Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2010,2,Mod(401,2010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2010, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2010.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2010 = 2 \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2010.d (of order \(2\), degree \(1\), 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: | \(16.0499308063\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} + 2 x^{18} + 2 x^{17} - 9 x^{16} + 4 x^{15} + 14 x^{14} - 28 x^{13} - 16 x^{12} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 401.15 | ||
Root | \(1.16984 - 1.27729i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2010.401 |
Dual form | 2010.2.d.c.401.16 |
$q$-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 \(\left(\mathbb{Z}/2010\mathbb{Z}\right)^\times\).
\(n\) | \(671\) | \(1141\) | \(1207\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.16984 | − | 1.27729i | 0.675405 | − | 0.737447i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.16984 | + | 1.27729i | −0.477584 | + | 0.521453i | ||||
\(7\) | 1.10570i | 0.417917i | 0.977925 | + | 0.208959i | \(0.0670074\pi\) | ||||
−0.977925 | + | 0.208959i | \(0.932993\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.262965 | − | 2.98845i | −0.0876550 | − | 0.996151i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0.357335 | 0.107741 | 0.0538703 | − | 0.998548i | \(-0.482844\pi\) | ||||
0.0538703 | + | 0.998548i | \(0.482844\pi\) | |||||||
\(12\) | 1.16984 | − | 1.27729i | 0.337703 | − | 0.368723i | ||||
\(13\) | − | 2.58786i | − | 0.717744i | −0.933387 | − | 0.358872i | \(-0.883161\pi\) | ||
0.933387 | − | 0.358872i | \(-0.116839\pi\) | |||||||
\(14\) | − | 1.10570i | − | 0.295512i | ||||||
\(15\) | −1.16984 | + | 1.27729i | −0.302050 | + | 0.329796i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 2.15051i | − | 0.521574i | −0.965396 | − | 0.260787i | \(-0.916018\pi\) | ||
0.965396 | − | 0.260787i | \(-0.0839821\pi\) | |||||||
\(18\) | 0.262965 | + | 2.98845i | 0.0619814 | + | 0.704385i | ||||
\(19\) | 5.30796 | 1.21773 | 0.608865 | − | 0.793274i | \(-0.291625\pi\) | ||||
0.608865 | + | 0.793274i | \(0.291625\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 1.41231 | + | 1.29349i | 0.308191 | + | 0.282263i | ||||
\(22\) | −0.357335 | −0.0761841 | ||||||||
\(23\) | − | 0.834453i | − | 0.173995i | −0.996209 | − | 0.0869977i | \(-0.972273\pi\) | ||
0.996209 | − | 0.0869977i | \(-0.0277273\pi\) | |||||||
\(24\) | −1.16984 | + | 1.27729i | −0.238792 | + | 0.260727i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.58786i | 0.507522i | ||||||||
\(27\) | −4.12476 | − | 3.16012i | −0.793811 | − | 0.608165i | ||||
\(28\) | 1.10570i | 0.208959i | ||||||||
\(29\) | 3.88309i | 0.721071i | 0.932745 | + | 0.360536i | \(0.117406\pi\) | ||||
−0.932745 | + | 0.360536i | \(0.882594\pi\) | |||||||
\(30\) | 1.16984 | − | 1.27729i | 0.213582 | − | 0.233201i | ||||
\(31\) | − | 2.99195i | − | 0.537370i | −0.963228 | − | 0.268685i | \(-0.913411\pi\) | ||
0.963228 | − | 0.268685i | \(-0.0865890\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.418024 | − | 0.456423i | 0.0727686 | − | 0.0794530i | ||||
\(34\) | 2.15051i | 0.368809i | ||||||||
\(35\) | − | 1.10570i | − | 0.186898i | ||||||
\(36\) | −0.262965 | − | 2.98845i | −0.0438275 | − | 0.498075i | ||||
\(37\) | 2.73596 | 0.449790 | 0.224895 | − | 0.974383i | \(-0.427796\pi\) | ||||
0.224895 | + | 0.974383i | \(0.427796\pi\) | |||||||
\(38\) | −5.30796 | −0.861065 | ||||||||
\(39\) | −3.30546 | − | 3.02738i | −0.529298 | − | 0.484768i | ||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −6.20196 | −0.968583 | −0.484292 | − | 0.874907i | \(-0.660923\pi\) | ||||
−0.484292 | + | 0.874907i | \(0.660923\pi\) | |||||||
\(42\) | −1.41231 | − | 1.29349i | −0.217924 | − | 0.199590i | ||||
\(43\) | 6.90875i | 1.05357i | 0.849997 | + | 0.526787i | \(0.176603\pi\) | ||||
−0.849997 | + | 0.526787i | \(0.823397\pi\) | |||||||
\(44\) | 0.357335 | 0.0538703 | ||||||||
\(45\) | 0.262965 | + | 2.98845i | 0.0392005 | + | 0.445492i | ||||
\(46\) | 0.834453i | 0.123033i | ||||||||
\(47\) | − | 9.75513i | − | 1.42293i | −0.702720 | − | 0.711466i | \(-0.748031\pi\) | ||
0.702720 | − | 0.711466i | \(-0.251969\pi\) | |||||||
\(48\) | 1.16984 | − | 1.27729i | 0.168851 | − | 0.184362i | ||||
\(49\) | 5.77742 | 0.825345 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −2.74683 | − | 2.51574i | −0.384633 | − | 0.352274i | ||||
\(52\) | − | 2.58786i | − | 0.358872i | ||||||
\(53\) | −11.7716 | −1.61695 | −0.808476 | − | 0.588529i | \(-0.799707\pi\) | ||||
−0.808476 | + | 0.588529i | \(0.799707\pi\) | |||||||
\(54\) | 4.12476 | + | 3.16012i | 0.561309 | + | 0.430038i | ||||
\(55\) | −0.357335 | −0.0481831 | ||||||||
\(56\) | − | 1.10570i | − | 0.147756i | ||||||
\(57\) | 6.20945 | − | 6.77983i | 0.822462 | − | 0.898011i | ||||
\(58\) | − | 3.88309i | − | 0.509874i | ||||||
\(59\) | − | 9.47707i | − | 1.23381i | −0.787038 | − | 0.616905i | \(-0.788386\pi\) | ||
0.787038 | − | 0.616905i | \(-0.211614\pi\) | |||||||
\(60\) | −1.16984 | + | 1.27729i | −0.151025 | + | 0.164898i | ||||
\(61\) | − | 15.2529i | − | 1.95293i | −0.215677 | − | 0.976465i | \(-0.569196\pi\) | ||
0.215677 | − | 0.976465i | \(-0.430804\pi\) | |||||||
\(62\) | 2.99195i | 0.379978i | ||||||||
\(63\) | 3.30435 | − | 0.290761i | 0.416308 | − | 0.0366325i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.58786i | 0.320985i | ||||||||
\(66\) | −0.418024 | + | 0.456423i | −0.0514552 | + | 0.0561817i | ||||
\(67\) | 7.79466 | − | 2.49867i | 0.952269 | − | 0.305261i | ||||
\(68\) | − | 2.15051i | − | 0.260787i | ||||||
\(69\) | −1.06584 | − | 0.976173i | −0.128312 | − | 0.117517i | ||||
\(70\) | 1.10570i | 0.132157i | ||||||||
\(71\) | 15.8888i | 1.88566i | 0.333279 | + | 0.942828i | \(0.391845\pi\) | ||||
−0.333279 | + | 0.942828i | \(0.608155\pi\) | |||||||
\(72\) | 0.262965 | + | 2.98845i | 0.0309907 | + | 0.352193i | ||||
\(73\) | −12.0792 | −1.41377 | −0.706883 | − | 0.707330i | \(-0.749899\pi\) | ||||
−0.706883 | + | 0.707330i | \(0.749899\pi\) | |||||||
\(74\) | −2.73596 | −0.318049 | ||||||||
\(75\) | 1.16984 | − | 1.27729i | 0.135081 | − | 0.147489i | ||||
\(76\) | 5.30796 | 0.608865 | ||||||||
\(77\) | 0.395107i | 0.0450266i | ||||||||
\(78\) | 3.30546 | + | 3.02738i | 0.374270 | + | 0.342783i | ||||
\(79\) | − | 9.34458i | − | 1.05135i | −0.850686 | − | 0.525674i | \(-0.823813\pi\) | ||
0.850686 | − | 0.525674i | \(-0.176187\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −8.86170 | + | 1.57172i | −0.984633 | + | 0.174635i | ||||
\(82\) | 6.20196 | 0.684892 | ||||||||
\(83\) | − | 4.47970i | − | 0.491711i | −0.969307 | − | 0.245855i | \(-0.920931\pi\) | ||
0.969307 | − | 0.245855i | \(-0.0790689\pi\) | |||||||
\(84\) | 1.41231 | + | 1.29349i | 0.154096 | + | 0.141132i | ||||
\(85\) | 2.15051i | 0.233255i | ||||||||
\(86\) | − | 6.90875i | − | 0.744989i | ||||||
\(87\) | 4.95985 | + | 4.54258i | 0.531752 | + | 0.487015i | ||||
\(88\) | −0.357335 | −0.0380921 | ||||||||
\(89\) | − | 6.97529i | − | 0.739379i | −0.929155 | − | 0.369689i | \(-0.879464\pi\) | ||
0.929155 | − | 0.369689i | \(-0.120536\pi\) | |||||||
\(90\) | −0.262965 | − | 2.98845i | −0.0277189 | − | 0.315011i | ||||
\(91\) | 2.86141 | 0.299957 | ||||||||
\(92\) | − | 0.834453i | − | 0.0869977i | ||||||
\(93\) | −3.82160 | − | 3.50009i | −0.396281 | − | 0.362942i | ||||
\(94\) | 9.75513i | 1.00617i | ||||||||
\(95\) | −5.30796 | −0.544585 | ||||||||
\(96\) | −1.16984 | + | 1.27729i | −0.119396 | + | 0.130363i | ||||
\(97\) | − | 14.6528i | − | 1.48777i | −0.668310 | − | 0.743883i | \(-0.732982\pi\) | ||
0.668310 | − | 0.743883i | \(-0.267018\pi\) | |||||||
\(98\) | −5.77742 | −0.583607 | ||||||||
\(99\) | −0.0939666 | − | 1.06788i | −0.00944400 | − | 0.107326i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 4.74192 | 0.471838 | 0.235919 | − | 0.971773i | \(-0.424190\pi\) | ||||
0.235919 | + | 0.971773i | \(0.424190\pi\) | |||||||
\(102\) | 2.74683 | + | 2.51574i | 0.271977 | + | 0.249095i | ||||
\(103\) | 18.2963 | 1.80279 | 0.901396 | − | 0.432996i | \(-0.142544\pi\) | ||||
0.901396 | + | 0.432996i | \(0.142544\pi\) | |||||||
\(104\) | 2.58786i | 0.253761i | ||||||||
\(105\) | −1.41231 | − | 1.29349i | −0.137827 | − | 0.126232i | ||||
\(106\) | 11.7716 | 1.14336 | ||||||||
\(107\) | − | 14.5849i | − | 1.40998i | −0.709219 | − | 0.704988i | \(-0.750952\pi\) | ||
0.709219 | − | 0.704988i | \(-0.249048\pi\) | |||||||
\(108\) | −4.12476 | − | 3.16012i | −0.396905 | − | 0.304082i | ||||
\(109\) | − | 1.55580i | − | 0.149018i | −0.997220 | − | 0.0745091i | \(-0.976261\pi\) | ||
0.997220 | − | 0.0745091i | \(-0.0237390\pi\) | |||||||
\(110\) | 0.357335 | 0.0340706 | ||||||||
\(111\) | 3.20063 | − | 3.49463i | 0.303790 | − | 0.331696i | ||||
\(112\) | 1.10570i | 0.104479i | ||||||||
\(113\) | 9.97721 | 0.938577 | 0.469288 | − | 0.883045i | \(-0.344510\pi\) | ||||
0.469288 | + | 0.883045i | \(0.344510\pi\) | |||||||
\(114\) | −6.20945 | + | 6.77983i | −0.581568 | + | 0.634990i | ||||
\(115\) | 0.834453i | 0.0778131i | ||||||||
\(116\) | 3.88309i | 0.360536i | ||||||||
\(117\) | −7.73371 | + | 0.680517i | −0.714981 | + | 0.0629138i | ||||
\(118\) | 9.47707i | 0.872435i | ||||||||
\(119\) | 2.37782 | 0.217975 | ||||||||
\(120\) | 1.16984 | − | 1.27729i | 0.106791 | − | 0.116601i | ||||
\(121\) | −10.8723 | −0.988392 | ||||||||
\(122\) | 15.2529i | 1.38093i | ||||||||
\(123\) | −7.25528 | + | 7.92173i | −0.654186 | + | 0.714278i | ||||
\(124\) | − | 2.99195i | − | 0.268685i | ||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −3.30435 | + | 0.290761i | −0.294374 | + | 0.0259031i | ||||
\(127\) | −22.0307 | −1.95491 | −0.977454 | − | 0.211148i | \(-0.932280\pi\) | ||||
−0.977454 | + | 0.211148i | \(0.932280\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 8.82451 | + | 8.08210i | 0.776955 | + | 0.711590i | ||||
\(130\) | − | 2.58786i | − | 0.226971i | ||||||
\(131\) | − | 3.60469i | − | 0.314943i | −0.987524 | − | 0.157472i | \(-0.949666\pi\) | ||
0.987524 | − | 0.157472i | \(-0.0503343\pi\) | |||||||
\(132\) | 0.418024 | − | 0.456423i | 0.0363843 | − | 0.0397265i | ||||
\(133\) | 5.86904i | 0.508910i | ||||||||
\(134\) | −7.79466 | + | 2.49867i | −0.673356 | + | 0.215852i | ||||
\(135\) | 4.12476 | + | 3.16012i | 0.355003 | + | 0.271980i | ||||
\(136\) | 2.15051i | 0.184404i | ||||||||
\(137\) | −22.9849 | −1.96373 | −0.981865 | − | 0.189583i | \(-0.939286\pi\) | ||||
−0.981865 | + | 0.189583i | \(0.939286\pi\) | |||||||
\(138\) | 1.06584 | + | 0.976173i | 0.0907305 | + | 0.0830974i | ||||
\(139\) | 8.81597i | 0.747761i | 0.927477 | + | 0.373881i | \(0.121973\pi\) | ||||
−0.927477 | + | 0.373881i | \(0.878027\pi\) | |||||||
\(140\) | − | 1.10570i | − | 0.0934491i | ||||||
\(141\) | −12.4602 | − | 11.4119i | −1.04934 | − | 0.961056i | ||||
\(142\) | − | 15.8888i | − | 1.33336i | ||||||
\(143\) | − | 0.924735i | − | 0.0773302i | ||||||
\(144\) | −0.262965 | − | 2.98845i | −0.0219137 | − | 0.249038i | ||||
\(145\) | − | 3.88309i | − | 0.322473i | ||||||
\(146\) | 12.0792 | 0.999684 | ||||||||
\(147\) | 6.75863 | − | 7.37947i | 0.557443 | − | 0.608648i | ||||
\(148\) | 2.73596 | 0.224895 | ||||||||
\(149\) | 10.1468i | 0.831256i | 0.909535 | + | 0.415628i | \(0.136438\pi\) | ||||
−0.909535 | + | 0.415628i | \(0.863562\pi\) | |||||||
\(150\) | −1.16984 | + | 1.27729i | −0.0955168 | + | 0.104291i | ||||
\(151\) | 1.34157 | 0.109176 | 0.0545879 | − | 0.998509i | \(-0.482615\pi\) | ||||
0.0545879 | + | 0.998509i | \(0.482615\pi\) | |||||||
\(152\) | −5.30796 | −0.430533 | ||||||||
\(153\) | −6.42669 | + | 0.565508i | −0.519567 | + | 0.0457186i | ||||
\(154\) | − | 0.395107i | − | 0.0318386i | ||||||
\(155\) | 2.99195i | 0.240319i | ||||||||
\(156\) | −3.30546 | − | 3.02738i | −0.264649 | − | 0.242384i | ||||
\(157\) | 16.5368 | 1.31978 | 0.659888 | − | 0.751364i | \(-0.270604\pi\) | ||||
0.659888 | + | 0.751364i | \(0.270604\pi\) | |||||||
\(158\) | 9.34458i | 0.743415i | ||||||||
\(159\) | −13.7708 | + | 15.0358i | −1.09210 | + | 1.19242i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0.922658 | 0.0727156 | ||||||||
\(162\) | 8.86170 | − | 1.57172i | 0.696241 | − | 0.123486i | ||||
\(163\) | −14.0394 | −1.09965 | −0.549825 | − | 0.835280i | \(-0.685306\pi\) | ||||
−0.549825 | + | 0.835280i | \(0.685306\pi\) | |||||||
\(164\) | −6.20196 | −0.484292 | ||||||||
\(165\) | −0.418024 | + | 0.456423i | −0.0325431 | + | 0.0355324i | ||||
\(166\) | 4.47970i | 0.347692i | ||||||||
\(167\) | 9.21767i | 0.713285i | 0.934241 | + | 0.356642i | \(0.116079\pi\) | ||||
−0.934241 | + | 0.356642i | \(0.883921\pi\) | |||||||
\(168\) | −1.41231 | − | 1.29349i | −0.108962 | − | 0.0997952i | ||||
\(169\) | 6.30297 | 0.484844 | ||||||||
\(170\) | − | 2.15051i | − | 0.164936i | ||||||
\(171\) | −1.39581 | − | 15.8626i | −0.106740 | − | 1.21304i | ||||
\(172\) | 6.90875i | 0.526787i | ||||||||
\(173\) | 6.73609i | 0.512135i | 0.966659 | + | 0.256068i | \(0.0824270\pi\) | ||||
−0.966659 | + | 0.256068i | \(0.917573\pi\) | |||||||
\(174\) | −4.95985 | − | 4.54258i | −0.376005 | − | 0.344372i | ||||
\(175\) | 1.10570i | 0.0835834i | ||||||||
\(176\) | 0.357335 | 0.0269352 | ||||||||
\(177\) | −12.1050 | − | 11.0866i | −0.909868 | − | 0.833321i | ||||
\(178\) | 6.97529i | 0.522820i | ||||||||
\(179\) | 19.0886 | 1.42675 | 0.713374 | − | 0.700784i | \(-0.247166\pi\) | ||||
0.713374 | + | 0.700784i | \(0.247166\pi\) | |||||||
\(180\) | 0.262965 | + | 2.98845i | 0.0196002 | + | 0.222746i | ||||
\(181\) | 12.3626 | 0.918908 | 0.459454 | − | 0.888201i | \(-0.348045\pi\) | ||||
0.459454 | + | 0.888201i | \(0.348045\pi\) | |||||||
\(182\) | −2.86141 | −0.212102 | ||||||||
\(183\) | −19.4824 | − | 17.8434i | −1.44018 | − | 1.31902i | ||||
\(184\) | 0.834453i | 0.0615167i | ||||||||
\(185\) | −2.73596 | −0.201152 | ||||||||
\(186\) | 3.82160 | + | 3.50009i | 0.280213 | + | 0.256639i | ||||
\(187\) | − | 0.768452i | − | 0.0561947i | ||||||
\(188\) | − | 9.75513i | − | 0.711466i | ||||||
\(189\) | 3.49416 | − | 4.56077i | 0.254162 | − | 0.331747i | ||||
\(190\) | 5.30796 | 0.385080 | ||||||||
\(191\) | −11.6132 | −0.840300 | −0.420150 | − | 0.907455i | \(-0.638023\pi\) | ||||
−0.420150 | + | 0.907455i | \(0.638023\pi\) | |||||||
\(192\) | 1.16984 | − | 1.27729i | 0.0844257 | − | 0.0921808i | ||||
\(193\) | −0.896082 | −0.0645014 | −0.0322507 | − | 0.999480i | \(-0.510267\pi\) | ||||
−0.0322507 | + | 0.999480i | \(0.510267\pi\) | |||||||
\(194\) | 14.6528i | 1.05201i | ||||||||
\(195\) | 3.30546 | + | 3.02738i | 0.236709 | + | 0.216795i | ||||
\(196\) | 5.77742 | 0.412673 | ||||||||
\(197\) | −4.56961 | −0.325571 | −0.162785 | − | 0.986661i | \(-0.552048\pi\) | ||||
−0.162785 | + | 0.986661i | \(0.552048\pi\) | |||||||
\(198\) | 0.0939666 | + | 1.06788i | 0.00667792 | + | 0.0758909i | ||||
\(199\) | 1.24326 | 0.0881324 | 0.0440662 | − | 0.999029i | \(-0.485969\pi\) | ||||
0.0440662 | + | 0.999029i | \(0.485969\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 5.92694 | − | 12.8791i | 0.418054 | − | 0.908422i | ||||
\(202\) | −4.74192 | −0.333640 | ||||||||
\(203\) | −4.29355 | −0.301348 | ||||||||
\(204\) | −2.74683 | − | 2.51574i | −0.192317 | − | 0.176137i | ||||
\(205\) | 6.20196 | 0.433164 | ||||||||
\(206\) | −18.2963 | −1.27477 | ||||||||
\(207\) | −2.49372 | + | 0.219432i | −0.173326 | + | 0.0152516i | ||||
\(208\) | − | 2.58786i | − | 0.179436i | ||||||
\(209\) | 1.89672 | 0.131199 | ||||||||
\(210\) | 1.41231 | + | 1.29349i | 0.0974587 | + | 0.0892595i | ||||
\(211\) | 1.28602 | 0.0885332 | 0.0442666 | − | 0.999020i | \(-0.485905\pi\) | ||||
0.0442666 | + | 0.999020i | \(0.485905\pi\) | |||||||
\(212\) | −11.7716 | −0.808476 | ||||||||
\(213\) | 20.2947 | + | 18.5873i | 1.39057 | + | 1.27358i | ||||
\(214\) | 14.5849i | 0.997003i | ||||||||
\(215\) | − | 6.90875i | − | 0.471173i | ||||||
\(216\) | 4.12476 | + | 3.16012i | 0.280654 | + | 0.215019i | ||||
\(217\) | 3.30821 | 0.224576 | ||||||||
\(218\) | 1.55580i | 0.105372i | ||||||||
\(219\) | −14.1307 | + | 15.4287i | −0.954865 | + | 1.04258i | ||||
\(220\) | −0.357335 | −0.0240915 | ||||||||
\(221\) | −5.56521 | −0.374357 | ||||||||
\(222\) | −3.20063 | + | 3.49463i | −0.214812 | + | 0.234544i | ||||
\(223\) | −23.6116 | −1.58115 | −0.790574 | − | 0.612366i | \(-0.790218\pi\) | ||||
−0.790574 | + | 0.612366i | \(0.790218\pi\) | |||||||
\(224\) | − | 1.10570i | − | 0.0738780i | ||||||
\(225\) | −0.262965 | − | 2.98845i | −0.0175310 | − | 0.199230i | ||||
\(226\) | −9.97721 | −0.663674 | ||||||||
\(227\) | − | 16.9703i | − | 1.12636i | −0.826335 | − | 0.563178i | \(-0.809578\pi\) | ||
0.826335 | − | 0.563178i | \(-0.190422\pi\) | |||||||
\(228\) | 6.20945 | − | 6.77983i | 0.411231 | − | 0.449005i | ||||
\(229\) | 19.9276i | 1.31685i | 0.752646 | + | 0.658425i | \(0.228777\pi\) | ||||
−0.752646 | + | 0.658425i | \(0.771223\pi\) | |||||||
\(230\) | − | 0.834453i | − | 0.0550222i | ||||||
\(231\) | 0.504668 | + | 0.462211i | 0.0332047 | + | 0.0304112i | ||||
\(232\) | − | 3.88309i | − | 0.254937i | ||||||
\(233\) | 25.2606 | 1.65488 | 0.827440 | − | 0.561555i | \(-0.189797\pi\) | ||||
0.827440 | + | 0.561555i | \(0.189797\pi\) | |||||||
\(234\) | 7.73371 | − | 0.680517i | 0.505568 | − | 0.0444868i | ||||
\(235\) | 9.75513i | 0.636355i | ||||||||
\(236\) | − | 9.47707i | − | 0.616905i | ||||||
\(237\) | −11.9358 | − | 10.9316i | −0.775312 | − | 0.710086i | ||||
\(238\) | −2.37782 | −0.154131 | ||||||||
\(239\) | 4.75090 | 0.307310 | 0.153655 | − | 0.988125i | \(-0.450896\pi\) | ||||
0.153655 | + | 0.988125i | \(0.450896\pi\) | |||||||
\(240\) | −1.16984 | + | 1.27729i | −0.0755126 | + | 0.0824490i | ||||
\(241\) | 18.6505 | 1.20139 | 0.600693 | − | 0.799480i | \(-0.294891\pi\) | ||||
0.600693 | + | 0.799480i | \(0.294891\pi\) | |||||||
\(242\) | 10.8723 | 0.698899 | ||||||||
\(243\) | −8.35919 | + | 13.1577i | −0.536243 | + | 0.844064i | ||||
\(244\) | − | 15.2529i | − | 0.976465i | ||||||
\(245\) | −5.77742 | −0.369106 | ||||||||
\(246\) | 7.25528 | − | 7.92173i | 0.462580 | − | 0.505071i | ||||
\(247\) | − | 13.7363i | − | 0.874018i | ||||||
\(248\) | 2.99195i | 0.189989i | ||||||||
\(249\) | −5.72190 | − | 5.24052i | −0.362611 | − | 0.332104i | ||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 8.50442 | 0.536794 | 0.268397 | − | 0.963308i | \(-0.413506\pi\) | ||||
0.268397 | + | 0.963308i | \(0.413506\pi\) | |||||||
\(252\) | 3.30435 | − | 0.290761i | 0.208154 | − | 0.0183162i | ||||
\(253\) | − | 0.298179i | − | 0.0187464i | ||||||
\(254\) | 22.0307 | 1.38233 | ||||||||
\(255\) | 2.74683 | + | 2.51574i | 0.172013 | + | 0.157542i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 21.3562i | − | 1.33217i | −0.745878 | − | 0.666083i | \(-0.767970\pi\) | ||
0.745878 | − | 0.666083i | \(-0.232030\pi\) | |||||||
\(258\) | −8.82451 | − | 8.08210i | −0.549390 | − | 0.503170i | ||||
\(259\) | 3.02517i | 0.187975i | ||||||||
\(260\) | 2.58786i | 0.160492i | ||||||||
\(261\) | 11.6044 | − | 1.02112i | 0.718296 | − | 0.0632055i | ||||
\(262\) | 3.60469i | 0.222699i | ||||||||
\(263\) | − | 16.0248i | − | 0.988134i | −0.869424 | − | 0.494067i | \(-0.835510\pi\) | ||
0.869424 | − | 0.494067i | \(-0.164490\pi\) | |||||||
\(264\) | −0.418024 | + | 0.456423i | −0.0257276 | + | 0.0280909i | ||||
\(265\) | 11.7716 | 0.723123 | ||||||||
\(266\) | − | 5.86904i | − | 0.359854i | ||||||
\(267\) | −8.90950 | − | 8.15995i | −0.545252 | − | 0.499381i | ||||
\(268\) | 7.79466 | − | 2.49867i | 0.476134 | − | 0.152630i | ||||
\(269\) | 5.66646i | 0.345490i | 0.984967 | + | 0.172745i | \(0.0552637\pi\) | ||||
−0.984967 | + | 0.172745i | \(0.944736\pi\) | |||||||
\(270\) | −4.12476 | − | 3.16012i | −0.251025 | − | 0.192319i | ||||
\(271\) | 14.0485i | 0.853388i | 0.904396 | + | 0.426694i | \(0.140322\pi\) | ||||
−0.904396 | + | 0.426694i | \(0.859678\pi\) | |||||||
\(272\) | − | 2.15051i | − | 0.130394i | ||||||
\(273\) | 3.34738 | − | 3.65487i | 0.202593 | − | 0.221203i | ||||
\(274\) | 22.9849 | 1.38857 | ||||||||
\(275\) | 0.357335 | 0.0215481 | ||||||||
\(276\) | −1.06584 | − | 0.976173i | −0.0641562 | − | 0.0587587i | ||||
\(277\) | −25.5204 | −1.53337 | −0.766685 | − | 0.642023i | \(-0.778095\pi\) | ||||
−0.766685 | + | 0.642023i | \(0.778095\pi\) | |||||||
\(278\) | − | 8.81597i | − | 0.528747i | ||||||
\(279\) | −8.94129 | + | 0.786777i | −0.535301 | + | 0.0471031i | ||||
\(280\) | 1.10570i | 0.0660785i | ||||||||
\(281\) | 10.2431 | 0.611053 | 0.305526 | − | 0.952184i | \(-0.401168\pi\) | ||||
0.305526 | + | 0.952184i | \(0.401168\pi\) | |||||||
\(282\) | 12.4602 | + | 11.4119i | 0.741993 | + | 0.679569i | ||||
\(283\) | −8.28611 | −0.492558 | −0.246279 | − | 0.969199i | \(-0.579208\pi\) | ||||
−0.246279 | + | 0.969199i | \(0.579208\pi\) | |||||||
\(284\) | 15.8888i | 0.942828i | ||||||||
\(285\) | −6.20945 | + | 6.77983i | −0.367816 | + | 0.401603i | ||||
\(286\) | 0.924735i | 0.0546807i | ||||||||
\(287\) | − | 6.85753i | − | 0.404787i | ||||||
\(288\) | 0.262965 | + | 2.98845i | 0.0154954 | + | 0.176096i | ||||
\(289\) | 12.3753 | 0.727960 | ||||||||
\(290\) | 3.88309i | 0.228023i | ||||||||
\(291\) | −18.7159 | − | 17.1414i | −1.09715 | − | 1.00484i | ||||
\(292\) | −12.0792 | −0.706883 | ||||||||
\(293\) | − | 26.8620i | − | 1.56930i | −0.619941 | − | 0.784648i | \(-0.712844\pi\) | ||
0.619941 | − | 0.784648i | \(-0.287156\pi\) | |||||||
\(294\) | −6.75863 | + | 7.37947i | −0.394172 | + | 0.430379i | ||||
\(295\) | 9.47707i | 0.551776i | ||||||||
\(296\) | −2.73596 | −0.159025 | ||||||||
\(297\) | −1.47392 | − | 1.12922i | −0.0855257 | − | 0.0655241i | ||||
\(298\) | − | 10.1468i | − | 0.587787i | ||||||
\(299\) | −2.15945 | −0.124884 | ||||||||
\(300\) | 1.16984 | − | 1.27729i | 0.0675405 | − | 0.0737447i | ||||
\(301\) | −7.63903 | −0.440306 | ||||||||
\(302\) | −1.34157 | −0.0771989 | ||||||||
\(303\) | 5.54727 | − | 6.05683i | 0.318682 | − | 0.347956i | ||||
\(304\) | 5.30796 | 0.304433 | ||||||||
\(305\) | 15.2529i | 0.873377i | ||||||||
\(306\) | 6.42669 | − | 0.565508i | 0.367389 | − | 0.0323279i | ||||
\(307\) | −5.37690 | −0.306876 | −0.153438 | − | 0.988158i | \(-0.549034\pi\) | ||||
−0.153438 | + | 0.988158i | \(0.549034\pi\) | |||||||
\(308\) | 0.395107i | 0.0225133i | ||||||||
\(309\) | 21.4037 | − | 23.3698i | 1.21762 | − | 1.32946i | ||||
\(310\) | − | 2.99195i | − | 0.169931i | ||||||
\(311\) | 12.7194 | 0.721249 | 0.360625 | − | 0.932711i | \(-0.382564\pi\) | ||||
0.360625 | + | 0.932711i | \(0.382564\pi\) | |||||||
\(312\) | 3.30546 | + | 3.02738i | 0.187135 | + | 0.171391i | ||||
\(313\) | − | 1.01542i | − | 0.0573951i | −0.999588 | − | 0.0286975i | \(-0.990864\pi\) | ||
0.999588 | − | 0.0286975i | \(-0.00913596\pi\) | |||||||
\(314\) | −16.5368 | −0.933223 | ||||||||
\(315\) | −3.30435 | + | 0.290761i | −0.186179 | + | 0.0163826i | ||||
\(316\) | − | 9.34458i | − | 0.525674i | ||||||
\(317\) | 12.9163i | 0.725453i | 0.931896 | + | 0.362726i | \(0.118154\pi\) | ||||
−0.931896 | + | 0.362726i | \(0.881846\pi\) | |||||||
\(318\) | 13.7708 | − | 15.0358i | 0.772230 | − | 0.843165i | ||||
\(319\) | 1.38756i | 0.0776887i | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −18.6292 | − | 17.0620i | −1.03978 | − | 0.952305i | ||||
\(322\) | −0.922658 | −0.0514177 | ||||||||
\(323\) | − | 11.4148i | − | 0.635137i | ||||||
\(324\) | −8.86170 | + | 1.57172i | −0.492317 | + | 0.0873176i | ||||
\(325\) | − | 2.58786i | − | 0.143549i | ||||||
\(326\) | 14.0394 | 0.777571 | ||||||||
\(327\) | −1.98721 | − | 1.82003i | −0.109893 | − | 0.100648i | ||||
\(328\) | 6.20196 | 0.342446 | ||||||||
\(329\) | 10.7863 | 0.594668 | ||||||||
\(330\) | 0.418024 | − | 0.456423i | 0.0230115 | − | 0.0251252i | ||||
\(331\) | 0.685019i | 0.0376520i | 0.999823 | + | 0.0188260i | \(0.00599286\pi\) | ||||
−0.999823 | + | 0.0188260i | \(0.994007\pi\) | |||||||
\(332\) | − | 4.47970i | − | 0.245855i | ||||||
\(333\) | −0.719462 | − | 8.17630i | −0.0394263 | − | 0.448058i | ||||
\(334\) | − | 9.21767i | − | 0.504368i | ||||||
\(335\) | −7.79466 | + | 2.49867i | −0.425868 | + | 0.136517i | ||||
\(336\) | 1.41231 | + | 1.29349i | 0.0770479 | + | 0.0705659i | ||||
\(337\) | − | 5.93774i | − | 0.323449i | −0.986836 | − | 0.161725i | \(-0.948294\pi\) | ||
0.986836 | − | 0.161725i | \(-0.0517056\pi\) | |||||||
\(338\) | −6.30297 | −0.342836 | ||||||||
\(339\) | 11.6717 | − | 12.7438i | 0.633920 | − | 0.692150i | ||||
\(340\) | 2.15051i | 0.116628i | ||||||||
\(341\) | − | 1.06913i | − | 0.0578965i | ||||||
\(342\) | 1.39581 | + | 15.8626i | 0.0754766 | + | 0.857751i | ||||
\(343\) | 14.1280i | 0.762843i | ||||||||
\(344\) | − | 6.90875i | − | 0.372495i | ||||||
\(345\) | 1.06584 | + | 0.976173i | 0.0573830 | + | 0.0525554i | ||||
\(346\) | − | 6.73609i | − | 0.362134i | ||||||
\(347\) | 8.25511 | 0.443158 | 0.221579 | − | 0.975142i | \(-0.428879\pi\) | ||||
0.221579 | + | 0.975142i | \(0.428879\pi\) | |||||||
\(348\) | 4.95985 | + | 4.54258i | 0.265876 | + | 0.243508i | ||||
\(349\) | −12.0824 | −0.646756 | −0.323378 | − | 0.946270i | \(-0.604819\pi\) | ||||
−0.323378 | + | 0.946270i | \(0.604819\pi\) | |||||||
\(350\) | − | 1.10570i | − | 0.0591024i | ||||||
\(351\) | −8.17795 | + | 10.6743i | −0.436507 | + | 0.569753i | ||||
\(352\) | −0.357335 | −0.0190460 | ||||||||
\(353\) | 31.3728 | 1.66980 | 0.834902 | − | 0.550398i | \(-0.185524\pi\) | ||||
0.834902 | + | 0.550398i | \(0.185524\pi\) | |||||||
\(354\) | 12.1050 | + | 11.0866i | 0.643374 | + | 0.589247i | ||||
\(355\) | − | 15.8888i | − | 0.843291i | ||||||
\(356\) | − | 6.97529i | − | 0.369689i | ||||||
\(357\) | 2.78167 | − | 3.03718i | 0.147221 | − | 0.160745i | ||||
\(358\) | −19.0886 | −1.00886 | ||||||||
\(359\) | 25.9535i | 1.36977i | 0.728649 | + | 0.684887i | \(0.240148\pi\) | ||||
−0.728649 | + | 0.684887i | \(0.759852\pi\) | |||||||
\(360\) | −0.262965 | − | 2.98845i | −0.0138595 | − | 0.157505i | ||||
\(361\) | 9.17446 | 0.482867 | ||||||||
\(362\) | −12.3626 | −0.649766 | ||||||||
\(363\) | −12.7188 | + | 13.8871i | −0.667565 | + | 0.728886i | ||||
\(364\) | 2.86141 | 0.149979 | ||||||||
\(365\) | 12.0792 | 0.632255 | ||||||||
\(366\) | 19.4824 | + | 17.8434i | 1.01836 | + | 0.932688i | ||||
\(367\) | 5.72011i | 0.298587i | 0.988793 | + | 0.149294i | \(0.0477000\pi\) | ||||
−0.988793 | + | 0.149294i | \(0.952300\pi\) | |||||||
\(368\) | − | 0.834453i | − | 0.0434988i | ||||||
\(369\) | 1.63090 | + | 18.5343i | 0.0849011 | + | 0.964855i | ||||
\(370\) | 2.73596 | 0.142236 | ||||||||
\(371\) | − | 13.0159i | − | 0.675752i | ||||||
\(372\) | −3.82160 | − | 3.50009i | −0.198141 | − | 0.181471i | ||||
\(373\) | 19.4974i | 1.00953i | 0.863255 | + | 0.504767i | \(0.168422\pi\) | ||||
−0.863255 | + | 0.504767i | \(0.831578\pi\) | |||||||
\(374\) | 0.768452i | 0.0397357i | ||||||||
\(375\) | −1.16984 | + | 1.27729i | −0.0604101 | + | 0.0659592i | ||||
\(376\) | 9.75513i | 0.503083i | ||||||||
\(377\) | 10.0489 | 0.517545 | ||||||||
\(378\) | −3.49416 | + | 4.56077i | −0.179720 | + | 0.234581i | ||||
\(379\) | 7.66723i | 0.393839i | 0.980420 | + | 0.196920i | \(0.0630938\pi\) | ||||
−0.980420 | + | 0.196920i | \(0.936906\pi\) | |||||||
\(380\) | −5.30796 | −0.272293 | ||||||||
\(381\) | −25.7723 | + | 28.1397i | −1.32036 | + | 1.44164i | ||||
\(382\) | 11.6132 | 0.594182 | ||||||||
\(383\) | 19.2226 | 0.982229 | 0.491115 | − | 0.871095i | \(-0.336590\pi\) | ||||
0.491115 | + | 0.871095i | \(0.336590\pi\) | |||||||
\(384\) | −1.16984 | + | 1.27729i | −0.0596980 | + | 0.0651817i | ||||
\(385\) | − | 0.395107i | − | 0.0201365i | ||||||
\(386\) | 0.896082 | 0.0456094 | ||||||||
\(387\) | 20.6465 | − | 1.81676i | 1.04952 | − | 0.0923510i | ||||
\(388\) | − | 14.6528i | − | 0.743883i | ||||||
\(389\) | 28.5043i | 1.44522i | 0.691254 | + | 0.722611i | \(0.257058\pi\) | ||||
−0.691254 | + | 0.722611i | \(0.742942\pi\) | |||||||
\(390\) | −3.30546 | − | 3.02738i | −0.167379 | − | 0.153297i | ||||
\(391\) | −1.79450 | −0.0907515 | ||||||||
\(392\) | −5.77742 | −0.291804 | ||||||||
\(393\) | −4.60425 | − | 4.21690i | −0.232254 | − | 0.212714i | ||||
\(394\) | 4.56961 | 0.230213 | ||||||||
\(395\) | 9.34458i | 0.470177i | ||||||||
\(396\) | −0.0939666 | − | 1.06788i | −0.00472200 | − | 0.0536630i | ||||
\(397\) | 8.75968 | 0.439636 | 0.219818 | − | 0.975541i | \(-0.429454\pi\) | ||||
0.219818 | + | 0.975541i | \(0.429454\pi\) | |||||||
\(398\) | −1.24326 | −0.0623190 | ||||||||
\(399\) | 7.49649 | + | 6.86581i | 0.375294 | + | 0.343721i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 9.07728 | 0.453298 | 0.226649 | − | 0.973977i | \(-0.427223\pi\) | ||||
0.226649 | + | 0.973977i | \(0.427223\pi\) | |||||||
\(402\) | −5.92694 | + | 12.8791i | −0.295609 | + | 0.642351i | ||||
\(403\) | −7.74275 | −0.385694 | ||||||||
\(404\) | 4.74192 | 0.235919 | ||||||||
\(405\) | 8.86170 | − | 1.57172i | 0.440341 | − | 0.0780992i | ||||
\(406\) | 4.29355 | 0.213085 | ||||||||
\(407\) | 0.977656 | 0.0484606 | ||||||||
\(408\) | 2.74683 | + | 2.51574i | 0.135988 | + | 0.124548i | ||||
\(409\) | 20.5072i | 1.01402i | 0.861941 | + | 0.507008i | \(0.169249\pi\) | ||||
−0.861941 | + | 0.507008i | \(0.830751\pi\) | |||||||
\(410\) | −6.20196 | −0.306293 | ||||||||
\(411\) | −26.8885 | + | 29.3585i | −1.32631 | + | 1.44815i | ||||
\(412\) | 18.2963 | 0.901396 | ||||||||
\(413\) | 10.4788 | 0.515630 | ||||||||
\(414\) | 2.49372 | − | 0.219432i | 0.122560 | − | 0.0107845i | ||||
\(415\) | 4.47970i | 0.219900i | ||||||||
\(416\) | 2.58786i | 0.126880i | ||||||||
\(417\) | 11.2606 | + | 10.3132i | 0.551434 | + | 0.505042i | ||||
\(418\) | −1.89672 | −0.0927717 | ||||||||
\(419\) | − | 5.35904i | − | 0.261806i | −0.991395 | − | 0.130903i | \(-0.958212\pi\) | ||
0.991395 | − | 0.130903i | \(-0.0417877\pi\) | |||||||
\(420\) | −1.41231 | − | 1.29349i | −0.0689137 | − | 0.0631160i | ||||
\(421\) | −4.50590 | −0.219604 | −0.109802 | − | 0.993953i | \(-0.535022\pi\) | ||||
−0.109802 | + | 0.993953i | \(0.535022\pi\) | |||||||
\(422\) | −1.28602 | −0.0626025 | ||||||||
\(423\) | −29.1528 | + | 2.56526i | −1.41746 | + | 0.124727i | ||||
\(424\) | 11.7716 | 0.571679 | ||||||||
\(425\) | − | 2.15051i | − | 0.104315i | ||||||
\(426\) | −20.2947 | − | 18.5873i | −0.983282 | − | 0.900559i | ||||
\(427\) | 16.8652 | 0.816163 | ||||||||
\(428\) | − | 14.5849i | − | 0.704988i | ||||||
\(429\) | −1.18116 | − | 1.08179i | −0.0570269 | − | 0.0522292i | ||||
\(430\) | 6.90875i | 0.333169i | ||||||||
\(431\) | − | 15.8178i | − | 0.761917i | −0.924592 | − | 0.380959i | \(-0.875594\pi\) | ||
0.924592 | − | 0.380959i | \(-0.124406\pi\) | |||||||
\(432\) | −4.12476 | − | 3.16012i | −0.198453 | − | 0.152041i | ||||
\(433\) | 3.60619i | 0.173302i | 0.996239 | + | 0.0866512i | \(0.0276166\pi\) | ||||
−0.996239 | + | 0.0866512i | \(0.972383\pi\) | |||||||
\(434\) | −3.30821 | −0.158799 | ||||||||
\(435\) | −4.95985 | − | 4.54258i | −0.237807 | − | 0.217800i | ||||
\(436\) | − | 1.55580i | − | 0.0745091i | ||||||
\(437\) | − | 4.42924i | − | 0.211879i | ||||||
\(438\) | 14.1307 | − | 15.4287i | 0.675192 | − | 0.737213i | ||||
\(439\) | −2.26867 | −0.108278 | −0.0541389 | − | 0.998533i | \(-0.517241\pi\) | ||||
−0.0541389 | + | 0.998533i | \(0.517241\pi\) | |||||||
\(440\) | 0.357335 | 0.0170353 | ||||||||
\(441\) | −1.51926 | − | 17.2655i | −0.0723456 | − | 0.822169i | ||||
\(442\) | 5.56521 | 0.264710 | ||||||||
\(443\) | 9.02705 | 0.428888 | 0.214444 | − | 0.976736i | \(-0.431206\pi\) | ||||
0.214444 | + | 0.976736i | \(0.431206\pi\) | |||||||
\(444\) | 3.20063 | − | 3.49463i | 0.151895 | − | 0.165848i | ||||
\(445\) | 6.97529i | 0.330660i | ||||||||
\(446\) | 23.6116 | 1.11804 | ||||||||
\(447\) | 12.9604 | + | 11.8701i | 0.613007 | + | 0.561435i | ||||
\(448\) | 1.10570i | 0.0522396i | ||||||||
\(449\) | 18.8339i | 0.888827i | 0.895822 | + | 0.444413i | \(0.146588\pi\) | ||||
−0.895822 | + | 0.444413i | \(0.853412\pi\) | |||||||
\(450\) | 0.262965 | + | 2.98845i | 0.0123963 | + | 0.140877i | ||||
\(451\) | −2.21618 | −0.104356 | ||||||||
\(452\) | 9.97721 | 0.469288 | ||||||||
\(453\) | 1.56942 | − | 1.71359i | 0.0737379 | − | 0.0805113i | ||||
\(454\) | 16.9703i | 0.796454i | ||||||||
\(455\) | −2.86141 | −0.134145 | ||||||||
\(456\) | −6.20945 | + | 6.77983i | −0.290784 | + | 0.317495i | ||||
\(457\) | 7.12233 | 0.333169 | 0.166584 | − | 0.986027i | \(-0.446726\pi\) | ||||
0.166584 | + | 0.986027i | \(0.446726\pi\) | |||||||
\(458\) | − | 19.9276i | − | 0.931154i | ||||||
\(459\) | −6.79585 | + | 8.87032i | −0.317203 | + | 0.414031i | ||||
\(460\) | 0.834453i | 0.0389066i | ||||||||
\(461\) | − | 1.06535i | − | 0.0496181i | −0.999692 | − | 0.0248090i | \(-0.992102\pi\) | ||
0.999692 | − | 0.0248090i | \(-0.00789777\pi\) | |||||||
\(462\) | −0.504668 | − | 0.462211i | −0.0234793 | − | 0.0215040i | ||||
\(463\) | 14.4915i | 0.673478i | 0.941598 | + | 0.336739i | \(0.109324\pi\) | ||||
−0.941598 | + | 0.336739i | \(0.890676\pi\) | |||||||
\(464\) | 3.88309i | 0.180268i | ||||||||
\(465\) | 3.82160 | + | 3.50009i | 0.177222 | + | 0.162313i | ||||
\(466\) | −25.2606 | −1.17018 | ||||||||
\(467\) | 14.8441i | 0.686903i | 0.939170 | + | 0.343451i | \(0.111596\pi\) | ||||
−0.939170 | + | 0.343451i | \(0.888404\pi\) | |||||||
\(468\) | −7.73371 | + | 0.680517i | −0.357491 | + | 0.0314569i | ||||
\(469\) | 2.76279 | + | 8.61859i | 0.127574 | + | 0.397969i | ||||
\(470\) | − | 9.75513i | − | 0.449971i | ||||||
\(471\) | 19.3453 | − | 21.1223i | 0.891384 | − | 0.973265i | ||||
\(472\) | 9.47707i | 0.436217i | ||||||||
\(473\) | 2.46874i | 0.113513i | ||||||||
\(474\) | 11.9358 | + | 10.9316i | 0.548229 | + | 0.502106i | ||||
\(475\) | 5.30796 | 0.243546 | ||||||||
\(476\) | 2.37782 | 0.108987 | ||||||||
\(477\) | 3.09551 | + | 35.1788i | 0.141734 | + | 1.61073i | ||||
\(478\) | −4.75090 | −0.217301 | ||||||||
\(479\) | − | 3.58488i | − | 0.163797i | −0.996641 | − | 0.0818986i | \(-0.973902\pi\) | ||
0.996641 | − | 0.0818986i | \(-0.0260984\pi\) | |||||||
\(480\) | 1.16984 | − | 1.27729i | 0.0533955 | − | 0.0583003i | ||||
\(481\) | − | 7.08030i | − | 0.322834i | ||||||
\(482\) | −18.6505 | −0.849508 | ||||||||
\(483\) | 1.07936 | − | 1.17851i | 0.0491125 | − | 0.0536239i | ||||
\(484\) | −10.8723 | −0.494196 | ||||||||
\(485\) | 14.6528i | 0.665349i | ||||||||
\(486\) | 8.35919 | − | 13.1577i | 0.379181 | − | 0.596843i | ||||
\(487\) | 40.8238i | 1.84990i | 0.380088 | + | 0.924951i | \(0.375894\pi\) | ||||
−0.380088 | + | 0.924951i | \(0.624106\pi\) | |||||||
\(488\) | 15.2529i | 0.690465i | ||||||||
\(489\) | −16.4238 | + | 17.9325i | −0.742710 | + | 0.810934i | ||||
\(490\) | 5.77742 | 0.260997 | ||||||||
\(491\) | − | 5.82397i | − | 0.262832i | −0.991327 | − | 0.131416i | \(-0.958048\pi\) | ||
0.991327 | − | 0.131416i | \(-0.0419524\pi\) | |||||||
\(492\) | −7.25528 | + | 7.92173i | −0.327093 | + | 0.357139i | ||||
\(493\) | 8.35060 | 0.376092 | ||||||||
\(494\) | 13.7363i | 0.618024i | ||||||||
\(495\) | 0.0939666 | + | 1.06788i | 0.00422349 | + | 0.0479976i | ||||
\(496\) | − | 2.99195i | − | 0.134342i | ||||||
\(497\) | −17.5683 | −0.788048 | ||||||||
\(498\) | 5.72190 | + | 5.24052i | 0.256404 | + | 0.234833i | ||||
\(499\) | − | 26.6192i | − | 1.19164i | −0.803119 | − | 0.595819i | \(-0.796828\pi\) | ||
0.803119 | − | 0.595819i | \(-0.203172\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 11.7737 | + | 10.7832i | 0.526009 | + | 0.481756i | ||||
\(502\) | −8.50442 | −0.379571 | ||||||||
\(503\) | −1.50927 | −0.0672951 | −0.0336475 | − | 0.999434i | \(-0.510712\pi\) | ||||
−0.0336475 | + | 0.999434i | \(0.510712\pi\) | |||||||
\(504\) | −3.30435 | + | 0.290761i | −0.147187 | + | 0.0129515i | ||||
\(505\) | −4.74192 | −0.211013 | ||||||||
\(506\) | 0.298179i | 0.0132557i | ||||||||
\(507\) | 7.37344 | − | 8.05075i | 0.327466 | − | 0.357546i | ||||
\(508\) | −22.0307 | −0.977454 | ||||||||
\(509\) | 26.3815i | 1.16934i | 0.811272 | + | 0.584669i | \(0.198775\pi\) | ||||
−0.811272 | + | 0.584669i | \(0.801225\pi\) | |||||||
\(510\) | −2.74683 | − | 2.51574i | −0.121632 | − | 0.111399i | ||||
\(511\) | − | 13.3561i | − | 0.590837i | ||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −21.8941 | − | 16.7738i | −0.966647 | − | 0.740581i | ||||
\(514\) | 21.3562i | 0.941984i | ||||||||
\(515\) | −18.2963 | −0.806233 | ||||||||
\(516\) | 8.82451 | + | 8.08210i | 0.388477 | + | 0.355795i | ||||
\(517\) | − | 3.48585i | − | 0.153308i | ||||||
\(518\) | − | 3.02517i | − | 0.132918i | ||||||
\(519\) | 8.60397 | + | 7.88012i | 0.377673 | + | 0.345899i | ||||
\(520\) | − | 2.58786i | − | 0.113485i | ||||||
\(521\) | 19.9200 | 0.872709 | 0.436355 | − | 0.899775i | \(-0.356269\pi\) | ||||
0.436355 | + | 0.899775i | \(0.356269\pi\) | |||||||
\(522\) | −11.6044 | + | 1.02112i | −0.507912 | + | 0.0446930i | ||||
\(523\) | 26.8214 | 1.17282 | 0.586408 | − | 0.810016i | \(-0.300541\pi\) | ||||
0.586408 | + | 0.810016i | \(0.300541\pi\) | |||||||
\(524\) | − | 3.60469i | − | 0.157472i | ||||||
\(525\) | 1.41231 | + | 1.29349i | 0.0616383 | + | 0.0564527i | ||||
\(526\) | 16.0248i | 0.698716i | ||||||||
\(527\) | −6.43420 | −0.280278 | ||||||||
\(528\) | 0.418024 | − | 0.456423i | 0.0181922 | − | 0.0198632i | ||||
\(529\) | 22.3037 | 0.969726 | ||||||||
\(530\) | −11.7716 | −0.511325 | ||||||||
\(531\) | −28.3218 | + | 2.49214i | −1.22906 | + | 0.108149i | ||||
\(532\) | 5.86904i | 0.254455i | ||||||||
\(533\) | 16.0498i | 0.695195i | ||||||||
\(534\) | 8.90950 | + | 8.15995i | 0.385552 | + | 0.353115i | ||||
\(535\) | 14.5849i | 0.630560i | ||||||||
\(536\) | −7.79466 | + | 2.49867i | −0.336678 | + | 0.107926i | ||||
\(537\) | 22.3305 | − | 24.3817i | 0.963633 | − | 1.05215i | ||||
\(538\) | − | 5.66646i | − | 0.244298i | ||||||
\(539\) | 2.06447 | 0.0889232 | ||||||||
\(540\) | 4.12476 | + | 3.16012i | 0.177501 | + | 0.135990i | ||||
\(541\) | 15.3414i | 0.659580i | 0.944054 | + | 0.329790i | \(0.106978\pi\) | ||||
−0.944054 | + | 0.329790i | \(0.893022\pi\) | |||||||
\(542\) | − | 14.0485i | − | 0.603436i | ||||||
\(543\) | 14.4623 | − | 15.7907i | 0.620636 | − | 0.677646i | ||||
\(544\) | 2.15051i | 0.0922022i | ||||||||
\(545\) | 1.55580i | 0.0666430i | ||||||||
\(546\) | −3.34738 | + | 3.65487i | −0.143255 | + | 0.156414i | ||||
\(547\) | 22.7451i | 0.972508i | 0.873817 | + | 0.486254i | \(0.161637\pi\) | ||||
−0.873817 | + | 0.486254i | \(0.838363\pi\) | |||||||
\(548\) | −22.9849 | −0.981865 | ||||||||
\(549\) | −45.5825 | + | 4.01097i | −1.94541 | + | 0.171184i | ||||
\(550\) | −0.357335 | −0.0152368 | ||||||||
\(551\) | 20.6113i | 0.878070i | ||||||||
\(552\) | 1.06584 | + | 0.976173i | 0.0453653 | + | 0.0415487i | ||||
\(553\) | 10.3323 | 0.439376 | ||||||||
\(554\) | 25.5204 | 1.08426 | ||||||||
\(555\) | −3.20063 | + | 3.49463i | −0.135859 | + | 0.148339i | ||||
\(556\) | 8.81597i | 0.373881i | ||||||||
\(557\) | 16.7579i | 0.710055i | 0.934856 | + | 0.355027i | \(0.115528\pi\) | ||||
−0.934856 | + | 0.355027i | \(0.884472\pi\) | |||||||
\(558\) | 8.94129 | − | 0.786777i | 0.378515 | − | 0.0333069i | ||||
\(559\) | 17.8789 | 0.756196 | ||||||||
\(560\) | − | 1.10570i | − | 0.0467245i | ||||||
\(561\) | −0.981539 | − | 0.898963i | −0.0414406 | − | 0.0379542i | ||||
\(562\) | −10.2431 | −0.432079 | ||||||||
\(563\) | −11.6538 | −0.491148 | −0.245574 | − | 0.969378i | \(-0.578976\pi\) | ||||
−0.245574 | + | 0.969378i | \(0.578976\pi\) | |||||||
\(564\) | −12.4602 | − | 11.4119i | −0.524668 | − | 0.480528i | ||||
\(565\) | −9.97721 | −0.419744 | ||||||||
\(566\) | 8.28611 | 0.348291 | ||||||||
\(567\) | −1.73785 | − | 9.79842i | −0.0729830 | − | 0.411495i | ||||
\(568\) | − | 15.8888i | − | 0.666680i | ||||||
\(569\) | 47.2424i | 1.98051i | 0.139282 | + | 0.990253i | \(0.455521\pi\) | ||||
−0.139282 | + | 0.990253i | \(0.544479\pi\) | |||||||
\(570\) | 6.20945 | − | 6.77983i | 0.260085 | − | 0.283976i | ||||
\(571\) | 15.8046 | 0.661401 | 0.330700 | − | 0.943736i | \(-0.392715\pi\) | ||||
0.330700 | + | 0.943736i | \(0.392715\pi\) | |||||||
\(572\) | − | 0.924735i | − | 0.0386651i | ||||||
\(573\) | −13.5855 | + | 14.8335i | −0.567543 | + | 0.619676i | ||||
\(574\) | 6.85753i | 0.286228i | ||||||||
\(575\) | − | 0.834453i | − | 0.0347991i | ||||||
\(576\) | −0.262965 | − | 2.98845i | −0.0109569 | − | 0.124519i | ||||
\(577\) | − | 36.9474i | − | 1.53814i | −0.639164 | − | 0.769070i | \(-0.720720\pi\) | ||
0.639164 | − | 0.769070i | \(-0.279280\pi\) | |||||||
\(578\) | −12.3753 | −0.514746 | ||||||||
\(579\) | −1.04827 | + | 1.14456i | −0.0435646 | + | 0.0475663i | ||||
\(580\) | − | 3.88309i | − | 0.161236i | ||||||
\(581\) | 4.95322 | 0.205494 | ||||||||
\(582\) | 18.7159 | + | 17.1414i | 0.775800 | + | 0.710533i | ||||
\(583\) | −4.20640 | −0.174211 | ||||||||
\(584\) | 12.0792 | 0.499842 | ||||||||
\(585\) | 7.73371 | − | 0.680517i | 0.319749 | − | 0.0281359i | ||||
\(586\) | 26.8620i | 1.10966i | ||||||||
\(587\) | 17.7172 | 0.731266 | 0.365633 | − | 0.930759i | \(-0.380852\pi\) | ||||
0.365633 | + | 0.930759i | \(0.380852\pi\) | |||||||
\(588\) | 6.75863 | − | 7.37947i | 0.278721 | − | 0.304324i | ||||
\(589\) | − | 15.8811i | − | 0.654371i | ||||||
\(590\) | − | 9.47707i | − | 0.390165i | ||||||
\(591\) | −5.34569 | + | 5.83673i | −0.219892 | + | 0.240091i | ||||
\(592\) | 2.73596 | 0.112447 | ||||||||
\(593\) | 40.8538 | 1.67766 | 0.838832 | − | 0.544391i | \(-0.183239\pi\) | ||||
0.838832 | + | 0.544391i | \(0.183239\pi\) | |||||||
\(594\) | 1.47392 | + | 1.12922i | 0.0604758 | + | 0.0463325i | ||||
\(595\) | −2.37782 | −0.0974813 | ||||||||
\(596\) | 10.1468i | 0.415628i | ||||||||
\(597\) | 1.45441 | − | 1.58801i | 0.0595251 | − | 0.0649929i | ||||
\(598\) | 2.15945 | 0.0883064 | ||||||||
\(599\) | 13.4434 | 0.549282 | 0.274641 | − | 0.961547i | \(-0.411441\pi\) | ||||
0.274641 | + | 0.961547i | \(0.411441\pi\) | |||||||
\(600\) | −1.16984 | + | 1.27729i | −0.0477584 | + | 0.0521453i | ||||
\(601\) | 5.47259 | 0.223232 | 0.111616 | − | 0.993751i | \(-0.464397\pi\) | ||||
0.111616 | + | 0.993751i | \(0.464397\pi\) | |||||||
\(602\) | 7.63903 | 0.311344 | ||||||||
\(603\) | −9.51687 | − | 22.6369i | −0.387557 | − | 0.921846i | ||||
\(604\) | 1.34157 | 0.0545879 | ||||||||
\(605\) | 10.8723 | 0.442022 | ||||||||
\(606\) | −5.54727 | + | 6.05683i | −0.225342 | + | 0.246042i | ||||
\(607\) | −10.4948 | −0.425971 | −0.212985 | − | 0.977055i | \(-0.568319\pi\) | ||||
−0.212985 | + | 0.977055i | \(0.568319\pi\) | |||||||
\(608\) | −5.30796 | −0.215266 | ||||||||
\(609\) | −5.02275 | + | 5.48413i | −0.203532 | + | 0.222228i | ||||
\(610\) | − | 15.2529i | − | 0.617571i | ||||||
\(611\) | −25.2449 | −1.02130 | ||||||||
\(612\) | −6.42669 | + | 0.565508i | −0.259783 | + | 0.0228593i | ||||
\(613\) | −0.227267 | −0.00917921 | −0.00458960 | − | 0.999989i | \(-0.501461\pi\) | ||||
−0.00458960 | + | 0.999989i | \(0.501461\pi\) | |||||||
\(614\) | 5.37690 | 0.216994 | ||||||||
\(615\) | 7.25528 | − | 7.92173i | 0.292561 | − | 0.319435i | ||||
\(616\) | − | 0.395107i | − | 0.0159193i | ||||||
\(617\) | 13.2924i | 0.535131i | 0.963540 | + | 0.267566i | \(0.0862192\pi\) | ||||
−0.963540 | + | 0.267566i | \(0.913781\pi\) | |||||||
\(618\) | −21.4037 | + | 23.3698i | −0.860984 | + | 0.940072i | ||||
\(619\) | −27.9019 | −1.12147 | −0.560736 | − | 0.827995i | \(-0.689482\pi\) | ||||
−0.560736 | + | 0.827995i | \(0.689482\pi\) | |||||||
\(620\) | 2.99195i | 0.120159i | ||||||||
\(621\) | −2.63697 | + | 3.44192i | −0.105818 | + | 0.138119i | ||||
\(622\) | −12.7194 | −0.510000 | ||||||||
\(623\) | 7.71261 | 0.308999 | ||||||||
\(624\) | −3.30546 | − | 3.02738i | −0.132324 | − | 0.121192i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.01542i | 0.0405844i | ||||||||
\(627\) | 2.21885 | − | 2.42267i | 0.0886125 | − | 0.0967523i | ||||
\(628\) | 16.5368 | 0.659888 | ||||||||
\(629\) | − | 5.88371i | − | 0.234599i | ||||||
\(630\) | 3.30435 | − | 0.290761i | 0.131648 | − | 0.0115842i | ||||
\(631\) | − | 8.34969i | − | 0.332396i | −0.986092 | − | 0.166198i | \(-0.946851\pi\) | ||
0.986092 | − | 0.166198i | \(-0.0531491\pi\) | |||||||
\(632\) | 9.34458i | 0.371707i | ||||||||
\(633\) | 1.50443 | − | 1.64263i | 0.0597958 | − | 0.0652885i | ||||
\(634\) | − | 12.9163i | − | 0.512973i | ||||||
\(635\) | 22.0307 | 0.874262 | ||||||||
\(636\) | −13.7708 | + | 15.0358i | −0.546049 | + | 0.596208i | ||||
\(637\) | − | 14.9512i | − | 0.592387i | ||||||
\(638\) | − | 1.38756i | − | 0.0549342i | ||||||
\(639\) | 47.4830 | − | 4.17820i | 1.87840 | − | 0.165287i | ||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −37.1089 | −1.46572 | −0.732858 | − | 0.680382i | \(-0.761814\pi\) | ||||
−0.732858 | + | 0.680382i | \(0.761814\pi\) | |||||||
\(642\) | 18.6292 | + | 17.0620i | 0.735237 | + | 0.673382i | ||||
\(643\) | −9.38800 | −0.370227 | −0.185113 | − | 0.982717i | \(-0.559265\pi\) | ||||
−0.185113 | + | 0.982717i | \(0.559265\pi\) | |||||||
\(644\) | 0.922658 | 0.0363578 | ||||||||
\(645\) | −8.82451 | − | 8.08210i | −0.347465 | − | 0.318233i | ||||
\(646\) | 11.4148i | 0.449109i | ||||||||
\(647\) | −5.26994 | −0.207183 | −0.103591 | − | 0.994620i | \(-0.533033\pi\) | ||||
−0.103591 | + | 0.994620i | \(0.533033\pi\) | |||||||
\(648\) | 8.86170 | − | 1.57172i | 0.348120 | − | 0.0617428i | ||||
\(649\) | − | 3.38649i | − | 0.132931i | ||||||
\(650\) | 2.58786i | 0.101504i | ||||||||
\(651\) | 3.87006 | − | 4.22556i | 0.151680 | − | 0.165613i | ||||
\(652\) | −14.0394 | −0.549825 | ||||||||
\(653\) | 3.08390 | 0.120682 | 0.0603412 | − | 0.998178i | \(-0.480781\pi\) | ||||
0.0603412 | + | 0.998178i | \(0.480781\pi\) | |||||||
\(654\) | 1.98721 | + | 1.82003i | 0.0777061 | + | 0.0711687i | ||||
\(655\) | 3.60469i | 0.140847i | ||||||||
\(656\) | −6.20196 | −0.242146 | ||||||||
\(657\) | 3.17641 | + | 36.0982i | 0.123924 | + | 1.40832i | ||||
\(658\) | −10.7863 | −0.420494 | ||||||||
\(659\) | − | 0.0528055i | − | 0.00205701i | −0.999999 | − | 0.00102850i | \(-0.999673\pi\) | ||
0.999999 | − | 0.00102850i | \(-0.000327383\pi\) | |||||||
\(660\) | −0.418024 | + | 0.456423i | −0.0162716 | + | 0.0177662i | ||||
\(661\) | 32.0793i | 1.24774i | 0.781528 | + | 0.623870i | \(0.214441\pi\) | ||||
−0.781528 | + | 0.623870i | \(0.785559\pi\) | |||||||
\(662\) | − | 0.685019i | − | 0.0266240i | ||||||
\(663\) | −6.51039 | + | 7.10842i | −0.252843 | + | 0.276068i | ||||
\(664\) | 4.47970i | 0.173846i | ||||||||
\(665\) | − | 5.86904i | − | 0.227592i | ||||||
\(666\) | 0.719462 | + | 8.17630i | 0.0278786 | + | 0.316825i | ||||
\(667\) | 3.24025 | 0.125463 | ||||||||
\(668\) | 9.21767i | 0.356642i | ||||||||
\(669\) | −27.6217 | + | 30.1590i | −1.06792 | + | 1.16601i | ||||
\(670\) | 7.79466 | − | 2.49867i | 0.301134 | − | 0.0965319i | ||||
\(671\) | − | 5.45039i | − | 0.210410i | ||||||
\(672\) | −1.41231 | − | 1.29349i | −0.0544811 | − | 0.0498976i | ||||
\(673\) | − | 35.6698i | − | 1.37497i | −0.726199 | − | 0.687485i | \(-0.758715\pi\) | ||
0.726199 | − | 0.687485i | \(-0.241285\pi\) | |||||||
\(674\) | 5.93774i | 0.228713i | ||||||||
\(675\) | −4.12476 | − | 3.16012i | −0.158762 | − | 0.121633i | ||||
\(676\) | 6.30297 | 0.242422 | ||||||||
\(677\) | 5.61881 | 0.215948 | 0.107974 | − | 0.994154i | \(-0.465564\pi\) | ||||
0.107974 | + | 0.994154i | \(0.465564\pi\) | |||||||
\(678\) | −11.6717 | + | 12.7438i | −0.448249 | + | 0.489424i | ||||
\(679\) | 16.2017 | 0.621762 | ||||||||
\(680\) | − | 2.15051i | − | 0.0824681i | ||||||
\(681\) | −21.6760 | − | 19.8524i | −0.830628 | − | 0.760747i | ||||
\(682\) | 1.06913i | 0.0409390i | ||||||||
\(683\) | −13.4427 | −0.514371 | −0.257185 | − | 0.966362i | \(-0.582795\pi\) | ||||
−0.257185 | + | 0.966362i | \(0.582795\pi\) | |||||||
\(684\) | −1.39581 | − | 15.8626i | −0.0533700 | − | 0.606521i | ||||
\(685\) | 22.9849 | 0.878206 | ||||||||
\(686\) | − | 14.1280i | − | 0.539411i | ||||||
\(687\) | 25.4534 | + | 23.3120i | 0.971107 | + | 0.889408i | ||||
\(688\) | 6.90875i | 0.263393i | ||||||||
\(689\) | 30.4633i | 1.16056i | ||||||||
\(690\) | −1.06584 | − | 0.976173i | −0.0405759 | − | 0.0371623i | ||||
\(691\) | −24.5919 | −0.935519 | −0.467759 | − | 0.883856i | \(-0.654939\pi\) | ||||
−0.467759 | + | 0.883856i | \(0.654939\pi\) | |||||||
\(692\) | 6.73609i | 0.256068i | ||||||||
\(693\) | 1.18076 | − | 0.103899i | 0.0448533 | − | 0.00394681i | ||||
\(694\) | −8.25511 | −0.313360 | ||||||||
\(695\) | − | 8.81597i | − | 0.334409i | ||||||
\(696\) | −4.95985 | − | 4.54258i | −0.188003 | − | 0.172186i | ||||
\(697\) | 13.3373i | 0.505188i | ||||||||
\(698\) | 12.0824 | 0.457325 | ||||||||
\(699\) | 29.5508 | − | 32.2653i | 1.11771 | − | 1.22039i | ||||
\(700\) | 1.10570i | 0.0417917i | ||||||||
\(701\) | 22.9680 | 0.867489 | 0.433744 | − | 0.901036i | \(-0.357192\pi\) | ||||
0.433744 | + | 0.901036i | \(0.357192\pi\) | |||||||
\(702\) | 8.17795 | − | 10.6743i | 0.308657 | − | 0.402876i | ||||
\(703\) | 14.5224 | 0.547723 | ||||||||
\(704\) | 0.357335 | 0.0134676 | ||||||||
\(705\) | 12.4602 | + | 11.4119i | 0.469278 | + | 0.429797i | ||||
\(706\) | −31.3728 | −1.18073 | ||||||||
\(707\) | 5.24316i | 0.197189i | ||||||||
\(708\) | −12.1050 | − | 11.0866i | −0.454934 | − | 0.416661i | ||||
\(709\) | 52.1284 | 1.95772 | 0.978861 | − | 0.204526i | \(-0.0655652\pi\) | ||||
0.978861 | + | 0.204526i | \(0.0655652\pi\) | |||||||
\(710\) | 15.8888i | 0.596297i | ||||||||
\(711\) | −27.9258 | + | 2.45730i | −1.04730 | + | 0.0921558i | ||||
\(712\) | 6.97529i | 0.261410i | ||||||||
\(713\) | −2.49664 | −0.0934998 | ||||||||
\(714\) | −2.78167 | + | 3.03718i | −0.104101 | + | 0.113664i | ||||
\(715\) | 0.924735i | 0.0345831i | ||||||||
\(716\) | 19.0886 | 0.713374 | ||||||||
\(717\) | 5.55778 | − | 6.06830i | 0.207559 | − | 0.226625i | ||||
\(718\) | − | 25.9535i | − | 0.968576i | ||||||
\(719\) | − | 37.8793i | − | 1.41266i | −0.707884 | − | 0.706329i | \(-0.750350\pi\) | ||
0.707884 | − | 0.706329i | \(-0.249650\pi\) | |||||||
\(720\) | 0.262965 | + | 2.98845i | 0.00980012 | + | 0.111373i | ||||
\(721\) | 20.2303i | 0.753417i | ||||||||
\(722\) | −9.17446 | −0.341438 | ||||||||
\(723\) | 21.8181 | − | 23.8222i | 0.811423 | − | 0.885958i | ||||
\(724\) | 12.3626 | 0.459454 | ||||||||
\(725\) | 3.88309i | 0.144214i | ||||||||
\(726\) | 12.7188 | − | 13.8871i | 0.472040 | − | 0.515400i | ||||
\(727\) | − | 20.6312i | − | 0.765170i | −0.923920 | − | 0.382585i | \(-0.875034\pi\) | ||
0.923920 | − | 0.382585i | \(-0.124966\pi\) | |||||||
\(728\) | −2.86141 | −0.106051 | ||||||||
\(729\) | 7.02732 | + | 26.0695i | 0.260271 | + | 0.965536i | ||||
\(730\) | −12.0792 | −0.447072 | ||||||||
\(731\) | 14.8573 | 0.549517 | ||||||||
\(732\) | −19.4824 | − | 17.8434i | −0.720091 | − | 0.659510i | ||||
\(733\) | − | 13.3520i | − | 0.493166i | −0.969122 | − | 0.246583i | \(-0.920692\pi\) | ||
0.969122 | − | 0.246583i | \(-0.0793077\pi\) | |||||||
\(734\) | − | 5.72011i | − | 0.211133i | ||||||
\(735\) | −6.75863 | + | 7.37947i | −0.249296 | + | 0.272196i | ||||
\(736\) | 0.834453i | 0.0307583i | ||||||||
\(737\) | 2.78531 | − | 0.892861i | 0.102598 | − | 0.0328890i | ||||
\(738\) | −1.63090 | − | 18.5343i | −0.0600342 | − | 0.682255i | ||||
\(739\) | − | 41.7359i | − | 1.53528i | −0.640881 | − | 0.767640i | \(-0.721431\pi\) | ||
0.640881 | − | 0.767640i | \(-0.278569\pi\) | |||||||
\(740\) | −2.73596 | −0.100576 | ||||||||
\(741\) | −17.5453 | − | 16.0692i | −0.644542 | − | 0.590317i | ||||
\(742\) | 13.0159i | 0.477829i | ||||||||
\(743\) | 39.1259i | 1.43539i | 0.696358 | + | 0.717695i | \(0.254803\pi\) | ||||
−0.696358 | + | 0.717695i | \(0.745197\pi\) | |||||||
\(744\) | 3.82160 | + | 3.50009i | 0.140107 | + | 0.128319i | ||||
\(745\) | − | 10.1468i | − | 0.371749i | ||||||
\(746\) | − | 19.4974i | − | 0.713849i | ||||||
\(747\) | −13.3874 | + | 1.17800i | −0.489818 | + | 0.0431009i | ||||
\(748\) | − | 0.768452i | − | 0.0280974i | ||||||
\(749\) | 16.1266 | 0.589253 | ||||||||
\(750\) | 1.16984 | − | 1.27729i | 0.0427164 | − | 0.0466402i | ||||
\(751\) | 39.9206 | 1.45673 | 0.728363 | − | 0.685192i | \(-0.240282\pi\) | ||||
0.728363 | + | 0.685192i | \(0.240282\pi\) | |||||||
\(752\) | − | 9.75513i | − | 0.355733i | ||||||
\(753\) | 9.94878 | − | 10.8627i | 0.362554 | − | 0.395857i | ||||
\(754\) | −10.0489 | −0.365959 | ||||||||
\(755\) | −1.34157 | −0.0488249 | ||||||||
\(756\) | 3.49416 | − | 4.56077i | 0.127081 | − | 0.165873i | ||||
\(757\) | 8.22832i | 0.299063i | 0.988757 | + | 0.149532i | \(0.0477766\pi\) | ||||
−0.988757 | + | 0.149532i | \(0.952223\pi\) | |||||||
\(758\) | − | 7.66723i | − | 0.278486i | ||||||
\(759\) | −0.380863 | − | 0.348821i | −0.0138244 | − | 0.0126614i | ||||
\(760\) | 5.30796 | 0.192540 | ||||||||
\(761\) | 33.0672i | 1.19868i | 0.800493 | + | 0.599342i | \(0.204571\pi\) | ||||
−0.800493 | + | 0.599342i | \(0.795429\pi\) | |||||||
\(762\) | 25.7723 | − | 28.1397i | 0.933633 | − | 1.01939i | ||||
\(763\) | 1.72025 | 0.0622773 | ||||||||
\(764\) | −11.6132 | −0.420150 | ||||||||
\(765\) | 6.42669 | − | 0.565508i | 0.232357 | − | 0.0204460i | ||||
\(766\) | −19.2226 | −0.694541 | ||||||||
\(767\) | −24.5254 | −0.885559 | ||||||||
\(768\) | 1.16984 | − | 1.27729i | 0.0422128 | − | 0.0460904i | ||||
\(769\) | 25.2179i | 0.909382i | 0.890649 | + | 0.454691i | \(0.150250\pi\) | ||||
−0.890649 | + | 0.454691i | \(0.849750\pi\) | |||||||
\(770\) | 0.395107i | 0.0142387i | ||||||||
\(771\) | −27.2782 | − | 24.9833i | −0.982401 | − | 0.899752i | ||||
\(772\) | −0.896082 | −0.0322507 | ||||||||
\(773\) | − | 20.0081i | − | 0.719641i | −0.933021 | − | 0.359821i | \(-0.882838\pi\) | ||
0.933021 | − | 0.359821i | \(-0.117162\pi\) | |||||||
\(774\) | −20.6465 | + | 1.81676i | −0.742122 | + | 0.0653020i | ||||
\(775\) | − | 2.99195i | − | 0.107474i | ||||||
\(776\) | 14.6528i | 0.526004i | ||||||||
\(777\) | 3.86403 | + | 3.53895i | 0.138621 | + | 0.126959i | ||||
\(778\) | − | 28.5043i | − | 1.02193i | ||||||
\(779\) | −32.9198 | −1.17947 | ||||||||
\(780\) | 3.30546 | + | 3.02738i | 0.118355 | + | 0.108397i | ||||
\(781\) | 5.67764i | 0.203162i | ||||||||
\(782\) | 1.79450 | 0.0641710 | ||||||||
\(783\) | 12.2710 | − | 16.0168i | 0.438530 | − | 0.572394i | ||||
\(784\) | 5.77742 | 0.206336 | ||||||||
\(785\) | −16.5368 | −0.590222 | ||||||||
\(786\) | 4.60425 | + | 4.21690i | 0.164228 | + | 0.150412i | ||||
\(787\) | 2.81803i | 0.100452i | 0.998738 | + | 0.0502259i | \(0.0159941\pi\) | ||||
−0.998738 | + | 0.0502259i | \(0.984006\pi\) | |||||||
\(788\) | −4.56961 | −0.162785 | ||||||||
\(789\) | −20.4685 | − | 18.7464i | −0.728696 | − | 0.667391i | ||||
\(790\) | − | 9.34458i | − | 0.332465i | ||||||
\(791\) | 11.0318i | 0.392247i | ||||||||
\(792\) | 0.0939666 | + | 1.06788i | 0.00333896 | + | 0.0379454i | ||||
\(793\) | −39.4723 | −1.40170 | ||||||||
\(794\) | −8.75968 | −0.310870 | ||||||||
\(795\) | 13.7708 | − | 15.0358i | 0.488401 | − | 0.533265i | ||||
\(796\) | 1.24326 | 0.0440662 | ||||||||
\(797\) | − | 34.3198i | − | 1.21567i | −0.794063 | − | 0.607836i | \(-0.792038\pi\) | ||
0.794063 | − | 0.607836i | \(-0.207962\pi\) | |||||||
\(798\) | −7.49649 | − | 6.86581i | −0.265373 | − | 0.243047i | ||||
\(799\) | −20.9785 | −0.742165 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −20.8453 | + | 1.83426i | −0.736533 | + | 0.0648102i | ||||
\(802\) | −9.07728 | −0.320530 | ||||||||
\(803\) | −4.31633 | −0.152320 | ||||||||
\(804\) | 5.92694 | − | 12.8791i | 0.209027 | − | 0.454211i | ||||
\(805\) | −0.922658 | −0.0325194 | ||||||||
\(806\) | 7.74275 | 0.272727 | ||||||||
\(807\) | 7.23774 | + | 6.62883i | 0.254780 | + | 0.233346i | ||||
\(808\) | −4.74192 | −0.166820 | ||||||||
\(809\) | −6.24459 | −0.219548 | −0.109774 | − | 0.993957i | \(-0.535013\pi\) | ||||
−0.109774 | + | 0.993957i | \(0.535013\pi\) | |||||||
\(810\) | −8.86170 | + | 1.57172i | −0.311368 | + | 0.0552245i | ||||
\(811\) | − | 42.1703i | − | 1.48080i | −0.672166 | − | 0.740400i | \(-0.734636\pi\) | ||
0.672166 | − | 0.740400i | \(-0.265364\pi\) | |||||||
\(812\) | −4.29355 | −0.150674 | ||||||||
\(813\) | 17.9441 | + | 16.4345i | 0.629328 | + | 0.576383i | ||||
\(814\) | −0.977656 | −0.0342668 | ||||||||
\(815\) | 14.0394 | 0.491779 | ||||||||
\(816\) | −2.74683 | − | 2.51574i | −0.0961583 | − | 0.0880685i | ||||
\(817\) | 36.6714i | 1.28297i | ||||||||
\(818\) | − | 20.5072i | − | 0.717018i | ||||||
\(819\) | −0.752451 | − | 8.55119i | −0.0262928 | − | 0.298803i | ||||
\(820\) | 6.20196 | 0.216582 | ||||||||
\(821\) | 23.5569i | 0.822143i | 0.911603 | + | 0.411072i | \(0.134845\pi\) | ||||
−0.911603 | + | 0.411072i | \(0.865155\pi\) | |||||||
\(822\) | 26.8885 | − | 29.3585i | 0.937845 | − | 1.02399i | ||||
\(823\) | 26.0001 | 0.906306 | 0.453153 | − | 0.891433i | \(-0.350299\pi\) | ||||
0.453153 | + | 0.891433i | \(0.350299\pi\) | |||||||
\(824\) | −18.2963 | −0.637383 | ||||||||
\(825\) | 0.418024 | − | 0.456423i | 0.0145537 | − | 0.0158906i | ||||
\(826\) | −10.4788 | −0.364605 | ||||||||
\(827\) | − | 54.3627i | − | 1.89038i | −0.326527 | − | 0.945188i | \(-0.605879\pi\) | ||
0.326527 | − | 0.945188i | \(-0.394121\pi\) | |||||||
\(828\) | −2.49372 | + | 0.219432i | −0.0866628 | + | 0.00762578i | ||||
\(829\) | −31.7307 | −1.10205 | −0.551026 | − | 0.834488i | \(-0.685764\pi\) | ||||
−0.551026 | + | 0.834488i | \(0.685764\pi\) | |||||||
\(830\) | − | 4.47970i | − | 0.155493i | ||||||
\(831\) | −29.8547 | + | 32.5971i | −1.03565 | + | 1.13078i | ||||
\(832\) | − | 2.58786i | − | 0.0897180i | ||||||
\(833\) | − | 12.4244i | − | 0.430479i | ||||||
\(834\) | −11.2606 | − | 10.3132i | −0.389923 | − | 0.357119i | ||||
\(835\) | − | 9.21767i | − | 0.318991i | ||||||
\(836\) | 1.89672 | 0.0655995 | ||||||||
\(837\) | −9.45490 | + | 12.3411i | −0.326809 | + | 0.426570i | ||||
\(838\) | 5.35904i | 0.185125i | ||||||||
\(839\) | − | 24.8638i | − | 0.858392i | −0.903211 | − | 0.429196i | \(-0.858797\pi\) | ||
0.903211 | − | 0.429196i | \(-0.141203\pi\) | |||||||
\(840\) | 1.41231 | + | 1.29349i | 0.0487293 | + | 0.0446298i | ||||
\(841\) | 13.9216 | 0.480056 | ||||||||
\(842\) | 4.50590 | 0.155284 | ||||||||
\(843\) | 11.9828 | − | 13.0835i | 0.412708 | − | 0.450619i | ||||
\(844\) | 1.28602 | 0.0442666 | ||||||||
\(845\) | −6.30297 | −0.216829 | ||||||||
\(846\) | 29.1528 | − | 2.56526i | 1.00229 | − | 0.0881954i | ||||
\(847\) | − | 12.0216i | − | 0.413066i | ||||||
\(848\) | −11.7716 | −0.404238 | ||||||||
\(849\) | −9.69339 | + | 10.5838i | −0.332676 | + | 0.363235i | ||||
\(850\) | 2.15051i | 0.0737617i | ||||||||
\(851\) | − | 2.28303i | − | 0.0782613i | ||||||
\(852\) | 20.2947 | + | 18.5873i | 0.695285 | + | 0.636791i | ||||
\(853\) | 6.68029 | 0.228729 | 0.114364 | − | 0.993439i | \(-0.463517\pi\) | ||||
0.114364 | + | 0.993439i | \(0.463517\pi\) | |||||||
\(854\) | −16.8652 | −0.577114 | ||||||||
\(855\) | 1.39581 | + | 15.8626i | 0.0477356 | + | 0.542489i | ||||
\(856\) | 14.5849i | 0.498502i | ||||||||
\(857\) | −5.16006 | −0.176264 | −0.0881321 | − | 0.996109i | \(-0.528090\pi\) | ||||
−0.0881321 | + | 0.996109i | \(0.528090\pi\) | |||||||
\(858\) | 1.18116 | + | 1.08179i | 0.0403241 | + | 0.0369316i | ||||
\(859\) | −38.6569 | −1.31896 | −0.659478 | − | 0.751724i | \(-0.729223\pi\) | ||||
−0.659478 | + | 0.751724i | \(0.729223\pi\) | |||||||
\(860\) | − | 6.90875i | − | 0.235586i | ||||||
\(861\) | −8.75909 | − | 8.02219i | −0.298509 | − | 0.273396i | ||||
\(862\) | 15.8178i | 0.538757i | ||||||||
\(863\) | 27.1070i | 0.922731i | 0.887210 | + | 0.461366i | \(0.152640\pi\) | ||||
−0.887210 | + | 0.461366i | \(0.847360\pi\) | |||||||
\(864\) | 4.12476 | + | 3.16012i | 0.140327 | + | 0.107509i | ||||
\(865\) | − | 6.73609i | − | 0.229034i | ||||||
\(866\) | − | 3.60619i | − | 0.122543i | ||||||
\(867\) | 14.4771 | − | 15.8069i | 0.491668 | − | 0.536832i | ||||
\(868\) | 3.30821 | 0.112288 | ||||||||
\(869\) | − | 3.33915i | − | 0.113273i | ||||||
\(870\) | 4.95985 | + | 4.54258i | 0.168155 | + | 0.154008i | ||||
\(871\) | −6.46620 | − | 20.1715i | −0.219099 | − | 0.683485i | ||||
\(872\) | 1.55580i | 0.0526859i | ||||||||
\(873\) | −43.7892 | + | 3.85317i | −1.48204 | + | 0.130410i | ||||
\(874\) | 4.42924i | 0.149821i | ||||||||
\(875\) | − | 1.10570i | − | 0.0373796i | ||||||
\(876\) | −14.1307 | + | 15.4287i | −0.477433 | + | 0.521289i | ||||
\(877\) | 34.3329 | 1.15934 | 0.579671 | − | 0.814851i | \(-0.303181\pi\) | ||||
0.579671 | + | 0.814851i | \(0.303181\pi\) | |||||||
\(878\) | 2.26867 | 0.0765639 | ||||||||
\(879\) | −34.3107 | − | 31.4242i | −1.15727 | − | 1.05991i | ||||
\(880\) | −0.357335 | −0.0120458 | ||||||||
\(881\) | − | 21.3255i | − | 0.718474i | −0.933246 | − | 0.359237i | \(-0.883037\pi\) | ||
0.933246 | − | 0.359237i | \(-0.116963\pi\) | |||||||
\(882\) | 1.51926 | + | 17.2655i | 0.0511561 | + | 0.581361i | ||||
\(883\) | − | 51.3084i | − | 1.72667i | −0.504634 | − | 0.863333i | \(-0.668373\pi\) | ||
0.504634 | − | 0.863333i | \(-0.331627\pi\) | |||||||
\(884\) | −5.56521 | −0.187178 | ||||||||
\(885\) | 12.1050 | + | 11.0866i | 0.406906 | + | 0.372673i | ||||
\(886\) | −9.02705 | −0.303270 | ||||||||
\(887\) | 51.2841i | 1.72195i | 0.508645 | + | 0.860976i | \(0.330147\pi\) | ||||
−0.508645 | + | 0.860976i | \(0.669853\pi\) | |||||||
\(888\) | −3.20063 | + | 3.49463i | −0.107406 | + | 0.117272i | ||||
\(889\) | − | 24.3594i | − | 0.816989i | ||||||
\(890\) | − | 6.97529i | − | 0.233812i | ||||||
\(891\) | −3.16660 | + | 0.561630i | −0.106085 | + | 0.0188153i | ||||
\(892\) | −23.6116 | −0.790574 | ||||||||
\(893\) | − | 51.7799i | − | 1.73275i | ||||||
\(894\) | −12.9604 | − | 11.8701i | −0.433461 | − | 0.396994i | ||||
\(895\) | −19.0886 | −0.638061 | ||||||||
\(896\) | − | 1.10570i | − | 0.0369390i | ||||||
\(897\) | −2.52620 | + | 2.75825i | −0.0843474 | + | 0.0920954i | ||||
\(898\) | − | 18.8339i | − | 0.628495i | ||||||
\(899\) | 11.6180 | 0.387482 | ||||||||
\(900\) | −0.262965 | − | 2.98845i | −0.00876550 | − | 0.0996151i | ||||
\(901\) | 25.3149i | 0.843361i | ||||||||
\(902\) | 2.21618 | 0.0737907 | ||||||||
\(903\) | −8.93642 | + | 9.75730i | −0.297385 | + | 0.324702i | ||||
\(904\) | −9.97721 | −0.331837 | ||||||||
\(905\) | −12.3626 | −0.410948 | ||||||||
\(906\) | −1.56942 | + | 1.71359i | −0.0521406 | + | 0.0569301i | ||||
\(907\) | −47.9347 | −1.59165 | −0.795823 | − | 0.605529i | \(-0.792962\pi\) | ||||
−0.795823 | + | 0.605529i | \(0.792962\pi\) | |||||||
\(908\) | − | 16.9703i | − | 0.563178i | ||||||
\(909\) | −1.24696 | − | 14.1710i | −0.0413590 | − | 0.470022i | ||||
\(910\) | 2.86141 | 0.0948549 | ||||||||
\(911\) | − | 54.9975i | − | 1.82215i | −0.412244 | − | 0.911074i | \(-0.635255\pi\) | ||
0.412244 | − | 0.911074i | \(-0.364745\pi\) | |||||||
\(912\) | 6.20945 | − | 6.77983i | 0.205615 | − | 0.224503i | ||||
\(913\) | − | 1.60075i | − | 0.0529772i | ||||||
\(914\) | −7.12233 | −0.235586 | ||||||||
\(915\) | 19.4824 | + | 17.8434i | 0.644069 | + | 0.589883i | ||||
\(916\) | 19.9276i | 0.658425i | ||||||||
\(917\) | 3.98572 | 0.131620 | ||||||||
\(918\) | 6.79585 | − | 8.87032i | 0.224297 | − | 0.292764i | ||||
\(919\) | 43.8279i | 1.44575i | 0.690979 | + | 0.722874i | \(0.257180\pi\) | ||||
−0.690979 | + | 0.722874i | \(0.742820\pi\) | |||||||
\(920\) | − | 0.834453i | − | 0.0275111i | ||||||
\(921\) | −6.29009 | + | 6.86788i | −0.207266 | + | 0.226304i | ||||
\(922\) | 1.06535i | 0.0350853i | ||||||||
\(923\) | 41.1181 | 1.35342 | ||||||||
\(924\) | 0.504668 | + | 0.462211i | 0.0166024 | + | 0.0152056i | ||||
\(925\) | 2.73596 | 0.0899579 | ||||||||
\(926\) | − | 14.4915i | − | 0.476221i | ||||||
\(927\) | −4.81129 | − | 54.6777i | −0.158024 | − | 1.79585i | ||||
\(928\) | − | 3.88309i | − | 0.127469i | ||||||
\(929\) | 51.5178 | 1.69024 | 0.845121 | − | 0.534574i | \(-0.179528\pi\) | ||||
0.845121 | + | 0.534574i | \(0.179528\pi\) | |||||||
\(930\) | −3.82160 | − | 3.50009i | −0.125315 | − | 0.114772i | ||||
\(931\) | 30.6663 | 1.00505 | ||||||||
\(932\) | 25.2606 | 0.827440 | ||||||||
\(933\) | 14.8796 | − | 16.2464i | 0.487136 | − | 0.531883i | ||||
\(934\) | − | 14.8441i | − | 0.485714i | ||||||
\(935\) | 0.768452i | 0.0251311i | ||||||||
\(936\) | 7.73371 | − | 0.680517i | 0.252784 | − | 0.0222434i | ||||
\(937\) | − | 40.7276i | − | 1.33051i | −0.746615 | − | 0.665257i | \(-0.768322\pi\) | ||
0.746615 | − | 0.665257i | \(-0.231678\pi\) | |||||||
\(938\) | −2.76279 | − | 8.61859i | −0.0902082 | − | 0.281407i | ||||
\(939\) | −1.29699 | − | 1.18788i | −0.0423258 | − | 0.0387649i | ||||
\(940\) | 9.75513i | 0.318177i | ||||||||
\(941\) | −0.0284249 | −0.000926625 | −0.000463313 | − | 1.00000i | \(-0.500147\pi\) | ||||
−0.000463313 | 1.00000i | \(0.500147\pi\) | ||||||||
\(942\) | −19.3453 | + | 21.1223i | −0.630304 | + | 0.688202i | ||||
\(943\) | 5.17524i | 0.168529i | ||||||||
\(944\) | − | 9.47707i | − | 0.308452i | ||||||
\(945\) | −3.49416 | + | 4.56077i | −0.113665 | + | 0.148362i | ||||
\(946\) | − | 2.46874i | − | 0.0802656i | ||||||
\(947\) | − | 5.63009i | − | 0.182953i | −0.995807 | − | 0.0914767i | \(-0.970841\pi\) | ||
0.995807 | − | 0.0914767i | \(-0.0291587\pi\) | |||||||
\(948\) | −11.9358 | − | 10.9316i | −0.387656 | − | 0.355043i | ||||
\(949\) | 31.2594i | 1.01472i | ||||||||
\(950\) | −5.30796 | −0.172213 | ||||||||
\(951\) | 16.4980 | + | 15.1100i | 0.534983 | + | 0.489975i | ||||
\(952\) | −2.37782 | −0.0770657 | ||||||||
\(953\) | 43.1847i | 1.39889i | 0.714686 | + | 0.699445i | \(0.246569\pi\) | ||||
−0.714686 | + | 0.699445i | \(0.753431\pi\) | |||||||
\(954\) | −3.09551 | − | 35.1788i | −0.100221 | − | 1.13896i | ||||
\(955\) | 11.6132 | 0.375794 | ||||||||
\(956\) | 4.75090 | 0.153655 | ||||||||
\(957\) | 1.77233 | + | 1.62322i | 0.0572912 | + | 0.0524713i | ||||
\(958\) | 3.58488i | 0.115822i | ||||||||
\(959\) | − | 25.4145i | − | 0.820676i | ||||||
\(960\) | −1.16984 | + | 1.27729i | −0.0377563 | + | 0.0412245i | ||||
\(961\) | 22.0483 | 0.711234 | ||||||||
\(962\) | 7.08030i | 0.228278i | ||||||||
\(963\) | −43.5863 | + | 3.83532i | −1.40455 | + | 0.123591i | ||||
\(964\) | 18.6505 | 0.600693 | ||||||||
\(965\) | 0.896082 | 0.0288459 | ||||||||
\(966\) | −1.07936 | + | 1.17851i | −0.0347278 | + | 0.0379178i | ||||
\(967\) | −22.0124 | −0.707873 | −0.353936 | − | 0.935270i | \(-0.615157\pi\) | ||||
−0.353936 | + | 0.935270i | \(0.615157\pi\) | |||||||
\(968\) | 10.8723 | 0.349449 | ||||||||
\(969\) | −14.5801 | − | 13.3535i | −0.468379 | − | 0.428975i | ||||
\(970\) | − | 14.6528i | − | 0.470473i | ||||||
\(971\) | 2.80062i | 0.0898761i | 0.998990 | + | 0.0449380i | \(0.0143090\pi\) | ||||
−0.998990 | + | 0.0449380i | \(0.985691\pi\) | |||||||
\(972\) | −8.35919 | + | 13.1577i | −0.268121 | + | 0.422032i | ||||
\(973\) | −9.74786 | −0.312502 | ||||||||
\(974\) | − | 40.8238i | − | 1.30808i | ||||||
\(975\) | −3.30546 | − | 3.02738i | −0.105860 | − | 0.0969536i | ||||
\(976\) | − | 15.2529i | − | 0.488232i | ||||||
\(977\) | 17.7902i | 0.569158i | 0.958653 | + | 0.284579i | \(0.0918538\pi\) | ||||
−0.958653 | + | 0.284579i | \(0.908146\pi\) | |||||||
\(978\) | 16.4238 | − | 17.9325i | 0.525175 | − | 0.573417i | ||||
\(979\) | − | 2.49252i | − | 0.0796612i | ||||||
\(980\) | −5.77742 | −0.184553 | ||||||||
\(981\) | −4.64942 | + | 0.409120i | −0.148445 | + | 0.0130622i | ||||
\(982\) | 5.82397i | 0.185850i | ||||||||
\(983\) | −59.2259 | −1.88901 | −0.944506 | − | 0.328494i | \(-0.893459\pi\) | ||||
−0.944506 | + | 0.328494i | \(0.893459\pi\) | |||||||
\(984\) | 7.25528 | − | 7.92173i | 0.231290 | − | 0.252536i | ||||
\(985\) | 4.56961 | 0.145600 | ||||||||
\(986\) | −8.35060 | −0.265937 | ||||||||
\(987\) | 12.6182 | − | 13.7773i | 0.401642 | − | 0.438536i | ||||
\(988\) | − | 13.7363i | − | 0.437009i | ||||||
\(989\) | 5.76502 | 0.183317 | ||||||||
\(990\) | −0.0939666 | − | 1.06788i | −0.00298646 | − | 0.0339394i | ||||
\(991\) | − | 44.7858i | − | 1.42267i | −0.702854 | − | 0.711334i | \(-0.748091\pi\) | ||
0.702854 | − | 0.711334i | \(-0.251909\pi\) | |||||||
\(992\) | 2.99195i | 0.0949944i | ||||||||
\(993\) | 0.874971 | + | 0.801360i | 0.0277664 | + | 0.0254304i | ||||
\(994\) | 17.5683 | 0.557234 | ||||||||
\(995\) | −1.24326 | −0.0394140 | ||||||||
\(996\) | −5.72190 | − | 5.24052i | −0.181305 | − | 0.166052i | ||||
\(997\) | −53.5257 | −1.69518 | −0.847588 | − | 0.530654i | \(-0.821946\pi\) | ||||
−0.847588 | + | 0.530654i | \(0.821946\pi\) | |||||||
\(998\) | 26.6192i | 0.842616i | ||||||||
\(999\) | −11.2852 | − | 8.64597i | −0.357048 | − | 0.273546i |
(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 | 2010.2.d.c.401.15 | ✓ | 20 | |
3.2 | odd | 2 | 2010.2.d.d.401.5 | yes | 20 | ||
67.66 | odd | 2 | 2010.2.d.d.401.6 | yes | 20 | ||
201.200 | even | 2 | inner | 2010.2.d.c.401.16 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2010.2.d.c.401.15 | ✓ | 20 | 1.1 | even | 1 | trivial | |
2010.2.d.c.401.16 | yes | 20 | 201.200 | even | 2 | inner | |
2010.2.d.d.401.5 | yes | 20 | 3.2 | odd | 2 | ||
2010.2.d.d.401.6 | yes | 20 | 67.66 | odd | 2 |