Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,3,Mod(19,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.f (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.94278685509\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.4 | ||
Root | \(-0.523926 - 1.93016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.19 |
Dual form | 108.3.f.c.91.4 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.523926 | − | 1.93016i | −0.261963 | − | 0.965078i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.45100 | + | 2.02252i | −0.862751 | + | 0.505629i | ||||
\(5\) | 4.03104 | + | 6.98197i | 0.806209 | + | 1.39639i | 0.915472 | + | 0.402382i | \(0.131818\pi\) |
−0.109263 | + | 0.994013i | \(0.534849\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.90254 | + | 2.25313i | 0.557506 | + | 0.321876i | 0.752144 | − | 0.658999i | \(-0.229020\pi\) |
−0.194638 | + | 0.980875i | \(0.562353\pi\) | |||||||
\(8\) | 5.71184 | + | 5.60133i | 0.713980 | + | 0.700166i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 11.3643 | − | 11.4386i | 1.13643 | − | 1.14386i | ||||
\(11\) | 3.25842 | + | 1.88125i | 0.296220 | + | 0.171023i | 0.640744 | − | 0.767755i | \(-0.278626\pi\) |
−0.344523 | + | 0.938778i | \(0.611959\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.52605 | − | 6.10730i | −0.271235 | − | 0.469792i | 0.697944 | − | 0.716153i | \(-0.254099\pi\) |
−0.969178 | + | 0.246361i | \(0.920765\pi\) | |||||||
\(14\) | 2.30426 | − | 8.71299i | 0.164590 | − | 0.622357i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.81885 | − | 13.9594i | 0.488678 | − | 0.872464i | ||||
\(17\) | −0.517890 | −0.0304641 | −0.0152321 | − | 0.999884i | \(-0.504849\pi\) | ||||
−0.0152321 | + | 0.999884i | \(0.504849\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 16.4164i | 0.864023i | 0.901868 | + | 0.432012i | \(0.142196\pi\) | ||||
−0.901868 | + | 0.432012i | \(0.857804\pi\) | |||||||
\(20\) | −28.0323 | − | 15.9420i | −1.40162 | − | 0.797098i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.92394 | − | 7.27490i | 0.0874517 | − | 0.330677i | ||||
\(23\) | 27.7049 | − | 15.9954i | 1.20456 | − | 0.695454i | 0.242996 | − | 0.970027i | \(-0.421870\pi\) |
0.961566 | + | 0.274573i | \(0.0885366\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −19.9986 | + | 34.6387i | −0.799946 | + | 1.38555i | ||||
\(26\) | −9.94065 | + | 10.0056i | −0.382333 | + | 0.384831i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −18.0247 | + | 0.117384i | −0.643739 | + | 0.00419230i | ||||
\(29\) | −9.48394 | + | 16.4267i | −0.327032 | + | 0.566437i | −0.981922 | − | 0.189288i | \(-0.939382\pi\) |
0.654889 | + | 0.755725i | \(0.272715\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 13.1355 | − | 7.58377i | 0.423725 | − | 0.244638i | −0.272945 | − | 0.962030i | \(-0.587998\pi\) |
0.696670 | + | 0.717392i | \(0.254664\pi\) | |||||||
\(32\) | −31.0404 | − | 7.77790i | −0.970011 | − | 0.243059i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.271336 | + | 0.999608i | 0.00798047 | + | 0.0294002i | ||||
\(35\) | 36.3299i | 1.03800i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.592061 | 0.0160017 | 0.00800083 | − | 0.999968i | \(-0.497453\pi\) | ||||
0.00800083 | + | 0.999968i | \(0.497453\pi\) | |||||||
\(38\) | 31.6863 | − | 8.60099i | 0.833850 | − | 0.226342i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −16.0836 | + | 62.4591i | −0.402091 | + | 1.56148i | ||||
\(41\) | −12.3766 | − | 21.4369i | −0.301868 | − | 0.522850i | 0.674691 | − | 0.738100i | \(-0.264277\pi\) |
−0.976559 | + | 0.215250i | \(0.930943\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −27.8686 | − | 16.0900i | −0.648107 | − | 0.374185i | 0.139623 | − | 0.990205i | \(-0.455411\pi\) |
−0.787731 | + | 0.616020i | \(0.788744\pi\) | |||||||
\(44\) | −15.0497 | + | 0.0980099i | −0.342039 | + | 0.00222750i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −45.3890 | − | 45.0944i | −0.986718 | − | 0.980313i | ||||
\(47\) | −52.4682 | − | 30.2925i | −1.11634 | − | 0.644521i | −0.175879 | − | 0.984412i | \(-0.556277\pi\) |
−0.940465 | + | 0.339890i | \(0.889610\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.3468 | − | 24.8493i | −0.292791 | − | 0.507129i | ||||
\(50\) | 77.3358 | + | 20.4524i | 1.54672 | + | 0.409048i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 24.5205 | + | 13.9448i | 0.471548 | + | 0.268169i | ||||
\(53\) | 0.664765 | 0.0125427 | 0.00627137 | − | 0.999980i | \(-0.498004\pi\) | ||||
0.00627137 | + | 0.999980i | \(0.498004\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 30.3336i | 0.551521i | ||||||||
\(56\) | 9.67017 | + | 34.7290i | 0.172682 | + | 0.620160i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 36.6749 | + | 9.69913i | 0.632326 | + | 0.167226i | ||||
\(59\) | −30.5921 | + | 17.6623i | −0.518510 | + | 0.299362i | −0.736325 | − | 0.676628i | \(-0.763440\pi\) |
0.217815 | + | 0.975990i | \(0.430107\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 33.7750 | − | 58.5000i | 0.553688 | − | 0.959016i | −0.444316 | − | 0.895870i | \(-0.646553\pi\) |
0.998004 | − | 0.0631460i | \(-0.0201134\pi\) | |||||||
\(62\) | −21.5199 | − | 21.3802i | −0.347095 | − | 0.344842i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.25029 | + | 63.9878i | 0.0195357 | + | 0.999809i | ||||
\(65\) | 28.4273 | − | 49.2376i | 0.437343 | − | 0.757501i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 74.4692 | − | 42.9948i | 1.11148 | − | 0.641714i | 0.172269 | − | 0.985050i | \(-0.444890\pi\) |
0.939213 | + | 0.343336i | \(0.111557\pi\) | |||||||
\(68\) | 1.78724 | − | 1.04744i | 0.0262829 | − | 0.0154035i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 70.1224 | − | 19.0342i | 1.00175 | − | 0.271917i | ||||
\(71\) | − | 56.4434i | − | 0.794977i | −0.917607 | − | 0.397489i | \(-0.869882\pi\) | ||
0.917607 | − | 0.397489i | \(-0.130118\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 131.921 | 1.80713 | 0.903567 | − | 0.428447i | \(-0.140939\pi\) | ||||
0.903567 | + | 0.428447i | \(0.140939\pi\) | |||||||
\(74\) | −0.310196 | − | 1.14277i | −0.00419184 | − | 0.0154429i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −33.2025 | − | 56.6532i | −0.436875 | − | 0.745437i | ||||
\(77\) | 8.47743 | + | 14.6833i | 0.110096 | + | 0.190693i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −126.869 | − | 73.2481i | −1.60594 | − | 0.927191i | −0.990265 | − | 0.139192i | \(-0.955549\pi\) |
−0.615677 | − | 0.787999i | \(-0.711117\pi\) | |||||||
\(80\) | 128.982 | − | 1.68005i | 1.61228 | − | 0.0210006i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −34.8921 | + | 35.1201i | −0.425513 | + | 0.428293i | ||||
\(83\) | 87.1029 | + | 50.2889i | 1.04943 | + | 0.605890i | 0.922491 | − | 0.386020i | \(-0.126150\pi\) |
0.126942 | + | 0.991910i | \(0.459484\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.08764 | − | 3.61589i | −0.0245604 | − | 0.0425399i | ||||
\(86\) | −16.4550 | + | 62.2207i | −0.191338 | + | 0.723497i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.07410 | + | 28.9969i | 0.0917511 | + | 0.329510i | ||||
\(89\) | 25.8362 | 0.290295 | 0.145147 | − | 0.989410i | \(-0.453634\pi\) | ||||
0.145147 | + | 0.989410i | \(0.453634\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 31.7786i | − | 0.349216i | ||||||
\(92\) | −63.2587 | + | 111.234i | −0.687595 | + | 1.20907i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −30.9798 | + | 117.143i | −0.329573 | + | 1.24620i | ||||
\(95\) | −114.619 | + | 66.1754i | −1.20652 | + | 0.696583i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −48.2534 | + | 83.5773i | −0.497457 | + | 0.861621i | −0.999996 | − | 0.00293363i | \(-0.999066\pi\) |
0.502538 | + | 0.864555i | \(0.332400\pi\) | |||||||
\(98\) | −40.4465 | + | 40.7107i | −0.412719 | + | 0.415415i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.04189 | − | 159.986i | −0.0104189 | − | 1.59986i | ||||
\(101\) | 21.6600 | − | 37.5163i | 0.214456 | − | 0.371448i | −0.738648 | − | 0.674091i | \(-0.764536\pi\) |
0.953104 | + | 0.302643i | \(0.0978689\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −125.439 | + | 72.4223i | −1.21786 | + | 0.703129i | −0.964459 | − | 0.264233i | \(-0.914881\pi\) |
−0.253397 | + | 0.967362i | \(0.581548\pi\) | |||||||
\(104\) | 14.0687 | − | 54.6345i | 0.135276 | − | 0.525331i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.348288 | − | 1.28310i | −0.00328573 | − | 0.0121047i | ||||
\(107\) | − | 54.9861i | − | 0.513889i | −0.966426 | − | 0.256944i | \(-0.917284\pi\) | ||
0.966426 | − | 0.256944i | \(-0.0827158\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −63.9235 | −0.586454 | −0.293227 | − | 0.956043i | \(-0.594729\pi\) | ||||
−0.293227 | + | 0.956043i | \(0.594729\pi\) | |||||||
\(110\) | 58.5487 | − | 15.8926i | 0.532261 | − | 0.144478i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 61.9659 | − | 36.8603i | 0.553267 | − | 0.329110i | ||||
\(113\) | −17.8239 | − | 30.8720i | −0.157734 | − | 0.273203i | 0.776317 | − | 0.630342i | \(-0.217086\pi\) |
−0.934051 | + | 0.357139i | \(0.883752\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 223.360 | + | 128.957i | 1.94226 | + | 1.12136i | ||||
\(116\) | −0.494097 | − | 75.8699i | −0.00425945 | − | 0.654051i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 50.1190 | + | 49.7937i | 0.424738 | + | 0.421981i | ||||
\(119\) | −2.02109 | − | 1.16688i | −0.0169839 | − | 0.00980568i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −53.4218 | − | 92.5292i | −0.441502 | − | 0.764704i | ||||
\(122\) | −130.610 | − | 34.5413i | −1.07057 | − | 0.283126i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −29.9923 | + | 52.7383i | −0.241873 | + | 0.425309i | ||||
\(125\) | −120.909 | −0.967276 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.81219i | − | 0.0772613i | −0.999254 | − | 0.0386307i | \(-0.987700\pi\) | ||
0.999254 | − | 0.0386307i | \(-0.0122996\pi\) | |||||||
\(128\) | 122.851 | − | 35.9381i | 0.959776 | − | 0.280766i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −109.930 | − | 29.0723i | −0.845615 | − | 0.223633i | ||||
\(131\) | 101.561 | − | 58.6365i | 0.775278 | − | 0.447607i | −0.0594761 | − | 0.998230i | \(-0.518943\pi\) |
0.834754 | + | 0.550623i | \(0.185610\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −36.9884 | + | 64.0659i | −0.278109 | + | 0.481698i | ||||
\(134\) | −122.003 | − | 121.211i | −0.910471 | − | 0.904561i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.95811 | − | 2.90087i | −0.0217508 | − | 0.0213299i | ||||
\(137\) | −125.606 | + | 217.556i | −0.916831 | + | 1.58800i | −0.112634 | + | 0.993637i | \(0.535929\pi\) |
−0.804198 | + | 0.594362i | \(0.797405\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 133.073 | − | 76.8298i | 0.957361 | − | 0.552732i | 0.0620009 | − | 0.998076i | \(-0.480252\pi\) |
0.895360 | + | 0.445344i | \(0.146919\pi\) | |||||||
\(140\) | −73.4779 | − | 125.375i | −0.524842 | − | 0.895534i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −108.945 | + | 29.5721i | −0.767215 | + | 0.208255i | ||||
\(143\) | − | 26.5335i | − | 0.185549i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −152.921 | −1.05463 | ||||||||
\(146\) | −69.1167 | − | 254.628i | −0.473402 | − | 1.74403i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.04321 | + | 1.19745i | −0.0138054 | + | 0.00809091i | ||||
\(149\) | 45.8643 | + | 79.4393i | 0.307814 | + | 0.533150i | 0.977884 | − | 0.209148i | \(-0.0670691\pi\) |
−0.670070 | + | 0.742298i | \(0.733736\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −36.0215 | − | 20.7970i | −0.238553 | − | 0.137729i | 0.375958 | − | 0.926637i | \(-0.377314\pi\) |
−0.614512 | + | 0.788908i | \(0.710647\pi\) | |||||||
\(152\) | −91.9538 | + | 93.7681i | −0.604959 | + | 0.616895i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 23.8996 | − | 24.0557i | 0.155192 | − | 0.156206i | ||||
\(155\) | 105.899 | + | 61.1410i | 0.683222 | + | 0.394458i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 112.909 | + | 195.565i | 0.719167 | + | 1.24563i | 0.961330 | + | 0.275399i | \(0.0888099\pi\) |
−0.242163 | + | 0.970236i | \(0.577857\pi\) | |||||||
\(158\) | −74.9101 | + | 283.254i | −0.474114 | + | 1.79275i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −70.8200 | − | 248.076i | −0.442625 | − | 1.55048i | ||||
\(161\) | 144.160 | 0.895401 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 125.175i | 0.767945i | 0.923344 | + | 0.383973i | \(0.125444\pi\) | ||||
−0.923344 | + | 0.383973i | \(0.874556\pi\) | |||||||
\(164\) | 86.0681 | + | 48.9469i | 0.524805 | + | 0.298457i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 51.4299 | − | 194.470i | 0.309819 | − | 1.17151i | ||||
\(167\) | 154.373 | − | 89.1274i | 0.924390 | − | 0.533697i | 0.0393573 | − | 0.999225i | \(-0.487469\pi\) |
0.885033 | + | 0.465528i | \(0.154136\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 59.6340 | − | 103.289i | 0.352864 | − | 0.611178i | ||||
\(170\) | −5.88547 | + | 5.92393i | −0.0346204 | + | 0.0348466i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 128.717 | − | 0.838258i | 0.748354 | − | 0.00487359i | ||||
\(173\) | 75.5904 | − | 130.926i | 0.436939 | − | 0.756800i | −0.560513 | − | 0.828146i | \(-0.689396\pi\) |
0.997452 | + | 0.0713455i | \(0.0227293\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −156.091 | + | 90.1193i | −0.891949 | + | 0.514967i | ||||
\(176\) | 51.7383 | − | 30.7765i | 0.293968 | − | 0.174866i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.5363 | − | 49.8680i | −0.0760465 | − | 0.280157i | ||||
\(179\) | 276.827i | 1.54652i | 0.634088 | + | 0.773261i | \(0.281376\pi\) | ||||
−0.634088 | + | 0.773261i | \(0.718624\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −104.729 | −0.578612 | −0.289306 | − | 0.957237i | \(-0.593425\pi\) | ||||
−0.289306 | + | 0.957237i | \(0.593425\pi\) | |||||||
\(182\) | −61.3377 | + | 16.6497i | −0.337021 | + | 0.0914816i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 247.842 | + | 63.8209i | 1.34697 | + | 0.346852i | ||||
\(185\) | 2.38663 | + | 4.13376i | 0.0129007 | + | 0.0223446i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.68751 | − | 0.974282i | −0.00902409 | − | 0.00521006i | ||||
\(188\) | 242.335 | − | 1.57819i | 1.28902 | − | 0.00839461i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 187.781 | + | 186.562i | 0.988320 | + | 0.981904i | ||||
\(191\) | −192.972 | − | 111.413i | −1.01033 | − | 0.583312i | −0.0990389 | − | 0.995084i | \(-0.531577\pi\) |
−0.911287 | + | 0.411772i | \(0.864910\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 56.6790 | + | 98.1709i | 0.293674 | + | 0.508657i | 0.974675 | − | 0.223624i | \(-0.0717888\pi\) |
−0.681002 | + | 0.732282i | \(0.738455\pi\) | |||||||
\(194\) | 186.598 | + | 49.3482i | 0.961847 | + | 0.254372i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 99.7690 | + | 56.7386i | 0.509025 | + | 0.289482i | ||||
\(197\) | 120.998 | 0.614201 | 0.307100 | − | 0.951677i | \(-0.400641\pi\) | ||||
0.307100 | + | 0.951677i | \(0.400641\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 82.2364i | − | 0.413248i | −0.978420 | − | 0.206624i | \(-0.933752\pi\) | ||
0.978420 | − | 0.206624i | \(-0.0662477\pi\) | |||||||
\(200\) | −308.252 | + | 85.8317i | −1.54126 | + | 0.429158i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −83.7605 | − | 22.1515i | −0.414656 | − | 0.109661i | ||||
\(203\) | −74.0230 | + | 42.7372i | −0.364645 | + | 0.210528i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 99.7811 | − | 172.826i | 0.486737 | − | 0.843053i | ||||
\(206\) | 205.507 | + | 204.173i | 0.997607 | + | 0.991132i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −112.824 | + | 1.46958i | −0.542423 | + | 0.00706527i | ||||
\(209\) | −30.8835 | + | 53.4917i | −0.147768 | + | 0.255941i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −93.5819 | + | 54.0295i | −0.443516 | + | 0.256064i | −0.705088 | − | 0.709120i | \(-0.749093\pi\) |
0.261572 | + | 0.965184i | \(0.415759\pi\) | |||||||
\(212\) | −2.29411 | + | 1.34450i | −0.0108213 | + | 0.00634198i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −106.132 | + | 28.8086i | −0.495943 | + | 0.134620i | ||||
\(215\) | − | 259.437i | − | 1.20668i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 68.3490 | 0.314972 | ||||||||
\(218\) | 33.4912 | + | 123.382i | 0.153629 | + | 0.565974i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −61.3503 | − | 104.682i | −0.278865 | − | 0.475825i | ||||
\(221\) | 1.82611 | + | 3.16291i | 0.00826292 | + | 0.0143118i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 141.400 | + | 81.6371i | 0.634079 | + | 0.366086i | 0.782330 | − | 0.622864i | \(-0.214031\pi\) |
−0.148251 | + | 0.988950i | \(0.547364\pi\) | |||||||
\(224\) | −103.612 | − | 100.292i | −0.462552 | − | 0.447731i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −50.2493 | + | 50.5776i | −0.222342 | + | 0.223795i | ||||
\(227\) | 9.56722 | + | 5.52364i | 0.0421463 | + | 0.0243332i | 0.520925 | − | 0.853602i | \(-0.325587\pi\) |
−0.478779 | + | 0.877936i | \(0.658920\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.1725 | − | 28.0116i | −0.0706222 | − | 0.122321i | 0.828552 | − | 0.559912i | \(-0.189165\pi\) |
−0.899174 | + | 0.437591i | \(0.855832\pi\) | |||||||
\(230\) | 131.883 | − | 498.683i | 0.573403 | − | 2.16818i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −146.182 | + | 40.7039i | −0.630094 | + | 0.175448i | ||||
\(233\) | −181.049 | −0.777036 | −0.388518 | − | 0.921441i | \(-0.627013\pi\) | ||||
−0.388518 | + | 0.921441i | \(0.627013\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 488.442i | − | 2.07848i | ||||||
\(236\) | 69.8510 | − | 122.826i | 0.295979 | − | 0.520448i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.19335 | + | 4.51237i | −0.00501408 | + | 0.0189595i | ||||
\(239\) | −39.6432 | + | 22.8880i | −0.165871 | + | 0.0957658i | −0.580638 | − | 0.814162i | \(-0.697197\pi\) |
0.414766 | + | 0.909928i | \(0.363863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 169.216 | − | 293.090i | 0.702140 | − | 1.21614i | −0.265573 | − | 0.964091i | \(-0.585561\pi\) |
0.967714 | − | 0.252052i | \(-0.0811054\pi\) | |||||||
\(242\) | −150.607 | + | 151.591i | −0.622342 | + | 0.626408i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.75962 | + | 270.194i | 0.00721154 | + | 1.10735i | ||||
\(245\) | 115.665 | − | 200.338i | 0.472102 | − | 0.817704i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 100.260 | − | 57.8852i | 0.405911 | − | 0.234353i | ||||
\(248\) | 117.507 | + | 30.2588i | 0.473818 | + | 0.122011i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 63.3476 | + | 233.374i | 0.253390 | + | 0.933496i | ||||
\(251\) | 282.587i | 1.12585i | 0.826510 | + | 0.562923i | \(0.190323\pi\) | ||||
−0.826510 | + | 0.562923i | \(0.809677\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 120.366 | 0.475754 | ||||||||
\(254\) | −18.9391 | + | 5.14086i | −0.0745632 | + | 0.0202396i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −133.731 | − | 218.293i | −0.522387 | − | 0.852708i | ||||
\(257\) | −38.8897 | − | 67.3589i | −0.151322 | − | 0.262097i | 0.780392 | − | 0.625291i | \(-0.215020\pi\) |
−0.931714 | + | 0.363194i | \(0.881686\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.31055 | + | 1.33399i | 0.00892102 | + | 0.00515056i | ||||
\(260\) | 1.48101 | + | 227.414i | 0.00569620 | + | 0.874668i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −166.388 | − | 165.308i | −0.635070 | − | 0.630947i | ||||
\(263\) | −195.201 | − | 112.700i | −0.742211 | − | 0.428516i | 0.0806619 | − | 0.996742i | \(-0.474297\pi\) |
−0.822873 | + | 0.568226i | \(0.807630\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.67970 | + | 4.64138i | 0.0101121 | + | 0.0175146i | ||||
\(266\) | 143.036 | + | 37.8277i | 0.537730 | + | 0.142209i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −170.036 | + | 298.991i | −0.634462 | + | 1.11564i | ||||
\(269\) | −425.808 | −1.58293 | −0.791465 | − | 0.611214i | \(-0.790681\pi\) | ||||
−0.791465 | + | 0.611214i | \(0.790681\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 56.3665i | 0.207995i | 0.994578 | + | 0.103997i | \(0.0331633\pi\) | ||||
−0.994578 | + | 0.103997i | \(0.966837\pi\) | |||||||
\(272\) | −4.04931 | + | 7.22945i | −0.0148872 | + | 0.0265788i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 485.725 | + | 128.456i | 1.77272 | + | 0.468817i | ||||
\(275\) | −130.328 | + | 75.2450i | −0.473920 | + | 0.273618i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −209.641 | + | 363.109i | −0.756828 | + | 1.31086i | 0.187633 | + | 0.982239i | \(0.439918\pi\) |
−0.944461 | + | 0.328625i | \(0.893415\pi\) | |||||||
\(278\) | −218.014 | − | 216.599i | −0.784223 | − | 0.779132i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −203.496 | + | 207.511i | −0.726771 | + | 0.741110i | ||||
\(281\) | 73.9638 | − | 128.109i | 0.263216 | − | 0.455904i | −0.703878 | − | 0.710320i | \(-0.748550\pi\) |
0.967095 | + | 0.254416i | \(0.0818833\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −229.852 | + | 132.705i | −0.812198 | + | 0.468923i | −0.847719 | − | 0.530446i | \(-0.822024\pi\) |
0.0355207 | + | 0.999369i | \(0.488691\pi\) | |||||||
\(284\) | 114.158 | + | 194.786i | 0.401964 | + | 0.685867i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −51.2139 | + | 13.9016i | −0.179070 | + | 0.0486070i | ||||
\(287\) | − | 111.544i | − | 0.388656i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −288.732 | −0.999072 | ||||||||
\(290\) | 80.1191 | + | 295.161i | 0.276273 | + | 1.01780i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −455.259 | + | 266.812i | −1.55911 | + | 0.913740i | ||||
\(293\) | −124.844 | − | 216.236i | −0.426088 | − | 0.738006i | 0.570433 | − | 0.821344i | \(-0.306775\pi\) |
−0.996521 | + | 0.0833379i | \(0.973442\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −246.636 | − | 142.395i | −0.836054 | − | 0.482696i | ||||
\(296\) | 3.38176 | + | 3.31633i | 0.0114249 | + | 0.0112038i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 129.301 | − | 130.146i | 0.433895 | − | 0.436730i | ||||
\(299\) | −195.378 | − | 112.801i | −0.653438 | − | 0.377262i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −72.5056 | − | 125.583i | −0.240883 | − | 0.417221i | ||||
\(302\) | −21.2689 | + | 80.4232i | −0.0704269 | + | 0.266302i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 229.164 | + | 128.358i | 0.753829 | + | 0.422229i | ||||
\(305\) | 544.594 | 1.78555 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 259.968i | 0.846801i | 0.905943 | + | 0.423401i | \(0.139164\pi\) | ||||
−0.905943 | + | 0.423401i | \(0.860836\pi\) | |||||||
\(308\) | −58.9529 | − | 33.5265i | −0.191406 | − | 0.108852i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 62.5283 | − | 236.436i | 0.201704 | − | 0.762695i | ||||
\(311\) | −16.5959 | + | 9.58164i | −0.0533630 | + | 0.0308091i | −0.526444 | − | 0.850210i | \(-0.676475\pi\) |
0.473081 | + | 0.881019i | \(0.343142\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.9358 | + | 37.9939i | −0.0700823 | + | 0.121386i | −0.898937 | − | 0.438078i | \(-0.855660\pi\) |
0.828855 | + | 0.559464i | \(0.188993\pi\) | |||||||
\(314\) | 318.314 | − | 320.394i | 1.01374 | − | 1.02036i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 585.972 | − | 3.81610i | 1.85434 | − | 0.0120763i | ||||
\(317\) | −68.9690 | + | 119.458i | −0.217568 | + | 0.376838i | −0.954064 | − | 0.299603i | \(-0.903146\pi\) |
0.736496 | + | 0.676442i | \(0.236479\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −61.8054 | + | 35.6834i | −0.193747 | + | 0.111860i | ||||
\(320\) | −441.721 | + | 266.667i | −1.38038 | + | 0.833335i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −75.5289 | − | 278.250i | −0.234562 | − | 0.864132i | ||||
\(323\) | − | 8.50191i | − | 0.0263217i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 282.065 | 0.867892 | ||||||||
\(326\) | 241.607 | − | 65.5824i | 0.741127 | − | 0.201173i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 49.3818 | − | 191.769i | 0.150554 | − | 0.584662i | ||||
\(329\) | −136.506 | − | 236.436i | −0.414912 | − | 0.718649i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 51.7490 | + | 29.8773i | 0.156341 | + | 0.0902638i | 0.576130 | − | 0.817358i | \(-0.304562\pi\) |
−0.419788 | + | 0.907622i | \(0.637896\pi\) | |||||||
\(332\) | −402.303 | + | 2.61996i | −1.21176 | + | 0.00789145i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −252.910 | − | 251.268i | −0.757215 | − | 0.752300i | ||||
\(335\) | 600.378 | + | 346.628i | 1.79217 | + | 1.03471i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 224.356 | + | 388.595i | 0.665743 | + | 1.15310i | 0.979083 | + | 0.203460i | \(0.0652188\pi\) |
−0.313340 | + | 0.949641i | \(0.601448\pi\) | |||||||
\(338\) | −230.608 | − | 60.9870i | −0.682271 | − | 0.180435i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 14.5177 | + | 8.25618i | 0.0426990 | + | 0.0242829i | ||||
\(341\) | 57.0679 | 0.167355 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 350.108i | − | 1.02072i | ||||||
\(344\) | −69.0561 | − | 248.004i | −0.200744 | − | 0.720943i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −292.312 | − | 77.3056i | −0.844833 | − | 0.223426i | ||||
\(347\) | 500.441 | − | 288.930i | 1.44219 | − | 0.832651i | 0.444198 | − | 0.895929i | \(-0.353489\pi\) |
0.997996 | + | 0.0632779i | \(0.0201555\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 66.1311 | − | 114.542i | 0.189487 | − | 0.328202i | −0.755592 | − | 0.655042i | \(-0.772651\pi\) |
0.945079 | + | 0.326841i | \(0.105984\pi\) | |||||||
\(350\) | 255.724 | + | 254.064i | 0.730641 | + | 0.725898i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −86.5105 | − | 83.7384i | −0.245768 | − | 0.237893i | ||||
\(353\) | −270.562 | + | 468.628i | −0.766465 | + | 1.32756i | 0.173003 | + | 0.984921i | \(0.444653\pi\) |
−0.939468 | + | 0.342636i | \(0.888680\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 394.086 | − | 227.526i | 1.11010 | − | 0.640918i | ||||
\(356\) | −89.1609 | + | 52.2542i | −0.250452 | + | 0.146782i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 534.320 | − | 145.037i | 1.49251 | − | 0.405131i | ||||
\(359\) | 292.754i | 0.815470i | 0.913100 | + | 0.407735i | \(0.133681\pi\) | ||||
−0.913100 | + | 0.407735i | \(0.866319\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 91.5006 | 0.253464 | ||||||||
\(362\) | 54.8701 | + | 202.143i | 0.151575 | + | 0.558406i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 64.2728 | + | 109.668i | 0.176574 | + | 0.301286i | ||||
\(365\) | 531.779 | + | 921.067i | 1.45693 | + | 2.52347i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 378.870 | + | 218.741i | 1.03234 | + | 0.596024i | 0.917655 | − | 0.397377i | \(-0.130080\pi\) |
0.114689 | + | 0.993401i | \(0.463413\pi\) | |||||||
\(368\) | −6.66653 | − | 511.811i | −0.0181156 | − | 1.39079i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.72838 | − | 6.77234i | 0.0181848 | − | 0.0183036i | ||||
\(371\) | 2.59428 | + | 1.49781i | 0.00699266 | + | 0.00403721i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −352.979 | − | 611.377i | −0.946323 | − | 1.63908i | −0.753080 | − | 0.657929i | \(-0.771433\pi\) |
−0.193243 | − | 0.981151i | \(-0.561901\pi\) | |||||||
\(374\) | −0.996388 | + | 3.76760i | −0.00266414 | + | 0.0100738i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −130.012 | − | 466.917i | −0.345776 | − | 1.24180i | ||||
\(377\) | 133.763 | 0.354810 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 541.432i | 1.42858i | 0.699850 | + | 0.714290i | \(0.253250\pi\) | ||||
−0.699850 | + | 0.714290i | \(0.746750\pi\) | |||||||
\(380\) | 261.710 | − | 460.191i | 0.688711 | − | 1.21103i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −113.941 | + | 430.838i | −0.298274 | + | 1.12785i | ||||
\(383\) | −311.941 | + | 180.099i | −0.814467 | + | 0.470233i | −0.848505 | − | 0.529188i | \(-0.822497\pi\) |
0.0340377 | + | 0.999421i | \(0.489163\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −68.3458 | + | 118.378i | −0.177521 | + | 0.307476i | ||||
\(386\) | 159.790 | − | 160.834i | 0.413963 | − | 0.416667i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.51391 | − | 386.019i | −0.00647916 | − | 0.994893i | ||||
\(389\) | 43.9057 | − | 76.0468i | 0.112868 | − | 0.195493i | −0.804057 | − | 0.594552i | \(-0.797330\pi\) |
0.916926 | + | 0.399058i | \(0.130663\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.3481 | + | 8.28388i | −0.0366959 | + | 0.0211864i | ||||
\(392\) | 57.2428 | − | 222.296i | 0.146027 | − | 0.567083i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −63.3937 | − | 233.544i | −0.160898 | − | 0.592751i | ||||
\(395\) | − | 1181.07i | − | 2.99004i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −48.4128 | −0.121947 | −0.0609733 | − | 0.998139i | \(-0.519420\pi\) | ||||
−0.0609733 | + | 0.998139i | \(0.519420\pi\) | |||||||
\(398\) | −158.729 | + | 43.0858i | −0.398817 | + | 0.108256i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 327.169 | + | 550.004i | 0.817924 | + | 1.37501i | ||||
\(401\) | −217.859 | − | 377.343i | −0.543290 | − | 0.941005i | −0.998712 | − | 0.0507299i | \(-0.983845\pi\) |
0.455423 | − | 0.890275i | \(-0.349488\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −92.6326 | − | 53.4815i | −0.229858 | − | 0.132708i | ||||
\(404\) | 1.12845 | + | 173.277i | 0.00279319 | + | 0.428902i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 121.272 | + | 120.485i | 0.298699 | + | 0.296761i | ||||
\(407\) | 1.92919 | + | 1.11382i | 0.00474002 | + | 0.00273665i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.1145 | − | 46.9636i | −0.0662945 | − | 0.114825i | 0.830973 | − | 0.556313i | \(-0.187784\pi\) |
−0.897267 | + | 0.441487i | \(0.854451\pi\) | |||||||
\(410\) | −385.859 | − | 102.045i | −0.941119 | − | 0.248891i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 286.415 | − | 503.632i | 0.695183 | − | 1.22241i | ||||
\(413\) | −159.182 | −0.385430 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 810.867i | 1.95390i | ||||||||
\(416\) | 61.9479 | + | 216.998i | 0.148913 | + | 0.521630i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 119.428 | + | 31.5842i | 0.285713 | + | 0.0755603i | ||||
\(419\) | −552.029 | + | 318.714i | −1.31749 | + | 0.760655i | −0.983325 | − | 0.181859i | \(-0.941789\pi\) |
−0.334168 | + | 0.942514i | \(0.608455\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −95.7757 | + | 165.888i | −0.227496 | + | 0.394034i | −0.957065 | − | 0.289873i | \(-0.906387\pi\) |
0.729570 | + | 0.683907i | \(0.239720\pi\) | |||||||
\(422\) | 153.315 | + | 152.320i | 0.363307 | + | 0.360948i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.79704 | + | 3.72357i | 0.00895527 | + | 0.00878200i | ||||
\(425\) | 10.3571 | − | 17.9390i | 0.0243696 | − | 0.0422095i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 263.617 | − | 152.199i | 0.617369 | − | 0.356438i | ||||
\(428\) | 111.210 | + | 189.757i | 0.259837 | + | 0.443358i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −500.754 | + | 135.926i | −1.16454 | + | 0.316107i | ||||
\(431\) | 481.190i | 1.11645i | 0.829689 | + | 0.558225i | \(0.188518\pi\) | ||||
−0.829689 | + | 0.558225i | \(0.811482\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −360.347 | −0.832209 | −0.416105 | − | 0.909317i | \(-0.636605\pi\) | ||||
−0.416105 | + | 0.909317i | \(0.636605\pi\) | |||||||
\(434\) | −35.8098 | − | 131.924i | −0.0825110 | − | 0.303973i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 220.600 | − | 129.286i | 0.505964 | − | 0.296528i | ||||
\(437\) | 262.588 | + | 454.816i | 0.600888 | + | 1.04077i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −488.267 | − | 281.901i | −1.11223 | − | 0.642144i | −0.172821 | − | 0.984953i | \(-0.555288\pi\) |
−0.939405 | + | 0.342809i | \(0.888622\pi\) | |||||||
\(440\) | −169.909 | + | 173.261i | −0.386156 | + | 0.393775i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.14816 | − | 5.18180i | 0.0116474 | − | 0.0117235i | ||||
\(443\) | 569.917 | + | 329.042i | 1.28649 | + | 0.742757i | 0.978027 | − | 0.208478i | \(-0.0668509\pi\) |
0.308467 | + | 0.951235i | \(0.400184\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 104.147 | + | 180.388i | 0.234038 | + | 0.405366i | ||||
\(446\) | 83.4895 | − | 315.695i | 0.187196 | − | 0.707837i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −139.294 | + | 252.532i | −0.310924 | + | 0.563688i | ||||
\(449\) | −227.569 | −0.506836 | −0.253418 | − | 0.967357i | \(-0.581555\pi\) | ||||
−0.253418 | + | 0.967357i | \(0.581555\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 93.1339i | − | 0.206505i | ||||||
\(452\) | 123.950 | + | 70.4901i | 0.274225 | + | 0.155951i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.64897 | − | 21.3602i | 0.0124427 | − | 0.0470489i | ||||
\(455\) | 221.878 | − | 128.101i | 0.487643 | − | 0.281541i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −358.879 | + | 621.596i | −0.785292 | + | 1.36017i | 0.143532 | + | 0.989646i | \(0.454154\pi\) |
−0.928824 | + | 0.370520i | \(0.879179\pi\) | |||||||
\(458\) | −45.5935 | + | 45.8914i | −0.0995492 | + | 0.100200i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1031.63 | + | 6.71842i | −2.24268 | + | 0.0146053i | ||||
\(461\) | 200.873 | − | 347.922i | 0.435733 | − | 0.754712i | −0.561622 | − | 0.827394i | \(-0.689822\pi\) |
0.997355 | + | 0.0726819i | \(0.0231558\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 396.754 | − | 229.066i | 0.856920 | − | 0.494743i | −0.00605956 | − | 0.999982i | \(-0.501929\pi\) |
0.862980 | + | 0.505239i | \(0.168595\pi\) | |||||||
\(464\) | 155.153 | + | 260.828i | 0.334382 | + | 0.562129i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 94.8565 | + | 349.454i | 0.203555 | + | 0.749900i | ||||
\(467\) | 204.395i | 0.437677i | 0.975761 | + | 0.218838i | \(0.0702267\pi\) | ||||
−0.975761 | + | 0.218838i | \(0.929773\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 387.493 | 0.826210 | ||||||||
\(470\) | −942.769 | + | 255.907i | −2.00589 | + | 0.544483i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −273.670 | − | 70.4717i | −0.579808 | − | 0.149304i | ||||
\(473\) | −60.5385 | − | 104.856i | −0.127988 | − | 0.221682i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −568.643 | − | 328.306i | −1.19714 | − | 0.691172i | ||||
\(476\) | 9.33481 | − | 0.0607922i | 0.0196109 | − | 0.000127715i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 64.9475 | + | 64.5259i | 0.135874 | + | 0.134992i | ||||
\(479\) | 78.4548 | + | 45.2959i | 0.163789 | + | 0.0945634i | 0.579654 | − | 0.814863i | \(-0.303188\pi\) |
−0.415865 | + | 0.909426i | \(0.636521\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.08764 | − | 3.61589i | −0.00434020 | − | 0.00751745i | ||||
\(482\) | −654.367 | − | 173.055i | −1.35761 | − | 0.359036i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 371.501 | + | 211.272i | 0.767563 | + | 0.436513i | ||||
\(485\) | −778.046 | −1.60422 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 301.289i | − | 0.618663i | −0.950954 | − | 0.309332i | \(-0.899895\pi\) | ||
0.950954 | − | 0.309332i | \(-0.100105\pi\) | |||||||
\(488\) | 520.595 | − | 144.958i | 1.06679 | − | 0.297045i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −447.283 | − | 118.289i | −0.912822 | − | 0.241407i | ||||
\(491\) | 389.556 | − | 224.911i | 0.793394 | − | 0.458066i | −0.0477620 | − | 0.998859i | \(-0.515209\pi\) |
0.841156 | + | 0.540792i | \(0.181876\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.91164 | − | 8.50721i | 0.00996276 | − | 0.0172560i | ||||
\(494\) | −164.256 | − | 163.190i | −0.332502 | − | 0.330344i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.16074 | − | 242.660i | −0.00637246 | − | 0.489234i | ||||
\(497\) | 127.175 | − | 220.273i | 0.255884 | − | 0.443205i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −552.630 | + | 319.061i | −1.10748 | + | 0.639401i | −0.938174 | − | 0.346163i | \(-0.887484\pi\) |
−0.169301 | + | 0.985564i | \(0.554151\pi\) | |||||||
\(500\) | 417.259 | − | 244.541i | 0.834518 | − | 0.489083i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 545.437 | − | 148.055i | 1.08653 | − | 0.294930i | ||||
\(503\) | − | 182.179i | − | 0.362185i | −0.983466 | − | 0.181093i | \(-0.942037\pi\) | ||
0.983466 | − | 0.181093i | \(-0.0579634\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 349.250 | 0.691585 | ||||||||
\(506\) | −63.0628 | − | 232.325i | −0.124630 | − | 0.459140i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 19.8453 | + | 33.8619i | 0.0390656 | + | 0.0666573i | ||||
\(509\) | −471.123 | − | 816.009i | −0.925585 | − | 1.60316i | −0.790617 | − | 0.612311i | \(-0.790240\pi\) |
−0.134968 | − | 0.990850i | \(-0.543093\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 514.827 | + | 297.235i | 1.00749 | + | 0.581674i | ||||
\(512\) | −351.275 | + | 372.491i | −0.686084 | + | 0.727522i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −109.638 | + | 110.354i | −0.213303 | + | 0.214697i | ||||
\(515\) | −1011.30 | − | 583.875i | −1.96369 | − | 1.13374i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −113.976 | − | 197.412i | −0.220456 | − | 0.381841i | ||||
\(518\) | 1.36426 | − | 5.15863i | 0.00263371 | − | 0.00995874i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 438.168 | − | 122.007i | 0.842631 | − | 0.234628i | ||||
\(521\) | 634.330 | 1.21752 | 0.608762 | − | 0.793353i | \(-0.291666\pi\) | ||||
0.608762 | + | 0.793353i | \(0.291666\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 534.777i | − | 1.02252i | −0.859426 | − | 0.511259i | \(-0.829179\pi\) | ||
0.859426 | − | 0.511259i | \(-0.170821\pi\) | |||||||
\(524\) | −231.896 | + | 407.765i | −0.442549 | + | 0.778177i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −115.257 | + | 435.815i | −0.219119 | + | 0.828546i | ||||
\(527\) | −6.80273 | + | 3.92756i | −0.0129084 | + | 0.00745267i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 247.208 | − | 428.178i | 0.467313 | − | 0.809409i | ||||
\(530\) | 7.55461 | − | 7.60397i | 0.0142540 | − | 0.0143471i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.92703 | − | 295.901i | −0.00362224 | − | 0.556205i | ||||
\(533\) | −87.2809 | + | 151.175i | −0.163754 | + | 0.283630i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 383.912 | − | 221.652i | 0.717592 | − | 0.414302i | ||||
\(536\) | 666.185 | + | 171.547i | 1.24288 | + | 0.320050i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 223.092 | + | 821.876i | 0.414669 | + | 1.52765i | ||||
\(539\) | − | 107.960i | − | 0.200296i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −61.0097 | −0.112772 | −0.0563860 | − | 0.998409i | \(-0.517958\pi\) | ||||
−0.0563860 | + | 0.998409i | \(0.517958\pi\) | |||||||
\(542\) | 108.796 | − | 29.5319i | 0.200731 | − | 0.0544869i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16.0755 | + | 4.02810i | 0.0295505 | + | 0.00740459i | ||||
\(545\) | −257.678 | − | 446.312i | −0.472805 | − | 0.818921i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −104.430 | − | 60.2925i | −0.190914 | − | 0.110224i | 0.401497 | − | 0.915861i | \(-0.368490\pi\) |
−0.592410 | + | 0.805637i | \(0.701823\pi\) | |||||||
\(548\) | −6.54385 | − | 1004.83i | −0.0119413 | − | 1.83362i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 213.517 | + | 212.131i | 0.388212 | + | 0.385692i | ||||
\(551\) | −269.667 | − | 155.693i | −0.489415 | − | 0.282564i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −330.076 | − | 571.708i | −0.596882 | − | 1.03383i | ||||
\(554\) | 810.694 | + | 214.398i | 1.46335 | + | 0.387000i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −303.846 | + | 534.283i | −0.546486 | + | 0.960940i | ||||
\(557\) | 527.461 | 0.946968 | 0.473484 | − | 0.880802i | \(-0.342996\pi\) | ||||
0.473484 | + | 0.880802i | \(0.342996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 226.936i | 0.405967i | ||||||||
\(560\) | 507.145 | + | 284.058i | 0.905616 | + | 0.507247i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −286.022 | − | 75.6420i | −0.508936 | − | 0.134594i | ||||
\(563\) | −595.478 | + | 343.800i | −1.05769 | + | 0.610656i | −0.924792 | − | 0.380474i | \(-0.875761\pi\) |
−0.132896 | + | 0.991130i | \(0.542428\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 143.698 | − | 248.893i | 0.254333 | − | 0.440518i | ||||
\(566\) | 376.567 | + | 374.123i | 0.665313 | + | 0.660994i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 316.158 | − | 322.396i | 0.556616 | − | 0.567598i | ||||
\(569\) | −293.677 | + | 508.664i | −0.516128 | + | 0.893961i | 0.483696 | + | 0.875236i | \(0.339294\pi\) |
−0.999825 | + | 0.0187248i | \(0.994039\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −742.245 | + | 428.535i | −1.29990 | + | 0.750500i | −0.980387 | − | 0.197081i | \(-0.936854\pi\) |
−0.319517 | + | 0.947581i | \(0.603521\pi\) | |||||||
\(572\) | 53.6645 | + | 91.5674i | 0.0938191 | + | 0.160083i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −215.298 | + | 58.4410i | −0.375084 | + | 0.101814i | ||||
\(575\) | 1279.55i | 2.22530i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 871.732 | 1.51080 | 0.755401 | − | 0.655263i | \(-0.227442\pi\) | ||||
0.755401 | + | 0.655263i | \(0.227442\pi\) | |||||||
\(578\) | 151.274 | + | 557.297i | 0.261720 | + | 0.964182i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 527.730 | − | 309.285i | 0.909880 | − | 0.533250i | ||||
\(581\) | 226.615 | + | 392.509i | 0.390044 | + | 0.675575i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.16609 | + | 1.25059i | 0.00371542 | + | 0.00214510i | ||||
\(584\) | 753.511 | + | 738.931i | 1.29026 | + | 1.26529i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −351.960 | + | 354.259i | −0.600614 | + | 0.604538i | ||||
\(587\) | −700.071 | − | 404.186i | −1.19263 | − | 0.688563i | −0.233725 | − | 0.972303i | \(-0.575091\pi\) |
−0.958901 | + | 0.283740i | \(0.908425\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 124.498 | + | 215.638i | 0.211373 | + | 0.366108i | ||||
\(590\) | −145.626 | + | 550.651i | −0.246824 | + | 0.933306i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.62924 | − | 8.26484i | 0.00781966 | − | 0.0139609i | ||||
\(593\) | 445.123 | 0.750628 | 0.375314 | − | 0.926898i | \(-0.377535\pi\) | ||||
0.375314 | + | 0.926898i | \(0.377535\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 18.8149i | − | 0.0316217i | ||||||
\(596\) | −318.945 | − | 181.384i | −0.535143 | − | 0.304336i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −115.361 | + | 436.209i | −0.192911 | + | 0.729447i | ||||
\(599\) | 684.932 | − | 395.445i | 1.14346 | − | 0.660176i | 0.196174 | − | 0.980569i | \(-0.437148\pi\) |
0.947285 | + | 0.320393i | \(0.103815\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 193.532 | − | 335.208i | 0.322017 | − | 0.557750i | −0.658887 | − | 0.752242i | \(-0.728972\pi\) |
0.980904 | + | 0.194492i | \(0.0623057\pi\) | |||||||
\(602\) | −204.408 | + | 205.744i | −0.339548 | + | 0.341767i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 166.373 | − | 1.08349i | 0.275451 | − | 0.00179385i | ||||
\(605\) | 430.691 | − | 745.979i | 0.711886 | − | 1.23302i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 902.512 | − | 521.066i | 1.48684 | − | 0.858428i | 0.486953 | − | 0.873428i | \(-0.338108\pi\) |
0.999887 | + | 0.0150003i | \(0.00477491\pi\) | |||||||
\(608\) | 127.685 | − | 509.572i | 0.210009 | − | 0.838112i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −285.327 | − | 1051.15i | −0.467749 | − | 1.72320i | ||||
\(611\) | 427.251i | 0.699266i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 256.336 | 0.418166 | 0.209083 | − | 0.977898i | \(-0.432952\pi\) | ||||
0.209083 | + | 0.977898i | \(0.432952\pi\) | |||||||
\(614\) | 501.779 | − | 136.204i | 0.817229 | − | 0.221831i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −33.8244 | + | 131.354i | −0.0549098 | + | 0.213237i | ||||
\(617\) | 253.519 | + | 439.108i | 0.410890 | + | 0.711683i | 0.994987 | − | 0.100001i | \(-0.0318846\pi\) |
−0.584097 | + | 0.811684i | \(0.698551\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −662.787 | − | 382.660i | −1.07074 | − | 0.618191i | −0.142355 | − | 0.989816i | \(-0.545468\pi\) |
−0.928383 | + | 0.371624i | \(0.878801\pi\) | |||||||
\(620\) | −489.118 | + | 3.18534i | −0.788900 | + | 0.00513764i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 27.1891 | + | 27.0126i | 0.0437123 | + | 0.0434286i | ||||
\(623\) | 100.827 | + | 58.2125i | 0.161841 | + | 0.0934390i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.5746 | + | 21.7799i | 0.0201194 | + | 0.0348479i | ||||
\(626\) | 84.8268 | + | 22.4335i | 0.135506 | + | 0.0358362i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −785.183 | − | 446.533i | −1.25029 | − | 0.711040i | ||||
\(629\) | −0.306623 | −0.000487477 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 719.756i | − | 1.14066i | −0.821416 | − | 0.570330i | \(-0.806815\pi\) | ||
0.821416 | − | 0.570330i | \(-0.193185\pi\) | |||||||
\(632\) | −314.372 | − | 1129.02i | −0.497423 | − | 1.78642i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 266.707 | + | 70.5338i | 0.420673 | + | 0.111252i | ||||
\(635\) | 68.5084 | − | 39.5534i | 0.107887 | − | 0.0622888i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −101.175 | + | 175.240i | −0.158830 | + | 0.275102i | ||||
\(638\) | 101.256 | + | 100.599i | 0.158708 | + | 0.157678i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 746.138 | + | 712.877i | 1.16584 | + | 1.11387i | ||||
\(641\) | −351.516 | + | 608.844i | −0.548388 | + | 0.949835i | 0.449998 | + | 0.893030i | \(0.351425\pi\) |
−0.998385 | + | 0.0568054i | \(0.981909\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −507.224 | + | 292.846i | −0.788841 | + | 0.455437i | −0.839554 | − | 0.543276i | \(-0.817184\pi\) |
0.0507136 | + | 0.998713i | \(0.483850\pi\) | |||||||
\(644\) | −497.495 | + | 291.565i | −0.772508 | + | 0.452741i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.4100 | + | 4.45437i | −0.0254025 | + | 0.00689531i | ||||
\(647\) | − | 791.553i | − | 1.22342i | −0.791082 | − | 0.611710i | \(-0.790482\pi\) | ||
0.791082 | − | 0.611710i | \(-0.209518\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −132.909 | −0.204791 | ||||||||
\(650\) | −147.781 | − | 544.429i | −0.227355 | − | 0.837583i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −253.169 | − | 431.980i | −0.388296 | − | 0.662545i | ||||
\(653\) | 196.385 | + | 340.148i | 0.300742 | + | 0.520901i | 0.976304 | − | 0.216402i | \(-0.0694323\pi\) |
−0.675562 | + | 0.737303i | \(0.736099\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 818.797 | + | 472.733i | 1.25007 | + | 0.721730i | ||||
\(656\) | −396.017 | + | 5.15827i | −0.603685 | + | 0.00786322i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −384.838 | + | 387.353i | −0.584861 | + | 0.588682i | ||||
\(659\) | 372.557 | + | 215.096i | 0.565337 | + | 0.326398i | 0.755285 | − | 0.655397i | \(-0.227499\pi\) |
−0.189948 | + | 0.981794i | \(0.560832\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 453.865 | + | 786.117i | 0.686633 | + | 1.18928i | 0.972920 | + | 0.231140i | \(0.0742456\pi\) |
−0.286287 | + | 0.958144i | \(0.592421\pi\) | |||||||
\(662\) | 30.5552 | − | 115.537i | 0.0461559 | − | 0.174527i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 215.834 | + | 775.134i | 0.325051 | + | 1.16737i | ||||
\(665\) | −596.408 | −0.896854 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 606.799i | 0.909744i | ||||||||
\(668\) | −352.481 | + | 619.801i | −0.527666 | + | 0.927846i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 354.493 | − | 1340.43i | 0.529094 | − | 2.00064i | ||||
\(671\) | 220.106 | − | 127.078i | 0.328027 | − | 0.189387i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.8528 | + | 60.3668i | −0.0517872 | + | 0.0896980i | −0.890757 | − | 0.454480i | \(-0.849825\pi\) |
0.838970 | + | 0.544178i | \(0.183158\pi\) | |||||||
\(674\) | 632.504 | − | 636.636i | 0.938433 | − | 0.944564i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.10682 | + | 477.062i | 0.00459589 | + | 0.705712i | ||||
\(677\) | 144.502 | − | 250.285i | 0.213444 | − | 0.369697i | −0.739346 | − | 0.673326i | \(-0.764865\pi\) |
0.952790 | + | 0.303629i | \(0.0981984\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −376.622 | + | 217.443i | −0.554671 | + | 0.320239i | ||||
\(680\) | 8.32955 | − | 32.3470i | 0.0122493 | − | 0.0475691i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −29.8993 | − | 110.150i | −0.0438407 | − | 0.161510i | ||||
\(683\) | − | 522.729i | − | 0.765343i | −0.923884 | − | 0.382672i | \(-0.875004\pi\) | ||
0.923884 | − | 0.382672i | \(-0.124996\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2025.29 | −2.95663 | ||||||||
\(686\) | −675.763 | + | 183.431i | −0.985077 | + | 0.267392i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −442.507 | + | 263.225i | −0.643179 | + | 0.382594i | ||||
\(689\) | −2.34400 | − | 4.05992i | −0.00340203 | − | 0.00589248i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 485.917 | + | 280.544i | 0.703208 | + | 0.405997i | 0.808541 | − | 0.588440i | \(-0.200258\pi\) |
−0.105333 | + | 0.994437i | \(0.533591\pi\) | |||||||
\(692\) | 3.93813 | + | 604.711i | 0.00569093 | + | 0.873859i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −819.874 | − | 814.552i | −1.18137 | − | 1.17371i | ||||
\(695\) | 1072.85 | + | 619.409i | 1.54367 | + | 0.891236i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.40971 | + | 11.1019i | 0.00919614 | + | 0.0159282i | ||||
\(698\) | −255.733 | − | 67.6316i | −0.366379 | − | 0.0968934i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 356.403 | − | 626.699i | 0.509148 | − | 0.895284i | ||||
\(701\) | −1203.11 | −1.71627 | −0.858137 | − | 0.513421i | \(-0.828378\pi\) | ||||
−0.858137 | + | 0.513421i | \(0.828378\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.71954i | 0.0138258i | ||||||||
\(704\) | −116.303 | + | 210.851i | −0.165203 | + | 0.299505i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1046.28 | + | 276.701i | 1.48198 | + | 0.391928i | ||||
\(707\) | 169.058 | − | 97.6059i | 0.239121 | − | 0.138056i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 89.2724 | − | 154.624i | 0.125913 | − | 0.218088i | −0.796176 | − | 0.605065i | \(-0.793147\pi\) |
0.922090 | + | 0.386977i | \(0.126481\pi\) | |||||||
\(710\) | −645.632 | − | 641.441i | −0.909341 | − | 0.903439i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 147.572 | + | 144.717i | 0.207265 | + | 0.203254i | ||||
\(713\) | 242.611 | − | 420.215i | 0.340269 | − | 0.589362i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 185.257 | − | 106.958i | 0.259100 | − | 0.149591i | ||||
\(716\) | −559.888 | − | 955.332i | −0.781966 | − | 1.33426i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 565.061 | − | 153.381i | 0.786993 | − | 0.213623i | ||||
\(719\) | 53.0278i | 0.0737521i | 0.999320 | + | 0.0368760i | \(0.0117407\pi\) | ||||
−0.999320 | + | 0.0368760i | \(0.988259\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −652.709 | −0.905282 | ||||||||
\(722\) | −47.9395 | − | 176.610i | −0.0663982 | − | 0.244613i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 361.419 | − | 211.816i | 0.499198 | − | 0.292563i | ||||
\(725\) | −379.332 | − | 657.022i | −0.523216 | − | 0.906238i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 436.956 | + | 252.277i | 0.601041 | + | 0.347011i | 0.769451 | − | 0.638706i | \(-0.220530\pi\) |
−0.168410 | + | 0.985717i | \(0.553863\pi\) | |||||||
\(728\) | 178.003 | − | 181.515i | 0.244509 | − | 0.249333i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1499.19 | − | 1508.99i | 2.05369 | − | 2.06710i | ||||
\(731\) | 14.4329 | + | 8.33283i | 0.0197440 | + | 0.0113992i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 410.964 | + | 711.811i | 0.560660 | + | 0.971092i | 0.997439 | + | 0.0715233i | \(0.0227860\pi\) |
−0.436779 | + | 0.899569i | \(0.643881\pi\) | |||||||
\(734\) | 223.704 | − | 845.883i | 0.304774 | − | 1.15243i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −984.382 | + | 281.018i | −1.33748 | + | 0.381818i | ||||
\(737\) | 323.536 | 0.438991 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 190.298i | 0.257507i | 0.991677 | + | 0.128754i | \(0.0410977\pi\) | ||||
−0.991677 | + | 0.128754i | \(0.958902\pi\) | |||||||
\(740\) | −16.5969 | − | 9.43862i | −0.0224282 | − | 0.0127549i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.53179 | − | 5.79210i | 0.00206441 | − | 0.00780606i | ||||
\(743\) | −664.128 | + | 383.435i | −0.893847 | + | 0.516063i | −0.875199 | − | 0.483763i | \(-0.839270\pi\) |
−0.0186481 | + | 0.999826i | \(0.505936\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −369.762 | + | 640.447i | −0.496325 | + | 0.859660i | ||||
\(746\) | −995.118 | + | 1001.62i | −1.33394 | + | 1.34265i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.79409 | − | 0.0507583i | 0.0104199 | − | 6.78587e-5i | ||||
\(749\) | 123.891 | − | 214.586i | 0.165409 | − | 0.286496i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −519.601 | + | 299.992i | −0.691879 | + | 0.399456i | −0.804315 | − | 0.594202i | \(-0.797468\pi\) |
0.112437 | + | 0.993659i | \(0.464134\pi\) | |||||||
\(752\) | −833.107 | + | 495.573i | −1.10785 | + | 0.659006i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −70.0821 | − | 258.184i | −0.0929471 | − | 0.342419i | ||||
\(755\) | − | 335.335i | − | 0.444152i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −343.082 | −0.453213 | −0.226606 | − | 0.973986i | \(-0.572763\pi\) | ||||
−0.226606 | + | 0.973986i | \(0.572763\pi\) | |||||||
\(758\) | 1045.05 | − | 283.670i | 1.37869 | − | 0.374235i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1025.36 | − | 264.036i | −1.34915 | − | 0.347416i | ||||
\(761\) | 149.365 | + | 258.708i | 0.196275 | + | 0.339958i | 0.947318 | − | 0.320295i | \(-0.103782\pi\) |
−0.751043 | + | 0.660253i | \(0.770449\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −249.464 | − | 144.028i | −0.326952 | − | 0.188766i | ||||
\(764\) | 891.282 | − | 5.80440i | 1.16660 | − | 0.00759738i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 511.053 | + | 507.736i | 0.667171 | + | 0.662841i | ||||
\(767\) | 215.738 | + | 124.557i | 0.281275 | + | 0.162394i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −466.241 | − | 807.553i | −0.606295 | − | 1.05013i | −0.991845 | − | 0.127447i | \(-0.959322\pi\) |
0.385550 | − | 0.922687i | \(-0.374012\pi\) | |||||||
\(770\) | 264.297 | + | 69.8965i | 0.343243 | + | 0.0907747i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −394.152 | − | 224.154i | −0.510559 | − | 0.290355i | ||||
\(773\) | 173.239 | 0.224113 | 0.112056 | − | 0.993702i | \(-0.464256\pi\) | ||||
0.112056 | + | 0.993702i | \(0.464256\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 606.660i | 0.782787i | ||||||||
\(776\) | −743.759 | + | 207.097i | −0.958452 | + | 0.266878i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −169.786 | − | 44.9019i | −0.218233 | − | 0.0577145i | ||||
\(779\) | 351.917 | − | 203.179i | 0.451755 | − | 0.260821i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 106.184 | − | 183.916i | 0.135959 | − | 0.235488i | ||||
\(782\) | 23.5065 | + | 23.3539i | 0.0300595 | + | 0.0298644i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −459.058 | + | 5.97940i | −0.585533 | + | 0.00762679i | ||||
\(785\) | −910.285 | + | 1576.66i | −1.15960 | + | 2.00848i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.1896 | − | 24.9355i | 0.0548788 | − | 0.0316843i | −0.472310 | − | 0.881433i | \(-0.656580\pi\) |
0.527188 | + | 0.849748i | \(0.323246\pi\) | |||||||
\(788\) | −417.563 | + | 244.719i | −0.529902 | + | 0.310558i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2279.64 | + | 618.791i | −2.88562 | + | 0.783279i | ||||
\(791\) | − | 160.639i | − | 0.203083i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −476.369 | −0.600717 | ||||||||
\(794\) | 25.3647 | + | 93.4443i | 0.0319455 | + | 0.117688i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 166.324 | + | 283.798i | 0.208950 | + | 0.356530i | ||||
\(797\) | 513.753 | + | 889.846i | 0.644608 | + | 1.11649i | 0.984392 | + | 0.175991i | \(0.0563129\pi\) |
−0.339784 | + | 0.940504i | \(0.610354\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.1727 | + | 15.6882i | 0.0340084 | + | 0.0196348i | ||||
\(800\) | 890.181 | − | 919.649i | 1.11273 | − | 1.14956i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −614.189 | + | 618.202i | −0.765822 | + | 0.770825i | ||||
\(803\) | 429.854 | + | 248.176i | 0.535310 | + | 0.309061i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 581.114 | + | 1006.52i | 0.721880 | + | 1.25033i | ||||
\(806\) | −54.6950 | + | 206.816i | −0.0678598 | + | 0.256595i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 333.860 | − | 92.9621i | 0.413193 | − | 0.115052i | ||||
\(809\) | 637.363 | 0.787841 | 0.393920 | − | 0.919145i | \(-0.371119\pi\) | ||||
0.393920 | + | 0.919145i | \(0.371119\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1486.54i | − | 1.83298i | −0.400061 | − | 0.916489i | \(-0.631011\pi\) | ||
0.400061 | − | 0.916489i | \(-0.368989\pi\) | |||||||
\(812\) | 169.017 | − | 297.199i | 0.208149 | − | 0.366009i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.13909 | − | 4.30719i | 0.00139937 | − | 0.00529139i | ||||
\(815\) | −873.969 | + | 504.586i | −1.07235 | + | 0.619124i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 264.140 | − | 457.503i | 0.323304 | − | 0.559980i | ||||
\(818\) | −76.4412 | + | 76.9406i | −0.0934488 | + | 0.0940594i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.19842 | + | 798.232i | 0.00633954 | + | 0.973454i | ||||
\(821\) | −517.865 | + | 896.969i | −0.630773 | + | 1.09253i | 0.356620 | + | 0.934249i | \(0.383929\pi\) |
−0.987394 | + | 0.158282i | \(0.949404\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 278.230 | − | 160.636i | 0.338068 | − | 0.195184i | −0.321349 | − | 0.946961i | \(-0.604136\pi\) |
0.659417 | + | 0.751777i | \(0.270803\pi\) | |||||||
\(824\) | −1122.15 | − | 288.961i | −1.36183 | − | 0.350680i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 83.3998 | + | 307.247i | 0.100968 | + | 0.371970i | ||||
\(827\) | − | 119.865i | − | 0.144939i | −0.997371 | − | 0.0724695i | \(-0.976912\pi\) | ||
0.997371 | − | 0.0724695i | \(-0.0230880\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 810.947 | 0.978223 | 0.489112 | − | 0.872221i | \(-0.337321\pi\) | ||||
0.489112 | + | 0.872221i | \(0.337321\pi\) | |||||||
\(830\) | 1565.10 | − | 424.834i | 1.88566 | − | 0.511848i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 386.384 | − | 233.260i | 0.464404 | − | 0.280361i | ||||
\(833\) | 7.43005 | + | 12.8692i | 0.00891963 | + | 0.0154492i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1244.57 | + | 718.553i | 1.49050 | + | 0.860543i | ||||
\(836\) | −1.60897 | − | 247.062i | −0.00192461 | − | 0.295529i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 904.391 | + | 898.520i | 1.07923 | + | 1.07222i | ||||
\(839\) | −51.3491 | − | 29.6464i | −0.0612027 | − | 0.0353354i | 0.469086 | − | 0.883152i | \(-0.344583\pi\) |
−0.530289 | + | 0.847817i | \(0.677917\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 240.610 | + | 416.748i | 0.286100 | + | 0.495539i | ||||
\(842\) | 370.370 | + | 97.9488i | 0.439869 | + | 0.116329i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 213.676 | − | 375.727i | 0.253170 | − | 0.445174i | ||||
\(845\) | 961.549 | 1.13793 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 481.466i | − | 0.568437i | ||||||
\(848\) | 5.19770 | − | 9.27974i | 0.00612937 | − | 0.0109431i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −40.0515 | − | 10.5921i | −0.0471194 | − | 0.0124613i | ||||
\(851\) | 16.4030 | − | 9.47029i | 0.0192750 | − | 0.0111284i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 547.729 | − | 948.694i | 0.642121 | − | 1.11219i | −0.342838 | − | 0.939395i | \(-0.611388\pi\) |
0.984959 | − | 0.172791i | \(-0.0552785\pi\) | |||||||
\(854\) | −431.884 | − | 429.080i | −0.505718 | − | 0.502436i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 307.995 | − | 314.072i | 0.359807 | − | 0.366907i | ||||
\(857\) | 692.162 | − | 1198.86i | 0.807658 | − | 1.39890i | −0.106825 | − | 0.994278i | \(-0.534068\pi\) |
0.914482 | − | 0.404626i | \(-0.132598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 414.983 | − | 239.591i | 0.483101 | − | 0.278918i | −0.238607 | − | 0.971116i | \(-0.576691\pi\) |
0.721708 | + | 0.692198i | \(0.243357\pi\) | |||||||
\(860\) | 524.716 | + | 895.319i | 0.610135 | + | 1.04107i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 928.772 | − | 252.108i | 1.07746 | − | 0.292469i | ||||
\(863\) | − | 4.93230i | − | 0.00571530i | −0.999996 | − | 0.00285765i | \(-0.999090\pi\) | ||
0.999996 | − | 0.00285765i | \(-0.000909619\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1218.83 | 1.40906 | ||||||||
\(866\) | 188.795 | + | 695.525i | 0.218008 | + | 0.803147i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −235.873 | + | 138.237i | −0.271743 | + | 0.159259i | ||||
\(869\) | −275.596 | − | 477.347i | −0.317142 | − | 0.549306i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −525.164 | − | 303.204i | −0.602944 | − | 0.348110i | ||||
\(872\) | −365.121 | − | 358.056i | −0.418717 | − | 0.410615i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 740.289 | − | 745.126i | 0.847013 | − | 0.852547i | ||||
\(875\) | −471.854 | − | 272.425i | −0.539262 | − | 0.311343i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −839.494 | − | 1454.05i | −0.957234 | − | 1.65798i | −0.729172 | − | 0.684331i | \(-0.760095\pi\) |
−0.228062 | − | 0.973647i | \(-0.573239\pi\) | |||||||
\(878\) | −288.298 | + | 1090.13i | −0.328357 | + | 1.24160i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 423.440 | + | 237.174i | 0.481182 | + | 0.269516i | ||||
\(881\) | −830.879 | −0.943109 | −0.471555 | − | 0.881837i | \(-0.656307\pi\) | ||||
−0.471555 | + | 0.881837i | \(0.656307\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1228.46i | 1.39123i | 0.718414 | + | 0.695615i | \(0.244868\pi\) | ||||
−0.718414 | + | 0.695615i | \(0.755132\pi\) | |||||||
\(884\) | −12.6989 | − | 7.22188i | −0.0143653 | − | 0.00816954i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 336.507 | − | 1272.42i | 0.379805 | − | 1.43614i | ||||
\(887\) | 660.079 | − | 381.097i | 0.744170 | − | 0.429647i | −0.0794134 | − | 0.996842i | \(-0.525305\pi\) |
0.823584 | + | 0.567195i | \(0.191971\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.1082 | − | 38.2925i | 0.0248686 | − | 0.0430737i | ||||
\(890\) | 293.612 | − | 295.530i | 0.329901 | − | 0.332056i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −653.083 | + | 4.25315i | −0.732156 | + | 0.00476810i | ||||
\(893\) | 497.295 | − | 861.340i | 0.556881 | − | 0.964547i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1932.80 | + | 1115.90i | −2.15955 | + | 1.24682i | ||||
\(896\) | 560.406 | + | 136.551i | 0.625453 | + | 0.152400i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 119.229 | + | 439.244i | 0.132772 | + | 0.489136i | ||||
\(899\) | 287.696i | 0.320018i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.344275 | −0.000382104 | ||||||||
\(902\) | −179.763 | + | 48.7952i | −0.199294 | + | 0.0540967i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 71.1164 | − | 276.173i | 0.0786686 | − | 0.305502i | ||||
\(905\) | −422.166 | − | 731.214i | −0.466482 | − | 0.807971i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −324.076 | − | 187.106i | −0.357306 | − | 0.206291i | 0.310592 | − | 0.950543i | \(-0.399473\pi\) |
−0.667898 | + | 0.744253i | \(0.732806\pi\) | |||||||
\(908\) | −44.1882 | + | 0.287772i | −0.0486654 | + | 0.000316929i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −363.503 | − | 361.143i | −0.399453 | − | 0.396861i | ||||
\(911\) | −1265.50 | − | 730.639i | −1.38914 | − | 0.802018i | −0.395918 | − | 0.918286i | \(-0.629574\pi\) |
−0.993218 | + | 0.116268i | \(0.962907\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 189.212 | + | 327.725i | 0.207242 | + | 0.358954i | ||||
\(914\) | 1387.80 | + | 367.021i | 1.51838 | + | 0.401555i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 112.465 | + | 63.9589i | 0.122779 | + | 0.0698241i | ||||
\(917\) | 528.464 | 0.576296 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1112.72i | − | 1.21080i | −0.795923 | − | 0.605398i | \(-0.793014\pi\) | ||
0.795923 | − | 0.605398i | \(-0.206986\pi\) | |||||||
\(920\) | 553.466 | + | 1987.69i | 0.601593 | + | 2.16053i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −776.787 | − | 205.431i | −0.842502 | − | 0.222810i | ||||
\(923\) | −344.717 | + | 199.022i | −0.373474 | + | 0.215625i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.8404 | + | 20.5082i | −0.0128005 | + | 0.0221710i | ||||
\(926\) | −650.003 | − | 645.784i | −0.701947 | − | 0.697390i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 422.150 | − | 436.125i | 0.454903 | − | 0.469962i | ||||
\(929\) | 508.204 | − | 880.234i | 0.547044 | − | 0.947507i | −0.451432 | − | 0.892306i | \(-0.649086\pi\) |
0.998475 | − | 0.0552017i | \(-0.0175802\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 407.938 | − | 235.523i | 0.438171 | − | 0.252978i | ||||
\(932\) | 624.802 | − | 366.175i | 0.670389 | − | 0.392892i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 394.514 | − | 107.088i | 0.422392 | − | 0.114655i | ||||
\(935\) | − | 15.7095i | − | 0.0168016i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 170.282 | 0.181731 | 0.0908654 | − | 0.995863i | \(-0.471037\pi\) | ||||
0.0908654 | + | 0.995863i | \(0.471037\pi\) | |||||||
\(938\) | −203.017 | − | 747.921i | −0.216436 | − | 0.797357i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 987.882 | + | 1685.61i | 1.05094 | + | 1.79321i | ||||
\(941\) | 150.929 | + | 261.417i | 0.160392 | + | 0.277808i | 0.935009 | − | 0.354623i | \(-0.115391\pi\) |
−0.774617 | + | 0.632430i | \(0.782057\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −685.784 | − | 395.938i | −0.727237 | − | 0.419870i | ||||
\(944\) | 7.36126 | + | 565.147i | 0.00779794 | + | 0.598673i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −170.670 | + | 171.785i | −0.180413 | + | 0.181591i | ||||
\(947\) | 730.155 | + | 421.555i | 0.771019 | + | 0.445148i | 0.833238 | − | 0.552914i | \(-0.186484\pi\) |
−0.0622189 | + | 0.998063i | \(0.519818\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −465.159 | − | 805.679i | −0.490157 | − | 0.848977i | ||||
\(950\) | −335.756 | + | 1269.58i | −0.353427 | + | 1.33640i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.00808 | − | 17.9858i | −0.00526059 | − | 0.0188926i | ||||
\(953\) | −306.171 | −0.321270 | −0.160635 | − | 0.987014i | \(-0.551354\pi\) | ||||
−0.160635 | + | 0.987014i | \(0.551354\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1796.44i | − | 1.88109i | ||||||
\(956\) | 90.5175 | − | 159.166i | 0.0946835 | − | 0.166491i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 46.3236 | − | 175.162i | 0.0483545 | − | 0.182841i | ||||
\(959\) | −980.365 | + | 566.014i | −1.02228 | + | 0.590213i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −365.473 | + | 633.018i | −0.380305 | + | 0.658707i | ||||
\(962\) | −5.88547 | + | 5.92393i | −0.00611796 | + | 0.00615793i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.81584 | + | 1353.70i | 0.00914507 | + | 1.40425i | ||||
\(965\) | −456.951 | + | 791.462i | −0.473524 | + | 0.820168i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 103.822 | − | 59.9417i | 0.107365 | − | 0.0619873i | −0.445356 | − | 0.895354i | \(-0.646923\pi\) |
0.552721 | + | 0.833366i | \(0.313590\pi\) | |||||||
\(968\) | 213.150 | − | 827.745i | 0.220196 | − | 0.855109i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 407.638 | + | 1501.75i | 0.420246 | + | 1.54820i | ||||
\(971\) | 62.7602i | 0.0646346i | 0.999478 | + | 0.0323173i | \(0.0102887\pi\) | ||||
−0.999478 | + | 0.0323173i | \(0.989711\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 692.431 | 0.711646 | ||||||||
\(974\) | −581.535 | + | 157.853i | −0.597058 | + | 0.162067i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −552.545 | − | 928.882i | −0.566132 | − | 0.951723i | ||||
\(977\) | −618.115 | − | 1070.61i | −0.632666 | − | 1.09581i | −0.987004 | − | 0.160693i | \(-0.948627\pi\) |
0.354338 | − | 0.935117i | \(-0.384706\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 84.1854 | + | 48.6045i | 0.0859912 | + | 0.0496471i | ||||
\(980\) | 6.02594 | + | 925.300i | 0.00614892 | + | 0.944184i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −638.211 | − | 634.068i | −0.649909 | − | 0.645691i | ||||
\(983\) | 490.618 | + | 283.258i | 0.499103 | + | 0.288157i | 0.728343 | − | 0.685213i | \(-0.240291\pi\) |
−0.229240 | + | 0.973370i | \(0.573624\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 487.746 | + | 844.801i | 0.495174 | + | 0.857666i | ||||
\(986\) | −18.9936 | − | 5.02308i | −0.0192633 | − | 0.00509441i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −228.924 | + | 402.540i | −0.231705 | + | 0.407429i | ||||
\(989\) | −1029.46 | −1.04091 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 457.774i | 0.461931i | 0.972962 | + | 0.230966i | \(0.0741885\pi\) | ||||
−0.972962 | + | 0.230966i | \(0.925812\pi\) | |||||||
\(992\) | −466.716 | + | 133.237i | −0.470479 | + | 0.134311i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −491.791 | − | 130.060i | −0.494759 | − | 0.130845i | ||||
\(995\) | 574.172 | − | 331.498i | 0.577057 | − | 0.333164i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.3798 | − | 33.5667i | 0.0194381 | − | 0.0336677i | −0.856143 | − | 0.516739i | \(-0.827146\pi\) |
0.875581 | + | 0.483072i | \(0.160479\pi\) | |||||||
\(998\) | 905.375 | + | 899.498i | 0.907190 | + | 0.901301i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.3.f.c.19.4 | 16 | ||
3.2 | odd | 2 | 36.3.f.c.7.5 | yes | 16 | ||
4.3 | odd | 2 | inner | 108.3.f.c.19.8 | 16 | ||
8.3 | odd | 2 | 1728.3.o.g.127.1 | 16 | |||
8.5 | even | 2 | 1728.3.o.g.127.2 | 16 | |||
9.2 | odd | 6 | 324.3.d.i.163.5 | 8 | |||
9.4 | even | 3 | inner | 108.3.f.c.91.8 | 16 | ||
9.5 | odd | 6 | 36.3.f.c.31.1 | yes | 16 | ||
9.7 | even | 3 | 324.3.d.g.163.4 | 8 | |||
12.11 | even | 2 | 36.3.f.c.7.1 | ✓ | 16 | ||
24.5 | odd | 2 | 576.3.o.g.511.1 | 16 | |||
24.11 | even | 2 | 576.3.o.g.511.8 | 16 | |||
36.7 | odd | 6 | 324.3.d.g.163.3 | 8 | |||
36.11 | even | 6 | 324.3.d.i.163.6 | 8 | |||
36.23 | even | 6 | 36.3.f.c.31.5 | yes | 16 | ||
36.31 | odd | 6 | inner | 108.3.f.c.91.4 | 16 | ||
72.5 | odd | 6 | 576.3.o.g.319.8 | 16 | |||
72.13 | even | 6 | 1728.3.o.g.1279.1 | 16 | |||
72.59 | even | 6 | 576.3.o.g.319.1 | 16 | |||
72.67 | odd | 6 | 1728.3.o.g.1279.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.3.f.c.7.1 | ✓ | 16 | 12.11 | even | 2 | ||
36.3.f.c.7.5 | yes | 16 | 3.2 | odd | 2 | ||
36.3.f.c.31.1 | yes | 16 | 9.5 | odd | 6 | ||
36.3.f.c.31.5 | yes | 16 | 36.23 | even | 6 | ||
108.3.f.c.19.4 | 16 | 1.1 | even | 1 | trivial | ||
108.3.f.c.19.8 | 16 | 4.3 | odd | 2 | inner | ||
108.3.f.c.91.4 | 16 | 36.31 | odd | 6 | inner | ||
108.3.f.c.91.8 | 16 | 9.4 | even | 3 | inner | ||
324.3.d.g.163.3 | 8 | 36.7 | odd | 6 | |||
324.3.d.g.163.4 | 8 | 9.7 | even | 3 | |||
324.3.d.i.163.5 | 8 | 9.2 | odd | 6 | |||
324.3.d.i.163.6 | 8 | 36.11 | even | 6 | |||
576.3.o.g.319.1 | 16 | 72.59 | even | 6 | |||
576.3.o.g.319.8 | 16 | 72.5 | odd | 6 | |||
576.3.o.g.511.1 | 16 | 24.5 | odd | 2 | |||
576.3.o.g.511.8 | 16 | 24.11 | even | 2 | |||
1728.3.o.g.127.1 | 16 | 8.3 | odd | 2 | |||
1728.3.o.g.127.2 | 16 | 8.5 | even | 2 | |||
1728.3.o.g.1279.1 | 16 | 72.13 | even | 6 | |||
1728.3.o.g.1279.2 | 16 | 72.67 | odd | 6 |