Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,2,Mod(43,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("700.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.k (of order \(4\), 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: | \(5.58952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.4 | ||
Character | \(\chi\) | \(=\) | 700.43 |
Dual form | 700.2.k.b.407.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.26992 | − | 0.622342i | −0.897967 | − | 0.440062i | ||||
\(3\) | 2.09607 | − | 2.09607i | 1.21017 | − | 1.21017i | 0.239197 | − | 0.970971i | \(-0.423116\pi\) |
0.970971 | − | 0.239197i | \(-0.0768843\pi\) | |||||||
\(4\) | 1.22538 | + | 1.58065i | 0.612691 | + | 0.790323i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.96631 | + | 1.35737i | −1.61924 | + | 0.554143i | ||||
\(7\) | −0.707107 | − | 0.707107i | −0.267261 | − | 0.267261i | ||||
\(8\) | −0.572433 | − | 2.76990i | −0.202386 | − | 0.979306i | ||||
\(9\) | − | 5.78704i | − | 1.92901i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.214920i | 0.0648009i | 0.999475 | + | 0.0324005i | \(0.0103152\pi\) | ||||
−0.999475 | + | 0.0324005i | \(0.989685\pi\) | |||||||
\(12\) | 5.88164 | + | 0.744658i | 1.69788 | + | 0.214964i | ||||
\(13\) | −4.29923 | − | 4.29923i | −1.19239 | − | 1.19239i | −0.976394 | − | 0.215999i | \(-0.930699\pi\) |
−0.215999 | − | 0.976394i | \(-0.569301\pi\) | |||||||
\(14\) | 0.457905 | + | 1.33803i | 0.122380 | + | 0.357603i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.996878 | + | 3.87379i | −0.249220 | + | 0.968447i | ||||
\(17\) | −2.00932 | + | 2.00932i | −0.487331 | + | 0.487331i | −0.907463 | − | 0.420132i | \(-0.861984\pi\) |
0.420132 | + | 0.907463i | \(0.361984\pi\) | |||||||
\(18\) | −3.60152 | + | 7.34907i | −0.848886 | + | 1.73219i | ||||
\(19\) | 0.877903 | 0.201405 | 0.100702 | − | 0.994917i | \(-0.467891\pi\) | ||||
0.100702 | + | 0.994917i | \(0.467891\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.96429 | −0.646862 | ||||||||
\(22\) | 0.133754 | − | 0.272931i | 0.0285164 | − | 0.0581891i | ||||
\(23\) | 0.0902398 | − | 0.0902398i | 0.0188163 | − | 0.0188163i | −0.697636 | − | 0.716452i | \(-0.745765\pi\) |
0.716452 | + | 0.697636i | \(0.245765\pi\) | |||||||
\(24\) | −7.00576 | − | 4.60604i | −1.43005 | − | 0.940204i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.78408 | + | 8.13526i | 0.546003 | + | 1.59546i | ||||
\(27\) | −5.84185 | − | 5.84185i | −1.12426 | − | 1.12426i | ||||
\(28\) | 0.251209 | − | 1.98416i | 0.0474740 | − | 0.374971i | ||||
\(29\) | − | 4.03098i | − | 0.748534i | −0.927321 | − | 0.374267i | \(-0.877894\pi\) | ||
0.927321 | − | 0.374267i | \(-0.122106\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.60152i | − | 1.54488i | −0.635088 | − | 0.772440i | \(-0.719036\pi\) | ||
0.635088 | − | 0.772440i | \(-0.280964\pi\) | |||||||
\(32\) | 3.67677 | − | 4.29899i | 0.649968 | − | 0.759962i | ||||
\(33\) | 0.450489 | + | 0.450489i | 0.0784200 | + | 0.0784200i | ||||
\(34\) | 3.80215 | − | 1.30119i | 0.652064 | − | 0.223152i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9.14726 | − | 7.09134i | 1.52454 | − | 1.18189i | ||||
\(37\) | 1.29227 | − | 1.29227i | 0.212448 | − | 0.212448i | −0.592858 | − | 0.805307i | \(-0.702001\pi\) |
0.805307 | + | 0.592858i | \(0.202001\pi\) | |||||||
\(38\) | −1.11487 | − | 0.546356i | −0.180855 | − | 0.0886306i | ||||
\(39\) | −18.0230 | −2.88599 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.91481 | 0.455217 | 0.227608 | − | 0.973753i | \(-0.426909\pi\) | ||||
0.227608 | + | 0.973753i | \(0.426909\pi\) | |||||||
\(42\) | 3.76441 | + | 1.84480i | 0.580861 | + | 0.284659i | ||||
\(43\) | 2.06108 | − | 2.06108i | 0.314312 | − | 0.314312i | −0.532265 | − | 0.846578i | \(-0.678659\pi\) |
0.846578 | + | 0.532265i | \(0.178659\pi\) | |||||||
\(44\) | −0.339713 | + | 0.263360i | −0.0512136 | + | 0.0397030i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.170757 | + | 0.0584371i | −0.0251768 | + | 0.00861609i | ||||
\(47\) | 4.88813 | + | 4.88813i | 0.713007 | + | 0.713007i | 0.967163 | − | 0.254156i | \(-0.0817977\pi\) |
−0.254156 | + | 0.967163i | \(0.581798\pi\) | |||||||
\(48\) | 6.03021 | + | 10.2093i | 0.870386 | + | 1.47358i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.42336i | 1.17951i | ||||||||
\(52\) | 1.52736 | − | 12.0638i | 0.211807 | − | 1.67294i | ||||
\(53\) | 2.77420 | + | 2.77420i | 0.381066 | + | 0.381066i | 0.871486 | − | 0.490420i | \(-0.163157\pi\) |
−0.490420 | + | 0.871486i | \(0.663157\pi\) | |||||||
\(54\) | 3.78304 | + | 11.0543i | 0.514807 | + | 1.50430i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.55384 | + | 2.36338i | −0.207641 | + | 0.315820i | ||||
\(57\) | 1.84015 | − | 1.84015i | 0.243734 | − | 0.243734i | ||||
\(58\) | −2.50864 | + | 5.11901i | −0.329401 | + | 0.672159i | ||||
\(59\) | 10.4920 | 1.36594 | 0.682972 | − | 0.730445i | \(-0.260687\pi\) | ||||
0.682972 | + | 0.730445i | \(0.260687\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.32686 | −1.06615 | −0.533073 | − | 0.846069i | \(-0.678963\pi\) | ||||
−0.533073 | + | 0.846069i | \(0.678963\pi\) | |||||||
\(62\) | −5.35309 | + | 10.9232i | −0.679843 | + | 1.38725i | ||||
\(63\) | −4.09206 | + | 4.09206i | −0.515551 | + | 0.515551i | ||||
\(64\) | −7.34464 | + | 3.17116i | −0.918080 | + | 0.396395i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.291726 | − | 0.852442i | −0.0359090 | − | 0.104928i | ||||
\(67\) | 0.555822 | + | 0.555822i | 0.0679045 | + | 0.0679045i | 0.740243 | − | 0.672339i | \(-0.234710\pi\) |
−0.672339 | + | 0.740243i | \(0.734710\pi\) | |||||||
\(68\) | −5.63820 | − | 0.713837i | −0.683732 | − | 0.0865654i | ||||
\(69\) | − | 0.378298i | − | 0.0455418i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.75036i | 0.207729i | 0.994591 | + | 0.103865i | \(0.0331209\pi\) | ||||
−0.994591 | + | 0.103865i | \(0.966879\pi\) | |||||||
\(72\) | −16.0295 | + | 3.31270i | −1.88910 | + | 0.390405i | ||||
\(73\) | −4.18728 | − | 4.18728i | −0.490084 | − | 0.490084i | 0.418249 | − | 0.908333i | \(-0.362644\pi\) |
−0.908333 | + | 0.418249i | \(0.862644\pi\) | |||||||
\(74\) | −2.44532 | + | 0.836846i | −0.284262 | + | 0.0972813i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.07577 | + | 1.38765i | 0.123399 | + | 0.159175i | ||||
\(77\) | 0.151972 | − | 0.151972i | 0.0173188 | − | 0.0173188i | ||||
\(78\) | 22.8877 | + | 11.2165i | 2.59153 | + | 1.27002i | ||||
\(79\) | 12.4127 | 1.39654 | 0.698270 | − | 0.715834i | \(-0.253953\pi\) | ||||
0.698270 | + | 0.715834i | \(0.253953\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.12875 | −0.792083 | ||||||||
\(82\) | −3.70157 | − | 1.81401i | −0.408770 | − | 0.200324i | ||||
\(83\) | −5.30716 | + | 5.30716i | −0.582537 | + | 0.582537i | −0.935600 | − | 0.353063i | \(-0.885140\pi\) |
0.353063 | + | 0.935600i | \(0.385140\pi\) | |||||||
\(84\) | −3.63239 | − | 4.68550i | −0.396327 | − | 0.511230i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.90010 | + | 1.33471i | −0.420559 | + | 0.143925i | ||||
\(87\) | −8.44922 | − | 8.44922i | −0.905852 | − | 0.905852i | ||||
\(88\) | 0.595307 | − | 0.123028i | 0.0634599 | − | 0.0131148i | ||||
\(89\) | 12.7409i | 1.35053i | 0.737576 | + | 0.675264i | \(0.235971\pi\) | ||||
−0.737576 | + | 0.675264i | \(0.764029\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.08003i | 0.637361i | ||||||||
\(92\) | 0.253215 | + | 0.0320589i | 0.0263995 | + | 0.00334237i | ||||
\(93\) | −18.0294 | − | 18.0294i | −1.86956 | − | 1.86956i | ||||
\(94\) | −3.16544 | − | 9.24961i | −0.326490 | − | 0.954024i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.30422 | − | 16.7178i | −0.133111 | − | 1.70625i | ||||
\(97\) | 2.58579 | − | 2.58579i | 0.262547 | − | 0.262547i | −0.563541 | − | 0.826088i | \(-0.690561\pi\) |
0.826088 | + | 0.563541i | \(0.190561\pi\) | |||||||
\(98\) | 0.622342 | − | 1.26992i | 0.0628660 | − | 0.128281i | ||||
\(99\) | 1.24375 | 0.125002 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.1945 | −1.51190 | −0.755952 | − | 0.654627i | \(-0.772826\pi\) | ||||
−0.755952 | + | 0.654627i | \(0.772826\pi\) | |||||||
\(102\) | 5.24221 | − | 10.6970i | 0.519056 | − | 1.05916i | ||||
\(103\) | 1.08907 | − | 1.08907i | 0.107309 | − | 0.107309i | −0.651414 | − | 0.758723i | \(-0.725824\pi\) |
0.758723 | + | 0.651414i | \(0.225824\pi\) | |||||||
\(104\) | −9.44740 | + | 14.3694i | −0.926394 | + | 1.40904i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.79651 | − | 5.24951i | −0.174492 | − | 0.509877i | ||||
\(107\) | 9.68529 | + | 9.68529i | 0.936312 | + | 0.936312i | 0.998090 | − | 0.0617779i | \(-0.0196771\pi\) |
−0.0617779 | + | 0.998090i | \(0.519677\pi\) | |||||||
\(108\) | 2.07539 | − | 16.3924i | 0.199705 | − | 1.57736i | ||||
\(109\) | − | 12.0416i | − | 1.15337i | −0.816966 | − | 0.576686i | \(-0.804345\pi\) | ||
0.816966 | − | 0.576686i | \(-0.195655\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 5.41740i | − | 0.514197i | ||||||
\(112\) | 3.44408 | − | 2.03428i | 0.325435 | − | 0.192222i | ||||
\(113\) | 3.14409 | + | 3.14409i | 0.295771 | + | 0.295771i | 0.839355 | − | 0.543584i | \(-0.182933\pi\) |
−0.543584 | + | 0.839355i | \(0.682933\pi\) | |||||||
\(114\) | −3.48204 | + | 1.19164i | −0.326123 | + | 0.111607i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.37154 | − | 4.93949i | 0.591583 | − | 0.458620i | ||||
\(117\) | −24.8798 | + | 24.8798i | −2.30014 | + | 2.30014i | ||||
\(118\) | −13.3240 | − | 6.52961i | −1.22657 | − | 0.601100i | ||||
\(119\) | 2.84161 | 0.260490 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9538 | 0.995801 | ||||||||
\(122\) | 10.5744 | + | 5.18215i | 0.957364 | + | 0.469170i | ||||
\(123\) | 6.10965 | − | 6.10965i | 0.550889 | − | 0.550889i | ||||
\(124\) | 13.5960 | − | 10.5402i | 1.22095 | − | 0.946534i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.74323 | − | 2.64992i | 0.689822 | − | 0.236074i | ||||
\(127\) | −2.21268 | − | 2.21268i | −0.196344 | − | 0.196344i | 0.602087 | − | 0.798431i | \(-0.294336\pi\) |
−0.798431 | + | 0.602087i | \(0.794336\pi\) | |||||||
\(128\) | 11.3006 | + | 0.543764i | 0.998844 | + | 0.0480624i | ||||
\(129\) | − | 8.64036i | − | 0.760741i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.71791i | 0.324835i | 0.986722 | + | 0.162418i | \(0.0519292\pi\) | ||||
−0.986722 | + | 0.162418i | \(0.948071\pi\) | |||||||
\(132\) | −0.160042 | + | 1.26408i | −0.0139299 | + | 0.110024i | ||||
\(133\) | −0.620772 | − | 0.620772i | −0.0538277 | − | 0.0538277i | ||||
\(134\) | −0.359937 | − | 1.05176i | −0.0310939 | − | 0.0908582i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.71580 | + | 4.41540i | 0.575875 | + | 0.378618i | ||||
\(137\) | −1.84961 | + | 1.84961i | −0.158023 | + | 0.158023i | −0.781690 | − | 0.623667i | \(-0.785642\pi\) |
0.623667 | + | 0.781690i | \(0.285642\pi\) | |||||||
\(138\) | −0.235431 | + | 0.480408i | −0.0200412 | + | 0.0408950i | ||||
\(139\) | 10.9071 | 0.925130 | 0.462565 | − | 0.886585i | \(-0.346929\pi\) | ||||
0.462565 | + | 0.886585i | \(0.346929\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.4918 | 1.72572 | ||||||||
\(142\) | 1.08932 | − | 2.22281i | 0.0914137 | − | 0.186534i | ||||
\(143\) | 0.923993 | − | 0.923993i | 0.0772682 | − | 0.0772682i | ||||
\(144\) | 22.4178 | + | 5.76898i | 1.86815 | + | 0.480748i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.71158 | + | 7.92342i | 0.224412 | + | 0.655747i | ||||
\(147\) | 2.09607 | + | 2.09607i | 0.172881 | + | 0.172881i | ||||
\(148\) | 3.62615 | + | 0.459097i | 0.298068 | + | 0.0377376i | ||||
\(149\) | − | 11.2422i | − | 0.920997i | −0.887661 | − | 0.460498i | \(-0.847671\pi\) | ||
0.887661 | − | 0.460498i | \(-0.152329\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 9.08107i | − | 0.739007i | −0.929229 | − | 0.369504i | \(-0.879528\pi\) | ||
0.929229 | − | 0.369504i | \(-0.120472\pi\) | |||||||
\(152\) | −0.502541 | − | 2.43170i | −0.0407615 | − | 0.197237i | ||||
\(153\) | 11.6280 | + | 11.6280i | 0.940069 | + | 0.940069i | ||||
\(154\) | −0.287570 | + | 0.0984132i | −0.0231730 | + | 0.00793036i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −22.0851 | − | 28.4880i | −1.76822 | − | 2.28086i | ||||
\(157\) | −14.8107 | + | 14.8107i | −1.18202 | + | 1.18202i | −0.202799 | + | 0.979220i | \(0.565004\pi\) |
−0.979220 | + | 0.202799i | \(0.934996\pi\) | |||||||
\(158\) | −15.7631 | − | 7.72495i | −1.25405 | − | 0.614564i | ||||
\(159\) | 11.6299 | 0.922307 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.127618 | −0.0100577 | ||||||||
\(162\) | 9.05292 | + | 4.43652i | 0.711265 | + | 0.348566i | ||||
\(163\) | 11.2444 | − | 11.2444i | 0.880727 | − | 0.880727i | −0.112882 | − | 0.993608i | \(-0.536008\pi\) |
0.993608 | + | 0.112882i | \(0.0360082\pi\) | |||||||
\(164\) | 3.57176 | + | 4.60728i | 0.278907 | + | 0.359768i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.0425 | − | 3.43679i | 0.779452 | − | 0.266747i | ||||
\(167\) | 12.0570 | + | 12.0570i | 0.932995 | + | 0.932995i | 0.997892 | − | 0.0648970i | \(-0.0206719\pi\) |
−0.0648970 | + | 0.997892i | \(0.520672\pi\) | |||||||
\(168\) | 1.69686 | + | 8.21079i | 0.130916 | + | 0.633476i | ||||
\(169\) | 23.9668i | 1.84360i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 5.08047i | − | 0.388513i | ||||||
\(172\) | 5.78345 | + | 0.732227i | 0.440984 | + | 0.0558318i | ||||
\(173\) | 0.321011 | + | 0.321011i | 0.0244060 | + | 0.0244060i | 0.719204 | − | 0.694798i | \(-0.244506\pi\) |
−0.694798 | + | 0.719204i | \(0.744506\pi\) | |||||||
\(174\) | 5.47151 | + | 15.9881i | 0.414794 | + | 1.21206i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.832556 | − | 0.214249i | −0.0627563 | − | 0.0161497i | ||||
\(177\) | 21.9920 | − | 21.9920i | 1.65302 | − | 1.65302i | ||||
\(178\) | 7.92917 | − | 16.1798i | 0.594316 | − | 1.21273i | ||||
\(179\) | 4.85521 | 0.362895 | 0.181448 | − | 0.983401i | \(-0.441922\pi\) | ||||
0.181448 | + | 0.983401i | \(0.441922\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.88269 | 0.511586 | 0.255793 | − | 0.966732i | \(-0.417663\pi\) | ||||
0.255793 | + | 0.966732i | \(0.417663\pi\) | |||||||
\(182\) | 3.78386 | − | 7.72114i | 0.280478 | − | 0.572329i | ||||
\(183\) | −17.4537 | + | 17.4537i | −1.29022 | + | 1.29022i | ||||
\(184\) | −0.301611 | − | 0.198299i | −0.0222351 | − | 0.0146188i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 11.6754 | + | 34.1163i | 0.856084 | + | 2.50153i | ||||
\(187\) | −0.431844 | − | 0.431844i | −0.0315795 | − | 0.0315795i | ||||
\(188\) | −1.73657 | + | 13.7162i | −0.126653 | + | 1.00036i | ||||
\(189\) | 8.26162i | 0.600944i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.2429i | 1.24765i | 0.781563 | + | 0.623826i | \(0.214423\pi\) | ||||
−0.781563 | + | 0.623826i | \(0.785577\pi\) | |||||||
\(192\) | −8.74792 | + | 22.0419i | −0.631327 | + | 1.59074i | ||||
\(193\) | 14.3334 | + | 14.3334i | 1.03174 | + | 1.03174i | 0.999480 | + | 0.0322597i | \(0.0102704\pi\) |
0.0322597 | + | 0.999480i | \(0.489730\pi\) | |||||||
\(194\) | −4.89299 | + | 1.67450i | −0.351296 | + | 0.120222i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.58065 | + | 1.22538i | −0.112903 | + | 0.0875273i | ||||
\(197\) | 12.9394 | − | 12.9394i | 0.921891 | − | 0.921891i | −0.0752724 | − | 0.997163i | \(-0.523983\pi\) |
0.997163 | + | 0.0752724i | \(0.0239826\pi\) | |||||||
\(198\) | −1.57947 | − | 0.774040i | −0.112248 | − | 0.0550086i | ||||
\(199\) | −21.8858 | −1.55144 | −0.775720 | − | 0.631077i | \(-0.782613\pi\) | ||||
−0.775720 | + | 0.631077i | \(0.782613\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.33009 | 0.164352 | ||||||||
\(202\) | 19.2957 | + | 9.45614i | 1.35764 | + | 0.665332i | ||||
\(203\) | −2.85033 | + | 2.85033i | −0.200054 | + | 0.200054i | ||||
\(204\) | −13.3143 | + | 10.3218i | −0.932190 | + | 0.722673i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.06081 | + | 0.705257i | −0.143583 | + | 0.0491376i | ||||
\(207\) | −0.522222 | − | 0.522222i | −0.0362969 | − | 0.0362969i | ||||
\(208\) | 20.9401 | − | 12.3685i | 1.45194 | − | 0.857602i | ||||
\(209\) | 0.188679i | 0.0130512i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3.39701i | − | 0.233860i | −0.993140 | − | 0.116930i | \(-0.962695\pi\) | ||
0.993140 | − | 0.116930i | \(-0.0373053\pi\) | |||||||
\(212\) | −0.985571 | + | 7.78448i | −0.0676893 | + | 0.534640i | ||||
\(213\) | 3.66888 | + | 3.66888i | 0.251387 | + | 0.251387i | ||||
\(214\) | −6.27196 | − | 18.3271i | −0.428742 | − | 1.25281i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −12.8372 | + | 19.5254i | −0.873464 | + | 1.32853i | ||||
\(217\) | −6.08220 | + | 6.08220i | −0.412886 | + | 0.412886i | ||||
\(218\) | −7.49397 | + | 15.2918i | −0.507555 | + | 1.03569i | ||||
\(219\) | −17.5537 | −1.18617 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.2771 | 1.16218 | ||||||||
\(222\) | −3.37147 | + | 6.87965i | −0.226278 | + | 0.461732i | ||||
\(223\) | 19.7618 | − | 19.7618i | 1.32335 | − | 1.32335i | 0.412300 | − | 0.911048i | \(-0.364725\pi\) |
0.911048 | − | 0.412300i | \(-0.135275\pi\) | |||||||
\(224\) | −5.63972 | + | 0.439976i | −0.376820 | + | 0.0293972i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.03604 | − | 5.94944i | −0.135435 | − | 0.395751i | ||||
\(227\) | −14.7580 | − | 14.7580i | −0.979521 | − | 0.979521i | 0.0202733 | − | 0.999794i | \(-0.493546\pi\) |
−0.999794 | + | 0.0202733i | \(0.993546\pi\) | |||||||
\(228\) | 5.16351 | + | 0.653738i | 0.341962 | + | 0.0432948i | ||||
\(229\) | − | 3.25813i | − | 0.215303i | −0.994189 | − | 0.107652i | \(-0.965667\pi\) | ||
0.994189 | − | 0.107652i | \(-0.0343331\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 0.637087i | − | 0.0419173i | ||||||
\(232\) | −11.1654 | + | 2.30746i | −0.733043 | + | 0.151492i | ||||
\(233\) | −4.88513 | − | 4.88513i | −0.320035 | − | 0.320035i | 0.528745 | − | 0.848781i | \(-0.322663\pi\) |
−0.848781 | + | 0.528745i | \(0.822663\pi\) | |||||||
\(234\) | 47.0791 | − | 16.1116i | 3.07766 | − | 1.05325i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.8567 | + | 16.5841i | 0.836901 | + | 1.07954i | ||||
\(237\) | 26.0180 | − | 26.0180i | 1.69005 | − | 1.69005i | ||||
\(238\) | −3.60861 | − | 1.76845i | −0.233911 | − | 0.114632i | ||||
\(239\) | 10.2770 | 0.664761 | 0.332380 | − | 0.943145i | \(-0.392148\pi\) | ||||
0.332380 | + | 0.943145i | \(0.392148\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.78849 | 0.308454 | 0.154227 | − | 0.988035i | \(-0.450711\pi\) | ||||
0.154227 | + | 0.988035i | \(0.450711\pi\) | |||||||
\(242\) | −13.9104 | − | 6.81701i | −0.894197 | − | 0.438214i | ||||
\(243\) | 2.58317 | − | 2.58317i | 0.165710 | − | 0.165710i | ||||
\(244\) | −10.2036 | − | 13.1618i | −0.653218 | − | 0.842599i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.5611 | + | 3.95647i | −0.737106 | + | 0.252255i | ||||
\(247\) | −3.77431 | − | 3.77431i | −0.240154 | − | 0.240154i | ||||
\(248\) | −23.8253 | + | 4.92380i | −1.51291 | + | 0.312661i | ||||
\(249\) | 22.2484i | 1.40994i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 26.2656i | − | 1.65787i | −0.559347 | − | 0.828934i | \(-0.688948\pi\) | ||
0.559347 | − | 0.828934i | \(-0.311052\pi\) | |||||||
\(252\) | −11.4824 | − | 1.45376i | −0.723325 | − | 0.0915781i | ||||
\(253\) | 0.0193944 | + | 0.0193944i | 0.00121931 | + | 0.00121931i | ||||
\(254\) | 1.43288 | + | 4.18697i | 0.0899069 | + | 0.262714i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.0125 | − | 7.72339i | −0.875779 | − | 0.482712i | ||||
\(257\) | 16.3898 | − | 16.3898i | 1.02237 | − | 1.02237i | 0.0226254 | − | 0.999744i | \(-0.492798\pi\) |
0.999744 | − | 0.0226254i | \(-0.00720250\pi\) | |||||||
\(258\) | −5.37725 | + | 10.9725i | −0.334773 | + | 0.683121i | ||||
\(259\) | −1.82755 | −0.113558 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −23.3274 | −1.44393 | ||||||||
\(262\) | 2.31381 | − | 4.72144i | 0.142948 | − | 0.291691i | ||||
\(263\) | 4.21519 | − | 4.21519i | 0.259920 | − | 0.259920i | −0.565102 | − | 0.825021i | \(-0.691163\pi\) |
0.825021 | + | 0.565102i | \(0.191163\pi\) | |||||||
\(264\) | 0.989932 | − | 1.50568i | 0.0609261 | − | 0.0926683i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.401997 | + | 1.17466i | 0.0246480 | + | 0.0720231i | ||||
\(267\) | 26.7058 | + | 26.7058i | 1.63437 | + | 1.63437i | ||||
\(268\) | −0.197463 | + | 1.55965i | −0.0120620 | + | 0.0952710i | ||||
\(269\) | − | 0.0668035i | − | 0.00407308i | −0.999998 | − | 0.00203654i | \(-0.999352\pi\) | ||
0.999998 | − | 0.00203654i | \(-0.000648251\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.78031i | − | 0.168892i | −0.996428 | − | 0.0844459i | \(-0.973088\pi\) | ||
0.996428 | − | 0.0844459i | \(-0.0269120\pi\) | |||||||
\(272\) | −5.78063 | − | 9.78672i | −0.350502 | − | 0.593407i | ||||
\(273\) | 12.7442 | + | 12.7442i | 0.771314 | + | 0.771314i | ||||
\(274\) | 3.49994 | − | 1.19776i | 0.211439 | − | 0.0723596i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.597955 | − | 0.463560i | 0.0359927 | − | 0.0279030i | ||||
\(277\) | −4.05025 | + | 4.05025i | −0.243356 | + | 0.243356i | −0.818237 | − | 0.574881i | \(-0.805048\pi\) |
0.574881 | + | 0.818237i | \(0.305048\pi\) | |||||||
\(278\) | −13.8511 | − | 6.78796i | −0.830737 | − | 0.407115i | ||||
\(279\) | −49.7774 | −2.98010 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.9229 | −1.36746 | −0.683732 | − | 0.729734i | \(-0.739644\pi\) | ||||
−0.683732 | + | 0.729734i | \(0.739644\pi\) | |||||||
\(282\) | −26.0228 | − | 12.7529i | −1.54964 | − | 0.759422i | ||||
\(283\) | −0.402053 | + | 0.402053i | −0.0238995 | + | 0.0238995i | −0.718956 | − | 0.695056i | \(-0.755380\pi\) |
0.695056 | + | 0.718956i | \(0.255380\pi\) | |||||||
\(284\) | −2.76669 | + | 2.14486i | −0.164173 | + | 0.127274i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.74843 | + | 0.598356i | −0.103387 | + | 0.0353815i | ||||
\(287\) | −2.06108 | − | 2.06108i | −0.121662 | − | 0.121662i | ||||
\(288\) | −24.8785 | − | 21.2776i | −1.46598 | − | 1.25380i | ||||
\(289\) | 8.92528i | 0.525016i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 10.8400i | − | 0.635453i | ||||||
\(292\) | 1.48759 | − | 11.7496i | 0.0870544 | − | 0.687594i | ||||
\(293\) | 1.43269 | + | 1.43269i | 0.0836989 | + | 0.0836989i | 0.747717 | − | 0.664018i | \(-0.231150\pi\) |
−0.664018 | + | 0.747717i | \(0.731150\pi\) | |||||||
\(294\) | −1.35737 | − | 3.96631i | −0.0791632 | − | 0.231320i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.31920 | − | 2.83972i | −0.251049 | − | 0.165056i | ||||
\(297\) | 1.25553 | − | 1.25553i | 0.0728534 | − | 0.0728534i | ||||
\(298\) | −6.99649 | + | 14.2767i | −0.405296 | + | 0.827025i | ||||
\(299\) | −0.775924 | −0.0448728 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.91481 | −0.168007 | ||||||||
\(302\) | −5.65153 | + | 11.5322i | −0.325209 | + | 0.663604i | ||||
\(303\) | −31.8487 | + | 31.8487i | −1.82966 | + | 1.82966i | ||||
\(304\) | −0.875163 | + | 3.40081i | −0.0501940 | + | 0.195050i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −7.53003 | − | 22.0032i | −0.430463 | − | 1.25784i | ||||
\(307\) | −1.51038 | − | 1.51038i | −0.0862017 | − | 0.0862017i | 0.662691 | − | 0.748893i | \(-0.269414\pi\) |
−0.748893 | + | 0.662691i | \(0.769414\pi\) | |||||||
\(308\) | 0.426437 | + | 0.0539899i | 0.0242985 | + | 0.00307636i | ||||
\(309\) | − | 4.56555i | − | 0.259725i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.7459i | 0.722753i | 0.932420 | + | 0.361376i | \(0.117693\pi\) | ||||
−0.932420 | + | 0.361376i | \(0.882307\pi\) | |||||||
\(312\) | 10.3170 | + | 49.9219i | 0.584083 | + | 2.82627i | ||||
\(313\) | 14.3977 | + | 14.3977i | 0.813804 | + | 0.813804i | 0.985202 | − | 0.171398i | \(-0.0548283\pi\) |
−0.171398 | + | 0.985202i | \(0.554828\pi\) | |||||||
\(314\) | 28.0256 | − | 9.59103i | 1.58158 | − | 0.541253i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.2103 | + | 19.6201i | 0.855648 | + | 1.10372i | ||||
\(317\) | −6.99137 | + | 6.99137i | −0.392674 | + | 0.392674i | −0.875640 | − | 0.482965i | \(-0.839560\pi\) |
0.482965 | + | 0.875640i | \(0.339560\pi\) | |||||||
\(318\) | −14.7690 | − | 7.23774i | −0.828202 | − | 0.405872i | ||||
\(319\) | 0.866339 | 0.0485057 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 40.6021 | 2.26619 | ||||||||
\(322\) | 0.162065 | + | 0.0794222i | 0.00903152 | + | 0.00442603i | ||||
\(323\) | −1.76399 | + | 1.76399i | −0.0981509 | + | 0.0981509i | ||||
\(324\) | −8.73544 | − | 11.2680i | −0.485302 | − | 0.626001i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −21.2773 | + | 7.28158i | −1.17844 | + | 0.403290i | ||||
\(327\) | −25.2400 | − | 25.2400i | −1.39578 | − | 1.39578i | ||||
\(328\) | −1.66853 | − | 8.07372i | −0.0921294 | − | 0.445797i | ||||
\(329\) | − | 6.91286i | − | 0.381118i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 29.3504i | − | 1.61324i | −0.591069 | − | 0.806621i | \(-0.701294\pi\) | ||
0.591069 | − | 0.806621i | \(-0.298706\pi\) | |||||||
\(332\) | −14.8920 | − | 1.88544i | −0.817307 | − | 0.103477i | ||||
\(333\) | −7.47844 | − | 7.47844i | −0.409816 | − | 0.409816i | ||||
\(334\) | −7.80779 | − | 22.8149i | −0.427224 | − | 1.24837i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.95504 | − | 11.4831i | 0.161211 | − | 0.626452i | ||||
\(337\) | −21.9434 | + | 21.9434i | −1.19533 | + | 1.19533i | −0.219784 | + | 0.975549i | \(0.570535\pi\) |
−0.975549 | + | 0.219784i | \(0.929465\pi\) | |||||||
\(338\) | 14.9155 | − | 30.4359i | 0.811298 | − | 1.65549i | ||||
\(339\) | 13.1805 | 0.715866 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.84864 | 0.100110 | ||||||||
\(342\) | −3.16179 | + | 6.45177i | −0.170970 | + | 0.348872i | ||||
\(343\) | 0.707107 | − | 0.707107i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | −6.88881 | − | 4.52915i | −0.371420 | − | 0.244195i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.207879 | − | 0.607435i | −0.0111756 | − | 0.0326559i | ||||
\(347\) | −5.74445 | − | 5.74445i | −0.308378 | − | 0.308378i | 0.535902 | − | 0.844280i | \(-0.319972\pi\) |
−0.844280 | + | 0.535902i | \(0.819972\pi\) | |||||||
\(348\) | 3.00170 | − | 23.7087i | 0.160908 | − | 1.27092i | ||||
\(349\) | 8.46417i | 0.453076i | 0.974002 | + | 0.226538i | \(0.0727408\pi\) | ||||
−0.974002 | + | 0.226538i | \(0.927259\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 50.2309i | 2.68113i | ||||||||
\(352\) | 0.923941 | + | 0.790213i | 0.0492462 | + | 0.0421185i | ||||
\(353\) | −14.7063 | − | 14.7063i | −0.782739 | − | 0.782739i | 0.197553 | − | 0.980292i | \(-0.436700\pi\) |
−0.980292 | + | 0.197553i | \(0.936700\pi\) | |||||||
\(354\) | −41.6146 | + | 14.2415i | −2.21179 | + | 0.756928i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −20.1388 | + | 15.6124i | −1.06735 | + | 0.827457i | ||||
\(357\) | 5.95621 | − | 5.95621i | 0.315236 | − | 0.315236i | ||||
\(358\) | −6.16571 | − | 3.02160i | −0.325868 | − | 0.159696i | ||||
\(359\) | 23.5648 | 1.24370 | 0.621851 | − | 0.783135i | \(-0.286381\pi\) | ||||
0.621851 | + | 0.783135i | \(0.286381\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.2293 | −0.959436 | ||||||||
\(362\) | −8.74045 | − | 4.28338i | −0.459388 | − | 0.225130i | ||||
\(363\) | 22.9600 | − | 22.9600i | 1.20509 | − | 1.20509i | ||||
\(364\) | −9.61038 | + | 7.45036i | −0.503721 | + | 0.390505i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 33.0269 | − | 11.3026i | 1.72635 | − | 0.590797i | ||||
\(367\) | 3.77172 | + | 3.77172i | 0.196882 | + | 0.196882i | 0.798662 | − | 0.601780i | \(-0.205542\pi\) |
−0.601780 | + | 0.798662i | \(0.705542\pi\) | |||||||
\(368\) | 0.259612 | + | 0.439528i | 0.0135332 | + | 0.0229120i | ||||
\(369\) | − | 16.8681i | − | 0.878120i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 3.92331i | − | 0.203688i | ||||||
\(372\) | 6.40519 | − | 50.5911i | 0.332094 | − | 2.62302i | ||||
\(373\) | 22.7964 | + | 22.7964i | 1.18035 | + | 1.18035i | 0.979653 | + | 0.200699i | \(0.0643213\pi\) |
0.200699 | + | 0.979653i | \(0.435679\pi\) | |||||||
\(374\) | 0.279652 | + | 0.817160i | 0.0144604 | + | 0.0422543i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.7415 | − | 16.3377i | 0.553950 | − | 0.842554i | ||||
\(377\) | −17.3301 | + | 17.3301i | −0.892546 | + | 0.892546i | ||||
\(378\) | 5.14155 | − | 10.4916i | 0.264453 | − | 0.539629i | ||||
\(379\) | 3.18566 | 0.163637 | 0.0818183 | − | 0.996647i | \(-0.473927\pi\) | ||||
0.0818183 | + | 0.996647i | \(0.473927\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.27589 | −0.475218 | ||||||||
\(382\) | 10.7310 | − | 21.8971i | 0.549044 | − | 1.12035i | ||||
\(383\) | −19.9331 | + | 19.9331i | −1.01853 | + | 1.01853i | −0.0187081 | + | 0.999825i | \(0.505955\pi\) |
−0.999825 | + | 0.0187081i | \(0.994045\pi\) | |||||||
\(384\) | 24.8267 | − | 22.5472i | 1.26693 | − | 1.15061i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.28195 | − | 27.1225i | −0.472439 | − | 1.38050i | ||||
\(387\) | −11.9276 | − | 11.9276i | −0.606313 | − | 0.606313i | ||||
\(388\) | 7.25580 | + | 0.918636i | 0.368357 | + | 0.0466367i | ||||
\(389\) | 16.3461i | 0.828781i | 0.910099 | + | 0.414391i | \(0.136005\pi\) | ||||
−0.910099 | + | 0.414391i | \(0.863995\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.362641i | 0.0183395i | ||||||||
\(392\) | 2.76990 | − | 0.572433i | 0.139901 | − | 0.0289122i | ||||
\(393\) | 7.79301 | + | 7.79301i | 0.393105 | + | 0.393105i | ||||
\(394\) | −24.4846 | + | 8.37921i | −1.23352 | + | 0.422139i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.52407 | + | 1.96593i | 0.0765876 | + | 0.0987919i | ||||
\(397\) | 10.7408 | − | 10.7408i | 0.539067 | − | 0.539067i | −0.384188 | − | 0.923255i | \(-0.625519\pi\) |
0.923255 | + | 0.384188i | \(0.125519\pi\) | |||||||
\(398\) | 27.7931 | + | 13.6204i | 1.39314 | + | 0.682730i | ||||
\(399\) | −2.60236 | −0.130281 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.7605 | 1.18654 | 0.593271 | − | 0.805003i | \(-0.297836\pi\) | ||||
0.593271 | + | 0.805003i | \(0.297836\pi\) | |||||||
\(402\) | −2.95902 | − | 1.45011i | −0.147583 | − | 0.0723250i | ||||
\(403\) | −36.9800 | + | 36.9800i | −1.84210 | + | 1.84210i | ||||
\(404\) | −18.6190 | − | 24.0170i | −0.926330 | − | 1.19489i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.39357 | − | 1.84581i | 0.267678 | − | 0.0916058i | ||||
\(407\) | 0.277736 | + | 0.277736i | 0.0137669 | + | 0.0137669i | ||||
\(408\) | 23.3318 | − | 4.82181i | 1.15510 | − | 0.238715i | ||||
\(409\) | − | 22.5684i | − | 1.11593i | −0.829863 | − | 0.557967i | \(-0.811582\pi\) | ||
0.829863 | − | 0.557967i | \(-0.188418\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.75384i | 0.382469i | ||||||||
\(412\) | 3.05596 | + | 0.386907i | 0.150557 | + | 0.0190615i | ||||
\(413\) | −7.41897 | − | 7.41897i | −0.365064 | − | 0.365064i | ||||
\(414\) | 0.338178 | + | 0.988179i | 0.0166206 | + | 0.0485663i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −34.2897 | + | 2.67507i | −1.68119 | + | 0.131156i | ||||
\(417\) | 22.8621 | − | 22.8621i | 1.11956 | − | 1.11956i | ||||
\(418\) | 0.117423 | − | 0.239607i | 0.00574335 | − | 0.0117196i | ||||
\(419\) | −12.4351 | −0.607495 | −0.303748 | − | 0.952753i | \(-0.598238\pi\) | ||||
−0.303748 | + | 0.952753i | \(0.598238\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.2799 | −1.52449 | −0.762244 | − | 0.647289i | \(-0.775902\pi\) | ||||
−0.762244 | + | 0.647289i | \(0.775902\pi\) | |||||||
\(422\) | −2.11410 | + | 4.31392i | −0.102913 | + | 0.209998i | ||||
\(423\) | 28.2878 | − | 28.2878i | 1.37540 | − | 1.37540i | ||||
\(424\) | 6.09620 | − | 9.27229i | 0.296058 | − | 0.450302i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.37588 | − | 6.94246i | −0.115112 | − | 0.336364i | ||||
\(427\) | 5.88798 | + | 5.88798i | 0.284939 | + | 0.284939i | ||||
\(428\) | −3.44083 | + | 27.1772i | −0.166319 | + | 1.31366i | ||||
\(429\) | − | 3.87351i | − | 0.187015i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.1288i | 0.921402i | 0.887556 | + | 0.460701i | \(0.152402\pi\) | ||||
−0.887556 | + | 0.460701i | \(0.847598\pi\) | |||||||
\(432\) | 28.4537 | − | 16.8065i | 1.36898 | − | 0.808602i | ||||
\(433\) | −4.87478 | − | 4.87478i | −0.234267 | − | 0.234267i | 0.580204 | − | 0.814471i | \(-0.302973\pi\) |
−0.814471 | + | 0.580204i | \(0.802973\pi\) | |||||||
\(434\) | 11.5091 | − | 3.93869i | 0.552454 | − | 0.189063i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19.0334 | − | 14.7555i | 0.911536 | − | 0.706661i | ||||
\(437\) | 0.0792218 | − | 0.0792218i | 0.00378969 | − | 0.00378969i | ||||
\(438\) | 22.2917 | + | 10.9244i | 1.06514 | + | 0.521987i | ||||
\(439\) | −32.7840 | −1.56470 | −0.782349 | − | 0.622841i | \(-0.785978\pi\) | ||||
−0.782349 | + | 0.622841i | \(0.785978\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.78704 | 0.275574 | ||||||||
\(442\) | −21.9404 | − | 10.7522i | −1.04360 | − | 0.511431i | ||||
\(443\) | 8.51358 | − | 8.51358i | 0.404493 | − | 0.404493i | −0.475320 | − | 0.879813i | \(-0.657668\pi\) |
0.879813 | + | 0.475320i | \(0.157668\pi\) | |||||||
\(444\) | 8.56299 | − | 6.63838i | 0.406381 | − | 0.315044i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −37.3945 | + | 12.7973i | −1.77068 | + | 0.605968i | ||||
\(447\) | −23.5645 | − | 23.5645i | −1.11456 | − | 1.11456i | ||||
\(448\) | 7.43579 | + | 2.95110i | 0.351308 | + | 0.139426i | ||||
\(449\) | 5.52889i | 0.260925i | 0.991453 | + | 0.130462i | \(0.0416462\pi\) | ||||
−0.991453 | + | 0.130462i | \(0.958354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.626452i | 0.0294985i | ||||||||
\(452\) | −1.11698 | + | 8.82241i | −0.0525383 | + | 0.414971i | ||||
\(453\) | −19.0346 | − | 19.0346i | −0.894323 | − | 0.894323i | ||||
\(454\) | 9.55691 | + | 27.9259i | 0.448528 | + | 1.31063i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.15038 | − | 4.04366i | −0.288018 | − | 0.189362i | ||||
\(457\) | −19.0996 | + | 19.0996i | −0.893440 | + | 0.893440i | −0.994845 | − | 0.101405i | \(-0.967666\pi\) |
0.101405 | + | 0.994845i | \(0.467666\pi\) | |||||||
\(458\) | −2.02767 | + | 4.13755i | −0.0947467 | + | 0.193335i | ||||
\(459\) | 23.4763 | 1.09578 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.24886 | −0.384188 | −0.192094 | − | 0.981377i | \(-0.561528\pi\) | ||||
−0.192094 | + | 0.981377i | \(0.561528\pi\) | |||||||
\(462\) | −0.396486 | + | 0.809049i | −0.0184462 | + | 0.0376403i | ||||
\(463\) | −15.4884 | + | 15.4884i | −0.719806 | + | 0.719806i | −0.968565 | − | 0.248759i | \(-0.919977\pi\) |
0.248759 | + | 0.968565i | \(0.419977\pi\) | |||||||
\(464\) | 15.6152 | + | 4.01839i | 0.724915 | + | 0.186549i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.16349 | + | 9.24392i | 0.146546 | + | 0.428217i | ||||
\(467\) | 27.7817 | + | 27.7817i | 1.28558 | + | 1.28558i | 0.937442 | + | 0.348141i | \(0.113187\pi\) |
0.348141 | + | 0.937442i | \(0.386813\pi\) | |||||||
\(468\) | −69.8135 | − | 8.83889i | −3.22713 | − | 0.408578i | ||||
\(469\) | − | 0.786052i | − | 0.0362965i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 62.0885i | 2.86089i | ||||||||
\(472\) | −6.00597 | − | 29.0618i | −0.276447 | − | 1.33768i | ||||
\(473\) | 0.442969 | + | 0.442969i | 0.0203677 | + | 0.0203677i | ||||
\(474\) | −49.2328 | + | 16.8486i | −2.26134 | + | 0.773883i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.48205 | + | 4.49157i | 0.159600 | + | 0.205871i | ||||
\(477\) | 16.0544 | − | 16.0544i | 0.735082 | − | 0.735082i | ||||
\(478\) | −13.0509 | − | 6.39578i | −0.596934 | − | 0.292536i | ||||
\(479\) | −3.86716 | −0.176695 | −0.0883475 | − | 0.996090i | \(-0.528159\pi\) | ||||
−0.0883475 | + | 0.996090i | \(0.528159\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.1116 | −0.506644 | ||||||||
\(482\) | −6.08099 | − | 2.98008i | −0.276982 | − | 0.135739i | ||||
\(483\) | −0.267497 | + | 0.267497i | −0.0121716 | + | 0.0121716i | ||||
\(484\) | 13.4226 | + | 17.3141i | 0.610118 | + | 0.787004i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4.88803 | + | 1.67280i | −0.221725 | + | 0.0758797i | ||||
\(487\) | 0.314754 | + | 0.314754i | 0.0142629 | + | 0.0142629i | 0.714202 | − | 0.699939i | \(-0.246790\pi\) |
−0.699939 | + | 0.714202i | \(0.746790\pi\) | |||||||
\(488\) | 4.76657 | + | 23.0645i | 0.215773 | + | 1.04408i | ||||
\(489\) | − | 47.1380i | − | 2.13165i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 40.4240i | 1.82431i | 0.409844 | + | 0.912156i | \(0.365583\pi\) | ||||
−0.409844 | + | 0.912156i | \(0.634417\pi\) | |||||||
\(492\) | 17.1439 | + | 2.17054i | 0.772905 | + | 0.0978553i | ||||
\(493\) | 8.09952 | + | 8.09952i | 0.364784 | + | 0.364784i | ||||
\(494\) | 2.44415 | + | 7.14198i | 0.109968 | + | 0.321333i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 33.3205 | + | 8.57467i | 1.49613 | + | 0.385014i | ||||
\(497\) | 1.23769 | − | 1.23769i | 0.0555180 | − | 0.0555180i | ||||
\(498\) | 13.8461 | − | 28.2536i | 0.620459 | − | 1.26608i | ||||
\(499\) | 31.7874 | 1.42300 | 0.711501 | − | 0.702686i | \(-0.248016\pi\) | ||||
0.711501 | + | 0.702686i | \(0.248016\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 50.5445 | 2.25816 | ||||||||
\(502\) | −16.3461 | + | 33.3551i | −0.729564 | + | 1.48871i | ||||
\(503\) | −6.28613 | + | 6.28613i | −0.280285 | + | 0.280285i | −0.833222 | − | 0.552938i | \(-0.813507\pi\) |
0.552938 | + | 0.833222i | \(0.313507\pi\) | |||||||
\(504\) | 13.6770 | + | 8.99214i | 0.609222 | + | 0.400542i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.0125593 | − | 0.0366992i | −0.000558330 | − | 0.00163148i | ||||
\(507\) | 50.2362 | + | 50.2362i | 2.23107 | + | 2.23107i | ||||
\(508\) | 0.786085 | − | 6.20885i | 0.0348769 | − | 0.275473i | ||||
\(509\) | 3.09416i | 0.137146i | 0.997646 | + | 0.0685730i | \(0.0218446\pi\) | ||||
−0.997646 | + | 0.0685730i | \(0.978155\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.92171i | 0.261961i | ||||||||
\(512\) | 12.9881 | + | 18.5286i | 0.573998 | + | 0.818857i | ||||
\(513\) | −5.12858 | − | 5.12858i | −0.226432 | − | 0.226432i | ||||
\(514\) | −31.0138 | + | 10.6137i | −1.36796 | + | 0.468149i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 13.6573 | − | 10.5877i | 0.601231 | − | 0.466099i | ||||
\(517\) | −1.05056 | + | 1.05056i | −0.0462035 | + | 0.0462035i | ||||
\(518\) | 2.32084 | + | 1.13736i | 0.101972 | + | 0.0499728i | ||||
\(519\) | 1.34572 | 0.0590707 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.11386 | 0.224042 | 0.112021 | − | 0.993706i | \(-0.464268\pi\) | ||||
0.112021 | + | 0.993706i | \(0.464268\pi\) | |||||||
\(522\) | 29.6239 | + | 14.5176i | 1.29660 | + | 0.635420i | ||||
\(523\) | −17.9247 | + | 17.9247i | −0.783791 | + | 0.783791i | −0.980468 | − | 0.196677i | \(-0.936985\pi\) |
0.196677 | + | 0.980468i | \(0.436985\pi\) | |||||||
\(524\) | −5.87669 | + | 4.55586i | −0.256725 | + | 0.199024i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.97623 | + | 2.72966i | −0.347780 | + | 0.119019i | ||||
\(527\) | 17.2832 | + | 17.2832i | 0.752868 | + | 0.752868i | ||||
\(528\) | −2.19418 | + | 1.29602i | −0.0954895 | + | 0.0564018i | ||||
\(529\) | 22.9837i | 0.999292i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 60.7177i | − | 2.63493i | ||||||
\(532\) | 0.220537 | − | 1.74190i | 0.00956150 | − | 0.0755210i | ||||
\(533\) | −12.5314 | − | 12.5314i | −0.542797 | − | 0.542797i | ||||
\(534\) | −17.2940 | − | 50.5343i | −0.748386 | − | 2.18683i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.22140 | − | 1.85774i | 0.0527564 | − | 0.0802422i | ||||
\(537\) | 10.1769 | − | 10.1769i | 0.439164 | − | 0.439164i | ||||
\(538\) | −0.0415746 | + | 0.0848349i | −0.00179241 | + | 0.00365749i | ||||
\(539\) | −0.214920 | −0.00925728 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.00395 | 0.0431633 | 0.0215817 | − | 0.999767i | \(-0.493130\pi\) | ||||
0.0215817 | + | 0.999767i | \(0.493130\pi\) | |||||||
\(542\) | −1.73030 | + | 3.53077i | −0.0743229 | + | 0.151659i | ||||
\(543\) | 14.4266 | − | 14.4266i | 0.619105 | − | 0.619105i | ||||
\(544\) | 1.25024 | + | 16.0259i | 0.0536036 | + | 0.687103i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.25284 | − | 24.1153i | −0.353189 | − | 1.03204i | ||||
\(547\) | −11.1953 | − | 11.1953i | −0.478676 | − | 0.478676i | 0.426032 | − | 0.904708i | \(-0.359911\pi\) |
−0.904708 | + | 0.426032i | \(0.859911\pi\) | |||||||
\(548\) | −5.19006 | − | 0.657099i | −0.221708 | − | 0.0280699i | ||||
\(549\) | 48.1879i | 2.05661i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 3.53881i | − | 0.150758i | ||||||
\(552\) | −1.04785 | + | 0.216550i | −0.0445993 | + | 0.00921700i | ||||
\(553\) | −8.77712 | − | 8.77712i | −0.373241 | − | 0.373241i | ||||
\(554\) | 7.66412 | − | 2.62285i | 0.325617 | − | 0.111434i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.3654 | + | 17.2403i | 0.566819 | + | 0.731151i | ||||
\(557\) | 7.46496 | − | 7.46496i | 0.316301 | − | 0.316301i | −0.531044 | − | 0.847344i | \(-0.678200\pi\) |
0.847344 | + | 0.531044i | \(0.178200\pi\) | |||||||
\(558\) | 63.2132 | + | 30.9785i | 2.67603 | + | 1.31143i | ||||
\(559\) | −17.7221 | −0.749567 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.81035 | −0.0764331 | ||||||||
\(562\) | 29.1101 | + | 14.2658i | 1.22794 | + | 0.601769i | ||||
\(563\) | 5.26839 | − | 5.26839i | 0.222036 | − | 0.222036i | −0.587319 | − | 0.809355i | \(-0.699817\pi\) |
0.809355 | + | 0.587319i | \(0.199817\pi\) | |||||||
\(564\) | 25.1102 | + | 32.3902i | 1.05733 | + | 1.36387i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.760788 | − | 0.260360i | 0.0319783 | − | 0.0109437i | ||||
\(567\) | 5.04079 | + | 5.04079i | 0.211693 | + | 0.211693i | ||||
\(568\) | 4.84831 | − | 1.00196i | 0.203430 | − | 0.0420414i | ||||
\(569\) | 27.2916i | 1.14413i | 0.820210 | + | 0.572063i | \(0.193857\pi\) | ||||
−0.820210 | + | 0.572063i | \(0.806143\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 6.44056i | − | 0.269529i | −0.990878 | − | 0.134765i | \(-0.956972\pi\) | ||
0.990878 | − | 0.134765i | \(-0.0430278\pi\) | |||||||
\(572\) | 2.59275 | + | 0.328261i | 0.108408 | + | 0.0137253i | ||||
\(573\) | 36.1424 | + | 36.1424i | 1.50987 | + | 1.50987i | ||||
\(574\) | 1.33471 | + | 3.90010i | 0.0557096 | + | 0.162787i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 18.3516 | + | 42.5038i | 0.764652 | + | 1.77099i | ||||
\(577\) | 10.4727 | − | 10.4727i | 0.435984 | − | 0.435984i | −0.454674 | − | 0.890658i | \(-0.650244\pi\) |
0.890658 | + | 0.454674i | \(0.150244\pi\) | |||||||
\(578\) | 5.55457 | − | 11.3344i | 0.231040 | − | 0.471448i | ||||
\(579\) | 60.0876 | 2.49716 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.50546 | 0.311379 | ||||||||
\(582\) | −6.74619 | + | 13.7659i | −0.279639 | + | 0.570616i | ||||
\(583\) | −0.596232 | + | 0.596232i | −0.0246934 | + | 0.0246934i | ||||
\(584\) | −9.20139 | + | 13.9953i | −0.380756 | + | 0.579128i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.927778 | − | 2.71103i | −0.0383262 | − | 0.111992i | ||||
\(587\) | −15.0807 | − | 15.0807i | −0.622447 | − | 0.622447i | 0.323710 | − | 0.946156i | \(-0.395070\pi\) |
−0.946156 | + | 0.323710i | \(0.895070\pi\) | |||||||
\(588\) | −0.744658 | + | 5.88164i | −0.0307092 | + | 0.242555i | ||||
\(589\) | − | 7.55131i | − | 0.311146i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 54.2436i | − | 2.23129i | ||||||
\(592\) | 3.71775 | + | 6.29423i | 0.152799 | + | 0.258691i | ||||
\(593\) | −25.3176 | − | 25.3176i | −1.03967 | − | 1.03967i | −0.999180 | − | 0.0404897i | \(-0.987108\pi\) |
−0.0404897 | − | 0.999180i | \(-0.512892\pi\) | |||||||
\(594\) | −2.37579 | + | 0.813053i | −0.0974800 | + | 0.0333600i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.7699 | − | 13.7760i | 0.727884 | − | 0.564286i | ||||
\(597\) | −45.8741 | + | 45.8741i | −1.87750 | + | 1.87750i | ||||
\(598\) | 0.985359 | + | 0.482890i | 0.0402943 | + | 0.0197468i | ||||
\(599\) | −22.3540 | −0.913359 | −0.456680 | − | 0.889631i | \(-0.650961\pi\) | ||||
−0.456680 | + | 0.889631i | \(0.650961\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.6119 | −1.77897 | −0.889483 | − | 0.456969i | \(-0.848935\pi\) | ||||
−0.889483 | + | 0.456969i | \(0.848935\pi\) | |||||||
\(602\) | 3.70157 | + | 1.81401i | 0.150865 | + | 0.0739334i | ||||
\(603\) | 3.21657 | − | 3.21657i | 0.130989 | − | 0.130989i | ||||
\(604\) | 14.3540 | − | 11.1278i | 0.584054 | − | 0.452783i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 60.2660 | − | 20.6244i | 2.44814 | − | 0.837811i | ||||
\(607\) | −16.8823 | − | 16.8823i | −0.685232 | − | 0.685232i | 0.275943 | − | 0.961174i | \(-0.411010\pi\) |
−0.961174 | + | 0.275943i | \(0.911010\pi\) | |||||||
\(608\) | 3.22785 | − | 3.77410i | 0.130907 | − | 0.153060i | ||||
\(609\) | 11.9490i | 0.484198i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 42.0304i | − | 1.70037i | ||||||
\(612\) | −4.13101 | + | 32.6285i | −0.166986 | + | 1.31893i | ||||
\(613\) | 20.8003 | + | 20.8003i | 0.840115 | + | 0.840115i | 0.988874 | − | 0.148759i | \(-0.0475278\pi\) |
−0.148759 | + | 0.988874i | \(0.547528\pi\) | |||||||
\(614\) | 0.978084 | + | 2.85802i | 0.0394722 | + | 0.115340i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.507939 | − | 0.333952i | −0.0204655 | − | 0.0134553i | ||||
\(617\) | −12.8248 | + | 12.8248i | −0.516307 | + | 0.516307i | −0.916452 | − | 0.400145i | \(-0.868960\pi\) |
0.400145 | + | 0.916452i | \(0.368960\pi\) | |||||||
\(618\) | −2.84133 | + | 5.79787i | −0.114295 | + | 0.233224i | ||||
\(619\) | 14.7614 | 0.593309 | 0.296655 | − | 0.954985i | \(-0.404129\pi\) | ||||
0.296655 | + | 0.954985i | \(0.404129\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.05433 | −0.0423090 | ||||||||
\(622\) | 7.93229 | − | 16.1862i | 0.318056 | − | 0.649008i | ||||
\(623\) | 9.00915 | − | 9.00915i | 0.360944 | − | 0.360944i | ||||
\(624\) | 17.9667 | − | 69.8173i | 0.719245 | − | 2.79493i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.32359 | − | 27.2441i | −0.372645 | − | 1.08889i | ||||
\(627\) | 0.395486 | + | 0.395486i | 0.0157942 | + | 0.0157942i | ||||
\(628\) | −41.5591 | − | 5.26168i | −1.65839 | − | 0.209964i | ||||
\(629\) | 5.19318i | 0.207066i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 31.4840i | − | 1.25336i | −0.779278 | − | 0.626678i | \(-0.784414\pi\) | ||
0.779278 | − | 0.626678i | \(-0.215586\pi\) | |||||||
\(632\) | −7.10545 | − | 34.3819i | −0.282640 | − | 1.36764i | ||||
\(633\) | −7.12038 | − | 7.12038i | −0.283010 | − | 0.283010i | ||||
\(634\) | 13.2295 | − | 4.52744i | 0.525410 | − | 0.179808i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 14.2510 | + | 18.3827i | 0.565089 | + | 0.728920i | ||||
\(637\) | 4.29923 | − | 4.29923i | 0.170342 | − | 0.170342i | ||||
\(638\) | −1.10018 | − | 0.539159i | −0.0435565 | − | 0.0213455i | ||||
\(639\) | 10.1294 | 0.400713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.8470 | −0.902403 | −0.451201 | − | 0.892422i | \(-0.649004\pi\) | ||||
−0.451201 | + | 0.892422i | \(0.649004\pi\) | |||||||
\(642\) | −51.5614 | − | 25.2684i | −2.03496 | − | 0.997264i | ||||
\(643\) | 13.3643 | − | 13.3643i | 0.527038 | − | 0.527038i | −0.392650 | − | 0.919688i | \(-0.628442\pi\) |
0.919688 | + | 0.392650i | \(0.128442\pi\) | |||||||
\(644\) | −0.156381 | − | 0.201719i | −0.00616228 | − | 0.00794885i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.33792 | − | 1.14232i | 0.131329 | − | 0.0449438i | ||||
\(647\) | −16.5557 | − | 16.5557i | −0.650872 | − | 0.650872i | 0.302331 | − | 0.953203i | \(-0.402235\pi\) |
−0.953203 | + | 0.302331i | \(0.902235\pi\) | |||||||
\(648\) | 4.08073 | + | 19.7459i | 0.160306 | + | 0.775692i | ||||
\(649\) | 2.25495i | 0.0885144i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25.4975i | 0.999324i | ||||||||
\(652\) | 31.5520 | + | 3.99471i | 1.23567 | + | 0.156445i | ||||
\(653\) | −15.6135 | − | 15.6135i | −0.611004 | − | 0.611004i | 0.332204 | − | 0.943208i | \(-0.392208\pi\) |
−0.943208 | + | 0.332204i | \(0.892208\pi\) | |||||||
\(654\) | 16.3448 | + | 47.7606i | 0.639133 | + | 1.86759i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.90571 | + | 11.2914i | −0.113449 | + | 0.440853i | ||||
\(657\) | −24.2320 | + | 24.2320i | −0.945379 | + | 0.945379i | ||||
\(658\) | −4.30216 | + | 8.77876i | −0.167716 | + | 0.342232i | ||||
\(659\) | −23.8406 | −0.928696 | −0.464348 | − | 0.885653i | \(-0.653711\pi\) | ||||
−0.464348 | + | 0.885653i | \(0.653711\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0247 | 0.856662 | 0.428331 | − | 0.903622i | \(-0.359102\pi\) | ||||
0.428331 | + | 0.903622i | \(0.359102\pi\) | |||||||
\(662\) | −18.2660 | + | 37.2725i | −0.709926 | + | 1.44864i | ||||
\(663\) | 36.2140 | − | 36.2140i | 1.40643 | − | 1.40643i | ||||
\(664\) | 17.7383 | + | 11.6623i | 0.688379 | + | 0.452585i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.84286 | + | 14.1512i | 0.187657 | + | 0.548346i | ||||
\(667\) | −0.363755 | − | 0.363755i | −0.0140846 | − | 0.0140846i | ||||
\(668\) | −4.28339 | + | 33.8321i | −0.165729 | + | 1.30900i | ||||
\(669\) | − | 82.8444i | − | 3.20295i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.78961i | − | 0.0690872i | ||||||
\(672\) | −10.8990 | + | 12.7435i | −0.420440 | + | 0.491591i | ||||
\(673\) | −15.2135 | − | 15.2135i | −0.586437 | − | 0.586437i | 0.350227 | − | 0.936665i | \(-0.386104\pi\) |
−0.936665 | + | 0.350227i | \(0.886104\pi\) | |||||||
\(674\) | 41.5226 | − | 14.2100i | 1.59939 | − | 0.547349i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −37.8830 | + | 29.3685i | −1.45704 | + | 1.12956i | ||||
\(677\) | 8.40158 | − | 8.40158i | 0.322899 | − | 0.322899i | −0.526979 | − | 0.849878i | \(-0.676675\pi\) |
0.849878 | + | 0.526979i | \(0.176675\pi\) | |||||||
\(678\) | −16.7381 | − | 8.20277i | −0.642825 | − | 0.315026i | ||||
\(679\) | −3.65686 | −0.140337 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −61.8676 | −2.37077 | ||||||||
\(682\) | −2.34762 | − | 1.15049i | −0.0898952 | − | 0.0440544i | ||||
\(683\) | 25.3664 | − | 25.3664i | 0.970617 | − | 0.970617i | −0.0289635 | − | 0.999580i | \(-0.509221\pi\) |
0.999580 | + | 0.0289635i | \(0.00922064\pi\) | |||||||
\(684\) | 8.03041 | − | 6.22551i | 0.307051 | − | 0.238038i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.33803 | + | 0.457905i | −0.0510862 | + | 0.0174829i | ||||
\(687\) | −6.82927 | − | 6.82927i | −0.260553 | − | 0.260553i | ||||
\(688\) | 5.92955 | + | 10.0388i | 0.226062 | + | 0.382727i | ||||
\(689\) | − | 23.8539i | − | 0.908760i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.8205i | 1.66701i | 0.552512 | + | 0.833505i | \(0.313669\pi\) | ||||
−0.552512 | + | 0.833505i | \(0.686331\pi\) | |||||||
\(692\) | −0.114043 | + | 0.900764i | −0.00433527 | + | 0.0342419i | ||||
\(693\) | −0.879467 | − | 0.879467i | −0.0334082 | − | 0.0334082i | ||||
\(694\) | 3.71997 | + | 10.8700i | 0.141208 | + | 0.412619i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −18.5668 | + | 28.2401i | −0.703775 | + | 1.07044i | ||||
\(697\) | −5.85678 | + | 5.85678i | −0.221841 | + | 0.221841i | ||||
\(698\) | 5.26760 | − | 10.7488i | 0.199382 | − | 0.406848i | ||||
\(699\) | −20.4792 | −0.774593 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.4455 | 1.45207 | 0.726033 | − | 0.687660i | \(-0.241362\pi\) | ||||
0.726033 | + | 0.687660i | \(0.241362\pi\) | |||||||
\(702\) | 31.2608 | − | 63.7891i | 1.17986 | − | 2.40757i | ||||
\(703\) | 1.13449 | − | 1.13449i | 0.0427882 | − | 0.0427882i | ||||
\(704\) | −0.681547 | − | 1.57851i | −0.0256868 | − | 0.0594925i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.52347 | + | 27.8282i | 0.358420 | + | 1.04733i | ||||
\(707\) | 10.7441 | + | 10.7441i | 0.404073 | + | 0.404073i | ||||
\(708\) | 61.7102 | + | 7.81296i | 2.31921 | + | 0.293629i | ||||
\(709\) | 39.0425i | 1.46627i | 0.680082 | + | 0.733137i | \(0.261944\pi\) | ||||
−0.680082 | + | 0.733137i | \(0.738056\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 71.8330i | − | 2.69395i | ||||||
\(712\) | 35.2909 | − | 7.29329i | 1.32258 | − | 0.273328i | ||||
\(713\) | −0.776200 | − | 0.776200i | −0.0290689 | − | 0.0290689i | ||||
\(714\) | −11.2707 | + | 3.85710i | −0.421795 | + | 0.144348i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.94948 | + | 7.67436i | 0.222343 | + | 0.286804i | ||||
\(717\) | 21.5412 | − | 21.5412i | 0.804473 | − | 0.804473i | ||||
\(718\) | −29.9254 | − | 14.6654i | −1.11680 | − | 0.547306i | ||||
\(719\) | −4.65847 | −0.173732 | −0.0868659 | − | 0.996220i | \(-0.527685\pi\) | ||||
−0.0868659 | + | 0.996220i | \(0.527685\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.54018 | −0.0573593 | ||||||||
\(722\) | 23.1497 | + | 11.3448i | 0.861542 | + | 0.422211i | ||||
\(723\) | 10.0370 | − | 10.0370i | 0.373281 | − | 0.373281i | ||||
\(724\) | 8.43392 | + | 10.8791i | 0.313444 | + | 0.404318i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −43.4462 | + | 14.8683i | −1.61244 | + | 0.551816i | ||||
\(727\) | −8.55868 | − | 8.55868i | −0.317424 | − | 0.317424i | 0.530353 | − | 0.847777i | \(-0.322059\pi\) |
−0.847777 | + | 0.530353i | \(0.822059\pi\) | |||||||
\(728\) | 16.8411 | − | 3.48041i | 0.624171 | − | 0.128993i | ||||
\(729\) | − | 32.2153i | − | 1.19316i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.28274i | 0.306348i | ||||||||
\(732\) | −48.9756 | − | 6.20066i | −1.81019 | − | 0.229183i | ||||
\(733\) | 0.785057 | + | 0.785057i | 0.0289967 | + | 0.0289967i | 0.721456 | − | 0.692460i | \(-0.243473\pi\) |
−0.692460 | + | 0.721456i | \(0.743473\pi\) | |||||||
\(734\) | −2.44248 | − | 7.13708i | −0.0901535 | − | 0.263434i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.0561491 | − | 0.719731i | −0.00206968 | − | 0.0265297i | ||||
\(737\) | −0.119458 | + | 0.119458i | −0.00440028 | + | 0.00440028i | ||||
\(738\) | −10.4977 | + | 21.4211i | −0.386427 | + | 0.788523i | ||||
\(739\) | 4.86588 | 0.178994 | 0.0894972 | − | 0.995987i | \(-0.471474\pi\) | ||||
0.0894972 | + | 0.995987i | \(0.471474\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.8225 | −0.581253 | ||||||||
\(742\) | −2.44164 | + | 4.98228i | −0.0896354 | + | 0.182905i | ||||
\(743\) | 24.8474 | − | 24.8474i | 0.911564 | − | 0.911564i | −0.0848314 | − | 0.996395i | \(-0.527035\pi\) |
0.996395 | + | 0.0848314i | \(0.0270352\pi\) | |||||||
\(744\) | −39.6190 | + | 60.2603i | −1.45250 | + | 2.20925i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14.7624 | − | 43.1367i | −0.540490 | − | 1.57935i | ||||
\(747\) | 30.7128 | + | 30.7128i | 1.12372 | + | 1.12372i | ||||
\(748\) | 0.153418 | − | 1.21176i | 0.00560952 | − | 0.0443065i | ||||
\(749\) | − | 13.6971i | − | 0.500480i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.0268i | 0.730789i | 0.930853 | + | 0.365394i | \(0.119066\pi\) | ||||
−0.930853 | + | 0.365394i | \(0.880934\pi\) | |||||||
\(752\) | −23.8084 | + | 14.0627i | −0.868205 | + | 0.512814i | ||||
\(753\) | −55.0545 | − | 55.0545i | −2.00630 | − | 2.00630i | ||||
\(754\) | 32.7931 | − | 11.2226i | 1.19425 | − | 0.408702i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −13.0587 | + | 10.1236i | −0.474940 | + | 0.368193i | ||||
\(757\) | −10.7543 | + | 10.7543i | −0.390871 | + | 0.390871i | −0.874998 | − | 0.484127i | \(-0.839137\pi\) |
0.484127 | + | 0.874998i | \(0.339137\pi\) | |||||||
\(758\) | −4.04553 | − | 1.98257i | −0.146940 | − | 0.0720102i | ||||
\(759\) | 0.0813040 | 0.00295115 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.6034 | 0.746874 | 0.373437 | − | 0.927655i | \(-0.378179\pi\) | ||||
0.373437 | + | 0.927655i | \(0.378179\pi\) | |||||||
\(762\) | 11.7796 | + | 5.77277i | 0.426730 | + | 0.209125i | ||||
\(763\) | −8.51467 | + | 8.51467i | −0.308252 | + | 0.308252i | ||||
\(764\) | −27.2549 | + | 21.1291i | −0.986048 | + | 0.764426i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 37.7186 | − | 12.9082i | 1.36283 | − | 0.466392i | ||||
\(767\) | −45.1076 | − | 45.1076i | −1.62874 | − | 1.62874i | ||||
\(768\) | −45.5599 | + | 13.1824i | −1.64400 | + | 0.475678i | ||||
\(769\) | − | 9.33534i | − | 0.336641i | −0.985732 | − | 0.168320i | \(-0.946166\pi\) | ||
0.985732 | − | 0.168320i | \(-0.0538343\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 68.7086i | − | 2.47448i | ||||||
\(772\) | −5.09212 | + | 40.2199i | −0.183269 | + | 1.44754i | ||||
\(773\) | 10.3739 | + | 10.3739i | 0.373125 | + | 0.373125i | 0.868614 | − | 0.495489i | \(-0.165011\pi\) |
−0.495489 | + | 0.868614i | \(0.665011\pi\) | |||||||
\(774\) | 7.72401 | + | 22.5701i | 0.277634 | + | 0.811264i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.64256 | − | 5.68218i | −0.310250 | − | 0.203978i | ||||
\(777\) | −3.83068 | + | 3.83068i | −0.137425 | + | 0.137425i | ||||
\(778\) | 10.1729 | − | 20.7582i | 0.364715 | − | 0.744218i | ||||
\(779\) | 2.55892 | 0.0916829 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.376187 | −0.0134610 | ||||||||
\(782\) | 0.225687 | − | 0.460524i | 0.00807053 | − | 0.0164683i | ||||
\(783\) | −23.5484 | + | 23.5484i | −0.841550 | + | 0.841550i | ||||
\(784\) | −3.87379 | − | 0.996878i | −0.138350 | − | 0.0356028i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.04657 | − | 14.7464i | −0.180005 | − | 0.525986i | ||||
\(787\) | −20.1167 | − | 20.1167i | −0.717081 | − | 0.717081i | 0.250925 | − | 0.968007i | \(-0.419265\pi\) |
−0.968007 | + | 0.250925i | \(0.919265\pi\) | |||||||
\(788\) | 36.3082 | + | 4.59688i | 1.29342 | + | 0.163757i | ||||
\(789\) | − | 17.6707i | − | 0.629093i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 4.44642i | − | 0.158096i | ||||||
\(792\) | −0.711966 | − | 3.44507i | −0.0252986 | − | 0.122415i | ||||
\(793\) | 35.7991 | + | 35.7991i | 1.27126 | + | 1.27126i | ||||
\(794\) | −20.3244 | + | 6.95551i | −0.721287 | + | 0.246842i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −26.8184 | − | 34.5936i | −0.950553 | − | 1.22614i | ||||
\(797\) | 4.43257 | − | 4.43257i | 0.157010 | − | 0.157010i | −0.624231 | − | 0.781240i | \(-0.714587\pi\) |
0.781240 | + | 0.624231i | \(0.214587\pi\) | |||||||
\(798\) | 3.30479 | + | 1.61956i | 0.116988 | + | 0.0573318i | ||||
\(799\) | −19.6436 | −0.694941 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 73.7319 | 2.60519 | ||||||||
\(802\) | −30.1739 | − | 14.7871i | −1.06548 | − | 0.522152i | ||||
\(803\) | 0.899932 | − | 0.899932i | 0.0317579 | − | 0.0317579i | ||||
\(804\) | 2.85525 | + | 3.68304i | 0.100697 | + | 0.129891i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 69.9757 | − | 23.9473i | 2.46479 | − | 0.843509i | ||||
\(807\) | −0.140025 | − | 0.140025i | −0.00492911 | − | 0.00492911i | ||||
\(808\) | 8.69781 | + | 42.0870i | 0.305988 | + | 1.48062i | ||||
\(809\) | − | 2.61396i | − | 0.0919020i | −0.998944 | − | 0.0459510i | \(-0.985368\pi\) | ||
0.998944 | − | 0.0459510i | \(-0.0146318\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.5143i | 0.720354i | 0.932884 | + | 0.360177i | \(0.117284\pi\) | ||||
−0.932884 | + | 0.360177i | \(0.882716\pi\) | |||||||
\(812\) | −7.99811 | − | 1.01262i | −0.280679 | − | 0.0355359i | ||||
\(813\) | −5.82774 | − | 5.82774i | −0.204388 | − | 0.204388i | ||||
\(814\) | −0.179855 | − | 0.525548i | −0.00630392 | − | 0.0184205i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −32.6303 | − | 8.39706i | −1.14229 | − | 0.293956i | ||||
\(817\) | 1.80943 | − | 1.80943i | 0.0633040 | − | 0.0633040i | ||||
\(818\) | −14.0452 | + | 28.6600i | −0.491080 | + | 1.00207i | ||||
\(819\) | 35.1854 | 1.22948 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.11902 | −0.248456 | −0.124228 | − | 0.992254i | \(-0.539645\pi\) | ||||
−0.124228 | + | 0.992254i | \(0.539645\pi\) | |||||||
\(822\) | 4.82554 | − | 9.84674i | 0.168310 | − | 0.343444i | ||||
\(823\) | 15.9450 | − | 15.9450i | 0.555807 | − | 0.555807i | −0.372304 | − | 0.928111i | \(-0.621432\pi\) |
0.928111 | + | 0.372304i | \(0.121432\pi\) | |||||||
\(824\) | −3.64003 | − | 2.39319i | −0.126807 | − | 0.0833708i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.80435 | + | 14.0386i | 0.167165 | + | 0.488466i | ||||
\(827\) | −27.0197 | − | 27.0197i | −0.939566 | − | 0.939566i | 0.0587089 | − | 0.998275i | \(-0.481302\pi\) |
−0.998275 | + | 0.0587089i | \(0.981302\pi\) | |||||||
\(828\) | 0.185526 | − | 1.46537i | 0.00644748 | − | 0.0509251i | ||||
\(829\) | − | 22.0054i | − | 0.764278i | −0.924105 | − | 0.382139i | \(-0.875188\pi\) | ||
0.924105 | − | 0.382139i | \(-0.124812\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.9792i | 0.589003i | ||||||||
\(832\) | 45.2099 | + | 17.9428i | 1.56737 | + | 0.622054i | ||||
\(833\) | −2.00932 | − | 2.00932i | −0.0696188 | − | 0.0696188i | ||||
\(834\) | −43.2611 | + | 14.8050i | −1.49801 | + | 0.512654i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.298235 | + | 0.231204i | −0.0103147 | + | 0.00799637i | ||||
\(837\) | −50.2488 | + | 50.2488i | −1.73685 | + | 1.73685i | ||||
\(838\) | 15.7916 | + | 7.73889i | 0.545511 | + | 0.267335i | ||||
\(839\) | 47.2741 | 1.63208 | 0.816041 | − | 0.577994i | \(-0.196164\pi\) | ||||
0.816041 | + | 0.577994i | \(0.196164\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.7512 | 0.439697 | ||||||||
\(842\) | 39.7229 | + | 19.4668i | 1.36894 | + | 0.670869i | ||||
\(843\) | −48.0480 | + | 48.0480i | −1.65486 | + | 1.65486i | ||||
\(844\) | 5.36947 | − | 4.16263i | 0.184825 | − | 0.143284i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −53.5279 | + | 18.3185i | −1.84033 | + | 0.629804i | ||||
\(847\) | −7.74551 | − | 7.74551i | −0.266139 | − | 0.266139i | ||||
\(848\) | −13.5122 | + | 7.98113i | −0.464011 | + | 0.274073i | ||||
\(849\) | 1.68546i | 0.0578449i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 0.233229i | − | 0.00799499i | ||||||
\(852\) | −1.30342 | + | 10.2950i | −0.0446543 | + | 0.352700i | ||||
\(853\) | −11.2255 | − | 11.2255i | −0.384355 | − | 0.384355i | 0.488313 | − | 0.872668i | \(-0.337612\pi\) |
−0.872668 | + | 0.488313i | \(0.837612\pi\) | |||||||
\(854\) | −3.81292 | − | 11.1416i | −0.130475 | − | 0.381257i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 21.2831 | − | 32.3714i | 0.727440 | − | 1.10643i | ||||
\(857\) | −3.34445 | + | 3.34445i | −0.114244 | + | 0.114244i | −0.761918 | − | 0.647674i | \(-0.775742\pi\) |
0.647674 | + | 0.761918i | \(0.275742\pi\) | |||||||
\(858\) | −2.41065 | + | 4.91904i | −0.0822982 | + | 0.167933i | ||||
\(859\) | −5.60701 | −0.191309 | −0.0956543 | − | 0.995415i | \(-0.530494\pi\) | ||||
−0.0956543 | + | 0.995415i | \(0.530494\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.64036 | −0.294463 | ||||||||
\(862\) | 11.9046 | − | 24.2920i | 0.405474 | − | 0.827389i | ||||
\(863\) | −35.2995 | + | 35.2995i | −1.20161 | + | 1.20161i | −0.227931 | + | 0.973677i | \(0.573196\pi\) |
−0.973677 | + | 0.227931i | \(0.926804\pi\) | |||||||
\(864\) | −46.5932 | + | 3.63492i | −1.58513 | + | 0.123662i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.15679 | + | 9.22435i | 0.107272 | + | 0.313456i | ||||
\(867\) | 18.7080 | + | 18.7080i | 0.635358 | + | 0.635358i | ||||
\(868\) | −17.0668 | − | 2.16078i | −0.579285 | − | 0.0733417i | ||||
\(869\) | 2.66775i | 0.0904971i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 4.77922i | − | 0.161938i | ||||||
\(872\) | −33.3539 | + | 6.89299i | −1.12950 | + | 0.233426i | ||||
\(873\) | −14.9641 | − | 14.9641i | −0.506458 | − | 0.506458i | ||||
\(874\) | −0.149908 | + | 0.0513022i | −0.00507072 | + | 0.00173532i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −21.5100 | − | 27.7461i | −0.726754 | − | 0.937455i | ||||
\(877\) | −19.6457 | + | 19.6457i | −0.663389 | + | 0.663389i | −0.956177 | − | 0.292789i | \(-0.905417\pi\) |
0.292789 | + | 0.956177i | \(0.405417\pi\) | |||||||
\(878\) | 41.6330 | + | 20.4029i | 1.40505 | + | 0.688564i | ||||
\(879\) | 6.00606 | 0.202579 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.05077 | −0.102783 | −0.0513915 | − | 0.998679i | \(-0.516366\pi\) | ||||
−0.0513915 | + | 0.998679i | \(0.516366\pi\) | |||||||
\(882\) | −7.34907 | − | 3.60152i | −0.247456 | − | 0.121269i | ||||
\(883\) | −15.9128 | + | 15.9128i | −0.535509 | + | 0.535509i | −0.922207 | − | 0.386697i | \(-0.873616\pi\) |
0.386697 | + | 0.922207i | \(0.373616\pi\) | |||||||
\(884\) | 21.1710 | + | 27.3089i | 0.712058 | + | 0.918498i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.1099 | + | 5.51319i | −0.541223 | + | 0.185219i | ||||
\(887\) | 27.6148 | + | 27.6148i | 0.927215 | + | 0.927215i | 0.997525 | − | 0.0703102i | \(-0.0223989\pi\) |
−0.0703102 | + | 0.997525i | \(0.522399\pi\) | |||||||
\(888\) | −15.0056 | + | 3.10110i | −0.503556 | + | 0.104066i | ||||
\(889\) | 3.12921i | 0.104950i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1.53211i | − | 0.0513277i | ||||||
\(892\) | 55.4522 | + | 7.02064i | 1.85668 | + | 0.235068i | ||||
\(893\) | 4.29131 | + | 4.29131i | 0.143603 | + | 0.143603i | ||||
\(894\) | 15.2598 | + | 44.5901i | 0.510364 | + | 1.49132i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7.60626 | − | 8.37525i | −0.254107 | − | 0.279798i | ||||
\(897\) | −1.62639 | + | 1.62639i | −0.0543037 | + | 0.0543037i | ||||
\(898\) | 3.44086 | − | 7.02124i | 0.114823 | − | 0.234302i | ||||
\(899\) | −34.6725 | −1.15639 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.1485 | −0.371411 | ||||||||
\(902\) | 0.389867 | − | 0.795543i | 0.0129812 | − | 0.0264887i | ||||
\(903\) | −6.10965 | + | 6.10965i | −0.203317 | + | 0.203317i | ||||
\(904\) | 6.90903 | − | 10.5086i | 0.229791 | − | 0.349511i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 12.3263 | + | 36.0184i | 0.409516 | + | 1.19663i | ||||
\(907\) | 34.9739 | + | 34.9739i | 1.16129 | + | 1.16129i | 0.984193 | + | 0.177098i | \(0.0566708\pi\) |
0.177098 | + | 0.984193i | \(0.443329\pi\) | |||||||
\(908\) | 5.24297 | − | 41.4113i | 0.173994 | − | 1.37428i | ||||
\(909\) | 87.9310i | 2.91649i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.9032i | 0.990736i | 0.868683 | + | 0.495368i | \(0.164967\pi\) | ||||
−0.868683 | + | 0.495368i | \(0.835033\pi\) | |||||||
\(912\) | 5.29395 | + | 8.96276i | 0.175300 | + | 0.296786i | ||||
\(913\) | −1.14062 | − | 1.14062i | −0.0377489 | − | 0.0377489i | ||||
\(914\) | 36.1413 | − | 12.3684i | 1.19545 | − | 0.409111i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.14994 | − | 3.99245i | 0.170159 | − | 0.131914i | ||||
\(917\) | 2.62896 | − | 2.62896i | 0.0868159 | − | 0.0868159i | ||||
\(918\) | −29.8129 | − | 14.6103i | −0.983973 | − | 0.482210i | ||||
\(919\) | −46.1221 | −1.52143 | −0.760714 | − | 0.649087i | \(-0.775151\pi\) | ||||
−0.760714 | + | 0.649087i | \(0.775151\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.33172 | −0.208637 | ||||||||
\(922\) | 10.4754 | + | 5.13361i | 0.344988 | + | 0.169066i | ||||
\(923\) | 7.52519 | − | 7.52519i | 0.247695 | − | 0.247695i | ||||
\(924\) | 1.00701 | − | 0.780675i | 0.0331282 | − | 0.0256823i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 29.3080 | − | 10.0299i | 0.963122 | − | 0.329603i | ||||
\(927\) | −6.30250 | − | 6.30250i | −0.207001 | − | 0.207001i | ||||
\(928\) | −17.3291 | − | 14.8210i | −0.568857 | − | 0.486523i | ||||
\(929\) | − | 36.7649i | − | 1.20622i | −0.797659 | − | 0.603108i | \(-0.793929\pi\) | ||
0.797659 | − | 0.603108i | \(-0.206071\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.877903i | 0.0287721i | ||||||||
\(932\) | 1.73551 | − | 13.7078i | 0.0568484 | − | 0.449014i | ||||
\(933\) | 26.7163 | + | 26.7163i | 0.874652 | + | 0.874652i | ||||
\(934\) | −17.9908 | − | 52.5701i | −0.588675 | − | 1.72015i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 83.1566 | + | 54.6725i | 2.71806 | + | 1.78703i | ||||
\(937\) | −25.1593 | + | 25.1593i | −0.821917 | + | 0.821917i | −0.986383 | − | 0.164465i | \(-0.947410\pi\) |
0.164465 | + | 0.986383i | \(0.447410\pi\) | |||||||
\(938\) | −0.489193 | + | 0.998221i | −0.0159727 | + | 0.0325931i | ||||
\(939\) | 60.3571 | 1.96968 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.6403 | −0.835851 | −0.417926 | − | 0.908481i | \(-0.637243\pi\) | ||||
−0.417926 | + | 0.908481i | \(0.637243\pi\) | |||||||
\(942\) | 38.6402 | − | 78.8472i | 1.25897 | − | 2.56898i | ||||
\(943\) | 0.263032 | − | 0.263032i | 0.00856550 | − | 0.00856550i | ||||
\(944\) | −10.4593 | + | 40.6438i | −0.340420 | + | 1.32284i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.286856 | − | 0.838211i | −0.00932649 | − | 0.0272526i | ||||
\(947\) | 2.04606 | + | 2.04606i | 0.0664879 | + | 0.0664879i | 0.739569 | − | 0.673081i | \(-0.235029\pi\) |
−0.673081 | + | 0.739569i | \(0.735029\pi\) | |||||||
\(948\) | 73.0071 | + | 9.24323i | 2.37116 | + | 0.300206i | ||||
\(949\) | 36.0042i | 1.16874i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.3088i | 0.950404i | ||||||||
\(952\) | −1.62663 | − | 7.87095i | −0.0527193 | − | 0.255099i | ||||
\(953\) | 29.4048 | + | 29.4048i | 0.952513 | + | 0.952513i | 0.998923 | − | 0.0464091i | \(-0.0147778\pi\) |
−0.0464091 | + | 0.998923i | \(0.514778\pi\) | |||||||
\(954\) | −30.3791 | + | 10.3965i | −0.983561 | + | 0.336598i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.5932 | + | 16.2442i | 0.407293 | + | 0.525376i | ||||
\(957\) | 1.81591 | − | 1.81591i | 0.0587000 | − | 0.0587000i | ||||
\(958\) | 4.91097 | + | 2.40669i | 0.158666 | + | 0.0777567i | ||||
\(959\) | 2.61574 | 0.0844668 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −42.9862 | −1.38665 | ||||||||
\(962\) | 14.1108 | + | 6.91519i | 0.454950 | + | 0.222955i | ||||
\(963\) | 56.0492 | − | 56.0492i | 1.80616 | − | 1.80616i | ||||
\(964\) | 5.86774 | + | 7.56891i | 0.188987 | + | 0.243778i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.506174 | − | 0.173225i | 0.0162859 | − | 0.00557342i | ||||
\(967\) | 33.9934 | + | 33.9934i | 1.09315 | + | 1.09315i | 0.995190 | + | 0.0979625i | \(0.0312325\pi\) |
0.0979625 | + | 0.995190i | \(0.468767\pi\) | |||||||
\(968\) | −6.27032 | − | 30.3409i | −0.201536 | − | 0.975194i | ||||
\(969\) | 7.39489i | 0.237558i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.5798i | 0.435796i | 0.975972 | + | 0.217898i | \(0.0699200\pi\) | ||||
−0.975972 | + | 0.217898i | \(0.930080\pi\) | |||||||
\(972\) | 7.24844 | + | 0.917705i | 0.232494 | + | 0.0294354i | ||||
\(973\) | −7.71250 | − | 7.71250i | −0.247251 | − | 0.247251i | ||||
\(974\) | −0.203827 | − | 0.595596i | −0.00653104 | − | 0.0190841i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.30087 | − | 32.2565i | 0.265704 | − | 1.03251i | ||||
\(977\) | 29.3429 | − | 29.3429i | 0.938764 | − | 0.938764i | −0.0594666 | − | 0.998230i | \(-0.518940\pi\) |
0.998230 | + | 0.0594666i | \(0.0189400\pi\) | |||||||
\(978\) | −29.3359 | + | 59.8614i | −0.938060 | + | 1.91416i | ||||
\(979\) | −2.73827 | −0.0875155 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −69.6851 | −2.22487 | ||||||||
\(982\) | 25.1576 | − | 51.3352i | 0.802810 | − | 1.63817i | ||||
\(983\) | 1.45861 | − | 1.45861i | 0.0465225 | − | 0.0465225i | −0.683463 | − | 0.729985i | \(-0.739527\pi\) |
0.729985 | + | 0.683463i | \(0.239527\pi\) | |||||||
\(984\) | −20.4205 | − | 13.4257i | −0.650981 | − | 0.427997i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.24505 | − | 15.3264i | −0.167037 | − | 0.488092i | ||||
\(987\) | −14.4899 | − | 14.4899i | −0.461217 | − | 0.461217i | ||||
\(988\) | 1.34087 | − | 10.5908i | 0.0426589 | − | 0.336939i | ||||
\(989\) | − | 0.371983i | − | 0.0118284i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.9628i | 0.951798i | 0.879500 | + | 0.475899i | \(0.157877\pi\) | ||||
−0.879500 | + | 0.475899i | \(0.842123\pi\) | |||||||
\(992\) | −36.9779 | − | 31.6258i | −1.17405 | − | 1.00412i | ||||
\(993\) | −61.5205 | − | 61.5205i | −1.95229 | − | 1.95229i | ||||
\(994\) | −2.34203 | + | 0.801498i | −0.0742846 | + | 0.0254220i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −35.1668 | + | 27.2628i | −1.11430 | + | 0.863855i | ||||
\(997\) | 41.4242 | − | 41.4242i | 1.31192 | − | 1.31192i | 0.391919 | − | 0.920000i | \(-0.371811\pi\) |
0.920000 | − | 0.391919i | \(-0.128189\pi\) | |||||||
\(998\) | −40.3674 | − | 19.7826i | −1.27781 | − | 0.626209i | ||||
\(999\) | −15.0985 | −0.477696 |
(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 | 700.2.k.b.43.4 | 36 | ||
4.3 | odd | 2 | inner | 700.2.k.b.43.12 | 36 | ||
5.2 | odd | 4 | inner | 700.2.k.b.407.12 | 36 | ||
5.3 | odd | 4 | 140.2.k.a.127.7 | yes | 36 | ||
5.4 | even | 2 | 140.2.k.a.43.15 | yes | 36 | ||
20.3 | even | 4 | 140.2.k.a.127.15 | yes | 36 | ||
20.7 | even | 4 | inner | 700.2.k.b.407.4 | 36 | ||
20.19 | odd | 2 | 140.2.k.a.43.7 | ✓ | 36 | ||
35.3 | even | 12 | 980.2.x.l.667.6 | 72 | |||
35.4 | even | 6 | 980.2.x.k.863.4 | 72 | |||
35.9 | even | 6 | 980.2.x.k.263.10 | 72 | |||
35.13 | even | 4 | 980.2.k.l.687.7 | 36 | |||
35.18 | odd | 12 | 980.2.x.k.667.6 | 72 | |||
35.19 | odd | 6 | 980.2.x.l.263.10 | 72 | |||
35.23 | odd | 12 | 980.2.x.k.67.18 | 72 | |||
35.24 | odd | 6 | 980.2.x.l.863.4 | 72 | |||
35.33 | even | 12 | 980.2.x.l.67.18 | 72 | |||
35.34 | odd | 2 | 980.2.k.l.883.15 | 36 | |||
140.3 | odd | 12 | 980.2.x.l.667.10 | 72 | |||
140.19 | even | 6 | 980.2.x.l.263.6 | 72 | |||
140.23 | even | 12 | 980.2.x.k.67.4 | 72 | |||
140.39 | odd | 6 | 980.2.x.k.863.18 | 72 | |||
140.59 | even | 6 | 980.2.x.l.863.18 | 72 | |||
140.79 | odd | 6 | 980.2.x.k.263.6 | 72 | |||
140.83 | odd | 4 | 980.2.k.l.687.15 | 36 | |||
140.103 | odd | 12 | 980.2.x.l.67.4 | 72 | |||
140.123 | even | 12 | 980.2.x.k.667.10 | 72 | |||
140.139 | even | 2 | 980.2.k.l.883.7 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.2.k.a.43.7 | ✓ | 36 | 20.19 | odd | 2 | ||
140.2.k.a.43.15 | yes | 36 | 5.4 | even | 2 | ||
140.2.k.a.127.7 | yes | 36 | 5.3 | odd | 4 | ||
140.2.k.a.127.15 | yes | 36 | 20.3 | even | 4 | ||
700.2.k.b.43.4 | 36 | 1.1 | even | 1 | trivial | ||
700.2.k.b.43.12 | 36 | 4.3 | odd | 2 | inner | ||
700.2.k.b.407.4 | 36 | 20.7 | even | 4 | inner | ||
700.2.k.b.407.12 | 36 | 5.2 | odd | 4 | inner | ||
980.2.k.l.687.7 | 36 | 35.13 | even | 4 | |||
980.2.k.l.687.15 | 36 | 140.83 | odd | 4 | |||
980.2.k.l.883.7 | 36 | 140.139 | even | 2 | |||
980.2.k.l.883.15 | 36 | 35.34 | odd | 2 | |||
980.2.x.k.67.4 | 72 | 140.23 | even | 12 | |||
980.2.x.k.67.18 | 72 | 35.23 | odd | 12 | |||
980.2.x.k.263.6 | 72 | 140.79 | odd | 6 | |||
980.2.x.k.263.10 | 72 | 35.9 | even | 6 | |||
980.2.x.k.667.6 | 72 | 35.18 | odd | 12 | |||
980.2.x.k.667.10 | 72 | 140.123 | even | 12 | |||
980.2.x.k.863.4 | 72 | 35.4 | even | 6 | |||
980.2.x.k.863.18 | 72 | 140.39 | odd | 6 | |||
980.2.x.l.67.4 | 72 | 140.103 | odd | 12 | |||
980.2.x.l.67.18 | 72 | 35.33 | even | 12 | |||
980.2.x.l.263.6 | 72 | 140.19 | even | 6 | |||
980.2.x.l.263.10 | 72 | 35.19 | odd | 6 | |||
980.2.x.l.667.6 | 72 | 35.3 | even | 12 | |||
980.2.x.l.667.10 | 72 | 140.3 | odd | 12 | |||
980.2.x.l.863.4 | 72 | 35.24 | odd | 6 | |||
980.2.x.l.863.18 | 72 | 140.59 | even | 6 |