Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(101,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.t (of order \(6\), 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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 131.2 | ||
Character | \(\chi\) | \(=\) | 315.131 |
Dual form | 315.2.t.c.101.15 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.44435i | − | 1.72842i | −0.503135 | − | 0.864208i | \(-0.667820\pi\) | ||
0.503135 | − | 0.864208i | \(-0.332180\pi\) | |||||||
\(3\) | 0.807396 | − | 1.53235i | 0.466150 | − | 0.884705i | ||||
\(4\) | −3.97484 | −1.98742 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | −3.74561 | − | 1.97356i | −1.52914 | − | 0.805702i | ||||
\(7\) | 0.510801 | − | 2.59597i | 0.193065 | − | 0.981186i | ||||
\(8\) | 4.82720i | 1.70667i | ||||||||
\(9\) | −1.69622 | − | 2.47444i | −0.565408 | − | 0.824812i | ||||
\(10\) | −2.11687 | + | 1.22217i | −0.669413 | + | 0.386486i | ||||
\(11\) | 3.79537 | + | 2.19126i | 1.14435 | + | 0.660689i | 0.947503 | − | 0.319745i | \(-0.103597\pi\) |
0.196844 | + | 0.980435i | \(0.436931\pi\) | |||||||
\(12\) | −3.20927 | + | 6.09087i | −0.926437 | + | 1.75828i | ||||
\(13\) | 1.54497 | + | 0.891986i | 0.428496 | + | 0.247393i | 0.698706 | − | 0.715409i | \(-0.253760\pi\) |
−0.270209 | + | 0.962802i | \(0.587093\pi\) | |||||||
\(14\) | −6.34547 | − | 1.24858i | −1.69590 | − | 0.333696i | ||||
\(15\) | −1.73076 | + | 0.0669518i | −0.446879 | + | 0.0172869i | ||||
\(16\) | 3.84969 | 0.962422 | ||||||||
\(17\) | 3.92956 | + | 6.80619i | 0.953058 | + | 1.65074i | 0.738752 | + | 0.673978i | \(0.235416\pi\) |
0.214306 | + | 0.976767i | \(0.431251\pi\) | |||||||
\(18\) | −6.04838 | + | 4.14616i | −1.42562 | + | 0.977259i | ||||
\(19\) | −3.33955 | − | 1.92809i | −0.766146 | − | 0.442335i | 0.0653519 | − | 0.997862i | \(-0.479183\pi\) |
−0.831498 | + | 0.555528i | \(0.812516\pi\) | |||||||
\(20\) | 1.98742 | + | 3.44231i | 0.444401 | + | 0.769725i | ||||
\(21\) | −3.56554 | − | 2.87871i | −0.778064 | − | 0.628186i | ||||
\(22\) | 5.35620 | − | 9.27721i | 1.14195 | − | 1.97791i | ||||
\(23\) | −1.96471 | + | 1.13433i | −0.409670 | + | 0.236523i | −0.690648 | − | 0.723191i | \(-0.742675\pi\) |
0.280978 | + | 0.959714i | \(0.409341\pi\) | |||||||
\(24\) | 7.39699 | + | 3.89747i | 1.50990 | + | 0.795567i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 2.18033 | − | 3.77644i | 0.427597 | − | 0.740620i | ||||
\(27\) | −5.16124 | + | 0.601365i | −0.993280 | + | 0.115733i | ||||
\(28\) | −2.03035 | + | 10.3186i | −0.383701 | + | 1.95003i | ||||
\(29\) | 0.771716 | − | 0.445550i | 0.143304 | − | 0.0827366i | −0.426634 | − | 0.904425i | \(-0.640301\pi\) |
0.569938 | + | 0.821688i | \(0.306967\pi\) | |||||||
\(30\) | 0.163653 | + | 4.23057i | 0.0298789 | + | 0.772393i | ||||
\(31\) | − | 7.07941i | − | 1.27150i | −0.771895 | − | 0.635750i | \(-0.780691\pi\) | ||
0.771895 | − | 0.635750i | \(-0.219309\pi\) | |||||||
\(32\) | 0.244430i | 0.0432095i | ||||||||
\(33\) | 6.42215 | − | 4.04664i | 1.11795 | − | 0.704430i | ||||
\(34\) | 16.6367 | − | 9.60521i | 2.85317 | − | 1.64728i | ||||
\(35\) | −2.50358 | + | 0.855621i | −0.423182 | + | 0.144626i | ||||
\(36\) | 6.74222 | + | 9.83549i | 1.12370 | + | 1.63925i | ||||
\(37\) | 2.58988 | − | 4.48580i | 0.425774 | − | 0.737461i | −0.570719 | − | 0.821146i | \(-0.693335\pi\) |
0.996492 | + | 0.0836841i | \(0.0266687\pi\) | |||||||
\(38\) | −4.71293 | + | 8.16304i | −0.764538 | + | 1.32422i | ||||
\(39\) | 2.61424 | − | 1.64725i | 0.418613 | − | 0.263771i | ||||
\(40\) | 4.18048 | − | 2.41360i | 0.660992 | − | 0.381624i | ||||
\(41\) | 1.78706 | − | 3.09527i | 0.279091 | − | 0.483400i | −0.692068 | − | 0.721832i | \(-0.743300\pi\) |
0.971159 | + | 0.238432i | \(0.0766335\pi\) | |||||||
\(42\) | −7.03657 | + | 8.71541i | −1.08577 | + | 1.34482i | ||||
\(43\) | 2.68755 | + | 4.65498i | 0.409848 | + | 0.709877i | 0.994872 | − | 0.101138i | \(-0.0322485\pi\) |
−0.585025 | + | 0.811016i | \(0.698915\pi\) | |||||||
\(44\) | −15.0860 | − | 8.70991i | −2.27430 | − | 1.31307i | ||||
\(45\) | −1.29481 | + | 2.70619i | −0.193019 | + | 0.403415i | ||||
\(46\) | 2.77269 | + | 4.80244i | 0.408811 | + | 0.708081i | ||||
\(47\) | 0.599871 | 0.0875002 | 0.0437501 | − | 0.999043i | \(-0.486069\pi\) | ||||
0.0437501 | + | 0.999043i | \(0.486069\pi\) | |||||||
\(48\) | 3.10822 | − | 5.89909i | 0.448633 | − | 0.851460i | ||||
\(49\) | −6.47817 | − | 2.65205i | −0.925452 | − | 0.378865i | ||||
\(50\) | 2.11687 | + | 1.22217i | 0.299370 | + | 0.172842i | ||||
\(51\) | 13.6022 | − | 0.526181i | 1.90469 | − | 0.0736801i | ||||
\(52\) | −6.14099 | − | 3.54551i | −0.851603 | − | 0.491673i | ||||
\(53\) | 11.9100 | − | 6.87623i | 1.63596 | − | 0.944523i | 0.653758 | − | 0.756703i | \(-0.273191\pi\) |
0.982203 | − | 0.187820i | \(-0.0601421\pi\) | |||||||
\(54\) | 1.46995 | + | 12.6159i | 0.200034 | + | 1.71680i | ||||
\(55\) | − | 4.38252i | − | 0.590939i | ||||||
\(56\) | 12.5313 | + | 2.46574i | 1.67457 | + | 0.329498i | ||||
\(57\) | −5.65086 | + | 3.56065i | −0.748475 | + | 0.471619i | ||||
\(58\) | −1.08908 | − | 1.88634i | −0.143003 | − | 0.247689i | ||||
\(59\) | −8.92852 | −1.16239 | −0.581197 | − | 0.813763i | \(-0.697416\pi\) | ||||
−0.581197 | + | 0.813763i | \(0.697416\pi\) | |||||||
\(60\) | 6.87948 | − | 0.266123i | 0.888137 | − | 0.0343563i | ||||
\(61\) | 4.34422i | 0.556220i | 0.960549 | + | 0.278110i | \(0.0897081\pi\) | ||||
−0.960549 | + | 0.278110i | \(0.910292\pi\) | |||||||
\(62\) | −17.3045 | −2.19768 | ||||||||
\(63\) | −7.29000 | + | 3.13941i | −0.918454 | + | 0.395528i | ||||
\(64\) | 8.29685 | 1.03711 | ||||||||
\(65\) | − | 1.78397i | − | 0.221275i | ||||||
\(66\) | −9.89141 | − | 15.6980i | −1.21755 | − | 1.93229i | ||||
\(67\) | −6.48717 | −0.792534 | −0.396267 | − | 0.918135i | \(-0.629695\pi\) | ||||
−0.396267 | + | 0.918135i | \(0.629695\pi\) | |||||||
\(68\) | −15.6194 | − | 27.0535i | −1.89413 | − | 3.28072i | ||||
\(69\) | 0.151890 | + | 3.92648i | 0.0182854 | + | 0.472693i | ||||
\(70\) | 2.09144 | + | 6.11962i | 0.249974 | + | 0.731435i | ||||
\(71\) | 0.343987i | 0.0408237i | 0.999792 | + | 0.0204119i | \(0.00649775\pi\) | ||||
−0.999792 | + | 0.0204119i | \(0.993502\pi\) | |||||||
\(72\) | 11.9446 | − | 8.18801i | 1.40768 | − | 0.964967i | ||||
\(73\) | −3.38926 | + | 1.95679i | −0.396683 | + | 0.229025i | −0.685052 | − | 0.728494i | \(-0.740220\pi\) |
0.288369 | + | 0.957519i | \(0.406887\pi\) | |||||||
\(74\) | −10.9649 | − | 6.33057i | −1.27464 | − | 0.735914i | ||||
\(75\) | 0.923360 | + | 1.46540i | 0.106620 | + | 0.169210i | ||||
\(76\) | 13.2742 | + | 7.66386i | 1.52266 | + | 0.879105i | ||||
\(77\) | 7.62713 | − | 8.73339i | 0.869192 | − | 0.995262i | ||||
\(78\) | −4.02645 | − | 6.39011i | −0.455906 | − | 0.723538i | ||||
\(79\) | 6.87481 | 0.773477 | 0.386739 | − | 0.922189i | \(-0.373602\pi\) | ||||
0.386739 | + | 0.922189i | \(0.373602\pi\) | |||||||
\(80\) | −1.92484 | − | 3.33393i | −0.215204 | − | 0.372744i | ||||
\(81\) | −3.24566 | + | 8.39439i | −0.360629 | + | 0.932709i | ||||
\(82\) | −7.56592 | − | 4.36819i | −0.835517 | − | 0.482386i | ||||
\(83\) | −3.09467 | − | 5.36013i | −0.339685 | − | 0.588351i | 0.644689 | − | 0.764445i | \(-0.276987\pi\) |
−0.984373 | + | 0.176094i | \(0.943654\pi\) | |||||||
\(84\) | 14.1724 | + | 11.4424i | 1.54634 | + | 1.24847i | ||||
\(85\) | 3.92956 | − | 6.80619i | 0.426220 | − | 0.738235i | ||||
\(86\) | 11.3784 | − | 6.56931i | 1.22696 | − | 0.708387i | ||||
\(87\) | −0.0596608 | − | 1.54228i | −0.00639631 | − | 0.165350i | ||||
\(88\) | −10.5777 | + | 18.3210i | −1.12758 | + | 1.95303i | ||||
\(89\) | −1.69019 | + | 2.92749i | −0.179160 | + | 0.310313i | −0.941593 | − | 0.336753i | \(-0.890671\pi\) |
0.762433 | + | 0.647067i | \(0.224004\pi\) | |||||||
\(90\) | 6.61487 | + | 3.16497i | 0.697269 | + | 0.333617i | ||||
\(91\) | 3.10474 | − | 3.55506i | 0.325466 | − | 0.372672i | ||||
\(92\) | 7.80941 | − | 4.50877i | 0.814187 | − | 0.470071i | ||||
\(93\) | −10.8482 | − | 5.71589i | −1.12490 | − | 0.592710i | ||||
\(94\) | − | 1.46629i | − | 0.151237i | ||||||
\(95\) | 3.85618i | 0.395636i | ||||||||
\(96\) | 0.374553 | + | 0.197352i | 0.0382277 | + | 0.0201421i | ||||
\(97\) | −10.3098 | + | 5.95238i | −1.04680 | + | 0.604373i | −0.921753 | − | 0.387777i | \(-0.873243\pi\) |
−0.125052 | + | 0.992150i | \(0.539910\pi\) | |||||||
\(98\) | −6.48254 | + | 15.8349i | −0.654835 | + | 1.59957i | ||||
\(99\) | −1.01567 | − | 13.1083i | −0.102078 | − | 1.31743i | ||||
\(100\) | 1.98742 | − | 3.44231i | 0.198742 | − | 0.344231i | ||||
\(101\) | −8.42730 | + | 14.5965i | −0.838547 | + | 1.45241i | 0.0525616 | + | 0.998618i | \(0.483261\pi\) |
−0.891109 | + | 0.453789i | \(0.850072\pi\) | |||||||
\(102\) | −1.28617 | − | 33.2486i | −0.127350 | − | 3.29210i | ||||
\(103\) | 11.5186 | − | 6.65028i | 1.13496 | − | 0.655272i | 0.189785 | − | 0.981826i | \(-0.439221\pi\) |
0.945179 | + | 0.326554i | \(0.105887\pi\) | |||||||
\(104\) | −4.30580 | + | 7.45786i | −0.422218 | + | 0.731304i | ||||
\(105\) | −0.710267 | + | 4.52720i | −0.0693149 | + | 0.441809i | ||||
\(106\) | −16.8079 | − | 29.1122i | −1.63253 | − | 2.82762i | ||||
\(107\) | 16.8326 | + | 9.71828i | 1.62726 | + | 0.939502i | 0.984905 | + | 0.173098i | \(0.0553779\pi\) |
0.642360 | + | 0.766403i | \(0.277955\pi\) | |||||||
\(108\) | 20.5151 | − | 2.39033i | 1.97407 | − | 0.230010i | ||||
\(109\) | 4.51255 | + | 7.81596i | 0.432224 | + | 0.748633i | 0.997064 | − | 0.0765667i | \(-0.0243958\pi\) |
−0.564841 | + | 0.825200i | \(0.691062\pi\) | |||||||
\(110\) | −10.7124 | −1.02139 | ||||||||
\(111\) | −4.78278 | − | 7.59043i | −0.453962 | − | 0.720452i | ||||
\(112\) | 1.96642 | − | 9.99369i | 0.185810 | − | 0.944315i | ||||
\(113\) | 11.4033 | + | 6.58371i | 1.07273 | + | 0.619343i | 0.928927 | − | 0.370263i | \(-0.120732\pi\) |
0.143806 | + | 0.989606i | \(0.454066\pi\) | |||||||
\(114\) | 8.70346 | + | 13.8127i | 0.815154 | + | 1.29368i | ||||
\(115\) | 1.96471 | + | 1.13433i | 0.183210 | + | 0.105776i | ||||
\(116\) | −3.06745 | + | 1.77099i | −0.284806 | + | 0.164433i | ||||
\(117\) | −0.413443 | − | 5.33592i | −0.0382229 | − | 0.493306i | ||||
\(118\) | 21.8244i | 2.00910i | ||||||||
\(119\) | 19.6759 | − | 6.72442i | 1.80369 | − | 0.616427i | ||||
\(120\) | −0.323190 | − | 8.35471i | −0.0295031 | − | 0.762678i | ||||
\(121\) | 4.10323 | + | 7.10700i | 0.373021 | + | 0.646091i | ||||
\(122\) | 10.6188 | 0.961380 | ||||||||
\(123\) | −3.30019 | − | 5.23751i | −0.297568 | − | 0.472251i | ||||
\(124\) | 28.1395i | 2.52700i | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 7.67381 | + | 17.8193i | 0.683637 | + | 1.58747i | ||||
\(127\) | 3.16484 | 0.280834 | 0.140417 | − | 0.990092i | \(-0.455156\pi\) | ||||
0.140417 | + | 0.990092i | \(0.455156\pi\) | |||||||
\(128\) | − | 19.7915i | − | 1.74934i | ||||||
\(129\) | 9.30299 | − | 0.359873i | 0.819083 | − | 0.0316850i | ||||
\(130\) | −4.36065 | −0.382454 | ||||||||
\(131\) | −2.94131 | − | 5.09450i | −0.256984 | − | 0.445109i | 0.708449 | − | 0.705762i | \(-0.249395\pi\) |
−0.965432 | + | 0.260653i | \(0.916062\pi\) | |||||||
\(132\) | −25.5271 | + | 16.0848i | −2.22184 | + | 1.40000i | ||||
\(133\) | −6.71112 | + | 7.68452i | −0.581928 | + | 0.666333i | ||||
\(134\) | 15.8569i | 1.36983i | ||||||||
\(135\) | 3.10142 | + | 4.16908i | 0.266927 | + | 0.358817i | ||||
\(136\) | −32.8549 | + | 18.9688i | −2.81728 | + | 1.62656i | ||||
\(137\) | 0.431132 | + | 0.248914i | 0.0368341 | + | 0.0212662i | 0.518304 | − | 0.855196i | \(-0.326564\pi\) |
−0.481470 | + | 0.876463i | \(0.659897\pi\) | |||||||
\(138\) | 9.59769 | − | 0.371273i | 0.817010 | − | 0.0316048i | ||||
\(139\) | −9.77690 | − | 5.64470i | −0.829266 | − | 0.478777i | 0.0243354 | − | 0.999704i | \(-0.492253\pi\) |
−0.853601 | + | 0.520927i | \(0.825586\pi\) | |||||||
\(140\) | 9.95134 | − | 3.40096i | 0.841041 | − | 0.287433i | ||||
\(141\) | 0.484334 | − | 0.919216i | 0.0407883 | − | 0.0774119i | ||||
\(142\) | 0.840824 | 0.0705604 | ||||||||
\(143\) | 3.90915 | + | 6.77084i | 0.326899 | + | 0.566206i | ||||
\(144\) | −6.52993 | − | 9.52580i | −0.544160 | − | 0.793817i | ||||
\(145\) | −0.771716 | − | 0.445550i | −0.0640875 | − | 0.0370009i | ||||
\(146\) | 4.78308 | + | 8.28454i | 0.395851 | + | 0.685633i | ||||
\(147\) | −9.29433 | + | 7.78559i | −0.766583 | + | 0.642145i | ||||
\(148\) | −10.2944 | + | 17.8304i | −0.846191 | + | 1.46565i | ||||
\(149\) | −9.75448 | + | 5.63175i | −0.799118 | + | 0.461371i | −0.843163 | − | 0.537659i | \(-0.819309\pi\) |
0.0440448 | + | 0.999030i | \(0.485976\pi\) | |||||||
\(150\) | 3.58196 | − | 2.25701i | 0.292466 | − | 0.184284i | ||||
\(151\) | 1.16713 | − | 2.02154i | 0.0949800 | − | 0.164510i | −0.814620 | − | 0.579995i | \(-0.803055\pi\) |
0.909600 | + | 0.415484i | \(0.136388\pi\) | |||||||
\(152\) | 9.30729 | − | 16.1207i | 0.754921 | − | 1.30756i | ||||
\(153\) | 10.1761 | − | 21.2683i | 0.822687 | − | 1.71944i | ||||
\(154\) | −21.3475 | − | 18.6434i | −1.72023 | − | 1.50233i | ||||
\(155\) | −6.13095 | + | 3.53970i | −0.492450 | + | 0.284316i | ||||
\(156\) | −10.3912 | + | 6.54756i | −0.831961 | + | 0.524224i | ||||
\(157\) | 24.0107i | 1.91626i | 0.286328 | + | 0.958132i | \(0.407565\pi\) | ||||
−0.286328 | + | 0.958132i | \(0.592435\pi\) | |||||||
\(158\) | − | 16.8044i | − | 1.33689i | ||||||
\(159\) | −0.920752 | − | 23.8022i | −0.0730204 | − | 1.88763i | ||||
\(160\) | 0.211683 | − | 0.122215i | 0.0167350 | − | 0.00966194i | ||||
\(161\) | 1.94111 | + | 5.67975i | 0.152981 | + | 0.447627i | ||||
\(162\) | 20.5188 | + | 7.93352i | 1.61211 | + | 0.623316i | ||||
\(163\) | 6.10651 | − | 10.5768i | 0.478299 | − | 0.828438i | −0.521392 | − | 0.853318i | \(-0.674587\pi\) |
0.999690 | + | 0.0248796i | \(0.00792025\pi\) | |||||||
\(164\) | −7.10327 | + | 12.3032i | −0.554672 | + | 0.960720i | ||||
\(165\) | −6.71557 | − | 3.53843i | −0.522807 | − | 0.275466i | ||||
\(166\) | −13.1020 | + | 7.56447i | −1.01692 | + | 0.587116i | ||||
\(167\) | −8.16312 | + | 14.1389i | −0.631681 | + | 1.09410i | 0.355527 | + | 0.934666i | \(0.384301\pi\) |
−0.987208 | + | 0.159438i | \(0.949032\pi\) | |||||||
\(168\) | 13.8961 | − | 17.2116i | 1.07211 | − | 1.32790i | ||||
\(169\) | −4.90872 | − | 8.50215i | −0.377594 | − | 0.654012i | ||||
\(170\) | −16.6367 | − | 9.60521i | −1.27598 | − | 0.736686i | ||||
\(171\) | 0.893688 | + | 11.5340i | 0.0683420 | + | 0.882026i | ||||
\(172\) | −10.6826 | − | 18.5028i | −0.814540 | − | 1.41083i | ||||
\(173\) | 4.49971 | 0.342106 | 0.171053 | − | 0.985262i | \(-0.445283\pi\) | ||||
0.171053 | + | 0.985262i | \(0.445283\pi\) | |||||||
\(174\) | −3.76987 | + | 0.145832i | −0.285793 | + | 0.0110555i | ||||
\(175\) | 1.99278 | + | 1.74035i | 0.150640 | + | 0.131558i | ||||
\(176\) | 14.6110 | + | 8.43566i | 1.10134 | + | 0.635862i | ||||
\(177\) | −7.20886 | + | 13.6817i | −0.541851 | + | 1.02838i | ||||
\(178\) | 7.15581 | + | 4.13141i | 0.536351 | + | 0.309662i | ||||
\(179\) | 7.40489 | − | 4.27521i | 0.553467 | − | 0.319545i | −0.197052 | − | 0.980393i | \(-0.563137\pi\) |
0.750519 | + | 0.660849i | \(0.229803\pi\) | |||||||
\(180\) | 5.14667 | − | 10.7567i | 0.383610 | − | 0.801755i | ||||
\(181\) | 0.872879i | 0.0648806i | 0.999474 | + | 0.0324403i | \(0.0103279\pi\) | ||||
−0.999474 | + | 0.0324403i | \(0.989672\pi\) | |||||||
\(182\) | −8.68982 | − | 7.58908i | −0.644132 | − | 0.562540i | ||||
\(183\) | 6.65689 | + | 3.50751i | 0.492091 | + | 0.259282i | ||||
\(184\) | −5.47562 | − | 9.48405i | −0.403668 | − | 0.699174i | ||||
\(185\) | −5.17976 | −0.380823 | ||||||||
\(186\) | −13.9716 | + | 26.5167i | −1.02445 | + | 1.94430i | ||||
\(187\) | 34.4427i | 2.51870i | ||||||||
\(188\) | −2.38439 | −0.173900 | ||||||||
\(189\) | −1.07523 | + | 13.7056i | −0.0782118 | + | 0.996937i | ||||
\(190\) | 9.42586 | 0.683824 | ||||||||
\(191\) | 15.5264i | 1.12345i | 0.827324 | + | 0.561726i | \(0.189862\pi\) | ||||
−0.827324 | + | 0.561726i | \(0.810138\pi\) | |||||||
\(192\) | 6.69884 | − | 12.7137i | 0.483447 | − | 0.917533i | ||||
\(193\) | −10.5140 | −0.756811 | −0.378406 | − | 0.925640i | \(-0.623528\pi\) | ||||
−0.378406 | + | 0.925640i | \(0.623528\pi\) | |||||||
\(194\) | 14.5497 | + | 25.2008i | 1.04461 | + | 1.80931i | ||||
\(195\) | −2.73368 | − | 1.44037i | −0.195763 | − | 0.103147i | ||||
\(196\) | 25.7497 | + | 10.5415i | 1.83926 | + | 0.752963i | ||||
\(197\) | 6.18325i | 0.440538i | 0.975439 | + | 0.220269i | \(0.0706936\pi\) | ||||
−0.975439 | + | 0.220269i | \(0.929306\pi\) | |||||||
\(198\) | −32.0412 | + | 2.48265i | −2.27707 | + | 0.176434i | ||||
\(199\) | 11.5085 | − | 6.64441i | 0.815813 | − | 0.471010i | −0.0331573 | − | 0.999450i | \(-0.510556\pi\) |
0.848971 | + | 0.528440i | \(0.177223\pi\) | |||||||
\(200\) | −4.18048 | − | 2.41360i | −0.295605 | − | 0.170667i | ||||
\(201\) | −5.23772 | + | 9.94064i | −0.369440 | + | 0.701159i | ||||
\(202\) | 35.6790 | + | 20.5993i | 2.51036 | + | 1.44936i | ||||
\(203\) | −0.762444 | − | 2.23094i | −0.0535131 | − | 0.156581i | ||||
\(204\) | −54.0666 | + | 2.09149i | −3.78542 | + | 0.146433i | ||||
\(205\) | −3.57411 | −0.249627 | ||||||||
\(206\) | −16.2556 | − | 28.1555i | −1.13258 | − | 1.96169i | ||||
\(207\) | 6.13940 | + | 2.93748i | 0.426718 | + | 0.204169i | ||||
\(208\) | 5.94763 | + | 3.43387i | 0.412394 | + | 0.238096i | ||||
\(209\) | −8.44990 | − | 14.6357i | −0.584492 | − | 1.01237i | ||||
\(210\) | 11.0661 | + | 1.73614i | 0.763630 | + | 0.119805i | ||||
\(211\) | 7.79496 | − | 13.5013i | 0.536627 | − | 0.929466i | −0.462455 | − | 0.886643i | \(-0.653031\pi\) |
0.999083 | − | 0.0428232i | \(-0.0136352\pi\) | |||||||
\(212\) | −47.3403 | + | 27.3319i | −3.25135 | + | 1.87717i | ||||
\(213\) | 0.527110 | + | 0.277734i | 0.0361170 | + | 0.0190300i | ||||
\(214\) | 23.7549 | − | 41.1446i | 1.62385 | − | 2.81259i | ||||
\(215\) | 2.68755 | − | 4.65498i | 0.183290 | − | 0.317467i | ||||
\(216\) | −2.90291 | − | 24.9143i | −0.197518 | − | 1.69521i | ||||
\(217\) | −18.3780 | − | 3.61617i | −1.24758 | − | 0.245481i | ||||
\(218\) | 19.1049 | − | 11.0302i | 1.29395 | − | 0.747062i | ||||
\(219\) | 0.262021 | + | 6.77346i | 0.0177058 | + | 0.457708i | ||||
\(220\) | 17.4198i | 1.17444i | ||||||||
\(221\) | 14.0204i | 0.943117i | ||||||||
\(222\) | −18.5537 | + | 11.6908i | −1.24524 | + | 0.784634i | ||||
\(223\) | −2.92075 | + | 1.68630i | −0.195588 | + | 0.112923i | −0.594596 | − | 0.804025i | \(-0.702688\pi\) |
0.399008 | + | 0.916947i | \(0.369355\pi\) | |||||||
\(224\) | 0.634534 | + | 0.124855i | 0.0423966 | + | 0.00834223i | ||||
\(225\) | 2.99103 | − | 0.231754i | 0.199402 | − | 0.0154503i | ||||
\(226\) | 16.0929 | − | 27.8737i | 1.07048 | − | 1.85413i | ||||
\(227\) | 9.68429 | − | 16.7737i | 0.642769 | − | 1.11331i | −0.342043 | − | 0.939684i | \(-0.611119\pi\) |
0.984812 | − | 0.173624i | \(-0.0555478\pi\) | |||||||
\(228\) | 22.4613 | − | 14.1530i | 1.48754 | − | 0.937306i | ||||
\(229\) | 9.06892 | − | 5.23594i | 0.599291 | − | 0.346001i | −0.169472 | − | 0.985535i | \(-0.554206\pi\) |
0.768763 | + | 0.639534i | \(0.220873\pi\) | |||||||
\(230\) | 2.77269 | − | 4.80244i | 0.182826 | − | 0.316663i | ||||
\(231\) | −7.22454 | − | 18.7388i | −0.475340 | − | 1.23292i | ||||
\(232\) | 2.15076 | + | 3.72523i | 0.141204 | + | 0.244573i | ||||
\(233\) | 10.9648 | + | 6.33051i | 0.718326 | + | 0.414726i | 0.814136 | − | 0.580674i | \(-0.197211\pi\) |
−0.0958104 | + | 0.995400i | \(0.530544\pi\) | |||||||
\(234\) | −13.0429 | + | 1.01060i | −0.852639 | + | 0.0660650i | ||||
\(235\) | −0.299936 | − | 0.519504i | −0.0195656 | − | 0.0338887i | ||||
\(236\) | 35.4895 | 2.31017 | ||||||||
\(237\) | 5.55070 | − | 10.5347i | 0.360557 | − | 0.684299i | ||||
\(238\) | −16.4368 | − | 48.0948i | −1.06544 | − | 3.11752i | ||||
\(239\) | 16.9811 | + | 9.80401i | 1.09841 | + | 0.634169i | 0.935804 | − | 0.352522i | \(-0.114676\pi\) |
0.162609 | + | 0.986691i | \(0.448009\pi\) | |||||||
\(240\) | −6.66287 | + | 0.257743i | −0.430086 | + | 0.0166373i | ||||
\(241\) | −1.52294 | − | 0.879268i | −0.0981009 | − | 0.0566386i | 0.450147 | − | 0.892955i | \(-0.351372\pi\) |
−0.548248 | + | 0.836316i | \(0.684705\pi\) | |||||||
\(242\) | 17.3720 | − | 10.0297i | 1.11671 | − | 0.644735i | ||||
\(243\) | 10.2426 | + | 11.7511i | 0.657066 | + | 0.753833i | ||||
\(244\) | − | 17.2676i | − | 1.10544i | ||||||
\(245\) | 0.942339 | + | 6.93628i | 0.0602038 | + | 0.443143i | ||||
\(246\) | −12.8023 | + | 8.06682i | −0.816246 | + | 0.514322i | ||||
\(247\) | −3.43966 | − | 5.95767i | −0.218861 | − | 0.379078i | ||||
\(248\) | 34.1737 | 2.17004 | ||||||||
\(249\) | −10.7123 | + | 0.414388i | −0.678862 | + | 0.0262608i | ||||
\(250\) | − | 2.44435i | − | 0.154594i | ||||||
\(251\) | −7.21616 | −0.455480 | −0.227740 | − | 0.973722i | \(-0.573134\pi\) | ||||
−0.227740 | + | 0.973722i | \(0.573134\pi\) | |||||||
\(252\) | 28.9766 | − | 12.4786i | 1.82535 | − | 0.786081i | ||||
\(253\) | −9.94241 | −0.625074 | ||||||||
\(254\) | − | 7.73598i | − | 0.485399i | ||||||
\(255\) | −7.25679 | − | 11.5168i | −0.454438 | − | 0.721208i | ||||
\(256\) | −31.7837 | −1.98648 | ||||||||
\(257\) | −6.76721 | − | 11.7212i | −0.422127 | − | 0.731146i | 0.574020 | − | 0.818841i | \(-0.305383\pi\) |
−0.996147 | + | 0.0876955i | \(0.972050\pi\) | |||||||
\(258\) | −0.879654 | − | 22.7398i | −0.0547649 | − | 1.41572i | ||||
\(259\) | −10.3221 | − | 9.01461i | −0.641385 | − | 0.560141i | ||||
\(260\) | 7.09101i | 0.439766i | ||||||||
\(261\) | −2.41149 | − | 1.15381i | −0.149267 | − | 0.0714189i | ||||
\(262\) | −12.4527 | + | 7.18960i | −0.769333 | + | 0.444175i | ||||
\(263\) | −3.78633 | − | 2.18604i | −0.233475 | − | 0.134797i | 0.378699 | − | 0.925520i | \(-0.376372\pi\) |
−0.612174 | + | 0.790723i | \(0.709705\pi\) | |||||||
\(264\) | 19.5340 | + | 31.0011i | 1.20223 | + | 1.90798i | ||||
\(265\) | −11.9100 | − | 6.87623i | −0.731624 | − | 0.422404i | ||||
\(266\) | 18.7837 | + | 16.4043i | 1.15170 | + | 1.00581i | ||||
\(267\) | 3.12130 | + | 4.95361i | 0.191021 | + | 0.303156i | ||||
\(268\) | 25.7855 | 1.57510 | ||||||||
\(269\) | −10.5229 | − | 18.2262i | −0.641592 | − | 1.11127i | −0.985077 | − | 0.172112i | \(-0.944941\pi\) |
0.343486 | − | 0.939158i | \(-0.388392\pi\) | |||||||
\(270\) | 10.1907 | − | 7.58094i | 0.620185 | − | 0.461361i | ||||
\(271\) | 2.86462 | + | 1.65389i | 0.174013 | + | 0.100467i | 0.584477 | − | 0.811410i | \(-0.301300\pi\) |
−0.410464 | + | 0.911877i | \(0.634633\pi\) | |||||||
\(272\) | 15.1276 | + | 26.2017i | 0.917243 | + | 1.58871i | ||||
\(273\) | −2.94086 | − | 7.62791i | −0.177989 | − | 0.461662i | ||||
\(274\) | 0.608433 | − | 1.05384i | 0.0367568 | − | 0.0636646i | ||||
\(275\) | −3.79537 | + | 2.19126i | −0.228870 | + | 0.132138i | ||||
\(276\) | −0.603740 | − | 15.6072i | −0.0363409 | − | 0.939440i | ||||
\(277\) | 12.7847 | − | 22.1438i | 0.768159 | − | 1.33049i | −0.170401 | − | 0.985375i | \(-0.554506\pi\) |
0.938560 | − | 0.345116i | \(-0.112160\pi\) | |||||||
\(278\) | −13.7976 | + | 23.8982i | −0.827525 | + | 1.43332i | ||||
\(279\) | −17.5175 | + | 12.0083i | −1.04875 | + | 0.718915i | ||||
\(280\) | −4.13026 | − | 12.0853i | −0.246830 | − | 0.722234i | ||||
\(281\) | 5.65129 | − | 3.26278i | 0.337128 | − | 0.194641i | −0.321873 | − | 0.946783i | \(-0.604313\pi\) |
0.659001 | + | 0.752142i | \(0.270979\pi\) | |||||||
\(282\) | −2.24688 | − | 1.18388i | −0.133800 | − | 0.0704991i | ||||
\(283\) | 4.69297i | 0.278968i | 0.990224 | + | 0.139484i | \(0.0445444\pi\) | ||||
−0.990224 | + | 0.139484i | \(0.955456\pi\) | |||||||
\(284\) | − | 1.36729i | − | 0.0811340i | ||||||
\(285\) | 5.90904 | + | 3.11347i | 0.350022 | + | 0.184426i | ||||
\(286\) | 16.5503 | − | 9.55532i | 0.978639 | − | 0.565018i | ||||
\(287\) | −7.12242 | − | 6.22022i | −0.420423 | − | 0.367168i | ||||
\(288\) | 0.604826 | − | 0.414608i | 0.0356397 | − | 0.0244310i | ||||
\(289\) | −22.3828 | + | 38.7682i | −1.31664 | + | 2.28048i | ||||
\(290\) | −1.08908 | + | 1.88634i | −0.0639530 | + | 0.110770i | ||||
\(291\) | 0.797045 | + | 20.6043i | 0.0467236 | + | 1.20784i | ||||
\(292\) | 13.4718 | − | 7.77794i | 0.788376 | − | 0.455169i | ||||
\(293\) | −5.27136 | + | 9.13027i | −0.307956 | + | 0.533396i | −0.977915 | − | 0.209002i | \(-0.932978\pi\) |
0.669959 | + | 0.742398i | \(0.266312\pi\) | |||||||
\(294\) | 19.0307 | + | 22.7186i | 1.10989 | + | 1.32497i | ||||
\(295\) | 4.46426 | + | 7.73233i | 0.259919 | + | 0.450194i | ||||
\(296\) | 21.6539 | + | 12.5019i | 1.25861 | + | 0.726657i | ||||
\(297\) | −20.9066 | − | 9.02720i | −1.21312 | − | 0.523811i | ||||
\(298\) | 13.7660 | + | 23.8433i | 0.797441 | + | 1.38121i | ||||
\(299\) | −4.04721 | −0.234056 | ||||||||
\(300\) | −3.67021 | − | 5.82475i | −0.211900 | − | 0.336292i | ||||
\(301\) | 13.4570 | − | 4.59905i | 0.775649 | − | 0.265085i | ||||
\(302\) | −4.94134 | − | 2.85288i | −0.284342 | − | 0.164165i | ||||
\(303\) | 15.5629 | + | 24.6988i | 0.894063 | + | 1.41891i | ||||
\(304\) | −12.8562 | − | 7.42255i | −0.737356 | − | 0.425712i | ||||
\(305\) | 3.76221 | − | 2.17211i | 0.215423 | − | 0.124375i | ||||
\(306\) | −51.9870 | − | 24.8739i | −2.97190 | − | 1.42195i | ||||
\(307\) | − | 12.9619i | − | 0.739776i | −0.929076 | − | 0.369888i | \(-0.879396\pi\) | ||
0.929076 | − | 0.369888i | \(-0.120604\pi\) | |||||||
\(308\) | −30.3166 | + | 34.7138i | −1.72745 | + | 1.97801i | ||||
\(309\) | −0.890496 | − | 23.0200i | −0.0506585 | − | 1.30956i | ||||
\(310\) | 8.65227 | + | 14.9862i | 0.491416 | + | 0.851158i | ||||
\(311\) | −11.3292 | −0.642418 | −0.321209 | − | 0.947008i | \(-0.604089\pi\) | ||||
−0.321209 | + | 0.947008i | \(0.604089\pi\) | |||||||
\(312\) | 7.95161 | + | 12.6195i | 0.450171 | + | 0.714437i | ||||
\(313\) | − | 5.07321i | − | 0.286755i | −0.989668 | − | 0.143377i | \(-0.954204\pi\) | ||
0.989668 | − | 0.143377i | \(-0.0457963\pi\) | |||||||
\(314\) | 58.6906 | 3.31210 | ||||||||
\(315\) | 6.36381 | + | 4.74362i | 0.358560 | + | 0.267273i | ||||
\(316\) | −27.3263 | −1.53722 | ||||||||
\(317\) | 9.97253i | 0.560113i | 0.959984 | + | 0.280056i | \(0.0903532\pi\) | ||||
−0.959984 | + | 0.280056i | \(0.909647\pi\) | |||||||
\(318\) | −58.1808 | + | 2.25064i | −3.26262 | + | 0.126210i | ||||
\(319\) | 3.90527 | 0.218653 | ||||||||
\(320\) | −4.14842 | − | 7.18528i | −0.231904 | − | 0.401669i | ||||
\(321\) | 28.4824 | − | 17.9469i | 1.58973 | − | 1.00170i | ||||
\(322\) | 13.8833 | − | 4.74474i | 0.773686 | − | 0.264414i | ||||
\(323\) | − | 30.3062i | − | 1.68628i | ||||||
\(324\) | 12.9010 | − | 33.3664i | 0.716721 | − | 1.85369i | ||||
\(325\) | −1.54497 | + | 0.891986i | −0.0856993 | + | 0.0494785i | ||||
\(326\) | −25.8534 | − | 14.9264i | −1.43189 | − | 0.826699i | ||||
\(327\) | 15.6202 | − | 0.604246i | 0.863801 | − | 0.0334149i | ||||
\(328\) | 14.9415 | + | 8.62648i | 0.825007 | + | 0.476318i | ||||
\(329\) | 0.306415 | − | 1.55725i | 0.0168932 | − | 0.0858540i | ||||
\(330\) | −8.64915 | + | 16.4152i | −0.476120 | + | 0.903627i | ||||
\(331\) | −25.0196 | −1.37520 | −0.687600 | − | 0.726089i | \(-0.741336\pi\) | ||||
−0.687600 | + | 0.726089i | \(0.741336\pi\) | |||||||
\(332\) | 12.3008 | + | 21.3057i | 0.675097 | + | 1.16930i | ||||
\(333\) | −15.4928 | + | 1.20043i | −0.849002 | + | 0.0657832i | ||||
\(334\) | 34.5605 | + | 19.9535i | 1.89107 | + | 1.09181i | ||||
\(335\) | 3.24358 | + | 5.61805i | 0.177216 | + | 0.306947i | ||||
\(336\) | −13.7262 | − | 11.0821i | −0.748825 | − | 0.604579i | ||||
\(337\) | −8.94751 | + | 15.4975i | −0.487402 | + | 0.844205i | −0.999895 | − | 0.0144863i | \(-0.995389\pi\) |
0.512493 | + | 0.858691i | \(0.328722\pi\) | |||||||
\(338\) | −20.7822 | + | 11.9986i | −1.13040 | + | 0.652639i | ||||
\(339\) | 19.2956 | − | 12.1583i | 1.04799 | − | 0.660346i | ||||
\(340\) | −15.6194 | + | 27.0535i | −0.847079 | + | 1.46718i | ||||
\(341\) | 15.5128 | − | 26.8690i | 0.840066 | − | 1.45504i | ||||
\(342\) | 28.1931 | − | 2.18448i | 1.52451 | − | 0.118123i | ||||
\(343\) | −10.1937 | + | 15.4625i | −0.550409 | + | 0.834895i | ||||
\(344\) | −22.4705 | + | 12.9734i | −1.21153 | + | 0.699477i | ||||
\(345\) | 3.32449 | − | 2.09478i | 0.178984 | − | 0.112779i | ||||
\(346\) | − | 10.9989i | − | 0.591302i | ||||||
\(347\) | 26.5501i | 1.42528i | 0.701528 | + | 0.712642i | \(0.252502\pi\) | ||||
−0.701528 | + | 0.712642i | \(0.747498\pi\) | |||||||
\(348\) | 0.237142 | + | 6.13031i | 0.0127122 | + | 0.328619i | ||||
\(349\) | −9.98709 | + | 5.76605i | −0.534597 | + | 0.308649i | −0.742886 | − | 0.669418i | \(-0.766544\pi\) |
0.208290 | + | 0.978067i | \(0.433210\pi\) | |||||||
\(350\) | 4.25403 | − | 4.87105i | 0.227388 | − | 0.260368i | ||||
\(351\) | −8.51034 | − | 3.67466i | −0.454248 | − | 0.196139i | ||||
\(352\) | −0.535609 | + | 0.927703i | −0.0285481 | + | 0.0494467i | ||||
\(353\) | −13.3299 | + | 23.0881i | −0.709480 | + | 1.22886i | 0.255570 | + | 0.966791i | \(0.417737\pi\) |
−0.965050 | + | 0.262065i | \(0.915596\pi\) | |||||||
\(354\) | 33.4428 | + | 17.6210i | 1.77746 | + | 0.936544i | ||||
\(355\) | 0.297901 | − | 0.171993i | 0.0158110 | − | 0.00912847i | ||||
\(356\) | 6.71823 | − | 11.6363i | 0.356065 | − | 0.616723i | ||||
\(357\) | 5.58207 | − | 35.5798i | 0.295434 | − | 1.88308i | ||||
\(358\) | −10.4501 | − | 18.1001i | −0.552306 | − | 0.956622i | ||||
\(359\) | −17.8292 | − | 10.2937i | −0.940992 | − | 0.543282i | −0.0507207 | − | 0.998713i | \(-0.516152\pi\) |
−0.890271 | + | 0.455431i | \(0.849485\pi\) | |||||||
\(360\) | −13.0633 | − | 6.25032i | −0.688498 | − | 0.329421i | ||||
\(361\) | −2.06492 | − | 3.57655i | −0.108680 | − | 0.188239i | ||||
\(362\) | 2.13362 | 0.112141 | ||||||||
\(363\) | 14.2034 | − | 0.549437i | 0.745484 | − | 0.0288380i | ||||
\(364\) | −12.3409 | + | 14.1308i | −0.646837 | + | 0.740656i | ||||
\(365\) | 3.38926 | + | 1.95679i | 0.177402 | + | 0.102423i | ||||
\(366\) | 8.57357 | − | 16.2718i | 0.448148 | − | 0.850538i | ||||
\(367\) | 15.6251 | + | 9.02113i | 0.815621 | + | 0.470899i | 0.848904 | − | 0.528547i | \(-0.177263\pi\) |
−0.0332829 | + | 0.999446i | \(0.510596\pi\) | |||||||
\(368\) | −7.56352 | + | 4.36680i | −0.394276 | + | 0.227635i | ||||
\(369\) | −10.6903 | + | 0.828316i | −0.556514 | + | 0.0431204i | ||||
\(370\) | 12.6611i | 0.658221i | ||||||||
\(371\) | −11.7669 | − | 34.4304i | −0.610907 | − | 1.78754i | ||||
\(372\) | 43.1197 | + | 22.7198i | 2.23565 | + | 1.17796i | ||||
\(373\) | 4.77327 | + | 8.26755i | 0.247151 | + | 0.428078i | 0.962734 | − | 0.270450i | \(-0.0871724\pi\) |
−0.715583 | + | 0.698527i | \(0.753839\pi\) | |||||||
\(374\) | 84.1900 | 4.35336 | ||||||||
\(375\) | 0.807396 | − | 1.53235i | 0.0416938 | − | 0.0791305i | ||||
\(376\) | 2.89570i | 0.149334i | ||||||||
\(377\) | 1.58970 | 0.0818737 | ||||||||
\(378\) | 33.5013 | + | 2.62825i | 1.72312 | + | 0.135183i | ||||
\(379\) | 0.905456 | 0.0465101 | 0.0232551 | − | 0.999730i | \(-0.492597\pi\) | ||||
0.0232551 | + | 0.999730i | \(0.492597\pi\) | |||||||
\(380\) | − | 15.3277i | − | 0.786296i | ||||||
\(381\) | 2.55528 | − | 4.84966i | 0.130911 | − | 0.248456i | ||||
\(382\) | 37.9520 | 1.94179 | ||||||||
\(383\) | −3.06888 | − | 5.31546i | −0.156812 | − | 0.271607i | 0.776905 | − | 0.629618i | \(-0.216788\pi\) |
−0.933718 | + | 0.358011i | \(0.883455\pi\) | |||||||
\(384\) | −30.3276 | − | 15.9796i | −1.54765 | − | 0.815456i | ||||
\(385\) | −11.3769 | − | 2.23859i | −0.579821 | − | 0.114089i | ||||
\(386\) | 25.6998i | 1.30808i | ||||||||
\(387\) | 6.95975 | − | 14.5460i | 0.353784 | − | 0.739417i | ||||
\(388\) | 40.9800 | − | 23.6598i | 2.08044 | − | 1.20114i | ||||
\(389\) | −7.24609 | − | 4.18353i | −0.367391 | − | 0.212114i | 0.304927 | − | 0.952376i | \(-0.401368\pi\) |
−0.672318 | + | 0.740262i | \(0.734701\pi\) | |||||||
\(390\) | −3.52077 | + | 6.68207i | −0.178281 | + | 0.338360i | ||||
\(391\) | −15.4409 | − | 8.91480i | −0.780879 | − | 0.450841i | ||||
\(392\) | 12.8020 | − | 31.2714i | 0.646598 | − | 1.57945i | ||||
\(393\) | −10.1814 | + | 0.393852i | −0.513583 | + | 0.0198672i | ||||
\(394\) | 15.1140 | 0.761433 | ||||||||
\(395\) | −3.43741 | − | 5.95376i | −0.172955 | − | 0.299566i | ||||
\(396\) | 4.03712 | + | 52.1033i | 0.202873 | + | 2.61829i | ||||
\(397\) | −17.1060 | − | 9.87616i | −0.858526 | − | 0.495670i | 0.00499248 | − | 0.999988i | \(-0.498411\pi\) |
−0.863518 | + | 0.504317i | \(0.831744\pi\) | |||||||
\(398\) | −16.2413 | − | 28.1307i | −0.814101 | − | 1.41006i | ||||
\(399\) | 6.35688 | + | 16.4883i | 0.318242 | + | 0.825447i | ||||
\(400\) | −1.92484 | + | 3.33393i | −0.0962422 | + | 0.166696i | ||||
\(401\) | −13.3743 | + | 7.72163i | −0.667879 | + | 0.385600i | −0.795272 | − | 0.606252i | \(-0.792672\pi\) |
0.127394 | + | 0.991852i | \(0.459339\pi\) | |||||||
\(402\) | 24.2984 | + | 12.8028i | 1.21189 | + | 0.638546i | ||||
\(403\) | 6.31474 | − | 10.9374i | 0.314559 | − | 0.544833i | ||||
\(404\) | 33.4972 | − | 58.0188i | 1.66655 | − | 2.88654i | ||||
\(405\) | 8.89258 | − | 1.38637i | 0.441876 | − | 0.0688893i | ||||
\(406\) | −5.45320 | + | 1.86368i | −0.270638 | + | 0.0924929i | ||||
\(407\) | 19.6591 | − | 11.3502i | 0.974466 | − | 0.562608i | ||||
\(408\) | 2.53999 | + | 65.6606i | 0.125748 | + | 3.25069i | ||||
\(409\) | 4.73802i | 0.234280i | 0.993115 | + | 0.117140i | \(0.0373726\pi\) | ||||
−0.993115 | + | 0.117140i | \(0.962627\pi\) | |||||||
\(410\) | 8.73638i | 0.431459i | ||||||||
\(411\) | 0.729519 | − | 0.459675i | 0.0359845 | − | 0.0226741i | ||||
\(412\) | −45.7847 | + | 26.4338i | −2.25565 | + | 1.30230i | ||||
\(413\) | −4.56070 | + | 23.1782i | −0.224417 | + | 1.14053i | ||||
\(414\) | 7.18022 | − | 15.0068i | 0.352889 | − | 0.737546i | ||||
\(415\) | −3.09467 | + | 5.36013i | −0.151912 | + | 0.263119i | ||||
\(416\) | −0.218028 | + | 0.377636i | −0.0106897 | + | 0.0185151i | ||||
\(417\) | −16.5435 | + | 10.4242i | −0.810139 | + | 0.510474i | ||||
\(418\) | −35.7746 | + | 20.6545i | −1.74980 | + | 1.01024i | ||||
\(419\) | −0.120202 | + | 0.208195i | −0.00587224 | + | 0.0101710i | −0.868947 | − | 0.494906i | \(-0.835203\pi\) |
0.863074 | + | 0.505077i | \(0.168536\pi\) | |||||||
\(420\) | 2.82320 | − | 17.9949i | 0.137758 | − | 0.878061i | ||||
\(421\) | 6.23154 | + | 10.7933i | 0.303707 | + | 0.526035i | 0.976973 | − | 0.213365i | \(-0.0684424\pi\) |
−0.673266 | + | 0.739400i | \(0.735109\pi\) | |||||||
\(422\) | −33.0018 | − | 19.0536i | −1.60650 | − | 0.927515i | ||||
\(423\) | −1.01752 | − | 1.48434i | −0.0494733 | − | 0.0721712i | ||||
\(424\) | 33.1930 | + | 57.4919i | 1.61199 | + | 2.79205i | ||||
\(425\) | −7.85911 | −0.381223 | ||||||||
\(426\) | 0.678878 | − | 1.28844i | 0.0328918 | − | 0.0624252i | ||||
\(427\) | 11.2775 | + | 2.21903i | 0.545756 | + | 0.107386i | ||||
\(428\) | −66.9067 | − | 38.6286i | −3.23406 | − | 1.86719i | ||||
\(429\) | 13.5316 | − | 0.523448i | 0.653310 | − | 0.0252723i | ||||
\(430\) | −11.3784 | − | 6.56931i | −0.548715 | − | 0.316800i | ||||
\(431\) | 1.71946 | − | 0.992731i | 0.0828235 | − | 0.0478182i | −0.458016 | − | 0.888944i | \(-0.651440\pi\) |
0.540840 | + | 0.841126i | \(0.318107\pi\) | |||||||
\(432\) | −19.8691 | + | 2.31507i | −0.955955 | + | 0.111384i | ||||
\(433\) | 31.7870i | 1.52758i | 0.645463 | + | 0.763792i | \(0.276665\pi\) | ||||
−0.645463 | + | 0.763792i | \(0.723335\pi\) | |||||||
\(434\) | −8.83918 | + | 44.9222i | −0.424294 | + | 2.15633i | ||||
\(435\) | −1.30582 | + | 0.822807i | −0.0626094 | + | 0.0394506i | ||||
\(436\) | −17.9367 | − | 31.0672i | −0.859010 | − | 1.48785i | ||||
\(437\) | 8.74834 | 0.418490 | ||||||||
\(438\) | 16.5567 | − | 0.640471i | 0.791110 | − | 0.0306029i | ||||
\(439\) | 7.36913i | 0.351709i | 0.984416 | + | 0.175855i | \(0.0562689\pi\) | ||||
−0.984416 | + | 0.175855i | \(0.943731\pi\) | |||||||
\(440\) | 21.1553 | 1.00854 | ||||||||
\(441\) | 4.42608 | + | 20.5283i | 0.210766 | + | 0.977537i | ||||
\(442\) | 34.2709 | 1.63010 | ||||||||
\(443\) | − | 41.1425i | − | 1.95474i | −0.211537 | − | 0.977370i | \(-0.567847\pi\) | ||
0.211537 | − | 0.977370i | \(-0.432153\pi\) | |||||||
\(444\) | 19.0108 | + | 30.1708i | 0.902213 | + | 1.43184i | ||||
\(445\) | 3.38038 | 0.160245 | ||||||||
\(446\) | 4.12190 | + | 7.13934i | 0.195177 | + | 0.338057i | ||||
\(447\) | 0.754111 | + | 19.4944i | 0.0356682 | + | 0.922052i | ||||
\(448\) | 4.23804 | − | 21.5384i | 0.200228 | − | 1.01759i | ||||
\(449\) | 26.0169i | 1.22781i | 0.789379 | + | 0.613906i | \(0.210403\pi\) | ||||
−0.789379 | + | 0.613906i | \(0.789597\pi\) | |||||||
\(450\) | −0.566489 | − | 7.31113i | −0.0267045 | − | 0.344650i | ||||
\(451\) | 13.5651 | − | 7.83180i | 0.638755 | − | 0.368785i | ||||
\(452\) | −45.3264 | − | 26.1692i | −2.13197 | − | 1.23090i | ||||
\(453\) | −2.15537 | − | 3.42064i | −0.101268 | − | 0.160716i | ||||
\(454\) | −41.0007 | − | 23.6718i | −1.92426 | − | 1.11097i | ||||
\(455\) | −4.63115 | − | 0.911255i | −0.217112 | − | 0.0427203i | ||||
\(456\) | −17.1880 | − | 27.2779i | −0.804900 | − | 1.27740i | ||||
\(457\) | −30.7128 | −1.43668 | −0.718342 | − | 0.695690i | \(-0.755099\pi\) | ||||
−0.718342 | + | 0.695690i | \(0.755099\pi\) | |||||||
\(458\) | −12.7985 | − | 22.1676i | −0.598033 | − | 1.03582i | ||||
\(459\) | −24.3744 | − | 32.7653i | −1.13770 | − | 1.52935i | ||||
\(460\) | −7.80941 | − | 4.50877i | −0.364116 | − | 0.210222i | ||||
\(461\) | −15.7774 | − | 27.3273i | −0.734828 | − | 1.27276i | −0.954799 | − | 0.297253i | \(-0.903930\pi\) |
0.219971 | − | 0.975506i | \(-0.429404\pi\) | |||||||
\(462\) | −45.8041 | + | 17.6593i | −2.13100 | + | 0.821584i | ||||
\(463\) | −12.2485 | + | 21.2150i | −0.569234 | + | 0.985943i | 0.427408 | + | 0.904059i | \(0.359427\pi\) |
−0.996642 | + | 0.0818837i | \(0.973906\pi\) | |||||||
\(464\) | 2.97086 | − | 1.71523i | 0.137919 | − | 0.0796275i | ||||
\(465\) | 0.473979 | + | 12.2527i | 0.0219802 | + | 0.568207i | ||||
\(466\) | 15.4740 | − | 26.8017i | 0.716818 | − | 1.24157i | ||||
\(467\) | 1.33602 | − | 2.31405i | 0.0618236 | − | 0.107082i | −0.833457 | − | 0.552584i | \(-0.813642\pi\) |
0.895281 | + | 0.445503i | \(0.146975\pi\) | |||||||
\(468\) | 1.64337 | + | 21.2095i | 0.0759649 | + | 0.980408i | ||||
\(469\) | −3.31365 | + | 16.8405i | −0.153010 | + | 0.777623i | ||||
\(470\) | −1.26985 | + | 0.733147i | −0.0585737 | + | 0.0338176i | ||||
\(471\) | 36.7929 | + | 19.3862i | 1.69533 | + | 0.893267i | ||||
\(472\) | − | 43.0998i | − | 1.98383i | ||||||
\(473\) | 23.5565i | 1.08313i | ||||||||
\(474\) | −25.7504 | − | 13.5678i | −1.18275 | − | 0.623192i | ||||
\(475\) | 3.33955 | − | 1.92809i | 0.153229 | − | 0.0884669i | ||||
\(476\) | −78.2087 | + | 26.7285i | −3.58469 | + | 1.22510i | ||||
\(477\) | −37.2168 | − | 17.8069i | −1.70404 | − | 0.815320i | ||||
\(478\) | 23.9644 | − | 41.5076i | 1.09611 | − | 1.89851i | ||||
\(479\) | −1.78583 | + | 3.09315i | −0.0815968 | + | 0.141330i | −0.903936 | − | 0.427668i | \(-0.859335\pi\) |
0.822339 | + | 0.568998i | \(0.192669\pi\) | |||||||
\(480\) | −0.0163650 | − | 0.423049i | −0.000746957 | − | 0.0193094i | ||||
\(481\) | 8.00255 | − | 4.62027i | 0.364885 | − | 0.210666i | ||||
\(482\) | −2.14924 | + | 3.72259i | −0.0978951 | + | 0.169559i | ||||
\(483\) | 10.2706 | + | 1.61135i | 0.467330 | + | 0.0733189i | ||||
\(484\) | −16.3097 | − | 28.2492i | −0.741350 | − | 1.28406i | ||||
\(485\) | 10.3098 | + | 5.95238i | 0.468145 | + | 0.270284i | ||||
\(486\) | 28.7238 | − | 25.0366i | 1.30294 | − | 1.13568i | ||||
\(487\) | −8.17684 | − | 14.1627i | −0.370528 | − | 0.641773i | 0.619119 | − | 0.785297i | \(-0.287490\pi\) |
−0.989647 | + | 0.143524i | \(0.954157\pi\) | |||||||
\(488\) | −20.9704 | −0.949287 | ||||||||
\(489\) | −11.2770 | − | 17.8970i | −0.509964 | − | 0.809330i | ||||
\(490\) | 16.9547 | − | 2.30340i | 0.765935 | − | 0.104057i | ||||
\(491\) | −36.3236 | − | 20.9714i | −1.63926 | − | 0.946427i | −0.981089 | − | 0.193559i | \(-0.937997\pi\) |
−0.658172 | − | 0.752868i | \(-0.728670\pi\) | |||||||
\(492\) | 13.1177 | + | 20.8183i | 0.591394 | + | 0.938561i | ||||
\(493\) | 6.06500 | + | 3.50163i | 0.273154 | + | 0.157706i | ||||
\(494\) | −14.5626 | + | 8.40774i | −0.655204 | + | 0.378282i | ||||
\(495\) | −10.8443 | + | 7.43373i | −0.487413 | + | 0.334121i | ||||
\(496\) | − | 27.2535i | − | 1.22372i | ||||||
\(497\) | 0.892981 | + | 0.175709i | 0.0400557 | + | 0.00788162i | ||||
\(498\) | 1.01291 | + | 26.1845i | 0.0453895 | + | 1.17336i | ||||
\(499\) | 15.5412 | + | 26.9181i | 0.695718 | + | 1.20502i | 0.969938 | + | 0.243352i | \(0.0782470\pi\) |
−0.274220 | + | 0.961667i | \(0.588420\pi\) | |||||||
\(500\) | −3.97484 | −0.177760 | ||||||||
\(501\) | 15.0750 | + | 23.9245i | 0.673501 | + | 1.06887i | ||||
\(502\) | 17.6388i | 0.787259i | ||||||||
\(503\) | −16.2335 | −0.723815 | −0.361908 | − | 0.932214i | \(-0.617874\pi\) | ||||
−0.361908 | + | 0.932214i | \(0.617874\pi\) | |||||||
\(504\) | −15.1546 | − | 35.1903i | −0.675038 | − | 1.56750i | ||||
\(505\) | 16.8546 | 0.750020 | ||||||||
\(506\) | 24.3027i | 1.08039i | ||||||||
\(507\) | −16.9916 | + | 0.657295i | −0.754623 | + | 0.0291915i | ||||
\(508\) | −12.5798 | −0.558136 | ||||||||
\(509\) | −6.36136 | − | 11.0182i | −0.281962 | − | 0.488373i | 0.689906 | − | 0.723899i | \(-0.257652\pi\) |
−0.971868 | + | 0.235526i | \(0.924319\pi\) | |||||||
\(510\) | −28.1510 | + | 17.7381i | −1.24655 | + | 0.785458i | ||||
\(511\) | 3.34854 | + | 9.79797i | 0.148131 | + | 0.433437i | ||||
\(512\) | 38.1074i | 1.68413i | ||||||||
\(513\) | 18.3957 | + | 7.94305i | 0.812191 | + | 0.350694i | ||||
\(514\) | −28.6506 | + | 16.5414i | −1.26372 | + | 0.729611i | ||||
\(515\) | −11.5186 | − | 6.65028i | −0.507571 | − | 0.293046i | ||||
\(516\) | −36.9779 | + | 1.43044i | −1.62786 | + | 0.0629715i | ||||
\(517\) | 2.27673 | + | 1.31447i | 0.100131 | + | 0.0578105i | ||||
\(518\) | −22.0349 | + | 25.2309i | −0.968156 | + | 1.10858i | ||||
\(519\) | 3.63305 | − | 6.89515i | 0.159473 | − | 0.302663i | ||||
\(520\) | 8.61160 | 0.377644 | ||||||||
\(521\) | 3.53054 | + | 6.11507i | 0.154676 | + | 0.267906i | 0.932941 | − | 0.360030i | \(-0.117233\pi\) |
−0.778265 | + | 0.627936i | \(0.783900\pi\) | |||||||
\(522\) | −2.82031 | + | 5.89452i | −0.123442 | + | 0.257996i | ||||
\(523\) | 22.9186 | + | 13.2321i | 1.00216 | + | 0.578598i | 0.908887 | − | 0.417043i | \(-0.136934\pi\) |
0.0932737 | + | 0.995641i | \(0.470267\pi\) | |||||||
\(524\) | 11.6913 | + | 20.2498i | 0.510735 | + | 0.884619i | ||||
\(525\) | 4.27580 | − | 1.64849i | 0.186611 | − | 0.0719460i | ||||
\(526\) | −5.34345 | + | 9.25512i | −0.232985 | + | 0.403542i | ||||
\(527\) | 48.1838 | − | 27.8189i | 2.09892 | − | 1.21181i | ||||
\(528\) | 24.7233 | − | 15.5783i | 1.07594 | − | 0.677959i | ||||
\(529\) | −8.92661 | + | 15.4613i | −0.388113 | + | 0.672232i | ||||
\(530\) | −16.8079 | + | 29.1122i | −0.730089 | + | 1.26455i | ||||
\(531\) | 15.1448 | + | 22.0931i | 0.657227 | + | 0.958757i | ||||
\(532\) | 26.6757 | − | 30.5448i | 1.15654 | − | 1.32428i | ||||
\(533\) | 5.52188 | − | 3.18806i | 0.239179 | − | 0.138090i | ||||
\(534\) | 12.1084 | − | 7.62956i | 0.523980 | − | 0.330163i | ||||
\(535\) | − | 19.4366i | − | 0.840316i | ||||||
\(536\) | − | 31.3149i | − | 1.35260i | ||||||
\(537\) | −0.572466 | − | 14.7987i | −0.0247037 | − | 0.638611i | ||||
\(538\) | −44.5511 | + | 25.7216i | −1.92074 | + | 1.10894i | ||||
\(539\) | −18.7757 | − | 24.2609i | −0.808727 | − | 1.04499i | ||||
\(540\) | −12.3276 | − | 16.5714i | −0.530497 | − | 0.713121i | ||||
\(541\) | 16.1875 | − | 28.0376i | 0.695955 | − | 1.20543i | −0.273903 | − | 0.961757i | \(-0.588315\pi\) |
0.969858 | − | 0.243672i | \(-0.0783520\pi\) | |||||||
\(542\) | 4.04269 | − | 7.00214i | 0.173648 | − | 0.300768i | ||||
\(543\) | 1.33756 | + | 0.704759i | 0.0574002 | + | 0.0302441i | ||||
\(544\) | −1.66364 | + | 0.960501i | −0.0713279 | + | 0.0411812i | ||||
\(545\) | 4.51255 | − | 7.81596i | 0.193296 | − | 0.334799i | ||||
\(546\) | −18.6453 | + | 7.18849i | −0.797944 | + | 0.307639i | ||||
\(547\) | −2.71649 | − | 4.70510i | −0.116149 | − | 0.201176i | 0.802090 | − | 0.597204i | \(-0.203722\pi\) |
−0.918238 | + | 0.396028i | \(0.870388\pi\) | |||||||
\(548\) | −1.71368 | − | 0.989394i | −0.0732048 | − | 0.0422648i | ||||
\(549\) | 10.7495 | − | 7.36877i | 0.458777 | − | 0.314491i | ||||
\(550\) | 5.35620 | + | 9.27721i | 0.228389 | + | 0.395582i | ||||
\(551\) | −3.43625 | −0.146389 | ||||||||
\(552\) | −18.9539 | + | 0.733205i | −0.806733 | + | 0.0312073i | ||||
\(553\) | 3.51166 | − | 17.8468i | 0.149331 | − | 0.758925i | ||||
\(554\) | −54.1271 | − | 31.2503i | −2.29964 | − | 1.32770i | ||||
\(555\) | −4.18212 | + | 7.93723i | −0.177521 | + | 0.336917i | ||||
\(556\) | 38.8616 | + | 22.4368i | 1.64810 | + | 0.951531i | ||||
\(557\) | 22.1583 | − | 12.7931i | 0.938878 | − | 0.542061i | 0.0492696 | − | 0.998786i | \(-0.484311\pi\) |
0.889608 | + | 0.456724i | \(0.150977\pi\) | |||||||
\(558\) | 29.3524 | + | 42.8190i | 1.24258 | + | 1.81267i | ||||
\(559\) | 9.58904i | 0.405573i | ||||||||
\(560\) | −9.63800 | + | 3.29387i | −0.407280 | + | 0.139191i | ||||
\(561\) | 52.7784 | + | 27.8089i | 2.22831 | + | 1.17409i | ||||
\(562\) | −7.97537 | − | 13.8137i | −0.336420 | − | 0.582697i | ||||
\(563\) | −14.7083 | −0.619880 | −0.309940 | − | 0.950756i | \(-0.600309\pi\) | ||||
−0.309940 | + | 0.950756i | \(0.600309\pi\) | |||||||
\(564\) | −1.92515 | + | 3.65374i | −0.0810635 | + | 0.153850i | ||||
\(565\) | − | 13.1674i | − | 0.553957i | ||||||
\(566\) | 11.4713 | 0.482173 | ||||||||
\(567\) | 20.1337 | + | 12.7135i | 0.845537 | + | 0.533917i | ||||
\(568\) | −1.66050 | −0.0696728 | ||||||||
\(569\) | − | 0.139959i | − | 0.00586740i | −0.999996 | − | 0.00293370i | \(-0.999066\pi\) | ||
0.999996 | − | 0.00293370i | \(-0.000933826\pi\) | |||||||
\(570\) | 7.61040 | − | 14.4438i | 0.318765 | − | 0.604983i | ||||
\(571\) | 33.1340 | 1.38661 | 0.693307 | − | 0.720642i | \(-0.256153\pi\) | ||||
0.693307 | + | 0.720642i | \(0.256153\pi\) | |||||||
\(572\) | −15.5382 | − | 26.9130i | −0.649686 | − | 1.12529i | ||||
\(573\) | 23.7920 | + | 12.5360i | 0.993924 | + | 0.523697i | ||||
\(574\) | −15.2044 | + | 17.4097i | −0.634619 | + | 0.726666i | ||||
\(575\) | − | 2.26865i | − | 0.0946093i | ||||||
\(576\) | −14.0733 | − | 20.5300i | −0.586387 | − | 0.855417i | ||||
\(577\) | 26.9549 | − | 15.5624i | 1.12215 | − | 0.647871i | 0.180198 | − | 0.983630i | \(-0.442326\pi\) |
0.941948 | + | 0.335759i | \(0.108993\pi\) | |||||||
\(578\) | 94.7630 | + | 54.7115i | 3.94162 | + | 2.27570i | ||||
\(579\) | −8.48893 | + | 16.1111i | −0.352788 | + | 0.669555i | ||||
\(580\) | 3.06745 | + | 1.77099i | 0.127369 | + | 0.0735365i | ||||
\(581\) | −15.4955 | + | 5.29574i | −0.642863 | + | 0.219704i | ||||
\(582\) | 50.3640 | − | 1.94826i | 2.08765 | − | 0.0807578i | ||||
\(583\) | 60.2704 | 2.49615 | ||||||||
\(584\) | −9.44583 | − | 16.3607i | −0.390871 | − | 0.677009i | ||||
\(585\) | −4.41432 | + | 3.02601i | −0.182510 | + | 0.125110i | ||||
\(586\) | 22.3176 | + | 12.8851i | 0.921930 | + | 0.532277i | ||||
\(587\) | 9.74979 | + | 16.8871i | 0.402417 | + | 0.697007i | 0.994017 | − | 0.109225i | \(-0.0348369\pi\) |
−0.591600 | + | 0.806232i | \(0.701504\pi\) | |||||||
\(588\) | 36.9435 | − | 30.9465i | 1.52352 | − | 1.27621i | ||||
\(589\) | −13.6498 | + | 23.6421i | −0.562428 | + | 0.974154i | ||||
\(590\) | 18.9005 | − | 10.9122i | 0.778122 | − | 0.449249i | ||||
\(591\) | 9.47493 | + | 4.99233i | 0.389747 | + | 0.205357i | ||||
\(592\) | 9.97022 | − | 17.2689i | 0.409774 | − | 0.709749i | ||||
\(593\) | −16.3836 | + | 28.3772i | −0.672794 | + | 1.16531i | 0.304314 | + | 0.952572i | \(0.401573\pi\) |
−0.977108 | + | 0.212742i | \(0.931761\pi\) | |||||||
\(594\) | −22.0656 | + | 51.1029i | −0.905364 | + | 2.09678i | ||||
\(595\) | −15.6615 | − | 13.6776i | −0.642058 | − | 0.560728i | ||||
\(596\) | 38.7725 | − | 22.3853i | 1.58818 | − | 0.916938i | ||||
\(597\) | −0.889710 | − | 22.9997i | −0.0364134 | − | 0.941316i | ||||
\(598\) | 9.89280i | 0.404547i | ||||||||
\(599\) | − | 1.28048i | − | 0.0523189i | −0.999658 | − | 0.0261594i | \(-0.991672\pi\) | ||
0.999658 | − | 0.0261594i | \(-0.00832776\pi\) | |||||||
\(600\) | −7.07380 | + | 4.45725i | −0.288787 | + | 0.181966i | ||||
\(601\) | −16.8456 | + | 9.72583i | −0.687148 | + | 0.396725i | −0.802543 | − | 0.596595i | \(-0.796520\pi\) |
0.115395 | + | 0.993320i | \(0.463187\pi\) | |||||||
\(602\) | −11.2417 | − | 32.8936i | −0.458177 | − | 1.34064i | ||||
\(603\) | 11.0037 | + | 16.0521i | 0.448105 | + | 0.653691i | ||||
\(604\) | −4.63917 | + | 8.03529i | −0.188765 | + | 0.326951i | ||||
\(605\) | 4.10323 | − | 7.10700i | 0.166820 | − | 0.288941i | ||||
\(606\) | 60.3724 | − | 38.0411i | 2.45246 | − | 1.54531i | ||||
\(607\) | 19.6796 | − | 11.3620i | 0.798772 | − | 0.461171i | −0.0442698 | − | 0.999020i | \(-0.514096\pi\) |
0.843041 | + | 0.537849i | \(0.180763\pi\) | |||||||
\(608\) | 0.471284 | − | 0.816287i | 0.0191131 | − | 0.0331048i | ||||
\(609\) | −4.03419 | − | 0.632919i | −0.163474 | − | 0.0256472i | ||||
\(610\) | −5.30940 | − | 9.19614i | −0.214971 | − | 0.372341i | ||||
\(611\) | 0.926781 | + | 0.535077i | 0.0374935 | + | 0.0216469i | ||||
\(612\) | −40.4483 | + | 84.5379i | −1.63503 | + | 3.41724i | ||||
\(613\) | −22.1377 | − | 38.3437i | −0.894134 | − | 1.54869i | −0.834873 | − | 0.550443i | \(-0.814459\pi\) |
−0.0592614 | − | 0.998242i | \(-0.518875\pi\) | |||||||
\(614\) | −31.6835 | −1.27864 | ||||||||
\(615\) | −2.88572 | + | 5.47681i | −0.116364 | + | 0.220846i | ||||
\(616\) | 42.1579 | + | 36.8177i | 1.69859 | + | 1.48343i | ||||
\(617\) | −5.53420 | − | 3.19517i | −0.222798 | − | 0.128633i | 0.384447 | − | 0.923147i | \(-0.374392\pi\) |
−0.607245 | + | 0.794514i | \(0.707726\pi\) | |||||||
\(618\) | −56.2690 | + | 2.17668i | −2.26347 | + | 0.0875590i | ||||
\(619\) | 14.5285 | + | 8.38801i | 0.583948 | + | 0.337143i | 0.762701 | − | 0.646751i | \(-0.223873\pi\) |
−0.178753 | + | 0.983894i | \(0.557206\pi\) | |||||||
\(620\) | 24.3695 | − | 14.0698i | 0.978705 | − | 0.565055i | ||||
\(621\) | 9.45819 | − | 7.03603i | 0.379544 | − | 0.282346i | ||||
\(622\) | 27.6924i | 1.11036i | ||||||||
\(623\) | 6.73634 | + | 5.88305i | 0.269886 | + | 0.235699i | ||||
\(624\) | 10.0640 | − | 6.34139i | 0.402882 | − | 0.253859i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −12.4007 | −0.495632 | ||||||||
\(627\) | −29.2494 | + | 1.13147i | −1.16811 | + | 0.0451866i | ||||
\(628\) | − | 95.4388i | − | 3.80842i | ||||||
\(629\) | 40.7083 | 1.62315 | ||||||||
\(630\) | 11.5951 | − | 15.5554i | 0.461959 | − | 0.619741i | ||||
\(631\) | −12.0000 | −0.477713 | −0.238857 | − | 0.971055i | \(-0.576773\pi\) | ||||
−0.238857 | + | 0.971055i | \(0.576773\pi\) | |||||||
\(632\) | 33.1861i | 1.32007i | ||||||||
\(633\) | −14.3951 | − | 22.8455i | −0.572154 | − | 0.908028i | ||||
\(634\) | 24.3763 | 0.968108 | ||||||||
\(635\) | −1.58242 | − | 2.74083i | −0.0627965 | − | 0.108767i | ||||
\(636\) | 3.65984 | + | 94.6098i | 0.145122 | + | 3.75152i | ||||
\(637\) | −7.64295 | − | 9.87576i | −0.302825 | − | 0.391292i | ||||
\(638\) | − | 9.54583i | − | 0.377923i | ||||||
\(639\) | 0.851173 | − | 0.583478i | 0.0336719 | − | 0.0230821i | ||||
\(640\) | −17.1400 | + | 9.89576i | −0.677517 | + | 0.391164i | ||||
\(641\) | 1.66913 | + | 0.963673i | 0.0659267 | + | 0.0380628i | 0.532601 | − | 0.846366i | \(-0.321215\pi\) |
−0.466674 | + | 0.884429i | \(0.654548\pi\) | |||||||
\(642\) | −43.8686 | − | 69.6209i | −1.73136 | − | 2.74772i | ||||
\(643\) | 0.105313 | + | 0.0608025i | 0.00415314 | + | 0.00239782i | 0.502075 | − | 0.864824i | \(-0.332570\pi\) |
−0.497922 | + | 0.867222i | \(0.665903\pi\) | |||||||
\(644\) | −7.71559 | − | 22.5761i | −0.304037 | − | 0.889624i | ||||
\(645\) | −4.96316 | − | 7.87669i | −0.195424 | − | 0.310145i | ||||
\(646\) | −74.0789 | −2.91460 | ||||||||
\(647\) | 18.1842 | + | 31.4959i | 0.714894 | + | 1.23823i | 0.963000 | + | 0.269500i | \(0.0868583\pi\) |
−0.248107 | + | 0.968733i | \(0.579808\pi\) | |||||||
\(648\) | −40.5214 | − | 15.6675i | −1.59183 | − | 0.615476i | ||||
\(649\) | −33.8871 | − | 19.5647i | −1.33018 | − | 0.767982i | ||||
\(650\) | 2.18033 | + | 3.77644i | 0.0855194 | + | 0.148124i | ||||
\(651\) | −20.3795 | + | 25.2419i | −0.798738 | + | 0.989307i | ||||
\(652\) | −24.2724 | + | 42.0411i | −0.950581 | + | 1.64645i | ||||
\(653\) | 32.1477 | − | 18.5605i | 1.25804 | − | 0.726328i | 0.285345 | − | 0.958425i | \(-0.407892\pi\) |
0.972693 | + | 0.232097i | \(0.0745586\pi\) | |||||||
\(654\) | −1.47699 | − | 38.1813i | −0.0577548 | − | 1.49301i | ||||
\(655\) | −2.94131 | + | 5.09450i | −0.114927 | + | 0.199059i | ||||
\(656\) | 6.87960 | − | 11.9158i | 0.268603 | − | 0.465235i | ||||
\(657\) | 10.5909 | + | 5.06736i | 0.413190 | + | 0.197696i | ||||
\(658\) | −3.80646 | − | 0.748985i | −0.148391 | − | 0.0291985i | ||||
\(659\) | −34.3197 | + | 19.8145i | −1.33691 | + | 0.771863i | −0.986347 | − | 0.164677i | \(-0.947342\pi\) |
−0.350559 | + | 0.936541i | \(0.614008\pi\) | |||||||
\(660\) | 26.6933 | + | 14.0647i | 1.03904 | + | 0.547467i | ||||
\(661\) | 18.6155i | 0.724061i | 0.932166 | + | 0.362030i | \(0.117916\pi\) | ||||
−0.932166 | + | 0.362030i | \(0.882084\pi\) | |||||||
\(662\) | 61.1566i | 2.37692i | ||||||||
\(663\) | 21.4843 | + | 11.3201i | 0.834381 | + | 0.439635i | ||||
\(664\) | 25.8745 | − | 14.9386i | 1.00412 | − | 0.579731i | ||||
\(665\) | 10.0106 | + | 1.96974i | 0.388193 | + | 0.0763833i | ||||
\(666\) | 2.93427 | + | 37.8699i | 0.113701 | + | 1.46743i | ||||
\(667\) | −1.01080 | + | 1.75075i | −0.0391383 | + | 0.0677895i | ||||
\(668\) | 32.4471 | − | 56.2001i | 1.25542 | − | 2.17445i | ||||
\(669\) | 0.225801 | + | 5.83714i | 0.00872997 | + | 0.225677i | ||||
\(670\) | 13.7325 | − | 7.92845i | 0.530532 | − | 0.306303i | ||||
\(671\) | −9.51931 | + | 16.4879i | −0.367489 | + | 0.636510i | ||||
\(672\) | 0.703642 | − | 0.871524i | 0.0271436 | − | 0.0336198i | ||||
\(673\) | 17.5049 | + | 30.3194i | 0.674765 | + | 1.16873i | 0.976538 | + | 0.215347i | \(0.0690883\pi\) |
−0.301773 | + | 0.953380i | \(0.597578\pi\) | |||||||
\(674\) | 37.8814 | + | 21.8708i | 1.45914 | + | 0.842433i | ||||
\(675\) | 2.05982 | − | 4.77044i | 0.0792825 | − | 0.183614i | ||||
\(676\) | 19.5114 | + | 33.7947i | 0.750438 | + | 1.29980i | ||||
\(677\) | 42.2000 | 1.62188 | 0.810940 | − | 0.585130i | \(-0.198956\pi\) | ||||
0.810940 | + | 0.585130i | \(0.198956\pi\) | |||||||
\(678\) | −29.7190 | − | 47.1651i | −1.14135 | − | 1.81136i | ||||
\(679\) | 10.1860 | + | 29.8045i | 0.390901 | + | 1.14379i | ||||
\(680\) | 32.8549 | + | 18.9688i | 1.25993 | + | 0.727419i | ||||
\(681\) | −17.8842 | − | 28.3828i | −0.685323 | − | 1.08763i | ||||
\(682\) | −65.6772 | − | 37.9187i | −2.51491 | − | 1.45198i | ||||
\(683\) | −7.07680 | + | 4.08579i | −0.270786 | + | 0.156339i | −0.629245 | − | 0.777207i | \(-0.716636\pi\) |
0.358459 | + | 0.933546i | \(0.383302\pi\) | |||||||
\(684\) | −3.55227 | − | 45.8458i | −0.135824 | − | 1.75296i | ||||
\(685\) | − | 0.497828i | − | 0.0190210i | ||||||
\(686\) | 37.7957 | + | 24.9170i | 1.44305 | + | 0.951335i | ||||
\(687\) | −0.701111 | − | 18.1243i | −0.0267491 | − | 0.691484i | ||||
\(688\) | 10.3462 | + | 17.9202i | 0.394446 | + | 0.683201i | ||||
\(689\) | 24.5340 | 0.934672 | ||||||||
\(690\) | −5.12038 | − | 8.12621i | −0.194929 | − | 0.309360i | ||||
\(691\) | − | 37.7671i | − | 1.43673i | −0.695668 | − | 0.718364i | \(-0.744891\pi\) | ||
0.695668 | − | 0.718364i | \(-0.255109\pi\) | |||||||
\(692\) | −17.8856 | −0.679910 | ||||||||
\(693\) | −34.5475 | − | 4.05906i | −1.31235 | − | 0.154191i | ||||
\(694\) | 64.8977 | 2.46348 | ||||||||
\(695\) | 11.2894i | 0.428231i | ||||||||
\(696\) | 7.44489 | − | 0.287995i | 0.282198 | − | 0.0109164i | ||||
\(697\) | 28.0894 | 1.06396 | ||||||||
\(698\) | 14.0942 | + | 24.4119i | 0.533475 | + | 0.924005i | ||||
\(699\) | 18.5535 | − | 11.6907i | 0.701758 | − | 0.442182i | ||||
\(700\) | −7.92098 | − | 6.91763i | −0.299385 | − | 0.261462i | ||||
\(701\) | 35.4760i | 1.33991i | 0.742402 | + | 0.669954i | \(0.233686\pi\) | ||||
−0.742402 | + | 0.669954i | \(0.766314\pi\) | |||||||
\(702\) | −8.98216 | + | 20.8022i | −0.339010 | + | 0.785130i | ||||
\(703\) | −17.2981 | + | 9.98705i | −0.652410 | + | 0.376669i | ||||
\(704\) | 31.4896 | + | 18.1805i | 1.18681 | + | 0.685205i | ||||
\(705\) | −1.03823 | + | 0.0401624i | −0.0391020 | + | 0.00151260i | ||||
\(706\) | 56.4354 | + | 32.5830i | 2.12397 | + | 1.22628i | ||||
\(707\) | 33.5875 | + | 29.3330i | 1.26319 | + | 1.10318i | ||||
\(708\) | 28.6541 | − | 54.3825i | 1.07689 | − | 2.04382i | ||||
\(709\) | 0.383803 | 0.0144140 | 0.00720701 | − | 0.999974i | \(-0.497706\pi\) | ||||
0.00720701 | + | 0.999974i | \(0.497706\pi\) | |||||||
\(710\) | −0.420412 | − | 0.728175i | −0.0157778 | − | 0.0273279i | ||||
\(711\) | −11.6612 | − | 17.0113i | −0.437330 | − | 0.637973i | ||||
\(712\) | −14.1316 | − | 8.15888i | −0.529604 | − | 0.305767i | ||||
\(713\) | 8.03036 | + | 13.9090i | 0.300739 | + | 0.520896i | ||||
\(714\) | −86.9694 | − | 13.6445i | −3.25475 | − | 0.510633i | ||||
\(715\) | 3.90915 | − | 6.77084i | 0.146194 | − | 0.253215i | ||||
\(716\) | −29.4333 | + | 16.9933i | −1.09997 | + | 0.635070i | ||||
\(717\) | 28.7337 | − | 18.1053i | 1.07308 | − | 0.676154i | ||||
\(718\) | −25.1614 | + | 43.5809i | −0.939017 | + | 1.62642i | ||||
\(719\) | −20.4550 | + | 35.4291i | −0.762842 | + | 1.32128i | 0.178537 | + | 0.983933i | \(0.442863\pi\) |
−0.941380 | + | 0.337349i | \(0.890470\pi\) | |||||||
\(720\) | −4.98462 | + | 10.4180i | −0.185766 | + | 0.388255i | ||||
\(721\) | −11.3802 | − | 33.2990i | −0.423822 | − | 1.24012i | ||||
\(722\) | −8.74233 | + | 5.04739i | −0.325356 | + | 0.187844i | ||||
\(723\) | −2.57696 | + | 1.62376i | −0.0958383 | + | 0.0603883i | ||||
\(724\) | − | 3.46956i | − | 0.128945i | ||||||
\(725\) | 0.891101i | 0.0330947i | ||||||||
\(726\) | −1.34302 | − | 34.7180i | −0.0498440 | − | 1.28851i | ||||
\(727\) | 0.765637 | − | 0.442041i | 0.0283959 | − | 0.0163944i | −0.485735 | − | 0.874106i | \(-0.661448\pi\) |
0.514131 | + | 0.857712i | \(0.328115\pi\) | |||||||
\(728\) | 17.1610 | + | 14.9872i | 0.636030 | + | 0.555464i | ||||
\(729\) | 26.2767 | − | 6.20758i | 0.973212 | − | 0.229910i | ||||
\(730\) | 4.78308 | − | 8.28454i | 0.177030 | − | 0.306625i | ||||
\(731\) | −21.1218 | + | 36.5840i | −0.781217 | + | 1.35311i | ||||
\(732\) | −26.4601 | − | 13.9418i | −0.977993 | − | 0.515303i | ||||
\(733\) | 35.9939 | − | 20.7811i | 1.32946 | − | 0.767566i | 0.344247 | − | 0.938879i | \(-0.388134\pi\) |
0.985217 | + | 0.171313i | \(0.0548009\pi\) | |||||||
\(734\) | 22.0508 | − | 38.1931i | 0.813909 | − | 1.40973i | ||||
\(735\) | 11.3897 | + | 4.15633i | 0.420115 | + | 0.153309i | ||||
\(736\) | −0.277263 | − | 0.480234i | −0.0102201 | − | 0.0177017i | ||||
\(737\) | −24.6212 | − | 14.2151i | −0.906934 | − | 0.523619i | ||||
\(738\) | 2.02469 | + | 26.1308i | 0.0745300 | + | 0.961888i | ||||
\(739\) | −7.43979 | − | 12.8861i | −0.273677 | − | 0.474023i | 0.696123 | − | 0.717922i | \(-0.254907\pi\) |
−0.969800 | + | 0.243900i | \(0.921573\pi\) | |||||||
\(740\) | 20.5887 | 0.756857 | ||||||||
\(741\) | −11.9064 | + | 0.460583i | −0.437394 | + | 0.0169199i | ||||
\(742\) | −84.1599 | + | 28.7624i | −3.08961 | + | 1.05590i | ||||
\(743\) | 2.00964 | + | 1.16027i | 0.0737265 | + | 0.0425660i | 0.536410 | − | 0.843957i | \(-0.319780\pi\) |
−0.462684 | + | 0.886523i | \(0.653113\pi\) | |||||||
\(744\) | 27.5918 | − | 52.3663i | 1.01156 | − | 1.91984i | ||||
\(745\) | 9.75448 | + | 5.63175i | 0.357376 | + | 0.206331i | ||||
\(746\) | 20.2088 | − | 11.6675i | 0.739896 | − | 0.427179i | ||||
\(747\) | −8.01405 | + | 16.7496i | −0.293219 | + | 0.612834i | ||||
\(748\) | − | 136.904i | − | 5.00572i | ||||||
\(749\) | 33.8265 | − | 38.7328i | 1.23599 | − | 1.41526i | ||||
\(750\) | −3.74561 | − | 1.97356i | −0.136770 | − | 0.0720642i | ||||
\(751\) | −16.4458 | − | 28.4850i | −0.600116 | − | 1.03943i | −0.992803 | − | 0.119760i | \(-0.961788\pi\) |
0.392686 | − | 0.919672i | \(-0.371546\pi\) | |||||||
\(752\) | 2.30932 | 0.0842121 | ||||||||
\(753\) | −5.82630 | + | 11.0577i | −0.212322 | + | 0.402966i | ||||
\(754\) | − | 3.88578i | − | 0.141512i | ||||||
\(755\) | −2.33427 | −0.0849527 | ||||||||
\(756\) | 4.27389 | − | 54.4777i | 0.155440 | − | 1.98133i | ||||
\(757\) | −18.8340 | −0.684535 | −0.342268 | − | 0.939603i | \(-0.611195\pi\) | ||||
−0.342268 | + | 0.939603i | \(0.611195\pi\) | |||||||
\(758\) | − | 2.21325i | − | 0.0803889i | ||||||
\(759\) | −8.02746 | + | 15.2353i | −0.291378 | + | 0.553006i | ||||
\(760\) | −18.6146 | −0.675222 | ||||||||
\(761\) | −4.75297 | − | 8.23238i | −0.172295 | − | 0.298423i | 0.766927 | − | 0.641734i | \(-0.221785\pi\) |
−0.939222 | + | 0.343311i | \(0.888452\pi\) | |||||||
\(762\) | −11.8543 | − | 6.24600i | −0.429435 | − | 0.226269i | ||||
\(763\) | 22.5950 | − | 7.72206i | 0.817995 | − | 0.279557i | ||||
\(764\) | − | 61.7150i | − | 2.23277i | ||||||
\(765\) | −23.5069 | + | 1.82138i | −0.849893 | + | 0.0658523i | ||||
\(766\) | −12.9928 | + | 7.50142i | −0.469450 | + | 0.271037i | ||||
\(767\) | −13.7943 | − | 7.96412i | −0.498082 | − | 0.287568i | ||||
\(768\) | −25.6620 | + | 48.7039i | −0.925999 | + | 1.75745i | ||||
\(769\) | 14.2817 | + | 8.24557i | 0.515013 | + | 0.297343i | 0.734892 | − | 0.678184i | \(-0.237233\pi\) |
−0.219879 | + | 0.975527i | \(0.570566\pi\) | |||||||
\(770\) | −5.47190 | + | 27.8091i | −0.197194 | + | 1.00217i | ||||
\(771\) | −23.4248 | + | 0.906154i | −0.843623 | + | 0.0326343i | ||||
\(772\) | 41.7913 | 1.50410 | ||||||||
\(773\) | −19.5007 | − | 33.7762i | −0.701392 | − | 1.21485i | −0.967978 | − | 0.251036i | \(-0.919229\pi\) |
0.266585 | − | 0.963811i | \(-0.414105\pi\) | |||||||
\(774\) | −35.5556 | − | 17.0121i | −1.27802 | − | 0.611486i | ||||
\(775\) | 6.13095 | + | 3.53970i | 0.220230 | + | 0.127150i | ||||
\(776\) | −28.7334 | − | 49.7677i | −1.03147 | − | 1.78655i | ||||
\(777\) | −22.1476 | + | 8.53878i | −0.794542 | + | 0.306327i | ||||
\(778\) | −10.2260 | + | 17.7120i | −0.366620 | + | 0.635005i | ||||
\(779\) | −11.9359 | + | 6.89122i | −0.427649 | + | 0.246903i | ||||
\(780\) | 10.8659 | + | 5.72526i | 0.389063 | + | 0.204997i | ||||
\(781\) | −0.753764 | + | 1.30556i | −0.0269718 | + | 0.0467166i | ||||
\(782\) | −21.7909 | + | 37.7429i | −0.779240 | + | 1.34968i | ||||
\(783\) | −3.71507 | + | 2.76367i | −0.132766 | + | 0.0987657i | ||||
\(784\) | −24.9389 | − | 10.2096i | −0.890675 | − | 0.364627i | ||||
\(785\) | 20.7939 | − | 12.0054i | 0.742166 | − | 0.428490i | ||||
\(786\) | 0.962712 | + | 24.8869i | 0.0343388 | + | 0.887685i | ||||
\(787\) | − | 37.9768i | − | 1.35373i | −0.736108 | − | 0.676864i | \(-0.763338\pi\) | ||
0.736108 | − | 0.676864i | \(-0.236662\pi\) | |||||||
\(788\) | − | 24.5774i | − | 0.875535i | ||||||
\(789\) | −6.40686 | + | 4.03700i | −0.228090 | + | 0.143721i | ||||
\(790\) | −14.5531 | + | 8.40222i | −0.517775 | + | 0.298938i | ||||
\(791\) | 22.9160 | − | 26.2397i | 0.814798 | − | 0.932978i | ||||
\(792\) | 63.2763 | − | 4.90283i | 2.24842 | − | 0.174215i | ||||
\(793\) | −3.87499 | + | 6.71167i | −0.137605 | + | 0.238338i | ||||
\(794\) | −24.1408 | + | 41.8131i | −0.856724 | + | 1.48389i | ||||
\(795\) | −20.1529 | + | 12.6985i | −0.714750 | + | 0.450369i | ||||
\(796\) | −45.7443 | + | 26.4105i | −1.62136 | + | 0.936095i | ||||
\(797\) | 18.9269 | − | 32.7823i | 0.670425 | − | 1.16121i | −0.307359 | − | 0.951594i | \(-0.599445\pi\) |
0.977784 | − | 0.209616i | \(-0.0672215\pi\) | |||||||
\(798\) | 40.3031 | − | 15.5384i | 1.42671 | − | 0.550055i | ||||
\(799\) | 2.35723 | + | 4.08284i | 0.0833927 | + | 0.144440i | ||||
\(800\) | −0.211683 | − | 0.122215i | −0.00748411 | − | 0.00432095i | ||||
\(801\) | 10.1108 | − | 0.783417i | 0.357248 | − | 0.0276807i | ||||
\(802\) | 18.8744 | + | 32.6914i | 0.666477 | + | 1.15437i | ||||
\(803\) | −17.1513 | −0.605258 | ||||||||
\(804\) | 20.8191 | − | 39.5125i | 0.734233 | − | 1.39350i | ||||
\(805\) | 3.94826 | − | 4.52092i | 0.139158 | − | 0.159342i | ||||
\(806\) | −26.7349 | − | 15.4354i | −0.941698 | − | 0.543689i | ||||
\(807\) | −36.4251 | + | 1.40905i | −1.28222 | + | 0.0496010i | ||||
\(808\) | −70.4603 | − | 40.6803i | −2.47879 | − | 1.43113i | ||||
\(809\) | −45.8364 | + | 26.4637i | −1.61152 | + | 0.930413i | −0.622506 | + | 0.782615i | \(0.713885\pi\) |
−0.989018 | + | 0.147798i | \(0.952781\pi\) | |||||||
\(810\) | −3.38877 | − | 21.7366i | −0.119069 | − | 0.763745i | ||||
\(811\) | − | 16.7360i | − | 0.587682i | −0.955854 | − | 0.293841i | \(-0.905066\pi\) | ||
0.955854 | − | 0.293841i | \(-0.0949335\pi\) | |||||||
\(812\) | 3.03060 | + | 8.86764i | 0.106353 | + | 0.311193i | ||||
\(813\) | 4.84723 | − | 3.05427i | 0.170000 | − | 0.107118i | ||||
\(814\) | −27.7438 | − | 48.0537i | −0.972421 | − | 1.68428i | ||||
\(815\) | −12.2130 | −0.427803 | ||||||||
\(816\) | 52.3643 | − | 2.02563i | 1.83312 | − | 0.0709114i | ||||
\(817\) | − | 20.7274i | − | 0.725160i | ||||||
\(818\) | 11.5814 | 0.404933 | ||||||||
\(819\) | −14.0631 | − | 1.65231i | −0.491405 | − | 0.0577363i | ||||
\(820\) | 14.2065 | 0.496114 | ||||||||
\(821\) | 12.7579i | 0.445254i | 0.974904 | + | 0.222627i | \(0.0714632\pi\) | ||||
−0.974904 | + | 0.222627i | \(0.928537\pi\) | |||||||
\(822\) | −1.12361 | − | 1.78320i | −0.0391902 | − | 0.0621962i | ||||
\(823\) | −36.3966 | −1.26871 | −0.634353 | − | 0.773043i | \(-0.718733\pi\) | ||||
−0.634353 | + | 0.773043i | \(0.718733\pi\) | |||||||
\(824\) | 32.1023 | + | 55.6028i | 1.11834 | + | 1.93701i | ||||
\(825\) | 0.293417 | + | 7.58507i | 0.0102155 | + | 0.264078i | ||||
\(826\) | 56.6557 | + | 11.1479i | 1.97130 | + | 0.387886i | ||||
\(827\) | − | 14.5352i | − | 0.505439i | −0.967540 | − | 0.252720i | \(-0.918675\pi\) | ||
0.967540 | − | 0.252720i | \(-0.0813250\pi\) | |||||||
\(828\) | −24.4031 | − | 11.6760i | −0.848068 | − | 0.405769i | ||||
\(829\) | 2.33693 | − | 1.34923i | 0.0811651 | − | 0.0468607i | −0.458868 | − | 0.888504i | \(-0.651745\pi\) |
0.540033 | + | 0.841644i | \(0.318412\pi\) | |||||||
\(830\) | 13.1020 | + | 7.56447i | 0.454778 | + | 0.262566i | ||||
\(831\) | −23.6098 | − | 37.4695i | −0.819015 | − | 1.29980i | ||||
\(832\) | 12.8183 | + | 7.40067i | 0.444396 | + | 0.256572i | ||||
\(833\) | −7.40595 | − | 54.5130i | −0.256601 | − | 1.88876i | ||||
\(834\) | 25.4803 | + | 40.4381i | 0.882311 | + | 1.40026i | ||||
\(835\) | 16.3262 | 0.564993 | ||||||||
\(836\) | 33.5870 | + | 58.1744i | 1.16163 | + | 2.01200i | ||||
\(837\) | 4.25731 | + | 36.5385i | 0.147154 | + | 1.26296i | ||||
\(838\) | 0.508902 | + | 0.293815i | 0.0175797 | + | 0.0101497i | ||||
\(839\) | −10.6019 | − | 18.3631i | −0.366019 | − | 0.633964i | 0.622920 | − | 0.782286i | \(-0.285946\pi\) |
−0.988939 | + | 0.148322i | \(0.952613\pi\) | |||||||
\(840\) | −21.8537 | − | 3.42860i | −0.754025 | − | 0.118298i | ||||
\(841\) | −14.1030 | + | 24.4271i | −0.486309 | + | 0.842312i | ||||
\(842\) | 26.3827 | − | 15.2321i | 0.909208 | − | 0.524931i | ||||
\(843\) | −0.436897 | − | 11.2941i | −0.0150475 | − | 0.388991i | ||||
\(844\) | −30.9837 | + | 53.6654i | −1.06650 | + | 1.84724i | ||||
\(845\) | −4.90872 | + | 8.50215i | −0.168865 | + | 0.292483i | ||||
\(846\) | −3.62825 | + | 2.48716i | −0.124742 | + | 0.0855104i | ||||
\(847\) | 20.5455 | − | 7.02162i | 0.705953 | − | 0.241266i | ||||
\(848\) | 45.8497 | − | 26.4713i | 1.57449 | − | 0.909029i | ||||
\(849\) | 7.19129 | + | 3.78908i | 0.246804 | + | 0.130041i | ||||
\(850\) | 19.2104i | 0.658912i | ||||||||
\(851\) | 11.7511i | 0.402821i | ||||||||
\(852\) | −2.09518 | − | 1.10395i | −0.0717797 | − | 0.0378206i | ||||
\(853\) | −4.49048 | + | 2.59258i | −0.153751 | + | 0.0887682i | −0.574902 | − | 0.818222i | \(-0.694960\pi\) |
0.421151 | + | 0.906991i | \(0.361626\pi\) | |||||||
\(854\) | 5.42409 | − | 27.5661i | 0.185608 | − | 0.943293i | ||||
\(855\) | 9.54188 | − | 6.54095i | 0.326325 | − | 0.223696i | ||||
\(856\) | −46.9121 | + | 81.2542i | −1.60342 | + | 2.77721i | ||||
\(857\) | −25.3909 | + | 43.9783i | −0.867337 | + | 1.50227i | −0.00262895 | + | 0.999997i | \(0.500837\pi\) |
−0.864708 | + | 0.502275i | \(0.832497\pi\) | |||||||
\(858\) | −1.27949 | − | 33.0759i | −0.0436811 | − | 1.12919i | ||||
\(859\) | 30.4118 | − | 17.5583i | 1.03764 | − | 0.599080i | 0.118474 | − | 0.992957i | \(-0.462200\pi\) |
0.919163 | + | 0.393877i | \(0.128866\pi\) | |||||||
\(860\) | −10.6826 | + | 18.5028i | −0.364273 | + | 0.630940i | ||||
\(861\) | −15.2822 | + | 5.89189i | −0.520816 | + | 0.200795i | ||||
\(862\) | −2.42658 | − | 4.20296i | −0.0826497 | − | 0.143153i | ||||
\(863\) | −45.8409 | − | 26.4663i | −1.56044 | − | 0.900922i | −0.997212 | − | 0.0746216i | \(-0.976225\pi\) |
−0.563230 | − | 0.826300i | \(-0.690442\pi\) | |||||||
\(864\) | −0.146992 | − | 1.26156i | −0.00500076 | − | 0.0429192i | ||||
\(865\) | −2.24985 | − | 3.89686i | −0.0764973 | − | 0.132497i | ||||
\(866\) | 77.6984 | 2.64030 | ||||||||
\(867\) | 41.3348 | + | 65.5998i | 1.40380 | + | 2.22788i | ||||
\(868\) | 73.0495 | + | 14.3737i | 2.47946 | + | 0.487875i | ||||
\(869\) | 26.0925 | + | 15.0645i | 0.885127 | + | 0.511028i | ||||
\(870\) | 2.01123 | + | 3.19188i | 0.0681870 | + | 0.108215i | ||||
\(871\) | −10.0225 | − | 5.78647i | −0.339598 | − | 0.196067i | ||||
\(872\) | −37.7292 | + | 21.7830i | −1.27767 | + | 0.737665i | ||||
\(873\) | 32.2166 | + | 15.4144i | 1.09037 | + | 0.521700i | ||||
\(874\) | − | 21.3840i | − | 0.723324i | ||||||
\(875\) | 0.510801 | − | 2.59597i | 0.0172682 | − | 0.0877599i | ||||
\(876\) | −1.04149 | − | 26.9234i | −0.0351888 | − | 0.909658i | ||||
\(877\) | 9.65302 | + | 16.7195i | 0.325959 | + | 0.564578i | 0.981706 | − | 0.190403i | \(-0.0609795\pi\) |
−0.655747 | + | 0.754981i | \(0.727646\pi\) | |||||||
\(878\) | 18.0127 | 0.607900 | ||||||||
\(879\) | 9.73474 | + | 15.4493i | 0.328344 | + | 0.521094i | ||||
\(880\) | − | 16.8713i | − | 0.568732i | ||||||
\(881\) | −0.474565 | −0.0159885 | −0.00799424 | − | 0.999968i | \(-0.502545\pi\) | ||||
−0.00799424 | + | 0.999968i | \(0.502545\pi\) | |||||||
\(882\) | 50.1783 | − | 10.8189i | 1.68959 | − | 0.364291i | ||||
\(883\) | −43.6911 | −1.47032 | −0.735162 | − | 0.677892i | \(-0.762894\pi\) | ||||
−0.735162 | + | 0.677892i | \(0.762894\pi\) | |||||||
\(884\) | − | 55.7291i | − | 1.87437i | ||||||
\(885\) | 15.4531 | − | 0.597780i | 0.519450 | − | 0.0200942i | ||||
\(886\) | −100.567 | −3.37860 | ||||||||
\(887\) | −13.9301 | − | 24.1276i | −0.467726 | − | 0.810125i | 0.531594 | − | 0.846999i | \(-0.321593\pi\) |
−0.999320 | + | 0.0368743i | \(0.988260\pi\) | |||||||
\(888\) | 36.6406 | − | 23.0875i | 1.22958 | − | 0.774765i | ||||
\(889\) | 1.61660 | − | 8.21585i | 0.0542192 | − | 0.275551i | ||||
\(890\) | − | 8.26282i | − | 0.276970i | ||||||
\(891\) | −30.7127 | + | 24.7477i | −1.02892 | + | 0.829080i | ||||
\(892\) | 11.6095 | − | 6.70276i | 0.388716 | − | 0.224425i | ||||
\(893\) | −2.00330 | − | 1.15661i | −0.0670380 | − | 0.0387044i | ||||
\(894\) | 47.6510 | − | 1.84331i | 1.59369 | − | 0.0616495i | ||||
\(895\) | −7.40489 | − | 4.27521i | −0.247518 | − | 0.142905i | ||||
\(896\) | −51.3783 | − | 10.1095i | −1.71643 | − | 0.337736i | ||||
\(897\) | −3.26770 | + | 6.20177i | −0.109105 | + | 0.207071i | ||||
\(898\) | 63.5943 | 2.12217 | ||||||||
\(899\) | −3.15423 | − | 5.46329i | −0.105200 | − | 0.182211i | ||||
\(900\) | −11.8889 | + | 0.921187i | −0.396296 | + | 0.0307062i | ||||
\(901\) | 93.6019 | + | 54.0411i | 3.11833 | + | 1.80037i | ||||
\(902\) | −19.1437 | − | 33.1578i | −0.637414 | − | 1.10403i | ||||
\(903\) | 3.81776 | − | 24.3342i | 0.127047 | − | 0.809790i | ||||
\(904\) | −31.7809 | + | 55.0461i | −1.05702 | + | 1.83081i | ||||
\(905\) | 0.755935 | − | 0.436440i | 0.0251281 | − | 0.0145077i | ||||
\(906\) | −8.36125 | + | 5.26848i | −0.277784 | + | 0.175033i | ||||
\(907\) | 2.13062 | − | 3.69034i | 0.0707461 | − | 0.122536i | −0.828482 | − | 0.560015i | \(-0.810795\pi\) |
0.899229 | + | 0.437479i | \(0.144129\pi\) | |||||||
\(908\) | −38.4935 | + | 66.6727i | −1.27745 | + | 2.21261i | ||||
\(909\) | 50.4127 | − | 3.90613i | 1.67208 | − | 0.129558i | ||||
\(910\) | −2.22742 | + | 11.3201i | −0.0738384 | + | 0.375259i | ||||
\(911\) | 3.52078 | − | 2.03273i | 0.116649 | − | 0.0673472i | −0.440540 | − | 0.897733i | \(-0.645213\pi\) |
0.557189 | + | 0.830386i | \(0.311880\pi\) | |||||||
\(912\) | −21.7541 | + | 13.7074i | −0.720349 | + | 0.453897i | ||||
\(913\) | − | 27.1249i | − | 0.897704i | ||||||
\(914\) | 75.0728i | 2.48319i | ||||||||
\(915\) | −0.290853 | − | 7.51879i | −0.00961531 | − | 0.248563i | ||||
\(916\) | −36.0475 | + | 20.8120i | −1.19104 | + | 0.687649i | ||||
\(917\) | −14.7276 | + | 5.03330i | −0.486349 | + | 0.166214i | ||||
\(918\) | −80.0898 | + | 59.5795i | −2.64336 | + | 1.96642i | ||||
\(919\) | 11.2988 | − | 19.5700i | 0.372712 | − | 0.645556i | −0.617270 | − | 0.786751i | \(-0.711761\pi\) |
0.989982 | + | 0.141196i | \(0.0450947\pi\) | |||||||
\(920\) | −5.47562 | + | 9.48405i | −0.180526 | + | 0.312680i | ||||
\(921\) | −19.8623 | − | 10.4654i | −0.654484 | − | 0.344847i | ||||
\(922\) | −66.7974 | + | 38.5655i | −2.19986 | + | 1.27009i | ||||
\(923\) | −0.306832 | + | 0.531448i | −0.0100995 | + | 0.0174928i | ||||
\(924\) | 28.7164 | + | 74.4837i | 0.944700 | + | 2.45033i | ||||
\(925\) | 2.58988 | + | 4.48580i | 0.0851547 | + | 0.147492i | ||||
\(926\) | 51.8568 | + | 29.9395i | 1.70412 | + | 0.983874i | ||||
\(927\) | −35.9938 | − | 17.2217i | −1.18219 | − | 0.565636i | ||||
\(928\) | 0.108906 | + | 0.188631i | 0.00357501 | + | 0.00619210i | ||||
\(929\) | −4.91016 | −0.161097 | −0.0805486 | − | 0.996751i | \(-0.525667\pi\) | ||||
−0.0805486 | + | 0.996751i | \(0.525667\pi\) | |||||||
\(930\) | 29.9500 | − | 1.15857i | 0.982098 | − | 0.0379910i | ||||
\(931\) | 16.5208 | + | 21.3472i | 0.541447 | + | 0.699625i | ||||
\(932\) | −43.5832 | − | 25.1628i | −1.42762 | − | 0.824234i | ||||
\(933\) | −9.14712 | + | 17.3603i | −0.299463 | + | 0.568350i | ||||
\(934\) | −5.65635 | − | 3.26570i | −0.185082 | − | 0.106857i | ||||
\(935\) | 29.8283 | − | 17.2214i | 0.975488 | − | 0.563198i | ||||
\(936\) | 25.7576 | − | 1.99578i | 0.841913 | − | 0.0652340i | ||||
\(937\) | − | 53.9957i | − | 1.76396i | −0.471284 | − | 0.881982i | \(-0.656209\pi\) | ||
0.471284 | − | 0.881982i | \(-0.343791\pi\) | |||||||
\(938\) | 41.1641 | + | 8.09972i | 1.34406 | + | 0.264465i | ||||
\(939\) | −7.77396 | − | 4.09609i | −0.253694 | − | 0.133671i | ||||
\(940\) | 1.19220 | + | 2.06495i | 0.0388852 | + | 0.0673511i | ||||
\(941\) | 7.27482 | 0.237152 | 0.118576 | − | 0.992945i | \(-0.462167\pi\) | ||||
0.118576 | + | 0.992945i | \(0.462167\pi\) | |||||||
\(942\) | 47.3865 | − | 89.9348i | 1.54394 | − | 2.93023i | ||||
\(943\) | 8.10841i | 0.264046i | ||||||||
\(944\) | −34.3720 | −1.11871 | ||||||||
\(945\) | 12.4070 | − | 5.92163i | 0.403601 | − | 0.192631i | ||||
\(946\) | 57.5803 | 1.87210 | ||||||||
\(947\) | 24.4635i | 0.794957i | 0.917612 | + | 0.397478i | \(0.130115\pi\) | ||||
−0.917612 | + | 0.397478i | \(0.869885\pi\) | |||||||
\(948\) | −22.0632 | + | 41.8736i | −0.716578 | + | 1.35999i | ||||
\(949\) | −6.98173 | −0.226636 | ||||||||
\(950\) | −4.71293 | − | 8.16304i | −0.152908 | − | 0.264844i | ||||
\(951\) | 15.2814 | + | 8.05178i | 0.495535 | + | 0.261097i | ||||
\(952\) | 32.4601 | + | 94.9797i | 1.05204 | + | 3.07831i | ||||
\(953\) | 24.1698i | 0.782938i | 0.920191 | + | 0.391469i | \(0.128033\pi\) | ||||
−0.920191 | + | 0.391469i | \(0.871967\pi\) | |||||||
\(954\) | −43.5262 | + | 90.9708i | −1.40921 | + | 2.94529i | ||||
\(955\) | 13.4463 | − | 7.76320i | 0.435111 | − | 0.251211i | ||||
\(956\) | −67.4970 | − | 38.9694i | −2.18301 | − | 1.26036i | ||||
\(957\) | 3.15310 | − | 5.98425i | 0.101925 | − | 0.193443i | ||||
\(958\) | 7.56075 | + | 4.36520i | 0.244277 | + | 0.141033i | ||||
\(959\) | 0.866397 | − | 0.992062i | 0.0279774 | − | 0.0320353i | ||||
\(960\) | −14.3598 | + | 0.555488i | −0.463461 | + | 0.0179283i | ||||
\(961\) | −19.1180 | −0.616710 | ||||||||
\(962\) | −11.2936 | − | 19.5610i | −0.364119 | − | 0.630673i | ||||
\(963\) | −4.50451 | − | 58.1354i | −0.145156 | − | 1.87339i | ||||
\(964\) | 6.05343 | + | 3.49495i | 0.194968 | + | 0.112565i | ||||
\(965\) | 5.25698 | + | 9.10536i | 0.169228 | + | 0.293112i | ||||
\(966\) | 3.93870 | − | 25.1050i | 0.126725 | − | 0.807741i | ||||
\(967\) | −1.86561 | + | 3.23133i | −0.0599939 | + | 0.103913i | −0.894462 | − | 0.447143i | \(-0.852441\pi\) |
0.834469 | + | 0.551056i | \(0.185775\pi\) | |||||||
\(968\) | −34.3070 | + | 19.8071i | −1.10267 | + | 0.636625i | ||||
\(969\) | −46.4398 | − | 24.4691i | −1.49186 | − | 0.786061i | ||||
\(970\) | 14.5497 | − | 25.2008i | 0.467163 | − | 0.809150i | ||||
\(971\) | −20.5327 | + | 35.5637i | −0.658926 | + | 1.14129i | 0.321968 | + | 0.946751i | \(0.395656\pi\) |
−0.980894 | + | 0.194543i | \(0.937678\pi\) | |||||||
\(972\) | −40.7129 | − | 46.7087i | −1.30587 | − | 1.49818i | ||||
\(973\) | −19.6475 | + | 22.4973i | −0.629871 | + | 0.721229i | ||||
\(974\) | −34.6186 | + | 19.9871i | −1.10925 | + | 0.640426i | ||||
\(975\) | 0.119440 | + | 3.08762i | 0.00382514 | + | 0.0988830i | ||||
\(976\) | 16.7239i | 0.535319i | ||||||||
\(977\) | − | 48.1446i | − | 1.54028i | −0.637874 | − | 0.770141i | \(-0.720186\pi\) | ||
0.637874 | − | 0.770141i | \(-0.279814\pi\) | |||||||
\(978\) | −43.7465 | + | 27.5650i | −1.39886 | + | 0.881430i | ||||
\(979\) | −12.8298 | + | 7.40728i | −0.410042 | + | 0.236738i | ||||
\(980\) | −3.74565 | − | 27.5706i | −0.119650 | − | 0.880711i | ||||
\(981\) | 11.6858 | − | 24.4236i | 0.373099 | − | 0.779786i | ||||
\(982\) | −51.2615 | + | 88.7875i | −1.63582 | + | 2.83332i | ||||
\(983\) | −2.82493 | + | 4.89292i | −0.0901013 | + | 0.156060i | −0.907554 | − | 0.419936i | \(-0.862052\pi\) |
0.817452 | + | 0.575996i | \(0.195386\pi\) | |||||||
\(984\) | 25.2825 | − | 15.9307i | 0.805978 | − | 0.507852i | ||||
\(985\) | 5.35485 | − | 3.09162i | 0.170620 | − | 0.0985073i | ||||
\(986\) | 8.55921 | − | 14.8250i | 0.272581 | − | 0.472124i | ||||
\(987\) | −2.13886 | − | 1.72685i | −0.0680807 | − | 0.0549664i | ||||
\(988\) | 13.6721 | + | 23.6808i | 0.434968 | + | 0.753387i | ||||
\(989\) | −10.5605 | − | 6.09712i | −0.335805 | − | 0.193877i | ||||
\(990\) | 18.1706 | + | 26.5071i | 0.577500 | + | 0.842452i | ||||
\(991\) | −12.8768 | − | 22.3033i | −0.409046 | − | 0.708489i | 0.585737 | − | 0.810501i | \(-0.300805\pi\) |
−0.994783 | + | 0.102013i | \(0.967472\pi\) | |||||||
\(992\) | 1.73042 | 0.0549409 | ||||||||
\(993\) | −20.2007 | + | 38.3389i | −0.641051 | + | 1.21665i | ||||
\(994\) | 0.429494 | − | 2.18276i | 0.0136227 | − | 0.0692329i | ||||
\(995\) | −11.5085 | − | 6.64441i | −0.364843 | − | 0.210642i | ||||
\(996\) | 42.5795 | − | 1.64713i | 1.34918 | − | 0.0521912i | ||||
\(997\) | −25.7278 | − | 14.8540i | −0.814809 | − | 0.470430i | 0.0338142 | − | 0.999428i | \(-0.489235\pi\) |
−0.848623 | + | 0.528998i | \(0.822568\pi\) | |||||||
\(998\) | 65.7972 | − | 37.9880i | 2.08277 | − | 1.20249i | ||||
\(999\) | −10.6694 | + | 24.7098i | −0.337564 | + | 0.781782i |
(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 | 315.2.t.c.131.2 | yes | 32 | |
3.2 | odd | 2 | 945.2.t.c.341.15 | 32 | |||
7.3 | odd | 6 | 315.2.be.c.311.15 | yes | 32 | ||
9.2 | odd | 6 | 315.2.be.c.236.15 | yes | 32 | ||
9.7 | even | 3 | 945.2.be.c.656.2 | 32 | |||
21.17 | even | 6 | 945.2.be.c.206.2 | 32 | |||
63.38 | even | 6 | inner | 315.2.t.c.101.15 | ✓ | 32 | |
63.52 | odd | 6 | 945.2.t.c.521.2 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.t.c.101.15 | ✓ | 32 | 63.38 | even | 6 | inner | |
315.2.t.c.131.2 | yes | 32 | 1.1 | even | 1 | trivial | |
315.2.be.c.236.15 | yes | 32 | 9.2 | odd | 6 | ||
315.2.be.c.311.15 | yes | 32 | 7.3 | odd | 6 | ||
945.2.t.c.341.15 | 32 | 3.2 | odd | 2 | |||
945.2.t.c.521.2 | 32 | 63.52 | odd | 6 | |||
945.2.be.c.206.2 | 32 | 21.17 | even | 6 | |||
945.2.be.c.656.2 | 32 | 9.7 | even | 3 |