Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [575,2,Mod(26,575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(575, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 16]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("575.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 575 = 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 575.k (of order \(11\), degree \(10\), 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: | \(4.59139811622\) |
Analytic rank: | \(0\) |
Dimension: | \(100\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{11})\) |
Twist minimal: | no (minimal twist has level 115) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{11}]$ |
Embedding invariants
Embedding label | 26.1 | ||
Character | \(\chi\) | \(=\) | 575.26 |
Dual form | 575.2.k.g.376.1 |
$q$-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 \(\left(\mathbb{Z}/575\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(e\left(\frac{8}{11}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.336428 | − | 2.33991i | −0.237890 | − | 1.65456i | −0.662408 | − | 0.749144i | \(-0.730465\pi\) |
0.424517 | − | 0.905420i | \(-0.360444\pi\) | |||||||
\(3\) | 1.10646 | − | 2.42282i | 0.638817 | − | 1.39881i | −0.262193 | − | 0.965015i | \(-0.584446\pi\) |
0.901010 | − | 0.433799i | \(-0.142827\pi\) | |||||||
\(4\) | −3.44299 | + | 1.01095i | −1.72150 | + | 0.505477i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −6.04141 | − | 1.77392i | −2.46639 | − | 0.724199i | ||||
\(7\) | 2.96780 | − | 1.90729i | 1.12172 | − | 0.720888i | 0.157907 | − | 0.987454i | \(-0.449525\pi\) |
0.963817 | + | 0.266566i | \(0.0858889\pi\) | |||||||
\(8\) | 1.55980 | + | 3.41548i | 0.551472 | + | 1.20755i | ||||
\(9\) | −2.68120 | − | 3.09427i | −0.893733 | − | 1.03142i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.318127 | + | 2.21262i | −0.0959189 | + | 0.667131i | 0.883964 | + | 0.467556i | \(0.154865\pi\) |
−0.979883 | + | 0.199575i | \(0.936044\pi\) | |||||||
\(12\) | −1.36019 | + | 9.46032i | −0.392653 | + | 2.73096i | ||||
\(13\) | −2.99626 | − | 1.92558i | −0.831012 | − | 0.534059i | 0.0545872 | − | 0.998509i | \(-0.482616\pi\) |
−0.885599 | + | 0.464450i | \(0.846252\pi\) | |||||||
\(14\) | −5.46133 | − | 6.30271i | −1.45960 | − | 1.68447i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.42973 | − | 0.918832i | 0.357433 | − | 0.229708i | ||||
\(17\) | −5.12944 | − | 1.50614i | −1.24407 | − | 0.365293i | −0.407528 | − | 0.913193i | \(-0.633609\pi\) |
−0.836544 | + | 0.547900i | \(0.815427\pi\) | |||||||
\(18\) | −6.33827 | + | 7.31475i | −1.49394 | + | 1.72410i | ||||
\(19\) | 2.61956 | − | 0.769172i | 0.600968 | − | 0.176460i | 0.0329235 | − | 0.999458i | \(-0.489518\pi\) |
0.568045 | + | 0.822998i | \(0.307700\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.33725 | − | 9.30079i | −0.291812 | − | 2.02960i | ||||
\(22\) | 5.28435 | 1.12663 | ||||||||
\(23\) | 1.35066 | + | 4.60171i | 0.281632 | + | 0.959522i | ||||
\(24\) | 10.0009 | 2.04143 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.49765 | + | 7.65878i | −0.685945 | + | 1.50201i | ||||
\(27\) | −2.79663 | + | 0.821163i | −0.538211 | + | 0.158033i | ||||
\(28\) | −8.28993 | + | 9.56709i | −1.56665 | + | 1.80801i | ||||
\(29\) | 4.25645 | + | 1.24981i | 0.790403 | + | 0.232083i | 0.651926 | − | 0.758282i | \(-0.273961\pi\) |
0.138477 | + | 0.990366i | \(0.455779\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.941375 | − | 2.06132i | −0.169076 | − | 0.370225i | 0.806059 | − | 0.591835i | \(-0.201596\pi\) |
−0.975135 | + | 0.221610i | \(0.928869\pi\) | |||||||
\(32\) | 2.28675 | + | 2.63905i | 0.404245 | + | 0.466523i | ||||
\(33\) | 5.00878 | + | 3.21895i | 0.871917 | + | 0.560347i | ||||
\(34\) | −1.79854 | + | 12.5091i | −0.308447 | + | 2.14530i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 12.3595 | + | 7.94297i | 2.05992 | + | 1.32383i | ||||
\(37\) | −4.24619 | − | 4.90036i | −0.698069 | − | 0.805614i | 0.290421 | − | 0.956899i | \(-0.406204\pi\) |
−0.988490 | + | 0.151285i | \(0.951659\pi\) | |||||||
\(38\) | −2.68108 | − | 5.87075i | −0.434929 | − | 0.952362i | ||||
\(39\) | −7.98057 | + | 5.12880i | −1.27791 | + | 0.821265i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.88742 | − | 2.17820i | 0.294765 | − | 0.340177i | −0.588978 | − | 0.808149i | \(-0.700470\pi\) |
0.883743 | + | 0.467972i | \(0.155015\pi\) | |||||||
\(42\) | −21.3131 | + | 6.25809i | −3.28868 | + | 0.965644i | ||||
\(43\) | 1.67327 | − | 3.66396i | 0.255172 | − | 0.558748i | −0.738082 | − | 0.674711i | \(-0.764268\pi\) |
0.993254 | + | 0.115963i | \(0.0369954\pi\) | |||||||
\(44\) | −1.14155 | − | 7.93965i | −0.172095 | − | 1.19695i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.3132 | − | 4.70856i | 1.52059 | − | 0.694239i | ||||
\(47\) | 11.8883 | 1.73409 | 0.867045 | − | 0.498230i | \(-0.166017\pi\) | ||||
0.867045 | + | 0.498230i | \(0.166017\pi\) | |||||||
\(48\) | −0.644217 | − | 4.48063i | −0.0929847 | − | 0.646723i | ||||
\(49\) | 2.26219 | − | 4.95350i | 0.323170 | − | 0.707643i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.32464 | + | 10.7612i | −1.30571 | + | 1.50687i | ||||
\(52\) | 12.2628 | + | 3.60067i | 1.70054 | + | 0.499323i | ||||
\(53\) | 6.11746 | − | 3.93145i | 0.840297 | − | 0.540026i | −0.0482374 | − | 0.998836i | \(-0.515360\pi\) |
0.888535 | + | 0.458810i | \(0.151724\pi\) | |||||||
\(54\) | 2.86231 | + | 6.26758i | 0.389511 | + | 0.852909i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11.1435 | + | 7.16148i | 1.48911 | + | 0.956994i | ||||
\(57\) | 1.03488 | − | 7.19777i | 0.137074 | − | 0.953368i | ||||
\(58\) | 1.49244 | − | 10.3802i | 0.195967 | − | 1.36298i | ||||
\(59\) | 5.02690 | + | 3.23060i | 0.654447 | + | 0.420588i | 0.825289 | − | 0.564711i | \(-0.191012\pi\) |
−0.170842 | + | 0.985298i | \(0.554649\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.60637 | − | 3.51746i | −0.205675 | − | 0.450364i | 0.778482 | − | 0.627667i | \(-0.215990\pi\) |
−0.984156 | + | 0.177303i | \(0.943263\pi\) | |||||||
\(62\) | −4.50660 | + | 2.89622i | −0.572339 | + | 0.367820i | ||||
\(63\) | −13.8589 | − | 4.06935i | −1.74606 | − | 0.512690i | ||||
\(64\) | 7.63171 | − | 8.80747i | 0.953964 | − | 1.10093i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.84694 | − | 12.8030i | 0.719709 | − | 1.57594i | ||||
\(67\) | 0.217129 | + | 1.51017i | 0.0265265 | + | 0.184496i | 0.998777 | − | 0.0494474i | \(-0.0157460\pi\) |
−0.972250 | + | 0.233943i | \(0.924837\pi\) | |||||||
\(68\) | 19.1833 | 2.32631 | ||||||||
\(69\) | 12.6436 | + | 1.81922i | 1.52210 | + | 0.219008i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.0271164 | − | 0.188599i | −0.00321812 | − | 0.0223825i | 0.988149 | − | 0.153497i | \(-0.0490535\pi\) |
−0.991367 | + | 0.131114i | \(0.958144\pi\) | |||||||
\(72\) | 6.38628 | − | 13.9840i | 0.752631 | − | 1.64803i | ||||
\(73\) | −4.32629 | + | 1.27031i | −0.506354 | + | 0.148679i | −0.524925 | − | 0.851148i | \(-0.675907\pi\) |
0.0185706 | + | 0.999828i | \(0.494088\pi\) | |||||||
\(74\) | −10.0378 | + | 11.5843i | −1.16688 | + | 1.34665i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.24152 | + | 5.29650i | −0.945367 | + | 0.607551i | ||||
\(77\) | 3.27598 | + | 7.17339i | 0.373332 | + | 0.817483i | ||||
\(78\) | 14.6858 | + | 16.9483i | 1.66284 | + | 1.91902i | ||||
\(79\) | −4.72198 | − | 3.03463i | −0.531264 | − | 0.341423i | 0.247349 | − | 0.968926i | \(-0.420440\pi\) |
−0.778614 | + | 0.627503i | \(0.784077\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.643205 | − | 4.47359i | 0.0714672 | − | 0.497065i | ||||
\(82\) | −5.73176 | − | 3.68358i | −0.632967 | − | 0.406783i | ||||
\(83\) | 4.89183 | + | 5.64548i | 0.536948 | + | 0.619672i | 0.957792 | − | 0.287462i | \(-0.0928114\pi\) |
−0.420844 | + | 0.907133i | \(0.638266\pi\) | |||||||
\(84\) | 14.0068 | + | 30.6706i | 1.52827 | + | 3.34644i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.13625 | − | 2.68265i | −0.985187 | − | 0.289277i | ||||
\(87\) | 7.73766 | − | 8.92974i | 0.829565 | − | 0.957368i | ||||
\(88\) | −8.05338 | + | 2.36469i | −0.858493 | + | 0.252076i | ||||
\(89\) | −2.09043 | + | 4.57740i | −0.221585 | + | 0.485203i | −0.987476 | − | 0.157767i | \(-0.949571\pi\) |
0.765892 | + | 0.642970i | \(0.222298\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.5649 | −1.31716 | ||||||||
\(92\) | −9.30242 | − | 14.4782i | −0.969845 | − | 1.50945i | ||||
\(93\) | −6.03581 | −0.625884 | ||||||||
\(94\) | −3.99956 | − | 27.8176i | −0.412523 | − | 2.86916i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.92415 | − | 2.62037i | 0.910817 | − | 0.267440i | ||||
\(97\) | −6.12879 | + | 7.07300i | −0.622284 | + | 0.718154i | −0.976139 | − | 0.217146i | \(-0.930325\pi\) |
0.353855 | + | 0.935300i | \(0.384871\pi\) | |||||||
\(98\) | −12.3518 | − | 3.62681i | −1.24772 | − | 0.366363i | ||||
\(99\) | 7.69941 | − | 4.94811i | 0.773819 | − | 0.497304i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.5966 | + | 13.3832i | 1.15391 | + | 1.33168i | 0.934466 | + | 0.356053i | \(0.115878\pi\) |
0.219441 | + | 0.975626i | \(0.429577\pi\) | |||||||
\(102\) | 28.3173 | + | 18.1984i | 2.80383 | + | 1.80191i | ||||
\(103\) | 0.283096 | − | 1.96898i | 0.0278943 | − | 0.194009i | −0.971110 | − | 0.238634i | \(-0.923300\pi\) |
0.999004 | + | 0.0446252i | \(0.0142094\pi\) | |||||||
\(104\) | 1.90322 | − | 13.2372i | 0.186626 | − | 1.29801i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.2573 | − | 12.9916i | −1.09341 | − | 1.26186i | ||||
\(107\) | −6.09336 | − | 13.3426i | −0.589067 | − | 1.28988i | −0.936004 | − | 0.351989i | \(-0.885505\pi\) |
0.346937 | − | 0.937889i | \(-0.387222\pi\) | |||||||
\(108\) | 8.79860 | − | 5.65452i | 0.846645 | − | 0.544106i | ||||
\(109\) | −12.9896 | − | 3.81410i | −1.24418 | − | 0.365325i | −0.407597 | − | 0.913162i | \(-0.633633\pi\) |
−0.836585 | + | 0.547837i | \(0.815451\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.5709 | + | 4.86566i | −1.57284 | + | 0.461828i | ||||
\(112\) | 2.49068 | − | 5.45382i | 0.235347 | − | 0.515338i | ||||
\(113\) | 0.306196 | + | 2.12964i | 0.0288045 | + | 0.200340i | 0.999142 | − | 0.0414142i | \(-0.0131863\pi\) |
−0.970338 | + | 0.241754i | \(0.922277\pi\) | |||||||
\(114\) | −17.1903 | −1.61002 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −15.9184 | −1.47799 | ||||||||
\(117\) | 2.07531 | + | 14.4341i | 0.191862 | + | 1.33443i | ||||
\(118\) | 5.86810 | − | 12.8493i | 0.540202 | − | 1.18288i | ||||
\(119\) | −18.0958 | + | 5.31341i | −1.65884 | + | 0.487080i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.75993 | + | 1.69127i | 0.523630 | + | 0.153752i | ||||
\(122\) | −7.69010 | + | 4.94212i | −0.696228 | + | 0.447439i | ||||
\(123\) | −3.18901 | − | 6.98297i | −0.287544 | − | 0.629633i | ||||
\(124\) | 5.32505 | + | 6.14543i | 0.478203 | + | 0.551876i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.85937 | + | 33.7977i | −0.432907 | + | 3.01093i | ||||
\(127\) | −1.23974 | + | 8.62257i | −0.110009 | + | 0.765129i | 0.857898 | + | 0.513820i | \(0.171770\pi\) |
−0.967907 | + | 0.251309i | \(0.919139\pi\) | |||||||
\(128\) | −17.3009 | − | 11.1186i | −1.52920 | − | 0.982756i | ||||
\(129\) | −7.02568 | − | 8.10807i | −0.618577 | − | 0.713876i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.63613 | + | 4.90744i | −0.667171 | + | 0.428765i | −0.829905 | − | 0.557905i | \(-0.811605\pi\) |
0.162733 | + | 0.986670i | \(0.447969\pi\) | |||||||
\(132\) | −20.4994 | − | 6.01917i | −1.78424 | − | 0.523901i | ||||
\(133\) | 6.30730 | − | 7.27901i | 0.546912 | − | 0.631170i | ||||
\(134\) | 3.46060 | − | 1.01612i | 0.298950 | − | 0.0877796i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.85670 | − | 19.8688i | −0.244960 | − | 1.70373i | ||||
\(137\) | 7.22132 | 0.616959 | 0.308479 | − | 0.951231i | \(-0.400180\pi\) | ||||
0.308479 | + | 0.951231i | \(0.400180\pi\) | |||||||
\(138\) | 0.00315700 | − | 30.1968i | 0.000268741 | − | 2.57052i | ||||
\(139\) | 8.06639 | 0.684182 | 0.342091 | − | 0.939667i | \(-0.388865\pi\) | ||||
0.342091 | + | 0.939667i | \(0.388865\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.1540 | − | 28.8032i | 1.10777 | − | 2.42567i | ||||
\(142\) | −0.432180 | + | 0.126900i | −0.0362678 | + | 0.0106492i | ||||
\(143\) | 5.21376 | − | 6.01701i | 0.435997 | − | 0.503167i | ||||
\(144\) | −6.67650 | − | 1.96040i | −0.556375 | − | 0.163367i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.42790 | + | 9.69575i | 0.366456 | + | 0.802426i | ||||
\(147\) | −9.49840 | − | 10.9617i | −0.783415 | − | 0.904109i | ||||
\(148\) | 19.5736 | + | 12.5792i | 1.60894 | + | 1.03400i | ||||
\(149\) | −1.16801 | + | 8.12372i | −0.0956875 | + | 0.665521i | 0.884367 | + | 0.466792i | \(0.154590\pi\) |
−0.980055 | + | 0.198729i | \(0.936319\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.93951 | − | 3.17443i | −0.401972 | − | 0.258332i | 0.323999 | − | 0.946058i | \(-0.394973\pi\) |
−0.725970 | + | 0.687726i | \(0.758609\pi\) | |||||||
\(152\) | 6.71308 | + | 7.74730i | 0.544502 | + | 0.628389i | ||||
\(153\) | 9.09265 | + | 19.9101i | 0.735097 | + | 1.60964i | ||||
\(154\) | 15.6829 | − | 10.0788i | 1.26377 | − | 0.812173i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 22.2921 | − | 25.7264i | 1.78479 | − | 2.05976i | ||||
\(157\) | 17.5505 | − | 5.15329i | 1.40068 | − | 0.411277i | 0.507764 | − | 0.861496i | \(-0.330472\pi\) |
0.892918 | + | 0.450219i | \(0.148654\pi\) | |||||||
\(158\) | −5.51215 | + | 12.0699i | −0.438523 | + | 0.960232i | ||||
\(159\) | −2.75644 | − | 19.1715i | −0.218600 | − | 1.52040i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.7853 | + | 11.0809i | 1.00762 | + | 0.873294i | ||||
\(162\) | −10.6842 | −0.839428 | ||||||||
\(163\) | −0.109527 | − | 0.761778i | −0.00857883 | − | 0.0596670i | 0.985082 | − | 0.172084i | \(-0.0550500\pi\) |
−0.993661 | + | 0.112417i | \(0.964141\pi\) | |||||||
\(164\) | −4.29631 | + | 9.40761i | −0.335485 | + | 0.734611i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.5641 | − | 13.3457i | 0.897551 | − | 1.03583i | ||||
\(167\) | −16.5934 | − | 4.87226i | −1.28403 | − | 0.377027i | −0.432647 | − | 0.901563i | \(-0.642420\pi\) |
−0.851388 | + | 0.524537i | \(0.824238\pi\) | |||||||
\(168\) | 29.6808 | − | 19.0747i | 2.28993 | − | 1.47165i | ||||
\(169\) | −0.130688 | − | 0.286167i | −0.0100529 | − | 0.0220128i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.40358 | − | 6.04332i | −0.719110 | − | 0.462144i | ||||
\(172\) | −2.05697 | + | 14.3066i | −0.156843 | + | 1.09087i | ||||
\(173\) | −1.26037 | + | 8.76606i | −0.0958241 | + | 0.666471i | 0.884129 | + | 0.467243i | \(0.154753\pi\) |
−0.979953 | + | 0.199228i | \(0.936156\pi\) | |||||||
\(174\) | −23.4979 | − | 15.1012i | −1.78137 | − | 1.14482i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.57819 | + | 3.45576i | 0.118961 | + | 0.260488i | ||||
\(177\) | 13.3892 | − | 8.60473i | 1.00640 | − | 0.646771i | ||||
\(178\) | 11.4140 | + | 3.35144i | 0.855512 | + | 0.251201i | ||||
\(179\) | 2.91404 | − | 3.36298i | 0.217806 | − | 0.251361i | −0.636323 | − | 0.771423i | \(-0.719545\pi\) |
0.854129 | + | 0.520061i | \(0.174091\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.78381 | + | 6.09569i | −0.206919 | + | 0.453089i | −0.984429 | − | 0.175781i | \(-0.943755\pi\) |
0.777510 | + | 0.628870i | \(0.216482\pi\) | |||||||
\(182\) | 4.22719 | + | 29.4008i | 0.313340 | + | 2.17933i | ||||
\(183\) | −10.2995 | −0.761364 | ||||||||
\(184\) | −13.6103 | + | 11.7909i | −1.00336 | + | 0.869236i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.03061 | + | 14.1232i | 0.148892 | + | 1.03556i | ||||
\(187\) | 4.96433 | − | 10.8704i | 0.363028 | − | 0.794920i | ||||
\(188\) | −40.9314 | + | 12.0185i | −2.98523 | + | 0.876542i | ||||
\(189\) | −6.73363 | + | 7.77103i | −0.489800 | + | 0.565259i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.26348 | − | 2.73997i | 0.308495 | − | 0.198257i | −0.377228 | − | 0.926120i | \(-0.623123\pi\) |
0.685723 | + | 0.727863i | \(0.259486\pi\) | |||||||
\(192\) | −12.8947 | − | 28.2354i | −0.930592 | − | 2.03771i | ||||
\(193\) | −3.61698 | − | 4.17422i | −0.260356 | − | 0.300467i | 0.610489 | − | 0.792025i | \(-0.290973\pi\) |
−0.870845 | + | 0.491558i | \(0.836428\pi\) | |||||||
\(194\) | 18.6120 | + | 11.9612i | 1.33627 | + | 0.858767i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.78093 | + | 19.3418i | −0.198638 | + | 1.38156i | ||||
\(197\) | −11.2558 | − | 7.23368i | −0.801945 | − | 0.515379i | 0.0743051 | − | 0.997236i | \(-0.476326\pi\) |
−0.876250 | + | 0.481857i | \(0.839963\pi\) | |||||||
\(198\) | −14.1684 | − | 16.3512i | −1.00690 | − | 1.16203i | ||||
\(199\) | 1.31471 | + | 2.87881i | 0.0931973 | + | 0.204074i | 0.950490 | − | 0.310756i | \(-0.100582\pi\) |
−0.857292 | + | 0.514830i | \(0.827855\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.89910 | + | 1.14488i | 0.275021 | + | 0.0807535i | ||||
\(202\) | 27.4140 | − | 31.6375i | 1.92884 | − | 2.22600i | ||||
\(203\) | 15.0161 | − | 4.40911i | 1.05392 | − | 0.309459i | ||||
\(204\) | 21.2256 | − | 46.4775i | 1.48609 | − | 3.25408i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.70246 | −0.327636 | ||||||||
\(207\) | 10.6175 | − | 16.5174i | 0.737969 | − | 1.14804i | ||||
\(208\) | −6.05312 | −0.419708 | ||||||||
\(209\) | 0.868534 | + | 6.04079i | 0.0600778 | + | 0.417850i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0764 | − | 5.60133i | 1.31327 | − | 0.385612i | 0.451212 | − | 0.892417i | \(-0.350992\pi\) |
0.862061 | + | 0.506805i | \(0.169174\pi\) | |||||||
\(212\) | −17.0878 | + | 19.7204i | −1.17360 | + | 1.35440i | ||||
\(213\) | −0.486943 | − | 0.142979i | −0.0333648 | − | 0.00979679i | ||||
\(214\) | −29.1704 | + | 18.7467i | −1.99405 | + | 1.28150i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7.16684 | − | 8.27097i | −0.487641 | − | 0.562768i | ||||
\(217\) | −6.72536 | − | 4.32213i | −0.456547 | − | 0.293405i | ||||
\(218\) | −4.55457 | + | 31.6777i | −0.308474 | + | 2.14549i | ||||
\(219\) | −1.70915 | + | 11.8874i | −0.115493 | + | 0.803274i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.4689 | + | 14.3899i | 0.838751 | + | 0.967971i | ||||
\(222\) | 16.9601 | + | 37.1375i | 1.13829 | + | 2.49250i | ||||
\(223\) | 16.6542 | − | 10.7030i | 1.11525 | − | 0.716726i | 0.152817 | − | 0.988254i | \(-0.451165\pi\) |
0.962431 | + | 0.271528i | \(0.0875290\pi\) | |||||||
\(224\) | 11.8201 | + | 3.47069i | 0.789762 | + | 0.231895i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.88015 | − | 1.43294i | 0.324623 | − | 0.0953179i | ||||
\(227\) | −3.80511 | + | 8.33203i | −0.252554 | + | 0.553016i | −0.992864 | − | 0.119249i | \(-0.961951\pi\) |
0.740310 | + | 0.672265i | \(0.234679\pi\) | |||||||
\(228\) | 3.71352 | + | 25.8281i | 0.245934 | + | 1.71051i | ||||
\(229\) | 1.05646 | 0.0698128 | 0.0349064 | − | 0.999391i | \(-0.488887\pi\) | ||||
0.0349064 | + | 0.999391i | \(0.488887\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21.0045 | 1.38200 | ||||||||
\(232\) | 2.37051 | + | 16.4873i | 0.155632 | + | 1.08244i | ||||
\(233\) | 9.63002 | − | 21.0868i | 0.630884 | − | 1.38144i | −0.276449 | − | 0.961029i | \(-0.589158\pi\) |
0.907332 | − | 0.420414i | \(-0.138115\pi\) | |||||||
\(234\) | 33.0762 | − | 9.71205i | 2.16226 | − | 0.634896i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −20.5736 | − | 6.04094i | −1.33923 | − | 0.393232i | ||||
\(237\) | −12.5771 | + | 8.08278i | −0.816968 | + | 0.525033i | ||||
\(238\) | 18.5208 | + | 40.5549i | 1.20053 | + | 2.62879i | ||||
\(239\) | 18.0896 | + | 20.8765i | 1.17012 | + | 1.35039i | 0.924573 | + | 0.381006i | \(0.124422\pi\) |
0.245547 | + | 0.969385i | \(0.421032\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.82110 | + | 12.6660i | −0.117307 | + | 0.815891i | 0.843193 | + | 0.537612i | \(0.180673\pi\) |
−0.960500 | + | 0.278280i | \(0.910236\pi\) | |||||||
\(242\) | 2.01961 | − | 14.0467i | 0.129825 | − | 0.902955i | ||||
\(243\) | −17.4830 | − | 11.2356i | −1.12153 | − | 0.720766i | ||||
\(244\) | 9.08670 | + | 10.4866i | 0.581716 | + | 0.671337i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.2666 | + | 9.81126i | −0.973364 | + | 0.625543i | ||||
\(247\) | −9.32997 | − | 2.73953i | −0.593652 | − | 0.174312i | ||||
\(248\) | 5.57206 | − | 6.43050i | 0.353826 | − | 0.408337i | ||||
\(249\) | 19.0906 | − | 5.60550i | 1.20982 | − | 0.355234i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.340194 | − | 2.36610i | −0.0214728 | − | 0.149347i | 0.976264 | − | 0.216583i | \(-0.0694911\pi\) |
−0.997737 | + | 0.0672358i | \(0.978582\pi\) | |||||||
\(252\) | 51.8301 | 3.26499 | ||||||||
\(253\) | −10.6115 | + | 1.52457i | −0.667141 | + | 0.0958492i | ||||
\(254\) | 20.5931 | 1.29212 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.5136 | + | 23.0215i | −0.657098 | + | 1.43884i | ||||
\(257\) | 14.0628 | − | 4.12920i | 0.877211 | − | 0.257572i | 0.188031 | − | 0.982163i | \(-0.439789\pi\) |
0.689179 | + | 0.724591i | \(0.257971\pi\) | |||||||
\(258\) | −16.6085 | + | 19.1672i | −1.03400 | + | 1.19330i | ||||
\(259\) | −21.9483 | − | 6.44459i | −1.36380 | − | 0.400447i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.54515 | − | 16.5216i | −0.467033 | − | 1.02266i | ||||
\(262\) | 14.0520 | + | 16.2168i | 0.868133 | + | 1.00188i | ||||
\(263\) | −24.9496 | − | 16.0341i | −1.53846 | − | 0.988706i | −0.988106 | − | 0.153771i | \(-0.950858\pi\) |
−0.550349 | − | 0.834934i | \(-0.685505\pi\) | |||||||
\(264\) | −3.18157 | + | 22.1283i | −0.195812 | + | 1.36190i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −19.1542 | − | 12.3096i | −1.17442 | − | 0.754752i | ||||
\(267\) | 8.77722 | + | 10.1294i | 0.537157 | + | 0.619912i | ||||
\(268\) | −2.27428 | − | 4.97998i | −0.138924 | − | 0.304201i | ||||
\(269\) | −21.6241 | + | 13.8970i | −1.31844 | + | 0.847313i | −0.995091 | − | 0.0989653i | \(-0.968447\pi\) |
−0.323354 | + | 0.946278i | \(0.604810\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.32741 | − | 4.99410i | 0.262872 | − | 0.303370i | −0.608935 | − | 0.793220i | \(-0.708403\pi\) |
0.871807 | + | 0.489850i | \(0.162948\pi\) | |||||||
\(272\) | −8.71761 | + | 2.55972i | −0.528583 | + | 0.155206i | ||||
\(273\) | −13.9026 | + | 30.4425i | −0.841426 | + | 1.84247i | ||||
\(274\) | −2.42945 | − | 16.8972i | −0.146769 | − | 1.02080i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −45.3708 | + | 6.51849i | −2.73100 | + | 0.392367i | ||||
\(277\) | −13.9516 | −0.838270 | −0.419135 | − | 0.907924i | \(-0.637667\pi\) | ||||
−0.419135 | + | 0.907924i | \(0.637667\pi\) | |||||||
\(278\) | −2.71376 | − | 18.8746i | −0.162760 | − | 1.13202i | ||||
\(279\) | −3.85428 | + | 8.43969i | −0.230749 | + | 0.505271i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.60330 | − | 3.00437i | 0.155300 | − | 0.179225i | −0.672768 | − | 0.739853i | \(-0.734895\pi\) |
0.828068 | + | 0.560628i | \(0.189440\pi\) | |||||||
\(282\) | −71.8222 | − | 21.0889i | −4.27695 | − | 1.25583i | ||||
\(283\) | −10.3371 | + | 6.64328i | −0.614480 | + | 0.394902i | −0.810535 | − | 0.585691i | \(-0.800823\pi\) |
0.196055 | + | 0.980593i | \(0.437187\pi\) | |||||||
\(284\) | 0.284026 | + | 0.621930i | 0.0168538 | + | 0.0369047i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.8333 | − | 10.1754i | −0.936242 | − | 0.601686i | ||||
\(287\) | 1.44703 | − | 10.0643i | 0.0854155 | − | 0.594078i | ||||
\(288\) | 2.03470 | − | 14.1516i | 0.119896 | − | 0.833894i | ||||
\(289\) | 9.74140 | + | 6.26042i | 0.573024 | + | 0.368260i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.3553 | + | 22.6749i | 0.607039 | + | 1.32923i | ||||
\(292\) | 13.6112 | − | 8.74736i | 0.796533 | − | 0.511901i | ||||
\(293\) | 8.13042 | + | 2.38731i | 0.474984 | + | 0.139468i | 0.510458 | − | 0.859903i | \(-0.329476\pi\) |
−0.0354738 | + | 0.999371i | \(0.511294\pi\) | |||||||
\(294\) | −22.4539 | + | 25.9132i | −1.30954 | + | 1.51129i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 10.1139 | − | 22.1463i | 0.587858 | − | 1.28723i | ||||
\(297\) | −0.927242 | − | 6.44911i | −0.0538040 | − | 0.374215i | ||||
\(298\) | 19.4017 | 1.12391 | ||||||||
\(299\) | 4.81402 | − | 16.3887i | 0.278402 | − | 0.947783i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.02229 | − | 14.0653i | −0.116563 | − | 0.810712i | ||||
\(302\) | −5.76608 | + | 12.6260i | −0.331801 | + | 0.726542i | ||||
\(303\) | 45.2563 | − | 13.2884i | 2.59991 | − | 0.763401i | ||||
\(304\) | 3.03852 | − | 3.50664i | 0.174271 | − | 0.201120i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 43.5288 | − | 27.9743i | 2.48838 | − | 1.59918i | ||||
\(307\) | 6.40985 | + | 14.0356i | 0.365829 | + | 0.801055i | 0.999620 | + | 0.0275503i | \(0.00877064\pi\) |
−0.633791 | + | 0.773504i | \(0.718502\pi\) | |||||||
\(308\) | −18.5311 | − | 21.3860i | −1.05591 | − | 1.21858i | ||||
\(309\) | −4.45724 | − | 2.86449i | −0.253563 | − | 0.162955i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.83372 | + | 26.6641i | −0.217391 | + | 1.51198i | 0.530227 | + | 0.847856i | \(0.322107\pi\) |
−0.747618 | + | 0.664129i | \(0.768802\pi\) | |||||||
\(312\) | −29.9654 | − | 19.2576i | −1.69646 | − | 1.09025i | ||||
\(313\) | 12.5004 | + | 14.4262i | 0.706562 | + | 0.815416i | 0.989623 | − | 0.143686i | \(-0.0458955\pi\) |
−0.283062 | + | 0.959102i | \(0.591350\pi\) | |||||||
\(314\) | −17.9627 | − | 39.3328i | −1.01369 | − | 2.21968i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.3256 | + | 5.67451i | 1.08715 | + | 0.319216i | ||||
\(317\) | −8.88647 | + | 10.2555i | −0.499114 | + | 0.576008i | −0.948278 | − | 0.317441i | \(-0.897176\pi\) |
0.449164 | + | 0.893449i | \(0.351722\pi\) | |||||||
\(318\) | −43.9321 | + | 12.8996i | −2.46359 | + | 0.723376i | ||||
\(319\) | −4.11944 | + | 9.02032i | −0.230645 | + | 0.505041i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −39.0687 | −2.18060 | ||||||||
\(322\) | 21.6268 | − | 33.6443i | 1.20522 | − | 1.87492i | ||||
\(323\) | −14.5954 | −0.812107 | ||||||||
\(324\) | 2.30804 | + | 16.0528i | 0.128224 | + | 0.891821i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.74564 | + | 0.512566i | −0.0966821 | + | 0.0283884i | ||||
\(327\) | −23.6134 | + | 27.2514i | −1.30583 | + | 1.50700i | ||||
\(328\) | 10.3836 | + | 3.04889i | 0.573337 | + | 0.168347i | ||||
\(329\) | 35.2822 | − | 22.6745i | 1.94517 | − | 1.25008i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.7178 | + | 21.6015i | 1.02883 | + | 1.18733i | 0.982088 | + | 0.188421i | \(0.0603370\pi\) |
0.0467377 | + | 0.998907i | \(0.485118\pi\) | |||||||
\(332\) | −22.5498 | − | 14.4919i | −1.23758 | − | 0.795347i | ||||
\(333\) | −3.77816 | + | 26.2777i | −0.207042 | + | 1.44001i | ||||
\(334\) | −5.81815 | + | 40.4661i | −0.318355 | + | 2.21421i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −10.4578 | − | 12.0689i | −0.570518 | − | 0.658413i | ||||
\(337\) | 10.1661 | + | 22.2607i | 0.553783 | + | 1.21262i | 0.954993 | + | 0.296629i | \(0.0958625\pi\) |
−0.401210 | + | 0.915986i | \(0.631410\pi\) | |||||||
\(338\) | −0.625636 | + | 0.402072i | −0.0340301 | + | 0.0218698i | ||||
\(339\) | 5.49853 | + | 1.61451i | 0.298639 | + | 0.0876884i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.86041 | − | 1.42714i | 0.263206 | − | 0.0772842i | ||||
\(342\) | −10.9772 | + | 24.0366i | −0.593577 | + | 1.29975i | ||||
\(343\) | 0.780401 | + | 5.42781i | 0.0421377 | + | 0.293074i | ||||
\(344\) | 15.1241 | 0.815439 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.9358 | 1.12551 | ||||||||
\(347\) | 2.02165 | + | 14.0609i | 0.108528 | + | 0.754826i | 0.969308 | + | 0.245850i | \(0.0790669\pi\) |
−0.860780 | + | 0.508977i | \(0.830024\pi\) | |||||||
\(348\) | −17.6132 | + | 38.5674i | −0.944164 | + | 2.06743i | ||||
\(349\) | 28.1361 | − | 8.26151i | 1.50609 | − | 0.442229i | 0.578456 | − | 0.815713i | \(-0.303655\pi\) |
0.927636 | + | 0.373485i | \(0.121837\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.96062 | + | 2.92470i | 0.531659 | + | 0.156109i | ||||
\(352\) | −6.56670 | + | 4.22016i | −0.350007 | + | 0.224936i | ||||
\(353\) | 0.182831 | + | 0.400343i | 0.00973109 | + | 0.0213081i | 0.914435 | − | 0.404732i | \(-0.132635\pi\) |
−0.904704 | + | 0.426041i | \(0.859908\pi\) | |||||||
\(354\) | −24.6388 | − | 28.4347i | −1.30954 | − | 1.51129i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.56979 | − | 17.8733i | 0.136198 | − | 0.947281i | ||||
\(357\) | −7.14894 | + | 49.7219i | −0.378362 | + | 2.63156i | ||||
\(358\) | −8.84943 | − | 5.68718i | −0.467707 | − | 0.300577i | ||||
\(359\) | 11.7154 | + | 13.5203i | 0.618317 | + | 0.713576i | 0.975387 | − | 0.220502i | \(-0.0707696\pi\) |
−0.357070 | + | 0.934078i | \(0.616224\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.71335 | + | 6.24239i | −0.511229 | + | 0.328547i | ||||
\(362\) | 15.1999 | + | 4.46309i | 0.798889 | + | 0.234575i | ||||
\(363\) | 10.4708 | − | 12.0839i | 0.549574 | − | 0.634242i | ||||
\(364\) | 43.2610 | − | 12.7026i | 2.26749 | − | 0.665795i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.46505 | + | 24.1000i | 0.181121 | + | 1.25973i | ||||
\(367\) | 14.3058 | 0.746756 | 0.373378 | − | 0.927679i | \(-0.378199\pi\) | ||||
0.373378 | + | 0.927679i | \(0.378199\pi\) | |||||||
\(368\) | 6.15928 | + | 5.33817i | 0.321075 | + | 0.278271i | ||||
\(369\) | −11.8005 | −0.614308 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.6570 | − | 23.3355i | 0.553283 | − | 1.21152i | ||||
\(372\) | 20.7812 | − | 6.10192i | 1.07746 | − | 0.316370i | ||||
\(373\) | −8.44615 | + | 9.74738i | −0.437325 | + | 0.504700i | −0.931037 | − | 0.364926i | \(-0.881094\pi\) |
0.493712 | + | 0.869626i | \(0.335640\pi\) | |||||||
\(374\) | −27.1058 | − | 7.95898i | −1.40161 | − | 0.411549i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.5434 | + | 40.6043i | 0.956301 | + | 2.09401i | ||||
\(377\) | −10.3468 | − | 11.9409i | −0.532889 | − | 0.614986i | ||||
\(378\) | 20.4489 | + | 13.1417i | 1.05178 | + | 0.675935i | ||||
\(379\) | 2.91401 | − | 20.2674i | 0.149683 | − | 1.04107i | −0.767056 | − | 0.641580i | \(-0.778279\pi\) |
0.916739 | − | 0.399487i | \(-0.130812\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.5192 | + | 12.5442i | 0.999998 | + | 0.642660i | ||||
\(382\) | −7.84563 | − | 9.05434i | −0.401417 | − | 0.463260i | ||||
\(383\) | 4.93623 | + | 10.8088i | 0.252230 | + | 0.552306i | 0.992815 | − | 0.119656i | \(-0.0381791\pi\) |
−0.740586 | + | 0.671962i | \(0.765452\pi\) | |||||||
\(384\) | −46.0812 | + | 29.6146i | −2.35157 | + | 1.51126i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.55042 | + | 9.86771i | −0.435205 | + | 0.502253i | ||||
\(387\) | −15.8236 | + | 4.64624i | −0.804361 | + | 0.236182i | ||||
\(388\) | 13.9509 | − | 30.5482i | 0.708249 | − | 1.55085i | ||||
\(389\) | 2.44932 | + | 17.0354i | 0.124186 | + | 0.863730i | 0.952733 | + | 0.303810i | \(0.0982588\pi\) |
−0.828547 | + | 0.559919i | \(0.810832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.00268044 | − | 25.6385i | 0.000135556 | − | 1.29659i | ||||
\(392\) | 20.4471 | 1.03274 | ||||||||
\(393\) | 3.44074 | + | 23.9308i | 0.173562 | + | 1.20715i | ||||
\(394\) | −13.1394 | + | 28.7712i | −0.661952 | + | 1.44947i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −21.5067 | + | 24.8200i | −1.08075 | + | 1.24725i | ||||
\(397\) | 33.2841 | + | 9.77310i | 1.67048 | + | 0.490498i | 0.973900 | − | 0.226978i | \(-0.0728846\pi\) |
0.696583 | + | 0.717476i | \(0.254703\pi\) | |||||||
\(398\) | 6.29385 | − | 4.04481i | 0.315482 | − | 0.202748i | ||||
\(399\) | −10.6569 | − | 23.3354i | −0.533513 | − | 1.16823i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.64422 | + | 5.55530i | 0.431672 | + | 0.277419i | 0.738380 | − | 0.674385i | \(-0.235591\pi\) |
−0.306708 | + | 0.951804i | \(0.599228\pi\) | |||||||
\(402\) | 1.36714 | − | 9.50869i | 0.0681869 | − | 0.474251i | ||||
\(403\) | −1.14864 | + | 7.98895i | −0.0572177 | + | 0.397958i | ||||
\(404\) | −53.4568 | − | 34.3546i | −2.65958 | − | 1.70921i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.3687 | − | 33.6528i | −0.762737 | − | 1.67016i | ||||
\(407\) | 12.1935 | − | 7.83627i | 0.604408 | − | 0.388429i | ||||
\(408\) | −51.2993 | − | 15.0628i | −2.53969 | − | 0.745721i | ||||
\(409\) | −7.07591 | + | 8.16604i | −0.349881 | + | 0.403784i | −0.903224 | − | 0.429169i | \(-0.858806\pi\) |
0.553343 | + | 0.832954i | \(0.313352\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.99013 | − | 17.4959i | 0.394124 | − | 0.863011i | ||||
\(412\) | 1.01585 | + | 7.06537i | 0.0500472 | + | 0.348086i | ||||
\(413\) | 21.0805 | 1.03731 | ||||||||
\(414\) | −42.2212 | − | 19.2871i | −2.07506 | − | 0.947910i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.77000 | − | 12.3106i | −0.0867812 | − | 0.603577i | ||||
\(417\) | 8.92516 | − | 19.5434i | 0.437067 | − | 0.957043i | ||||
\(418\) | 13.8427 | − | 4.06458i | 0.677068 | − | 0.198805i | ||||
\(419\) | 3.34511 | − | 3.86046i | 0.163419 | − | 0.188596i | −0.668134 | − | 0.744041i | \(-0.732907\pi\) |
0.831553 | + | 0.555445i | \(0.187452\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.7319 | + | 8.82497i | −0.669253 | + | 0.430103i | −0.830656 | − | 0.556786i | \(-0.812034\pi\) |
0.161403 | + | 0.986889i | \(0.448398\pi\) | |||||||
\(422\) | −19.5244 | − | 42.7525i | −0.950434 | − | 2.08116i | ||||
\(423\) | −31.8749 | − | 36.7856i | −1.54981 | − | 1.78858i | ||||
\(424\) | 22.9698 | + | 14.7618i | 1.11551 | + | 0.716896i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.170737 | + | 1.18750i | −0.00827224 | + | 0.0575347i | ||||
\(427\) | −11.4762 | − | 7.37531i | −0.555372 | − | 0.356916i | ||||
\(428\) | 34.4681 | + | 39.7783i | 1.66608 | + | 1.92276i | ||||
\(429\) | −8.80926 | − | 19.2896i | −0.425315 | − | 0.931310i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.4425 | − | 9.52599i | −1.56270 | − | 0.458851i | −0.617835 | − | 0.786307i | \(-0.711990\pi\) |
−0.944866 | + | 0.327457i | \(0.893808\pi\) | |||||||
\(432\) | −3.24391 | + | 3.74367i | −0.156073 | + | 0.180117i | ||||
\(433\) | −11.3572 | + | 3.33479i | −0.545794 | + | 0.160260i | −0.542994 | − | 0.839736i | \(-0.682709\pi\) |
−0.00279993 | + | 0.999996i | \(0.500891\pi\) | |||||||
\(434\) | −7.85077 | + | 17.1908i | −0.376849 | + | 0.825185i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 48.5791 | 2.32652 | ||||||||
\(437\) | 7.07764 | + | 11.0156i | 0.338570 | + | 0.526946i | ||||
\(438\) | 28.3903 | 1.35654 | ||||||||
\(439\) | −0.148592 | − | 1.03348i | −0.00709190 | − | 0.0493253i | 0.985968 | − | 0.166933i | \(-0.0533865\pi\) |
−0.993060 | + | 0.117608i | \(0.962477\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −21.3928 | + | 6.28150i | −1.01871 | + | 0.299119i | ||||
\(442\) | 29.4762 | − | 34.0173i | 1.40204 | − | 1.61804i | ||||
\(443\) | −17.2535 | − | 5.06609i | −0.819739 | − | 0.240697i | −0.155136 | − | 0.987893i | \(-0.549581\pi\) |
−0.664604 | + | 0.747196i | \(0.731400\pi\) | |||||||
\(444\) | 52.1346 | − | 33.5049i | 2.47420 | − | 1.59007i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −30.6470 | − | 35.3685i | −1.45118 | − | 1.67475i | ||||
\(447\) | 18.3899 | + | 11.8185i | 0.869813 | + | 0.558995i | ||||
\(448\) | 5.85102 | − | 40.6947i | 0.276435 | − | 1.92264i | ||||
\(449\) | 3.70353 | − | 25.7586i | 0.174780 | − | 1.21562i | −0.693834 | − | 0.720135i | \(-0.744080\pi\) |
0.868614 | − | 0.495489i | \(-0.165011\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.21909 | + | 4.86909i | 0.198669 | + | 0.229276i | ||||
\(452\) | −3.20720 | − | 7.02279i | −0.150854 | − | 0.330324i | ||||
\(453\) | −13.1565 | + | 8.45514i | −0.618144 | + | 0.397257i | ||||
\(454\) | 20.7763 | + | 6.10048i | 0.975081 | + | 0.286310i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 26.1981 | − | 7.69245i | 1.22684 | − | 0.360232i | ||||
\(457\) | 17.6798 | − | 38.7134i | 0.827028 | − | 1.81094i | 0.326588 | − | 0.945167i | \(-0.394101\pi\) |
0.500439 | − | 0.865772i | \(-0.333172\pi\) | |||||||
\(458\) | −0.355422 | − | 2.47202i | −0.0166078 | − | 0.115510i | ||||
\(459\) | 15.5819 | 0.727301 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.19201 | 0.195241 | 0.0976206 | − | 0.995224i | \(-0.468877\pi\) | ||||
0.0976206 | + | 0.995224i | \(0.468877\pi\) | |||||||
\(462\) | −7.06651 | − | 49.1487i | −0.328764 | − | 2.28660i | ||||
\(463\) | −9.41743 | + | 20.6213i | −0.437665 | + | 0.958353i | 0.554356 | + | 0.832280i | \(0.312965\pi\) |
−0.992021 | + | 0.126073i | \(0.959763\pi\) | |||||||
\(464\) | 7.23394 | − | 2.12408i | 0.335827 | − | 0.0986078i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −52.5810 | − | 15.4392i | −2.43577 | − | 0.715205i | ||||
\(467\) | 23.7113 | − | 15.2384i | 1.09723 | − | 0.705147i | 0.138756 | − | 0.990327i | \(-0.455690\pi\) |
0.958474 | + | 0.285180i | \(0.0920533\pi\) | |||||||
\(468\) | −21.7374 | − | 47.5984i | −1.00481 | − | 2.20023i | ||||
\(469\) | 3.52472 | + | 4.06774i | 0.162756 | + | 0.187831i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.93350 | − | 48.2236i | 0.319479 | − | 2.22202i | ||||
\(472\) | −3.19308 | + | 22.2084i | −0.146973 | + | 1.02222i | ||||
\(473\) | 7.57464 | + | 4.86792i | 0.348282 | + | 0.223827i | ||||
\(474\) | 23.1442 | + | 26.7099i | 1.06305 | + | 1.22682i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 56.9321 | − | 36.5880i | 2.60948 | − | 1.67701i | ||||
\(477\) | −28.5671 | − | 8.38805i | −1.30800 | − | 0.384062i | ||||
\(478\) | 42.7633 | − | 49.3514i | 1.95595 | − | 2.25728i | ||||
\(479\) | −35.4090 | + | 10.3970i | −1.61788 | + | 0.475052i | −0.960447 | − | 0.278463i | \(-0.910175\pi\) |
−0.657431 | + | 0.753514i | \(0.728357\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.28664 | + | 22.8591i | 0.149858 | + | 1.04229i | ||||
\(482\) | 30.2500 | 1.37785 | ||||||||
\(483\) | 40.9933 | − | 18.7159i | 1.86526 | − | 0.851601i | ||||
\(484\) | −21.5412 | −0.979145 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −20.4086 | + | 44.6885i | −0.925751 | + | 2.02711i | ||||
\(487\) | −36.0854 | + | 10.5956i | −1.63519 | + | 0.480134i | −0.965042 | − | 0.262097i | \(-0.915586\pi\) |
−0.670145 | + | 0.742231i | \(0.733768\pi\) | |||||||
\(488\) | 9.50820 | − | 10.9730i | 0.430416 | − | 0.496727i | ||||
\(489\) | −1.96684 | − | 0.577515i | −0.0889434 | − | 0.0261161i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.61449 | + | 16.6734i | 0.343637 | + | 0.752460i | 0.999998 | − | 0.00198684i | \(-0.000632432\pi\) |
−0.656361 | + | 0.754447i | \(0.727905\pi\) | |||||||
\(492\) | 18.0392 | + | 20.8183i | 0.813270 | + | 0.938563i | ||||
\(493\) | −19.9508 | − | 12.8216i | −0.898541 | − | 0.577457i | ||||
\(494\) | −3.27138 | + | 22.7529i | −0.147186 | + | 1.02370i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.23992 | − | 2.08217i | −0.145477 | − | 0.0934923i | ||||
\(497\) | −0.440188 | − | 0.508004i | −0.0197451 | − | 0.0227871i | ||||
\(498\) | −19.5390 | − | 42.7843i | −0.875561 | − | 1.91721i | ||||
\(499\) | 26.7787 | − | 17.2096i | 1.19878 | − | 0.770407i | 0.220033 | − | 0.975492i | \(-0.429383\pi\) |
0.978744 | + | 0.205085i | \(0.0657471\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.1646 | + | 34.8118i | −1.34765 | + | 1.55527i | ||||
\(502\) | −5.42200 | + | 1.59204i | −0.241996 | + | 0.0710564i | ||||
\(503\) | 9.46207 | − | 20.7190i | 0.421893 | − | 0.923817i | −0.572680 | − | 0.819779i | \(-0.694096\pi\) |
0.994573 | − | 0.104038i | \(-0.0331764\pi\) | |||||||
\(504\) | −7.71835 | − | 53.6823i | −0.343803 | − | 2.39120i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.13737 | + | 24.3171i | 0.317295 | + | 1.08102i | ||||
\(507\) | −0.837931 | −0.0372138 | ||||||||
\(508\) | −4.44861 | − | 30.9407i | −0.197375 | − | 1.37277i | ||||
\(509\) | −7.55811 | + | 16.5500i | −0.335007 | + | 0.733564i | −0.999911 | − | 0.0133655i | \(-0.995745\pi\) |
0.664903 | + | 0.746930i | \(0.268473\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.4167 | + | 12.0215i | −0.460809 | + | 0.531802i | ||||
\(512\) | 17.9400 | + | 5.26767i | 0.792845 | + | 0.232800i | ||||
\(513\) | −6.69431 | + | 4.30217i | −0.295561 | + | 0.189946i | ||||
\(514\) | −14.3930 | − | 31.5164i | −0.634850 | − | 1.39013i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 32.3862 | + | 20.8134i | 1.42572 | + | 0.916258i | ||||
\(517\) | −3.78200 | + | 26.3044i | −0.166332 | + | 1.15686i | ||||
\(518\) | −7.69573 | + | 53.5250i | −0.338131 | + | 2.35175i | ||||
\(519\) | 19.8440 | + | 12.7530i | 0.871055 | + | 0.559793i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.6857 | − | 34.3469i | −0.687204 | − | 1.50477i | −0.854825 | − | 0.518916i | \(-0.826336\pi\) |
0.167621 | − | 0.985851i | \(-0.446391\pi\) | |||||||
\(522\) | −36.1206 | + | 23.2133i | −1.58095 | + | 1.01602i | ||||
\(523\) | 6.84693 | + | 2.01044i | 0.299396 | + | 0.0879105i | 0.427980 | − | 0.903788i | \(-0.359225\pi\) |
−0.128585 | + | 0.991699i | \(0.541043\pi\) | |||||||
\(524\) | 21.3299 | − | 24.6160i | 0.931802 | − | 1.07536i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −29.1246 | + | 63.7739i | −1.26989 | + | 2.78068i | ||||
\(527\) | 1.72409 | + | 11.9913i | 0.0751024 | + | 0.522348i | ||||
\(528\) | 10.1189 | 0.440368 | ||||||||
\(529\) | −19.3514 | + | 12.4307i | −0.841367 | + | 0.540465i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.48180 | − | 24.2165i | −0.151097 | − | 1.05090i | ||||
\(532\) | −14.3572 | + | 31.4380i | −0.622465 | + | 1.36301i | ||||
\(533\) | −9.84948 | + | 2.89207i | −0.426628 | + | 0.125269i | ||||
\(534\) | 20.7491 | − | 23.9457i | 0.897899 | − | 1.03623i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.81926 | + | 3.09715i | −0.208160 | + | 0.133777i | ||||
\(537\) | −4.92361 | − | 10.7812i | −0.212470 | − | 0.465244i | ||||
\(538\) | 39.7925 | + | 45.9230i | 1.71558 | + | 1.97988i | ||||
\(539\) | 10.2406 | + | 6.58121i | 0.441092 | + | 0.283473i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.63696 | − | 32.2508i | 0.199358 | − | 1.38657i | −0.606793 | − | 0.794860i | \(-0.707544\pi\) |
0.806152 | − | 0.591709i | \(-0.201547\pi\) | |||||||
\(542\) | −13.1416 | − | 8.44558i | −0.564479 | − | 0.362769i | ||||
\(543\) | 11.6886 | + | 13.4893i | 0.501604 | + | 0.578882i | ||||
\(544\) | −7.75498 | − | 16.9810i | −0.332492 | − | 0.728056i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 75.9099 | + | 22.2892i | 3.24864 | + | 0.953888i | ||||
\(547\) | −2.17243 | + | 2.50711i | −0.0928862 | + | 0.107196i | −0.800290 | − | 0.599614i | \(-0.795321\pi\) |
0.707403 | + | 0.706810i | \(0.249866\pi\) | |||||||
\(548\) | −24.8629 | + | 7.30042i | −1.06209 | + | 0.311858i | ||||
\(549\) | −6.57696 | + | 14.4015i | −0.280698 | + | 0.614643i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.1113 | 0.515961 | ||||||||
\(552\) | 13.5079 | + | 46.0214i | 0.574934 | + | 1.95880i | ||||
\(553\) | −19.8018 | −0.842060 | ||||||||
\(554\) | 4.69370 | + | 32.6454i | 0.199416 | + | 1.38697i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −27.7725 | + | 8.15474i | −1.17782 | + | 0.345838i | ||||
\(557\) | −14.5209 | + | 16.7580i | −0.615268 | + | 0.710057i | −0.974801 | − | 0.223075i | \(-0.928391\pi\) |
0.359533 | + | 0.933132i | \(0.382936\pi\) | |||||||
\(558\) | 21.0448 | + | 6.17930i | 0.890896 | + | 0.261591i | ||||
\(559\) | −12.0688 | + | 7.75614i | −0.510455 | + | 0.328050i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.8441 | − | 24.0553i | −0.880037 | − | 1.01562i | ||||
\(562\) | −7.90575 | − | 5.08072i | −0.333484 | − | 0.214317i | ||||
\(563\) | 3.60466 | − | 25.0710i | 0.151918 | − | 1.05662i | −0.761082 | − | 0.648656i | \(-0.775331\pi\) |
0.913000 | − | 0.407959i | \(-0.133760\pi\) | |||||||
\(564\) | −16.1704 | + | 112.467i | −0.680895 | + | 4.73573i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 19.0224 | + | 21.9530i | 0.799569 | + | 0.922752i | ||||
\(567\) | −6.62353 | − | 14.5035i | −0.278162 | − | 0.609090i | ||||
\(568\) | 0.601859 | − | 0.386791i | 0.0252534 | − | 0.0162294i | ||||
\(569\) | 7.77393 | + | 2.28263i | 0.325900 | + | 0.0956929i | 0.440590 | − | 0.897708i | \(-0.354769\pi\) |
−0.114690 | + | 0.993401i | \(0.536587\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.3509 | − | 10.3799i | 1.47939 | − | 0.434387i | 0.560250 | − | 0.828324i | \(-0.310705\pi\) |
0.919138 | + | 0.393937i | \(0.128887\pi\) | |||||||
\(572\) | −11.8680 | + | 25.9874i | −0.496227 | + | 1.08659i | ||||
\(573\) | −1.92107 | − | 13.3613i | −0.0802537 | − | 0.558177i | ||||
\(574\) | −24.0364 | −1.00326 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −47.7148 | −1.98812 | ||||||||
\(577\) | −2.55037 | − | 17.7382i | −0.106173 | − | 0.738452i | −0.971465 | − | 0.237183i | \(-0.923776\pi\) |
0.865291 | − | 0.501269i | \(-0.167133\pi\) | |||||||
\(578\) | 11.3715 | − | 24.9001i | 0.472993 | − | 1.03571i | ||||
\(579\) | −14.1154 | + | 4.14466i | −0.586617 | + | 0.172246i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.2856 | + | 7.42451i | 1.04902 | + | 0.308021i | ||||
\(582\) | 49.5734 | − | 31.8589i | 2.05489 | − | 1.32059i | ||||
\(583\) | 6.75268 | + | 14.7863i | 0.279668 | + | 0.612387i | ||||
\(584\) | −11.0869 | − | 12.7949i | −0.458778 | − | 0.529458i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.85078 | − | 19.8276i | 0.117764 | − | 0.819070i | ||||
\(587\) | 2.42196 | − | 16.8451i | 0.0999649 | − | 0.695271i | −0.876784 | − | 0.480884i | \(-0.840316\pi\) |
0.976749 | − | 0.214387i | \(-0.0687752\pi\) | |||||||
\(588\) | 43.7847 | + | 28.1387i | 1.80565 | + | 1.16042i | ||||
\(589\) | −4.05150 | − | 4.67568i | −0.166939 | − | 0.192658i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −29.9801 | + | 19.2670i | −1.23321 | + | 0.792539i | ||||
\(592\) | −10.5735 | − | 3.10466i | −0.434569 | − | 0.127601i | ||||
\(593\) | −21.7752 | + | 25.1299i | −0.894201 | + | 1.03196i | 0.105095 | + | 0.994462i | \(0.466485\pi\) |
−0.999297 | + | 0.0375010i | \(0.988060\pi\) | |||||||
\(594\) | −14.7784 | + | 4.33932i | −0.606363 | + | 0.178044i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.19124 | − | 29.1507i | −0.171680 | − | 1.19406i | ||||
\(597\) | 8.42952 | 0.344997 | ||||||||
\(598\) | −39.9676 | − | 5.75074i | −1.63440 | − | 0.235165i | ||||
\(599\) | −6.89064 | −0.281544 | −0.140772 | − | 0.990042i | \(-0.544958\pi\) | ||||
−0.140772 | + | 0.990042i | \(0.544958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.28839 | + | 13.7696i | −0.256509 | + | 0.561676i | −0.993448 | − | 0.114283i | \(-0.963543\pi\) |
0.736940 | + | 0.675959i | \(0.236270\pi\) | |||||||
\(602\) | −32.2312 | + | 9.46393i | −1.31364 | + | 0.385721i | ||||
\(603\) | 4.09069 | − | 4.72091i | 0.166586 | − | 0.192250i | ||||
\(604\) | 20.2159 | + | 5.93592i | 0.822573 | + | 0.241529i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −46.3192 | − | 101.425i | −1.88159 | − | 4.12010i | ||||
\(607\) | −21.5668 | − | 24.8894i | −0.875370 | − | 1.01023i | −0.999838 | − | 0.0180070i | \(-0.994268\pi\) |
0.124468 | − | 0.992224i | \(-0.460278\pi\) | |||||||
\(608\) | 8.02017 | + | 5.15425i | 0.325261 | + | 0.209032i | ||||
\(609\) | 5.93225 | − | 41.2597i | 0.240387 | − | 1.67193i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.6205 | − | 22.8919i | −1.44105 | − | 0.926106i | ||||
\(612\) | −51.4341 | − | 59.3581i | −2.07910 | − | 2.39941i | ||||
\(613\) | 18.8285 | + | 41.2287i | 0.760477 | + | 1.66521i | 0.746568 | + | 0.665309i | \(0.231700\pi\) |
0.0139091 | + | 0.999903i | \(0.495572\pi\) | |||||||
\(614\) | 30.6856 | − | 19.7204i | 1.23837 | − | 0.795851i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −19.3907 | + | 22.3781i | −0.781274 | + | 0.901638i | ||||
\(617\) | −29.8682 | + | 8.77009i | −1.20245 | + | 0.353070i | −0.820788 | − | 0.571233i | \(-0.806465\pi\) |
−0.381659 | + | 0.924303i | \(0.624647\pi\) | |||||||
\(618\) | −5.20310 | + | 11.3932i | −0.209299 | + | 0.458302i | ||||
\(619\) | 0.641572 | + | 4.46223i | 0.0257870 | + | 0.179352i | 0.998644 | − | 0.0520534i | \(-0.0165766\pi\) |
−0.972857 | + | 0.231406i | \(0.925668\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.55605 | − | 11.7601i | −0.303214 | − | 0.471918i | ||||
\(622\) | 63.6814 | 2.55339 | ||||||||
\(623\) | 2.52645 | + | 17.5719i | 0.101220 | + | 0.704002i | ||||
\(624\) | −6.69756 | + | 14.6656i | −0.268117 | + | 0.587094i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 29.5504 | − | 34.1030i | 1.18107 | − | 1.36303i | ||||
\(627\) | 15.5967 | + | 4.57961i | 0.622873 | + | 0.182892i | ||||
\(628\) | −55.2165 | + | 35.4855i | −2.20338 | + | 1.41602i | ||||
\(629\) | 14.3999 | + | 31.5315i | 0.574163 | + | 1.25724i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.70287 | + | 4.30767i | 0.266837 | + | 0.171486i | 0.667217 | − | 0.744864i | \(-0.267485\pi\) |
−0.400380 | + | 0.916349i | \(0.631122\pi\) | |||||||
\(632\) | 2.99939 | − | 20.8612i | 0.119310 | − | 0.829816i | ||||
\(633\) | 7.53632 | − | 52.4163i | 0.299542 | − | 2.08336i | ||||
\(634\) | 26.9866 | + | 17.3433i | 1.07178 | + | 0.688789i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 28.8719 | + | 63.2206i | 1.14484 | + | 2.50686i | ||||
\(637\) | −16.3164 | + | 10.4859i | −0.646481 | + | 0.415468i | ||||
\(638\) | 22.4926 | + | 6.60442i | 0.890491 | + | 0.261472i | ||||
\(639\) | −0.510870 | + | 0.589575i | −0.0202097 | + | 0.0233232i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.3922 | + | 27.1351i | −0.489462 | + | 1.07177i | 0.490291 | + | 0.871559i | \(0.336891\pi\) |
−0.979752 | + | 0.200213i | \(0.935837\pi\) | |||||||
\(642\) | 13.1438 | + | 91.4172i | 0.518745 | + | 3.60795i | ||||
\(643\) | −29.0966 | −1.14746 | −0.573728 | − | 0.819046i | \(-0.694503\pi\) | ||||
−0.573728 | + | 0.819046i | \(0.694503\pi\) | |||||||
\(644\) | −55.2219 | − | 25.2260i | −2.17605 | − | 0.994042i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.91028 | + | 34.1518i | 0.193192 | + | 1.34368i | ||||
\(647\) | −10.1294 | + | 22.1804i | −0.398229 | + | 0.872001i | 0.599217 | + | 0.800586i | \(0.295479\pi\) |
−0.997447 | + | 0.0714143i | \(0.977249\pi\) | |||||||
\(648\) | 16.2827 | − | 4.78104i | 0.639646 | − | 0.187817i | ||||
\(649\) | −8.74728 | + | 10.0949i | −0.343361 | + | 0.396259i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.9131 | + | 11.5120i | −0.702069 | + | 0.451192i | ||||
\(652\) | 1.14722 | + | 2.51207i | 0.0449287 | + | 0.0983802i | ||||
\(653\) | 16.4632 | + | 18.9996i | 0.644256 | + | 0.743511i | 0.980121 | − | 0.198399i | \(-0.0635741\pi\) |
−0.335865 | + | 0.941910i | \(0.609029\pi\) | |||||||
\(654\) | 71.7098 | + | 46.0851i | 2.80408 | + | 1.80207i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.697103 | − | 4.84846i | 0.0272173 | − | 0.189300i | ||||
\(657\) | 15.5303 | + | 9.98075i | 0.605897 | + | 0.389386i | ||||
\(658\) | −64.9261 | − | 74.9287i | −2.53108 | − | 2.92102i | ||||
\(659\) | 11.3454 | + | 24.8431i | 0.441956 | + | 0.967748i | 0.991235 | + | 0.132110i | \(0.0421751\pi\) |
−0.549279 | + | 0.835639i | \(0.685098\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.8051 | − | 7.57707i | −1.00370 | − | 0.294714i | −0.261729 | − | 0.965142i | \(-0.584293\pi\) |
−0.741975 | + | 0.670428i | \(0.766111\pi\) | |||||||
\(662\) | 44.2484 | − | 51.0654i | 1.71976 | − | 1.98471i | ||||
\(663\) | 48.6606 | − | 14.2880i | 1.88982 | − | 0.554901i | ||||
\(664\) | −11.6517 | + | 25.5138i | −0.452175 | + | 0.990126i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 62.7584 | 2.43184 | ||||||||
\(667\) | −0.00222425 | + | 21.2750i | −8.61233e−5 | + | 0.823772i | ||||
\(668\) | 62.0565 | 2.40104 | ||||||||
\(669\) | −7.50416 | − | 52.1926i | −0.290128 | − | 2.01788i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.29383 | − | 2.43529i | 0.320180 | − | 0.0940133i | ||||
\(672\) | 21.4873 | − | 24.7977i | 0.828891 | − | 0.956591i | ||||
\(673\) | −32.1719 | − | 9.44653i | −1.24014 | − | 0.364137i | −0.405070 | − | 0.914286i | \(-0.632753\pi\) |
−0.835067 | + | 0.550149i | \(0.814571\pi\) | |||||||
\(674\) | 48.6677 | − | 31.2768i | 1.87461 | − | 1.20474i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.739259 | + | 0.853150i | 0.0284330 | + | 0.0328135i | ||||
\(677\) | −8.25789 | − | 5.30702i | −0.317376 | − | 0.203965i | 0.372247 | − | 0.928134i | \(-0.378587\pi\) |
−0.689623 | + | 0.724168i | \(0.742224\pi\) | |||||||
\(678\) | 1.92795 | − | 13.4092i | 0.0740426 | − | 0.514978i | ||||
\(679\) | −4.69877 | + | 32.6807i | −0.180322 | + | 1.25417i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.9768 | + | 18.4382i | 0.612231 | + | 0.706552i | ||||
\(682\) | −4.97456 | − | 10.8928i | −0.190486 | − | 0.417106i | ||||
\(683\) | 3.61887 | − | 2.32570i | 0.138472 | − | 0.0889906i | −0.469571 | − | 0.882895i | \(-0.655591\pi\) |
0.608043 | + | 0.793904i | \(0.291955\pi\) | |||||||
\(684\) | 38.4860 | + | 11.3005i | 1.47155 | + | 0.432085i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12.4380 | − | 3.65213i | 0.474886 | − | 0.139439i | ||||
\(687\) | 1.16893 | − | 2.55961i | 0.0445976 | − | 0.0976552i | ||||
\(688\) | −0.974231 | − | 6.77593i | −0.0371422 | − | 0.258330i | ||||
\(689\) | −25.8998 | −0.986703 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.1512 | 1.37526 | 0.687628 | − | 0.726063i | \(-0.258652\pi\) | ||||
0.687628 | + | 0.726063i | \(0.258652\pi\) | |||||||
\(692\) | −4.52264 | − | 31.4556i | −0.171925 | − | 1.19576i | ||||
\(693\) | 13.4128 | − | 29.3700i | 0.509512 | − | 1.11567i | ||||
\(694\) | 32.2209 | − | 9.46092i | 1.22309 | − | 0.359132i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 42.5685 | + | 12.4993i | 1.61356 | + | 0.473783i | ||||
\(697\) | −12.9621 | + | 8.33022i | −0.490974 | + | 0.315530i | ||||
\(698\) | −28.7969 | − | 63.0565i | −1.08998 | − | 2.38672i | ||||
\(699\) | −40.4342 | − | 46.6636i | −1.52936 | − | 1.76498i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.83086 | + | 19.6891i | −0.106920 | + | 0.743645i | 0.863870 | + | 0.503715i | \(0.168034\pi\) |
−0.970790 | + | 0.239930i | \(0.922875\pi\) | |||||||
\(702\) | 3.49250 | − | 24.2909i | 0.131816 | − | 0.916800i | ||||
\(703\) | −14.8924 | − | 9.57074i | −0.561676 | − | 0.360967i | ||||
\(704\) | 17.0597 | + | 19.6880i | 0.642963 | + | 0.742019i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.875256 | − | 0.562493i | 0.0329407 | − | 0.0211697i | ||||
\(707\) | 59.9421 | + | 17.6006i | 2.25436 | + | 0.661939i | ||||
\(708\) | −37.4000 | + | 43.1619i | −1.40558 | + | 1.62212i | ||||
\(709\) | 22.6013 | − | 6.63633i | 0.848809 | − | 0.249233i | 0.171731 | − | 0.985144i | \(-0.445064\pi\) |
0.677078 | + | 0.735911i | \(0.263246\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.27060 | + | 22.7475i | 0.122657 | + | 0.853099i | ||||
\(712\) | −18.8947 | −0.708107 | ||||||||
\(713\) | 8.21413 | − | 7.11608i | 0.307622 | − | 0.266499i | ||||
\(714\) | 118.750 | 4.44410 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.63320 | + | 14.5247i | −0.247894 | + | 0.542813i | ||||
\(717\) | 70.5955 | − | 20.7287i | 2.63644 | − | 0.774128i | ||||
\(718\) | 27.6949 | − | 31.9616i | 1.03356 | − | 1.19280i | ||||
\(719\) | 6.30658 | + | 1.85178i | 0.235196 | + | 0.0690597i | 0.397206 | − | 0.917729i | \(-0.369980\pi\) |
−0.162011 | + | 0.986789i | \(0.551798\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.91524 | − | 6.38348i | −0.108569 | − | 0.237733i | ||||
\(722\) | 17.8744 | + | 20.6282i | 0.665218 | + | 0.767703i | ||||
\(723\) | 28.6725 | + | 18.4267i | 1.06634 | + | 0.685296i | ||||
\(724\) | 3.42217 | − | 23.8017i | 0.127184 | − | 0.884584i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −31.7979 | − | 20.4353i | −1.18013 | − | 0.758425i | ||||
\(727\) | −14.4754 | − | 16.7055i | −0.536864 | − | 0.619574i | 0.420908 | − | 0.907103i | \(-0.361712\pi\) |
−0.957772 | + | 0.287529i | \(0.907166\pi\) | |||||||
\(728\) | −19.5988 | − | 42.9153i | −0.726378 | − | 1.59055i | ||||
\(729\) | −35.1598 | + | 22.5958i | −1.30221 | + | 0.836883i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.1014 | + | 16.2739i | −0.521559 | + | 0.601911i | ||||
\(732\) | 35.4612 | − | 10.4124i | 1.31069 | − | 0.384852i | ||||
\(733\) | 9.93068 | − | 21.7452i | 0.366798 | − | 0.803176i | −0.632786 | − | 0.774327i | \(-0.718089\pi\) |
0.999584 | − | 0.0288488i | \(-0.00918415\pi\) | |||||||
\(734\) | −4.81286 | − | 33.4742i | −0.177646 | − | 1.23556i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.05552 | + | 14.0874i | −0.333791 | + | 0.519270i | ||||
\(737\) | −3.41050 | −0.125627 | ||||||||
\(738\) | 3.97001 | + | 27.6120i | 0.146138 | + | 1.01641i | ||||
\(739\) | 10.5665 | − | 23.1373i | 0.388693 | − | 0.851120i | −0.609599 | − | 0.792710i | \(-0.708670\pi\) |
0.998293 | − | 0.0584100i | \(-0.0186031\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.9606 | + | 19.5736i | −0.623065 | + | 0.719055i | ||||
\(742\) | −58.1883 | − | 17.0856i | −2.13616 | − | 0.627233i | ||||
\(743\) | 2.96587 | − | 1.90605i | 0.108807 | − | 0.0699261i | −0.485106 | − | 0.874456i | \(-0.661219\pi\) |
0.593913 | + | 0.804530i | \(0.297582\pi\) | |||||||
\(744\) | −9.41464 | − | 20.6152i | −0.345157 | − | 0.755789i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 25.6495 | + | 16.4839i | 0.939094 | + | 0.603519i | ||||
\(747\) | 4.35264 | − | 30.2733i | 0.159255 | − | 1.10764i | ||||
\(748\) | −6.10271 | + | 42.4453i | −0.223137 | + | 1.55195i | ||||
\(749\) | −43.5321 | − | 27.9764i | −1.59063 | − | 1.02223i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.61807 | − | 16.6812i | −0.277987 | − | 0.608707i | 0.718211 | − | 0.695826i | \(-0.244961\pi\) |
−0.996198 | + | 0.0871186i | \(0.972234\pi\) | |||||||
\(752\) | 16.9971 | − | 10.9234i | 0.619820 | − | 0.398334i | ||||
\(753\) | −6.10904 | − | 1.79378i | −0.222626 | − | 0.0653688i | ||||
\(754\) | −24.4596 | + | 28.2278i | −0.890765 | + | 1.02800i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 15.3277 | − | 33.5630i | 0.557463 | − | 1.22067i | ||||
\(757\) | −0.0678232 | − | 0.471721i | −0.00246508 | − | 0.0171450i | 0.988552 | − | 0.150882i | \(-0.0482113\pi\) |
−0.991017 | + | 0.133737i | \(0.957302\pi\) | |||||||
\(758\) | −48.4042 | −1.75812 | ||||||||
\(759\) | −8.04750 | + | 27.3967i | −0.292106 | + | 0.994436i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.96300 | − | 20.6081i | −0.107409 | − | 0.747043i | −0.970344 | − | 0.241728i | \(-0.922286\pi\) |
0.862935 | − | 0.505314i | \(-0.168623\pi\) | |||||||
\(762\) | 22.7855 | − | 49.8933i | 0.825431 | − | 1.80744i | ||||
\(763\) | −45.8253 | + | 13.4555i | −1.65899 | + | 0.487123i | ||||
\(764\) | −11.9091 | + | 13.7439i | −0.430857 | + | 0.497236i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.6310 | − | 15.1867i | 0.853822 | − | 0.548718i | ||||
\(767\) | −8.84114 | − | 19.3594i | −0.319235 | − | 0.699027i | ||||
\(768\) | 44.1440 | + | 50.9449i | 1.59291 | + | 1.83831i | ||||
\(769\) | −10.8385 | − | 6.96550i | −0.390847 | − | 0.251182i | 0.330427 | − | 0.943831i | \(-0.392807\pi\) |
−0.721275 | + | 0.692649i | \(0.756444\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.55564 | − | 38.6403i | 0.200081 | − | 1.39160i | ||||
\(772\) | 16.6732 | + | 10.7152i | 0.600080 | + | 0.385648i | ||||
\(773\) | 25.9803 | + | 29.9828i | 0.934446 | + | 1.07841i | 0.996767 | + | 0.0803519i | \(0.0256044\pi\) |
−0.0623206 | + | 0.998056i | \(0.519850\pi\) | |||||||
\(774\) | 16.1953 | + | 35.4627i | 0.582127 | + | 1.27468i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −33.7174 | − | 9.90031i | −1.21038 | − | 0.355400i | ||||
\(777\) | −39.8990 | + | 46.0459i | −1.43137 | + | 1.65189i | ||||
\(778\) | 39.0372 | − | 11.4624i | 1.39955 | − | 0.410946i | ||||
\(779\) | 3.26880 | − | 7.15767i | 0.117117 | − | 0.256450i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.425924 | 0.0152408 | ||||||||
\(782\) | −59.9925 | + | 8.61922i | −2.14533 | + | 0.308223i | ||||
\(783\) | −12.9300 | −0.462080 | ||||||||
\(784\) | −1.31712 | − | 9.16074i | −0.0470399 | − | 0.327169i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 54.8384 | − | 16.1020i | 1.95602 | − | 0.574339i | ||||
\(787\) | −32.0522 | + | 36.9902i | −1.14254 | + | 1.31856i | −0.201796 | + | 0.979428i | \(0.564678\pi\) |
−0.940740 | + | 0.339129i | \(0.889868\pi\) | |||||||
\(788\) | 46.0666 | + | 13.5264i | 1.64106 | + | 0.481858i | ||||
\(789\) | −66.4535 | + | 42.7071i | −2.36581 | + | 1.52041i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.97058 | + | 5.73636i | 0.176733 | + | 0.203961i | ||||
\(792\) | 28.9097 | + | 18.5791i | 1.02726 | + | 0.660180i | ||||
\(793\) | −1.96004 | + | 13.6324i | −0.0696032 | + | 0.484101i | ||||
\(794\) | 11.6704 | − | 81.1697i | 0.414168 | − | 2.88060i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.43688 | − | 8.58262i | −0.263593 | − | 0.304203i | ||||
\(797\) | 17.2590 | + | 37.7919i | 0.611344 | + | 1.33866i | 0.921651 | + | 0.388020i | \(0.126841\pi\) |
−0.310307 | + | 0.950636i | \(0.600432\pi\) | |||||||
\(798\) | −51.0174 | + | 32.7869i | −1.80599 | + | 1.16064i | ||||
\(799\) | −60.9804 | − | 17.9055i | −2.15733 | − | 0.633450i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.7685 | − | 5.80457i | 0.698487 | − | 0.205094i | ||||
\(802\) | 10.0907 | − | 22.0956i | 0.356316 | − | 0.780224i | ||||
\(803\) | −1.43441 | − | 9.97658i | −0.0506194 | − | 0.352066i | ||||
\(804\) | −14.5820 | −0.514267 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 19.0798 | 0.672058 | ||||||||
\(807\) | 9.74353 | + | 67.7677i | 0.342988 | + | 2.38554i | ||||
\(808\) | −27.6217 | + | 60.4831i | −0.971728 | + | 2.12779i | ||||
\(809\) | 39.8880 | − | 11.7122i | 1.40239 | − | 0.411778i | 0.508885 | − | 0.860835i | \(-0.330058\pi\) |
0.893504 | + | 0.449056i | \(0.148240\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.376831 | − | 0.110647i | −0.0132323 | − | 0.00388536i | 0.275110 | − | 0.961413i | \(-0.411286\pi\) |
−0.288342 | + | 0.957527i | \(0.593104\pi\) | |||||||
\(812\) | −47.2427 | + | 30.3611i | −1.65789 | + | 1.06546i | ||||
\(813\) | −7.31167 | − | 16.0103i | −0.256431 | − | 0.561506i | ||||
\(814\) | −22.4384 | − | 25.8952i | −0.786464 | − | 0.907628i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.44398 | + | 23.9534i | −0.120563 | + | 0.838537i | ||||
\(817\) | 1.56503 | − | 10.8850i | 0.0547533 | − | 0.380818i | ||||
\(818\) | 21.4883 | + | 13.8097i | 0.751320 | + | 0.482844i | ||||
\(819\) | 33.6891 | + | 38.8793i | 1.17719 | + | 1.35855i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.225917 | + | 0.145188i | −0.00788457 | + | 0.00506710i | −0.544577 | − | 0.838711i | \(-0.683310\pi\) |
0.536693 | + | 0.843778i | \(0.319673\pi\) | |||||||
\(822\) | −43.6269 | − | 12.8100i | −1.52166 | − | 0.446801i | ||||
\(823\) | −6.84511 | + | 7.89968i | −0.238606 | + | 0.275366i | −0.862405 | − | 0.506219i | \(-0.831043\pi\) |
0.623799 | + | 0.781585i | \(0.285588\pi\) | |||||||
\(824\) | 7.16658 | − | 2.10430i | 0.249659 | − | 0.0733066i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.09208 | − | 49.3265i | −0.246765 | − | 1.71629i | ||||
\(827\) | −30.9322 | −1.07562 | −0.537809 | − | 0.843067i | \(-0.680748\pi\) | ||||
−0.537809 | + | 0.843067i | \(0.680748\pi\) | |||||||
\(828\) | −19.8577 | + | 67.6031i | −0.690104 | + | 2.34937i | ||||
\(829\) | 29.2137 | 1.01463 | 0.507316 | − | 0.861760i | \(-0.330638\pi\) | ||||
0.507316 | + | 0.861760i | \(0.330638\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.4369 | + | 33.8021i | −0.535501 | + | 1.17258i | ||||
\(832\) | −39.8260 | + | 11.6940i | −1.38072 | + | 0.405416i | ||||
\(833\) | −19.0644 | + | 22.0015i | −0.660543 | + | 0.762308i | ||||
\(834\) | −48.7323 | − | 14.3091i | −1.68746 | − | 0.495484i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9.09731 | − | 19.9203i | −0.314637 | − | 0.688959i | ||||
\(837\) | 4.32536 | + | 4.99173i | 0.149506 | + | 0.172539i | ||||
\(838\) | −10.1585 | − | 6.52847i | −0.350920 | − | 0.225522i | ||||
\(839\) | −4.71976 | + | 32.8267i | −0.162944 | + | 1.13330i | 0.730102 | + | 0.683338i | \(0.239472\pi\) |
−0.893047 | + | 0.449964i | \(0.851437\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.84098 | − | 5.03909i | −0.270379 | − | 0.173762i | ||||
\(842\) | 25.2694 | + | 29.1625i | 0.870841 | + | 1.00500i | ||||
\(843\) | −4.39857 | − | 9.63153i | −0.151495 | − | 0.331728i | ||||
\(844\) | −60.0171 | + | 38.5707i | −2.06587 | + | 1.32766i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −75.3513 | + | 86.9601i | −2.59063 | + | 2.98975i | ||||
\(847\) | 20.3201 | − | 5.96651i | 0.698206 | − | 0.205012i | ||||
\(848\) | 5.13397 | − | 11.2418i | 0.176301 | − | 0.386046i | ||||
\(849\) | 4.65778 | + | 32.3956i | 0.159855 | + | 1.11181i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.8149 | − | 26.1584i | 0.576406 | − | 0.896700i | ||||
\(852\) | 1.82109 | 0.0623894 | ||||||||
\(853\) | 7.59008 | + | 52.7902i | 0.259879 | + | 1.80750i | 0.533650 | + | 0.845705i | \(0.320820\pi\) |
−0.273771 | + | 0.961795i | \(0.588271\pi\) | |||||||
\(854\) | −13.3966 | + | 29.3345i | −0.458423 | + | 1.00381i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 36.0670 | − | 41.6235i | 1.23274 | − | 1.42266i | ||||
\(857\) | 5.53794 | + | 1.62608i | 0.189172 | + | 0.0555460i | 0.374946 | − | 0.927046i | \(-0.377661\pi\) |
−0.185774 | + | 0.982592i | \(0.559479\pi\) | |||||||
\(858\) | −42.1722 | + | 27.1024i | −1.43973 | + | 0.925261i | ||||
\(859\) | −13.4507 | − | 29.4529i | −0.458931 | − | 1.00492i | −0.987730 | − | 0.156172i | \(-0.950085\pi\) |
0.528799 | − | 0.848747i | \(-0.322643\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.7829 | − | 14.6417i | −0.776440 | − | 0.498987i | ||||
\(862\) | −11.3753 | + | 79.1173i | −0.387446 | + | 2.69474i | ||||
\(863\) | −2.20431 | + | 15.3313i | −0.0750355 | + | 0.521883i | 0.917289 | + | 0.398222i | \(0.130373\pi\) |
−0.992325 | + | 0.123661i | \(0.960536\pi\) | |||||||
\(864\) | −8.56228 | − | 5.50265i | −0.291295 | − | 0.187204i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11.6240 | + | 25.4530i | 0.394999 | + | 0.864927i | ||||
\(867\) | 25.9464 | − | 16.6747i | 0.881184 | − | 0.566303i | ||||
\(868\) | 27.5248 | + | 8.08202i | 0.934253 | + | 0.274322i | ||||
\(869\) | 8.21668 | − | 9.48256i | 0.278732 | − | 0.321674i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.25737 | − | 4.94294i | 0.0764879 | − | 0.167485i | ||||
\(872\) | −7.23422 | − | 50.3151i | −0.244982 | − | 1.70388i | ||||
\(873\) | 38.3183 | 1.29688 | ||||||||
\(874\) | 23.3943 | − | 20.2670i | 0.791322 | − | 0.685540i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.13301 | − | 42.6560i | −0.207215 | − | 1.44121i | ||||
\(877\) | 20.1907 | − | 44.2114i | 0.681791 | − | 1.49291i | −0.178944 | − | 0.983859i | \(-0.557268\pi\) |
0.860735 | − | 0.509054i | \(-0.170005\pi\) | |||||||
\(878\) | −2.36825 | + | 0.695382i | −0.0799247 | + | 0.0234680i | ||||
\(879\) | 14.7800 | − | 17.0571i | 0.498518 | − | 0.575320i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.53735 | + | 1.63066i | −0.0854857 | + | 0.0549383i | −0.582685 | − | 0.812698i | \(-0.697998\pi\) |
0.497200 | + | 0.867636i | \(0.334362\pi\) | |||||||
\(882\) | 21.8953 | + | 47.9440i | 0.737252 | + | 1.61436i | ||||
\(883\) | −23.0188 | − | 26.5651i | −0.774645 | − | 0.893988i | 0.222065 | − | 0.975032i | \(-0.428720\pi\) |
−0.996711 | + | 0.0810434i | \(0.974175\pi\) | |||||||
\(884\) | −57.4780 | − | 36.9388i | −1.93319 | − | 1.24239i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.04961 | + | 42.0760i | −0.203241 | + | 1.41357i | ||||
\(887\) | −2.92897 | − | 1.88233i | −0.0983450 | − | 0.0632025i | 0.490544 | − | 0.871416i | \(-0.336798\pi\) |
−0.588889 | + | 0.808214i | \(0.700434\pi\) | |||||||
\(888\) | −42.4659 | − | 49.0082i | −1.42506 | − | 1.64461i | ||||
\(889\) | 12.7664 | + | 27.9546i | 0.428173 | + | 0.937568i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.69374 | + | 2.84634i | 0.324752 | + | 0.0953559i | ||||
\(892\) | −46.5200 | + | 53.6870i | −1.55761 | + | 1.79757i | ||||
\(893\) | 31.1422 | − | 9.14416i | 1.04213 | − | 0.305998i | ||||
\(894\) | 21.4673 | − | 47.0067i | 0.717973 | − | 1.57214i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −72.5521 | −2.42380 | ||||||||
\(897\) | −34.3803 | − | 29.7970i | −1.14792 | − | 0.994892i | ||||
\(898\) | −61.5187 | −2.05291 | ||||||||
\(899\) | −1.43066 | − | 9.95046i | −0.0477152 | − | 0.331867i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.3004 | + | 10.9524i | −1.24266 | + | 0.364877i | ||||
\(902\) | 9.97379 | − | 11.5104i | 0.332091 | − | 0.383253i | ||||
\(903\) | −36.3153 | − | 10.6631i | −1.20850 | − | 0.354847i | ||||
\(904\) | −6.79615 | + | 4.36762i | −0.226037 | + | 0.145265i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 24.2104 | + | 27.9403i | 0.804338 | + | 0.928255i | ||||
\(907\) | −20.6296 | − | 13.2578i | −0.684994 | − | 0.440219i | 0.151309 | − | 0.988486i | \(-0.451651\pi\) |
−0.836303 | + | 0.548268i | \(0.815287\pi\) | |||||||
\(908\) | 4.67767 | − | 32.5339i | 0.155234 | − | 1.07968i | ||||
\(909\) | 10.3184 | − | 71.7661i | 0.342240 | − | 2.38033i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.79940 | − | 6.69286i | −0.192143 | − | 0.221744i | 0.651501 | − | 0.758648i | \(-0.274139\pi\) |
−0.843644 | + | 0.536903i | \(0.819594\pi\) | |||||||
\(912\) | −5.13394 | − | 11.2418i | −0.170002 | − | 0.372252i | ||||
\(913\) | −14.0475 | + | 9.02780i | −0.464905 | + | 0.298777i | ||||
\(914\) | −96.5338 | − | 28.3449i | −3.19305 | − | 0.937565i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.63738 | + | 1.06803i | −0.120182 | + | 0.0352888i | ||||
\(917\) | −13.3026 | + | 29.1286i | −0.439291 | + | 0.961912i | ||||
\(918\) | −5.24219 | − | 36.4602i | −0.173018 | − | 1.20337i | ||||
\(919\) | 3.15448 | 0.104057 | 0.0520283 | − | 0.998646i | \(-0.483431\pi\) | ||||
0.0520283 | + | 0.998646i | \(0.483431\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 41.0980 | 1.35422 | ||||||||
\(922\) | −1.41031 | − | 9.80890i | −0.0464460 | − | 0.323039i | ||||
\(923\) | −0.281913 | + | 0.617304i | −0.00927930 | + | 0.0203188i | ||||
\(924\) | −72.3185 | + | 21.2346i | −2.37910 | + | 0.698568i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 51.4202 | + | 15.0983i | 1.68977 | + | 0.496162i | ||||
\(927\) | −6.85158 | + | 4.40324i | −0.225035 | + | 0.144621i | ||||
\(928\) | 6.43515 | + | 14.0910i | 0.211244 | + | 0.462560i | ||||
\(929\) | 16.4053 | + | 18.9327i | 0.538239 | + | 0.621161i | 0.958102 | − | 0.286426i | \(-0.0924673\pi\) |
−0.419863 | + | 0.907588i | \(0.637922\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.11584 | − | 14.7160i | 0.0693439 | − | 0.482298i | ||||
\(932\) | −11.8383 | + | 82.3372i | −0.387776 | + | 2.69704i | ||||
\(933\) | 60.3605 | + | 38.7913i | 1.97611 | + | 1.26997i | ||||
\(934\) | −43.6335 | − | 50.3557i | −1.42773 | − | 1.64769i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −46.0622 | + | 29.6024i | −1.50559 | + | 0.967585i | ||||
\(937\) | −33.2911 | − | 9.77514i | −1.08757 | − | 0.319340i | −0.311668 | − | 0.950191i | \(-0.600888\pi\) |
−0.775904 | + | 0.630851i | \(0.782706\pi\) | |||||||
\(938\) | 8.33233 | − | 9.61602i | 0.272060 | − | 0.313974i | ||||
\(939\) | 48.7832 | − | 14.3240i | 1.59198 | − | 0.467447i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.68698 | − | 53.4641i | −0.250588 | − | 1.74288i | −0.594697 | − | 0.803950i | \(-0.702728\pi\) |
0.344109 | − | 0.938930i | \(-0.388181\pi\) | |||||||
\(942\) | −115.171 | −3.75248 | ||||||||
\(943\) | 12.5727 | + | 5.74334i | 0.409423 | + | 0.187029i | ||||
\(944\) | 10.1555 | 0.330533 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.84217 | − | 19.3616i | 0.287484 | − | 0.629501i | ||||
\(947\) | 29.9505 | − | 8.79427i | 0.973261 | − | 0.285775i | 0.243821 | − | 0.969820i | \(-0.421599\pi\) |
0.729440 | + | 0.684045i | \(0.239781\pi\) | |||||||
\(948\) | 35.1314 | − | 40.5438i | 1.14101 | − | 1.31680i | ||||
\(949\) | 15.4088 | + | 4.52443i | 0.500190 | + | 0.146869i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.0147 | + | 32.8777i | 0.486886 | + | 1.06613i | ||||
\(952\) | −46.3737 | − | 53.5181i | −1.50298 | − | 1.73453i | ||||
\(953\) | −25.1341 | − | 16.1527i | −0.814172 | − | 0.523236i | 0.0660403 | − | 0.997817i | \(-0.478963\pi\) |
−0.880212 | + | 0.474580i | \(0.842600\pi\) | |||||||
\(954\) | −10.0165 | + | 69.6662i | −0.324296 | + | 2.25553i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −83.3876 | − | 53.5899i | −2.69695 | − | 1.73322i | ||||
\(957\) | 17.2966 | + | 19.9613i | 0.559119 | + | 0.645258i | ||||
\(958\) | 36.2406 | + | 79.3559i | 1.17088 | + | 2.56387i | ||||
\(959\) | 21.4314 | − | 13.7732i | 0.692058 | − | 0.444758i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.9378 | − | 19.5473i | 0.546381 | − | 0.630557i | ||||
\(962\) | 52.3824 | − | 15.3809i | 1.68888 | − | 0.495899i | ||||
\(963\) | −24.9481 | + | 54.6286i | −0.803940 | + | 1.76038i | ||||
\(964\) | −6.53474 | − | 45.4501i | −0.210470 | − | 1.46385i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −57.5846 | − | 89.6240i | −1.85276 | − | 2.88361i | ||||
\(967\) | 1.88281 | 0.0605471 | 0.0302735 | − | 0.999542i | \(-0.490362\pi\) | ||||
0.0302735 | + | 0.999542i | \(0.490362\pi\) | |||||||
\(968\) | 3.20783 | + | 22.3110i | 0.103104 | + | 0.717102i | ||||
\(969\) | −16.1492 | + | 35.3619i | −0.518788 | + | 1.13599i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.60934 | + | 7.62758i | −0.212104 | + | 0.244781i | −0.851825 | − | 0.523826i | \(-0.824504\pi\) |
0.639722 | + | 0.768607i | \(0.279050\pi\) | |||||||
\(972\) | 71.5525 | + | 21.0097i | 2.29505 | + | 0.673886i | ||||
\(973\) | 23.9394 | − | 15.3849i | 0.767463 | − | 0.493219i | ||||
\(974\) | 36.9329 | + | 80.8718i | 1.18341 | + | 2.59130i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.52863 | − | 3.55303i | −0.176967 | − | 0.113730i | ||||
\(977\) | 4.48086 | − | 31.1651i | 0.143355 | − | 0.997059i | −0.783433 | − | 0.621476i | \(-0.786533\pi\) |
0.926789 | − | 0.375583i | \(-0.122558\pi\) | |||||||
\(978\) | −0.689633 | + | 4.79650i | −0.0220520 | + | 0.153375i | ||||
\(979\) | −9.46303 | − | 6.08152i | −0.302440 | − | 0.194366i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.0259 | + | 50.4198i | 0.735162 | + | 1.60978i | ||||
\(982\) | 36.4525 | − | 23.4266i | 1.16325 | − | 0.747572i | ||||
\(983\) | −55.9596 | − | 16.4312i | −1.78483 | − | 0.524075i | −0.788930 | − | 0.614483i | \(-0.789365\pi\) |
−0.995905 | + | 0.0904084i | \(0.971183\pi\) | |||||||
\(984\) | 18.8760 | − | 21.7840i | 0.601744 | − | 0.694449i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −23.2894 | + | 50.9966i | −0.741685 | + | 1.62406i | ||||
\(987\) | −15.8977 | − | 110.571i | −0.506029 | − | 3.51951i | ||||
\(988\) | 34.8925 | 1.11008 | ||||||||
\(989\) | 19.1205 | + | 2.75115i | 0.607996 | + | 0.0874815i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.99082 | + | 41.6671i | 0.190305 | + | 1.32360i | 0.831202 | + | 0.555971i | \(0.187653\pi\) |
−0.640897 | + | 0.767627i | \(0.721438\pi\) | |||||||
\(992\) | 3.28725 | − | 7.19808i | 0.104370 | − | 0.228539i | ||||
\(993\) | 73.0472 | − | 21.4486i | 2.31808 | − | 0.680651i | ||||
\(994\) | −1.04059 | + | 1.20091i | −0.0330055 | + | 0.0380904i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −60.0618 | + | 38.5994i | −1.90313 | + | 1.22307i | ||||
\(997\) | 23.3798 | + | 51.1947i | 0.740446 | + | 1.62135i | 0.782819 | + | 0.622250i | \(0.213781\pi\) |
−0.0423723 | + | 0.999102i | \(0.513492\pi\) | |||||||
\(998\) | −49.2779 | − | 56.8698i | −1.55987 | − | 1.80018i | ||||
\(999\) | 15.8990 | + | 10.2177i | 0.503022 | + | 0.323272i |
(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 | 575.2.k.g.26.1 | 100 | ||
5.2 | odd | 4 | 115.2.j.a.49.10 | yes | 100 | ||
5.3 | odd | 4 | 115.2.j.a.49.1 | ✓ | 100 | ||
5.4 | even | 2 | inner | 575.2.k.g.26.10 | 100 | ||
23.8 | even | 11 | inner | 575.2.k.g.376.1 | 100 | ||
115.8 | odd | 44 | 115.2.j.a.54.10 | yes | 100 | ||
115.54 | even | 22 | inner | 575.2.k.g.376.10 | 100 | ||
115.77 | odd | 44 | 115.2.j.a.54.1 | yes | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.2.j.a.49.1 | ✓ | 100 | 5.3 | odd | 4 | ||
115.2.j.a.49.10 | yes | 100 | 5.2 | odd | 4 | ||
115.2.j.a.54.1 | yes | 100 | 115.77 | odd | 44 | ||
115.2.j.a.54.10 | yes | 100 | 115.8 | odd | 44 | ||
575.2.k.g.26.1 | 100 | 1.1 | even | 1 | trivial | ||
575.2.k.g.26.10 | 100 | 5.4 | even | 2 | inner | ||
575.2.k.g.376.1 | 100 | 23.8 | even | 11 | inner | ||
575.2.k.g.376.10 | 100 | 115.54 | even | 22 | inner |