i | −0.777591 | + | 1.34683i | ||||
\(246\) | 1.24436 | 0.0793377 | ||||||||
\(247\) | −12.7404 | −0.810655 | ||||||||
\(248\) | 5.24424 | + | 9.08329i | 0.333010 | + | 0.576790i | ||||
\(249\) | 18.4250 | 1.16764 | ||||||||
\(250\) | −29.9228 | − | 51.8278i | −1.89248 | − | 3.27788i | ||||
\(251\) | 1.19974 | + | 2.07801i | 0.0757271 | + | 0.131163i | 0.901402 | − | 0.432983i | \(-0.142539\pi\) |
−0.825675 | + | 0.564146i | \(0.809206\pi\) | |||||||
\(252\) | −1.09537 | − | 1.89724i | −0.0690018 | − | 0.119515i | ||||
\(253\) | 0.344095 | + | 0.595990i | 0.0216331 | + | 0.0374696i | ||||
\(254\) | 11.6577 | − | 20.1917i | 0.731470 | − | 1.26694i | ||||
\(255\) | −8.46433 | + | 14.6607i | −0.530057 | + | 0.918086i | ||||
\(256\) | −7.41200 | + | 12.8380i | −0.463250 | + | 0.802372i | ||||
\(257\) | 11.6268 | + | 20.1383i | 0.725262 | + | 1.25619i | 0.958866 | + | 0.283858i | \(0.0916145\pi\) |
−0.233605 | + | 0.972332i | \(0.575052\pi\) | |||||||
\(258\) | −15.8283 | −0.985424 | ||||||||
\(259\) | −4.35611 | + | 7.54500i | −0.270675 | + | 0.468824i | ||||
\(260\) | 7.86903 | + | 13.6296i | 0.488016 | + | 0.845269i | ||||
\(261\) | 9.06268 | − | 15.6970i | 0.560966 | − | 0.971621i | ||||
\(262\) | 2.80924 | 0.173556 | ||||||||
\(263\) | −9.25296 | + | 16.0266i | −0.570562 | + | 0.988242i | 0.425947 | + | 0.904748i | \(0.359941\pi\) |
−0.996508 | + | 0.0834937i | \(0.973392\pi\) | |||||||
\(264\) | 0.464834 | 0.0286085 | ||||||||
\(265\) | 19.8940 | − | 34.4574i | 1.22208 | − | 2.11670i | ||||
\(266\) | 4.56053 | 0.279624 | ||||||||
\(267\) | 12.5486 | 0.767963 | ||||||||
\(268\) | −5.12708 | −0.313186 | ||||||||
\(269\) | −13.5863 | −0.828369 | −0.414185 | − | 0.910193i | \(-0.635933\pi\) | ||||
−0.414185 | + | 0.910193i | \(0.635933\pi\) | |||||||
\(270\) | 2.17595 | + | 3.76885i | 0.132424 | + | 0.229365i | ||||
\(271\) | −15.8122 | −0.960523 | −0.480261 | − | 0.877125i | \(-0.659458\pi\) | ||||
−0.480261 | + | 0.877125i | \(0.659458\pi\) | |||||||
\(272\) | −4.02895 | − | 6.97834i | −0.244291 | − | 0.423124i | ||||
\(273\) | −7.34800 | + | 12.7271i | −0.444721 | + | 0.770280i | ||||
\(274\) | −18.2152 | −1.10042 | ||||||||
\(275\) | −0.608940 | − | 1.05471i | −0.0367204 | − | 0.0636017i | ||||
\(276\) | 6.30474 | + | 10.9201i | 0.379501 | + | 0.657314i | ||||
\(277\) | 24.6245 | 1.47955 | 0.739773 | − | 0.672857i | \(-0.234933\pi\) | ||||
0.739773 | + | 0.672857i | \(0.234933\pi\) | |||||||
\(278\) | −15.5723 | − | 26.9721i | −0.933966 | − | 1.61768i | ||||
\(279\) | 6.69585 | − | 11.5976i | 0.400870 | − | 0.694328i | ||||
\(280\) | 5.34187 | + | 9.25239i | 0.319238 | + | 0.552936i | ||||
\(281\) | 8.59410 | 0.512681 | 0.256340 | − | 0.966587i | \(-0.417483\pi\) | ||||
0.256340 | + | 0.966587i | \(0.417483\pi\) | |||||||
\(282\) | 4.24727 | 0.252921 | ||||||||
\(283\) | −0.986664 | − | 1.70895i | −0.0586511 | − | 0.101587i | 0.835209 | − | 0.549933i | \(-0.185347\pi\) |
−0.893860 | + | 0.448346i | \(0.852013\pi\) | |||||||
\(284\) | −10.0176 | −0.594436 | ||||||||
\(285\) | 24.7621 | 1.46678 | ||||||||
\(286\) | 0.392626 | + | 0.680049i | 0.0232165 | + | 0.0402121i | ||||
\(287\) | 0.183119 | + | 0.317171i | 0.0108091 | + | 0.0187220i | ||||
\(288\) | 10.2799 | 0.605748 | ||||||||
\(289\) | −14.3004 | −0.841198 | ||||||||
\(290\) | 23.3049 | − | 40.3653i | 1.36851 | − | 2.37033i | ||||
\(291\) | −2.69442 | − | 4.66687i | −0.157949 | − | 0.273577i | ||||
\(292\) | −3.18298 | + | 5.51308i | −0.186270 | + | 0.322629i | ||||
\(293\) | 8.55612 | + | 14.8196i | 0.499854 | + | 0.865773i | 1.00000 | 0.000168528i | \(-5.36440e-5\pi\) | |
−0.500146 | + | 0.865941i | \(0.666720\pi\) | |||||||
\(294\) | −11.1271 | + | 19.2727i | −0.648944 | + | 1.12400i | ||||
\(295\) | −8.93271 | − | 15.4719i | −0.520083 | − | 0.900810i | ||||
\(296\) | −8.08796 | − | 14.0088i | −0.470103 | − | 0.814242i | ||||
\(297\) | 0.0278636 | + | 0.0482613i | 0.00161681 | + | 0.00280040i | ||||
\(298\) | 5.29963 | 0.306999 | ||||||||
\(299\) | 20.1985 | − | 34.9849i | 1.16811 | − | 2.02323i | ||||
\(300\) | −11.1574 | − | 19.3252i | −0.644172 | − | 1.11574i | ||||
\(301\) | −2.32926 | − | 4.03440i | −0.134256 | − | 0.232539i | ||||
\(302\) | −32.1965 | −1.85270 | ||||||||
\(303\) | −6.81432 | + | 11.8027i | −0.391472 | + | 0.678050i | ||||
\(304\) | −5.89327 | + | 10.2074i | −0.338002 | + | 0.585437i | ||||
\(305\) | −45.3287 | −2.59551 | ||||||||
\(306\) | −3.69560 | + | 6.40096i | −0.211263 | + | 0.365918i | ||||
\(307\) | 15.9840 | + | 27.6851i | 0.912255 | + | 1.58007i | 0.810872 | + | 0.585224i | \(0.198993\pi\) |
0.101383 | + | 0.994847i | \(0.467673\pi\) | |||||||
\(308\) | −0.0360696 | − | 0.0624744i | −0.00205526 | − | 0.00355981i | ||||
\(309\) | −3.92846 | + | 6.80429i | −0.223482 | + | 0.387083i | ||||
\(310\) | 17.2186 | − | 29.8234i | 0.977949 | − | 1.69386i | ||||
\(311\) | −3.45514 | + | 5.98449i | −0.195923 | + | 0.339349i | −0.947203 | − | 0.320635i | \(-0.896104\pi\) |
0.751280 | + | 0.659984i | \(0.229437\pi\) | |||||||
\(312\) | −13.6430 | − | 23.6303i | −0.772382 | − | 1.33780i | ||||
\(313\) | −0.475084 | − | 0.822869i | −0.0268533 | − | 0.0465113i | 0.852286 | − | 0.523075i | \(-0.175215\pi\) |
−0.879140 | + | 0.476564i | \(0.841882\pi\) | |||||||
\(314\) | −8.52102 | −0.480869 | ||||||||
\(315\) | 6.82051 | − | 11.8135i | 0.384292 | − | 0.665614i | ||||
\(316\) | 3.36355 | − | 5.82584i | 0.189214 | − | 0.327729i | ||||
\(317\) | −1.30502 | −0.0732970 | −0.0366485 | − | 0.999328i | \(-0.511668\pi\) | ||||
−0.0366485 | + | 0.999328i | \(0.511668\pi\) | |||||||
\(318\) | 18.1873 | − | 31.5014i | 1.01990 | − | 1.76651i | ||||
\(319\) | 0.298426 | − | 0.516889i | 0.0167087 | − | 0.0289402i | ||||
\(320\) | −15.7365 | −0.879697 | ||||||||
\(321\) | −4.29601 | − | 7.44091i | −0.239780 | − | 0.415311i | ||||
\(322\) | −7.23021 | + | 12.5231i | −0.402924 | + | 0.697885i | ||||
\(323\) | −1.97442 | − | 3.41980i | −0.109860 | − | 0.190283i | ||||
\(324\) | 3.35107 | + | 5.80423i | 0.186171 | + | 0.322457i | ||||
\(325\) | −35.7451 | + | 61.9123i | −1.98278 | + | 3.43427i | ||||
\(326\) | −30.3335 | −1.68002 | ||||||||
\(327\) | −8.14096 | − | 14.1006i | −0.450196 | − | 0.779763i | ||||
\(328\) | −0.679990 | −0.0375462 | ||||||||
\(329\) | 0.625021 | + | 1.08257i | 0.0344585 | + | 0.0596839i | ||||
\(330\) | −0.763101 | − | 1.32173i | −0.0420073 | − | 0.0727588i | ||||
\(331\) | −7.93631 | + | 13.7461i | −0.436219 | + | 0.755554i | −0.997394 | − | 0.0721433i | \(-0.977016\pi\) |
0.561175 | + | 0.827697i | \(0.310349\pi\) | |||||||
\(332\) | 5.30910 | 0.291375 | ||||||||
\(333\) | −10.3267 | + | 17.8864i | −0.565900 | + | 0.980168i | ||||
\(334\) | 17.2788 | 0.945453 | ||||||||
\(335\) | −15.9623 | − | 27.6476i | −0.872115 | − | 1.51055i | ||||
\(336\) | 6.79784 | + | 11.7742i | 0.370853 | + | 0.642335i | ||||
\(337\) | 12.5264 | + | 21.6963i | 0.682356 | + | 1.18187i | 0.974260 | + | 0.225427i | \(0.0723777\pi\) |
−0.291904 | + | 0.956447i | \(0.594289\pi\) | |||||||
\(338\) | 12.3856 | − | 21.4524i | 0.673686 | − | 1.16686i | ||||
\(339\) | 49.4581 | 2.68620 | ||||||||
\(340\) | −2.43897 | + | 4.22442i | −0.132272 | + | 0.229101i | ||||
\(341\) | 0.220489 | − | 0.381898i | 0.0119401 | − | 0.0206809i | ||||
\(342\) | 10.8113 | 0.584609 | ||||||||
\(343\) | −14.6478 | −0.790907 | ||||||||
\(344\) | 8.64945 | 0.466347 | ||||||||
\(345\) | −39.2575 | + | 67.9960i | −2.11355 | + | 3.66078i | ||||
\(346\) | 8.37606 | 0.450300 | ||||||||
\(347\) | 3.55935 | 0.191076 | 0.0955379 | − | 0.995426i | \(-0.469543\pi\) | ||||
0.0955379 | + | 0.995426i | \(0.469543\pi\) | |||||||
\(348\) | 5.46796 | − | 9.47079i | 0.293114 | − | 0.507688i | ||||
\(349\) | 8.26310 | − | 14.3121i | 0.442314 | − | 0.766109i | −0.555547 | − | 0.831485i | \(-0.687491\pi\) |
0.997861 | + | 0.0653755i | \(0.0208245\pi\) | |||||||
\(350\) | 12.7952 | − | 22.1619i | 0.683932 | − | 1.18460i | ||||
\(351\) | 1.63561 | − | 2.83296i | 0.0873024 | − | 0.151212i | ||||
\(352\) | 0.338508 | 0.0180425 | ||||||||
\(353\) | 17.5329 | − | 30.3678i | 0.933181 | − | 1.61632i | 0.155336 | − | 0.987862i | \(-0.450354\pi\) |
0.777845 | − | 0.628456i | \(-0.216313\pi\) | |||||||
\(354\) | −8.16639 | − | 14.1446i | −0.434039 | − | 0.751777i | ||||
\(355\) | −31.1882 | − | 54.0196i | −1.65530 | − | 2.86706i | ||||
\(356\) | 3.61584 | 0.191639 | ||||||||
\(357\) | −4.55496 | −0.241074 | ||||||||
\(358\) | 6.04325 | 0.319396 | ||||||||
\(359\) | −7.37120 | + | 12.7673i | −0.389037 | + | 0.673832i | −0.992320 | − | 0.123695i | \(-0.960526\pi\) |
0.603283 | + | 0.797527i | \(0.293859\pi\) | |||||||
\(360\) | 12.6636 | + | 21.9340i | 0.667430 | + | 1.15602i | ||||
\(361\) | 6.61195 | − | 11.4522i | 0.347998 | − | 0.602749i | ||||
\(362\) | −2.25695 | + | 3.90915i | −0.118623 | + | 0.205460i | ||||
\(363\) | 13.1702 | + | 22.8114i | 0.691254 | + | 1.19729i | ||||
\(364\) | −2.11730 | + | 3.66728i | −0.110977 | + | 0.192217i | ||||
\(365\) | −39.6387 | −2.07478 | ||||||||
\(366\) | −41.4400 | −2.16611 | ||||||||
\(367\) | 3.35392 | 0.175073 | 0.0875367 | − | 0.996161i | \(-0.472101\pi\) | ||||
0.0875367 | + | 0.996161i | \(0.472101\pi\) | |||||||
\(368\) | −18.6862 | − | 32.3655i | −0.974087 | − | 1.68717i | ||||
\(369\) | 0.434106 | + | 0.751894i | 0.0225987 | + | 0.0391420i | ||||
\(370\) | −26.5554 | + | 45.9954i | −1.38055 | + | 2.39118i | ||||
\(371\) | 10.7057 | 0.555811 | ||||||||
\(372\) | 4.03994 | − | 6.99738i | 0.209461 | − | 0.362797i | ||||
\(373\) | 9.76601 | − | 16.9152i | 0.505665 | − | 0.875837i | −0.494314 | − | 0.869284i | \(-0.664581\pi\) |
0.999979 | − | 0.00655376i | \(-0.00208614\pi\) | |||||||
\(374\) | −0.121693 | + | 0.210778i | −0.00629258 | + | 0.0108991i | ||||
\(375\) | 43.7156 | − | 75.7176i | 2.25746 | − | 3.91004i | ||||
\(376\) | −2.32095 | −0.119694 | ||||||||
\(377\) | −35.0355 | −1.80442 | ||||||||
\(378\) | −0.585478 | + | 1.01408i | −0.0301137 | + | 0.0521585i | ||||
\(379\) | −30.0491 | −1.54352 | −0.771759 | − | 0.635915i | \(-0.780623\pi\) | ||||
−0.771759 | + | 0.635915i | \(0.780623\pi\) | |||||||
\(380\) | 7.13511 | 0.366024 | ||||||||
\(381\) | 34.0625 | 1.74508 | ||||||||
\(382\) | −7.29918 | + | 12.6425i | −0.373458 | + | 0.646849i | ||||
\(383\) | −2.32304 | + | 4.02363i | −0.118702 | + | 0.205598i | −0.919254 | − | 0.393666i | \(-0.871207\pi\) |
0.800552 | + | 0.599264i | \(0.204540\pi\) | |||||||
\(384\) | −32.3513 | −1.65092 | ||||||||
\(385\) | 0.224593 | − | 0.389007i | 0.0114463 | − | 0.0198256i | ||||
\(386\) | 16.5181 | + | 28.6102i | 0.840748 | + | 1.45622i | ||||
\(387\) | −5.52181 | − | 9.56406i | −0.280689 | − | 0.486168i | ||||
\(388\) | −0.776387 | − | 1.34474i | −0.0394151 | − | 0.0682690i | ||||
\(389\) | 3.30184 | 0.167410 | 0.0837050 | − | 0.996491i | \(-0.473325\pi\) | ||||
0.0837050 | + | 0.996491i | \(0.473325\pi\) | |||||||
\(390\) | −44.7944 | + | 77.5862i | −2.26825 | + | 3.92873i | ||||
\(391\) | 12.5209 | 0.633209 | ||||||||
\(392\) | 6.08046 | − | 10.5317i | 0.307110 | − | 0.531929i | ||||
\(393\) | 2.05207 | + | 3.55430i | 0.103513 | + | 0.179291i | ||||
\(394\) | 10.2675 | + | 17.7839i | 0.517271 | + | 0.895939i | ||||
\(395\) | 41.8874 | 2.10758 | ||||||||
\(396\) | −0.0855076 | − | 0.148104i | −0.00429692 | − | 0.00744248i | ||||
\(397\) | −19.1459 | −0.960904 | −0.480452 | − | 0.877021i | \(-0.659527\pi\) | ||||
−0.480452 | + | 0.877021i | \(0.659527\pi\) | |||||||
\(398\) | 0.668146 | − | 1.15726i | 0.0334911 | − | 0.0580083i | ||||
\(399\) | 3.33134 | + | 5.77005i | 0.166776 | + | 0.288864i | ||||
\(400\) | 33.0687 | + | 57.2768i | 1.65344 | + | 2.86384i | ||||
\(401\) | −10.3082 | + | 17.8543i | −0.514766 | + | 0.891601i | 0.485087 | + | 0.874466i | \(0.338788\pi\) |
−0.999853 | + | 0.0171349i | \(0.994546\pi\) | |||||||
\(402\) | −14.5929 | − | 25.2757i | −0.727830 | − | 1.26064i | ||||
\(403\) | −25.8856 | −1.28945 | ||||||||
\(404\) | −1.96352 | + | 3.40092i | −0.0976889 | + | 0.169202i | ||||
\(405\) | −20.8660 | + | 36.1410i | −1.03684 | + | 1.79586i | ||||
\(406\) | 12.5412 | 0.622410 | ||||||||
\(407\) | −0.340050 | + | 0.588984i | −0.0168556 | + | 0.0291948i | ||||
\(408\) | 4.22858 | − | 7.32412i | 0.209346 | − | 0.362598i | ||||
\(409\) | −9.39333 | −0.464470 | −0.232235 | − | 0.972660i | \(-0.574604\pi\) | ||||
−0.232235 | + | 0.972660i | \(0.574604\pi\) | |||||||
\(410\) | 1.11632 | + | 1.93352i | 0.0551309 | + | 0.0954895i | ||||
\(411\) | −13.3057 | − | 23.0462i | −0.656322 | − | 1.13678i | ||||
\(412\) | −1.13197 | + | 1.96064i | −0.0557683 | + | 0.0965936i | ||||
\(413\) | 2.40351 | − | 4.16299i | 0.118269 | − | 0.204848i | ||||
\(414\) | −17.1401 | + | 29.6876i | −0.842392 | + | 1.45907i | ||||
\(415\) | 16.5290 | + | 28.6291i | 0.811377 | + | 1.40535i | ||||
\(416\) | −9.93528 | − | 17.2084i | −0.487117 | − | 0.843712i | ||||
\(417\) | 22.7503 | − | 39.4047i | 1.11409 | − | 1.92966i | ||||
\(418\) | 0.356008 | 0.0174129 | ||||||||
\(419\) | −7.06199 | + | 12.2317i | −0.345001 | + | 0.597559i | −0.985354 | − | 0.170522i | \(-0.945455\pi\) |
0.640353 | + | 0.768081i | \(0.278788\pi\) | |||||||
\(420\) | 4.11515 | − | 7.12765i | 0.200799 | − | 0.347794i | ||||
\(421\) | 12.5287 | 0.610611 | 0.305306 | − | 0.952254i | \(-0.401241\pi\) | ||||
0.305306 | + | 0.952254i | \(0.401241\pi\) | |||||||
\(422\) | 8.56429 | + | 14.8338i | 0.416903 | + | 0.722098i | ||||
\(423\) | 1.48169 | + | 2.56637i | 0.0720424 | + | 0.124781i | ||||
\(424\) | −9.93858 | + | 17.2141i | −0.482660 | + | 0.835992i | ||||
\(425\) | −22.1580 | −1.07482 | ||||||||
\(426\) | −28.5126 | − | 49.3853i | −1.38144 | − | 2.39273i | ||||
\(427\) | −6.09825 | − | 10.5625i | −0.295115 | − | 0.511154i | ||||
\(428\) | −1.23788 | − | 2.14407i | −0.0598353 | − | 0.103638i | ||||
\(429\) | −0.573605 | + | 0.993513i | −0.0276939 | + | 0.0479673i | ||||
\(430\) | −14.1995 | − | 24.5942i | −0.684760 | − | 1.18604i | ||||
\(431\) | 9.57080 | − | 16.5771i | 0.461009 | − | 0.798491i | −0.538002 | − | 0.842943i | \(-0.680821\pi\) |
0.999012 | + | 0.0444521i | \(0.0141542\pi\) | |||||||
\(432\) | −1.51315 | − | 2.62085i | −0.0728014 | − | 0.126096i | ||||
\(433\) | 9.84110 | − | 17.0453i | 0.472933 | − | 0.819144i | −0.526587 | − | 0.850121i | \(-0.676529\pi\) |
0.999520 | + | 0.0309769i | \(0.00986184\pi\) | |||||||
\(434\) | 9.26593 | 0.444779 | ||||||||
\(435\) | 68.0944 | 3.26488 | ||||||||
\(436\) | −2.34579 | − | 4.06303i | −0.112343 | − | 0.194584i | ||||
\(437\) | −9.15735 | − | 15.8610i | −0.438056 | − | 0.758734i | ||||
\(438\) | −36.2382 | −1.73153 | ||||||||
\(439\) | 33.9634 | 1.62098 | 0.810492 | − | 0.585750i | \(-0.199200\pi\) | ||||
0.810492 | + | 0.585750i | \(0.199200\pi\) | |||||||
\(440\) | 0.417001 | + | 0.722267i | 0.0198798 | + | 0.0344327i | ||||
\(441\) | −15.5271 | −0.739385 | ||||||||
\(442\) | 14.2868 | 0.679556 | ||||||||
\(443\) | 2.65655 | + | 4.60128i | 0.126217 | + | 0.218613i | 0.922208 | − | 0.386695i | \(-0.126383\pi\) |
−0.795991 | + | 0.605308i | \(0.793050\pi\) | |||||||
\(444\) | −6.23062 | + | 10.7917i | −0.295692 | + | 0.512154i | ||||
\(445\) | 11.2573 | + | 19.4983i | 0.533649 | + | 0.924307i | ||||
\(446\) | −7.27927 | −0.344684 | ||||||||
\(447\) | 3.87123 | + | 6.70517i | 0.183103 | + | 0.317144i | ||||
\(448\) | −2.11709 | − | 3.66691i | −0.100023 | − | 0.173245i | ||||
\(449\) | 34.9719 | 1.65043 | 0.825214 | − | 0.564820i | \(-0.191055\pi\) | ||||
0.825214 | + | 0.564820i | \(0.191055\pi\) | |||||||
\(450\) | 30.3327 | − | 52.5377i | 1.42990 | − | 2.47665i | ||||
\(451\) | 0.0142947 | + | 0.0247592i | 0.000673113 | + | 0.00116587i | ||||
\(452\) | 14.2512 | 0.670320 | ||||||||
\(453\) | −23.5186 | − | 40.7354i | −1.10500 | − | 1.91392i | ||||
\(454\) | 27.4087 | 1.28635 | ||||||||
\(455\) | −26.3675 | −1.23613 | ||||||||
\(456\) | −12.3706 | −0.579304 | ||||||||
\(457\) | −16.2143 | −0.758472 | −0.379236 | − | 0.925300i | \(-0.623813\pi\) | ||||
−0.379236 | + | 0.925300i | \(0.623813\pi\) | |||||||
\(458\) | 14.3130 | − | 24.7909i | 0.668804 | − | 1.15840i | ||||
\(459\) | 1.01390 | 0.0473248 | ||||||||
\(460\) | −11.3119 | + | 19.5928i | −0.527421 | + | 0.913520i | ||||
\(461\) | 4.64564 | 0.216369 | 0.108184 | − | 0.994131i | \(-0.465496\pi\) | ||||
0.108184 | + | 0.994131i | \(0.465496\pi\) | |||||||
\(462\) | 0.205326 | − | 0.355635i | 0.00955263 | − | 0.0165456i | ||||
\(463\) | −7.57873 | − | 13.1267i | −0.352213 | − | 0.610051i | 0.634424 | − | 0.772986i | \(-0.281238\pi\) |
−0.986637 | + | 0.162934i | \(0.947904\pi\) | |||||||
\(464\) | −16.2062 | + | 28.0699i | −0.752353 | + | 1.30311i | ||||
\(465\) | 50.3107 | 2.33311 | ||||||||
\(466\) | 3.87766 | + | 6.71630i | 0.179629 | + | 0.311126i | ||||
\(467\) | 3.83598 | − | 6.64411i | 0.177508 | − | 0.307453i | −0.763518 | − | 0.645786i | \(-0.776530\pi\) |
0.941026 | + | 0.338333i | \(0.109863\pi\) | |||||||
\(468\) | −5.01934 | + | 8.69375i | −0.232019 | + | 0.401869i | ||||
\(469\) | 4.29495 | − | 7.43907i | 0.198322 | − | 0.343504i | ||||
\(470\) | 3.81021 | + | 6.59948i | 0.175752 | + | 0.304412i | ||||
\(471\) | −6.22437 | − | 10.7809i | −0.286804 | − | 0.496759i | ||||
\(472\) | 4.46257 | + | 7.72941i | 0.205407 | + | 0.355775i | ||||
\(473\) | −0.181829 | − | 0.314936i | −0.00836048 | − | 0.0144808i | ||||
\(474\) | 38.2940 | 1.75890 | ||||||||
\(475\) | 16.2056 | + | 28.0690i | 0.743565 | + | 1.28789i | ||||
\(476\) | −1.31250 | −0.0601582 | ||||||||
\(477\) | 25.3792 | 1.16203 | ||||||||
\(478\) | −8.13699 | + | 14.0937i | −0.372177 | + | 0.644630i | ||||
\(479\) | 8.48232 | − | 14.6918i | 0.387567 | − | 0.671286i | −0.604555 | − | 0.796564i | \(-0.706649\pi\) |
0.992122 | + | 0.125278i | \(0.0399822\pi\) | |||||||
\(480\) | 19.3100 | + | 33.4459i | 0.881378 | + | 1.52659i | ||||
\(481\) | 39.9222 | 1.82029 | ||||||||
\(482\) | −6.17752 | + | 24.7032i | −0.281378 | + | 1.12520i | ||||
\(483\) | −21.1259 | −0.961260 | ||||||||
\(484\) | 3.79494 | + | 6.57302i | 0.172497 | + | 0.298774i | ||||
\(485\) | 4.83431 | − | 8.37327i | 0.219515 | − | 0.380211i | ||||
\(486\) | −17.5577 | + | 30.4108i | −0.796433 | + | 1.37946i | ||||
\(487\) | 30.8789 | 1.39926 | 0.699629 | − | 0.714506i | \(-0.253348\pi\) | ||||
0.699629 | + | 0.714506i | \(0.253348\pi\) | |||||||
\(488\) | 22.6452 | 1.02510 | ||||||||
\(489\) | −22.1578 | − | 38.3784i | −1.00201 | − | 1.73553i | ||||
\(490\) | −39.9283 | −1.80378 | ||||||||
\(491\) | −17.8819 | − | 30.9724i | −0.807000 | − | 1.39777i | −0.914932 | − | 0.403607i | \(-0.867756\pi\) |
0.107932 | − | 0.994158i | \(-0.465577\pi\) | |||||||
\(492\) | 0.261918 | + | 0.453655i | 0.0118082 | + | 0.0204523i | ||||
\(493\) | −5.42955 | − | 9.40426i | −0.244535 | − | 0.423547i | ||||
\(494\) | −10.4489 | − | 18.0980i | −0.470119 | − | 0.814269i | ||||
\(495\) | 0.532428 | − | 0.922192i | 0.0239308 | − | 0.0414494i | ||||
\(496\) | −11.9737 | + | 20.7391i | −0.537637 | + | 0.931214i | ||||
\(497\) | 8.39175 | − | 14.5349i | 0.376421 | − | 0.651981i | ||||
\(498\) | 15.1110 | + | 26.1730i | 0.677141 | + | 1.17284i | ||||
\(499\) | −42.4545 | −1.90052 | −0.950262 | − | 0.311453i | \(-0.899184\pi\) | ||||
−0.950262 | + | 0.311453i | \(0.899184\pi\) | |||||||
\(500\) | 12.5965 | − | 21.8178i | 0.563332 | − | 0.975720i | ||||
\(501\) | 12.6217 | + | 21.8614i | 0.563895 | + | 0.976694i | ||||
\(502\) | −1.96791 | + | 3.40851i | −0.0878320 | + | 0.152129i | ||||
\(503\) | 26.7535 | 1.19288 | 0.596441 | − | 0.802657i | \(-0.296581\pi\) | ||||
0.596441 | + | 0.802657i | \(0.296581\pi\) | |||||||
\(504\) | −3.40737 | + | 5.90173i | −0.151776 | + | 0.262884i | ||||
\(505\) | −24.4524 | −1.08812 | ||||||||
\(506\) | −0.564410 | + | 0.977587i | −0.0250911 | + | 0.0434591i | ||||
\(507\) | 36.1893 | 1.60722 | ||||||||
\(508\) | 9.81501 | 0.435471 | ||||||||
\(509\) | −15.7611 | −0.698600 | −0.349300 | − | 0.937011i | \(-0.613581\pi\) | ||||
−0.349300 | + | 0.937011i | \(0.613581\pi\) | |||||||
\(510\) | −27.7677 | −1.22957 | ||||||||
\(511\) | −5.33275 | − | 9.23660i | −0.235907 | − | 0.408603i | ||||
\(512\) | 2.68508 | 0.118665 | ||||||||
\(513\) | −0.741531 | − | 1.28437i | −0.0327394 | − | 0.0567063i | ||||
\(514\) | −19.0712 | + | 33.0323i | −0.841194 | + | 1.45699i | ||||
\(515\) | −14.0969 | −0.621182 | ||||||||
\(516\) | −3.33158 | − | 5.77047i | −0.146665 | − | 0.254031i | ||||
\(517\) | 0.0487909 | + | 0.0845083i | 0.00214582 | + | 0.00371667i | ||||
\(518\) | −14.2904 | −0.627885 | ||||||||
\(519\) | 6.11848 | + | 10.5975i | 0.268571 | + | 0.465179i | ||||
\(520\) | 24.4782 | − | 42.3974i | 1.07344 | − | 1.85925i | ||||
\(521\) | −1.28159 | − | 2.21977i | −0.0561473 | − | 0.0972499i | 0.836586 | − | 0.547836i | \(-0.184548\pi\) |
−0.892733 | + | 0.450586i | \(0.851215\pi\) | |||||||
\(522\) | 29.7306 | 1.30127 | ||||||||
\(523\) | 31.8308 | 1.39187 | 0.695933 | − | 0.718107i | \(-0.254991\pi\) | ||||
0.695933 | + | 0.718107i | \(0.254991\pi\) | |||||||
\(524\) | 0.591299 | + | 1.02416i | 0.0258310 | + | 0.0447406i | ||||
\(525\) | 37.3861 | 1.63166 | ||||||||
\(526\) | −30.3548 | −1.32353 | ||||||||
\(527\) | −4.01156 | − | 6.94823i | −0.174746 | − | 0.302670i | ||||
\(528\) | 0.530658 | + | 0.919127i | 0.0230939 | + | 0.0399999i | ||||
\(529\) | 35.0718 | 1.52486 | ||||||||
\(530\) | 65.2633 | 2.83485 | ||||||||
\(531\) | 5.69782 | − | 9.86891i | 0.247264 | − | 0.428274i | ||||
\(532\) | 0.959915 | + | 1.66262i | 0.0416176 | + | 0.0720838i | ||||
\(533\) | 0.839108 | − | 1.45338i | 0.0363458 | − | 0.0629528i | ||||
\(534\) | 10.2916 | + | 17.8256i | 0.445361 | + | 0.771387i | ||||
\(535\) | 7.70788 | − | 13.3504i | 0.333241 | − | 0.577190i | ||||
\(536\) | 7.97440 | + | 13.8121i | 0.344442 | + | 0.596591i | ||||
\(537\) | 4.41443 | + | 7.64601i | 0.190497 | + | 0.329950i | ||||
\(538\) | −11.1426 | − | 19.2996i | −0.480392 | − | 0.832063i | ||||
\(539\) | −0.511293 | −0.0220230 | ||||||||
\(540\) | −0.916001 | + | 1.58656i | −0.0394184 | + | 0.0682747i | ||||
\(541\) | 10.7238 | + | 18.5742i | 0.461053 | + | 0.798567i | 0.999014 | − | 0.0444027i | \(-0.0141385\pi\) |
−0.537961 | + | 0.842970i | \(0.680805\pi\) | |||||||
\(542\) | −12.9682 | − | 22.4615i | −0.557031 | − | 0.964806i | ||||
\(543\) | −6.59455 | −0.282999 | ||||||||
\(544\) | 3.07940 | − | 5.33367i | 0.132028 | − | 0.228679i | ||||
\(545\) | 14.6065 | − | 25.2992i | 0.625672 | − | 1.08370i | ||||
\(546\) | −24.1055 | −1.03162 | ||||||||
\(547\) | −9.77321 | + | 16.9277i | −0.417872 | + | 0.723776i | −0.995725 | − | 0.0923647i | \(-0.970557\pi\) |
0.577853 | + | 0.816141i | \(0.303891\pi\) | |||||||
\(548\) | −3.83400 | − | 6.64067i | −0.163780 | − | 0.283676i | ||||
\(549\) | −14.4567 | − | 25.0397i | −0.616996 | − | 1.06867i | ||||
\(550\) | 0.998828 | − | 1.73002i | 0.0425902 | − | 0.0737684i | ||||
\(551\) | −7.94197 | + | 13.7559i | −0.338339 | + | 0.586021i | ||||
\(552\) | 19.6121 | − | 33.9692i | 0.834748 | − | 1.44583i | ||||
\(553\) | 5.63528 | + | 9.76059i | 0.239636 | + | 0.415063i | ||||
\(554\) | 20.1955 | + | 34.9796i | 0.858025 | + | 1.48614i | ||||
\(555\) | −77.5920 | −3.29360 | ||||||||
\(556\) | 6.55543 | − | 11.3543i | 0.278012 | − | 0.481531i | ||||
\(557\) | −0.142737 | + | 0.247229i | −0.00604798 | + | 0.0104754i | −0.869034 | − | 0.494753i | \(-0.835258\pi\) |
0.862986 | + | 0.505229i | \(0.168592\pi\) | |||||||
\(558\) | 21.9661 | 0.929898 | ||||||||
\(559\) | −10.6734 | + | 18.4869i | −0.451438 | + | 0.781913i | ||||
\(560\) | −12.1967 | + | 21.1252i | −0.515403 | + | 0.892703i | ||||
\(561\) | −0.355573 | −0.0150123 | ||||||||
\(562\) | 7.04834 | + | 12.2081i | 0.297316 | + | 0.514967i | ||||
\(563\) | 4.83849 | − | 8.38051i | 0.203918 | − | 0.353196i | −0.745870 | − | 0.666092i | \(-0.767966\pi\) |
0.949787 | + | 0.312896i | \(0.101299\pi\) | |||||||
\(564\) | 0.893979 | + | 1.54842i | 0.0376433 | + | 0.0652001i | ||||
\(565\) | 44.3688 | + | 76.8489i | 1.86661 | + | 3.23306i | ||||
\(566\) | 1.61840 | − | 2.80315i | 0.0680264 | − | 0.117825i | ||||
\(567\) | −11.2288 | −0.471563 | ||||||||
\(568\) | 15.5809 | + | 26.9869i | 0.653760 | + | 1.13235i | ||||
\(569\) | 22.0217 | 0.923197 | 0.461598 | − | 0.887089i | \(-0.347276\pi\) | ||||
0.461598 | + | 0.887089i | \(0.347276\pi\) | |||||||
\(570\) | 20.3083 | + | 35.1750i | 0.850621 | + | 1.47332i | ||||
\(571\) | −19.7217 | − | 34.1590i | −0.825328 | − | 1.42951i | −0.901668 | − | 0.432429i | \(-0.857657\pi\) |
0.0763397 | − | 0.997082i | \(-0.475677\pi\) | |||||||
\(572\) | −0.165282 | + | 0.286278i | −0.00691081 | + | 0.0119699i | ||||
\(573\) | −21.3274 | −0.890964 | ||||||||
\(574\) | −0.300365 | + | 0.520247i | −0.0125370 | + | 0.0217147i | ||||
\(575\) | −102.769 | −4.28576 | ||||||||
\(576\) | −5.01884 | − | 8.69289i | −0.209118 | − | 0.362204i | ||||
\(577\) | 7.75662 | + | 13.4349i | 0.322912 | + | 0.559300i | 0.981088 | − | 0.193564i | \(-0.0620048\pi\) |
−0.658175 | + | 0.752865i | \(0.728672\pi\) | |||||||
\(578\) | −11.7283 | − | 20.3139i | −0.487831 | − | 0.844949i | ||||
\(579\) | −24.1320 | + | 41.7978i | −1.00289 | + | 1.73706i | ||||
\(580\) | 19.6212 | 0.814725 | ||||||||
\(581\) | −4.44742 | + | 7.70316i | −0.184510 | + | 0.319581i | ||||
\(582\) | 4.41958 | − | 7.65494i | 0.183198 | − | 0.317308i | ||||
\(583\) | 0.835714 | 0.0346118 | ||||||||
\(584\) | 19.8026 | 0.819436 | ||||||||
\(585\) | −62.5075 | −2.58437 | ||||||||
\(586\) | −14.0344 | + | 24.3083i | −0.579755 | + | 1.00417i | ||||
\(587\) | −33.1316 | −1.36749 | −0.683744 | − | 0.729722i | \(-0.739649\pi\) | ||||
−0.683744 | + | 0.729722i | \(0.739649\pi\) | |||||||
\(588\) | −9.36825 | −0.386340 | ||||||||
\(589\) | −5.86783 | + | 10.1634i | −0.241780 | + | 0.418775i | ||||
\(590\) | 14.6521 | − | 25.3782i | 0.603217 | − | 1.04480i | ||||
\(591\) | −15.0003 | + | 25.9813i | −0.617029 | + | 1.06873i | ||||
\(592\) | 18.4666 | − | 31.9850i | 0.758971 | − | 1.31458i | ||||
\(593\) | −12.7907 | −0.525251 | −0.262625 | − | 0.964898i | \(-0.584588\pi\) | ||||
−0.262625 | + | 0.964898i | \(0.584588\pi\) | |||||||
\(594\) | −0.0457040 | + | 0.0791617i | −0.00187526 | + | 0.00324804i | ||||
\(595\) | −4.08624 | − | 7.07758i | −0.167520 | − | 0.290153i | ||||
\(596\) | 1.11548 | + | 1.93207i | 0.0456919 | + | 0.0791408i | ||||
\(597\) | 1.95225 | 0.0799002 | ||||||||
\(598\) | 66.2623 | 2.70967 | ||||||||
\(599\) | 13.2353 | 0.540778 | 0.270389 | − | 0.962751i | \(-0.412848\pi\) | ||||
0.270389 | + | 0.962751i | \(0.412848\pi\) | |||||||
\(600\) | −34.7073 | + | 60.1148i | −1.41692 | + | 2.45418i | ||||
\(601\) | −3.41285 | − | 5.91122i | −0.139213 | − | 0.241124i | 0.787986 | − | 0.615693i | \(-0.211124\pi\) |
−0.927199 | + | 0.374569i | \(0.877791\pi\) | |||||||
\(602\) | 3.82063 | − | 6.61752i | 0.155717 | − | 0.269710i | ||||
\(603\) | 10.1817 | − | 17.6353i | 0.414632 | − | 0.718164i | ||||
\(604\) | −6.77681 | − | 11.7378i | −0.275745 | − | 0.477604i | ||||
\(605\) | −23.6298 | + | 40.9281i | −0.960689 | + | 1.66396i | ||||
\(606\) | −22.3547 | −0.908097 | ||||||||
\(607\) | −44.0468 | −1.78780 | −0.893902 | − | 0.448262i | \(-0.852043\pi\) | ||||
−0.893902 | + | 0.448262i | \(0.852043\pi\) | |||||||
\(608\) | −9.00865 | −0.365349 | ||||||||
\(609\) | 9.16101 | + | 15.8673i | 0.371223 | + | 0.642977i | ||||
\(610\) | −37.1758 | − | 64.3903i | −1.50520 | − | 2.60709i | ||||
\(611\) | 2.86405 | − | 4.96068i | 0.115867 | − | 0.200687i | ||||
\(612\) | −3.11144 | −0.125773 | ||||||||
\(613\) | 1.76404 | − | 3.05541i | 0.0712489 | − | 0.123407i | −0.828200 | − | 0.560433i | \(-0.810635\pi\) |
0.899449 | + | 0.437026i | \(0.143968\pi\) | |||||||
\(614\) | −26.2181 | + | 45.4111i | −1.05808 | + | 1.83264i | ||||
\(615\) | −1.63087 | + | 2.82476i | −0.0657632 | + | 0.113905i | ||||
\(616\) | −0.112202 | + | 0.194339i | −0.00452073 | + | 0.00783014i | ||||
\(617\) | 11.5683 | 0.465722 | 0.232861 | − | 0.972510i | \(-0.425191\pi\) | ||||
0.232861 | + | 0.972510i | \(0.425191\pi\) | |||||||
\(618\) | −12.8875 | −0.518412 | ||||||||
\(619\) | 5.00259 | − | 8.66473i | 0.201071 | − | 0.348265i | −0.747803 | − | 0.663921i | \(-0.768891\pi\) |
0.948874 | + | 0.315656i | \(0.102225\pi\) | |||||||
\(620\) | 14.4969 | 0.582209 | ||||||||
\(621\) | 4.70246 | 0.188703 | ||||||||
\(622\) | −11.3348 | −0.454483 | ||||||||
\(623\) | −3.02899 | + | 5.24636i | −0.121354 | + | 0.210191i | ||||
\(624\) | 31.1499 | − | 53.9532i | 1.24699 | − | 2.15986i | ||||
\(625\) | 89.4392 | 3.57757 | ||||||||
\(626\) | 0.779267 | − | 1.34973i | 0.0311458 | − | 0.0539461i | ||||
\(627\) | 0.260054 | + | 0.450426i | 0.0103855 | + | 0.0179883i | ||||
\(628\) | −1.79353 | − | 3.10649i | −0.0715697 | − | 0.123962i | ||||
\(629\) | 6.18685 | + | 10.7159i | 0.246686 | + | 0.427272i | ||||
\(630\) | 22.3750 | 0.891442 | ||||||||
\(631\) | −9.12074 | + | 15.7976i | −0.363091 | + | 0.628892i | −0.988468 | − | 0.151431i | \(-0.951612\pi\) |
0.625377 | + | 0.780323i | \(0.284945\pi\) | |||||||
\(632\) | −20.9260 | −0.832391 | ||||||||
\(633\) | −12.5120 | + | 21.6713i | −0.497306 | + | 0.861359i | ||||
\(634\) | −1.07029 | − | 1.85380i | −0.0425067 | − | 0.0736238i | ||||
\(635\) | 30.5574 | + | 52.9270i | 1.21263 | + | 2.10034i | ||||
\(636\) | 15.3125 | 0.607181 | ||||||||
\(637\) | 15.0066 | + | 25.9922i | 0.594582 | + | 1.02985i | ||||
\(638\) | 0.979002 | 0.0387591 | ||||||||
\(639\) | 19.8937 | − | 34.4569i | 0.786983 | − | 1.36309i | ||||
\(640\) | −29.0223 | − | 50.2681i | −1.14721 | − | 1.98702i | ||||
\(641\) | −6.12843 | − | 10.6147i | −0.242058 | − | 0.419257i | 0.719242 | − | 0.694760i | \(-0.244489\pi\) |
−0.961300 | + | 0.275502i | \(0.911156\pi\) | |||||||
\(642\) | 7.04663 | − | 12.2051i | 0.278108 | − | 0.481698i | ||||
\(643\) | 19.6171 | + | 33.9778i | 0.773623 | + | 1.33995i | 0.935565 | + | 0.353154i | \(0.114891\pi\) |
−0.161942 | + | 0.986800i | \(0.551776\pi\) | |||||||
\(644\) | −6.08735 | −0.239875 | ||||||||
\(645\) | 20.7447 | − | 35.9308i | 0.816820 | − | 1.41477i | ||||
\(646\) | 3.23859 | − | 5.60941i | 0.127421 | − | 0.220699i | ||||
\(647\) | −9.93362 | −0.390531 | −0.195265 | − | 0.980750i | \(-0.562557\pi\) | ||||
−0.195265 | + | 0.980750i | \(0.562557\pi\) | |||||||
\(648\) | 10.4242 | − | 18.0552i | 0.409500 | − | 0.709276i | ||||
\(649\) | 0.187624 | − | 0.324975i | 0.00736490 | − | 0.0127564i | ||||
\(650\) | −117.263 | −4.59945 | ||||||||
\(651\) | 6.76850 | + | 11.7234i | 0.265279 | + | 0.459476i | ||||
\(652\) | −6.38469 | − | 11.0586i | −0.250044 | − | 0.433088i | ||||
\(653\) | 0.132167 | − | 0.228920i | 0.00517209 | − | 0.00895832i | −0.863428 | − | 0.504472i | \(-0.831687\pi\) |
0.868600 | + | 0.495514i | \(0.165020\pi\) | |||||||
\(654\) | 13.3534 | − | 23.1288i | 0.522160 | − | 0.904407i | ||||
\(655\) | −3.68182 | + | 6.37710i | −0.143861 | + | 0.249174i | ||||
\(656\) | −0.776282 | − | 1.34456i | −0.0303087 | − | 0.0524963i | ||||
\(657\) | −12.6420 | − | 21.8965i | −0.493210 | − | 0.854265i | ||||
\(658\) | −1.02521 | + | 1.77571i | −0.0399667 | + | 0.0692244i | ||||
\(659\) | 31.5798 | 1.23017 | 0.615087 | − | 0.788459i | \(-0.289121\pi\) | ||||
0.615087 | + | 0.788459i | \(0.289121\pi\) | |||||||
\(660\) | 0.321240 | − | 0.556404i | 0.0125042 | − | 0.0216580i | ||||
\(661\) | −7.07757 | + | 12.2587i | −0.275286 | + | 0.476809i | −0.970207 | − | 0.242277i | \(-0.922106\pi\) |
0.694921 | + | 0.719086i | \(0.255439\pi\) | |||||||
\(662\) | −26.0355 | −1.01190 | ||||||||
\(663\) | 10.4361 | + | 18.0759i | 0.405306 | + | 0.702011i | ||||
\(664\) | −8.25750 | − | 14.3024i | −0.320453 | − | 0.555041i | ||||
\(665\) | −5.97707 | + | 10.3526i | −0.231781 | + | 0.401456i | ||||
\(666\) | −33.8773 | −1.31272 | ||||||||
\(667\) | −25.1822 | − | 43.6169i | −0.975060 | − | 1.68885i | ||||
\(668\) | 3.63689 | + | 6.29928i | 0.140716 | + | 0.243727i | ||||
\(669\) | −5.31731 | − | 9.20984i | −0.205579 | − | 0.356073i | ||||
\(670\) | 26.1826 | − | 45.3496i | 1.01152 | − | 1.75201i | ||||
\(671\) | −0.476046 | − | 0.824536i | −0.0183776 | − | 0.0318309i | ||||
\(672\) | −5.19571 | + | 8.99923i | −0.200429 | + | 0.347153i | ||||
\(673\) | −9.21752 | − | 15.9652i | −0.355309 | − | 0.615414i | 0.631861 | − | 0.775081i | \(-0.282291\pi\) |
−0.987171 | + | 0.159667i | \(0.948958\pi\) | |||||||
\(674\) | −20.5467 | + | 35.5879i | −0.791430 | + | 1.37080i | ||||
\(675\) | −8.32187 | −0.320309 | ||||||||
\(676\) | 10.4278 | 0.401070 | ||||||||
\(677\) | 2.58725 | + | 4.48124i | 0.0994360 | + | 0.172228i | 0.911451 | − | 0.411408i | \(-0.134963\pi\) |
−0.812015 | + | 0.583636i | \(0.801629\pi\) | |||||||
\(678\) | 40.5624 | + | 70.2562i | 1.55779 | + | 2.69817i | ||||
\(679\) | 2.60151 | 0.0998370 | ||||||||
\(680\) | 15.1738 | 0.581889 | ||||||||
\(681\) | 20.0213 | + | 34.6778i | 0.767216 | + | 1.32886i | ||||
\(682\) | 0.723324 | 0.0276975 | ||||||||
\(683\) | 8.54870 | 0.327107 | 0.163553 | − | 0.986534i | \(-0.447704\pi\) | ||||
0.163553 | + | 0.986534i | \(0.447704\pi\) | |||||||
\(684\) | 2.27560 | + | 3.94146i | 0.0870098 | + | 0.150705i | ||||
\(685\) | 23.8730 | − | 41.3493i | 0.912141 | − | 1.57988i | ||||
\(686\) | −12.0132 | − | 20.8075i | −0.458667 | − | 0.794434i | ||||
\(687\) | 41.8211 | 1.59557 | ||||||||
\(688\) | 9.87428 | + | 17.1028i | 0.376453 | + | 0.652036i | ||||
\(689\) | −24.5284 | − | 42.4845i | −0.934459 | − | 1.61853i | ||||
\(690\) | −128.786 | −4.90281 | ||||||||
\(691\) | −9.89997 | + | 17.1473i | −0.376613 | + | 0.652312i | −0.990567 | − | 0.137029i | \(-0.956245\pi\) |
0.613954 | + | 0.789342i | \(0.289578\pi\) | |||||||
\(692\) | 1.76302 | + | 3.05364i | 0.0670199 | + | 0.116082i | ||||
\(693\) | 0.286518 | 0.0108839 | ||||||||
\(694\) | 2.91915 | + | 5.05612i | 0.110810 | + | 0.191928i | ||||
\(695\) | 81.6369 | 3.09667 | ||||||||
\(696\) | −34.0184 | −1.28946 | ||||||||
\(697\) | 0.520156 | 0.0197023 | ||||||||
\(698\) | 27.1075 | 1.02603 | ||||||||
\(699\) | −5.66504 | + | 9.81214i | −0.214271 | + | 0.371129i | ||||
\(700\) | 10.7727 | 0.407170 | ||||||||
\(701\) | 7.73917 | − | 13.4046i | 0.292304 | − | 0.506286i | −0.682050 | − | 0.731306i | \(-0.738911\pi\) |
0.974354 | + | 0.225020i | \(0.0722447\pi\) | |||||||
\(702\) | 5.36570 | 0.202515 | ||||||||
\(703\) | 9.04970 | − | 15.6745i | 0.341316 | − | 0.591176i | ||||
\(704\) | −0.165266 | − | 0.286249i | −0.00622870 | − | 0.0107884i | ||||
\(705\) | −5.56651 | + | 9.64148i | −0.209647 | + | 0.363119i | ||||
\(706\) | 57.5175 | 2.16470 | ||||||||
\(707\) | −3.28968 | − | 5.69789i | −0.123721 | − | 0.214291i | ||||
\(708\) | 3.43778 | − | 5.95440i | 0.129200 | − | 0.223780i | ||||
\(709\) | 14.7059 | − | 25.4713i | 0.552290 | − | 0.956594i | −0.445819 | − | 0.895123i | \(-0.647087\pi\) |
0.998109 | − | 0.0614711i | \(-0.0195792\pi\) | |||||||
\(710\) | 51.1572 | − | 88.6069i | 1.91990 | − | 3.32536i | ||||
\(711\) | 13.3592 | + | 23.1387i | 0.501007 | + | 0.867770i | ||||
\(712\) | −5.62390 | − | 9.74088i | −0.210765 | − | 0.365055i | ||||
\(713\) | −18.6056 | − | 32.2258i | −0.696785 | − | 1.20687i | ||||
\(714\) | −3.73569 | − | 6.47041i | −0.139805 | − | 0.242149i | ||||
\(715\) | −2.05832 | −0.0769768 | ||||||||
\(716\) | 1.27200 | + | 2.20317i | 0.0475370 | + | 0.0823364i | ||||
\(717\) | −23.7754 | −0.887907 | ||||||||
\(718\) | −24.1816 | −0.902449 | ||||||||
\(719\) | 24.1951 | − | 41.9071i | 0.902324 | − | 1.56287i | 0.0778545 | − | 0.996965i | \(-0.475193\pi\) |
0.824470 | − | 0.565906i | \(-0.191474\pi\) | |||||||
\(720\) | −28.9137 | + | 50.0801i | −1.07755 | + | 1.86637i | ||||
\(721\) | −1.89651 | − | 3.28484i | −0.0706295 | − | 0.122334i | ||||
\(722\) | 21.6908 | 0.807249 | ||||||||
\(723\) | −35.7674 | + | 10.2291i | −1.33020 | + | 0.380425i | ||||
\(724\) | −1.90020 | −0.0706204 | ||||||||
\(725\) | 44.5646 | + | 77.1882i | 1.65509 | + | 2.86670i | ||||
\(726\) | −21.6027 | + | 37.4169i | −0.801750 | + | 1.38867i | ||||
\(727\) | −13.1230 | + | 22.7298i | −0.486706 | + | 0.843000i | −0.999883 | − | 0.0152828i | \(-0.995135\pi\) |
0.513177 | + | 0.858283i | \(0.328468\pi\) | |||||||
\(728\) | 13.1726 | 0.488208 | ||||||||
\(729\) | −22.1830 | −0.821592 | ||||||||
\(730\) | −32.5092 | − | 56.3076i | −1.20322 | − | 2.08404i | ||||
\(731\) | −6.61636 | −0.244715 | ||||||||
\(732\) | −8.72243 | − | 15.1077i | −0.322390 | − | 0.558396i | ||||
\(733\) | 7.34601 | + | 12.7237i | 0.271331 | + | 0.469959i | 0.969203 | − | 0.246263i | \(-0.0792028\pi\) |
−0.697872 | + | 0.716223i | \(0.745870\pi\) | |||||||
\(734\) | 2.75068 | + | 4.76431i | 0.101529 | + | 0.175854i | ||||
\(735\) | −29.1665 | − | 50.5179i | −1.07582 | − | 1.86338i | ||||
\(736\) | 14.2822 | − | 24.7375i | 0.526449 | − | 0.911837i | ||||
\(737\) | 0.335276 | − | 0.580714i | 0.0123500 | − | 0.0213909i | ||||
\(738\) | −0.712053 | + | 1.23331i | −0.0262110 | + | 0.0453988i | ||||
\(739\) | −21.0132 | − | 36.3960i | −0.772985 | − | 1.33885i | −0.935920 | − | 0.352212i | \(-0.885430\pi\) |
0.162936 | − | 0.986637i | \(-0.447904\pi\) | |||||||
\(740\) | −22.3579 | −0.821892 | ||||||||
\(741\) | 15.2653 | − | 26.4402i | 0.560784 | − | 0.971306i | ||||
\(742\) | 8.78012 | + | 15.2076i | 0.322328 | + | 0.558289i | ||||
\(743\) | 0.0333676 | − | 0.0577944i | 0.00122414 | − | 0.00212027i | −0.865413 | − | 0.501060i | \(-0.832944\pi\) |
0.866637 | + | 0.498939i | \(0.166277\pi\) | |||||||
\(744\) | −25.1341 | −0.921460 | ||||||||
\(745\) | −6.94574 | + | 12.0304i | −0.254472 | + | 0.440759i | ||||
\(746\) | 32.0379 | 1.17299 | ||||||||
\(747\) | −10.5432 | + | 18.2613i | −0.385755 | + | 0.668148i | ||||
\(748\) | −0.102457 | −0.00374620 | ||||||||
\(749\) | 4.14789 | 0.151560 | ||||||||
\(750\) | 143.411 | 5.23663 | ||||||||
\(751\) | −27.5221 | −1.00430 | −0.502149 | − | 0.864781i | \(-0.667457\pi\) | ||||
−0.502149 | + | 0.864781i | \(0.667457\pi\) | |||||||
\(752\) | −2.64961 | − | 4.58926i | −0.0966214 | − | 0.167353i | ||||
\(753\) | −5.75000 | −0.209542 | ||||||||
\(754\) | −28.7339 | − | 49.7686i | −1.04643 | − | 1.81247i | ||||
\(755\) | 42.1970 | − | 73.0873i | 1.53571 | − | 2.65992i | ||||
\(756\) | −0.492933 | −0.0179278 | ||||||||
\(757\) | −8.42193 | − | 14.5872i | −0.306100 | − | 0.530181i | 0.671405 | − | 0.741090i | \(-0.265691\pi\) |
−0.977506 | + | 0.210909i | \(0.932358\pi\) | |||||||
\(758\) | −24.6444 | − | 42.6853i | −0.895124 | − | 1.55040i | ||||
\(759\) | −1.64914 | −0.0598601 | ||||||||
\(760\) | −11.0976 | − | 19.2216i | −0.402552 | − | 0.697241i | ||||
\(761\) | −10.0795 | + | 17.4582i | −0.365382 | + | 0.632861i | −0.988837 | − | 0.148998i | \(-0.952395\pi\) |
0.623455 | + | 0.781859i | \(0.285728\pi\) | |||||||
\(762\) | 27.9360 | + | 48.3865i | 1.01201 | + | 1.75286i | ||||
\(763\) | 7.86026 | 0.284561 | ||||||||
\(764\) | −6.14542 | −0.222333 | ||||||||
\(765\) | −9.68696 | − | 16.7783i | −0.350233 | − | 0.606621i | ||||
\(766\) | −7.62086 | −0.275353 | ||||||||
\(767\) | −22.0273 | −0.795359 | ||||||||
\(768\) | −17.7617 | − | 30.7642i | −0.640921 | − | 1.11011i | ||||
\(769\) | 20.6804 | + | 35.8195i | 0.745754 | + | 1.29168i | 0.949841 | + | 0.312732i | \(0.101244\pi\) |
−0.204087 | + | 0.978953i | \(0.565423\pi\) | |||||||
\(770\) | 0.736790 | 0.0265521 | ||||||||
\(771\) | −55.7239 | −2.00685 | ||||||||
\(772\) | −6.95356 | + | 12.0439i | −0.250264 | + | 0.433470i | ||||
\(773\) | −9.48547 | − | 16.4293i | −0.341169 | − | 0.590922i | 0.643481 | − | 0.765462i | \(-0.277489\pi\) |
−0.984650 | + | 0.174540i | \(0.944156\pi\) | |||||||
\(774\) | 9.05729 | − | 15.6877i | 0.325557 | − | 0.563882i | ||||
\(775\) | 32.9260 | + | 57.0296i | 1.18274 | + | 2.04856i | ||||
\(776\) | −2.41511 | + | 4.18309i | −0.0866973 | + | 0.150164i | ||||
\(777\) | −10.4388 | − | 18.0805i | −0.374488 | − | 0.648633i | ||||
\(778\) | 2.70796 | + | 4.69033i | 0.0970851 | + | 0.168156i | ||||
\(779\) | −0.380424 | − | 0.658913i | −0.0136301 | − | 0.0236080i | ||||
\(780\) | −37.7139 | −1.35037 | ||||||||
\(781\) | 0.655083 | − | 1.13464i | 0.0234407 | − | 0.0406005i | ||||
\(782\) | 10.2689 | + | 17.7862i | 0.367213 | + | 0.636032i | ||||
\(783\) | −2.03917 | − | 3.53195i | −0.0728740 | − | 0.126222i | ||||
\(784\) | 27.7660 | 0.991643 | ||||||||
\(785\) | 11.1677 | − | 19.3431i | 0.398594 | − | 0.690384i | ||||
\(786\) | −3.36597 | + | 5.83002i | −0.120060 | + | 0.207950i | ||||
\(787\) | 27.0008 | 0.962474 | 0.481237 | − | 0.876591i | \(-0.340188\pi\) | ||||
0.481237 | + | 0.876591i | \(0.340188\pi\) | |||||||
\(788\) | −4.32228 | + | 7.48642i | −0.153975 | + | 0.266693i | ||||
\(789\) | −22.1733 | − | 38.4053i | −0.789391 | − | 1.36727i | ||||
\(790\) | 34.3534 | + | 59.5019i | 1.22224 | + | 2.11698i | ||||
\(791\) | −11.9382 | + | 20.6776i | −0.424474 | + | 0.735210i | ||||
\(792\) | −0.265988 | + | 0.460705i | −0.00945149 | + | 0.0163705i | ||||
\(793\) | −27.9441 | + | 48.4007i | −0.992325 | + | 1.71876i | ||||
\(794\) | −15.7022 | − | 27.1971i | −0.557252 | − | 0.965189i | ||||
\(795\) | 47.6730 | + | 82.5720i | 1.69079 | + | 2.92853i | ||||
\(796\) | 0.562534 | 0.0199385 | ||||||||
\(797\) | 23.2739 | − | 40.3116i | 0.824403 | − | 1.42791i | −0.0779711 | − | 0.996956i | \(-0.524844\pi\) |
0.902374 | − | 0.430953i | \(-0.141822\pi\) | |||||||
\(798\) | −5.46431 | + | 9.46447i | −0.193435 | + | 0.335038i | ||||
\(799\) | 1.77540 | 0.0628091 | ||||||||
\(800\) | −25.2750 | + | 43.7776i | −0.893607 | + | 1.54777i | ||||
\(801\) | −7.18060 | + | 12.4372i | −0.253714 | + | 0.439446i | ||||
\(802\) | −33.8165 | −1.19410 | ||||||||
\(803\) | −0.416289 | − | 0.721034i | −0.0146905 | − | 0.0254447i | ||||
\(804\) | 6.14314 | − | 10.6402i | 0.216652 | − | 0.375252i | ||||
\(805\) | −18.9520 | − | 32.8258i | −0.667969 | − | 1.15696i | ||||
\(806\) | −21.2297 | − | 36.7710i | −0.747786 | − | 1.29520i | ||||
\(807\) | 16.2787 | − | 28.1956i | 0.573038 | − | 0.992531i | ||||
\(808\) | 12.2159 | 0.429752 | ||||||||
\(809\) | 9.33892 | + | 16.1755i | 0.328339 | + | 0.568700i | 0.982182 | − | 0.187930i | \(-0.0601778\pi\) |
−0.653843 | + | 0.756630i | \(0.726844\pi\) | |||||||
\(810\) | −68.4520 | −2.40516 | ||||||||
\(811\) | 5.85160 | + | 10.1353i | 0.205478 | + | 0.355898i | 0.950285 | − | 0.311382i | \(-0.100792\pi\) |
−0.744807 | + | 0.667280i | \(0.767459\pi\) | |||||||
\(812\) | 2.63971 | + | 4.57212i | 0.0926358 | + | 0.160450i | ||||
\(813\) | 18.9458 | − | 32.8151i | 0.664458 | − | 1.15087i | ||||
\(814\) | −1.11555 | −0.0391000 | ||||||||
\(815\) | 39.7554 | − | 68.8583i | 1.39257 | − | 2.41200i | ||||
\(816\) | 19.3095 | 0.675969 | ||||||||
\(817\) | 4.83898 | + | 8.38135i | 0.169294 | + | 0.293226i | ||||
\(818\) | −7.70382 | − | 13.3434i | −0.269358 | − | 0.466541i | ||||
\(819\) | −8.40938 | − | 14.5655i | −0.293848 | − | 0.508959i | ||||
\(820\) | −0.469931 | + | 0.813945i | −0.0164107 | + | 0.0284242i | ||||
\(821\) | 6.39468 | 0.223176 | 0.111588 | − | 0.993755i | \(-0.464406\pi\) | ||||
0.111588 | + | 0.993755i | \(0.464406\pi\) | |||||||
\(822\) | 21.8250 | − | 37.8020i | 0.761234 | − | 1.31850i | ||||
\(823\) | 4.61846 | − | 7.99941i | 0.160989 | − | 0.278842i | −0.774234 | − | 0.632899i | \(-0.781865\pi\) |
0.935224 | + | 0.354057i | \(0.115198\pi\) | |||||||
\(824\) | 7.04246 | 0.245336 | ||||||||
\(825\) | 2.91846 | 0.101608 | ||||||||
\(826\) | 7.88482 | 0.274348 | ||||||||
\(827\) | −6.13183 | + | 10.6206i | −0.213225 | + | 0.369316i | −0.952722 | − | 0.303844i | \(-0.901730\pi\) |
0.739497 | + | 0.673160i | \(0.235063\pi\) | |||||||
\(828\) | −14.4309 | −0.501507 | ||||||||
\(829\) | −53.1162 | −1.84480 | −0.922400 | − | 0.386236i | \(-0.873775\pi\) | ||||
−0.922400 | + | 0.386236i | \(0.873775\pi\) | |||||||
\(830\) | −27.1121 | + | 46.9595i | −0.941075 | + | 1.62999i | ||||
\(831\) | −29.5045 | + | 51.1033i | −1.02350 | + | 1.77275i | ||||
\(832\) | −9.70120 | + | 16.8030i | −0.336329 | + | 0.582538i | ||||
\(833\) | −4.65122 | + | 8.05615i | −0.161155 | + | 0.279129i | ||||
\(834\) | 74.6335 | 2.58435 | ||||||||
\(835\) | −22.6457 | + | 39.2236i | −0.783688 | + | 1.35739i | ||||
\(836\) | 0.0749336 | + | 0.129789i | 0.00259163 | + | 0.00448884i | ||||
\(837\) | −1.50662 | − | 2.60954i | −0.0520763 | − | 0.0901989i | ||||
\(838\) | −23.1672 | −0.800297 | ||||||||
\(839\) | 1.64179 | 0.0566809 | 0.0283405 | − | 0.999598i | \(-0.490978\pi\) | ||||
0.0283405 | + | 0.999598i | \(0.490978\pi\) | |||||||
\(840\) | −25.6020 | −0.883352 | ||||||||
\(841\) | −7.34000 | + | 12.7133i | −0.253104 | + | 0.438388i | ||||
\(842\) | 10.2753 | + | 17.7973i | 0.354109 | + | 0.613334i | ||||
\(843\) | −10.2972 | + | 17.8353i | −0.354655 | + | 0.614281i | ||||
\(844\) | −3.60528 | + | 6.24453i | −0.124099 | + | 0.214946i | ||||
\(845\) | 32.4653 | + | 56.2315i | 1.11684 | + | 1.93442i | ||||
\(846\) | −2.43038 | + | 4.20955i | −0.0835583 | + | 0.144727i | ||||
\(847\) | −12.7161 | −0.436929 | ||||||||
\(848\) | −45.3839 | −1.55849 | ||||||||
\(849\) | 4.72879 | 0.162292 | ||||||||
\(850\) | −18.1726 | − | 31.4759i | −0.623316 | − | 1.07962i | ||||
\(851\) | 28.6946 | + | 49.7005i | 0.983637 | + | 1.70371i | ||||
\(852\) | 12.0029 | − | 20.7896i | 0.411211 | − | 0.712239i | ||||
\(853\) | −3.12352 | −0.106947 | −0.0534736 | − | 0.998569i | \(-0.517029\pi\) | ||||
−0.0534736 | + | 0.998569i | \(0.517029\pi\) | |||||||
\(854\) | 10.0028 | − | 17.3254i | 0.342289 | − | 0.592862i | ||||
\(855\) | −14.1694 | + | 24.5422i | −0.484584 | + | 0.839324i | ||||
\(856\) | −3.85068 | + | 6.66957i | −0.131613 | + | 0.227961i | ||||
\(857\) | −26.3721 | + | 45.6778i | −0.900854 | + | 1.56033i | −0.0744665 | + | 0.997224i | \(0.523725\pi\) |
−0.826388 | + | 0.563102i | \(0.809608\pi\) | |||||||
\(858\) | −1.88174 | −0.0642415 | ||||||||
\(859\) | 11.9733 | 0.408524 | 0.204262 | − | 0.978916i | \(-0.434521\pi\) | ||||
0.204262 | + | 0.978916i | \(0.434521\pi\) | |||||||
\(860\) | 5.97751 | − | 10.3533i | 0.203831 | − | 0.353046i | ||||
\(861\) | −0.877632 | −0.0299096 | ||||||||
\(862\) | 31.3975 | 1.06940 | ||||||||
\(863\) | 30.9314 | 1.05292 | 0.526458 | − | 0.850201i | \(-0.323520\pi\) | ||||
0.526458 | + | 0.850201i | \(0.323520\pi\) | |||||||
\(864\) | 1.15653 | − | 2.00316i | 0.0393458 | − | 0.0681489i | ||||
\(865\) | −10.9777 | + | 19.0140i | −0.373254 | + | 0.646495i | ||||
\(866\) | 32.2842 | 1.09706 | ||||||||
\(867\) | 17.1343 | − | 29.6775i | 0.581913 | − | 1.00790i | ||||
\(868\) | 1.95032 | + | 3.37806i | 0.0661983 | + | 0.114659i | ||||
\(869\) | 0.439905 | + | 0.761939i | 0.0149228 | + | 0.0258470i | ||||
\(870\) | 55.8468 | + | 96.7294i | 1.89338 | + | 3.27943i | ||||
\(871\) | −39.3617 | −1.33372 | ||||||||
\(872\) | −7.29705 | + | 12.6389i | −0.247109 | + | 0.428006i | ||||
\(873\) | 6.16722 | 0.208729 | ||||||||
\(874\) | 15.0206 | − | 26.0164i | 0.508078 | − | 0.880018i | ||||
\(875\) | 21.1041 | + | 36.5534i | 0.713450 | + | 1.23573i | ||||
\(876\) | −7.62753 | − | 13.2113i | −0.257710 | − | 0.446367i | ||||
\(877\) | −13.7122 | −0.463030 | −0.231515 | − | 0.972831i | \(-0.574368\pi\) | ||||
−0.231515 | + | 0.972831i | \(0.574368\pi\) | |||||||
\(878\) | 27.8546 | + | 48.2456i | 0.940048 | + | 1.62821i | ||||
\(879\) | −41.0069 | −1.38313 | ||||||||
\(880\) | −0.952104 | + | 1.64909i | −0.0320954 | + | 0.0555909i | ||||
\(881\) | 14.0603 | + | 24.3531i | 0.473703 | + | 0.820478i | 0.999547 | − | 0.0301031i | \(-0.00958357\pi\) |
−0.525843 | + | 0.850581i | \(0.676250\pi\) | |||||||
\(882\) | −12.7343 | − | 22.0565i | −0.428787 | − | 0.742682i | ||||
\(883\) | −12.5366 | + | 21.7141i | −0.421891 | + | 0.730736i | −0.996124 | − | 0.0879553i | \(-0.971967\pi\) |
0.574234 | + | 0.818691i | \(0.305300\pi\) | |||||||
\(884\) | 3.00714 | + | 5.20852i | 0.101141 | + | 0.175182i | ||||
\(885\) | 42.8118 | 1.43910 | ||||||||
\(886\) | −4.35747 | + | 7.54736i | −0.146392 | + | 0.253559i | ||||
\(887\) | 4.89266 | − | 8.47433i | 0.164279 | − | 0.284540i | −0.772120 | − | 0.635477i | \(-0.780804\pi\) |
0.936399 | + | 0.350937i | \(0.114137\pi\) | |||||||
\(888\) | 38.7631 | 1.30081 | ||||||||
\(889\) | −8.22202 | + | 14.2410i | −0.275758 | + | 0.477626i | ||||
\(890\) | −18.4651 | + | 31.9825i | −0.618952 | + | 1.07206i | ||||
\(891\) | −0.876548 | −0.0293655 | ||||||||
\(892\) | −1.53216 | − | 2.65379i | −0.0513007 | − | 0.0888554i | ||||
\(893\) | −1.29846 | − | 2.24901i | −0.0434515 | − | 0.0752601i | ||||
\(894\) | −6.34988 | + | 10.9983i | −0.212372 | + | 0.367839i | ||||
\(895\) | −7.92034 | + | 13.7184i | −0.264748 | + | 0.458557i | ||||
\(896\) | 7.80896 | − | 13.5255i | 0.260879 | − | 0.451856i | ||||
\(897\) | 48.4028 | + | 83.8361i | 1.61612 | + | 2.79920i | ||||
\(898\) | 28.6818 | + | 49.6783i | 0.957124 | + | 1.65779i | ||||
\(899\) | −16.1362 | + | 27.9488i | −0.538173 | + | 0.932144i | ||||
\(900\) | 25.5381 | 0.851269 | ||||||||
\(901\) | 7.60247 | − | 13.1679i | 0.253275 | − | 0.438685i | ||||
\(902\) | −0.0234473 | + | 0.0406119i | −0.000780709 | + | 0.00135223i | ||||
\(903\) | 11.1634 | 0.371496 | ||||||||
\(904\) | −22.1656 | − | 38.3919i | −0.737217 | − | 1.27690i | ||||
\(905\) | −5.91596 | − | 10.2467i | −0.196653 | − | 0.340613i | ||||
\(906\) | 38.5770 | − | 66.8173i | 1.28163 | − | 2.21986i | ||||
\(907\) | 3.15903 | 0.104894 | 0.0524470 | − | 0.998624i | \(-0.483298\pi\) | ||||
0.0524470 | + | 0.998624i | \(0.483298\pi\) | |||||||
\(908\) | 5.76906 | + | 9.99231i | 0.191453 | + | 0.331606i | ||||
\(909\) | −7.79861 | − | 13.5076i | −0.258664 | − | 0.448019i | ||||
\(910\) | −21.6250 | − | 37.4555i | −0.716861 | − | 1.24164i | ||||
\(911\) | 21.4479 | − | 37.1488i | 0.710600 | − | 1.23080i | −0.254032 | − | 0.967196i | \(-0.581757\pi\) |
0.964632 | − | 0.263599i | \(-0.0849097\pi\) | |||||||
\(912\) | −14.1223 | − | 24.4606i | −0.467637 | − | 0.809971i | ||||
\(913\) | −0.347178 | + | 0.601330i | −0.0114899 | + | 0.0199011i | ||||
\(914\) | −13.2979 | − | 23.0327i | −0.439857 | − | 0.761854i | ||||
\(915\) | 54.3117 | − | 94.0706i | 1.79549 | − | 3.10988i | ||||
\(916\) | 12.0506 | 0.398164 | ||||||||
\(917\) | −1.98132 | −0.0654290 | ||||||||
\(918\) | 0.831537 | + | 1.44026i | 0.0274448 | + | 0.0475358i | ||||
\(919\) | −4.62491 | − | 8.01058i | −0.152562 | − | 0.264245i | 0.779607 | − | 0.626269i | \(-0.215419\pi\) |
−0.932168 | + | 0.362025i | \(0.882086\pi\) | |||||||
\(920\) | 70.3760 | 2.32023 | ||||||||
\(921\) | −76.6065 | −2.52427 | ||||||||
\(922\) | 3.81006 | + | 6.59922i | 0.125478 | + | 0.217334i | ||||
\(923\) | −76.9074 | −2.53144 | ||||||||
\(924\) | 0.172871 | 0.00568703 | ||||||||
\(925\) | −50.7803 | − | 87.9541i | −1.66965 | − | 2.89191i | ||||
\(926\) | 12.4312 | − | 21.5315i | 0.408514 | − | 0.707568i | ||||
\(927\) | −4.49591 | − | 7.78714i | −0.147665 | − | 0.255763i | ||||
\(928\) | −24.7733 | −0.813224 | ||||||||
\(929\) | −15.9273 | − | 27.5869i | −0.522558 | − | 0.905097i | −0.999656 | − | 0.0262464i | \(-0.991645\pi\) |
0.477098 | − | 0.878850i | \(-0.341689\pi\) | |||||||
\(930\) | 41.2617 | + | 71.4674i | 1.35303 | + | 2.34351i | ||||
\(931\) | 13.6070 | 0.445951 | ||||||||
\(932\) | −1.63236 | + | 2.82734i | −0.0534698 | + | 0.0926125i | ||||
\(933\) | −8.27973 | − | 14.3409i | −0.271066 | − | 0.469501i | ||||
\(934\) | 12.5841 | 0.411765 | ||||||||
\(935\) | −0.318983 | − | 0.552495i | −0.0104319 | − | 0.0180685i | ||||
\(936\) | 31.2273 | 1.02070 | ||||||||
\(937\) | 20.8821 | 0.682190 | 0.341095 | − | 0.940029i | \(-0.389202\pi\) | ||||
0.341095 | + | 0.940029i | \(0.389202\pi\) | |||||||
\(938\) | 14.0898 | 0.460048 | ||||||||
\(939\) | 2.27693 | 0.0743049 | ||||||||
\(940\) | −1.60397 | + | 2.77816i | −0.0523158 | + | 0.0906136i | ||||
\(941\) | −40.8680 | −1.33226 | −0.666130 | − | 0.745836i | \(-0.732050\pi\) | ||||
−0.666130 | + | 0.745836i | \(0.732050\pi\) | |||||||
\(942\) | 10.2097 | − | 17.6837i | 0.332649 | − | 0.576165i | ||||
\(943\) | 2.41248 | 0.0785611 | ||||||||
\(944\) | −10.1890 | + | 17.6479i | −0.331624 | + | 0.574390i | ||||
\(945\) | −1.53467 | − | 2.65812i | −0.0499227 | − | 0.0864686i | ||||
\(946\) | 0.298249 | − | 0.516582i | 0.00969690 | − | 0.0167955i | ||||
\(947\) | 3.73700 | 0.121436 | 0.0607181 | − | 0.998155i | \(-0.480661\pi\) | ||||
0.0607181 | + | 0.998155i | \(0.480661\pi\) | |||||||
\(948\) | 8.06024 | + | 13.9607i | 0.261784 | + | 0.453424i | ||||
\(949\) | −24.4364 | + | 42.3251i | −0.793239 | + | 1.37393i | ||||
\(950\) | −26.5817 | + | 46.0408i | −0.862423 | + | 1.49376i | ||||
\(951\) | 1.56364 | − | 2.70830i | 0.0507044 | − | 0.0878226i | ||||
\(952\) | 2.04139 | + | 3.53579i | 0.0661619 | + | 0.114596i | ||||
\(953\) | 24.8171 | + | 42.9844i | 0.803903 | + | 1.39240i | 0.917029 | + | 0.398821i | \(0.130580\pi\) |
−0.113126 | + | 0.993581i | \(0.536086\pi\) | |||||||
\(954\) | 20.8144 | + | 36.0516i | 0.673891 | + | 1.16721i | ||||
\(955\) | −19.1327 | − | 33.1389i | −0.619121 | − | 1.07235i | ||||
\(956\) | −6.85080 | −0.221571 | ||||||||
\(957\) | 0.715133 | + | 1.23865i | 0.0231170 | + | 0.0400398i | ||||
\(958\) | 27.8267 | 0.899039 | ||||||||
\(959\) | 12.8469 | 0.414849 | ||||||||
\(960\) | 18.8551 | − | 32.6579i | 0.608545 | − | 1.05403i | ||||
\(961\) | 3.57793 | − | 6.19716i | 0.115417 | − | 0.199908i | ||||
\(962\) | 32.7417 | + | 56.7102i | 1.05563 | + | 1.82841i | ||||
\(963\) | 9.83310 | 0.316867 | ||||||||
\(964\) | −10.3063 | + | 2.94749i | −0.331942 | + | 0.0949322i | ||||
\(965\) | −86.5950 | −2.78759 | ||||||||
\(966\) | −17.3261 | − | 30.0097i | −0.557459 | − | 0.965547i | ||||
\(967\) | 12.5369 | − | 21.7146i | 0.403161 | − | 0.698295i | −0.590945 | − | 0.806712i | \(-0.701245\pi\) |
0.994105 | + | 0.108417i | \(0.0345783\pi\) | |||||||
\(968\) | 11.8049 | − | 20.4467i | 0.379424 | − | 0.657182i | ||||
\(969\) | 9.46280 | 0.303989 | ||||||||
\(970\) | 15.8592 | 0.509208 | ||||||||
\(971\) | 4.37687 | + | 7.58096i | 0.140460 | + | 0.243284i | 0.927670 | − | 0.373401i | \(-0.121808\pi\) |
−0.787210 | + | 0.616685i | \(0.788475\pi\) | |||||||
\(972\) | −14.7824 | −0.474146 | ||||||||
\(973\) | 10.9829 | + | 19.0230i | 0.352097 | + | 0.609850i | ||||
\(974\) | 25.3250 | + | 43.8641i | 0.811465 | + | 1.40550i | ||||
\(975\) | −85.6576 | − | 148.363i | −2.74324 | − | 4.75143i | ||||
\(976\) | 25.8519 | + | 44.7768i | 0.827499 | + | 1.43327i | ||||
\(977\) | −28.1104 | + | 48.6887i | −0.899332 | + | 1.55769i | −0.0709815 | + | 0.997478i | \(0.522613\pi\) |
−0.828350 | + | 0.560211i | \(0.810720\pi\) | |||||||
\(978\) | 36.3448 | − | 62.9511i | 1.16218 | − | 2.01295i | ||||
\(979\) | −0.236451 | + | 0.409545i | −0.00755701 | + | 0.0130891i | ||||
\(980\) | −8.40424 | − | 14.5566i | −0.268464 | − | 0.464992i | ||||
\(981\) | 18.6338 | 0.594930 | ||||||||
\(982\) | 29.3313 | − | 50.8033i | 0.935999 | − | 1.62120i | ||||
\(983\) | −7.90132 | − | 13.6855i | −0.252013 | − | 0.436499i | 0.712067 | − | 0.702111i | \(-0.247759\pi\) |
−0.964080 | + | 0.265612i | \(0.914426\pi\) | |||||||
\(984\) | 0.814747 | − | 1.41118i | 0.0259732 | − | 0.0449869i | ||||
\(985\) | −53.8269 | −1.71507 | ||||||||
\(986\) | 8.90596 | − | 15.4256i | 0.283623 | − | 0.491250i | ||||
\(987\) | −2.99554 | −0.0953490 | ||||||||
\(988\) | 4.39864 | − | 7.61867i | 0.139939 | − | 0.242382i | ||||
\(989\) | −30.6866 | −0.975778 | ||||||||
\(990\) | 1.74666 | 0.0555123 | ||||||||
\(991\) | 39.6990 | 1.26108 | 0.630540 | − | 0.776157i | \(-0.282834\pi\) | ||||
0.630540 | + | 0.776157i | \(0.282834\pi\) | |||||||
\(992\) | −18.3035 | −0.581136 | ||||||||
\(993\) | −19.0182 | − | 32.9405i | −0.603524 | − | 1.04533i | ||||
\(994\) | 27.5295 | 0.873184 | ||||||||
\(995\) | 1.75136 | + | 3.03344i | 0.0555218 | + | 0.0961665i | ||||
\(996\) | −6.36123 | + | 11.0180i | −0.201563 | + | 0.349118i | ||||
\(997\) | −9.25494 | −0.293107 | −0.146554 | − | 0.989203i | \(-0.546818\pi\) | ||||
−0.146554 | + | 0.989203i | \(0.546818\pi\) | |||||||
\(998\) | −34.8185 | − | 60.3074i | −1.10216 | − | 1.90900i | ||||
\(999\) | 2.32359 | + | 4.02457i | 0.0735151 | + | 0.127332i |
(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 | 241.2.c.a.15.15 | ✓ | 38 | |
241.225 | even | 3 | inner | 241.2.c.a.225.15 | yes | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
241.2.c.a.15.15 | ✓ | 38 | 1.1 | even | 1 | trivial | |
241.2.c.a.225.15 | yes | 38 | 241.225 | even | 3 | inner |