Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,2,Mod(295,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.295");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.f (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.04280545828\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.3317760000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 295.2 | ||
Root | \(-1.72286 - 0.178197i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.295 |
Dual form | 882.2.f.p.589.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.707107 | + | 1.58114i | −0.408248 | + | 0.912871i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.72286 | − | 2.98408i | −0.770486 | − | 1.33452i | −0.937297 | − | 0.348532i | \(-0.886680\pi\) |
0.166810 | − | 0.985989i | \(-0.446653\pi\) | |||||||
\(6\) | −1.01575 | − | 1.40294i | −0.414679 | − | 0.572749i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.00000 | − | 2.23607i | −0.666667 | − | 0.745356i | ||||
\(10\) | 3.44572 | 1.08963 | ||||||||
\(11\) | −2.00000 | + | 3.46410i | −0.603023 | + | 1.04447i | 0.389338 | + | 0.921095i | \(0.372704\pi\) |
−0.992361 | + | 0.123371i | \(0.960630\pi\) | |||||||
\(12\) | 1.72286 | − | 0.178197i | 0.497347 | − | 0.0514410i | ||||
\(13\) | −2.12132 | − | 3.67423i | −0.588348 | − | 1.01905i | −0.994449 | − | 0.105221i | \(-0.966445\pi\) |
0.406100 | − | 0.913828i | \(-0.366888\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.93649 | − | 0.614017i | 1.53280 | − | 0.158538i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.41421 | −0.342997 | −0.171499 | − | 0.985184i | \(-0.554861\pi\) | ||||
−0.171499 | + | 0.985184i | \(0.554861\pi\) | |||||||
\(18\) | 2.93649 | − | 0.614017i | 0.692138 | − | 0.144725i | ||||
\(19\) | 6.27415 | 1.43939 | 0.719694 | − | 0.694291i | \(-0.244282\pi\) | ||||
0.719694 | + | 0.694291i | \(0.244282\pi\) | |||||||
\(20\) | −1.72286 | + | 2.98408i | −0.385243 | + | 0.667261i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | − | 3.46410i | −0.426401 | − | 0.738549i | ||||
\(23\) | 4.37298 | + | 7.57423i | 0.911830 | + | 1.57934i | 0.811477 | + | 0.584384i | \(0.198664\pi\) |
0.100353 | + | 0.994952i | \(0.468003\pi\) | |||||||
\(24\) | −0.707107 | + | 1.58114i | −0.144338 | + | 0.322749i | ||||
\(25\) | −3.43649 | + | 5.95218i | −0.687298 | + | 1.19044i | ||||
\(26\) | 4.24264 | 0.832050 | ||||||||
\(27\) | 4.94975 | − | 1.58114i | 0.952579 | − | 0.304290i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.563508 | + | 0.976025i | −0.104641 | + | 0.181243i | −0.913591 | − | 0.406633i | \(-0.866703\pi\) |
0.808951 | + | 0.587877i | \(0.200036\pi\) | |||||||
\(30\) | −2.43649 | + | 5.44816i | −0.444840 | + | 0.994694i | ||||
\(31\) | 2.73861 | + | 4.74342i | 0.491869 | + | 0.851943i | 0.999956 | − | 0.00936313i | \(-0.00298042\pi\) |
−0.508087 | + | 0.861306i | \(0.669647\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −4.06301 | − | 5.61177i | −0.707280 | − | 0.976883i | ||||
\(34\) | 0.707107 | − | 1.22474i | 0.121268 | − | 0.210042i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.936492 | + | 2.85008i | −0.156082 | + | 0.475014i | ||||
\(37\) | 5.74597 | 0.944631 | 0.472316 | − | 0.881430i | \(-0.343418\pi\) | ||||
0.472316 | + | 0.881430i | \(0.343418\pi\) | |||||||
\(38\) | −3.13707 | + | 5.43357i | −0.508900 | + | 0.881442i | ||||
\(39\) | 7.30948 | − | 0.756026i | 1.17045 | − | 0.121061i | ||||
\(40\) | −1.72286 | − | 2.98408i | −0.272408 | − | 0.471825i | ||||
\(41\) | 2.82843 | + | 4.89898i | 0.441726 | + | 0.765092i | 0.997818 | − | 0.0660290i | \(-0.0210330\pi\) |
−0.556092 | + | 0.831121i | \(0.687700\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.563508 | + | 0.976025i | −0.0859342 | + | 0.148842i | −0.905789 | − | 0.423729i | \(-0.860721\pi\) |
0.819855 | + | 0.572572i | \(0.194054\pi\) | |||||||
\(44\) | 4.00000 | 0.603023 | ||||||||
\(45\) | −3.22689 | + | 9.82059i | −0.481036 | + | 1.46397i | ||||
\(46\) | −8.74597 | −1.28952 | ||||||||
\(47\) | −2.03151 | + | 3.51867i | −0.296326 | + | 0.513251i | −0.975292 | − | 0.220918i | \(-0.929095\pi\) |
0.678967 | + | 0.734169i | \(0.262428\pi\) | |||||||
\(48\) | −1.01575 | − | 1.40294i | −0.146611 | − | 0.202497i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.43649 | − | 5.95218i | −0.485993 | − | 0.841765i | ||||
\(51\) | 1.00000 | − | 2.23607i | 0.140028 | − | 0.313112i | ||||
\(52\) | −2.12132 | + | 3.67423i | −0.294174 | + | 0.509525i | ||||
\(53\) | 12.6190 | 1.73335 | 0.866673 | − | 0.498877i | \(-0.166254\pi\) | ||||
0.866673 | + | 0.498877i | \(0.166254\pi\) | |||||||
\(54\) | −1.10557 | + | 5.07718i | −0.150449 | + | 0.690916i | ||||
\(55\) | 13.7829 | 1.85848 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.43649 | + | 9.92030i | −0.587628 | + | 1.31398i | ||||
\(58\) | −0.563508 | − | 0.976025i | −0.0739923 | − | 0.128158i | ||||
\(59\) | −4.15283 | − | 7.19291i | −0.540652 | − | 0.936437i | −0.998867 | − | 0.0475951i | \(-0.984844\pi\) |
0.458215 | − | 0.888842i | \(-0.348489\pi\) | |||||||
\(60\) | −3.50000 | − | 4.83414i | −0.451848 | − | 0.624085i | ||||
\(61\) | 3.13707 | − | 5.43357i | 0.401661 | − | 0.695697i | −0.592265 | − | 0.805743i | \(-0.701766\pi\) |
0.993927 | + | 0.110045i | \(0.0350997\pi\) | |||||||
\(62\) | −5.47723 | −0.695608 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.30948 | + | 12.6604i | −0.906629 | + | 1.57033i | ||||
\(66\) | 6.89144 | − | 0.712788i | 0.848278 | − | 0.0877381i | ||||
\(67\) | 3.43649 | + | 5.95218i | 0.419834 | + | 0.727174i | 0.995922 | − | 0.0902132i | \(-0.0287549\pi\) |
−0.576088 | + | 0.817388i | \(0.695422\pi\) | |||||||
\(68\) | 0.707107 | + | 1.22474i | 0.0857493 | + | 0.148522i | ||||
\(69\) | −15.0681 | + | 1.55850i | −1.81398 | + | 0.187622i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.87298 | −1.17171 | −0.585854 | − | 0.810417i | \(-0.699241\pi\) | ||||
−0.585854 | + | 0.810417i | \(0.699241\pi\) | |||||||
\(72\) | −2.00000 | − | 2.23607i | −0.235702 | − | 0.263523i | ||||
\(73\) | −4.42227 | −0.517587 | −0.258794 | − | 0.965933i | \(-0.583325\pi\) | ||||
−0.258794 | + | 0.965933i | \(0.583325\pi\) | |||||||
\(74\) | −2.87298 | + | 4.97615i | −0.333978 | + | 0.578466i | ||||
\(75\) | −6.98125 | − | 9.64240i | −0.806126 | − | 1.11341i | ||||
\(76\) | −3.13707 | − | 5.43357i | −0.359847 | − | 0.623273i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.00000 | + | 6.70820i | −0.339683 | + | 0.759555i | ||||
\(79\) | 0.936492 | − | 1.62205i | 0.105364 | − | 0.182495i | −0.808523 | − | 0.588464i | \(-0.799733\pi\) |
0.913887 | + | 0.405969i | \(0.133066\pi\) | |||||||
\(80\) | 3.44572 | 0.385243 | ||||||||
\(81\) | −1.00000 | + | 8.94427i | −0.111111 | + | 0.993808i | ||||
\(82\) | −5.65685 | −0.624695 | ||||||||
\(83\) | −1.32440 | + | 2.29393i | −0.145372 | + | 0.251791i | −0.929512 | − | 0.368793i | \(-0.879771\pi\) |
0.784140 | + | 0.620584i | \(0.213104\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.43649 | + | 4.22013i | 0.264275 | + | 0.457737i | ||||
\(86\) | −0.563508 | − | 0.976025i | −0.0607647 | − | 0.105247i | ||||
\(87\) | −1.14477 | − | 1.58114i | −0.122732 | − | 0.169516i | ||||
\(88\) | −2.00000 | + | 3.46410i | −0.213201 | + | 0.369274i | ||||
\(89\) | −7.07107 | −0.749532 | −0.374766 | − | 0.927119i | \(-0.622277\pi\) | ||||
−0.374766 | + | 0.927119i | \(0.622277\pi\) | |||||||
\(90\) | −6.89144 | − | 7.70486i | −0.726421 | − | 0.812164i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.37298 | − | 7.57423i | 0.455915 | − | 0.789668i | ||||
\(93\) | −9.43649 | + | 0.976025i | −0.978519 | + | 0.101209i | ||||
\(94\) | −2.03151 | − | 3.51867i | −0.209534 | − | 0.362923i | ||||
\(95\) | −10.8095 | − | 18.7226i | −1.10903 | − | 1.92089i | ||||
\(96\) | 1.72286 | − | 0.178197i | 0.175839 | − | 0.0181872i | ||||
\(97\) | 7.50873 | − | 13.0055i | 0.762396 | − | 1.32051i | −0.179216 | − | 0.983810i | \(-0.557356\pi\) |
0.941612 | − | 0.336699i | \(-0.109311\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.7460 | − | 2.45607i | 1.18051 | − | 0.246844i | ||||
\(100\) | 6.87298 | 0.687298 | ||||||||
\(101\) | −6.67261 | + | 11.5573i | −0.663949 | + | 1.14999i | 0.315620 | + | 0.948886i | \(0.397788\pi\) |
−0.979569 | + | 0.201108i | \(0.935546\pi\) | |||||||
\(102\) | 1.43649 | + | 1.98406i | 0.142234 | + | 0.196451i | ||||
\(103\) | 1.94169 | + | 3.36311i | 0.191321 | + | 0.331377i | 0.945688 | − | 0.325075i | \(-0.105390\pi\) |
−0.754368 | + | 0.656452i | \(0.772056\pi\) | |||||||
\(104\) | −2.12132 | − | 3.67423i | −0.208013 | − | 0.360288i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.30948 | + | 10.9283i | −0.612830 | + | 1.06145i | ||||
\(107\) | 0.254033 | 0.0245583 | 0.0122792 | − | 0.999925i | \(-0.496091\pi\) | ||||
0.0122792 | + | 0.999925i | \(0.496091\pi\) | |||||||
\(108\) | −3.84418 | − | 3.49604i | −0.369906 | − | 0.336406i | ||||
\(109\) | 16.8730 | 1.61614 | 0.808069 | − | 0.589087i | \(-0.200513\pi\) | ||||
0.808069 | + | 0.589087i | \(0.200513\pi\) | |||||||
\(110\) | −6.89144 | + | 11.9363i | −0.657073 | + | 1.13808i | ||||
\(111\) | −4.06301 | + | 9.08517i | −0.385644 | + | 0.862326i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.93649 | − | 3.35410i | −0.182170 | − | 0.315527i | 0.760449 | − | 0.649397i | \(-0.224979\pi\) |
−0.942619 | + | 0.333870i | \(0.891645\pi\) | |||||||
\(114\) | −6.37298 | − | 8.80226i | −0.596885 | − | 0.824407i | ||||
\(115\) | 15.0681 | − | 26.0987i | 1.40511 | − | 2.43371i | ||||
\(116\) | 1.12702 | 0.104641 | ||||||||
\(117\) | −3.97320 | + | 12.0919i | −0.367322 | + | 1.11790i | ||||
\(118\) | 8.30565 | 0.764597 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.93649 | − | 0.614017i | 0.541925 | − | 0.0560518i | ||||
\(121\) | −2.50000 | − | 4.33013i | −0.227273 | − | 0.393648i | ||||
\(122\) | 3.13707 | + | 5.43357i | 0.284017 | + | 0.491932i | ||||
\(123\) | −9.74597 | + | 1.00803i | −0.878764 | + | 0.0908914i | ||||
\(124\) | 2.73861 | − | 4.74342i | 0.245935 | − | 0.425971i | ||||
\(125\) | 6.45378 | 0.577243 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.745967 | −0.0661938 | −0.0330969 | − | 0.999452i | \(-0.510537\pi\) | ||||
−0.0330969 | + | 0.999452i | \(0.510537\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −1.14477 | − | 1.58114i | −0.100791 | − | 0.139212i | ||||
\(130\) | −7.30948 | − | 12.6604i | −0.641083 | − | 1.11039i | ||||
\(131\) | 6.67261 | + | 11.5573i | 0.582988 | + | 1.00977i | 0.995123 | + | 0.0986425i | \(0.0314500\pi\) |
−0.412135 | + | 0.911123i | \(0.635217\pi\) | |||||||
\(132\) | −2.82843 | + | 6.32456i | −0.246183 | + | 0.550482i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.87298 | −0.593735 | ||||||||
\(135\) | −13.2460 | − | 12.0464i | −1.14003 | − | 1.03679i | ||||
\(136\) | −1.41421 | −0.121268 | ||||||||
\(137\) | 7.74597 | − | 13.4164i | 0.661783 | − | 1.14624i | −0.318364 | − | 0.947968i | \(-0.603134\pi\) |
0.980147 | − | 0.198273i | \(-0.0635331\pi\) | |||||||
\(138\) | 6.18433 | − | 13.8286i | 0.526445 | − | 1.17717i | ||||
\(139\) | 9.93870 | + | 17.2143i | 0.842989 | + | 1.46010i | 0.887356 | + | 0.461085i | \(0.152540\pi\) |
−0.0443665 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.12702 | − | 5.70017i | −0.347558 | − | 0.480041i | ||||
\(142\) | 4.93649 | − | 8.55025i | 0.414261 | − | 0.717521i | ||||
\(143\) | 16.9706 | 1.41915 | ||||||||
\(144\) | 2.93649 | − | 0.614017i | 0.244708 | − | 0.0511681i | ||||
\(145\) | 3.88338 | 0.322497 | ||||||||
\(146\) | 2.21113 | − | 3.82980i | 0.182995 | − | 0.316956i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.87298 | − | 4.97615i | −0.236158 | − | 0.409037i | ||||
\(149\) | 7.87298 | + | 13.6364i | 0.644980 | + | 1.11714i | 0.984306 | + | 0.176469i | \(0.0564676\pi\) |
−0.339326 | + | 0.940669i | \(0.610199\pi\) | |||||||
\(150\) | 11.8412 | − | 1.22474i | 0.966829 | − | 0.100000i | ||||
\(151\) | −5.50000 | + | 9.52628i | −0.447584 | + | 0.775238i | −0.998228 | − | 0.0595022i | \(-0.981049\pi\) |
0.550645 | + | 0.834740i | \(0.314382\pi\) | |||||||
\(152\) | 6.27415 | 0.508900 | ||||||||
\(153\) | 2.82843 | + | 3.16228i | 0.228665 | + | 0.255655i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.43649 | − | 16.3445i | 0.757957 | − | 1.31282i | ||||
\(156\) | −4.30948 | − | 5.95218i | −0.345034 | − | 0.476556i | ||||
\(157\) | 5.96550 | + | 10.3325i | 0.476099 | + | 0.824627i | 0.999625 | − | 0.0273823i | \(-0.00871714\pi\) |
−0.523526 | + | 0.852010i | \(0.675384\pi\) | |||||||
\(158\) | 0.936492 | + | 1.62205i | 0.0745033 | + | 0.129043i | ||||
\(159\) | −8.92295 | + | 19.9523i | −0.707636 | + | 1.58232i | ||||
\(160\) | −1.72286 | + | 2.98408i | −0.136204 | + | 0.235912i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.24597 | − | 5.33816i | −0.569297 | − | 0.419406i | ||||
\(163\) | 10.0000 | 0.783260 | 0.391630 | − | 0.920123i | \(-0.371911\pi\) | ||||
0.391630 | + | 0.920123i | \(0.371911\pi\) | |||||||
\(164\) | 2.82843 | − | 4.89898i | 0.220863 | − | 0.382546i | ||||
\(165\) | −9.74597 | + | 21.7926i | −0.758722 | + | 1.69656i | ||||
\(166\) | −1.32440 | − | 2.29393i | −0.102793 | − | 0.178043i | ||||
\(167\) | 4.77012 | + | 8.26209i | 0.369123 | + | 0.639340i | 0.989429 | − | 0.145021i | \(-0.0463248\pi\) |
−0.620306 | + | 0.784360i | \(0.712991\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.50000 | + | 4.33013i | −0.192308 | + | 0.333087i | ||||
\(170\) | −4.87298 | −0.373741 | ||||||||
\(171\) | −12.5483 | − | 14.0294i | −0.959592 | − | 1.07286i | ||||
\(172\) | 1.12702 | 0.0859342 | ||||||||
\(173\) | 6.36396 | − | 11.0227i | 0.483843 | − | 0.838041i | −0.515985 | − | 0.856598i | \(-0.672574\pi\) |
0.999828 | + | 0.0185571i | \(0.00590724\pi\) | |||||||
\(174\) | 1.94169 | − | 0.200831i | 0.147199 | − | 0.0152250i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.00000 | − | 3.46410i | −0.150756 | − | 0.261116i | ||||
\(177\) | 14.3095 | − | 1.48004i | 1.07557 | − | 0.111247i | ||||
\(178\) | 3.53553 | − | 6.12372i | 0.264999 | − | 0.458993i | ||||
\(179\) | −6.87298 | −0.513711 | −0.256855 | − | 0.966450i | \(-0.582686\pi\) | ||||
−0.256855 | + | 0.966450i | \(0.582686\pi\) | |||||||
\(180\) | 10.1183 | − | 2.11573i | 0.754176 | − | 0.157697i | ||||
\(181\) | 13.3452 | 0.991942 | 0.495971 | − | 0.868339i | \(-0.334812\pi\) | ||||
0.495971 | + | 0.868339i | \(0.334812\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.37298 | + | 8.80226i | 0.471104 | + | 0.650682i | ||||
\(184\) | 4.37298 | + | 7.57423i | 0.322381 | + | 0.558380i | ||||
\(185\) | −9.89949 | − | 17.1464i | −0.727825 | − | 1.26063i | ||||
\(186\) | 3.87298 | − | 8.66025i | 0.283981 | − | 0.635001i | ||||
\(187\) | 2.82843 | − | 4.89898i | 0.206835 | − | 0.358249i | ||||
\(188\) | 4.06301 | 0.296326 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 21.6190 | 1.56840 | ||||||||
\(191\) | 3.06351 | − | 5.30615i | 0.221668 | − | 0.383940i | −0.733647 | − | 0.679531i | \(-0.762183\pi\) |
0.955314 | + | 0.295591i | \(0.0955167\pi\) | |||||||
\(192\) | −0.707107 | + | 1.58114i | −0.0510310 | + | 0.114109i | ||||
\(193\) | −11.9365 | − | 20.6746i | −0.859207 | − | 1.48819i | −0.872686 | − | 0.488282i | \(-0.837624\pi\) |
0.0134785 | − | 0.999909i | \(-0.495710\pi\) | |||||||
\(194\) | 7.50873 | + | 13.0055i | 0.539096 | + | 0.933741i | ||||
\(195\) | −14.8492 | − | 20.5095i | −1.06338 | − | 1.46872i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.6190 | 1.18405 | 0.592026 | − | 0.805919i | \(-0.298328\pi\) | ||||
0.592026 | + | 0.805919i | \(0.298328\pi\) | |||||||
\(198\) | −3.74597 | + | 11.4003i | −0.266214 | + | 0.810187i | ||||
\(199\) | −12.1890 | −0.864058 | −0.432029 | − | 0.901860i | \(-0.642202\pi\) | ||||
−0.432029 | + | 0.901860i | \(0.642202\pi\) | |||||||
\(200\) | −3.43649 | + | 5.95218i | −0.242997 | + | 0.420883i | ||||
\(201\) | −11.8412 | + | 1.22474i | −0.835213 | + | 0.0863868i | ||||
\(202\) | −6.67261 | − | 11.5573i | −0.469483 | − | 0.813168i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.43649 | + | 0.252009i | −0.170589 | + | 0.0176441i | ||||
\(205\) | 9.74597 | − | 16.8805i | 0.680688 | − | 1.17899i | ||||
\(206\) | −3.88338 | −0.270568 | ||||||||
\(207\) | 8.19052 | − | 24.9267i | 0.569281 | − | 1.73253i | ||||
\(208\) | 4.24264 | 0.294174 | ||||||||
\(209\) | −12.5483 | + | 21.7343i | −0.867984 | + | 1.50339i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.3095 | − | 17.8565i | −0.709734 | − | 1.22929i | −0.964956 | − | 0.262412i | \(-0.915482\pi\) |
0.255222 | − | 0.966882i | \(-0.417851\pi\) | |||||||
\(212\) | −6.30948 | − | 10.9283i | −0.433337 | − | 0.750561i | ||||
\(213\) | 6.98125 | − | 15.6106i | 0.478348 | − | 1.06962i | ||||
\(214\) | −0.127017 | + | 0.219999i | −0.00868268 | + | 0.0150388i | ||||
\(215\) | 3.88338 | 0.264845 | ||||||||
\(216\) | 4.94975 | − | 1.58114i | 0.336788 | − | 0.107583i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.43649 | + | 14.6124i | −0.571391 | + | 0.989679i | ||||
\(219\) | 3.12702 | − | 6.99222i | 0.211304 | − | 0.472491i | ||||
\(220\) | −6.89144 | − | 11.9363i | −0.464621 | − | 0.804747i | ||||
\(221\) | 3.00000 | + | 5.19615i | 0.201802 | + | 0.349531i | ||||
\(222\) | −5.83648 | − | 8.06126i | −0.391719 | − | 0.541036i | ||||
\(223\) | −11.2239 | + | 19.4404i | −0.751608 | + | 1.30182i | 0.195436 | + | 0.980717i | \(0.437388\pi\) |
−0.947043 | + | 0.321106i | \(0.895945\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 20.1825 | − | 4.22013i | 1.34550 | − | 0.281342i | ||||
\(226\) | 3.87298 | 0.257627 | ||||||||
\(227\) | 5.16858 | − | 8.95224i | 0.343051 | − | 0.594181i | −0.641947 | − | 0.766749i | \(-0.721873\pi\) |
0.984998 | + | 0.172568i | \(0.0552064\pi\) | |||||||
\(228\) | 10.8095 | − | 1.11803i | 0.715875 | − | 0.0740436i | ||||
\(229\) | 6.67261 | + | 11.5573i | 0.440938 | + | 0.763728i | 0.997759 | − | 0.0669049i | \(-0.0213124\pi\) |
−0.556821 | + | 0.830632i | \(0.687979\pi\) | |||||||
\(230\) | 15.0681 | + | 26.0987i | 0.993559 | + | 1.72090i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.563508 | + | 0.976025i | −0.0369961 | + | 0.0640792i | ||||
\(233\) | 7.25403 | 0.475228 | 0.237614 | − | 0.971360i | \(-0.423635\pi\) | ||||
0.237614 | + | 0.971360i | \(0.423635\pi\) | |||||||
\(234\) | −8.48528 | − | 9.48683i | −0.554700 | − | 0.620174i | ||||
\(235\) | 14.0000 | 0.913259 | ||||||||
\(236\) | −4.15283 | + | 7.19291i | −0.270326 | + | 0.468218i | ||||
\(237\) | 1.90249 | + | 2.62769i | 0.123580 | + | 0.170687i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.50000 | + | 12.9904i | 0.485135 | + | 0.840278i | 0.999854 | − | 0.0170808i | \(-0.00543724\pi\) |
−0.514719 | + | 0.857359i | \(0.672104\pi\) | |||||||
\(240\) | −2.43649 | + | 5.44816i | −0.157275 | + | 0.351677i | ||||
\(241\) | −11.8412 | + | 20.5095i | −0.762758 | + | 1.32114i | 0.178666 | + | 0.983910i | \(0.442822\pi\) |
−0.941424 | + | 0.337226i | \(0.890511\pi\) | |||||||
\(242\) | 5.00000 | 0.321412 | ||||||||
\(243\) | −13.4350 | − | 7.90569i | −0.861858 | − | 0.507151i | ||||
\(244\) | −6.27415 | −0.401661 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.00000 | − | 8.94427i | 0.255031 | − | 0.570266i | ||||
\(247\) | −13.3095 | − | 23.0527i | −0.846862 | − | 1.46681i | ||||
\(248\) | 2.73861 | + | 4.74342i | 0.173902 | + | 0.301207i | ||||
\(249\) | −2.69052 | − | 3.71611i | −0.170505 | − | 0.235499i | ||||
\(250\) | −3.22689 | + | 5.58913i | −0.204086 | + | 0.353488i | ||||
\(251\) | −9.46183 | −0.597225 | −0.298613 | − | 0.954374i | \(-0.596524\pi\) | ||||
−0.298613 | + | 0.954374i | \(0.596524\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −34.9839 | −2.19942 | ||||||||
\(254\) | 0.372983 | − | 0.646026i | 0.0234031 | − | 0.0405353i | ||||
\(255\) | −8.39547 | + | 0.868351i | −0.525745 | + | 0.0543782i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1.50403 | + | 2.60505i | 0.0938187 | + | 0.162499i | 0.909115 | − | 0.416545i | \(-0.136759\pi\) |
−0.815296 | + | 0.579044i | \(0.803426\pi\) | |||||||
\(258\) | 1.94169 | − | 0.200831i | 0.120884 | − | 0.0125032i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 14.6190 | 0.906629 | ||||||||
\(261\) | 3.30948 | − | 0.692007i | 0.204851 | − | 0.0428342i | ||||
\(262\) | −13.3452 | −0.824470 | ||||||||
\(263\) | 8.80948 | − | 15.2585i | 0.543216 | − | 0.940877i | −0.455501 | − | 0.890235i | \(-0.650540\pi\) |
0.998717 | − | 0.0506418i | \(-0.0161267\pi\) | |||||||
\(264\) | −4.06301 | − | 5.61177i | −0.250061 | − | 0.345380i | ||||
\(265\) | −21.7407 | − | 37.6560i | −1.33552 | − | 2.31319i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.00000 | − | 11.1803i | 0.305995 | − | 0.684226i | ||||
\(268\) | 3.43649 | − | 5.95218i | 0.209917 | − | 0.363587i | ||||
\(269\) | 2.03151 | 0.123863 | 0.0619316 | − | 0.998080i | \(-0.480274\pi\) | ||||
0.0619316 | + | 0.998080i | \(0.480274\pi\) | |||||||
\(270\) | 17.0554 | − | 5.44816i | 1.03796 | − | 0.331565i | ||||
\(271\) | −7.07107 | −0.429537 | −0.214768 | − | 0.976665i | \(-0.568900\pi\) | ||||
−0.214768 | + | 0.976665i | \(0.568900\pi\) | |||||||
\(272\) | 0.707107 | − | 1.22474i | 0.0428746 | − | 0.0742611i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.74597 | + | 13.4164i | 0.467951 | + | 0.810515i | ||||
\(275\) | −13.7460 | − | 23.8087i | −0.828913 | − | 1.43572i | ||||
\(276\) | 8.88374 | + | 12.2701i | 0.534738 | + | 0.738572i | ||||
\(277\) | −7.18246 | + | 12.4404i | −0.431552 | + | 0.747470i | −0.997007 | − | 0.0773089i | \(-0.975367\pi\) |
0.565455 | + | 0.824779i | \(0.308701\pi\) | |||||||
\(278\) | −19.8774 | −1.19217 | ||||||||
\(279\) | 5.12938 | − | 15.6106i | 0.307088 | − | 0.934580i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.37298 | + | 7.57423i | −0.260870 | + | 0.451841i | −0.966473 | − | 0.256767i | \(-0.917343\pi\) |
0.705603 | + | 0.708607i | \(0.250676\pi\) | |||||||
\(282\) | 7.00000 | − | 0.724016i | 0.416844 | − | 0.0431146i | ||||
\(283\) | 2.51978 | + | 4.36439i | 0.149785 | + | 0.259436i | 0.931148 | − | 0.364641i | \(-0.118808\pi\) |
−0.781363 | + | 0.624077i | \(0.785475\pi\) | |||||||
\(284\) | 4.93649 | + | 8.55025i | 0.292927 | + | 0.507364i | ||||
\(285\) | 37.2464 | − | 3.85243i | 2.20629 | − | 0.228198i | ||||
\(286\) | −8.48528 | + | 14.6969i | −0.501745 | + | 0.869048i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.936492 | + | 2.85008i | −0.0551833 | + | 0.167943i | ||||
\(289\) | −15.0000 | −0.882353 | ||||||||
\(290\) | −1.94169 | + | 3.36311i | −0.114020 | + | 0.197489i | ||||
\(291\) | 15.2540 | + | 21.0686i | 0.894207 | + | 1.23506i | ||||
\(292\) | 2.21113 | + | 3.82980i | 0.129397 | + | 0.224122i | ||||
\(293\) | −0.398461 | − | 0.690154i | −0.0232783 | − | 0.0403192i | 0.854152 | − | 0.520024i | \(-0.174077\pi\) |
−0.877430 | + | 0.479705i | \(0.840744\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.3095 | + | 24.7847i | −0.833130 | + | 1.44302i | ||||
\(296\) | 5.74597 | 0.333978 | ||||||||
\(297\) | −4.42227 | + | 20.3087i | −0.256606 | + | 1.17843i | ||||
\(298\) | −15.7460 | −0.912139 | ||||||||
\(299\) | 18.5530 | − | 32.1347i | 1.07295 | − | 1.85840i | ||||
\(300\) | −4.85993 | + | 10.8671i | −0.280588 | + | 0.627415i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.50000 | − | 9.52628i | −0.316489 | − | 0.548176i | ||||
\(303\) | −13.5554 | − | 18.7226i | −0.778740 | − | 1.07558i | ||||
\(304\) | −3.13707 | + | 5.43357i | −0.179923 | + | 0.311637i | ||||
\(305\) | −21.6190 | −1.23790 | ||||||||
\(306\) | −4.15283 | + | 0.868351i | −0.237401 | + | 0.0496403i | ||||
\(307\) | −14.2205 | −0.811609 | −0.405805 | − | 0.913960i | \(-0.633009\pi\) | ||||
−0.405805 | + | 0.913960i | \(0.633009\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.69052 | + | 0.692007i | −0.380611 | + | 0.0393669i | ||||
\(310\) | 9.43649 | + | 16.3445i | 0.535957 | + | 0.928304i | ||||
\(311\) | −0.707107 | − | 1.22474i | −0.0400963 | − | 0.0694489i | 0.845281 | − | 0.534322i | \(-0.179433\pi\) |
−0.885377 | + | 0.464873i | \(0.846100\pi\) | |||||||
\(312\) | 7.30948 | − | 0.756026i | 0.413818 | − | 0.0428015i | ||||
\(313\) | 7.86799 | − | 13.6278i | 0.444725 | − | 0.770286i | −0.553308 | − | 0.832977i | \(-0.686635\pi\) |
0.998033 | + | 0.0626904i | \(0.0199681\pi\) | |||||||
\(314\) | −11.9310 | −0.673305 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.87298 | −0.105364 | ||||||||
\(317\) | −12.3095 | + | 21.3206i | −0.691369 | + | 1.19749i | 0.280020 | + | 0.959994i | \(0.409659\pi\) |
−0.971389 | + | 0.237492i | \(0.923675\pi\) | |||||||
\(318\) | −12.8177 | − | 17.7037i | −0.718783 | − | 0.992772i | ||||
\(319\) | −2.25403 | − | 3.90410i | −0.126202 | − | 0.218588i | ||||
\(320\) | −1.72286 | − | 2.98408i | −0.0963108 | − | 0.166815i | ||||
\(321\) | −0.179629 | + | 0.401662i | −0.0100259 | + | 0.0224186i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.87298 | −0.493706 | ||||||||
\(324\) | 8.24597 | − | 3.60611i | 0.458109 | − | 0.200339i | ||||
\(325\) | 29.1596 | 1.61748 | ||||||||
\(326\) | −5.00000 | + | 8.66025i | −0.276924 | + | 0.479647i | ||||
\(327\) | −11.9310 | + | 26.6785i | −0.659786 | + | 1.47533i | ||||
\(328\) | 2.82843 | + | 4.89898i | 0.156174 | + | 0.270501i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −14.0000 | − | 19.3366i | −0.770675 | − | 1.06444i | ||||
\(331\) | −10.1825 | + | 17.6365i | −0.559679 | + | 0.969392i | 0.437844 | + | 0.899051i | \(0.355742\pi\) |
−0.997523 | + | 0.0703409i | \(0.977591\pi\) | |||||||
\(332\) | 2.64880 | 0.145372 | ||||||||
\(333\) | −11.4919 | − | 12.8484i | −0.629754 | − | 0.704086i | ||||
\(334\) | −9.54024 | −0.522019 | ||||||||
\(335\) | 11.8412 | − | 20.5095i | 0.646953 | − | 1.12056i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.87298 | − | 13.6364i | −0.428869 | − | 0.742822i | 0.567904 | − | 0.823095i | \(-0.307754\pi\) |
−0.996773 | + | 0.0802722i | \(0.974421\pi\) | |||||||
\(338\) | −2.50000 | − | 4.33013i | −0.135982 | − | 0.235528i | ||||
\(339\) | 6.67261 | − | 0.690154i | 0.362406 | − | 0.0374840i | ||||
\(340\) | 2.43649 | − | 4.22013i | 0.132137 | − | 0.228869i | ||||
\(341\) | −21.9089 | −1.18643 | ||||||||
\(342\) | 18.4240 | − | 3.85243i | 0.996255 | − | 0.208316i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.563508 | + | 0.976025i | −0.0303823 | + | 0.0526237i | ||||
\(345\) | 30.6109 | + | 42.2793i | 1.64803 | + | 2.27624i | ||||
\(346\) | 6.36396 | + | 11.0227i | 0.342129 | + | 0.592584i | ||||
\(347\) | −3.87298 | − | 6.70820i | −0.207913 | − | 0.360115i | 0.743144 | − | 0.669131i | \(-0.233334\pi\) |
−0.951057 | + | 0.309016i | \(0.900000\pi\) | |||||||
\(348\) | −0.796921 | + | 1.78197i | −0.0427195 | + | 0.0955236i | ||||
\(349\) | −8.21584 | + | 14.2302i | −0.439784 | + | 0.761728i | −0.997672 | − | 0.0681880i | \(-0.978278\pi\) |
0.557889 | + | 0.829916i | \(0.311612\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.3095 | − | 14.8324i | −0.870535 | − | 0.791697i | ||||
\(352\) | 4.00000 | 0.213201 | ||||||||
\(353\) | 1.94169 | − | 3.36311i | 0.103346 | − | 0.179000i | −0.809715 | − | 0.586823i | \(-0.800378\pi\) |
0.913061 | + | 0.407823i | \(0.133712\pi\) | |||||||
\(354\) | −5.87298 | + | 13.1324i | −0.312146 | + | 0.697979i | ||||
\(355\) | 17.0098 | + | 29.4618i | 0.902785 | + | 1.56367i | ||||
\(356\) | 3.53553 | + | 6.12372i | 0.187383 | + | 0.324557i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.43649 | − | 5.95218i | 0.181624 | − | 0.314582i | ||||
\(359\) | 18.2379 | 0.962560 | 0.481280 | − | 0.876567i | \(-0.340172\pi\) | ||||
0.481280 | + | 0.876567i | \(0.340172\pi\) | |||||||
\(360\) | −3.22689 | + | 9.82059i | −0.170072 | + | 0.517591i | ||||
\(361\) | 20.3649 | 1.07184 | ||||||||
\(362\) | −6.67261 | + | 11.5573i | −0.350704 | + | 0.607438i | ||||
\(363\) | 8.61430 | − | 0.890985i | 0.452133 | − | 0.0467646i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.61895 | + | 13.1964i | 0.398794 | + | 0.690732i | ||||
\(366\) | −10.8095 | + | 1.11803i | −0.565020 | + | 0.0584406i | ||||
\(367\) | 3.44572 | − | 5.96816i | 0.179865 | − | 0.311535i | −0.761969 | − | 0.647613i | \(-0.775767\pi\) |
0.941834 | + | 0.336078i | \(0.109101\pi\) | |||||||
\(368\) | −8.74597 | −0.455915 | ||||||||
\(369\) | 5.29760 | − | 16.1225i | 0.275782 | − | 0.839305i | ||||
\(370\) | 19.7990 | 1.02930 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.56351 | + | 7.68423i | 0.288454 | + | 0.398409i | ||||
\(373\) | 0.563508 | + | 0.976025i | 0.0291774 | + | 0.0505367i | 0.880245 | − | 0.474519i | \(-0.157378\pi\) |
−0.851068 | + | 0.525055i | \(0.824045\pi\) | |||||||
\(374\) | 2.82843 | + | 4.89898i | 0.146254 | + | 0.253320i | ||||
\(375\) | −4.56351 | + | 10.2043i | −0.235659 | + | 0.526949i | ||||
\(376\) | −2.03151 | + | 3.51867i | −0.104767 | + | 0.181462i | ||||
\(377\) | 4.78153 | 0.246261 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.3649 | 1.35427 | 0.677137 | − | 0.735857i | \(-0.263220\pi\) | ||||
0.677137 | + | 0.735857i | \(0.263220\pi\) | |||||||
\(380\) | −10.8095 | + | 18.7226i | −0.554514 | + | 0.960447i | ||||
\(381\) | 0.527478 | − | 1.17948i | 0.0270235 | − | 0.0604264i | ||||
\(382\) | 3.06351 | + | 5.30615i | 0.156743 | + | 0.271486i | ||||
\(383\) | −6.45378 | − | 11.1783i | −0.329773 | − | 0.571183i | 0.652694 | − | 0.757622i | \(-0.273639\pi\) |
−0.982467 | + | 0.186439i | \(0.940305\pi\) | |||||||
\(384\) | −1.01575 | − | 1.40294i | −0.0518349 | − | 0.0715936i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.8730 | 1.21510 | ||||||||
\(387\) | 3.30948 | − | 0.692007i | 0.168230 | − | 0.0351767i | ||||
\(388\) | −15.0175 | −0.762396 | ||||||||
\(389\) | −6.56351 | + | 11.3683i | −0.332783 | + | 0.576397i | −0.983056 | − | 0.183303i | \(-0.941321\pi\) |
0.650273 | + | 0.759700i | \(0.274654\pi\) | |||||||
\(390\) | 25.1864 | − | 2.60505i | 1.27536 | − | 0.131912i | ||||
\(391\) | −6.18433 | − | 10.7116i | −0.312755 | − | 0.541708i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.9919 | + | 2.37808i | −1.15979 | + | 0.119958i | ||||
\(394\) | −8.30948 | + | 14.3924i | −0.418625 | + | 0.725080i | ||||
\(395\) | −6.45378 | −0.324725 | ||||||||
\(396\) | −8.00000 | − | 8.94427i | −0.402015 | − | 0.449467i | ||||
\(397\) | −7.07107 | −0.354887 | −0.177443 | − | 0.984131i | \(-0.556783\pi\) | ||||
−0.177443 | + | 0.984131i | \(0.556783\pi\) | |||||||
\(398\) | 6.09452 | − | 10.5560i | 0.305491 | − | 0.529125i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.43649 | − | 5.95218i | −0.171825 | − | 0.297609i | ||||
\(401\) | 1.93649 | + | 3.35410i | 0.0967038 | + | 0.167496i | 0.910318 | − | 0.413909i | \(-0.135837\pi\) |
−0.813615 | + | 0.581405i | \(0.802503\pi\) | |||||||
\(402\) | 4.85993 | − | 10.8671i | 0.242391 | − | 0.542004i | ||||
\(403\) | 11.6190 | − | 20.1246i | 0.578781 | − | 1.00248i | ||||
\(404\) | 13.3452 | 0.663949 | ||||||||
\(405\) | 28.4133 | − | 12.4256i | 1.41187 | − | 0.617435i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.4919 | + | 19.9046i | −0.569634 | + | 0.986635i | ||||
\(408\) | 1.00000 | − | 2.23607i | 0.0495074 | − | 0.110702i | ||||
\(409\) | 11.5717 | + | 20.0428i | 0.572186 | + | 0.991055i | 0.996341 | + | 0.0854655i | \(0.0272378\pi\) |
−0.424155 | + | 0.905589i | \(0.639429\pi\) | |||||||
\(410\) | 9.74597 | + | 16.8805i | 0.481319 | + | 0.833669i | ||||
\(411\) | 15.7360 | + | 21.7343i | 0.776199 | + | 1.07207i | ||||
\(412\) | 1.94169 | − | 3.36311i | 0.0956603 | − | 0.165688i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 17.4919 | + | 19.5566i | 0.859682 | + | 0.961153i | ||||
\(415\) | 9.12702 | 0.448028 | ||||||||
\(416\) | −2.12132 | + | 3.67423i | −0.104006 | + | 0.180144i | ||||
\(417\) | −34.2460 | + | 3.54209i | −1.67703 | + | 0.173457i | ||||
\(418\) | −12.5483 | − | 21.7343i | −0.613757 | − | 1.06306i | ||||
\(419\) | −15.6854 | − | 27.1679i | −0.766280 | − | 1.32724i | −0.939567 | − | 0.342365i | \(-0.888772\pi\) |
0.173287 | − | 0.984871i | \(-0.444561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.43649 | − | 11.1483i | 0.313695 | − | 0.543336i | −0.665464 | − | 0.746430i | \(-0.731766\pi\) |
0.979159 | + | 0.203094i | \(0.0650996\pi\) | |||||||
\(422\) | 20.6190 | 1.00371 | ||||||||
\(423\) | 11.9310 | − | 2.49476i | 0.580105 | − | 0.121299i | ||||
\(424\) | 12.6190 | 0.612830 | ||||||||
\(425\) | 4.85993 | − | 8.41765i | 0.235741 | − | 0.408316i | ||||
\(426\) | 10.0285 | + | 13.8512i | 0.485883 | + | 0.671094i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.127017 | − | 0.219999i | −0.00613958 | − | 0.0106341i | ||||
\(429\) | −12.0000 | + | 26.8328i | −0.579365 | + | 1.29550i | ||||
\(430\) | −1.94169 | + | 3.36311i | −0.0936367 | + | 0.162183i | ||||
\(431\) | −21.4919 | −1.03523 | −0.517615 | − | 0.855614i | \(-0.673180\pi\) | ||||
−0.517615 | + | 0.855614i | \(0.673180\pi\) | |||||||
\(432\) | −1.10557 | + | 5.07718i | −0.0531916 | + | 0.244276i | ||||
\(433\) | 29.6985 | 1.42722 | 0.713609 | − | 0.700544i | \(-0.247059\pi\) | ||||
0.713609 | + | 0.700544i | \(0.247059\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.74597 | + | 6.14017i | −0.131659 | + | 0.294399i | ||||
\(436\) | −8.43649 | − | 14.6124i | −0.404035 | − | 0.699809i | ||||
\(437\) | 27.4367 | + | 47.5218i | 1.31248 | + | 2.27328i | ||||
\(438\) | 4.49193 | + | 6.20419i | 0.214633 | + | 0.296448i | ||||
\(439\) | −5.47723 | + | 9.48683i | −0.261414 | + | 0.452782i | −0.966618 | − | 0.256223i | \(-0.917522\pi\) |
0.705204 | + | 0.709004i | \(0.250855\pi\) | |||||||
\(440\) | 13.7829 | 0.657073 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.00000 | −0.285391 | ||||||||
\(443\) | 7.18246 | − | 12.4404i | 0.341249 | − | 0.591060i | −0.643416 | − | 0.765517i | \(-0.722483\pi\) |
0.984665 | + | 0.174456i | \(0.0558168\pi\) | |||||||
\(444\) | 9.89949 | − | 1.02391i | 0.469809 | − | 0.0485928i | ||||
\(445\) | 12.1825 | + | 21.1006i | 0.577504 | + | 1.00027i | ||||
\(446\) | −11.2239 | − | 19.4404i | −0.531467 | − | 0.920527i | ||||
\(447\) | −27.1281 | + | 2.80588i | −1.28311 | + | 0.132714i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.00000 | 0.424736 | 0.212368 | − | 0.977190i | \(-0.431882\pi\) | ||||
0.212368 | + | 0.977190i | \(0.431882\pi\) | |||||||
\(450\) | −6.43649 | + | 19.5886i | −0.303419 | + | 0.923415i | ||||
\(451\) | −22.6274 | −1.06548 | ||||||||
\(452\) | −1.93649 | + | 3.35410i | −0.0910849 | + | 0.157764i | ||||
\(453\) | −11.1733 | − | 15.4324i | −0.524967 | − | 0.725076i | ||||
\(454\) | 5.16858 | + | 8.95224i | 0.242573 | + | 0.420150i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.43649 | + | 9.92030i | −0.207758 | + | 0.464560i | ||||
\(457\) | −13.0635 | + | 22.6267i | −0.611085 | + | 1.05843i | 0.379973 | + | 0.924998i | \(0.375933\pi\) |
−0.991058 | + | 0.133433i | \(0.957400\pi\) | |||||||
\(458\) | −13.3452 | −0.623581 | ||||||||
\(459\) | −7.00000 | + | 2.23607i | −0.326732 | + | 0.104371i | ||||
\(460\) | −30.1361 | −1.40511 | ||||||||
\(461\) | 14.1813 | − | 24.5628i | 0.660491 | − | 1.14400i | −0.319996 | − | 0.947419i | \(-0.603682\pi\) |
0.980487 | − | 0.196585i | \(-0.0629851\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.809475 | + | 1.40205i | 0.0376195 | + | 0.0651589i | 0.884222 | − | 0.467067i | \(-0.154689\pi\) |
−0.846603 | + | 0.532226i | \(0.821356\pi\) | |||||||
\(464\) | −0.563508 | − | 0.976025i | −0.0261602 | − | 0.0453108i | ||||
\(465\) | 19.1703 | + | 26.4777i | 0.889001 | + | 1.22787i | ||||
\(466\) | −3.62702 | + | 6.28218i | −0.168018 | + | 0.291016i | ||||
\(467\) | −6.19574 | −0.286705 | −0.143352 | − | 0.989672i | \(-0.545788\pi\) | ||||
−0.143352 | + | 0.989672i | \(0.545788\pi\) | |||||||
\(468\) | 12.4585 | − | 2.60505i | 0.575893 | − | 0.120419i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7.00000 | + | 12.1244i | −0.322886 | + | 0.559255i | ||||
\(471\) | −20.5554 | + | 2.12607i | −0.947145 | + | 0.0979641i | ||||
\(472\) | −4.15283 | − | 7.19291i | −0.191149 | − | 0.331080i | ||||
\(473\) | −2.25403 | − | 3.90410i | −0.103641 | − | 0.179511i | ||||
\(474\) | −3.22689 | + | 0.333760i | −0.148216 | + | 0.0153301i | ||||
\(475\) | −21.5611 | + | 37.3448i | −0.989289 | + | 1.71350i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −25.2379 | − | 28.2168i | −1.15556 | − | 1.29196i | ||||
\(478\) | −15.0000 | −0.686084 | ||||||||
\(479\) | 1.94169 | − | 3.36311i | 0.0887182 | − | 0.153664i | −0.818251 | − | 0.574861i | \(-0.805056\pi\) |
0.906970 | + | 0.421196i | \(0.138390\pi\) | |||||||
\(480\) | −3.50000 | − | 4.83414i | −0.159752 | − | 0.220647i | ||||
\(481\) | −12.1890 | − | 21.1120i | −0.555772 | − | 0.962626i | ||||
\(482\) | −11.8412 | − | 20.5095i | −0.539351 | − | 0.934184i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.50000 | + | 4.33013i | −0.113636 | + | 0.196824i | ||||
\(485\) | −51.7460 | −2.34966 | ||||||||
\(486\) | 13.5640 | − | 7.68223i | 0.615278 | − | 0.348473i | ||||
\(487\) | −0.491933 | −0.0222916 | −0.0111458 | − | 0.999938i | \(-0.503548\pi\) | ||||
−0.0111458 | + | 0.999938i | \(0.503548\pi\) | |||||||
\(488\) | 3.13707 | − | 5.43357i | 0.142009 | − | 0.245966i | ||||
\(489\) | −7.07107 | + | 15.8114i | −0.319765 | + | 0.715016i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.872983 | − | 1.51205i | −0.0393972 | − | 0.0682379i | 0.845654 | − | 0.533731i | \(-0.179210\pi\) |
−0.885052 | + | 0.465493i | \(0.845877\pi\) | |||||||
\(492\) | 5.74597 | + | 7.93624i | 0.259048 | + | 0.357793i | ||||
\(493\) | 0.796921 | − | 1.38031i | 0.0358915 | − | 0.0621659i | ||||
\(494\) | 26.6190 | 1.19764 | ||||||||
\(495\) | −27.5658 | − | 30.8195i | −1.23899 | − | 1.38523i | ||||
\(496\) | −5.47723 | −0.245935 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.56351 | − | 0.472008i | 0.204496 | − | 0.0211512i | ||||
\(499\) | 14.8730 | + | 25.7608i | 0.665806 | + | 1.15321i | 0.979066 | + | 0.203543i | \(0.0652456\pi\) |
−0.313260 | + | 0.949667i | \(0.601421\pi\) | |||||||
\(500\) | −3.22689 | − | 5.58913i | −0.144311 | − | 0.249954i | ||||
\(501\) | −16.4365 | + | 1.70004i | −0.734328 | + | 0.0759523i | ||||
\(502\) | 4.73092 | − | 8.19419i | 0.211151 | − | 0.365724i | ||||
\(503\) | 3.88338 | 0.173152 | 0.0865758 | − | 0.996245i | \(-0.472408\pi\) | ||||
0.0865758 | + | 0.996245i | \(0.472408\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 45.9839 | 2.04626 | ||||||||
\(506\) | 17.4919 | − | 30.2969i | 0.777611 | − | 1.34686i | ||||
\(507\) | −5.07877 | − | 7.01471i | −0.225556 | − | 0.311534i | ||||
\(508\) | 0.372983 | + | 0.646026i | 0.0165485 | + | 0.0286628i | ||||
\(509\) | 11.4035 | + | 19.7515i | 0.505452 | + | 0.875469i | 0.999980 | + | 0.00630722i | \(0.00200766\pi\) |
−0.494528 | + | 0.869162i | \(0.664659\pi\) | |||||||
\(510\) | 3.44572 | − | 7.70486i | 0.152579 | − | 0.341177i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 31.0554 | − | 9.92030i | 1.37113 | − | 0.437992i | ||||
\(514\) | −3.00806 | −0.132680 | ||||||||
\(515\) | 6.69052 | − | 11.5883i | 0.294820 | − | 0.510643i | ||||
\(516\) | −0.796921 | + | 1.78197i | −0.0350825 | + | 0.0784468i | ||||
\(517\) | −8.12602 | − | 14.0747i | −0.357382 | − | 0.619004i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.9284 | + | 17.8565i | 0.567495 | + | 0.783815i | ||||
\(520\) | −7.30948 | + | 12.6604i | −0.320542 | + | 0.555194i | ||||
\(521\) | −1.41421 | −0.0619578 | −0.0309789 | − | 0.999520i | \(-0.509862\pi\) | ||||
−0.0309789 | + | 0.999520i | \(0.509862\pi\) | |||||||
\(522\) | −1.05544 | + | 3.21209i | −0.0461954 | + | 0.140589i | ||||
\(523\) | −18.2836 | −0.799484 | −0.399742 | − | 0.916628i | \(-0.630900\pi\) | ||||
−0.399742 | + | 0.916628i | \(0.630900\pi\) | |||||||
\(524\) | 6.67261 | − | 11.5573i | 0.291494 | − | 0.504883i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.80948 | + | 15.2585i | 0.384111 | + | 0.665300i | ||||
\(527\) | −3.87298 | − | 6.70820i | −0.168710 | − | 0.292214i | ||||
\(528\) | 6.89144 | − | 0.712788i | 0.299911 | − | 0.0310201i | ||||
\(529\) | −26.7460 | + | 46.3254i | −1.16287 | + | 2.01415i | ||||
\(530\) | 43.4814 | 1.88871 | ||||||||
\(531\) | −7.77817 | + | 23.6718i | −0.337544 | + | 1.02727i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | − | 20.7846i | 0.519778 | − | 0.900281i | ||||
\(534\) | 7.18246 | + | 9.92030i | 0.310815 | + | 0.429293i | ||||
\(535\) | −0.437664 | − | 0.758056i | −0.0189219 | − | 0.0327736i | ||||
\(536\) | 3.43649 | + | 5.95218i | 0.148434 | + | 0.257095i | ||||
\(537\) | 4.85993 | − | 10.8671i | 0.209722 | − | 0.468952i | ||||
\(538\) | −1.01575 | + | 1.75934i | −0.0437922 | + | 0.0758504i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.80948 | + | 17.4945i | −0.163934 | + | 0.752845i | ||||
\(541\) | −38.1109 | −1.63851 | −0.819257 | − | 0.573426i | \(-0.805614\pi\) | ||||
−0.819257 | + | 0.573426i | \(0.805614\pi\) | |||||||
\(542\) | 3.53553 | − | 6.12372i | 0.151864 | − | 0.263036i | ||||
\(543\) | −9.43649 | + | 21.1006i | −0.404959 | + | 0.905515i | ||||
\(544\) | 0.707107 | + | 1.22474i | 0.0303170 | + | 0.0525105i | ||||
\(545\) | −29.0698 | − | 50.3503i | −1.24521 | − | 2.15677i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.4919 | − | 28.5649i | 0.705144 | − | 1.22135i | −0.261495 | − | 0.965205i | \(-0.584216\pi\) |
0.966639 | − | 0.256141i | \(-0.0824511\pi\) | |||||||
\(548\) | −15.4919 | −0.661783 | ||||||||
\(549\) | −18.4240 | + | 3.85243i | −0.786316 | + | 0.164418i | ||||
\(550\) | 27.4919 | 1.17226 | ||||||||
\(551\) | −3.53553 | + | 6.12372i | −0.150619 | + | 0.260879i | ||||
\(552\) | −15.0681 | + | 1.55850i | −0.641340 | + | 0.0663344i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −7.18246 | − | 12.4404i | −0.305153 | − | 0.528541i | ||||
\(555\) | 34.1109 | − | 3.52812i | 1.44793 | − | 0.149760i | ||||
\(556\) | 9.93870 | − | 17.2143i | 0.421495 | − | 0.730050i | ||||
\(557\) | 26.6190 | 1.12788 | 0.563941 | − | 0.825815i | \(-0.309285\pi\) | ||||
0.563941 | + | 0.825815i | \(0.309285\pi\) | |||||||
\(558\) | 10.9545 | + | 12.2474i | 0.463739 | + | 0.518476i | ||||
\(559\) | 4.78153 | 0.202237 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.74597 | + | 7.93624i | 0.242595 | + | 0.335068i | ||||
\(562\) | −4.37298 | − | 7.57423i | −0.184463 | − | 0.319500i | ||||
\(563\) | −10.8254 | − | 18.7502i | −0.456238 | − | 0.790227i | 0.542521 | − | 0.840042i | \(-0.317470\pi\) |
−0.998758 | + | 0.0498156i | \(0.984137\pi\) | |||||||
\(564\) | −2.87298 | + | 6.42419i | −0.120974 | + | 0.270507i | ||||
\(565\) | −6.67261 | + | 11.5573i | −0.280719 | + | 0.486219i | ||||
\(566\) | −5.03956 | −0.211829 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.87298 | −0.414261 | ||||||||
\(569\) | 11.7460 | − | 20.3446i | 0.492417 | − | 0.852890i | −0.507545 | − | 0.861625i | \(-0.669447\pi\) |
0.999962 | + | 0.00873460i | \(0.00278035\pi\) | |||||||
\(570\) | −15.2869 | + | 34.1826i | −0.640298 | + | 1.43175i | ||||
\(571\) | −15.7460 | − | 27.2728i | −0.658948 | − | 1.14133i | −0.980888 | − | 0.194572i | \(-0.937668\pi\) |
0.321940 | − | 0.946760i | \(-0.395665\pi\) | |||||||
\(572\) | −8.48528 | − | 14.6969i | −0.354787 | − | 0.614510i | ||||
\(573\) | 6.22354 | + | 8.59585i | 0.259992 | + | 0.359097i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −60.1109 | −2.50680 | ||||||||
\(576\) | −2.00000 | − | 2.23607i | −0.0833333 | − | 0.0931695i | ||||
\(577\) | −24.2213 | −1.00834 | −0.504172 | − | 0.863603i | \(-0.668202\pi\) | ||||
−0.504172 | + | 0.863603i | \(0.668202\pi\) | |||||||
\(578\) | 7.50000 | − | 12.9904i | 0.311959 | − | 0.540329i | ||||
\(579\) | 41.1298 | − | 4.25409i | 1.70930 | − | 0.176794i | ||||
\(580\) | −1.94169 | − | 3.36311i | −0.0806244 | − | 0.139645i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −25.8730 | + | 2.67607i | −1.07247 | + | 0.110927i | ||||
\(583\) | −25.2379 | + | 43.7133i | −1.04525 | + | 1.81042i | ||||
\(584\) | −4.42227 | −0.182995 | ||||||||
\(585\) | 42.9284 | − | 8.97628i | 1.77487 | − | 0.371124i | ||||
\(586\) | 0.796921 | 0.0329205 | ||||||||
\(587\) | 4.28184 | − | 7.41637i | 0.176731 | − | 0.306106i | −0.764028 | − | 0.645183i | \(-0.776781\pi\) |
0.940759 | + | 0.339076i | \(0.110115\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.1825 | + | 29.7609i | 0.707991 | + | 1.22628i | ||||
\(590\) | −14.3095 | − | 24.7847i | −0.589112 | − | 1.02037i | ||||
\(591\) | −11.7514 | + | 26.2769i | −0.483387 | + | 1.08089i | ||||
\(592\) | −2.87298 | + | 4.97615i | −0.118079 | + | 0.204519i | ||||
\(593\) | −33.7615 | −1.38642 | −0.693209 | − | 0.720736i | \(-0.743804\pi\) | ||||
−0.693209 | + | 0.720736i | \(0.743804\pi\) | |||||||
\(594\) | −15.3767 | − | 13.9842i | −0.630914 | − | 0.573777i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.87298 | − | 13.6364i | 0.322490 | − | 0.558569i | ||||
\(597\) | 8.61895 | − | 19.2726i | 0.352750 | − | 0.788773i | ||||
\(598\) | 18.5530 | + | 32.1347i | 0.758688 | + | 1.31409i | ||||
\(599\) | 22.6190 | + | 39.1772i | 0.924185 | + | 1.60074i | 0.792866 | + | 0.609396i | \(0.208588\pi\) |
0.131319 | + | 0.991340i | \(0.458079\pi\) | |||||||
\(600\) | −6.98125 | − | 9.64240i | −0.285008 | − | 0.393649i | ||||
\(601\) | −2.39076 | + | 4.14092i | −0.0975213 | + | 0.168912i | −0.910658 | − | 0.413161i | \(-0.864425\pi\) |
0.813137 | + | 0.582073i | \(0.197758\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.43649 | − | 19.5886i | 0.262114 | − | 0.797709i | ||||
\(604\) | 11.0000 | 0.447584 | ||||||||
\(605\) | −8.61430 | + | 14.9204i | −0.350221 | + | 0.606601i | ||||
\(606\) | 22.9919 | − | 2.37808i | 0.933983 | − | 0.0966028i | ||||
\(607\) | 13.3452 | + | 23.1146i | 0.541666 | + | 0.938192i | 0.998809 | + | 0.0487991i | \(0.0155394\pi\) |
−0.457143 | + | 0.889393i | \(0.651127\pi\) | |||||||
\(608\) | −3.13707 | − | 5.43357i | −0.127225 | − | 0.220360i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.8095 | − | 18.7226i | 0.437663 | − | 0.758054i | ||||
\(611\) | 17.2379 | 0.697371 | ||||||||
\(612\) | 1.32440 | − | 4.03063i | 0.0535357 | − | 0.162929i | ||||
\(613\) | 26.6190 | 1.07513 | 0.537565 | − | 0.843223i | \(-0.319344\pi\) | ||||
0.537565 | + | 0.843223i | \(0.319344\pi\) | |||||||
\(614\) | 7.11027 | − | 12.3154i | 0.286947 | − | 0.497007i | ||||
\(615\) | 19.7990 | + | 27.3460i | 0.798372 | + | 1.10270i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.12702 | + | 10.6123i | 0.246664 | + | 0.427235i | 0.962598 | − | 0.270933i | \(-0.0873321\pi\) |
−0.715934 | + | 0.698168i | \(0.753999\pi\) | |||||||
\(618\) | 2.74597 | − | 6.14017i | 0.110459 | − | 0.246994i | ||||
\(619\) | −18.9515 | + | 32.8249i | −0.761723 | + | 1.31934i | 0.180238 | + | 0.983623i | \(0.442313\pi\) |
−0.941962 | + | 0.335721i | \(0.891020\pi\) | |||||||
\(620\) | −18.8730 | −0.757957 | ||||||||
\(621\) | 33.6211 | + | 30.5762i | 1.34917 | + | 1.22698i | ||||
\(622\) | 1.41421 | 0.0567048 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.00000 | + | 6.70820i | −0.120096 | + | 0.268543i | ||||
\(625\) | 6.06351 | + | 10.5023i | 0.242540 | + | 0.420092i | ||||
\(626\) | 7.86799 | + | 13.6278i | 0.314468 | + | 0.544675i | ||||
\(627\) | −25.4919 | − | 35.2091i | −1.01805 | − | 1.40611i | ||||
\(628\) | 5.96550 | − | 10.3325i | 0.238049 | − | 0.412314i | ||||
\(629\) | −8.12602 | −0.324006 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.38105 | −0.174407 | −0.0872034 | − | 0.996191i | \(-0.527793\pi\) | ||||
−0.0872034 | + | 0.996191i | \(0.527793\pi\) | |||||||
\(632\) | 0.936492 | − | 1.62205i | 0.0372516 | − | 0.0645217i | ||||
\(633\) | 35.5236 | − | 3.67423i | 1.41193 | − | 0.146038i | ||||
\(634\) | −12.3095 | − | 21.3206i | −0.488872 | − | 0.846751i | ||||
\(635\) | 1.28520 | + | 2.22602i | 0.0510014 | + | 0.0883371i | ||||
\(636\) | 21.7407 | − | 2.24866i | 0.862074 | − | 0.0891651i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.50807 | 0.178476 | ||||||||
\(639\) | 19.7460 | + | 22.0767i | 0.781138 | + | 0.873339i | ||||
\(640\) | 3.44572 | 0.136204 | ||||||||
\(641\) | −8.55544 | + | 14.8185i | −0.337920 | + | 0.585294i | −0.984041 | − | 0.177941i | \(-0.943057\pi\) |
0.646122 | + | 0.763234i | \(0.276390\pi\) | |||||||
\(642\) | −0.258035 | − | 0.356394i | −0.0101838 | − | 0.0140657i | ||||
\(643\) | 1.76206 | + | 3.05198i | 0.0694890 | + | 0.120358i | 0.898676 | − | 0.438612i | \(-0.144530\pi\) |
−0.829187 | + | 0.558971i | \(0.811196\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.74597 | + | 6.14017i | −0.108122 | + | 0.241769i | ||||
\(646\) | 4.43649 | − | 7.68423i | 0.174551 | − | 0.302332i | ||||
\(647\) | 5.47723 | 0.215332 | 0.107666 | − | 0.994187i | \(-0.465662\pi\) | ||||
0.107666 | + | 0.994187i | \(0.465662\pi\) | |||||||
\(648\) | −1.00000 | + | 8.94427i | −0.0392837 | + | 0.351364i | ||||
\(649\) | 33.2226 | 1.30410 | ||||||||
\(650\) | −14.5798 | + | 25.2530i | −0.571867 | + | 0.990502i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.00000 | − | 8.66025i | −0.195815 | − | 0.339162i | ||||
\(653\) | 7.25403 | + | 12.5644i | 0.283872 | + | 0.491681i | 0.972335 | − | 0.233590i | \(-0.0750475\pi\) |
−0.688463 | + | 0.725272i | \(0.741714\pi\) | |||||||
\(654\) | −17.1388 | − | 23.6718i | −0.670179 | − | 0.925641i | ||||
\(655\) | 22.9919 | − | 39.8232i | 0.898369 | − | 1.55602i | ||||
\(656\) | −5.65685 | −0.220863 | ||||||||
\(657\) | 8.84454 | + | 9.88849i | 0.345058 | + | 0.385787i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.5635 | + | 25.2247i | −0.567314 | + | 0.982616i | 0.429517 | + | 0.903059i | \(0.358684\pi\) |
−0.996830 | + | 0.0795572i | \(0.974649\pi\) | |||||||
\(660\) | 23.7460 | − | 2.45607i | 0.924310 | − | 0.0956023i | ||||
\(661\) | −23.1043 | − | 40.0178i | −0.898652 | − | 1.55651i | −0.829218 | − | 0.558925i | \(-0.811214\pi\) |
−0.0694345 | − | 0.997587i | \(-0.522119\pi\) | |||||||
\(662\) | −10.1825 | − | 17.6365i | −0.395752 | − | 0.685463i | ||||
\(663\) | −10.3372 | + | 1.06918i | −0.401462 | + | 0.0415236i | ||||
\(664\) | −1.32440 | + | 2.29393i | −0.0513967 | + | 0.0890216i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16.8730 | − | 3.52812i | 0.653815 | − | 0.136712i | ||||
\(667\) | −9.85685 | −0.381659 | ||||||||
\(668\) | 4.77012 | − | 8.26209i | 0.184561 | − | 0.319670i | ||||
\(669\) | −22.8014 | − | 31.4929i | −0.881553 | − | 1.21759i | ||||
\(670\) | 11.8412 | + | 20.5095i | 0.457465 | + | 0.792353i | ||||
\(671\) | 12.5483 | + | 21.7343i | 0.484421 | + | 0.839043i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.11895 | + | 12.3304i | −0.274415 | + | 0.475301i | −0.969987 | − | 0.243155i | \(-0.921818\pi\) |
0.695572 | + | 0.718456i | \(0.255151\pi\) | |||||||
\(674\) | 15.7460 | 0.606512 | ||||||||
\(675\) | −7.59855 | + | 34.8953i | −0.292468 | + | 1.34312i | ||||
\(676\) | 5.00000 | 0.192308 | ||||||||
\(677\) | 6.36396 | − | 11.0227i | 0.244587 | − | 0.423637i | −0.717428 | − | 0.696632i | \(-0.754681\pi\) |
0.962015 | + | 0.272995i | \(0.0880143\pi\) | |||||||
\(678\) | −2.73861 | + | 6.12372i | −0.105176 | + | 0.235180i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.43649 | + | 4.22013i | 0.0934352 | + | 0.161834i | ||||
\(681\) | 10.5000 | + | 14.5024i | 0.402361 | + | 0.555734i | ||||
\(682\) | 10.9545 | − | 18.9737i | 0.419468 | − | 0.726539i | ||||
\(683\) | 7.74597 | 0.296391 | 0.148196 | − | 0.988958i | \(-0.452653\pi\) | ||||
0.148196 | + | 0.988958i | \(0.452653\pi\) | |||||||
\(684\) | −5.87569 | + | 17.8819i | −0.224662 | + | 0.683730i | ||||
\(685\) | −53.3809 | −2.03958 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.9919 | + | 2.37808i | −0.877197 | + | 0.0907293i | ||||
\(688\) | −0.563508 | − | 0.976025i | −0.0214836 | − | 0.0372106i | ||||
\(689\) | −26.7688 | − | 46.3650i | −1.01981 | − | 1.76637i | ||||
\(690\) | −51.9204 | + | 5.37017i | −1.97657 | + | 0.204439i | ||||
\(691\) | 8.52448 | − | 14.7648i | 0.324287 | − | 0.561681i | −0.657081 | − | 0.753820i | \(-0.728209\pi\) |
0.981368 | + | 0.192139i | \(0.0615424\pi\) | |||||||
\(692\) | −12.7279 | −0.483843 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.74597 | 0.294033 | ||||||||
\(695\) | 34.2460 | − | 59.3158i | 1.29902 | − | 2.24997i | ||||
\(696\) | −1.14477 | − | 1.58114i | −0.0433924 | − | 0.0599329i | ||||
\(697\) | −4.00000 | − | 6.92820i | −0.151511 | − | 0.262424i | ||||
\(698\) | −8.21584 | − | 14.2302i | −0.310974 | − | 0.538623i | ||||
\(699\) | −5.12938 | + | 11.4696i | −0.194011 | + | 0.433821i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.2540 | −0.613906 | −0.306953 | − | 0.951725i | \(-0.599310\pi\) | ||||
−0.306953 | + | 0.951725i | \(0.599310\pi\) | |||||||
\(702\) | 21.0000 | − | 6.70820i | 0.792594 | − | 0.253185i | ||||
\(703\) | 36.0510 | 1.35969 | ||||||||
\(704\) | −2.00000 | + | 3.46410i | −0.0753778 | + | 0.130558i | ||||
\(705\) | −9.89949 | + | 22.1359i | −0.372837 | + | 0.833688i | ||||
\(706\) | 1.94169 | + | 3.36311i | 0.0730765 | + | 0.126572i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −8.43649 | − | 11.6523i | −0.317063 | − | 0.437922i | ||||
\(709\) | 26.3649 | − | 45.6654i | 0.990155 | − | 1.71500i | 0.373857 | − | 0.927486i | \(-0.378035\pi\) |
0.616298 | − | 0.787513i | \(-0.288632\pi\) | |||||||
\(710\) | −34.0195 | −1.27673 | ||||||||
\(711\) | −5.50000 | + | 1.15004i | −0.206266 | + | 0.0431300i | ||||
\(712\) | −7.07107 | −0.264999 | ||||||||
\(713\) | −23.9518 | + | 41.4858i | −0.897003 | + | 1.55365i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −29.2379 | − | 50.6415i | −1.09344 | − | 1.89389i | ||||
\(716\) | 3.43649 | + | 5.95218i | 0.128428 | + | 0.222443i | ||||
\(717\) | −25.8429 | + | 2.67295i | −0.965121 | + | 0.0998233i | ||||
\(718\) | −9.11895 | + | 15.7945i | −0.340316 | + | 0.589445i | ||||
\(719\) | 23.5027 | 0.876504 | 0.438252 | − | 0.898852i | \(-0.355598\pi\) | ||||
0.438252 | + | 0.898852i | \(0.355598\pi\) | |||||||
\(720\) | −6.89144 | − | 7.70486i | −0.256829 | − | 0.287143i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10.1825 | + | 17.6365i | −0.378952 | + | 0.656364i | ||||
\(723\) | −24.0554 | − | 33.2250i | −0.894632 | − | 1.23565i | ||||
\(724\) | −6.67261 | − | 11.5573i | −0.247985 | − | 0.429523i | ||||
\(725\) | −3.87298 | − | 6.70820i | −0.143839 | − | 0.249136i | ||||
\(726\) | −3.53553 | + | 7.90569i | −0.131216 | + | 0.293408i | ||||
\(727\) | 1.68366 | − | 2.91618i | 0.0624434 | − | 0.108155i | −0.833114 | − | 0.553102i | \(-0.813444\pi\) |
0.895557 | + | 0.444947i | \(0.146777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.0000 | − | 15.6525i | 0.814815 | − | 0.579721i | ||||
\(730\) | −15.2379 | −0.563980 | ||||||||
\(731\) | 0.796921 | − | 1.38031i | 0.0294752 | − | 0.0510525i | ||||
\(732\) | 4.43649 | − | 9.92030i | 0.163977 | − | 0.366665i | ||||
\(733\) | −18.5138 | − | 32.0668i | −0.683823 | − | 1.18442i | −0.973805 | − | 0.227384i | \(-0.926983\pi\) |
0.289983 | − | 0.957032i | \(-0.406350\pi\) | |||||||
\(734\) | 3.44572 | + | 5.96816i | 0.127184 | + | 0.220289i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.37298 | − | 7.57423i | 0.161190 | − | 0.279190i | ||||
\(737\) | −27.4919 | −1.01268 | ||||||||
\(738\) | 11.3137 | + | 12.6491i | 0.416463 | + | 0.465620i | ||||
\(739\) | −30.0000 | −1.10357 | −0.551784 | − | 0.833987i | \(-0.686053\pi\) | ||||
−0.551784 | + | 0.833987i | \(0.686053\pi\) | |||||||
\(740\) | −9.89949 | + | 17.1464i | −0.363913 | + | 0.630315i | ||||
\(741\) | 45.8607 | − | 4.74342i | 1.68474 | − | 0.174254i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.12702 | + | 10.6123i | 0.224778 | + | 0.389328i | 0.956253 | − | 0.292541i | \(-0.0945008\pi\) |
−0.731475 | + | 0.681869i | \(0.761167\pi\) | |||||||
\(744\) | −9.43649 | + | 0.976025i | −0.345959 | + | 0.0357828i | ||||
\(745\) | 27.1281 | − | 46.9872i | 0.993896 | − | 1.72148i | ||||
\(746\) | −1.12702 | −0.0412630 | ||||||||
\(747\) | 7.77817 | − | 1.62641i | 0.284589 | − | 0.0595071i | ||||
\(748\) | −5.65685 | −0.206835 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −6.55544 | − | 9.05427i | −0.239371 | − | 0.330615i | ||||
\(751\) | 6.50000 | + | 11.2583i | 0.237188 | + | 0.410822i | 0.959906 | − | 0.280321i | \(-0.0904408\pi\) |
−0.722718 | + | 0.691143i | \(0.757107\pi\) | |||||||
\(752\) | −2.03151 | − | 3.51867i | −0.0740814 | − | 0.128313i | ||||
\(753\) | 6.69052 | − | 14.9605i | 0.243816 | − | 0.545190i | ||||
\(754\) | −2.39076 | + | 4.14092i | −0.0870665 | + | 0.150804i | ||||
\(755\) | 37.9029 | 1.37943 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.2379 | 1.13536 | 0.567680 | − | 0.823249i | \(-0.307841\pi\) | ||||
0.567680 | + | 0.823249i | \(0.307841\pi\) | |||||||
\(758\) | −13.1825 | + | 22.8327i | −0.478808 | + | 0.829321i | ||||
\(759\) | 24.7373 | − | 55.3144i | 0.897908 | − | 2.00778i | ||||
\(760\) | −10.8095 | − | 18.7226i | −0.392101 | − | 0.679139i | ||||
\(761\) | −15.2869 | − | 26.4777i | −0.554150 | − | 0.959816i | −0.997969 | − | 0.0636995i | \(-0.979710\pi\) |
0.443819 | − | 0.896116i | \(-0.353623\pi\) | |||||||
\(762\) | 0.757718 | + | 1.04655i | 0.0274492 | + | 0.0379124i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6.12702 | −0.221668 | ||||||||
\(765\) | 4.56351 | − | 13.8884i | 0.164994 | − | 0.502137i | ||||
\(766\) | 12.9076 | 0.466369 | ||||||||
\(767\) | −17.6190 | + | 30.5169i | −0.636183 | + | 1.10190i | ||||
\(768\) | 1.72286 | − | 0.178197i | 0.0621683 | − | 0.00643013i | ||||
\(769\) | −0.617292 | − | 1.06918i | −0.0222601 | − | 0.0385557i | 0.854681 | − | 0.519154i | \(-0.173753\pi\) |
−0.876941 | + | 0.480598i | \(0.840420\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.18246 | + | 0.536026i | −0.186642 | + | 0.0193045i | ||||
\(772\) | −11.9365 | + | 20.6746i | −0.429604 | + | 0.744095i | ||||
\(773\) | 2.03151 | 0.0730682 | 0.0365341 | − | 0.999332i | \(-0.488368\pi\) | ||||
0.0365341 | + | 0.999332i | \(0.488368\pi\) | |||||||
\(774\) | −1.05544 | + | 3.21209i | −0.0379371 | + | 0.115456i | ||||
\(775\) | −37.6449 | −1.35224 | ||||||||
\(776\) | 7.50873 | − | 13.0055i | 0.269548 | − | 0.466870i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.56351 | − | 11.3683i | −0.235313 | − | 0.407574i | ||||
\(779\) | 17.7460 | + | 30.7369i | 0.635815 | + | 1.10126i | ||||
\(780\) | −10.3372 | + | 23.1146i | −0.370130 | + | 0.827635i | ||||
\(781\) | 19.7460 | − | 34.2010i | 0.706566 | − | 1.22381i | ||||
\(782\) | 12.3687 | 0.442303 | ||||||||
\(783\) | −1.24599 | + | 5.72206i | −0.0445282 | + | 0.204490i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.5554 | − | 35.6031i | 0.733655 | − | 1.27073i | ||||
\(786\) | 9.43649 | − | 21.1006i | 0.336589 | − | 0.752635i | ||||
\(787\) | 6.18433 | + | 10.7116i | 0.220448 | + | 0.381827i | 0.954944 | − | 0.296786i | \(-0.0959149\pi\) |
−0.734496 | + | 0.678613i | \(0.762582\pi\) | |||||||
\(788\) | −8.30948 | − | 14.3924i | −0.296013 | − | 0.512709i | ||||
\(789\) | 17.8965 | + | 24.7184i | 0.637132 | + | 0.879997i | ||||
\(790\) | 3.22689 | − | 5.58913i | 0.114808 | − | 0.198852i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 11.7460 | − | 2.45607i | 0.417375 | − | 0.0872726i | ||||
\(793\) | −26.6190 | −0.945267 | ||||||||
\(794\) | 3.53553 | − | 6.12372i | 0.125471 | − | 0.217323i | ||||
\(795\) | 74.9123 | − | 7.74825i | 2.65687 | − | 0.274802i | ||||
\(796\) | 6.09452 | + | 10.5560i | 0.216014 | + | 0.374148i | ||||
\(797\) | −10.2980 | − | 17.8366i | −0.364772 | − | 0.631804i | 0.623967 | − | 0.781450i | \(-0.285520\pi\) |
−0.988740 | + | 0.149646i | \(0.952187\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.87298 | − | 4.97615i | 0.101639 | − | 0.176044i | ||||
\(800\) | 6.87298 | 0.242997 | ||||||||
\(801\) | 14.1421 | + | 15.8114i | 0.499688 | + | 0.558668i | ||||
\(802\) | −3.87298 | −0.136760 | ||||||||
\(803\) | 8.84454 | − | 15.3192i | 0.312117 | − | 0.540602i | ||||
\(804\) | 6.98125 | + | 9.64240i | 0.246210 | + | 0.340061i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.6190 | + | 20.1246i | 0.409260 | + | 0.708859i | ||||
\(807\) | −1.43649 | + | 3.21209i | −0.0505669 | + | 0.113071i | ||||
\(808\) | −6.67261 | + | 11.5573i | −0.234742 | + | 0.406584i | ||||
\(809\) | 46.7298 | 1.64293 | 0.821467 | − | 0.570256i | \(-0.193156\pi\) | ||||
0.821467 | + | 0.570256i | \(0.193156\pi\) | |||||||
\(810\) | −3.44572 | + | 30.8195i | −0.121070 | + | 1.08289i | ||||
\(811\) | 3.00806 | 0.105627 | 0.0528136 | − | 0.998604i | \(-0.483181\pi\) | ||||
0.0528136 | + | 0.998604i | \(0.483181\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.00000 | − | 11.1803i | 0.175358 | − | 0.392112i | ||||
\(814\) | −11.4919 | − | 19.9046i | −0.402792 | − | 0.697656i | ||||
\(815\) | −17.2286 | − | 29.8408i | −0.603491 | − | 1.04528i | ||||
\(816\) | 1.43649 | + | 1.98406i | 0.0502873 | + | 0.0694560i | ||||
\(817\) | −3.53553 | + | 6.12372i | −0.123693 | + | 0.214242i | ||||
\(818\) | −23.1435 | −0.809193 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −19.4919 | −0.680688 | ||||||||
\(821\) | 4.74597 | − | 8.22026i | 0.165635 | − | 0.286889i | −0.771245 | − | 0.636538i | \(-0.780366\pi\) |
0.936881 | + | 0.349649i | \(0.113699\pi\) | |||||||
\(822\) | −26.6904 | + | 2.76062i | −0.930936 | + | 0.0962875i | ||||
\(823\) | 3.12702 | + | 5.41615i | 0.109001 | + | 0.188795i | 0.915366 | − | 0.402623i | \(-0.131902\pi\) |
−0.806365 | + | 0.591418i | \(0.798568\pi\) | |||||||
\(824\) | 1.94169 | + | 3.36311i | 0.0676420 | + | 0.117159i | ||||
\(825\) | 47.3647 | − | 4.89898i | 1.64903 | − | 0.170561i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.8730 | 1.69948 | 0.849740 | − | 0.527202i | \(-0.176759\pi\) | ||||
0.849740 | + | 0.527202i | \(0.176759\pi\) | |||||||
\(828\) | −25.6825 | + | 5.37017i | −0.892527 | + | 0.186626i | ||||
\(829\) | 10.6180 | 0.368779 | 0.184389 | − | 0.982853i | \(-0.440969\pi\) | ||||
0.184389 | + | 0.982853i | \(0.440969\pi\) | |||||||
\(830\) | −4.56351 | + | 7.90423i | −0.158402 | + | 0.274360i | ||||
\(831\) | −14.5912 | − | 20.1531i | −0.506163 | − | 0.699105i | ||||
\(832\) | −2.12132 | − | 3.67423i | −0.0735436 | − | 0.127381i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 14.0554 | − | 31.4289i | 0.486700 | − | 1.08829i | ||||
\(835\) | 16.4365 | − | 28.4688i | 0.568808 | − | 0.985205i | ||||
\(836\) | 25.0966 | 0.867984 | ||||||||
\(837\) | 21.0554 | + | 19.1486i | 0.727783 | + | 0.661872i | ||||
\(838\) | 31.3707 | 1.08368 | ||||||||
\(839\) | 12.8961 | − | 22.3368i | 0.445224 | − | 0.771151i | −0.552844 | − | 0.833285i | \(-0.686457\pi\) |
0.998068 | + | 0.0621340i | \(0.0197906\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.8649 | + | 24.0147i | 0.478101 | + | 0.828094i | ||||
\(842\) | 6.43649 | + | 11.1483i | 0.221816 | + | 0.384197i | ||||
\(843\) | −8.88374 | − | 12.2701i | −0.305972 | − | 0.422604i | ||||
\(844\) | −10.3095 | + | 17.8565i | −0.354867 | + | 0.614647i | ||||
\(845\) | 17.2286 | 0.592682 | ||||||||
\(846\) | −3.80498 | + | 11.5799i | −0.130818 | + | 0.398126i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.30948 | + | 10.9283i | −0.216668 | + | 0.375280i | ||||
\(849\) | −8.68246 | + | 0.898035i | −0.297981 | + | 0.0308205i | ||||
\(850\) | 4.85993 | + | 8.41765i | 0.166694 | + | 0.288723i | ||||
\(851\) | 25.1270 | + | 43.5213i | 0.861343 | + | 1.49189i | ||||
\(852\) | −17.0098 | + | 1.75934i | −0.582745 | + | 0.0602739i | ||||
\(853\) | −9.06337 | + | 15.6982i | −0.310324 | + | 0.537497i | −0.978432 | − | 0.206567i | \(-0.933771\pi\) |
0.668109 | + | 0.744064i | \(0.267104\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.2460 | + | 61.6158i | −0.692397 | + | 2.10722i | ||||
\(856\) | 0.254033 | 0.00868268 | ||||||||
\(857\) | 12.9076 | − | 22.3565i | 0.440914 | − | 0.763685i | −0.556844 | − | 0.830617i | \(-0.687988\pi\) |
0.997758 | + | 0.0669325i | \(0.0213212\pi\) | |||||||
\(858\) | −17.2379 | − | 23.8087i | −0.588492 | − | 0.812816i | ||||
\(859\) | 15.2869 | + | 26.4777i | 0.521583 | + | 0.903407i | 0.999685 | + | 0.0251033i | \(0.00799146\pi\) |
−0.478102 | + | 0.878304i | \(0.658675\pi\) | |||||||
\(860\) | −1.94169 | − | 3.36311i | −0.0662111 | − | 0.114681i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.7460 | − | 18.6126i | 0.366009 | − | 0.633946i | ||||
\(863\) | −43.8730 | −1.49345 | −0.746727 | − | 0.665131i | \(-0.768376\pi\) | ||||
−0.746727 | + | 0.665131i | \(0.768376\pi\) | |||||||
\(864\) | −3.84418 | − | 3.49604i | −0.130782 | − | 0.118938i | ||||
\(865\) | −43.8569 | −1.49118 | ||||||||
\(866\) | −14.8492 | + | 25.7196i | −0.504598 | + | 0.873989i | ||||
\(867\) | 10.6066 | − | 23.7171i | 0.360219 | − | 0.805474i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.74597 | + | 6.48820i | 0.127073 | + | 0.220097i | ||||
\(870\) | −3.94456 | − | 5.44816i | −0.133733 | − | 0.184710i | ||||
\(871\) | 14.5798 | − | 25.2530i | 0.494018 | − | 0.855664i | ||||
\(872\) | 16.8730 | 0.571391 | ||||||||
\(873\) | −44.0987 | + | 9.22097i | −1.49251 | + | 0.312083i | ||||
\(874\) | −54.8735 | −1.85612 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.61895 | + | 0.788035i | −0.257420 | + | 0.0266252i | ||||
\(877\) | −15.5635 | − | 26.9568i | −0.525542 | − | 0.910266i | −0.999557 | − | 0.0297493i | \(-0.990529\pi\) |
0.474015 | − | 0.880517i | \(-0.342804\pi\) | |||||||
\(878\) | −5.47723 | − | 9.48683i | −0.184847 | − | 0.320165i | ||||
\(879\) | 1.37298 | − | 0.142009i | 0.0463096 | − | 0.00478984i | ||||
\(880\) | −6.89144 | + | 11.9363i | −0.232310 | + | 0.402373i | ||||
\(881\) | −26.6904 | −0.899223 | −0.449612 | − | 0.893224i | \(-0.648438\pi\) | ||||
−0.449612 | + | 0.893224i | \(0.648438\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.4919 | 1.19440 | 0.597199 | − | 0.802093i | \(-0.296280\pi\) | ||||
0.597199 | + | 0.802093i | \(0.296280\pi\) | |||||||
\(884\) | 3.00000 | − | 5.19615i | 0.100901 | − | 0.174766i | ||||
\(885\) | −29.0698 | − | 40.1507i | −0.977170 | − | 1.34965i | ||||
\(886\) | 7.18246 | + | 12.4404i | 0.241299 | + | 0.417943i | ||||
\(887\) | 3.88338 | + | 6.72622i | 0.130391 | + | 0.225844i | 0.923827 | − | 0.382809i | \(-0.125043\pi\) |
−0.793436 | + | 0.608653i | \(0.791710\pi\) | |||||||
\(888\) | −4.06301 | + | 9.08517i | −0.136346 | + | 0.304878i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −24.3649 | −0.816714 | ||||||||
\(891\) | −28.9839 | − | 21.3526i | −0.970996 | − | 0.715341i | ||||
\(892\) | 22.4478 | 0.751608 | ||||||||
\(893\) | −12.7460 | + | 22.0767i | −0.426528 | + | 0.738767i | ||||
\(894\) | 11.1341 | − | 24.8966i | 0.372379 | − | 0.832666i | ||||
\(895\) | 11.8412 | + | 20.5095i | 0.395807 | + | 0.685558i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 37.6905 | + | 52.0576i | 1.25845 | + | 1.73815i | ||||
\(898\) | −4.50000 | + | 7.79423i | −0.150167 | + | 0.260097i | ||||
\(899\) | −6.17292 | −0.205879 | ||||||||
\(900\) | −13.7460 | − | 15.3685i | −0.458199 | − | 0.512282i | ||||
\(901\) | −17.8459 | −0.594533 | ||||||||
\(902\) | 11.3137 | − | 19.5959i | 0.376705 | − | 0.652473i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.93649 | − | 3.35410i | −0.0644068 | − | 0.111556i | ||||
\(905\) | −22.9919 | − | 39.8232i | −0.764278 | − | 1.32377i | ||||
\(906\) | 18.9515 | − | 1.96017i | 0.629620 | − | 0.0651222i | ||||
\(907\) | −9.30948 | + | 16.1245i | −0.309116 | + | 0.535405i | −0.978169 | − | 0.207810i | \(-0.933366\pi\) |
0.669053 | + | 0.743215i | \(0.266700\pi\) | |||||||
\(908\) | −10.3372 | −0.343051 | ||||||||
\(909\) | 39.1881 | − | 8.19419i | 1.29979 | − | 0.271784i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.3730 | − | 33.5550i | 0.641856 | − | 1.11173i | −0.343163 | − | 0.939276i | \(-0.611498\pi\) |
0.985018 | − | 0.172450i | \(-0.0551685\pi\) | |||||||
\(912\) | −6.37298 | − | 8.80226i | −0.211031 | − | 0.291472i | ||||
\(913\) | −5.29760 | − | 9.17571i | −0.175325 | − | 0.303672i | ||||
\(914\) | −13.0635 | − | 22.6267i | −0.432102 | − | 0.748423i | ||||
\(915\) | 15.2869 | − | 34.1826i | 0.505370 | − | 1.13004i | ||||
\(916\) | 6.67261 | − | 11.5573i | 0.220469 | − | 0.381864i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.56351 | − | 7.18021i | 0.0516035 | − | 0.236982i | ||||
\(919\) | −0.635083 | −0.0209495 | −0.0104747 | − | 0.999945i | \(-0.503334\pi\) | ||||
−0.0104747 | + | 0.999945i | \(0.503334\pi\) | |||||||
\(920\) | 15.0681 | − | 26.0987i | 0.496780 | − | 0.860448i | ||||
\(921\) | 10.0554 | − | 22.4847i | 0.331338 | − | 0.740894i | ||||
\(922\) | 14.1813 | + | 24.5628i | 0.467038 | + | 0.808933i | ||||
\(923\) | 20.9438 | + | 36.2757i | 0.689372 | + | 1.19403i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.7460 | + | 34.2010i | −0.649243 | + | 1.12452i | ||||
\(926\) | −1.61895 | −0.0532020 | ||||||||
\(927\) | 3.63676 | − | 11.0680i | 0.119447 | − | 0.363520i | ||||
\(928\) | 1.12702 | 0.0369961 | ||||||||
\(929\) | −27.2179 | + | 47.1428i | −0.892991 | + | 1.54671i | −0.0567186 | + | 0.998390i | \(0.518064\pi\) |
−0.836272 | + | 0.548315i | \(0.815270\pi\) | |||||||
\(930\) | −32.5155 | + | 3.36311i | −1.06623 | + | 0.110281i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.62702 | − | 6.28218i | −0.118807 | − | 0.205780i | ||||
\(933\) | 2.43649 | − | 0.252009i | 0.0797672 | − | 0.00825039i | ||||
\(934\) | 3.09787 | − | 5.36567i | 0.101365 | − | 0.175570i | ||||
\(935\) | −19.4919 | −0.637454 | ||||||||
\(936\) | −3.97320 | + | 12.0919i | −0.129868 | + | 0.395236i | ||||
\(937\) | 45.2320 | 1.47767 | 0.738833 | − | 0.673889i | \(-0.235377\pi\) | ||||
0.738833 | + | 0.673889i | \(0.235377\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.9839 | + | 22.0767i | 0.521614 | + | 0.720445i | ||||
\(940\) | −7.00000 | − | 12.1244i | −0.228315 | − | 0.395453i | ||||
\(941\) | 12.8569 | + | 22.2689i | 0.419124 | + | 0.725945i | 0.995852 | − | 0.0909922i | \(-0.0290038\pi\) |
−0.576727 | + | 0.816937i | \(0.695670\pi\) | |||||||
\(942\) | 8.43649 | − | 18.8646i | 0.274876 | − | 0.614641i | ||||
\(943\) | −24.7373 | + | 42.8463i | −0.805558 | + | 1.39527i | ||||
\(944\) | 8.30565 | 0.270326 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.50807 | 0.146570 | ||||||||
\(947\) | 28.8014 | − | 49.8855i | 0.935920 | − | 1.62106i | 0.162935 | − | 0.986637i | \(-0.447904\pi\) |
0.772985 | − | 0.634424i | \(-0.218763\pi\) | |||||||
\(948\) | 1.32440 | − | 2.96145i | 0.0430145 | − | 0.0961833i | ||||
\(949\) | 9.38105 | + | 16.2485i | 0.304522 | + | 0.527447i | ||||
\(950\) | −21.5611 | − | 37.3448i | −0.699533 | − | 1.21163i | ||||
\(951\) | −25.0068 | − | 34.5390i | −0.810900 | − | 1.12000i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −59.4919 | −1.92713 | −0.963566 | − | 0.267469i | \(-0.913813\pi\) | ||||
−0.963566 | + | 0.267469i | \(0.913813\pi\) | |||||||
\(954\) | 37.0554 | − | 7.74825i | 1.19971 | − | 0.250859i | ||||
\(955\) | −21.1120 | −0.683168 | ||||||||
\(956\) | 7.50000 | − | 12.9904i | 0.242567 | − | 0.420139i | ||||
\(957\) | 7.76677 | − | 0.803324i | 0.251064 | − | 0.0259678i | ||||
\(958\) | 1.94169 | + | 3.36311i | 0.0627332 | + | 0.108657i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 5.93649 | − | 0.614017i | 0.191599 | − | 0.0198173i | ||||
\(961\) | 0.500000 | − | 0.866025i | 0.0161290 | − | 0.0279363i | ||||
\(962\) | 24.3781 | 0.785981 | ||||||||
\(963\) | −0.508067 | − | 0.568036i | −0.0163722 | − | 0.0183047i | ||||
\(964\) | 23.6824 | 0.762758 | ||||||||
\(965\) | −41.1298 | + | 71.2389i | −1.32402 | + | 2.29326i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.2460 | − | 52.3876i | −0.972645 | − | 1.68467i | −0.687498 | − | 0.726186i | \(-0.741291\pi\) |
−0.285147 | − | 0.958484i | \(-0.592042\pi\) | |||||||
\(968\) | −2.50000 | − | 4.33013i | −0.0803530 | − | 0.139176i | ||||
\(969\) | 6.27415 | − | 14.0294i | 0.201555 | − | 0.450690i | ||||
\(970\) | 25.8730 | − | 44.8133i | 0.830731 | − | 1.43887i | ||||
\(971\) | −1.49262 | −0.0479005 | −0.0239502 | − | 0.999713i | \(-0.507624\pi\) | ||||
−0.0239502 | + | 0.999713i | \(0.507624\pi\) | |||||||
\(972\) | −0.129018 | + | 15.5879i | −0.00413824 | + | 0.499983i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.245967 | − | 0.426027i | 0.00788128 | − | 0.0136508i | ||||
\(975\) | −20.6190 | + | 46.1054i | −0.660335 | + | 1.47655i | ||||
\(976\) | 3.13707 | + | 5.43357i | 0.100415 | + | 0.173924i | ||||
\(977\) | −22.7460 | − | 39.3972i | −0.727708 | − | 1.26043i | −0.957850 | − | 0.287270i | \(-0.907252\pi\) |
0.230142 | − | 0.973157i | \(-0.426081\pi\) | |||||||
\(978\) | −10.1575 | − | 14.0294i | −0.324802 | − | 0.448611i | ||||
\(979\) | 14.1421 | − | 24.4949i | 0.451985 | − | 0.782860i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33.7460 | − | 37.7291i | −1.07743 | − | 1.20460i | ||||
\(982\) | 1.74597 | 0.0557160 | ||||||||
\(983\) | −4.94975 | + | 8.57321i | −0.157872 | + | 0.273443i | −0.934101 | − | 0.357008i | \(-0.883797\pi\) |
0.776229 | + | 0.630451i | \(0.217130\pi\) | |||||||
\(984\) | −9.74597 | + | 1.00803i | −0.310690 | + | 0.0321350i | ||||
\(985\) | −28.6321 | − | 49.5923i | −0.912295 | − | 1.58014i | ||||
\(986\) | 0.796921 | + | 1.38031i | 0.0253791 | + | 0.0439580i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13.3095 | + | 23.0527i | −0.423431 | + | 0.733404i | ||||
\(989\) | −9.85685 | −0.313430 | ||||||||
\(990\) | 40.4733 | − | 8.46292i | 1.28633 | − | 0.268969i | ||||
\(991\) | −11.7460 | −0.373123 | −0.186561 | − | 0.982443i | \(-0.559734\pi\) | ||||
−0.186561 | + | 0.982443i | \(0.559734\pi\) | |||||||
\(992\) | 2.73861 | − | 4.74342i | 0.0869510 | − | 0.150604i | ||||
\(993\) | −20.6857 | − | 28.5708i | −0.656442 | − | 0.906667i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.0000 | + | 36.3731i | 0.665745 | + | 1.15310i | ||||
\(996\) | −1.87298 | + | 4.18812i | −0.0593477 | + | 0.132706i | ||||
\(997\) | −13.5640 | + | 23.4936i | −0.429578 | + | 0.744050i | −0.996836 | − | 0.0794898i | \(-0.974671\pi\) |
0.567258 | + | 0.823540i | \(0.308004\pi\) | |||||||
\(998\) | −29.7460 | −0.941592 | ||||||||
\(999\) | 28.4411 | − | 9.08517i | 0.899836 | − | 0.287442i |
(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 | 882.2.f.p.295.2 | ✓ | 8 | |
3.2 | odd | 2 | 2646.2.f.s.883.4 | 8 | |||
7.2 | even | 3 | 882.2.e.t.655.2 | 8 | |||
7.3 | odd | 6 | 882.2.h.r.79.1 | 8 | |||
7.4 | even | 3 | 882.2.h.r.79.4 | 8 | |||
7.5 | odd | 6 | 882.2.e.t.655.3 | 8 | |||
7.6 | odd | 2 | inner | 882.2.f.p.295.3 | yes | 8 | |
9.2 | odd | 6 | 7938.2.a.cd.1.1 | 4 | |||
9.4 | even | 3 | inner | 882.2.f.p.589.1 | yes | 8 | |
9.5 | odd | 6 | 2646.2.f.s.1765.4 | 8 | |||
9.7 | even | 3 | 7938.2.a.cu.1.4 | 4 | |||
21.2 | odd | 6 | 2646.2.e.r.2125.4 | 8 | |||
21.5 | even | 6 | 2646.2.e.r.2125.1 | 8 | |||
21.11 | odd | 6 | 2646.2.h.s.667.1 | 8 | |||
21.17 | even | 6 | 2646.2.h.s.667.4 | 8 | |||
21.20 | even | 2 | 2646.2.f.s.883.1 | 8 | |||
63.4 | even | 3 | 882.2.e.t.373.2 | 8 | |||
63.5 | even | 6 | 2646.2.h.s.361.4 | 8 | |||
63.13 | odd | 6 | inner | 882.2.f.p.589.4 | yes | 8 | |
63.20 | even | 6 | 7938.2.a.cd.1.4 | 4 | |||
63.23 | odd | 6 | 2646.2.h.s.361.1 | 8 | |||
63.31 | odd | 6 | 882.2.e.t.373.3 | 8 | |||
63.32 | odd | 6 | 2646.2.e.r.1549.4 | 8 | |||
63.34 | odd | 6 | 7938.2.a.cu.1.1 | 4 | |||
63.40 | odd | 6 | 882.2.h.r.67.1 | 8 | |||
63.41 | even | 6 | 2646.2.f.s.1765.1 | 8 | |||
63.58 | even | 3 | 882.2.h.r.67.4 | 8 | |||
63.59 | even | 6 | 2646.2.e.r.1549.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.2.e.t.373.2 | 8 | 63.4 | even | 3 | |||
882.2.e.t.373.3 | 8 | 63.31 | odd | 6 | |||
882.2.e.t.655.2 | 8 | 7.2 | even | 3 | |||
882.2.e.t.655.3 | 8 | 7.5 | odd | 6 | |||
882.2.f.p.295.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
882.2.f.p.295.3 | yes | 8 | 7.6 | odd | 2 | inner | |
882.2.f.p.589.1 | yes | 8 | 9.4 | even | 3 | inner | |
882.2.f.p.589.4 | yes | 8 | 63.13 | odd | 6 | inner | |
882.2.h.r.67.1 | 8 | 63.40 | odd | 6 | |||
882.2.h.r.67.4 | 8 | 63.58 | even | 3 | |||
882.2.h.r.79.1 | 8 | 7.3 | odd | 6 | |||
882.2.h.r.79.4 | 8 | 7.4 | even | 3 | |||
2646.2.e.r.1549.1 | 8 | 63.59 | even | 6 | |||
2646.2.e.r.1549.4 | 8 | 63.32 | odd | 6 | |||
2646.2.e.r.2125.1 | 8 | 21.5 | even | 6 | |||
2646.2.e.r.2125.4 | 8 | 21.2 | odd | 6 | |||
2646.2.f.s.883.1 | 8 | 21.20 | even | 2 | |||
2646.2.f.s.883.4 | 8 | 3.2 | odd | 2 | |||
2646.2.f.s.1765.1 | 8 | 63.41 | even | 6 | |||
2646.2.f.s.1765.4 | 8 | 9.5 | odd | 6 | |||
2646.2.h.s.361.1 | 8 | 63.23 | odd | 6 | |||
2646.2.h.s.361.4 | 8 | 63.5 | even | 6 | |||
2646.2.h.s.667.1 | 8 | 21.11 | odd | 6 | |||
2646.2.h.s.667.4 | 8 | 21.17 | even | 6 | |||
7938.2.a.cd.1.1 | 4 | 9.2 | odd | 6 | |||
7938.2.a.cd.1.4 | 4 | 63.20 | even | 6 | |||
7938.2.a.cu.1.1 | 4 | 63.34 | odd | 6 | |||
7938.2.a.cu.1.4 | 4 | 9.7 | even | 3 |