Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(97,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.bd (of order \(12\), degree \(4\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 440.4 | ||
Character | \(\chi\) | \(=\) | 637.440 |
Dual form | 637.2.bd.b.97.4 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{7}{12}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0707322 | + | 0.263976i | −0.0500152 | + | 0.186659i | −0.986414 | − | 0.164278i | \(-0.947470\pi\) |
0.936399 | + | 0.350938i | \(0.114137\pi\) | |||||||
\(3\) | −2.17048 | + | 1.25313i | −1.25313 | + | 0.723493i | −0.971729 | − | 0.236099i | \(-0.924131\pi\) |
−0.281397 | + | 0.959591i | \(0.590798\pi\) | |||||||
\(4\) | 1.66737 | + | 0.962657i | 0.833685 | + | 0.481328i | ||||
\(5\) | −1.04692 | + | 1.04692i | −0.468196 | + | 0.468196i | −0.901330 | − | 0.433134i | \(-0.857408\pi\) |
0.433134 | + | 0.901330i | \(0.357408\pi\) | |||||||
\(6\) | −0.177273 | − | 0.661591i | −0.0723713 | − | 0.270093i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.758543 | + | 0.758543i | −0.268186 | + | 0.268186i | ||||
\(9\) | 1.64065 | − | 2.84169i | 0.546883 | − | 0.947230i | ||||
\(10\) | −0.202311 | − | 0.350412i | −0.0639763 | − | 0.110810i | ||||
\(11\) | −4.43396 | − | 1.18808i | −1.33689 | − | 0.358218i | −0.481609 | − | 0.876386i | \(-0.659948\pi\) |
−0.855279 | + | 0.518168i | \(0.826614\pi\) | |||||||
\(12\) | −4.82532 | −1.39295 | ||||||||
\(13\) | −2.80779 | − | 2.26193i | −0.778741 | − | 0.627346i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.960393 | − | 3.58423i | 0.247972 | − | 0.925445i | ||||
\(16\) | 1.77873 | + | 3.08085i | 0.444682 | + | 0.770213i | ||||
\(17\) | −1.17081 | + | 2.02791i | −0.283964 | + | 0.491840i | −0.972357 | − | 0.233497i | \(-0.924983\pi\) |
0.688393 | + | 0.725337i | \(0.258316\pi\) | |||||||
\(18\) | 0.634091 | + | 0.634091i | 0.149457 | + | 0.149457i | ||||
\(19\) | 0.438561 | + | 1.63673i | 0.100613 | + | 0.375492i | 0.997811 | − | 0.0661367i | \(-0.0210674\pi\) |
−0.897198 | + | 0.441629i | \(0.854401\pi\) | |||||||
\(20\) | −2.75342 | + | 0.737778i | −0.615684 | + | 0.164972i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.627247 | − | 1.08642i | 0.133730 | − | 0.231626i | ||||
\(23\) | 4.15065 | − | 2.39638i | 0.865471 | − | 0.499680i | −0.000369324 | − | 1.00000i | \(-0.500118\pi\) |
0.865841 | + | 0.500320i | \(0.166784\pi\) | |||||||
\(24\) | 0.695851 | − | 2.59695i | 0.142040 | − | 0.530101i | ||||
\(25\) | 2.80792i | 0.561585i | ||||||||
\(26\) | 0.795696 | − | 0.581199i | 0.156049 | − | 0.113982i | ||||
\(27\) | 0.705008i | 0.135679i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.87534 | − | 4.98024i | −0.533938 | − | 0.924808i | −0.999214 | − | 0.0396419i | \(-0.987378\pi\) |
0.465276 | − | 0.885166i | \(-0.345955\pi\) | |||||||
\(30\) | 0.878222 | + | 0.507042i | 0.160341 | + | 0.0925727i | ||||
\(31\) | 4.17096 | − | 4.17096i | 0.749127 | − | 0.749127i | −0.225189 | − | 0.974315i | \(-0.572300\pi\) |
0.974315 | + | 0.225189i | \(0.0722998\pi\) | |||||||
\(32\) | −3.01146 | + | 0.806919i | −0.532356 | + | 0.142644i | ||||
\(33\) | 11.1126 | − | 2.97762i | 1.93446 | − | 0.518336i | ||||
\(34\) | −0.452505 | − | 0.452505i | −0.0776040 | − | 0.0776040i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.47114 | − | 3.15877i | 0.911857 | − | 0.526461i | ||||
\(37\) | −8.24256 | − | 2.20859i | −1.35507 | − | 0.363090i | −0.493066 | − | 0.869992i | \(-0.664124\pi\) |
−0.862003 | + | 0.506902i | \(0.830790\pi\) | |||||||
\(38\) | −0.463079 | −0.0751214 | ||||||||
\(39\) | 8.92873 | + | 1.39095i | 1.42974 | + | 0.222730i | ||||
\(40\) | − | 1.58827i | − | 0.251127i | ||||||
\(41\) | −0.829479 | − | 0.222258i | −0.129543 | − | 0.0347109i | 0.193465 | − | 0.981107i | \(-0.438027\pi\) |
−0.323008 | + | 0.946396i | \(0.604694\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.70069 | + | 0.981895i | 0.259353 | + | 0.149738i | 0.624039 | − | 0.781393i | \(-0.285490\pi\) |
−0.364686 | + | 0.931130i | \(0.618824\pi\) | |||||||
\(44\) | −6.24934 | − | 6.24934i | −0.942123 | − | 0.942123i | ||||
\(45\) | 1.25739 | + | 4.69264i | 0.187441 | + | 0.699538i | ||||
\(46\) | 0.339003 | + | 1.26518i | 0.0499832 | + | 0.186540i | ||||
\(47\) | −5.67880 | − | 5.67880i | −0.828339 | − | 0.828339i | 0.158948 | − | 0.987287i | \(-0.449190\pi\) |
−0.987287 | + | 0.158948i | \(0.949190\pi\) | |||||||
\(48\) | −7.72139 | − | 4.45794i | −1.11449 | − | 0.643449i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.741225 | − | 0.198611i | −0.104825 | − | 0.0280878i | ||||
\(51\) | − | 5.86871i | − | 0.821783i | ||||||
\(52\) | −2.50417 | − | 6.47441i | −0.347266 | − | 0.897839i | ||||
\(53\) | −13.0827 | −1.79704 | −0.898521 | − | 0.438931i | \(-0.855357\pi\) | ||||
−0.898521 | + | 0.438931i | \(0.855357\pi\) | |||||||
\(54\) | −0.186105 | − | 0.0498668i | −0.0253257 | − | 0.00678601i | ||||
\(55\) | 5.88581 | − | 3.39817i | 0.793642 | − | 0.458210i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.00292 | − | 3.00292i | −0.397747 | − | 0.397747i | ||||
\(58\) | 1.51804 | − | 0.406759i | 0.199329 | − | 0.0534100i | ||||
\(59\) | −1.49637 | + | 0.400951i | −0.194811 | + | 0.0521994i | −0.354905 | − | 0.934902i | \(-0.615487\pi\) |
0.160094 | + | 0.987102i | \(0.448820\pi\) | |||||||
\(60\) | 5.05172 | − | 5.05172i | 0.652174 | − | 0.652174i | ||||
\(61\) | 8.45262 | + | 4.88012i | 1.08225 | + | 0.624836i | 0.931502 | − | 0.363737i | \(-0.118499\pi\) |
0.150746 | + | 0.988573i | \(0.451833\pi\) | |||||||
\(62\) | 0.806013 | + | 1.39606i | 0.102364 | + | 0.177299i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.26289i | 0.782861i | ||||||||
\(65\) | 5.30758 | − | 0.571475i | 0.658324 | − | 0.0708827i | ||||
\(66\) | 3.14408i | 0.387009i | ||||||||
\(67\) | −0.141189 | + | 0.526925i | −0.0172490 | + | 0.0643742i | −0.974014 | − | 0.226488i | \(-0.927276\pi\) |
0.956765 | + | 0.290862i | \(0.0939422\pi\) | |||||||
\(68\) | −3.90436 | + | 2.25418i | −0.473473 | + | 0.273360i | ||||
\(69\) | −6.00594 | + | 10.4026i | −0.723030 | + | 1.25232i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.77061 | − | 0.474435i | 0.210133 | − | 0.0563050i | −0.152217 | − | 0.988347i | \(-0.548641\pi\) |
0.362350 | + | 0.932042i | \(0.381975\pi\) | |||||||
\(72\) | 0.911040 | + | 3.40005i | 0.107367 | + | 0.400699i | ||||
\(73\) | −1.67079 | − | 1.67079i | −0.195551 | − | 0.195551i | 0.602538 | − | 0.798090i | \(-0.294156\pi\) |
−0.798090 | + | 0.602538i | \(0.794156\pi\) | |||||||
\(74\) | 1.16603 | − | 2.01962i | 0.135548 | − | 0.234776i | ||||
\(75\) | −3.51868 | − | 6.09453i | −0.406302 | − | 0.703736i | ||||
\(76\) | −0.844368 | + | 3.15123i | −0.0968557 | + | 0.361470i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.998725 | + | 2.25859i | −0.113083 | + | 0.255735i | ||||
\(79\) | 4.26678 | 0.480050 | 0.240025 | − | 0.970767i | \(-0.422844\pi\) | ||||
0.240025 | + | 0.970767i | \(0.422844\pi\) | |||||||
\(80\) | −5.08758 | − | 1.36321i | −0.568809 | − | 0.152412i | ||||
\(81\) | 4.03849 | + | 6.99486i | 0.448721 | + | 0.777207i | ||||
\(82\) | 0.117342 | − | 0.203242i | 0.0129582 | − | 0.0224443i | ||||
\(83\) | 3.88518 | − | 3.88518i | 0.426454 | − | 0.426454i | −0.460965 | − | 0.887419i | \(-0.652496\pi\) |
0.887419 | + | 0.460965i | \(0.152496\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.897309 | − | 3.34880i | −0.0973268 | − | 0.363228i | ||||
\(86\) | −0.379490 | + | 0.379490i | −0.0409215 | + | 0.0409215i | ||||
\(87\) | 12.4817 | + | 7.20634i | 1.33818 | + | 0.772600i | ||||
\(88\) | 4.26455 | − | 2.46214i | 0.454603 | − | 0.262465i | ||||
\(89\) | −3.63117 | + | 13.5517i | −0.384904 | + | 1.43648i | 0.453415 | + | 0.891299i | \(0.350205\pi\) |
−0.838319 | + | 0.545180i | \(0.816461\pi\) | |||||||
\(90\) | −1.32768 | −0.139950 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.22757 | 0.962041 | ||||||||
\(93\) | −3.82624 | + | 14.2797i | −0.396762 | + | 1.48074i | ||||
\(94\) | 1.90074 | − | 1.09739i | 0.196047 | − | 0.113188i | ||||
\(95\) | −2.17267 | − | 1.25439i | −0.222911 | − | 0.128698i | ||||
\(96\) | 5.52514 | − | 5.52514i | 0.563908 | − | 0.563908i | ||||
\(97\) | 0.734114 | + | 2.73975i | 0.0745380 | + | 0.278180i | 0.993128 | − | 0.117032i | \(-0.0373380\pi\) |
−0.918590 | + | 0.395212i | \(0.870671\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.6507 | + | 10.6507i | −1.07044 | + | 1.07044i | ||||
\(100\) | −2.70307 | + | 4.68185i | −0.270307 | + | 0.468185i | ||||
\(101\) | −5.32015 | − | 9.21476i | −0.529374 | − | 0.916903i | −0.999413 | − | 0.0342575i | \(-0.989093\pi\) |
0.470039 | − | 0.882646i | \(-0.344240\pi\) | |||||||
\(102\) | 1.54920 | + | 0.415107i | 0.153394 | + | 0.0411017i | ||||
\(103\) | −17.2155 | −1.69629 | −0.848145 | − | 0.529765i | \(-0.822280\pi\) | ||||
−0.848145 | + | 0.529765i | \(0.822280\pi\) | |||||||
\(104\) | 3.84560 | − | 0.414061i | 0.377092 | − | 0.0406020i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.925366 | − | 3.45351i | 0.0898794 | − | 0.335435i | ||||
\(107\) | 2.02845 | + | 3.51338i | 0.196097 | + | 0.339651i | 0.947260 | − | 0.320467i | \(-0.103840\pi\) |
−0.751162 | + | 0.660118i | \(0.770506\pi\) | |||||||
\(108\) | −0.678681 | + | 1.17551i | −0.0653061 | + | 0.113113i | ||||
\(109\) | −5.60132 | − | 5.60132i | −0.536509 | − | 0.536509i | 0.385993 | − | 0.922502i | \(-0.373859\pi\) |
−0.922502 | + | 0.385993i | \(0.873859\pi\) | |||||||
\(110\) | 0.480721 | + | 1.79407i | 0.0458349 | + | 0.171058i | ||||
\(111\) | 20.6579 | − | 5.53528i | 1.96077 | − | 0.525385i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.23138 | + | 15.9892i | −0.868415 | + | 1.50414i | −0.00479920 | + | 0.999988i | \(0.501528\pi\) |
−0.863616 | + | 0.504150i | \(0.831806\pi\) | |||||||
\(114\) | 1.00510 | − | 0.580297i | 0.0941365 | − | 0.0543497i | ||||
\(115\) | −1.83658 | + | 6.85421i | −0.171262 | + | 0.639159i | ||||
\(116\) | − | 11.0719i | − | 1.02800i | ||||||
\(117\) | −11.0343 | + | 4.26784i | −1.02012 | + | 0.394562i | ||||
\(118\) | − | 0.423366i | − | 0.0389740i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.99030 | + | 3.44730i | 0.181688 | + | 0.314694i | ||||
\(121\) | 8.72217 | + | 5.03575i | 0.792925 | + | 0.457795i | ||||
\(122\) | −1.88611 | + | 1.88611i | −0.170760 | + | 0.170760i | ||||
\(123\) | 2.07888 | − | 0.557035i | 0.187447 | − | 0.0502262i | ||||
\(124\) | 10.9697 | − | 2.93933i | 0.985112 | − | 0.263960i | ||||
\(125\) | −8.17426 | − | 8.17426i | −0.731128 | − | 0.731128i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.52084 | + | 1.45541i | −0.223689 | + | 0.129147i | −0.607657 | − | 0.794200i | \(-0.707890\pi\) |
0.383968 | + | 0.923346i | \(0.374557\pi\) | |||||||
\(128\) | −7.67618 | − | 2.05683i | −0.678485 | − | 0.181799i | ||||
\(129\) | −4.92175 | −0.433336 | ||||||||
\(130\) | −0.224561 | + | 1.44150i | −0.0196953 | + | 0.126428i | ||||
\(131\) | 9.91023i | 0.865861i | 0.901427 | + | 0.432931i | \(0.142520\pi\) | ||||
−0.901427 | + | 0.432931i | \(0.857480\pi\) | |||||||
\(132\) | 21.3953 | + | 5.73284i | 1.86222 | + | 0.498980i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.129109 | − | 0.0745412i | −0.0111533 | − | 0.00643938i | ||||
\(135\) | −0.738086 | − | 0.738086i | −0.0635243 | − | 0.0635243i | ||||
\(136\) | −0.650144 | − | 2.42637i | −0.0557493 | − | 0.208059i | ||||
\(137\) | −0.140972 | − | 0.526114i | −0.0120440 | − | 0.0449489i | 0.959642 | − | 0.281223i | \(-0.0907402\pi\) |
−0.971686 | + | 0.236275i | \(0.924074\pi\) | |||||||
\(138\) | −2.32122 | − | 2.32122i | −0.197596 | − | 0.197596i | ||||
\(139\) | 3.32499 | + | 1.91968i | 0.282022 | + | 0.162825i | 0.634338 | − | 0.773056i | \(-0.281273\pi\) |
−0.352317 | + | 0.935881i | \(0.614606\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.4420 | + | 5.20946i | 1.63731 | + | 0.438716i | ||||
\(142\) | 0.500958i | 0.0420394i | ||||||||
\(143\) | 9.76228 | + | 13.3652i | 0.816363 | + | 1.11765i | ||||
\(144\) | 11.6731 | 0.972757 | ||||||||
\(145\) | 8.22416 | + | 2.20366i | 0.682979 | + | 0.183004i | ||||
\(146\) | 0.559228 | − | 0.322870i | 0.0462820 | − | 0.0267210i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −11.6173 | − | 11.6173i | −0.954936 | − | 0.954936i | ||||
\(149\) | −22.5930 | + | 6.05379i | −1.85089 | + | 0.495946i | −0.999587 | − | 0.0287228i | \(-0.990856\pi\) |
−0.851307 | + | 0.524668i | \(0.824189\pi\) | |||||||
\(150\) | 1.85770 | − | 0.497768i | 0.151680 | − | 0.0406426i | ||||
\(151\) | −4.66151 | + | 4.66151i | −0.379348 | + | 0.379348i | −0.870867 | − | 0.491519i | \(-0.836442\pi\) |
0.491519 | + | 0.870867i | \(0.336442\pi\) | |||||||
\(152\) | −1.57420 | − | 0.908865i | −0.127685 | − | 0.0737187i | ||||
\(153\) | 3.84179 | + | 6.65417i | 0.310590 | + | 0.537958i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.73331i | 0.701476i | ||||||||
\(156\) | 13.5485 | + | 10.9145i | 1.08475 | + | 0.873861i | ||||
\(157\) | 10.9614i | 0.874816i | 0.899263 | + | 0.437408i | \(0.144103\pi\) | ||||
−0.899263 | + | 0.437408i | \(0.855897\pi\) | |||||||
\(158\) | −0.301799 | + | 1.12633i | −0.0240098 | + | 0.0896058i | ||||
\(159\) | 28.3956 | − | 16.3942i | 2.25192 | − | 1.30015i | ||||
\(160\) | 2.30798 | − | 3.99754i | 0.182462 | − | 0.316033i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.13213 | + | 0.571302i | −0.167516 | + | 0.0448857i | ||||
\(163\) | 1.00078 | + | 3.73496i | 0.0783870 | + | 0.292544i | 0.993980 | − | 0.109562i | \(-0.0349448\pi\) |
−0.915593 | + | 0.402106i | \(0.868278\pi\) | |||||||
\(164\) | −1.16909 | − | 1.16909i | −0.0912906 | − | 0.0912906i | ||||
\(165\) | −8.51668 | + | 14.7513i | −0.663023 | + | 1.14839i | ||||
\(166\) | 0.750788 | + | 1.30040i | 0.0582724 | + | 0.100931i | ||||
\(167\) | −6.30900 | + | 23.5455i | −0.488205 | + | 1.82201i | 0.0769673 | + | 0.997034i | \(0.475476\pi\) |
−0.565172 | + | 0.824973i | \(0.691190\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.76737 | + | 12.7020i | 0.212875 | + | 0.977079i | ||||
\(170\) | 0.947472 | 0.0726678 | ||||||||
\(171\) | 5.37061 | + | 1.43905i | 0.410701 | + | 0.110047i | ||||
\(172\) | 1.89046 | + | 3.27436i | 0.144146 | + | 0.249668i | ||||
\(173\) | −2.39991 | + | 4.15677i | −0.182462 | + | 0.316033i | −0.942718 | − | 0.333590i | \(-0.891740\pi\) |
0.760257 | + | 0.649623i | \(0.225073\pi\) | |||||||
\(174\) | −2.78516 | + | 2.78516i | −0.211143 | + | 0.211143i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.22653 | − | 15.7736i | −0.318587 | − | 1.18898i | ||||
\(177\) | 2.74540 | − | 2.74540i | 0.206357 | − | 0.206357i | ||||
\(178\) | −3.32049 | − | 1.91709i | −0.248881 | − | 0.143692i | ||||
\(179\) | 9.64786 | − | 5.57019i | 0.721115 | − | 0.416336i | −0.0940481 | − | 0.995568i | \(-0.529981\pi\) |
0.815163 | + | 0.579232i | \(0.196647\pi\) | |||||||
\(180\) | −2.42087 | + | 9.03481i | −0.180441 | + | 0.673415i | ||||
\(181\) | 4.32449 | 0.321437 | 0.160718 | − | 0.987000i | \(-0.448619\pi\) | ||||
0.160718 | + | 0.987000i | \(0.448619\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.4616 | −1.80826 | ||||||||
\(184\) | −1.33069 | + | 4.96621i | −0.0980999 | + | 0.366114i | ||||
\(185\) | 10.9415 | − | 6.31708i | 0.804435 | − | 0.464441i | ||||
\(186\) | −3.49887 | − | 2.02007i | −0.256549 | − | 0.148119i | ||||
\(187\) | 7.60064 | − | 7.60064i | 0.555814 | − | 0.555814i | ||||
\(188\) | −4.00193 | − | 14.9354i | −0.291871 | − | 1.08928i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.484806 | − | 0.484806i | 0.0351715 | − | 0.0351715i | ||||
\(191\) | 3.15973 | − | 5.47282i | 0.228630 | − | 0.395999i | −0.728772 | − | 0.684756i | \(-0.759909\pi\) |
0.957402 | + | 0.288757i | \(0.0932420\pi\) | |||||||
\(192\) | −7.84819 | − | 13.5935i | −0.566394 | − | 0.981024i | ||||
\(193\) | −11.5064 | − | 3.08313i | −0.828250 | − | 0.221929i | −0.180300 | − | 0.983612i | \(-0.557707\pi\) |
−0.647950 | + | 0.761683i | \(0.724373\pi\) | |||||||
\(194\) | −0.775155 | −0.0556529 | ||||||||
\(195\) | −10.8039 | + | 7.89144i | −0.773680 | + | 0.565118i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.533499 | + | 1.99105i | −0.0380103 | + | 0.141856i | −0.982323 | − | 0.187192i | \(-0.940061\pi\) |
0.944313 | + | 0.329048i | \(0.106728\pi\) | |||||||
\(198\) | −2.05819 | − | 3.56488i | −0.146269 | − | 0.253345i | ||||
\(199\) | 9.28142 | − | 16.0759i | 0.657942 | − | 1.13959i | −0.323205 | − | 0.946329i | \(-0.604760\pi\) |
0.981147 | − | 0.193261i | \(-0.0619063\pi\) | |||||||
\(200\) | −2.12993 | − | 2.12993i | −0.150609 | − | 0.150609i | ||||
\(201\) | −0.353856 | − | 1.32061i | −0.0249591 | − | 0.0931485i | ||||
\(202\) | 2.80878 | − | 0.752611i | 0.197625 | − | 0.0529536i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.64955 | − | 9.78531i | 0.395548 | − | 0.685109i | ||||
\(205\) | 1.10108 | − | 0.635711i | 0.0769030 | − | 0.0443999i | ||||
\(206\) | 1.21769 | − | 4.54447i | 0.0848403 | − | 0.316628i | ||||
\(207\) | − | 15.7265i | − | 1.09307i | ||||||
\(208\) | 1.97436 | − | 12.6737i | 0.136897 | − | 0.878766i | ||||
\(209\) | − | 7.77825i | − | 0.538033i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.40368 | − | 2.43124i | −0.0966332 | − | 0.167374i | 0.813656 | − | 0.581347i | \(-0.197474\pi\) |
−0.910289 | + | 0.413973i | \(0.864141\pi\) | |||||||
\(212\) | −21.8136 | − | 12.5941i | −1.49817 | − | 0.864967i | ||||
\(213\) | −3.24855 | + | 3.24855i | −0.222587 | + | 0.222587i | ||||
\(214\) | −1.07092 | + | 0.286953i | −0.0732069 | + | 0.0196157i | ||||
\(215\) | −2.80845 | + | 0.752522i | −0.191535 | + | 0.0513216i | ||||
\(216\) | −0.534779 | − | 0.534779i | −0.0363871 | − | 0.0363871i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.87481 | − | 1.08242i | 0.126978 | − | 0.0733108i | ||||
\(219\) | 5.72013 | + | 1.53270i | 0.386531 | + | 0.103571i | ||||
\(220\) | 13.0851 | 0.882197 | ||||||||
\(221\) | 7.87438 | − | 3.04565i | 0.529688 | − | 0.204872i | ||||
\(222\) | 5.84473i | 0.392272i | ||||||||
\(223\) | −15.6678 | − | 4.19816i | −1.04919 | − | 0.281130i | −0.307274 | − | 0.951621i | \(-0.599417\pi\) |
−0.741917 | + | 0.670491i | \(0.766083\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.97924 | + | 4.60682i | 0.531950 | + | 0.307121i | ||||
\(226\) | −3.56782 | − | 3.56782i | −0.237328 | − | 0.237328i | ||||
\(227\) | 0.454277 | + | 1.69538i | 0.0301514 | + | 0.112527i | 0.979362 | − | 0.202116i | \(-0.0647819\pi\) |
−0.949210 | + | 0.314643i | \(0.898115\pi\) | |||||||
\(228\) | −2.11620 | − | 7.89777i | −0.140149 | − | 0.523042i | ||||
\(229\) | −7.88016 | − | 7.88016i | −0.520736 | − | 0.520736i | 0.397058 | − | 0.917794i | \(-0.370031\pi\) |
−0.917794 | + | 0.397058i | \(0.870031\pi\) | |||||||
\(230\) | −1.67944 | − | 0.969627i | −0.110739 | − | 0.0639353i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.95880 | + | 1.59666i | 0.391214 | + | 0.104826i | ||||
\(233\) | − | 20.3654i | − | 1.33418i | −0.744976 | − | 0.667091i | \(-0.767539\pi\) | ||
0.744976 | − | 0.667091i | \(-0.232461\pi\) | |||||||
\(234\) | −0.346127 | − | 3.21466i | −0.0226271 | − | 0.210149i | ||||
\(235\) | 11.8905 | 0.775650 | ||||||||
\(236\) | −2.88098 | − | 0.771957i | −0.187536 | − | 0.0502501i | ||||
\(237\) | −9.26095 | + | 5.34681i | −0.601563 | + | 0.347313i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.6160 | + | 14.6160i | 0.945430 | + | 0.945430i | 0.998586 | − | 0.0531558i | \(-0.0169280\pi\) |
−0.0531558 | + | 0.998586i | \(0.516928\pi\) | |||||||
\(240\) | 12.7508 | − | 3.41656i | 0.823059 | − | 0.220538i | ||||
\(241\) | −13.7908 | + | 3.69524i | −0.888345 | + | 0.238031i | −0.674004 | − | 0.738728i | \(-0.735427\pi\) |
−0.214341 | + | 0.976759i | \(0.568760\pi\) | |||||||
\(242\) | −1.94626 | + | 1.94626i | −0.125110 | + | 0.125110i | ||||
\(243\) | −19.3626 | − | 11.1790i | −1.24211 | − | 0.717132i | ||||
\(244\) | 9.39577 | + | 16.2740i | 0.601503 | + | 1.04183i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.588176i | 0.0375007i | ||||||||
\(247\) | 2.47078 | − | 5.58760i | 0.157212 | − | 0.355530i | ||||
\(248\) | 6.32771i | 0.401810i | ||||||||
\(249\) | −3.56408 | + | 13.3013i | −0.225864 | + | 0.842937i | ||||
\(250\) | 2.73599 | − | 1.57963i | 0.173039 | − | 0.0999043i | ||||
\(251\) | −3.24540 | + | 5.62120i | −0.204848 | + | 0.354807i | −0.950084 | − | 0.311993i | \(-0.899003\pi\) |
0.745236 | + | 0.666801i | \(0.232337\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.2509 | + | 5.69416i | −1.33603 | + | 0.357989i | ||||
\(254\) | −0.205889 | − | 0.768387i | −0.0129186 | − | 0.0482129i | ||||
\(255\) | 6.14406 | + | 6.14406i | 0.384756 | + | 0.384756i | ||||
\(256\) | −5.17698 | + | 8.96680i | −0.323561 | + | 0.560425i | ||||
\(257\) | 11.0980 | + | 19.2224i | 0.692277 | + | 1.19906i | 0.971090 | + | 0.238713i | \(0.0767257\pi\) |
−0.278813 | + | 0.960345i | \(0.589941\pi\) | |||||||
\(258\) | 0.348126 | − | 1.29923i | 0.0216734 | − | 0.0808862i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 9.39984 | + | 4.15652i | 0.582953 | + | 0.257776i | ||||
\(261\) | −18.8697 | −1.16801 | ||||||||
\(262\) | −2.61607 | − | 0.700973i | −0.161621 | − | 0.0433062i | ||||
\(263\) | −5.05320 | − | 8.75240i | −0.311594 | − | 0.539696i | 0.667114 | − | 0.744956i | \(-0.267529\pi\) |
−0.978708 | + | 0.205260i | \(0.934196\pi\) | |||||||
\(264\) | −6.17075 | + | 10.6880i | −0.379783 | + | 0.657804i | ||||
\(265\) | 13.6965 | − | 13.6965i | 0.841368 | − | 0.841368i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.10063 | − | 33.9640i | −0.556950 | − | 2.07857i | ||||
\(268\) | −0.742663 | + | 0.742663i | −0.0453654 | + | 0.0453654i | ||||
\(269\) | −8.97049 | − | 5.17912i | −0.546940 | − | 0.315776i | 0.200947 | − | 0.979602i | \(-0.435598\pi\) |
−0.747887 | + | 0.663826i | \(0.768932\pi\) | |||||||
\(270\) | 0.247044 | − | 0.142631i | 0.0150346 | − | 0.00868022i | ||||
\(271\) | −0.846186 | + | 3.15801i | −0.0514022 | + | 0.191835i | −0.986853 | − | 0.161622i | \(-0.948327\pi\) |
0.935451 | + | 0.353458i | \(0.114994\pi\) | |||||||
\(272\) | −8.33024 | −0.505095 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.148853 | 0.00899252 | ||||||||
\(275\) | 3.33602 | − | 12.4502i | 0.201170 | − | 0.750776i | ||||
\(276\) | −20.0282 | + | 11.5633i | −1.20556 | + | 0.696030i | ||||
\(277\) | 14.4303 | + | 8.33132i | 0.867030 | + | 0.500580i | 0.866360 | − | 0.499420i | \(-0.166453\pi\) |
0.000670170 | 1.00000i | \(0.499787\pi\) | ||||||||
\(278\) | −0.741934 | + | 0.741934i | −0.0444982 | + | 0.0444982i | ||||
\(279\) | −5.00949 | − | 18.6957i | −0.299910 | − | 1.11928i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.02095 | − | 8.02095i | 0.478490 | − | 0.478490i | −0.426159 | − | 0.904648i | \(-0.640134\pi\) |
0.904648 | + | 0.426159i | \(0.140134\pi\) | |||||||
\(282\) | −2.75035 | + | 4.76374i | −0.163781 | + | 0.283677i | ||||
\(283\) | 7.22018 | + | 12.5057i | 0.429195 | + | 0.743388i | 0.996802 | − | 0.0799119i | \(-0.0254639\pi\) |
−0.567607 | + | 0.823300i | \(0.692131\pi\) | |||||||
\(284\) | 3.40899 | + | 0.913435i | 0.202286 | + | 0.0542024i | ||||
\(285\) | 6.28763 | 0.372447 | ||||||||
\(286\) | −4.21859 | + | 1.63166i | −0.249450 | + | 0.0964823i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.64774 | + | 9.88151i | −0.156020 | + | 0.582274i | ||||
\(289\) | 5.75839 | + | 9.97383i | 0.338729 | + | 0.586696i | ||||
\(290\) | −1.16343 | + | 2.01511i | −0.0683187 | + | 0.118331i | ||||
\(291\) | −5.02663 | − | 5.02663i | −0.294666 | − | 0.294666i | ||||
\(292\) | −1.17743 | − | 4.39423i | −0.0689039 | − | 0.257153i | ||||
\(293\) | 15.9091 | − | 4.26283i | 0.929420 | − | 0.249037i | 0.237812 | − | 0.971311i | \(-0.423570\pi\) |
0.691607 | + | 0.722274i | \(0.256903\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.14681 | − | 1.98634i | 0.0667701 | − | 0.115649i | ||||
\(296\) | 7.92765 | − | 4.57703i | 0.460785 | − | 0.266035i | ||||
\(297\) | 0.837602 | − | 3.12597i | 0.0486026 | − | 0.181387i | ||||
\(298\) | − | 6.39222i | − | 0.370292i | ||||||
\(299\) | −17.0746 | − | 2.65994i | −0.987450 | − | 0.153828i | ||||
\(300\) | − | 13.5491i | − | 0.782259i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.900809 | − | 1.56025i | −0.0518357 | − | 0.0897821i | ||||
\(303\) | 23.0945 | + | 13.3336i | 1.32675 | + | 0.765997i | ||||
\(304\) | −4.26245 | + | 4.26245i | −0.244468 | + | 0.244468i | ||||
\(305\) | −13.9583 | + | 3.74012i | −0.799250 | + | 0.214158i | ||||
\(306\) | −2.02828 | + | 0.543477i | −0.115949 | + | 0.0310685i | ||||
\(307\) | −8.27574 | − | 8.27574i | −0.472322 | − | 0.472322i | 0.430344 | − | 0.902665i | \(-0.358392\pi\) |
−0.902665 | + | 0.430344i | \(0.858392\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 37.3658 | − | 21.5731i | 2.12566 | − | 1.22725i | ||||
\(310\) | −2.30539 | − | 0.617726i | −0.130937 | − | 0.0350845i | ||||
\(311\) | −12.9025 | −0.731632 | −0.365816 | − | 0.930687i | \(-0.619210\pi\) | ||||
−0.365816 | + | 0.930687i | \(0.619210\pi\) | |||||||
\(312\) | −7.82792 | + | 5.71773i | −0.443169 | + | 0.323703i | ||||
\(313\) | − | 5.96180i | − | 0.336981i | −0.985703 | − | 0.168490i | \(-0.946111\pi\) | ||
0.985703 | − | 0.168490i | \(-0.0538892\pi\) | |||||||
\(314\) | −2.89355 | − | 0.775325i | −0.163293 | − | 0.0437541i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.11430 | + | 4.10744i | 0.400211 | + | 0.231062i | ||||
\(317\) | 9.14807 | + | 9.14807i | 0.513807 | + | 0.513807i | 0.915691 | − | 0.401884i | \(-0.131644\pi\) |
−0.401884 | + | 0.915691i | \(0.631644\pi\) | |||||||
\(318\) | 2.31920 | + | 8.65537i | 0.130054 | + | 0.485369i | ||||
\(319\) | 6.83225 | + | 25.4983i | 0.382532 | + | 1.42763i | ||||
\(320\) | −6.55673 | − | 6.55673i | −0.366533 | − | 0.366533i | ||||
\(321\) | −8.80540 | − | 5.08380i | −0.491470 | − | 0.283750i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.83262 | − | 1.02695i | −0.213253 | − | 0.0571409i | ||||
\(324\) | 15.5507i | 0.863928i | ||||||||
\(325\) | 6.35132 | − | 7.88406i | 0.352308 | − | 0.437329i | ||||
\(326\) | −1.05673 | −0.0585267 | ||||||||
\(327\) | 19.1767 | + | 5.13838i | 1.06047 | + | 0.284153i | ||||
\(328\) | 0.797788 | − | 0.460603i | 0.0440505 | − | 0.0254325i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.29159 | − | 3.29159i | −0.181196 | − | 0.181196i | ||||
\(331\) | 9.65252 | − | 2.58639i | 0.530551 | − | 0.142161i | 0.0164080 | − | 0.999865i | \(-0.494777\pi\) |
0.514142 | + | 0.857705i | \(0.328110\pi\) | |||||||
\(332\) | 10.2181 | − | 2.73794i | 0.560793 | − | 0.150264i | ||||
\(333\) | −19.7993 | + | 19.7993i | −1.08499 | + | 1.08499i | ||||
\(334\) | −5.76920 | − | 3.33085i | −0.315677 | − | 0.182256i | ||||
\(335\) | −0.403834 | − | 0.699462i | −0.0220638 | − | 0.0382157i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 17.5327i | − | 0.955069i | −0.878613 | − | 0.477534i | \(-0.841531\pi\) | ||
0.878613 | − | 0.477534i | \(-0.158469\pi\) | |||||||
\(338\) | −3.54878 | − | 0.167922i | −0.193028 | − | 0.00913374i | ||||
\(339\) | − | 46.2723i | − | 2.51317i | ||||||
\(340\) | 1.72760 | − | 6.44749i | 0.0936923 | − | 0.349664i | ||||
\(341\) | −23.4493 | + | 13.5384i | −1.26985 | + | 0.733148i | ||||
\(342\) | −0.759751 | + | 1.31593i | −0.0410826 | + | 0.0711572i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.03486 | + | 0.545238i | −0.109712 | + | 0.0293973i | ||||
\(345\) | −4.60294 | − | 17.1784i | −0.247814 | − | 0.924853i | ||||
\(346\) | −0.927536 | − | 0.927536i | −0.0498647 | − | 0.0498647i | ||||
\(347\) | 13.1271 | − | 22.7368i | 0.704700 | − | 1.22058i | −0.262100 | − | 0.965041i | \(-0.584415\pi\) |
0.966800 | − | 0.255535i | \(-0.0822516\pi\) | |||||||
\(348\) | 13.8745 | + | 24.0313i | 0.743749 | + | 1.28821i | ||||
\(349\) | 2.90133 | − | 10.8279i | 0.155304 | − | 0.579604i | −0.843775 | − | 0.536698i | \(-0.819672\pi\) |
0.999079 | − | 0.0429064i | \(-0.0136617\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.59468 | − | 1.97951i | 0.0851175 | − | 0.105659i | ||||
\(352\) | 14.3114 | 0.762799 | ||||||||
\(353\) | −6.76519 | − | 1.81273i | −0.360075 | − | 0.0964817i | 0.0742463 | − | 0.997240i | \(-0.476345\pi\) |
−0.434321 | + | 0.900758i | \(0.643012\pi\) | |||||||
\(354\) | 0.530531 | + | 0.918907i | 0.0281974 | + | 0.0488394i | ||||
\(355\) | −1.35699 | + | 2.35038i | −0.0720218 | + | 0.124745i | ||||
\(356\) | −19.1002 | + | 19.1002i | −1.01231 | + | 1.01231i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.787984 | + | 2.94080i | 0.0416463 | + | 0.155426i | ||||
\(359\) | 3.61441 | − | 3.61441i | 0.190761 | − | 0.190761i | −0.605264 | − | 0.796025i | \(-0.706932\pi\) |
0.796025 | + | 0.605264i | \(0.206932\pi\) | |||||||
\(360\) | −4.51336 | − | 2.60579i | −0.237875 | − | 0.137337i | ||||
\(361\) | 13.9679 | − | 8.06438i | 0.735154 | − | 0.424441i | ||||
\(362\) | −0.305881 | + | 1.14156i | −0.0160767 | + | 0.0599992i | ||||
\(363\) | −25.2417 | −1.32485 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.49837 | 0.183113 | ||||||||
\(366\) | 1.73023 | − | 6.45729i | 0.0904404 | − | 0.337528i | ||||
\(367\) | −15.9153 | + | 9.18868i | −0.830770 | + | 0.479645i | −0.854116 | − | 0.520082i | \(-0.825901\pi\) |
0.0233461 | + | 0.999727i | \(0.492568\pi\) | |||||||
\(368\) | 14.7658 | + | 8.52503i | 0.769720 | + | 0.444398i | ||||
\(369\) | −1.99247 | + | 1.99247i | −0.103724 | + | 0.103724i | ||||
\(370\) | 0.893642 | + | 3.33512i | 0.0464582 | + | 0.173385i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −20.1262 | + | 20.1262i | −1.04350 | + | 1.04350i | ||||
\(373\) | −10.4260 | + | 18.0583i | −0.539837 | + | 0.935025i | 0.459075 | + | 0.888397i | \(0.348181\pi\) |
−0.998912 | + | 0.0466277i | \(0.985153\pi\) | |||||||
\(374\) | 1.46878 | + | 2.54400i | 0.0759487 | + | 0.131547i | ||||
\(375\) | 27.9854 | + | 7.49867i | 1.44516 | + | 0.387230i | ||||
\(376\) | 8.61524 | 0.444297 | ||||||||
\(377\) | −3.19158 | + | 20.4873i | −0.164375 | + | 1.05515i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.22021 | − | 26.9462i | 0.370877 | − | 1.38413i | −0.488399 | − | 0.872620i | \(-0.662419\pi\) |
0.859276 | − | 0.511512i | \(-0.170914\pi\) | |||||||
\(380\) | −2.41509 | − | 4.18306i | −0.123892 | − | 0.214587i | ||||
\(381\) | 3.64762 | − | 6.31787i | 0.186873 | − | 0.323674i | ||||
\(382\) | 1.22120 | + | 1.22120i | 0.0624820 | + | 0.0624820i | ||||
\(383\) | −6.36142 | − | 23.7412i | −0.325054 | − | 1.21312i | −0.914258 | − | 0.405132i | \(-0.867225\pi\) |
0.589204 | − | 0.807984i | \(-0.299441\pi\) | |||||||
\(384\) | 19.2384 | − | 5.15492i | 0.981758 | − | 0.263061i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.62775 | − | 2.81934i | 0.0828502 | − | 0.143501i | ||||
\(387\) | 5.58048 | − | 3.22189i | 0.283672 | − | 0.163778i | ||||
\(388\) | −1.41340 | + | 5.27488i | −0.0717545 | + | 0.267792i | ||||
\(389\) | 24.4888i | 1.24163i | 0.783957 | + | 0.620815i | \(0.213198\pi\) | ||||
−0.783957 | + | 0.620815i | \(0.786802\pi\) | |||||||
\(390\) | −1.31897 | − | 3.41014i | −0.0667887 | − | 0.172679i | ||||
\(391\) | 11.2229i | 0.567565i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.4188 | − | 21.5099i | −0.626444 | − | 1.08503i | ||||
\(394\) | −0.487853 | − | 0.281662i | −0.0245777 | − | 0.0141899i | ||||
\(395\) | −4.46697 | + | 4.46697i | −0.224758 | + | 0.224758i | ||||
\(396\) | −28.0117 | + | 7.50570i | −1.40764 | + | 0.377176i | ||||
\(397\) | 18.7029 | − | 5.01142i | 0.938671 | − | 0.251516i | 0.243122 | − | 0.969996i | \(-0.421828\pi\) |
0.695548 | + | 0.718480i | \(0.255162\pi\) | |||||||
\(398\) | 3.58716 | + | 3.58716i | 0.179808 | + | 0.179808i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.65079 | + | 4.99454i | −0.432539 | + | 0.249727i | ||||
\(401\) | 12.7770 | + | 3.42360i | 0.638055 | + | 0.170966i | 0.563322 | − | 0.826237i | \(-0.309523\pi\) |
0.0747328 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(402\) | 0.373638 | 0.0186354 | ||||||||
\(403\) | −21.1456 | + | 2.27678i | −1.05334 | + | 0.113414i | ||||
\(404\) | − | 20.4859i | − | 1.01921i | ||||||
\(405\) | −11.5510 | − | 3.09509i | −0.573975 | − | 0.153796i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.9232 | + | 19.5856i | 1.68151 | + | 0.970821i | ||||
\(408\) | 4.45167 | + | 4.45167i | 0.220390 | + | 0.220390i | ||||
\(409\) | 6.44521 | + | 24.0538i | 0.318695 | + | 1.18939i | 0.920500 | + | 0.390743i | \(0.127782\pi\) |
−0.601805 | + | 0.798643i | \(0.705551\pi\) | |||||||
\(410\) | 0.0899304 | + | 0.335625i | 0.00444135 | + | 0.0165753i | ||||
\(411\) | 0.965263 | + | 0.965263i | 0.0476129 | + | 0.0476129i | ||||
\(412\) | −28.7045 | − | 16.5726i | −1.41417 | − | 0.816472i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.15142 | + | 1.11237i | 0.204031 | + | 0.0546700i | ||||
\(415\) | 8.13493i | 0.399328i | ||||||||
\(416\) | 10.2807 | + | 4.54605i | 0.504055 | + | 0.222888i | ||||
\(417\) | −9.62241 | −0.471212 | ||||||||
\(418\) | 2.05327 | + | 0.550173i | 0.100429 | + | 0.0269098i | ||||
\(419\) | 13.9899 | − | 8.07708i | 0.683452 | − | 0.394591i | −0.117703 | − | 0.993049i | \(-0.537553\pi\) |
0.801154 | + | 0.598458i | \(0.204220\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.8050 | − | 12.8050i | −0.624080 | − | 0.624080i | 0.322492 | − | 0.946572i | \(-0.395479\pi\) |
−0.946572 | + | 0.322492i | \(0.895479\pi\) | |||||||
\(422\) | 0.741075 | − | 0.198570i | 0.0360750 | − | 0.00966626i | ||||
\(423\) | −25.4543 | + | 6.82047i | −1.23763 | + | 0.331622i | ||||
\(424\) | 9.92376 | − | 9.92376i | 0.481941 | − | 0.481941i | ||||
\(425\) | −5.69421 | − | 3.28755i | −0.276210 | − | 0.159470i | ||||
\(426\) | −0.627763 | − | 1.08732i | −0.0304152 | − | 0.0526807i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.81080i | 0.377549i | ||||||||
\(429\) | −37.9370 | − | 16.7754i | −1.83162 | − | 0.809924i | ||||
\(430\) | − | 0.794591i | − | 0.0383186i | ||||||
\(431\) | 5.78727 | − | 21.5984i | 0.278763 | − | 1.04036i | −0.674515 | − | 0.738261i | \(-0.735647\pi\) |
0.953278 | − | 0.302096i | \(-0.0976863\pi\) | |||||||
\(432\) | −2.17202 | + | 1.25402i | −0.104502 | + | 0.0603340i | ||||
\(433\) | −9.21467 | + | 15.9603i | −0.442829 | + | 0.767002i | −0.997898 | − | 0.0648019i | \(-0.979358\pi\) |
0.555069 | + | 0.831804i | \(0.312692\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −20.6118 | + | 5.52292i | −0.988261 | + | 0.264804i | ||||
\(436\) | −3.94732 | − | 14.7316i | −0.189043 | − | 0.705517i | ||||
\(437\) | 5.74256 | + | 5.74256i | 0.274704 | + | 0.274704i | ||||
\(438\) | −0.809195 | + | 1.40157i | −0.0386648 | + | 0.0669694i | ||||
\(439\) | 7.79998 | + | 13.5100i | 0.372273 | + | 0.644795i | 0.989915 | − | 0.141664i | \(-0.0452453\pi\) |
−0.617642 | + | 0.786459i | \(0.711912\pi\) | |||||||
\(440\) | −1.88698 | + | 7.04230i | −0.0899582 | + | 0.335729i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.247006 | + | 2.29407i | 0.0117489 | + | 0.109118i | ||||
\(443\) | −29.5897 | −1.40585 | −0.702926 | − | 0.711263i | \(-0.748123\pi\) | ||||
−0.702926 | + | 0.711263i | \(0.748123\pi\) | |||||||
\(444\) | 39.7730 | + | 10.6571i | 1.88754 | + | 0.505766i | ||||
\(445\) | −10.3860 | − | 17.9891i | −0.492344 | − | 0.852765i | ||||
\(446\) | 2.21643 | − | 3.83897i | 0.104951 | − | 0.181781i | ||||
\(447\) | 41.4515 | − | 41.4515i | 1.96059 | − | 1.96059i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.50811 | − | 9.36041i | −0.118365 | − | 0.441745i | 0.881151 | − | 0.472834i | \(-0.156769\pi\) |
−0.999517 | + | 0.0310893i | \(0.990102\pi\) | |||||||
\(450\) | −1.78048 | + | 1.78048i | −0.0839326 | + | 0.0839326i | ||||
\(451\) | 3.41381 | + | 1.97097i | 0.160750 | + | 0.0928092i | ||||
\(452\) | −30.7843 | + | 17.7733i | −1.44797 | + | 0.835986i | ||||
\(453\) | 4.27625 | − | 15.9592i | 0.200916 | − | 0.749827i | ||||
\(454\) | −0.479673 | −0.0225122 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.55569 | 0.213340 | ||||||||
\(457\) | 8.97136 | − | 33.4816i | 0.419663 | − | 1.56620i | −0.355646 | − | 0.934621i | \(-0.615739\pi\) |
0.775309 | − | 0.631582i | \(-0.217594\pi\) | |||||||
\(458\) | 2.63756 | − | 1.52279i | 0.123245 | − | 0.0711555i | ||||
\(459\) | −1.42969 | − | 0.825433i | −0.0667323 | − | 0.0385279i | ||||
\(460\) | −9.66052 | + | 9.66052i | −0.450424 | + | 0.450424i | ||||
\(461\) | 2.45042 | + | 9.14508i | 0.114127 | + | 0.425929i | 0.999220 | − | 0.0394858i | \(-0.0125720\pi\) |
−0.885093 | + | 0.465414i | \(0.845905\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.59580 | − | 3.59580i | 0.167111 | − | 0.167111i | −0.618597 | − | 0.785708i | \(-0.712299\pi\) |
0.785708 | + | 0.618597i | \(0.212299\pi\) | |||||||
\(464\) | 10.2289 | − | 17.7170i | 0.474866 | − | 0.822491i | ||||
\(465\) | −10.9439 | − | 18.9555i | −0.507513 | − | 0.879038i | ||||
\(466\) | 5.37598 | + | 1.44049i | 0.249038 | + | 0.0667294i | ||||
\(467\) | 24.1247 | 1.11636 | 0.558179 | − | 0.829721i | \(-0.311500\pi\) | ||||
0.558179 | + | 0.829721i | \(0.311500\pi\) | |||||||
\(468\) | −22.5067 | − | 3.50617i | −1.04037 | − | 0.162073i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.841041 | + | 3.13881i | −0.0387943 | + | 0.144782i | ||||
\(471\) | −13.7360 | − | 23.7915i | −0.632923 | − | 1.09626i | ||||
\(472\) | 0.830922 | − | 1.43920i | 0.0382463 | − | 0.0662445i | ||||
\(473\) | −6.37423 | − | 6.37423i | −0.293087 | − | 0.293087i | ||||
\(474\) | −0.756384 | − | 2.82286i | −0.0347418 | − | 0.129658i | ||||
\(475\) | −4.59582 | + | 1.23145i | −0.210871 | + | 0.0565027i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.4641 | + | 37.1769i | −0.982772 | + | 1.70221i | ||||
\(478\) | −4.89210 | + | 2.82445i | −0.223759 | + | 0.129188i | ||||
\(479\) | 6.34020 | − | 23.6619i | 0.289691 | − | 1.08114i | −0.655652 | − | 0.755063i | \(-0.727606\pi\) |
0.945343 | − | 0.326078i | \(-0.105727\pi\) | |||||||
\(480\) | 11.5687i | 0.528039i | ||||||||
\(481\) | 18.1477 | + | 24.8453i | 0.827465 | + | 1.13285i | ||||
\(482\) | − | 3.90182i | − | 0.177723i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.69539 | + | 16.7929i | 0.440700 | + | 0.763314i | ||||
\(485\) | −3.63686 | − | 2.09974i | −0.165141 | − | 0.0953443i | ||||
\(486\) | 4.32054 | − | 4.32054i | 0.195984 | − | 0.195984i | ||||
\(487\) | 36.9186 | − | 9.89230i | 1.67294 | − | 0.448263i | 0.707039 | − | 0.707174i | \(-0.250030\pi\) |
0.965901 | + | 0.258911i | \(0.0833637\pi\) | |||||||
\(488\) | −10.1135 | + | 2.70989i | −0.457815 | + | 0.122671i | ||||
\(489\) | −6.85254 | − | 6.85254i | −0.309883 | − | 0.309883i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.2155 | − | 5.89793i | 0.461020 | − | 0.266170i | −0.251453 | − | 0.967869i | \(-0.580908\pi\) |
0.712473 | + | 0.701700i | \(0.247575\pi\) | |||||||
\(492\) | 4.00250 | + | 1.07247i | 0.180447 | + | 0.0483505i | ||||
\(493\) | 13.4660 | 0.606476 | ||||||||
\(494\) | 1.30023 | + | 1.04745i | 0.0585001 | + | 0.0471271i | ||||
\(495\) | − | 22.3009i | − | 1.00235i | ||||||
\(496\) | 20.2691 | + | 5.43109i | 0.910110 | + | 0.243863i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.25914 | − | 1.88166i | −0.146045 | − | 0.0843193i | ||||
\(499\) | 10.8271 | + | 10.8271i | 0.484686 | + | 0.484686i | 0.906625 | − | 0.421938i | \(-0.138650\pi\) |
−0.421938 | + | 0.906625i | \(0.638650\pi\) | |||||||
\(500\) | −5.76051 | − | 21.4985i | −0.257618 | − | 0.961443i | ||||
\(501\) | −15.8119 | − | 59.0110i | −0.706426 | − | 2.63642i | ||||
\(502\) | −1.25431 | − | 1.25431i | −0.0559826 | − | 0.0559826i | ||||
\(503\) | 21.5683 | + | 12.4524i | 0.961682 | + | 0.555227i | 0.896690 | − | 0.442659i | \(-0.145965\pi\) |
0.0649915 | + | 0.997886i | \(0.479298\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.2169 | + | 4.07735i | 0.677142 | + | 0.181440i | ||||
\(506\) | − | 6.01249i | − | 0.267288i | ||||||
\(507\) | −21.9238 | − | 24.1016i | −0.973669 | − | 1.07039i | ||||
\(508\) | −5.60424 | −0.248648 | ||||||||
\(509\) | −32.3493 | − | 8.66796i | −1.43386 | − | 0.384201i | −0.543478 | − | 0.839423i | \(-0.682893\pi\) |
−0.890378 | + | 0.455222i | \(0.849560\pi\) | |||||||
\(510\) | −2.05647 | + | 1.18730i | −0.0910619 | + | 0.0525746i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −13.2395 | − | 13.2395i | −0.585111 | − | 0.585111i | ||||
\(513\) | −1.15391 | + | 0.309189i | −0.0509464 | + | 0.0136510i | ||||
\(514\) | −5.85924 | + | 1.56998i | −0.258440 | + | 0.0692488i | ||||
\(515\) | 18.0232 | − | 18.0232i | 0.794196 | − | 0.794196i | ||||
\(516\) | −8.20638 | − | 4.73796i | −0.361266 | − | 0.208577i | ||||
\(517\) | 18.4327 | + | 31.9264i | 0.810670 | + | 1.40412i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 12.0296i | − | 0.528039i | ||||||
\(520\) | −3.59254 | + | 4.45952i | −0.157543 | + | 0.195563i | ||||
\(521\) | 22.9606i | 1.00592i | 0.864309 | + | 0.502962i | \(0.167756\pi\) | ||||
−0.864309 | + | 0.502962i | \(0.832244\pi\) | |||||||
\(522\) | 1.33470 | − | 4.98116i | 0.0584181 | − | 0.218019i | ||||
\(523\) | −2.92715 | + | 1.68999i | −0.127995 | + | 0.0738980i | −0.562630 | − | 0.826709i | \(-0.690211\pi\) |
0.434635 | + | 0.900607i | \(0.356877\pi\) | |||||||
\(524\) | −9.54015 | + | 16.5240i | −0.416764 | + | 0.721856i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.66785 | − | 0.714848i | 0.116324 | − | 0.0311688i | ||||
\(527\) | 3.57491 | + | 13.3417i | 0.155725 | + | 0.581175i | ||||
\(528\) | 28.9399 | + | 28.9399i | 1.25945 | + | 1.25945i | ||||
\(529\) | −0.0147097 | + | 0.0254780i | −0.000639552 | + | 0.00110774i | ||||
\(530\) | 2.64676 | + | 4.58433i | 0.114968 | + | 0.199130i | ||||
\(531\) | −1.31564 | + | 4.91004i | −0.0570939 | + | 0.213078i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.82627 | + | 2.50027i | 0.0791046 | + | 0.108299i | ||||
\(534\) | 9.60940 | 0.415840 | ||||||||
\(535\) | −5.80184 | − | 1.55460i | −0.250835 | − | 0.0672111i | ||||
\(536\) | −0.292598 | − | 0.506794i | −0.0126383 | − | 0.0218902i | ||||
\(537\) | −13.9603 | + | 24.1800i | −0.602432 | + | 1.04344i | ||||
\(538\) | 2.00167 | − | 2.00167i | 0.0862979 | − | 0.0862979i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.520139 | − | 1.94119i | −0.0223832 | − | 0.0835353i | ||||
\(541\) | −22.7480 | + | 22.7480i | −0.978012 | + | 0.978012i | −0.999763 | − | 0.0217516i | \(-0.993076\pi\) |
0.0217516 | + | 0.999763i | \(0.493076\pi\) | |||||||
\(542\) | −0.773787 | − | 0.446746i | −0.0332370 | − | 0.0191894i | ||||
\(543\) | −9.38621 | + | 5.41913i | −0.402801 | + | 0.232557i | ||||
\(544\) | 1.88950 | − | 7.05172i | 0.0810118 | − | 0.302340i | ||||
\(545\) | 11.7282 | 0.502383 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.1782 | −0.563460 | −0.281730 | − | 0.959494i | \(-0.590908\pi\) | ||||
−0.281730 | + | 0.959494i | \(0.590908\pi\) | |||||||
\(548\) | 0.271415 | − | 1.01293i | 0.0115943 | − | 0.0432704i | ||||
\(549\) | 27.7356 | − | 16.0132i | 1.18373 | − | 0.683425i | ||||
\(550\) | 3.05059 | + | 1.76126i | 0.130078 | + | 0.0751004i | ||||
\(551\) | 6.89031 | − | 6.89031i | 0.293537 | − | 0.293537i | ||||
\(552\) | −3.33505 | − | 12.4466i | −0.141949 | − | 0.529761i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.21995 | + | 3.21995i | −0.136803 | + | 0.136803i | ||||
\(555\) | −15.8322 | + | 27.4222i | −0.672039 | + | 1.16401i | ||||
\(556\) | 3.69599 | + | 6.40164i | 0.156745 | + | 0.271490i | ||||
\(557\) | 3.94410 | + | 1.05682i | 0.167117 | + | 0.0447788i | 0.341407 | − | 0.939916i | \(-0.389097\pi\) |
−0.174290 | + | 0.984694i | \(0.555763\pi\) | |||||||
\(558\) | 5.28954 | 0.223924 | ||||||||
\(559\) | −2.55421 | − | 6.60379i | −0.108032 | − | 0.279311i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.97247 | + | 26.0216i | −0.294378 | + | 1.09863i | ||||
\(562\) | 1.55000 | + | 2.68468i | 0.0653828 | + | 0.113246i | ||||
\(563\) | −10.2301 | + | 17.7191i | −0.431149 | + | 0.746772i | −0.996973 | − | 0.0777545i | \(-0.975225\pi\) |
0.565824 | + | 0.824526i | \(0.308558\pi\) | |||||||
\(564\) | 27.4021 | + | 27.4021i | 1.15383 | + | 1.15383i | ||||
\(565\) | −7.07491 | − | 26.4039i | −0.297644 | − | 1.11082i | ||||
\(566\) | −3.81191 | + | 1.02140i | −0.160227 | + | 0.0429326i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.983208 | + | 1.70297i | −0.0412545 | + | 0.0714549i | ||||
\(569\) | −8.00992 | + | 4.62453i | −0.335793 | + | 0.193870i | −0.658410 | − | 0.752659i | \(-0.728771\pi\) |
0.322617 | + | 0.946530i | \(0.395437\pi\) | |||||||
\(570\) | −0.444738 | + | 1.65978i | −0.0186280 | + | 0.0695207i | ||||
\(571\) | 40.7214i | 1.70414i | 0.523430 | + | 0.852069i | \(0.324652\pi\) | ||||
−0.523430 | + | 0.852069i | \(0.675348\pi\) | |||||||
\(572\) | 3.41129 | + | 31.6824i | 0.142633 | + | 1.32471i | ||||
\(573\) | 15.8382i | 0.661650i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.72885 | + | 11.6547i | 0.280613 | + | 0.486035i | ||||
\(576\) | 17.7972 | + | 10.2752i | 0.741549 | + | 0.428134i | ||||
\(577\) | −7.72857 | + | 7.72857i | −0.321745 | + | 0.321745i | −0.849436 | − | 0.527691i | \(-0.823058\pi\) |
0.527691 | + | 0.849436i | \(0.323058\pi\) | |||||||
\(578\) | −3.04016 | + | 0.814608i | −0.126454 | + | 0.0338832i | ||||
\(579\) | 28.8380 | − | 7.72711i | 1.19847 | − | 0.321128i | ||||
\(580\) | 11.5914 | + | 11.5914i | 0.481305 | + | 0.481305i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.68246 | − | 0.971367i | 0.0697401 | − | 0.0402644i | ||||
\(583\) | 58.0080 | + | 15.5432i | 2.40244 | + | 0.643733i | ||||
\(584\) | 2.53474 | 0.104888 | ||||||||
\(585\) | 7.08393 | − | 16.0201i | 0.292884 | − | 0.662349i | ||||
\(586\) | 4.50114i | 0.185941i | ||||||||
\(587\) | 15.6037 | + | 4.18099i | 0.644033 | + | 0.172568i | 0.566029 | − | 0.824385i | \(-0.308479\pi\) |
0.0780032 | + | 0.996953i | \(0.475146\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.65597 | + | 4.99753i | 0.356663 | + | 0.205920i | ||||
\(590\) | 0.443230 | + | 0.443230i | 0.0182475 | + | 0.0182475i | ||||
\(591\) | −1.33708 | − | 4.99007i | −0.0550003 | − | 0.205264i | ||||
\(592\) | −7.85696 | − | 29.3226i | −0.322919 | − | 1.20515i | ||||
\(593\) | 32.7121 | + | 32.7121i | 1.34333 | + | 1.34333i | 0.892726 | + | 0.450600i | \(0.148790\pi\) |
0.450600 | + | 0.892726i | \(0.351210\pi\) | |||||||
\(594\) | 0.765937 | + | 0.442214i | 0.0314268 | + | 0.0181443i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −43.4987 | − | 11.6554i | −1.78178 | − | 0.477425i | ||||
\(597\) | 46.5231i | 1.90407i | ||||||||
\(598\) | 1.90989 | − | 4.31915i | 0.0781010 | − | 0.176623i | ||||
\(599\) | −11.7977 | −0.482042 | −0.241021 | − | 0.970520i | \(-0.577482\pi\) | ||||
−0.241021 | + | 0.970520i | \(0.577482\pi\) | |||||||
\(600\) | 7.29204 | + | 1.95390i | 0.297696 | + | 0.0797675i | ||||
\(601\) | 11.5727 | − | 6.68152i | 0.472062 | − | 0.272545i | −0.245041 | − | 0.969513i | \(-0.578801\pi\) |
0.717102 | + | 0.696968i | \(0.245468\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.26572 | + | 1.26572i | 0.0515439 | + | 0.0515439i | ||||
\(604\) | −12.2599 | + | 3.28503i | −0.498848 | + | 0.133666i | ||||
\(605\) | −14.4034 | + | 3.85938i | −0.585582 | + | 0.156906i | ||||
\(606\) | −5.15329 | + | 5.15329i | −0.209338 | + | 0.209338i | ||||
\(607\) | −29.5465 | − | 17.0587i | −1.19926 | − | 0.692392i | −0.238868 | − | 0.971052i | \(-0.576776\pi\) |
−0.960390 | + | 0.278660i | \(0.910110\pi\) | |||||||
\(608\) | −2.64142 | − | 4.57508i | −0.107124 | − | 0.185544i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 3.94921i | − | 0.159899i | ||||||
\(611\) | 3.09985 | + | 28.7899i | 0.125407 | + | 1.16472i | ||||
\(612\) | 14.7933i | 0.597984i | ||||||||
\(613\) | −1.05301 | + | 3.92990i | −0.0425308 | + | 0.158727i | −0.983925 | − | 0.178580i | \(-0.942850\pi\) |
0.941395 | + | 0.337307i | \(0.109516\pi\) | |||||||
\(614\) | 2.76996 | − | 1.59924i | 0.111787 | − | 0.0645400i | ||||
\(615\) | −1.59325 | + | 2.75959i | −0.0642461 | + | 0.111277i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.7169 | + | 4.74724i | −0.713257 | + | 0.191117i | −0.597161 | − | 0.802121i | \(-0.703705\pi\) |
−0.116096 | + | 0.993238i | \(0.537038\pi\) | |||||||
\(618\) | 3.05183 | + | 11.3896i | 0.122763 | + | 0.458156i | ||||
\(619\) | −25.6416 | − | 25.6416i | −1.03062 | − | 1.03062i | −0.999516 | − | 0.0311060i | \(-0.990097\pi\) |
−0.0311060 | − | 0.999516i | \(-0.509903\pi\) | |||||||
\(620\) | −8.40718 | + | 14.5617i | −0.337641 | + | 0.584811i | ||||
\(621\) | 1.68947 | + | 2.92624i | 0.0677960 | + | 0.117426i | ||||
\(622\) | 0.912620 | − | 3.40595i | 0.0365927 | − | 0.136566i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 11.5965 | + | 29.9822i | 0.464231 | + | 1.20025i | ||||
\(625\) | 3.07595 | 0.123038 | ||||||||
\(626\) | 1.57377 | + | 0.421691i | 0.0629006 | + | 0.0168542i | ||||
\(627\) | 9.74713 | + | 16.8825i | 0.389263 | + | 0.674223i | ||||
\(628\) | −10.5521 | + | 18.2767i | −0.421074 | + | 0.729321i | ||||
\(629\) | 14.1293 | − | 14.1293i | 0.563373 | − | 0.563373i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.52992 | + | 24.3700i | 0.259952 | + | 0.970153i | 0.965268 | + | 0.261261i | \(0.0841383\pi\) |
−0.705316 | + | 0.708893i | \(0.749195\pi\) | |||||||
\(632\) | −3.23654 | + | 3.23654i | −0.128742 | + | 0.128742i | ||||
\(633\) | 6.09330 | + | 3.51797i | 0.242187 | + | 0.139827i | ||||
\(634\) | −3.06194 | + | 1.76781i | −0.121605 | + | 0.0702087i | ||||
\(635\) | 1.11542 | − | 4.16281i | 0.0442642 | − | 0.165196i | ||||
\(636\) | 63.1280 | 2.50319 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.21420 | −0.285613 | ||||||||
\(639\) | 1.55676 | − | 5.80992i | 0.0615846 | − | 0.229837i | ||||
\(640\) | 10.1897 | − | 5.88301i | 0.402782 | − | 0.232546i | ||||
\(641\) | 9.82660 | + | 5.67339i | 0.388127 | + | 0.224085i | 0.681348 | − | 0.731959i | \(-0.261394\pi\) |
−0.293221 | + | 0.956045i | \(0.594727\pi\) | |||||||
\(642\) | 1.96483 | − | 1.96483i | 0.0775456 | − | 0.0775456i | ||||
\(643\) | −2.92632 | − | 10.9212i | −0.115403 | − | 0.430690i | 0.883914 | − | 0.467650i | \(-0.154899\pi\) |
−0.999317 | + | 0.0369602i | \(0.988233\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.15267 | − | 5.15267i | 0.202886 | − | 0.202886i | ||||
\(646\) | 0.542179 | − | 0.939082i | 0.0213318 | − | 0.0369477i | ||||
\(647\) | 9.64081 | + | 16.6984i | 0.379020 | + | 0.656481i | 0.990920 | − | 0.134454i | \(-0.0429280\pi\) |
−0.611900 | + | 0.790935i | \(0.709595\pi\) | |||||||
\(648\) | −8.36927 | − | 2.24254i | −0.328776 | − | 0.0880953i | ||||
\(649\) | 7.11120 | 0.279139 | ||||||||
\(650\) | 1.63196 | + | 2.23425i | 0.0640108 | + | 0.0876346i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.92681 | + | 7.19096i | −0.0754598 | + | 0.281620i | ||||
\(653\) | −1.99409 | − | 3.45386i | −0.0780346 | − | 0.135160i | 0.824367 | − | 0.566055i | \(-0.191531\pi\) |
−0.902402 | + | 0.430895i | \(0.858198\pi\) | |||||||
\(654\) | −2.71282 | + | 4.69874i | −0.106080 | + | 0.183735i | ||||
\(655\) | −10.3752 | − | 10.3752i | −0.405393 | − | 0.405393i | ||||
\(656\) | −0.790674 | − | 2.95084i | −0.0308706 | − | 0.115211i | ||||
\(657\) | −7.48906 | + | 2.00669i | −0.292176 | + | 0.0782883i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.3526 | + | 23.1273i | −0.520143 | + | 0.900913i | 0.479583 | + | 0.877496i | \(0.340788\pi\) |
−0.999726 | + | 0.0234170i | \(0.992545\pi\) | |||||||
\(660\) | −28.4009 | + | 16.3973i | −1.10550 | + | 0.638263i | ||||
\(661\) | −3.67516 | + | 13.7159i | −0.142947 | + | 0.533486i | 0.856891 | + | 0.515498i | \(0.172393\pi\) |
−0.999838 | + | 0.0179886i | \(0.994274\pi\) | |||||||
\(662\) | 2.73098i | 0.106142i | ||||||||
\(663\) | −13.2746 | + | 16.4781i | −0.515542 | + | 0.639956i | ||||
\(664\) | 5.89415i | 0.228738i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.82609 | − | 6.62699i | −0.148258 | − | 0.256790i | ||||
\(667\) | −23.8691 | − | 13.7808i | −0.924216 | − | 0.533596i | ||||
\(668\) | −33.1857 | + | 33.1857i | −1.28399 | + | 1.28399i | ||||
\(669\) | 39.2674 | − | 10.5217i | 1.51816 | − | 0.406791i | ||||
\(670\) | 0.213205 | − | 0.0571282i | 0.00823684 | − | 0.00220705i | ||||
\(671\) | −31.6806 | − | 31.6806i | −1.22302 | − | 1.22302i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.5521 | − | 19.9487i | 1.33189 | − | 0.768965i | 0.346298 | − | 0.938124i | \(-0.387439\pi\) |
0.985589 | + | 0.169159i | \(0.0541052\pi\) | |||||||
\(674\) | 4.62822 | + | 1.24013i | 0.178273 | + | 0.0477680i | ||||
\(675\) | −1.97961 | −0.0761951 | ||||||||
\(676\) | −7.61346 | + | 23.8430i | −0.292825 | + | 0.917039i | ||||
\(677\) | − | 6.56822i | − | 0.252437i | −0.992002 | − | 0.126219i | \(-0.959716\pi\) | ||
0.992002 | − | 0.126219i | \(-0.0402841\pi\) | |||||||
\(678\) | 12.2148 | + | 3.27294i | 0.469106 | + | 0.125697i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.22086 | + | 1.85956i | 0.123514 | + | 0.0713110i | ||||
\(681\) | −3.11053 | − | 3.11053i | −0.119196 | − | 0.119196i | ||||
\(682\) | −1.91521 | − | 7.14765i | −0.0733371 | − | 0.273698i | ||||
\(683\) | 3.02219 | + | 11.2790i | 0.115641 | + | 0.431578i | 0.999334 | − | 0.0364888i | \(-0.0116173\pi\) |
−0.883693 | + | 0.468067i | \(0.844951\pi\) | |||||||
\(684\) | 7.56949 | + | 7.56949i | 0.289427 | + | 0.289427i | ||||
\(685\) | 0.698384 | + | 0.403212i | 0.0266839 | + | 0.0154060i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.9785 | + | 7.22888i | 1.02930 | + | 0.275799i | ||||
\(688\) | 6.98610i | 0.266343i | ||||||||
\(689\) | 36.7334 | + | 29.5920i | 1.39943 | + | 1.12737i | ||||
\(690\) | 4.86026 | 0.185027 | ||||||||
\(691\) | −19.0196 | − | 5.09630i | −0.723541 | − | 0.193872i | −0.121790 | − | 0.992556i | \(-0.538863\pi\) |
−0.601751 | + | 0.798684i | \(0.705530\pi\) | |||||||
\(692\) | −8.00308 | + | 4.62058i | −0.304231 | + | 0.175648i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.07347 | + | 5.07347i | 0.192586 | + | 0.192586i | ||||
\(695\) | −5.49074 | + | 1.47124i | −0.208276 | + | 0.0558073i | ||||
\(696\) | −14.9343 | + | 4.00162i | −0.566081 | + | 0.151681i | ||||
\(697\) | 1.42188 | − | 1.42188i | 0.0538577 | − | 0.0538577i | ||||
\(698\) | 2.65309 | + | 1.53176i | 0.100421 | + | 0.0579780i | ||||
\(699\) | 25.5204 | + | 44.2027i | 0.965271 | + | 1.67190i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.58634i | 0.0599153i | 0.999551 | + | 0.0299577i | \(0.00953725\pi\) | ||||
−0.999551 | + | 0.0299577i | \(0.990463\pi\) | |||||||
\(702\) | 0.409750 | + | 0.560972i | 0.0154650 | + | 0.0211725i | ||||
\(703\) | − | 14.4595i | − | 0.545350i | ||||||
\(704\) | 7.44078 | − | 27.7694i | 0.280435 | − | 1.04660i | ||||
\(705\) | −25.8081 | + | 14.9003i | −0.971988 | + | 0.561177i | ||||
\(706\) | 0.957033 | − | 1.65763i | 0.0360184 | − | 0.0623857i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7.22047 | − | 1.93472i | 0.271362 | − | 0.0727111i | ||||
\(709\) | −4.46614 | − | 16.6679i | −0.167730 | − | 0.625975i | −0.997676 | − | 0.0681325i | \(-0.978296\pi\) |
0.829947 | − | 0.557843i | \(-0.188371\pi\) | |||||||
\(710\) | −0.524462 | − | 0.524462i | −0.0196827 | − | 0.0196827i | ||||
\(711\) | 7.00029 | − | 12.1249i | 0.262531 | − | 0.454718i | ||||
\(712\) | −7.52517 | − | 13.0340i | −0.282017 | − | 0.488469i | ||||
\(713\) | 7.31700 | − | 27.3074i | 0.274024 | − | 1.02267i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.2125 | − | 3.77191i | −0.905498 | − | 0.141061i | ||||
\(716\) | 21.4487 | 0.801577 | ||||||||
\(717\) | −50.0394 | − | 13.4080i | −1.86876 | − | 0.500732i | ||||
\(718\) | 0.698463 | + | 1.20977i | 0.0260664 | + | 0.0451483i | ||||
\(719\) | 11.5856 | − | 20.0668i | 0.432069 | − | 0.748365i | −0.564983 | − | 0.825103i | \(-0.691117\pi\) |
0.997051 | + | 0.0767379i | \(0.0244505\pi\) | |||||||
\(720\) | −12.2208 | + | 12.2208i | −0.455441 | + | 0.455441i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.14082 | + | 4.25761i | 0.0424570 | + | 0.158452i | ||||
\(723\) | 25.3021 | − | 25.3021i | 0.940994 | − | 0.940994i | ||||
\(724\) | 7.21053 | + | 4.16300i | 0.267977 | + | 0.154717i | ||||
\(725\) | 13.9841 | − | 8.07374i | 0.519358 | − | 0.299851i | ||||
\(726\) | 1.78540 | − | 6.66321i | 0.0662625 | − | 0.247295i | ||||
\(727\) | −18.3365 | −0.680062 | −0.340031 | − | 0.940414i | \(-0.610438\pi\) | ||||
−0.340031 | + | 0.940414i | \(0.610438\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 31.8037 | 1.17792 | ||||||||
\(730\) | −0.247447 | + | 0.923485i | −0.00915843 | + | 0.0341797i | ||||
\(731\) | −3.98239 | + | 2.29923i | −0.147294 | + | 0.0850401i | ||||
\(732\) | −40.7866 | − | 23.5482i | −1.50752 | − | 0.870365i | ||||
\(733\) | −14.3713 | + | 14.3713i | −0.530816 | + | 0.530816i | −0.920815 | − | 0.389999i | \(-0.872475\pi\) |
0.389999 | + | 0.920815i | \(0.372475\pi\) | |||||||
\(734\) | −1.29987 | − | 4.85119i | −0.0479791 | − | 0.179061i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10.5659 | + | 10.5659i | −0.389463 | + | 0.389463i | ||||
\(737\) | 1.25205 | − | 2.16862i | 0.0461200 | − | 0.0798822i | ||||
\(738\) | −0.385033 | − | 0.666897i | −0.0141733 | − | 0.0245488i | ||||
\(739\) | 32.0846 | + | 8.59704i | 1.18025 | + | 0.316247i | 0.795026 | − | 0.606576i | \(-0.207457\pi\) |
0.385225 | + | 0.922823i | \(0.374124\pi\) | |||||||
\(740\) | 24.3247 | 0.894195 | ||||||||
\(741\) | 1.63919 | + | 15.2240i | 0.0602170 | + | 0.559266i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.88756 | − | 7.04445i | 0.0692477 | − | 0.258436i | −0.922620 | − | 0.385711i | \(-0.873956\pi\) |
0.991868 | + | 0.127275i | \(0.0406230\pi\) | |||||||
\(744\) | −7.92941 | − | 13.7341i | −0.290706 | − | 0.503518i | ||||
\(745\) | 17.3153 | − | 29.9909i | 0.634382 | − | 1.09878i | ||||
\(746\) | −4.02952 | − | 4.02952i | −0.147531 | − | 0.147531i | ||||
\(747\) | −4.66625 | − | 17.4147i | −0.170729 | − | 0.637170i | ||||
\(748\) | 19.9899 | − | 5.35628i | 0.730903 | − | 0.195845i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3.95894 | + | 6.85709i | −0.144560 | + | 0.250385i | ||||
\(751\) | −6.19866 | + | 3.57880i | −0.226192 | + | 0.130592i | −0.608814 | − | 0.793313i | \(-0.708355\pi\) |
0.382622 | + | 0.923905i | \(0.375021\pi\) | |||||||
\(752\) | 7.39449 | − | 27.5966i | 0.269649 | − | 1.00634i | ||||
\(753\) | − | 16.2676i | − | 0.592824i | ||||||
\(754\) | −5.18241 | − | 2.29161i | −0.188732 | − | 0.0834556i | ||||
\(755\) | − | 9.76045i | − | 0.355219i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.08185 | + | 12.2661i | 0.257394 | + | 0.445820i | 0.965543 | − | 0.260243i | \(-0.0838027\pi\) |
−0.708149 | + | 0.706063i | \(0.750469\pi\) | |||||||
\(758\) | 6.60245 | + | 3.81192i | 0.239812 | + | 0.138455i | ||||
\(759\) | 38.9891 | − | 38.9891i | 1.41522 | − | 1.41522i | ||||
\(760\) | 2.59957 | − | 0.696552i | 0.0942963 | − | 0.0252666i | ||||
\(761\) | −13.9443 | + | 3.73637i | −0.505481 | + | 0.135443i | −0.502543 | − | 0.864552i | \(-0.667602\pi\) |
−0.00293843 | + | 0.999996i | \(0.500935\pi\) | |||||||
\(762\) | 1.40976 | + | 1.40976i | 0.0510703 | + | 0.0510703i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.5369 | − | 6.08348i | 0.381212 | − | 0.220093i | ||||
\(765\) | −10.9884 | − | 2.94434i | −0.397287 | − | 0.106453i | ||||
\(766\) | 6.71706 | 0.242697 | ||||||||
\(767\) | 5.10842 | + | 2.25889i | 0.184454 | + | 0.0815639i | ||||
\(768\) | − | 25.9496i | − | 0.936377i | ||||||
\(769\) | −48.9223 | − | 13.1087i | −1.76418 | − | 0.472711i | −0.776625 | − | 0.629963i | \(-0.783070\pi\) |
−0.987559 | + | 0.157252i | \(0.949737\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −48.1761 | − | 27.8145i | −1.73502 | − | 1.00171i | ||||
\(772\) | −16.2175 | − | 16.2175i | −0.583679 | − | 0.583679i | ||||
\(773\) | −3.03164 | − | 11.3142i | −0.109040 | − | 0.406944i | 0.889732 | − | 0.456484i | \(-0.150891\pi\) |
−0.998772 | + | 0.0495394i | \(0.984225\pi\) | |||||||
\(774\) | 0.455783 | + | 1.70100i | 0.0163828 | + | 0.0611414i | ||||
\(775\) | 11.7117 | + | 11.7117i | 0.420698 | + | 0.420698i | ||||
\(776\) | −2.63508 | − | 1.52136i | −0.0945938 | − | 0.0546137i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.46445 | − | 1.73215i | −0.231762 | − | 0.0621004i | ||||
\(779\) | − | 1.45511i | − | 0.0521347i | ||||||
\(780\) | −25.6108 | + | 2.75755i | −0.917013 | + | 0.0987361i | ||||
\(781\) | −8.41449 | −0.301094 | ||||||||
\(782\) | −2.96257 | − | 0.793818i | −0.105941 | − | 0.0283869i | ||||
\(783\) | 3.51111 | − | 2.02714i | 0.125477 | − | 0.0724441i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.4757 | − | 11.4757i | −0.409586 | − | 0.409586i | ||||
\(786\) | 6.55652 | − | 1.75681i | 0.233863 | − | 0.0626635i | ||||
\(787\) | 33.9681 | − | 9.10172i | 1.21083 | − | 0.324441i | 0.403743 | − | 0.914872i | \(-0.367709\pi\) |
0.807088 | + | 0.590431i | \(0.201042\pi\) | |||||||
\(788\) | −2.80624 | + | 2.80624i | −0.0999680 | + | 0.0999680i | ||||
\(789\) | 21.9357 | + | 12.6646i | 0.780932 | + | 0.450871i | ||||
\(790\) | −0.863215 | − | 1.49513i | −0.0307118 | − | 0.0531944i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 16.1580i | − | 0.574151i | ||||||
\(793\) | −12.6947 | − | 32.8216i | −0.450802 | − | 1.16553i | ||||
\(794\) | 5.29158i | 0.187791i | ||||||||
\(795\) | −12.5645 | + | 46.8913i | −0.445617 | + | 1.66306i | ||||
\(796\) | 30.9511 | − | 17.8696i | 1.09703 | − | 0.633373i | ||||
\(797\) | 4.21417 | − | 7.29915i | 0.149273 | − | 0.258549i | −0.781686 | − | 0.623673i | \(-0.785640\pi\) |
0.930959 | + | 0.365123i | \(0.118973\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.1649 | − | 4.86727i | 0.642629 | − | 0.172192i | ||||
\(800\) | −2.26577 | − | 8.45596i | −0.0801069 | − | 0.298963i | ||||
\(801\) | 32.5523 | + | 32.5523i | 1.15018 | + | 1.15018i | ||||
\(802\) | −1.80750 | + | 3.13068i | −0.0638249 | + | 0.110548i | ||||
\(803\) | 5.42319 | + | 9.39325i | 0.191380 | + | 0.331480i | ||||
\(804\) | 0.681283 | − | 2.54258i | 0.0240270 | − | 0.0896700i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.894660 | − | 5.74297i | 0.0315130 | − | 0.202288i | ||||
\(807\) | 25.9603 | 0.913847 | ||||||||
\(808\) | 11.0254 | + | 2.95424i | 0.387871 | + | 0.103930i | ||||
\(809\) | −19.4561 | − | 33.6989i | −0.684040 | − | 1.18479i | −0.973738 | − | 0.227673i | \(-0.926888\pi\) |
0.289698 | − | 0.957118i | \(-0.406445\pi\) | |||||||
\(810\) | 1.63406 | − | 2.83027i | 0.0574149 | − | 0.0994456i | ||||
\(811\) | −33.4503 | + | 33.4503i | −1.17460 | + | 1.17460i | −0.193499 | + | 0.981101i | \(0.561984\pi\) |
−0.981101 | + | 0.193499i | \(0.938016\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.12076 | − | 7.91477i | −0.0743782 | − | 0.277583i | ||||
\(814\) | −7.56959 | + | 7.56959i | −0.265314 | + | 0.265314i | ||||
\(815\) | −4.95793 | − | 2.86246i | −0.173669 | − | 0.100268i | ||||
\(816\) | 18.0806 | − | 10.4388i | 0.632948 | − | 0.365433i | ||||
\(817\) | −0.861242 | + | 3.21420i | −0.0301311 | + | 0.112451i | ||||
\(818\) | −6.80553 | −0.237950 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.44788 | 0.0854838 | ||||||||
\(821\) | −12.3056 | + | 45.9251i | −0.429468 | + | 1.60280i | 0.324499 | + | 0.945886i | \(0.394804\pi\) |
−0.753968 | + | 0.656912i | \(0.771862\pi\) | |||||||
\(822\) | −0.323082 | + | 0.186531i | −0.0112688 | + | 0.00650603i | ||||
\(823\) | −31.5629 | − | 18.2229i | −1.10022 | − | 0.635210i | −0.163938 | − | 0.986471i | \(-0.552420\pi\) |
−0.936278 | + | 0.351261i | \(0.885753\pi\) | |||||||
\(824\) | 13.0587 | − | 13.0587i | 0.454920 | − | 0.454920i | ||||
\(825\) | 8.36092 | + | 31.2034i | 0.291090 | + | 1.08636i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.04107 | − | 4.04107i | 0.140522 | − | 0.140522i | −0.633347 | − | 0.773868i | \(-0.718319\pi\) |
0.773868 | + | 0.633347i | \(0.218319\pi\) | |||||||
\(828\) | 15.1392 | − | 26.2219i | 0.526124 | − | 0.911274i | ||||
\(829\) | −17.7840 | − | 30.8028i | −0.617664 | − | 1.06983i | −0.989911 | − | 0.141692i | \(-0.954746\pi\) |
0.372247 | − | 0.928134i | \(-0.378588\pi\) | |||||||
\(830\) | −2.14743 | − | 0.575402i | −0.0745383 | − | 0.0199725i | ||||
\(831\) | −41.7608 | −1.44866 | ||||||||
\(832\) | 14.1662 | − | 17.5849i | 0.491124 | − | 0.609646i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.680614 | − | 2.54009i | 0.0235677 | − | 0.0879560i | ||||
\(835\) | −18.0452 | − | 31.2552i | −0.624481 | − | 1.08163i | ||||
\(836\) | 7.48778 | − | 12.9692i | 0.258970 | − | 0.448550i | ||||
\(837\) | 2.94056 | + | 2.94056i | 0.101641 | + | 0.101641i | ||||
\(838\) | 1.14262 | + | 4.26431i | 0.0394711 | + | 0.147308i | ||||
\(839\) | −14.5158 | + | 3.88950i | −0.501142 | + | 0.134280i | −0.500530 | − | 0.865719i | \(-0.666861\pi\) |
−0.000611847 | 1.00000i | \(0.500195\pi\) | ||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.03520 | + | 3.52507i | −0.0701793 | + | 0.121554i | ||||
\(842\) | 4.28596 | − | 2.47450i | 0.147704 | − | 0.0852769i | ||||
\(843\) | −7.35803 | + | 27.4605i | −0.253424 | + | 0.945791i | ||||
\(844\) | − | 5.40504i | − | 0.186049i | ||||||
\(845\) | −16.1952 | − | 10.4008i | −0.557132 | − | 0.357798i | ||||
\(846\) | − | 7.20176i | − | 0.247602i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −23.2705 | − | 40.3057i | −0.799113 | − | 1.38410i | ||||
\(849\) | −31.3425 | − | 18.0956i | −1.07567 | − | 0.621039i | ||||
\(850\) | 1.27060 | − | 1.27060i | 0.0435812 | − | 0.0435812i | ||||
\(851\) | −39.5047 | + | 10.5852i | −1.35420 | + | 0.362857i | ||||
\(852\) | −8.54378 | + | 2.28930i | −0.292705 | + | 0.0784301i | ||||
\(853\) | 11.5963 | + | 11.5963i | 0.397050 | + | 0.397050i | 0.877191 | − | 0.480141i | \(-0.159415\pi\) |
−0.480141 | + | 0.877191i | \(0.659415\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.12916 | + | 4.11603i | −0.243812 | + | 0.140765i | ||||
\(856\) | −4.20371 | − | 1.12638i | −0.143680 | − | 0.0384989i | ||||
\(857\) | 46.8323 | 1.59976 | 0.799880 | − | 0.600160i | \(-0.204896\pi\) | ||||
0.799880 | + | 0.600160i | \(0.204896\pi\) | |||||||
\(858\) | 7.11168 | − | 8.82791i | 0.242789 | − | 0.301380i | ||||
\(859\) | 19.7674i | 0.674455i | 0.941423 | + | 0.337228i | \(0.109489\pi\) | ||||
−0.941423 | + | 0.337228i | \(0.890511\pi\) | |||||||
\(860\) | −5.40715 | − | 1.44884i | −0.184382 | − | 0.0494050i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.29211 | + | 3.05540i | 0.180250 | + | 0.104067i | ||||
\(863\) | 5.08332 | + | 5.08332i | 0.173038 | + | 0.173038i | 0.788313 | − | 0.615275i | \(-0.210955\pi\) |
−0.615275 | + | 0.788313i | \(0.710955\pi\) | |||||||
\(864\) | −0.568884 | − | 2.12311i | −0.0193538 | − | 0.0722295i | ||||
\(865\) | −1.83929 | − | 6.86431i | −0.0625376 | − | 0.233393i | ||||
\(866\) | −3.56136 | − | 3.56136i | −0.121020 | − | 0.121020i | ||||
\(867\) | −24.9969 | − | 14.4320i | −0.848940 | − | 0.490136i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.9187 | − | 5.06925i | −0.641773 | − | 0.171963i | ||||
\(870\) | − | 5.83168i | − | 0.197712i | ||||||
\(871\) | 1.58830 | − | 1.16014i | 0.0538174 | − | 0.0393097i | ||||
\(872\) | 8.49768 | 0.287768 | ||||||||
\(873\) | 8.98995 | + | 2.40885i | 0.304264 | + | 0.0815272i | ||||
\(874\) | −1.92208 | + | 1.10971i | −0.0650154 | + | 0.0375366i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.06211 | + | 8.06211i | 0.272393 | + | 0.272393i | ||||
\(877\) | 30.6945 | − | 8.22456i | 1.03648 | − | 0.277724i | 0.299825 | − | 0.953994i | \(-0.403072\pi\) |
0.736653 | + | 0.676270i | \(0.236405\pi\) | |||||||
\(878\) | −4.11802 | + | 1.10342i | −0.138976 | + | 0.0372386i | ||||
\(879\) | −29.1885 | + | 29.1885i | −0.984503 | + | 0.984503i | ||||
\(880\) | 20.9385 | + | 12.0889i | 0.705838 | + | 0.407516i | ||||
\(881\) | −8.45038 | − | 14.6365i | −0.284701 | − | 0.493116i | 0.687836 | − | 0.725866i | \(-0.258561\pi\) |
−0.972537 | + | 0.232750i | \(0.925228\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.1502i | 0.711760i | 0.934532 | + | 0.355880i | \(0.115819\pi\) | ||||
−0.934532 | + | 0.355880i | \(0.884181\pi\) | |||||||
\(884\) | 16.0614 | + | 2.50210i | 0.540204 | + | 0.0841548i | ||||
\(885\) | 5.74841i | 0.193231i | ||||||||
\(886\) | 2.09295 | − | 7.81099i | 0.0703140 | − | 0.262415i | ||||
\(887\) | −8.83730 | + | 5.10222i | −0.296727 | + | 0.171316i | −0.640972 | − | 0.767564i | \(-0.721468\pi\) |
0.344244 | + | 0.938880i | \(0.388135\pi\) | |||||||
\(888\) | −11.4712 | + | 19.8687i | −0.384948 | + | 0.666750i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.48332 | − | 1.46925i | 0.183801 | − | 0.0492494i | ||||
\(891\) | −9.59605 | − | 35.8129i | −0.321480 | − | 1.19978i | ||||
\(892\) | −22.0826 | − | 22.0826i | −0.739379 | − | 0.739379i | ||||
\(893\) | 6.80419 | − | 11.7852i | 0.227693 | − | 0.394377i | ||||
\(894\) | 8.01026 | + | 13.8742i | 0.267903 | + | 0.464022i | ||||
\(895\) | −4.26898 | + | 15.9321i | −0.142696 | + | 0.532550i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 40.3933 | − | 15.6233i | 1.34869 | − | 0.521647i | ||||
\(898\) | 2.64833 | 0.0883759 | ||||||||
\(899\) | −32.7653 | − | 8.77944i | −1.09278 | − | 0.292811i | ||||
\(900\) | 8.86957 | + | 15.3625i | 0.295652 | + | 0.512085i | ||||
\(901\) | 15.3174 | − | 26.5304i | 0.510295 | − | 0.883857i | ||||
\(902\) | −0.761755 | + | 0.761755i | −0.0253637 | + | 0.0253637i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.12611 | − | 19.1309i | −0.170492 | − | 0.636285i | ||||
\(905\) | −4.52739 | + | 4.52739i | −0.150496 | + | 0.150496i | ||||
\(906\) | 3.91037 | + | 2.25765i | 0.129913 | + | 0.0750056i | ||||
\(907\) | −13.5900 | + | 7.84622i | −0.451250 | + | 0.260529i | −0.708358 | − | 0.705853i | \(-0.750564\pi\) |
0.257108 | + | 0.966383i | \(0.417230\pi\) | |||||||
\(908\) | −0.874625 | + | 3.26415i | −0.0290255 | + | 0.108324i | ||||
\(909\) | −34.9140 | −1.15802 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.8232 | −0.789296 | −0.394648 | − | 0.918832i | \(-0.629134\pi\) | ||||
−0.394648 | + | 0.918832i | \(0.629134\pi\) | |||||||
\(912\) | 3.91017 | − | 14.5929i | 0.129479 | − | 0.483220i | ||||
\(913\) | −21.8426 | + | 12.6108i | −0.722885 | + | 0.417358i | ||||
\(914\) | 8.20378 | + | 4.73645i | 0.271357 | + | 0.156668i | ||||
\(915\) | 25.6094 | − | 25.6094i | 0.846619 | − | 0.846619i | ||||
\(916\) | −5.55326 | − | 20.7250i | −0.183485 | − | 0.684774i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.319020 | − | 0.319020i | 0.0105292 | − | 0.0105292i | ||||
\(919\) | 4.01647 | − | 6.95674i | 0.132491 | − | 0.229482i | −0.792145 | − | 0.610333i | \(-0.791036\pi\) |
0.924636 | + | 0.380851i | \(0.124369\pi\) | |||||||
\(920\) | −3.80609 | − | 6.59234i | −0.125483 | − | 0.217343i | ||||
\(921\) | 28.3329 | + | 7.59177i | 0.933600 | + | 0.250157i | ||||
\(922\) | −2.58741 | −0.0852117 | ||||||||
\(923\) | −6.04465 | − | 2.67289i | −0.198962 | − | 0.0879791i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.20155 | − | 23.1445i | 0.203906 | − | 0.760986i | ||||
\(926\) | 0.694867 | + | 1.20355i | 0.0228348 | + | 0.0395509i | ||||
\(927\) | −28.2445 | + | 48.9210i | −0.927672 | + | 1.60678i | ||||
\(928\) | 12.6776 | + | 12.6776i | 0.416164 | + | 0.416164i | ||||
\(929\) | 3.32217 | + | 12.3985i | 0.108997 | + | 0.406781i | 0.998768 | − | 0.0496256i | \(-0.0158028\pi\) |
−0.889771 | + | 0.456407i | \(0.849136\pi\) | |||||||
\(930\) | 5.77788 | − | 1.54818i | 0.189464 | − | 0.0507668i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 19.6049 | − | 33.9567i | 0.642180 | − | 1.11229i | ||||
\(933\) | 28.0045 | − | 16.1684i | 0.916827 | − | 0.529331i | ||||
\(934\) | −1.70639 | + | 6.36835i | −0.0558349 | + | 0.208379i | ||||
\(935\) | 15.9145i | 0.520460i | ||||||||
\(936\) | 5.13265 | − | 11.6073i | 0.167766 | − | 0.379397i | ||||
\(937\) | − | 19.3918i | − | 0.633501i | −0.948509 | − | 0.316751i | \(-0.897408\pi\) | ||
0.948509 | − | 0.316751i | \(-0.102592\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.47089 | + | 12.9400i | 0.243803 | + | 0.422279i | ||||
\(940\) | 19.8259 | + | 11.4465i | 0.646648 | + | 0.373342i | ||||
\(941\) | 1.88199 | − | 1.88199i | 0.0613512 | − | 0.0613512i | −0.675765 | − | 0.737117i | \(-0.736187\pi\) |
0.737117 | + | 0.675765i | \(0.236187\pi\) | |||||||
\(942\) | 7.25197 | − | 1.94316i | 0.236282 | − | 0.0633116i | ||||
\(943\) | −3.97550 | + | 1.06523i | −0.129460 | + | 0.0346887i | ||||
\(944\) | −3.89691 | − | 3.89691i | −0.126834 | − | 0.126834i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.13351 | − | 1.23178i | 0.0693663 | − | 0.0400487i | ||||
\(947\) | −19.4341 | − | 5.20734i | −0.631523 | − | 0.169216i | −0.0711620 | − | 0.997465i | \(-0.522671\pi\) |
−0.560360 | + | 0.828249i | \(0.689337\pi\) | |||||||
\(948\) | −20.5886 | −0.668686 | ||||||||
\(949\) | 0.912025 | + | 8.47044i | 0.0296056 | + | 0.274962i | ||||
\(950\) | − | 1.30029i | − | 0.0421870i | ||||||
\(951\) | −31.3194 | − | 8.39200i | −1.01560 | − | 0.272129i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.0417 | + | 13.8805i | 0.778788 | + | 0.449634i | 0.836001 | − | 0.548728i | \(-0.184888\pi\) |
−0.0572123 | + | 0.998362i | \(0.518221\pi\) | |||||||
\(954\) | −8.29560 | − | 8.29560i | −0.268580 | − | 0.268580i | ||||
\(955\) | 2.42161 | + | 9.03758i | 0.0783616 | + | 0.292449i | ||||
\(956\) | 10.3001 | + | 38.4405i | 0.333129 | + | 1.24325i | ||||
\(957\) | −46.7818 | − | 46.7818i | −1.51224 | − | 1.51224i | ||||
\(958\) | 5.79773 | + | 3.34732i | 0.187316 | + | 0.108147i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 22.4477 | + | 6.01483i | 0.724495 | + | 0.194128i | ||||
\(961\) | − | 3.79382i | − | 0.122381i | ||||||
\(962\) | −7.84220 | + | 3.03320i | −0.252843 | + | 0.0977944i | ||||
\(963\) | 13.3119 | 0.428970 | ||||||||
\(964\) | −26.5517 | − | 7.11450i | −0.855171 | − | 0.229143i | ||||
\(965\) | 15.2741 | − | 8.81849i | 0.491690 | − | 0.283877i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.10934 | − | 4.10934i | −0.132147 | − | 0.132147i | 0.637939 | − | 0.770087i | \(-0.279787\pi\) |
−0.770087 | + | 0.637939i | \(0.779787\pi\) | |||||||
\(968\) | −10.4360 | + | 2.79631i | −0.335425 | + | 0.0898768i | ||||
\(969\) | 9.60551 | − | 2.57379i | 0.308573 | − | 0.0826820i | ||||
\(970\) | 0.811524 | − | 0.811524i | 0.0260565 | − | 0.0260565i | ||||
\(971\) | 18.8523 | + | 10.8844i | 0.604999 | + | 0.349296i | 0.771006 | − | 0.636828i | \(-0.219754\pi\) |
−0.166007 | + | 0.986125i | \(0.553087\pi\) | |||||||
\(972\) | −21.5230 | − | 37.2790i | −0.690352 | − | 1.19572i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 10.4453i | 0.334690i | ||||||||
\(975\) | −3.90567 | + | 25.0712i | −0.125082 | + | 0.802920i | ||||
\(976\) | 34.7217i | 1.11141i | ||||||||
\(977\) | −2.39408 | + | 8.93483i | −0.0765934 | + | 0.285850i | −0.993590 | − | 0.113045i | \(-0.963940\pi\) |
0.916996 | + | 0.398895i | \(0.130606\pi\) | |||||||
\(978\) | 2.29360 | − | 1.32421i | 0.0733413 | − | 0.0423436i | ||||
\(979\) | 32.2009 | − | 55.7736i | 1.02915 | − | 1.78253i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.1070 | + | 6.72740i | −0.801605 | + | 0.214789i | ||||
\(982\) | 0.834347 | + | 3.11383i | 0.0266251 | + | 0.0993662i | ||||
\(983\) | −38.8850 | − | 38.8850i | −1.24024 | − | 1.24024i | −0.959902 | − | 0.280335i | \(-0.909554\pi\) |
−0.280335 | − | 0.959902i | \(-0.590446\pi\) | |||||||
\(984\) | −1.15439 | + | 1.99946i | −0.0368005 | + | 0.0637404i | ||||
\(985\) | −1.52593 | − | 2.64299i | −0.0486203 | − | 0.0842128i | ||||
\(986\) | −0.952477 | + | 3.55469i | −0.0303331 | + | 0.113205i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.49865 | − | 6.93808i | 0.302192 | − | 0.220730i | ||||
\(989\) | 9.41198 | 0.299284 | ||||||||
\(990\) | 5.88689 | + | 1.57739i | 0.187098 | + | 0.0501327i | ||||
\(991\) | 2.34950 | + | 4.06946i | 0.0746345 | + | 0.129271i | 0.900927 | − | 0.433970i | \(-0.142888\pi\) |
−0.826293 | + | 0.563241i | \(0.809554\pi\) | |||||||
\(992\) | −9.19506 | + | 15.9263i | −0.291944 | + | 0.505661i | ||||
\(993\) | −17.7095 | + | 17.7095i | −0.561995 | + | 0.561995i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.11326 | + | 26.5470i | 0.225505 | + | 0.841598i | ||||
\(996\) | −18.7472 | + | 18.7472i | −0.594029 | + | 0.594029i | ||||
\(997\) | 14.6274 | + | 8.44515i | 0.463255 | + | 0.267461i | 0.713412 | − | 0.700745i | \(-0.247149\pi\) |
−0.250157 | + | 0.968205i | \(0.580482\pi\) | |||||||
\(998\) | −3.62391 | + | 2.09227i | −0.114713 | + | 0.0662295i | ||||
\(999\) | 1.55707 | − | 5.81107i | 0.0492636 | − | 0.183854i |
(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 | 637.2.bd.b.440.4 | 28 | ||
7.2 | even | 3 | 637.2.x.a.570.4 | 28 | |||
7.3 | odd | 6 | 637.2.bb.a.362.4 | 28 | |||
7.4 | even | 3 | 91.2.ba.a.89.4 | yes | 28 | ||
7.5 | odd | 6 | 91.2.w.a.24.4 | yes | 28 | ||
7.6 | odd | 2 | 637.2.bd.a.440.4 | 28 | |||
13.6 | odd | 12 | 637.2.bd.a.97.4 | 28 | |||
21.5 | even | 6 | 819.2.gh.b.388.4 | 28 | |||
21.11 | odd | 6 | 819.2.et.b.271.4 | 28 | |||
91.6 | even | 12 | inner | 637.2.bd.b.97.4 | 28 | ||
91.19 | even | 12 | 91.2.ba.a.45.4 | yes | 28 | ||
91.32 | odd | 12 | 91.2.w.a.19.4 | ✓ | 28 | ||
91.45 | even | 12 | 637.2.x.a.19.4 | 28 | |||
91.58 | odd | 12 | 637.2.bb.a.227.4 | 28 | |||
273.32 | even | 12 | 819.2.gh.b.19.4 | 28 | |||
273.110 | odd | 12 | 819.2.et.b.136.4 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.w.a.19.4 | ✓ | 28 | 91.32 | odd | 12 | ||
91.2.w.a.24.4 | yes | 28 | 7.5 | odd | 6 | ||
91.2.ba.a.45.4 | yes | 28 | 91.19 | even | 12 | ||
91.2.ba.a.89.4 | yes | 28 | 7.4 | even | 3 | ||
637.2.x.a.19.4 | 28 | 91.45 | even | 12 | |||
637.2.x.a.570.4 | 28 | 7.2 | even | 3 | |||
637.2.bb.a.227.4 | 28 | 91.58 | odd | 12 | |||
637.2.bb.a.362.4 | 28 | 7.3 | odd | 6 | |||
637.2.bd.a.97.4 | 28 | 13.6 | odd | 12 | |||
637.2.bd.a.440.4 | 28 | 7.6 | odd | 2 | |||
637.2.bd.b.97.4 | 28 | 91.6 | even | 12 | inner | ||
637.2.bd.b.440.4 | 28 | 1.1 | even | 1 | trivial | ||
819.2.et.b.136.4 | 28 | 273.110 | odd | 12 | |||
819.2.et.b.271.4 | 28 | 21.11 | odd | 6 | |||
819.2.gh.b.19.4 | 28 | 273.32 | even | 12 | |||
819.2.gh.b.388.4 | 28 | 21.5 | even | 6 |