Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(149,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.q (of order \(4\), degree \(2\), not 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: | \(3.19401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.4767670494822400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 349.3 | ||
Root | \(1.35979 - 0.388551i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.349 |
Dual form | 400.2.q.e.149.3 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.388551 | + | 1.35979i | −0.274747 | + | 0.961516i | ||||
\(3\) | 1.03997 | − | 1.03997i | 0.600427 | − | 0.600427i | −0.339999 | − | 0.940426i | \(-0.610427\pi\) |
0.940426 | + | 0.339999i | \(0.110427\pi\) | |||||||
\(4\) | −1.69806 | − | 1.05670i | −0.849028 | − | 0.528348i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.01006 | + | 1.81822i | 0.412355 | + | 0.742286i | ||||
\(7\) | 1.49668 | 0.565693 | 0.282846 | − | 0.959165i | \(-0.408721\pi\) | ||||
0.282846 | + | 0.959165i | \(0.408721\pi\) | |||||||
\(8\) | 2.09667 | − | 1.89842i | 0.741283 | − | 0.671192i | ||||
\(9\) | 0.836925i | 0.278975i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.423260 | − | 0.423260i | 0.127618 | − | 0.127618i | −0.640413 | − | 0.768031i | \(-0.721237\pi\) |
0.768031 | + | 0.640413i | \(0.221237\pi\) | |||||||
\(12\) | −2.86486 | + | 0.666995i | −0.827014 | + | 0.192545i | ||||
\(13\) | 1.85704 | − | 1.85704i | 0.515051 | − | 0.515051i | −0.401019 | − | 0.916070i | \(-0.631344\pi\) |
0.916070 | + | 0.401019i | \(0.131344\pi\) | |||||||
\(14\) | −0.581538 | + | 2.03517i | −0.155422 | + | 0.543923i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.76679 | + | 3.58866i | 0.441697 | + | 0.897164i | ||||
\(17\) | − | 6.50950i | − | 1.57879i | −0.613888 | − | 0.789393i | \(-0.710395\pi\) | ||
0.613888 | − | 0.789393i | \(-0.289605\pi\) | |||||||
\(18\) | −1.13804 | − | 0.325188i | −0.268239 | − | 0.0766476i | ||||
\(19\) | 1.75725 | + | 1.75725i | 0.403141 | + | 0.403141i | 0.879338 | − | 0.476198i | \(-0.157985\pi\) |
−0.476198 | + | 0.879338i | \(0.657985\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.55650 | − | 1.55650i | 0.339657 | − | 0.339657i | ||||
\(22\) | 0.411086 | + | 0.740003i | 0.0876439 | + | 0.157769i | ||||
\(23\) | 7.19295 | 1.49983 | 0.749917 | − | 0.661532i | \(-0.230094\pi\) | ||||
0.749917 | + | 0.661532i | \(0.230094\pi\) | |||||||
\(24\) | 0.206172 | − | 4.15477i | 0.0420846 | − | 0.848088i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.80363 | + | 3.24674i | 0.353721 | + | 0.636739i | ||||
\(27\) | 3.99029 | + | 3.99029i | 0.767931 | + | 0.767931i | ||||
\(28\) | −2.54145 | − | 1.58154i | −0.480289 | − | 0.298883i | ||||
\(29\) | 6.57892 | + | 6.57892i | 1.22167 | + | 1.22167i | 0.967036 | + | 0.254639i | \(0.0819565\pi\) |
0.254639 | + | 0.967036i | \(0.418043\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.75252 | −1.21279 | −0.606394 | − | 0.795164i | \(-0.707385\pi\) | ||||
−0.606394 | + | 0.795164i | \(0.707385\pi\) | |||||||
\(32\) | −5.56631 | + | 1.00808i | −0.983993 | + | 0.178205i | ||||
\(33\) | − | 0.880355i | − | 0.153250i | ||||||
\(34\) | 8.85156 | + | 2.52928i | 1.51803 | + | 0.433767i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.884375 | − | 1.42115i | 0.147396 | − | 0.236858i | ||||
\(37\) | −1.95300 | − | 1.95300i | −0.321071 | − | 0.321071i | 0.528107 | − | 0.849178i | \(-0.322902\pi\) |
−0.849178 | + | 0.528107i | \(0.822902\pi\) | |||||||
\(38\) | −3.07227 | + | 1.70671i | −0.498388 | + | 0.276865i | ||||
\(39\) | − | 3.86254i | − | 0.618501i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.70745i | − | 1.20370i | −0.798609 | − | 0.601851i | \(-0.794430\pi\) | ||
0.798609 | − | 0.601851i | \(-0.205570\pi\) | |||||||
\(42\) | 1.51174 | + | 2.72130i | 0.233266 | + | 0.419906i | ||||
\(43\) | −6.13581 | − | 6.13581i | −0.935702 | − | 0.935702i | 0.0623522 | − | 0.998054i | \(-0.480140\pi\) |
−0.998054 | + | 0.0623522i | \(0.980140\pi\) | |||||||
\(44\) | −1.16598 | + | 0.271462i | −0.175778 | + | 0.0409244i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.79483 | + | 9.78090i | −0.412075 | + | 1.44211i | ||||
\(47\) | 6.65476i | 0.970697i | 0.874321 | + | 0.485348i | \(0.161307\pi\) | ||||
−0.874321 | + | 0.485348i | \(0.838693\pi\) | |||||||
\(48\) | 5.56950 | + | 1.89469i | 0.803888 | + | 0.273475i | ||||
\(49\) | −4.75994 | −0.679992 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.76969 | − | 6.76969i | −0.947946 | − | 0.947946i | ||||
\(52\) | −5.11569 | + | 1.19103i | −0.709419 | + | 0.165167i | ||||
\(53\) | 5.29390 | + | 5.29390i | 0.727173 | + | 0.727173i | 0.970056 | − | 0.242882i | \(-0.0780929\pi\) |
−0.242882 | + | 0.970056i | \(0.578093\pi\) | |||||||
\(54\) | −6.97638 | + | 3.87552i | −0.949365 | + | 0.527391i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.13804 | − | 2.84133i | 0.419338 | − | 0.379688i | ||||
\(57\) | 3.65497 | 0.484113 | ||||||||
\(58\) | −11.5022 | + | 6.38970i | −1.51031 | + | 0.839009i | ||||
\(59\) | −5.91841 | + | 5.91841i | −0.770511 | + | 0.770511i | −0.978196 | − | 0.207685i | \(-0.933407\pi\) |
0.207685 | + | 0.978196i | \(0.433407\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.43686 | − | 1.43686i | −0.183971 | − | 0.183971i | 0.609113 | − | 0.793084i | \(-0.291526\pi\) |
−0.793084 | + | 0.609113i | \(0.791526\pi\) | |||||||
\(62\) | 2.62370 | − | 9.18201i | 0.333210 | − | 1.16612i | ||||
\(63\) | 1.25261i | 0.157814i | ||||||||
\(64\) | 0.792016 | − | 7.96070i | 0.0990020 | − | 0.995087i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.19710 | + | 0.342063i | 0.147353 | + | 0.0421051i | ||||
\(67\) | −6.35614 | + | 6.35614i | −0.776526 | + | 0.776526i | −0.979238 | − | 0.202712i | \(-0.935024\pi\) |
0.202712 | + | 0.979238i | \(0.435024\pi\) | |||||||
\(68\) | −6.87857 | + | 11.0535i | −0.834149 | + | 1.34043i | ||||
\(69\) | 7.48045 | − | 7.48045i | 0.900540 | − | 0.900540i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.08932i | 0.485313i | 0.970112 | + | 0.242657i | \(0.0780188\pi\) | ||||
−0.970112 | + | 0.242657i | \(0.921981\pi\) | |||||||
\(72\) | 1.58883 | + | 1.75475i | 0.187246 | + | 0.206799i | ||||
\(73\) | −2.43800 | −0.285346 | −0.142673 | − | 0.989770i | \(-0.545570\pi\) | ||||
−0.142673 | + | 0.989770i | \(0.545570\pi\) | |||||||
\(74\) | 3.41451 | − | 1.89683i | 0.396929 | − | 0.220502i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.12703 | − | 4.84079i | −0.129279 | − | 0.555276i | ||||
\(77\) | 0.633485 | − | 0.633485i | 0.0721924 | − | 0.0721924i | ||||
\(78\) | 5.25224 | + | 1.50079i | 0.594699 | + | 0.169931i | ||||
\(79\) | −11.6722 | −1.31323 | −0.656615 | − | 0.754226i | \(-0.728012\pi\) | ||||
−0.656615 | + | 0.754226i | \(0.728012\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.78878 | 0.643198 | ||||||||
\(82\) | 10.4805 | + | 2.99474i | 1.15738 | + | 0.330714i | ||||
\(83\) | −2.81439 | + | 2.81439i | −0.308919 | + | 0.308919i | −0.844490 | − | 0.535571i | \(-0.820096\pi\) |
0.535571 | + | 0.844490i | \(0.320096\pi\) | |||||||
\(84\) | −4.28778 | + | 0.998279i | −0.467835 | + | 0.108921i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.7275 | − | 5.95933i | 1.15677 | − | 0.642611i | ||||
\(87\) | 13.6838 | 1.46705 | ||||||||
\(88\) | 0.0839103 | − | 1.69096i | 0.00894487 | − | 0.180257i | ||||
\(89\) | − | 10.5543i | − | 1.11876i | −0.828912 | − | 0.559379i | \(-0.811040\pi\) | ||
0.828912 | − | 0.559379i | \(-0.188960\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.77940 | − | 2.77940i | 0.291360 | − | 0.291360i | ||||
\(92\) | −12.2140 | − | 7.60076i | −1.27340 | − | 0.792434i | ||||
\(93\) | −7.02242 | + | 7.02242i | −0.728191 | + | 0.728191i | ||||
\(94\) | −9.04907 | − | 2.58572i | −0.933341 | − | 0.266696i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.74042 | + | 6.83717i | −0.483817 | + | 0.697815i | ||||
\(97\) | − | 18.1512i | − | 1.84298i | −0.388407 | − | 0.921488i | \(-0.626975\pi\) | ||
0.388407 | − | 0.921488i | \(-0.373025\pi\) | |||||||
\(98\) | 1.84948 | − | 6.47252i | 0.186826 | − | 0.653823i | ||||
\(99\) | 0.354237 | + | 0.354237i | 0.0356021 | + | 0.0356021i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.04036 | + | 1.04036i | −0.103520 | + | 0.103520i | −0.756970 | − | 0.653450i | \(-0.773321\pi\) |
0.653450 | + | 0.756970i | \(0.273321\pi\) | |||||||
\(102\) | 11.8357 | − | 6.57498i | 1.17191 | − | 0.651020i | ||||
\(103\) | 0.955267 | 0.0941253 | 0.0470626 | − | 0.998892i | \(-0.485014\pi\) | ||||
0.0470626 | + | 0.998892i | \(0.485014\pi\) | |||||||
\(104\) | 0.368154 | − | 7.41904i | 0.0361005 | − | 0.727497i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.25555 | + | 5.14164i | −0.898978 | + | 0.499400i | ||||
\(107\) | −7.20266 | − | 7.20266i | −0.696308 | − | 0.696308i | 0.267305 | − | 0.963612i | \(-0.413867\pi\) |
−0.963612 | + | 0.267305i | \(0.913867\pi\) | |||||||
\(108\) | −2.55921 | − | 10.9922i | −0.246260 | − | 1.05773i | ||||
\(109\) | 5.67807 | + | 5.67807i | 0.543861 | + | 0.543861i | 0.924658 | − | 0.380798i | \(-0.124351\pi\) |
−0.380798 | + | 0.924658i | \(0.624351\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.06212 | −0.385560 | ||||||||
\(112\) | 2.64432 | + | 5.37108i | 0.249865 | + | 0.507519i | ||||
\(113\) | 1.94751i | 0.183206i | 0.995796 | + | 0.0916029i | \(0.0291991\pi\) | ||||
−0.995796 | + | 0.0916029i | \(0.970801\pi\) | |||||||
\(114\) | −1.42014 | + | 4.97000i | −0.133009 | + | 0.465483i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.21946 | − | 18.1233i | −0.391767 | − | 1.68271i | ||||
\(117\) | 1.55420 | + | 1.55420i | 0.143686 | + | 0.143686i | ||||
\(118\) | −5.74818 | − | 10.3474i | −0.529163 | − | 0.952555i | ||||
\(119\) | − | 9.74266i | − | 0.893108i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6417i | 0.967427i | ||||||||
\(122\) | 2.51212 | − | 1.39553i | 0.227437 | − | 0.126346i | ||||
\(123\) | −8.01552 | − | 8.01552i | −0.722735 | − | 0.722735i | ||||
\(124\) | 11.4662 | + | 7.13536i | 1.02969 | + | 0.640774i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.70329 | − | 0.486703i | −0.151741 | − | 0.0433590i | ||||
\(127\) | 1.31796i | 0.116950i | 0.998289 | + | 0.0584750i | \(0.0186238\pi\) | ||||
−0.998289 | + | 0.0584750i | \(0.981376\pi\) | |||||||
\(128\) | 10.5171 | + | 4.17011i | 0.929592 | + | 0.368589i | ||||
\(129\) | −12.7621 | −1.12364 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.03026 | + | 1.03026i | 0.0900139 | + | 0.0900139i | 0.750680 | − | 0.660666i | \(-0.229726\pi\) |
−0.660666 | + | 0.750680i | \(0.729726\pi\) | |||||||
\(132\) | −0.930268 | + | 1.49489i | −0.0809694 | + | 0.130114i | ||||
\(133\) | 2.63004 | + | 2.63004i | 0.228054 | + | 0.228054i | ||||
\(134\) | −6.17333 | − | 11.1127i | −0.533294 | − | 0.959991i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.3578 | − | 13.6483i | −1.05967 | − | 1.17033i | ||||
\(137\) | −3.75559 | −0.320862 | −0.160431 | − | 0.987047i | \(-0.551288\pi\) | ||||
−0.160431 | + | 0.987047i | \(0.551288\pi\) | |||||||
\(138\) | 7.26530 | + | 13.0784i | 0.618463 | + | 1.11331i | ||||
\(139\) | −12.9485 | + | 12.9485i | −1.09828 | + | 1.09828i | −0.103669 | + | 0.994612i | \(0.533058\pi\) |
−0.994612 | + | 0.103669i | \(0.966942\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.92075 | + | 6.92075i | 0.582832 | + | 0.582832i | ||||
\(142\) | −5.56062 | − | 1.58891i | −0.466637 | − | 0.133338i | ||||
\(143\) | − | 1.57202i | − | 0.131459i | ||||||
\(144\) | −3.00344 | + | 1.47867i | −0.250286 | + | 0.123222i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.947288 | − | 3.31517i | 0.0783982 | − | 0.274365i | ||||
\(147\) | −4.95020 | + | 4.95020i | −0.408285 | + | 0.408285i | ||||
\(148\) | 1.25258 | + | 5.38003i | 0.102961 | + | 0.442236i | ||||
\(149\) | 15.8472 | − | 15.8472i | 1.29825 | − | 1.29825i | 0.368709 | − | 0.929545i | \(-0.379800\pi\) |
0.929545 | − | 0.368709i | \(-0.120200\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5316i | 0.938424i | 0.883085 | + | 0.469212i | \(0.155462\pi\) | ||||
−0.883085 | + | 0.469212i | \(0.844538\pi\) | |||||||
\(152\) | 7.02036 | + | 0.348371i | 0.569427 | + | 0.0282566i | ||||
\(153\) | 5.44797 | 0.440442 | ||||||||
\(154\) | 0.615265 | + | 1.10755i | 0.0495795 | + | 0.0892488i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.08153 | + | 6.55880i | −0.326784 | + | 0.525125i | ||||
\(157\) | −5.41891 | + | 5.41891i | −0.432476 | + | 0.432476i | −0.889470 | − | 0.456994i | \(-0.848926\pi\) |
0.456994 | + | 0.889470i | \(0.348926\pi\) | |||||||
\(158\) | 4.53526 | − | 15.8718i | 0.360806 | − | 1.26269i | ||||
\(159\) | 11.0110 | 0.873229 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.7656 | 0.848445 | ||||||||
\(162\) | −2.24924 | + | 7.87153i | −0.176717 | + | 0.618446i | ||||
\(163\) | −6.47288 | + | 6.47288i | −0.506995 | + | 0.506995i | −0.913603 | − | 0.406608i | \(-0.866711\pi\) |
0.406608 | + | 0.913603i | \(0.366711\pi\) | |||||||
\(164\) | −8.14443 | + | 13.0877i | −0.635973 | + | 1.02198i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.73344 | − | 4.92051i | −0.212156 | − | 0.381906i | ||||
\(167\) | −8.29734 | −0.642068 | −0.321034 | − | 0.947068i | \(-0.604030\pi\) | ||||
−0.321034 | + | 0.947068i | \(0.604030\pi\) | |||||||
\(168\) | 0.308573 | − | 6.21837i | 0.0238069 | − | 0.479757i | ||||
\(169\) | 6.10279i | 0.469445i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.47069 | + | 1.47069i | −0.112466 | + | 0.112466i | ||||
\(172\) | 3.93526 | + | 16.9026i | 0.300061 | + | 1.28881i | ||||
\(173\) | −11.9420 | + | 11.9420i | −0.907935 | + | 0.907935i | −0.996105 | − | 0.0881700i | \(-0.971898\pi\) |
0.0881700 | + | 0.996105i | \(0.471898\pi\) | |||||||
\(174\) | −5.31684 | + | 18.6070i | −0.403069 | + | 1.41060i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.26675 | + | 0.771125i | 0.170862 | + | 0.0581257i | ||||
\(177\) | 12.3099i | 0.925271i | ||||||||
\(178\) | 14.3517 | + | 4.10090i | 1.07570 | + | 0.307376i | ||||
\(179\) | 10.8703 | + | 10.8703i | 0.812481 | + | 0.812481i | 0.985005 | − | 0.172524i | \(-0.0551922\pi\) |
−0.172524 | + | 0.985005i | \(0.555192\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.09403 | + | 4.09403i | −0.304307 | + | 0.304307i | −0.842696 | − | 0.538389i | \(-0.819033\pi\) |
0.538389 | + | 0.842696i | \(0.319033\pi\) | |||||||
\(182\) | 2.69946 | + | 4.85934i | 0.200097 | + | 0.360198i | ||||
\(183\) | −2.98858 | −0.220922 | ||||||||
\(184\) | 15.0812 | − | 13.6552i | 1.11180 | − | 1.00668i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.82044 | − | 12.2776i | −0.500099 | − | 0.900236i | ||||
\(187\) | −2.75521 | − | 2.75521i | −0.201481 | − | 0.201481i | ||||
\(188\) | 7.03206 | − | 11.3002i | 0.512866 | − | 0.824148i | ||||
\(189\) | 5.97219 | + | 5.97219i | 0.434413 | + | 0.434413i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.2542 | 1.39319 | 0.696594 | − | 0.717466i | \(-0.254698\pi\) | ||||
0.696594 | + | 0.717466i | \(0.254698\pi\) | |||||||
\(192\) | −7.45521 | − | 9.10256i | −0.538034 | − | 0.656921i | ||||
\(193\) | − | 24.8152i | − | 1.78624i | −0.449820 | − | 0.893119i | \(-0.648512\pi\) | ||
0.449820 | − | 0.893119i | \(-0.351488\pi\) | |||||||
\(194\) | 24.6818 | + | 7.05267i | 1.77205 | + | 0.506352i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.08265 | + | 5.02981i | 0.577332 | + | 0.359272i | ||||
\(197\) | 2.81324 | + | 2.81324i | 0.200435 | + | 0.200435i | 0.800186 | − | 0.599751i | \(-0.204734\pi\) |
−0.599751 | + | 0.800186i | \(0.704734\pi\) | |||||||
\(198\) | −0.619327 | + | 0.344048i | −0.0440136 | + | 0.0244505i | ||||
\(199\) | − | 21.2194i | − | 1.50420i | −0.659048 | − | 0.752101i | \(-0.729041\pi\) | ||
0.659048 | − | 0.752101i | \(-0.270959\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.2204i | 0.932495i | ||||||||
\(202\) | −1.01044 | − | 1.81891i | −0.0710944 | − | 0.127978i | ||||
\(203\) | 9.84655 | + | 9.84655i | 0.691092 | + | 0.691092i | ||||
\(204\) | 4.34181 | + | 18.6488i | 0.303987 | + | 1.30568i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.371170 | + | 1.29896i | −0.0258607 | + | 0.0905030i | ||||
\(207\) | 6.01996i | 0.418416i | ||||||||
\(208\) | 9.94529 | + | 3.38329i | 0.689582 | + | 0.234589i | ||||
\(209\) | 1.48755 | 0.102896 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.5715 | + | 15.5715i | 1.07199 | + | 1.07199i | 0.997200 | + | 0.0747872i | \(0.0238278\pi\) |
0.0747872 | + | 0.997200i | \(0.476172\pi\) | |||||||
\(212\) | −3.39530 | − | 14.5834i | −0.233190 | − | 1.00159i | ||||
\(213\) | 4.25277 | + | 4.25277i | 0.291395 | + | 0.291395i | ||||
\(214\) | 12.5927 | − | 6.99550i | 0.860820 | − | 0.478203i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 15.9415 | + | 0.791065i | 1.08468 | + | 0.0538251i | ||||
\(217\) | −10.1064 | −0.686065 | ||||||||
\(218\) | −9.92721 | + | 5.51476i | −0.672355 | + | 0.373507i | ||||
\(219\) | −2.53545 | + | 2.53545i | −0.171330 | + | 0.171330i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0884 | − | 12.0884i | −0.813155 | − | 0.813155i | ||||
\(222\) | 1.57834 | − | 5.52363i | 0.105931 | − | 0.370722i | ||||
\(223\) | − | 7.88779i | − | 0.528205i | −0.964495 | − | 0.264103i | \(-0.914924\pi\) | ||
0.964495 | − | 0.264103i | \(-0.0850758\pi\) | |||||||
\(224\) | −8.33099 | + | 1.50878i | −0.556638 | + | 0.100809i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.64820 | − | 0.756705i | −0.176155 | − | 0.0503353i | ||||
\(227\) | −5.98838 | + | 5.98838i | −0.397463 | + | 0.397463i | −0.877337 | − | 0.479874i | \(-0.840682\pi\) |
0.479874 | + | 0.877337i | \(0.340682\pi\) | |||||||
\(228\) | −6.20635 | − | 3.86220i | −0.411026 | − | 0.255780i | ||||
\(229\) | −19.4584 | + | 19.4584i | −1.28585 | + | 1.28585i | −0.348563 | + | 0.937286i | \(0.613330\pi\) |
−0.937286 | + | 0.348563i | \(0.886670\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 1.31761i | − | 0.0866925i | ||||||
\(232\) | 26.2833 | + | 1.30426i | 1.72559 | + | 0.0856286i | ||||
\(233\) | 2.68717 | 0.176042 | 0.0880212 | − | 0.996119i | \(-0.471946\pi\) | ||||
0.0880212 | + | 0.996119i | \(0.471946\pi\) | |||||||
\(234\) | −2.71728 | + | 1.50950i | −0.177634 | + | 0.0986793i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 16.3037 | − | 3.79583i | 1.06128 | − | 0.247087i | ||||
\(237\) | −12.1388 | + | 12.1388i | −0.788499 | + | 0.788499i | ||||
\(238\) | 13.2480 | + | 3.78552i | 0.858738 | + | 0.245379i | ||||
\(239\) | 12.6359 | 0.817346 | 0.408673 | − | 0.912681i | \(-0.365992\pi\) | ||||
0.408673 | + | 0.912681i | \(0.365992\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.53314 | 0.485252 | 0.242626 | − | 0.970120i | \(-0.421991\pi\) | ||||
0.242626 | + | 0.970120i | \(0.421991\pi\) | |||||||
\(242\) | −14.4705 | − | 4.13485i | −0.930197 | − | 0.265798i | ||||
\(243\) | −5.95070 | + | 5.95070i | −0.381738 | + | 0.381738i | ||||
\(244\) | 0.921544 | + | 3.95819i | 0.0589958 | + | 0.253397i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 14.0139 | − | 7.78498i | 0.893491 | − | 0.496352i | ||||
\(247\) | 6.52658 | 0.415276 | ||||||||
\(248\) | −14.1578 | + | 12.8191i | −0.899020 | + | 0.814014i | ||||
\(249\) | 5.85376i | 0.370967i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.95683 | + | 9.95683i | −0.628470 | + | 0.628470i | −0.947683 | − | 0.319213i | \(-0.896581\pi\) |
0.319213 | + | 0.947683i | \(0.396581\pi\) | |||||||
\(252\) | 1.32363 | − | 2.12700i | 0.0833807 | − | 0.133989i | ||||
\(253\) | 3.04449 | − | 3.04449i | 0.191405 | − | 0.191405i | ||||
\(254\) | −1.79215 | − | 0.512094i | −0.112449 | − | 0.0321317i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.75692 | + | 12.6808i | −0.609808 | + | 0.792549i | ||||
\(257\) | − | 4.51630i | − | 0.281719i | −0.990030 | − | 0.140860i | \(-0.955013\pi\) | ||
0.990030 | − | 0.140860i | \(-0.0449866\pi\) | |||||||
\(258\) | 4.95874 | − | 17.3538i | 0.308717 | − | 1.08040i | ||||
\(259\) | −2.92302 | − | 2.92302i | −0.181628 | − | 0.181628i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.50606 | + | 5.50606i | −0.340817 | + | 0.340817i | ||||
\(262\) | −1.80124 | + | 1.00062i | −0.111281 | + | 0.0618188i | ||||
\(263\) | 20.2127 | 1.24637 | 0.623185 | − | 0.782075i | \(-0.285838\pi\) | ||||
0.623185 | + | 0.782075i | \(0.285838\pi\) | |||||||
\(264\) | −1.67128 | − | 1.84581i | −0.102860 | − | 0.113602i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.59821 | + | 2.55440i | −0.281935 | + | 0.156620i | ||||
\(267\) | −10.9762 | − | 10.9762i | −0.671732 | − | 0.671732i | ||||
\(268\) | 17.5096 | − | 4.07657i | 1.06957 | − | 0.249016i | ||||
\(269\) | −16.9430 | − | 16.9430i | −1.03304 | − | 1.03304i | −0.999435 | − | 0.0335999i | \(-0.989303\pi\) |
−0.0335999 | − | 0.999435i | \(-0.510697\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.64054 | −0.221147 | −0.110573 | − | 0.993868i | \(-0.535269\pi\) | ||||
−0.110573 | + | 0.993868i | \(0.535269\pi\) | |||||||
\(272\) | 23.3604 | − | 11.5009i | 1.41643 | − | 0.697345i | ||||
\(273\) | − | 5.78099i | − | 0.349881i | ||||||
\(274\) | 1.45924 | − | 5.10681i | 0.0881559 | − | 0.308514i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −20.6068 | + | 4.79766i | −1.24038 | + | 0.288785i | ||||
\(277\) | 16.0090 | + | 16.0090i | 0.961888 | + | 0.961888i | 0.999300 | − | 0.0374115i | \(-0.0119112\pi\) |
−0.0374115 | + | 0.999300i | \(0.511911\pi\) | |||||||
\(278\) | −12.5761 | − | 22.6385i | −0.754266 | − | 1.35777i | ||||
\(279\) | − | 5.65135i | − | 0.338338i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.51857i | − | 0.329210i | −0.986360 | − | 0.164605i | \(-0.947365\pi\) | ||
0.986360 | − | 0.164605i | \(-0.0526350\pi\) | |||||||
\(282\) | −12.0998 | + | 6.72170i | −0.720535 | + | 0.400271i | ||||
\(283\) | 2.36694 | + | 2.36694i | 0.140700 | + | 0.140700i | 0.773949 | − | 0.633249i | \(-0.218279\pi\) |
−0.633249 | + | 0.773949i | \(0.718279\pi\) | |||||||
\(284\) | 4.32117 | − | 6.94389i | 0.256414 | − | 0.412044i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.13762 | + | 0.610812i | 0.126400 | + | 0.0361180i | ||||
\(287\) | − | 11.5356i | − | 0.680925i | ||||||
\(288\) | −0.843689 | − | 4.65858i | −0.0497148 | − | 0.274509i | ||||
\(289\) | −25.3736 | −1.49257 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.8767 | − | 18.8767i | −1.10657 | − | 1.10657i | ||||
\(292\) | 4.13986 | + | 2.57623i | 0.242267 | + | 0.150762i | ||||
\(293\) | −19.1812 | − | 19.1812i | −1.12058 | − | 1.12058i | −0.991655 | − | 0.128922i | \(-0.958848\pi\) |
−0.128922 | − | 0.991655i | \(-0.541152\pi\) | |||||||
\(294\) | −4.80782 | − | 8.65463i | −0.280398 | − | 0.504749i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.80240 | − | 0.387177i | −0.453505 | − | 0.0225042i | ||||
\(297\) | 3.37786 | 0.196003 | ||||||||
\(298\) | 15.3914 | + | 27.7063i | 0.891601 | + | 1.60498i | ||||
\(299\) | 13.3576 | − | 13.3576i | 0.772491 | − | 0.772491i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.18335 | − | 9.18335i | −0.529320 | − | 0.529320i | ||||
\(302\) | −15.6805 | − | 4.48060i | −0.902311 | − | 0.257829i | ||||
\(303\) | 2.16390i | 0.124313i | ||||||||
\(304\) | −3.20148 | + | 9.41086i | −0.183618 | + | 0.539750i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.11681 | + | 7.40809i | −0.121010 | + | 0.423492i | ||||
\(307\) | 19.9292 | − | 19.9292i | 1.13742 | − | 1.13742i | 0.148507 | − | 0.988911i | \(-0.452553\pi\) |
0.988911 | − | 0.148507i | \(-0.0474469\pi\) | |||||||
\(308\) | −1.74510 | + | 0.406292i | −0.0994360 | + | 0.0231506i | ||||
\(309\) | 0.993449 | − | 0.993449i | 0.0565153 | − | 0.0565153i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.73314i | 0.325096i | 0.986701 | + | 0.162548i | \(0.0519713\pi\) | ||||
−0.986701 | + | 0.162548i | \(0.948029\pi\) | |||||||
\(312\) | −7.33271 | − | 8.09845i | −0.415133 | − | 0.458484i | ||||
\(313\) | 0.212621 | 0.0120180 | 0.00600902 | − | 0.999982i | \(-0.498087\pi\) | ||||
0.00600902 | + | 0.999982i | \(0.498087\pi\) | |||||||
\(314\) | −5.26306 | − | 9.47411i | −0.297011 | − | 0.534655i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.8201 | + | 12.3340i | 1.11497 | + | 0.693842i | ||||
\(317\) | −3.21582 | + | 3.21582i | −0.180618 | + | 0.180618i | −0.791625 | − | 0.611007i | \(-0.790765\pi\) |
0.611007 | + | 0.791625i | \(0.290765\pi\) | |||||||
\(318\) | −4.27834 | + | 14.9726i | −0.239917 | + | 0.839624i | ||||
\(319\) | 5.56919 | 0.311815 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.9811 | −0.836164 | ||||||||
\(322\) | −4.18297 | + | 14.6389i | −0.233108 | + | 0.815793i | ||||
\(323\) | 11.4388 | − | 11.4388i | 0.636473 | − | 0.636473i | ||||
\(324\) | −9.82968 | − | 6.11698i | −0.546093 | − | 0.339832i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.28671 | − | 11.3168i | −0.348188 | − | 0.626779i | ||||
\(327\) | 11.8101 | 0.653097 | ||||||||
\(328\) | −14.6320 | − | 16.1599i | −0.807915 | − | 0.892284i | ||||
\(329\) | 9.96006i | 0.549116i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.0295 | − | 22.0295i | 1.21085 | − | 1.21085i | 0.240106 | − | 0.970747i | \(-0.422818\pi\) |
0.970747 | − | 0.240106i | \(-0.0771824\pi\) | |||||||
\(332\) | 7.75295 | − | 1.80504i | 0.425498 | − | 0.0990643i | ||||
\(333\) | 1.63451 | − | 1.63451i | 0.0895708 | − | 0.0895708i | ||||
\(334\) | 3.22394 | − | 11.2826i | 0.176406 | − | 0.617359i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 8.33577 | + | 2.83575i | 0.454754 | + | 0.154703i | ||||
\(337\) | 11.2122i | 0.610767i | 0.952229 | + | 0.305384i | \(0.0987847\pi\) | ||||
−0.952229 | + | 0.305384i | \(0.901215\pi\) | |||||||
\(338\) | −8.29851 | − | 2.37125i | −0.451379 | − | 0.128979i | ||||
\(339\) | 2.02535 | + | 2.02535i | 0.110002 | + | 0.110002i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.85807 | + | 2.85807i | −0.154773 | + | 0.154773i | ||||
\(342\) | −1.42839 | − | 2.57126i | −0.0772383 | − | 0.139038i | ||||
\(343\) | −17.6009 | −0.950359 | ||||||||
\(344\) | −24.5131 | − | 1.21641i | −1.32166 | − | 0.0655844i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.5986 | − | 20.8787i | −0.623542 | − | 1.12245i | ||||
\(347\) | −1.23653 | − | 1.23653i | −0.0663803 | − | 0.0663803i | 0.673137 | − | 0.739518i | \(-0.264946\pi\) |
−0.739518 | + | 0.673137i | \(0.764946\pi\) | |||||||
\(348\) | −23.2358 | − | 14.4596i | −1.24557 | − | 0.775115i | ||||
\(349\) | 5.61778 | + | 5.61778i | 0.300713 | + | 0.300713i | 0.841293 | − | 0.540580i | \(-0.181795\pi\) |
−0.540580 | + | 0.841293i | \(0.681795\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.8203 | 0.791047 | ||||||||
\(352\) | −1.92931 | + | 2.78268i | −0.102833 | + | 0.148317i | ||||
\(353\) | 0.748709i | 0.0398497i | 0.999801 | + | 0.0199249i | \(0.00634270\pi\) | ||||
−0.999801 | + | 0.0199249i | \(0.993657\pi\) | |||||||
\(354\) | −16.7389 | − | 4.78304i | −0.889663 | − | 0.254216i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −11.1527 | + | 17.9219i | −0.591093 | + | 0.949856i | ||||
\(357\) | −10.1321 | − | 10.1321i | −0.536246 | − | 0.536246i | ||||
\(358\) | −19.0049 | + | 10.5576i | −1.00444 | + | 0.557987i | ||||
\(359\) | − | 2.69883i | − | 0.142439i | −0.997461 | − | 0.0712195i | \(-0.977311\pi\) | ||
0.997461 | − | 0.0712195i | \(-0.0226891\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 12.8241i | − | 0.674955i | ||||||
\(362\) | −3.97628 | − | 7.15776i | −0.208989 | − | 0.376204i | ||||
\(363\) | 11.0671 | + | 11.0671i | 0.580870 | + | 0.580870i | ||||
\(364\) | −7.65656 | + | 1.78260i | −0.401313 | + | 0.0934335i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.16122 | − | 4.06384i | 0.0606978 | − | 0.212420i | ||||
\(367\) | − | 20.6101i | − | 1.07584i | −0.842996 | − | 0.537920i | \(-0.819210\pi\) | ||
0.842996 | − | 0.537920i | \(-0.180790\pi\) | |||||||
\(368\) | 12.7084 | + | 25.8130i | 0.662472 | + | 1.34560i | ||||
\(369\) | 6.45056 | 0.335802 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.92329 | + | 7.92329i | 0.411357 | + | 0.411357i | ||||
\(372\) | 19.3450 | − | 4.50390i | 1.00299 | − | 0.233516i | ||||
\(373\) | 5.24143 | + | 5.24143i | 0.271391 | + | 0.271391i | 0.829660 | − | 0.558269i | \(-0.188534\pi\) |
−0.558269 | + | 0.829660i | \(0.688534\pi\) | |||||||
\(374\) | 4.81705 | − | 2.67597i | 0.249084 | − | 0.138371i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.6335 | + | 13.9528i | 0.651524 | + | 0.719561i | ||||
\(377\) | 24.4347 | 1.25845 | ||||||||
\(378\) | −10.4414 | + | 5.80042i | −0.537049 | + | 0.298341i | ||||
\(379\) | −5.41344 | + | 5.41344i | −0.278070 | + | 0.278070i | −0.832338 | − | 0.554268i | \(-0.812998\pi\) |
0.554268 | + | 0.832338i | \(0.312998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.37064 | + | 1.37064i | 0.0702199 | + | 0.0702199i | ||||
\(382\) | −7.48125 | + | 26.1817i | −0.382774 | + | 1.33957i | ||||
\(383\) | 29.5087i | 1.50782i | 0.656975 | + | 0.753912i | \(0.271836\pi\) | ||||
−0.656975 | + | 0.753912i | \(0.728164\pi\) | |||||||
\(384\) | 15.2743 | − | 6.60071i | 0.779463 | − | 0.336841i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 33.7435 | + | 9.64199i | 1.71750 | + | 0.490764i | ||||
\(387\) | 5.13521 | − | 5.13521i | 0.261037 | − | 0.261037i | ||||
\(388\) | −19.1803 | + | 30.8218i | −0.973732 | + | 1.56474i | ||||
\(389\) | −1.37884 | + | 1.37884i | −0.0699099 | + | 0.0699099i | −0.741197 | − | 0.671287i | \(-0.765742\pi\) |
0.671287 | + | 0.741197i | \(0.265742\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 46.8225i | − | 2.36792i | ||||||
\(392\) | −9.98001 | + | 9.03636i | −0.504067 | + | 0.456405i | ||||
\(393\) | 2.14287 | 0.108094 | ||||||||
\(394\) | −4.91850 | + | 2.73232i | −0.247790 | + | 0.137652i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.227193 | − | 0.975834i | −0.0114169 | − | 0.0490375i | ||||
\(397\) | 21.9750 | − | 21.9750i | 1.10289 | − | 1.10289i | 0.108832 | − | 0.994060i | \(-0.465289\pi\) |
0.994060 | − | 0.108832i | \(-0.0347111\pi\) | |||||||
\(398\) | 28.8539 | + | 8.24482i | 1.44632 | + | 0.413275i | ||||
\(399\) | 5.47033 | 0.273859 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.4584 | −1.57096 | −0.785479 | − | 0.618889i | \(-0.787583\pi\) | ||||
−0.785479 | + | 0.618889i | \(0.787583\pi\) | |||||||
\(402\) | −17.9770 | − | 5.13680i | −0.896609 | − | 0.256200i | ||||
\(403\) | −12.5397 | + | 12.5397i | −0.624648 | + | 0.624648i | ||||
\(404\) | 2.86595 | − | 0.667248i | 0.142586 | − | 0.0331968i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.2151 | + | 9.56335i | −0.854372 | + | 0.474621i | ||||
\(407\) | −1.65325 | −0.0819487 | ||||||||
\(408\) | −27.0455 | − | 1.34207i | −1.33895 | − | 0.0664426i | ||||
\(409\) | − | 12.8017i | − | 0.633003i | −0.948592 | − | 0.316502i | \(-0.897492\pi\) | ||
0.948592 | − | 0.316502i | \(-0.102508\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.90570 | + | 3.90570i | −0.192654 | + | 0.192654i | ||||
\(412\) | −1.62210 | − | 1.00943i | −0.0799150 | − | 0.0497309i | ||||
\(413\) | −8.85797 | + | 8.85797i | −0.435872 | + | 0.435872i | ||||
\(414\) | −8.18588 | − | 2.33906i | −0.402314 | − | 0.114959i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −8.46482 | + | 12.2089i | −0.415022 | + | 0.598592i | ||||
\(417\) | 26.9322i | 1.31888i | ||||||||
\(418\) | −0.577988 | + | 2.02275i | −0.0282703 | + | 0.0989360i | ||||
\(419\) | 11.4979 | + | 11.4979i | 0.561709 | + | 0.561709i | 0.929793 | − | 0.368084i | \(-0.119986\pi\) |
−0.368084 | + | 0.929793i | \(0.619986\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.5714 | − | 12.5714i | 0.612690 | − | 0.612690i | −0.330956 | − | 0.943646i | \(-0.607371\pi\) |
0.943646 | + | 0.330956i | \(0.107371\pi\) | |||||||
\(422\) | −27.2243 | + | 15.1236i | −1.32526 | + | 0.736208i | ||||
\(423\) | −5.56953 | −0.270800 | ||||||||
\(424\) | 21.1496 | + | 1.04950i | 1.02711 | + | 0.0509684i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.43529 | + | 4.13045i | −0.360241 | + | 0.200121i | ||||
\(427\) | −2.15052 | − | 2.15052i | −0.104071 | − | 0.104071i | ||||
\(428\) | 4.61950 | + | 19.8415i | 0.223292 | + | 0.959077i | ||||
\(429\) | −1.63486 | − | 1.63486i | −0.0789316 | − | 0.0789316i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.2579 | −0.734946 | −0.367473 | − | 0.930034i | \(-0.619777\pi\) | ||||
−0.367473 | + | 0.930034i | \(0.619777\pi\) | |||||||
\(432\) | −7.26978 | + | 21.3698i | −0.349768 | + | 1.02815i | ||||
\(433\) | 12.1705i | 0.584877i | 0.956284 | + | 0.292439i | \(0.0944667\pi\) | ||||
−0.956284 | + | 0.292439i | \(0.905533\pi\) | |||||||
\(434\) | 3.92684 | − | 13.7425i | 0.188495 | − | 0.659663i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.64169 | − | 15.6417i | −0.174405 | − | 0.749101i | ||||
\(437\) | 12.6398 | + | 12.6398i | 0.604644 | + | 0.604644i | ||||
\(438\) | −2.46252 | − | 4.43283i | −0.117664 | − | 0.211809i | ||||
\(439\) | 39.7535i | 1.89733i | 0.316283 | + | 0.948665i | \(0.397565\pi\) | ||||
−0.316283 | + | 0.948665i | \(0.602435\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 3.98371i | − | 0.189701i | ||||||
\(442\) | 21.1347 | − | 11.7407i | 1.00527 | − | 0.558450i | ||||
\(443\) | −3.62318 | − | 3.62318i | −0.172142 | − | 0.172142i | 0.615778 | − | 0.787920i | \(-0.288842\pi\) |
−0.787920 | + | 0.615778i | \(0.788842\pi\) | |||||||
\(444\) | 6.89771 | + | 4.29243i | 0.327351 | + | 0.203710i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.7257 | + | 3.06481i | 0.507878 | + | 0.145123i | ||||
\(447\) | − | 32.9612i | − | 1.55901i | ||||||
\(448\) | 1.18540 | − | 11.9146i | 0.0560047 | − | 0.562913i | ||||
\(449\) | 5.38425 | 0.254098 | 0.127049 | − | 0.991896i | \(-0.459449\pi\) | ||||
0.127049 | + | 0.991896i | \(0.459449\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.26225 | − | 3.26225i | −0.153614 | − | 0.153614i | ||||
\(452\) | 2.05792 | − | 3.30697i | 0.0967964 | − | 0.155547i | ||||
\(453\) | 11.9925 | + | 11.9925i | 0.563455 | + | 0.563455i | ||||
\(454\) | −5.81615 | − | 10.4697i | −0.272965 | − | 0.491369i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.66326 | − | 6.93867i | 0.358865 | − | 0.324933i | ||||
\(457\) | −14.3039 | −0.669108 | −0.334554 | − | 0.942377i | \(-0.608586\pi\) | ||||
−0.334554 | + | 0.942377i | \(0.608586\pi\) | |||||||
\(458\) | −18.8988 | − | 34.0199i | −0.883081 | − | 1.58965i | ||||
\(459\) | 25.9748 | − | 25.9748i | 1.21240 | − | 1.21240i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.50363 | − | 4.50363i | −0.209755 | − | 0.209755i | 0.594408 | − | 0.804163i | \(-0.297386\pi\) |
−0.804163 | + | 0.594408i | \(0.797386\pi\) | |||||||
\(462\) | 1.79167 | + | 0.511960i | 0.0833563 | + | 0.0238185i | ||||
\(463\) | − | 19.3500i | − | 0.899271i | −0.893212 | − | 0.449636i | \(-0.851554\pi\) | ||
0.893212 | − | 0.449636i | \(-0.148446\pi\) | |||||||
\(464\) | −11.9859 | + | 35.2330i | −0.556433 | + | 1.63565i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.04410 | + | 3.65399i | −0.0483672 | + | 0.169268i | ||||
\(467\) | 17.1773 | − | 17.1773i | 0.794871 | − | 0.794871i | −0.187410 | − | 0.982282i | \(-0.560009\pi\) |
0.982282 | + | 0.187410i | \(0.0600094\pi\) | |||||||
\(468\) | −0.996805 | − | 4.28145i | −0.0460773 | − | 0.197910i | ||||
\(469\) | −9.51312 | + | 9.51312i | −0.439275 | + | 0.439275i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.2710i | 0.519341i | ||||||||
\(472\) | −1.17331 | + | 23.6445i | −0.0540060 | + | 1.08833i | ||||
\(473\) | −5.19408 | −0.238824 | ||||||||
\(474\) | −11.7897 | − | 21.2227i | −0.541517 | − | 0.974792i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −10.2950 | + | 16.5436i | −0.471872 | + | 0.758273i | ||||
\(477\) | −4.43060 | + | 4.43060i | −0.202863 | + | 0.202863i | ||||
\(478\) | −4.90968 | + | 17.1821i | −0.224564 | + | 0.785892i | ||||
\(479\) | −5.54474 | −0.253346 | −0.126673 | − | 0.991945i | \(-0.540430\pi\) | ||||
−0.126673 | + | 0.991945i | \(0.540430\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.25361 | −0.330736 | ||||||||
\(482\) | −2.92701 | + | 10.2435i | −0.133322 | + | 0.466578i | ||||
\(483\) | 11.1959 | − | 11.1959i | 0.509429 | − | 0.509429i | ||||
\(484\) | 11.2450 | − | 18.0702i | 0.511138 | − | 0.821373i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −5.77955 | − | 10.4039i | −0.262166 | − | 0.471928i | ||||
\(487\) | −31.7138 | −1.43709 | −0.718546 | − | 0.695480i | \(-0.755192\pi\) | ||||
−0.718546 | + | 0.695480i | \(0.755192\pi\) | |||||||
\(488\) | −5.74037 | − | 0.284854i | −0.259855 | − | 0.0128947i | ||||
\(489\) | 13.4632i | 0.608827i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.39419 | − | 7.39419i | 0.333695 | − | 0.333695i | −0.520293 | − | 0.853988i | \(-0.674177\pi\) |
0.853988 | + | 0.520293i | \(0.174177\pi\) | |||||||
\(492\) | 5.14083 | + | 22.0808i | 0.231767 | + | 0.995477i | ||||
\(493\) | 42.8255 | − | 42.8255i | 1.92876 | − | 1.92876i | ||||
\(494\) | −2.53591 | + | 8.87477i | −0.114096 | + | 0.399295i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.9303 | − | 24.2325i | −0.535685 | − | 1.08807i | ||||
\(497\) | 6.12041i | 0.274538i | ||||||||
\(498\) | −7.95988 | − | 2.27449i | −0.356691 | − | 0.101922i | ||||
\(499\) | −14.0103 | − | 14.0103i | −0.627189 | − | 0.627189i | 0.320171 | − | 0.947360i | \(-0.396260\pi\) |
−0.947360 | + | 0.320171i | \(0.896260\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.62899 | + | 8.62899i | −0.385515 | + | 0.385515i | ||||
\(502\) | −9.67046 | − | 17.4079i | −0.431614 | − | 0.776954i | ||||
\(503\) | 8.43795 | 0.376230 | 0.188115 | − | 0.982147i | \(-0.439762\pi\) | ||||
0.188115 | + | 0.982147i | \(0.439762\pi\) | |||||||
\(504\) | 2.37798 | + | 2.62631i | 0.105924 | + | 0.116985i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.95692 | + | 5.32280i | 0.131451 | + | 0.236627i | ||||
\(507\) | 6.34671 | + | 6.34671i | 0.281868 | + | 0.281868i | ||||
\(508\) | 1.39268 | − | 2.23797i | 0.0617902 | − | 0.0992937i | ||||
\(509\) | −2.09367 | − | 2.09367i | −0.0928004 | − | 0.0928004i | 0.659183 | − | 0.751983i | \(-0.270902\pi\) |
−0.751983 | + | 0.659183i | \(0.770902\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.64891 | −0.161418 | ||||||||
\(512\) | −13.4521 | − | 18.1945i | −0.594506 | − | 0.804091i | ||||
\(513\) | 14.0239i | 0.619169i | ||||||||
\(514\) | 6.14122 | + | 1.75481i | 0.270878 | + | 0.0774016i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 21.6708 | + | 13.4857i | 0.954003 | + | 0.593674i | ||||
\(517\) | 2.81669 | + | 2.81669i | 0.123878 | + | 0.123878i | ||||
\(518\) | 5.11043 | − | 2.83895i | 0.224540 | − | 0.124736i | ||||
\(519\) | 24.8387i | 1.09030i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 28.2558i | − | 1.23791i | −0.785428 | − | 0.618954i | \(-0.787557\pi\) | ||
0.785428 | − | 0.618954i | \(-0.212443\pi\) | |||||||
\(522\) | −5.34770 | − | 9.62647i | −0.234062 | − | 0.421339i | ||||
\(523\) | −10.1929 | − | 10.1929i | −0.445703 | − | 0.445703i | 0.448220 | − | 0.893923i | \(-0.352058\pi\) |
−0.893923 | + | 0.448220i | \(0.852058\pi\) | |||||||
\(524\) | −0.660765 | − | 2.83810i | −0.0288657 | − | 0.123983i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.85368 | + | 27.4851i | −0.342437 | + | 1.19841i | ||||
\(527\) | 43.9555i | 1.91473i | ||||||||
\(528\) | 3.15929 | − | 1.55540i | 0.137491 | − | 0.0676901i | ||||
\(529\) | 28.7385 | 1.24950 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.95326 | − | 4.95326i | −0.214953 | − | 0.214953i | ||||
\(532\) | −1.68681 | − | 7.24512i | −0.0731323 | − | 0.314116i | ||||
\(533\) | −14.3131 | − | 14.3131i | −0.619967 | − | 0.619967i | ||||
\(534\) | 19.1901 | − | 10.6605i | 0.830438 | − | 0.461325i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.26009 | + | 25.3933i | −0.0544276 | + | 1.09682i | ||||
\(537\) | 22.6095 | 0.975671 | ||||||||
\(538\) | 29.6222 | − | 16.4557i | 1.27710 | − | 0.709457i | ||||
\(539\) | −2.01469 | + | 2.01469i | −0.0867790 | + | 0.0867790i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.86053 | + | 3.86053i | 0.165977 | + | 0.165977i | 0.785209 | − | 0.619231i | \(-0.212556\pi\) |
−0.619231 | + | 0.785209i | \(0.712556\pi\) | |||||||
\(542\) | 1.41453 | − | 4.95036i | 0.0607595 | − | 0.212636i | ||||
\(543\) | 8.51534i | 0.365428i | ||||||||
\(544\) | 6.56211 | + | 36.2339i | 0.281348 | + | 1.55352i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7.86093 | + | 2.24621i | 0.336417 | + | 0.0961289i | ||||
\(547\) | −20.6231 | + | 20.6231i | −0.881781 | + | 0.881781i | −0.993716 | − | 0.111935i | \(-0.964295\pi\) |
0.111935 | + | 0.993716i | \(0.464295\pi\) | |||||||
\(548\) | 6.37720 | + | 3.96852i | 0.272421 | + | 0.169527i | ||||
\(549\) | 1.20254 | − | 1.20254i | 0.0513233 | − | 0.0513233i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.1216i | 0.985014i | ||||||||
\(552\) | 1.48298 | − | 29.8850i | 0.0631199 | − | 1.27199i | ||||
\(553\) | −17.4696 | −0.742884 | ||||||||
\(554\) | −27.9892 | + | 15.5486i | −1.18915 | + | 0.660595i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 35.6700 | − | 8.30468i | 1.51275 | − | 0.352197i | ||||
\(557\) | 1.28512 | − | 1.28512i | 0.0544523 | − | 0.0544523i | −0.679356 | − | 0.733809i | \(-0.737741\pi\) |
0.733809 | + | 0.679356i | \(0.237741\pi\) | |||||||
\(558\) | 7.68465 | + | 2.19584i | 0.325317 | + | 0.0929573i | ||||
\(559\) | −22.7889 | −0.963868 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.73068 | −0.241949 | ||||||||
\(562\) | 7.50409 | + | 2.14425i | 0.316541 | + | 0.0904496i | ||||
\(563\) | 21.9152 | − | 21.9152i | 0.923615 | − | 0.923615i | −0.0736677 | − | 0.997283i | \(-0.523470\pi\) |
0.997283 | + | 0.0736677i | \(0.0234704\pi\) | |||||||
\(564\) | −4.43869 | − | 19.0650i | −0.186903 | − | 0.802779i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.13822 | + | 2.29886i | −0.173942 | + | 0.0966284i | ||||
\(567\) | 8.66397 | 0.363852 | ||||||||
\(568\) | 7.76324 | + | 8.57394i | 0.325738 | + | 0.359754i | ||||
\(569\) | − | 35.6668i | − | 1.49523i | −0.664132 | − | 0.747615i | \(-0.731199\pi\) | ||
0.664132 | − | 0.747615i | \(-0.268801\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.60524 | − | 5.60524i | 0.234572 | − | 0.234572i | −0.580026 | − | 0.814598i | \(-0.696958\pi\) |
0.814598 | + | 0.580026i | \(0.196958\pi\) | |||||||
\(572\) | −1.66115 | + | 2.66938i | −0.0694562 | + | 0.111613i | ||||
\(573\) | 20.0238 | − | 20.0238i | 0.836507 | − | 0.836507i | ||||
\(574\) | 15.6860 | + | 4.48217i | 0.654720 | + | 0.187082i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.66251 | + | 0.662858i | 0.277604 | + | 0.0276191i | ||||
\(577\) | − | 2.43681i | − | 0.101446i | −0.998713 | − | 0.0507230i | \(-0.983847\pi\) | ||
0.998713 | − | 0.0507230i | \(-0.0161526\pi\) | |||||||
\(578\) | 9.85896 | − | 34.5028i | 0.410079 | − | 1.43513i | ||||
\(579\) | −25.8071 | − | 25.8071i | −1.07251 | − | 1.07251i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.21225 | + | 4.21225i | −0.174753 | + | 0.174753i | ||||
\(582\) | 33.0029 | − | 18.3338i | 1.36802 | − | 0.759960i | ||||
\(583\) | 4.48139 | 0.185600 | ||||||||
\(584\) | −5.11167 | + | 4.62835i | −0.211523 | + | 0.191522i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 33.5353 | − | 18.6295i | 1.38533 | − | 0.769578i | ||||
\(587\) | 0.415982 | + | 0.415982i | 0.0171694 | + | 0.0171694i | 0.715639 | − | 0.698470i | \(-0.246135\pi\) |
−0.698470 | + | 0.715639i | \(0.746135\pi\) | |||||||
\(588\) | 13.6366 | − | 3.17486i | 0.562363 | − | 0.130929i | ||||
\(589\) | −11.8659 | − | 11.8659i | −0.488924 | − | 0.488924i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.85136 | 0.240693 | ||||||||
\(592\) | 3.55811 | − | 10.4592i | 0.146237 | − | 0.429870i | ||||
\(593\) | 15.3439i | 0.630098i | 0.949075 | + | 0.315049i | \(0.102021\pi\) | ||||
−0.949075 | + | 0.315049i | \(0.897979\pi\) | |||||||
\(594\) | −1.31247 | + | 4.59318i | −0.0538513 | + | 0.188460i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −43.6551 | + | 10.1638i | −1.78818 | + | 0.416324i | ||||
\(597\) | −22.0675 | − | 22.0675i | −0.903163 | − | 0.903163i | ||||
\(598\) | 12.9734 | + | 23.3537i | 0.530523 | + | 0.955002i | ||||
\(599\) | 43.3487i | 1.77118i | 0.464468 | + | 0.885590i | \(0.346246\pi\) | ||||
−0.464468 | + | 0.885590i | \(0.653754\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.7291i | 1.57979i | 0.613239 | + | 0.789897i | \(0.289866\pi\) | ||||
−0.613239 | + | 0.789897i | \(0.710134\pi\) | |||||||
\(602\) | 16.0556 | − | 8.91923i | 0.654379 | − | 0.363520i | ||||
\(603\) | −5.31961 | − | 5.31961i | −0.216631 | − | 0.216631i | ||||
\(604\) | 12.1853 | − | 19.5812i | 0.495815 | − | 0.796748i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.94244 | − | 0.840784i | −0.119529 | − | 0.0341545i | ||||
\(607\) | − | 34.9068i | − | 1.41682i | −0.705800 | − | 0.708412i | \(-0.749412\pi\) | ||
0.705800 | − | 0.708412i | \(-0.250588\pi\) | |||||||
\(608\) | −11.5528 | − | 8.00994i | −0.468530 | − | 0.324846i | ||||
\(609\) | 20.4802 | 0.829901 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.3582 | + | 12.3582i | 0.499958 | + | 0.499958i | ||||
\(612\) | −9.25095 | − | 5.75684i | −0.373947 | − | 0.232707i | ||||
\(613\) | 0.151779 | + | 0.151779i | 0.00613031 | + | 0.00613031i | 0.710165 | − | 0.704035i | \(-0.248620\pi\) |
−0.704035 | + | 0.710165i | \(0.748620\pi\) | |||||||
\(614\) | 19.3560 | + | 34.8430i | 0.781144 | + | 1.40615i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.125587 | − | 2.53083i | 0.00506004 | − | 0.101970i | ||||
\(617\) | 0.288199 | 0.0116025 | 0.00580123 | − | 0.999983i | \(-0.498153\pi\) | ||||
0.00580123 | + | 0.999983i | \(0.498153\pi\) | |||||||
\(618\) | 0.964876 | + | 1.73689i | 0.0388130 | + | 0.0698679i | ||||
\(619\) | 11.5307 | − | 11.5307i | 0.463460 | − | 0.463460i | −0.436328 | − | 0.899788i | \(-0.643721\pi\) |
0.899788 | + | 0.436328i | \(0.143721\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.7019 | + | 28.7019i | 1.15177 | + | 1.15177i | ||||
\(622\) | −7.79586 | − | 2.22762i | −0.312585 | − | 0.0893193i | ||||
\(623\) | − | 15.7965i | − | 0.632873i | ||||||
\(624\) | 13.8613 | − | 6.82428i | 0.554897 | − | 0.273190i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.0826141 | + | 0.289120i | −0.00330192 | + | 0.0115555i | ||||
\(627\) | 1.54700 | − | 1.54700i | 0.0617814 | − | 0.0617814i | ||||
\(628\) | 14.9278 | − | 3.47547i | 0.595682 | − | 0.138686i | ||||
\(629\) | −12.7131 | + | 12.7131i | −0.506903 | + | 0.506903i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 14.2062i | − | 0.565541i | −0.959188 | − | 0.282771i | \(-0.908746\pi\) | ||
0.959188 | − | 0.282771i | \(-0.0912536\pi\) | |||||||
\(632\) | −24.4728 | + | 22.1588i | −0.973475 | + | 0.881430i | ||||
\(633\) | 32.3878 | 1.28730 | ||||||||
\(634\) | −3.12332 | − | 5.62234i | −0.124043 | − | 0.223292i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −18.6973 | − | 11.6353i | −0.741396 | − | 0.461369i | ||||
\(637\) | −8.83942 | + | 8.83942i | −0.350230 | + | 0.350230i | ||||
\(638\) | −2.16391 | + | 7.57292i | −0.0856702 | + | 0.299815i | ||||
\(639\) | −3.42245 | −0.135390 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.7372 | 0.779572 | 0.389786 | − | 0.920905i | \(-0.372549\pi\) | ||||
0.389786 | + | 0.920905i | \(0.372549\pi\) | |||||||
\(642\) | 5.82093 | − | 20.3712i | 0.229734 | − | 0.803985i | ||||
\(643\) | −5.80043 | + | 5.80043i | −0.228747 | + | 0.228747i | −0.812169 | − | 0.583422i | \(-0.801713\pi\) |
0.583422 | + | 0.812169i | \(0.301713\pi\) | |||||||
\(644\) | −18.2805 | − | 11.3759i | −0.720353 | − | 0.448274i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.1098 | + | 19.9990i | 0.437110 | + | 0.786849i | ||||
\(647\) | −46.3186 | −1.82097 | −0.910485 | − | 0.413541i | \(-0.864292\pi\) | ||||
−0.910485 | + | 0.413541i | \(0.864292\pi\) | |||||||
\(648\) | 12.1371 | − | 10.9895i | 0.476792 | − | 0.431710i | ||||
\(649\) | 5.01005i | 0.196662i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.5103 | + | 10.5103i | −0.411932 | + | 0.411932i | ||||
\(652\) | 17.8312 | − | 4.15144i | 0.698322 | − | 0.162583i | ||||
\(653\) | −4.42354 | + | 4.42354i | −0.173106 | + | 0.173106i | −0.788343 | − | 0.615236i | \(-0.789061\pi\) |
0.615236 | + | 0.788343i | \(0.289061\pi\) | |||||||
\(654\) | −4.58881 | + | 16.0592i | −0.179437 | + | 0.627964i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 27.6594 | − | 13.6174i | 1.07992 | − | 0.531671i | ||||
\(657\) | − | 2.04042i | − | 0.0796045i | ||||||
\(658\) | −13.5436 | − | 3.86999i | −0.527984 | − | 0.150868i | ||||
\(659\) | 15.2461 | + | 15.2461i | 0.593905 | + | 0.593905i | 0.938684 | − | 0.344779i | \(-0.112046\pi\) |
−0.344779 | + | 0.938684i | \(0.612046\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.1271 | − | 19.1271i | 0.743958 | − | 0.743958i | −0.229379 | − | 0.973337i | \(-0.573670\pi\) |
0.973337 | + | 0.229379i | \(0.0736696\pi\) | |||||||
\(662\) | 21.3959 | + | 38.5151i | 0.831577 | + | 1.49693i | ||||
\(663\) | −25.1432 | −0.976481 | ||||||||
\(664\) | −0.557946 | + | 11.2437i | −0.0216525 | + | 0.436341i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.58750 | + | 2.85769i | 0.0615145 | + | 0.110733i | ||||
\(667\) | 47.3218 | + | 47.3218i | 1.83231 | + | 1.83231i | ||||
\(668\) | 14.0894 | + | 8.76777i | 0.545133 | + | 0.339235i | ||||
\(669\) | −8.20306 | − | 8.20306i | −0.317149 | − | 0.317149i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.21633 | −0.0469559 | ||||||||
\(672\) | −7.09490 | + | 10.2331i | −0.273692 | + | 0.394749i | ||||
\(673\) | 18.5586i | 0.715382i | 0.933840 | + | 0.357691i | \(0.116436\pi\) | ||||
−0.933840 | + | 0.357691i | \(0.883564\pi\) | |||||||
\(674\) | −15.2462 | − | 4.35651i | −0.587263 | − | 0.167807i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.44879 | − | 10.3629i | 0.248030 | − | 0.398572i | ||||
\(677\) | −2.71844 | − | 2.71844i | −0.104478 | − | 0.104478i | 0.652935 | − | 0.757414i | \(-0.273537\pi\) |
−0.757414 | + | 0.652935i | \(0.773537\pi\) | |||||||
\(678\) | −3.54100 | + | 1.96709i | −0.135991 | + | 0.0755458i | ||||
\(679\) | − | 27.1666i | − | 1.04256i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.4555i | 0.477295i | ||||||||
\(682\) | −2.77587 | − | 4.99688i | −0.106293 | − | 0.191340i | ||||
\(683\) | 12.6646 | + | 12.6646i | 0.484598 | + | 0.484598i | 0.906596 | − | 0.421999i | \(-0.138671\pi\) |
−0.421999 | + | 0.906596i | \(0.638671\pi\) | |||||||
\(684\) | 4.05138 | − | 0.943239i | 0.154908 | − | 0.0360657i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.83885 | − | 23.9335i | 0.261108 | − | 0.913786i | ||||
\(687\) | 40.4723i | 1.54412i | ||||||||
\(688\) | 11.1786 | − | 32.8600i | 0.426182 | − | 1.25278i | ||||
\(689\) | 19.6620 | 0.749063 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.8892 | + | 26.8892i | 1.02291 | + | 1.02291i | 0.999731 | + | 0.0231826i | \(0.00737991\pi\) |
0.0231826 | + | 0.999731i | \(0.492620\pi\) | |||||||
\(692\) | 32.8973 | − | 7.65914i | 1.25057 | − | 0.291157i | ||||
\(693\) | 0.530180 | + | 0.530180i | 0.0201399 | + | 0.0201399i | ||||
\(694\) | 2.16187 | − | 1.20096i | 0.0820636 | − | 0.0455880i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 28.6903 | − | 25.9775i | 1.08750 | − | 0.984675i | ||||
\(697\) | −50.1717 | −1.90039 | ||||||||
\(698\) | −9.82180 | + | 5.45621i | −0.371761 | + | 0.206521i | ||||
\(699\) | 2.79458 | − | 2.79458i | 0.105701 | − | 0.105701i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.3725 | + | 25.3725i | 0.958305 | + | 0.958305i | 0.999165 | − | 0.0408602i | \(-0.0130098\pi\) |
−0.0408602 | + | 0.999165i | \(0.513010\pi\) | |||||||
\(702\) | −5.75843 | + | 20.1524i | −0.217338 | + | 0.760605i | ||||
\(703\) | − | 6.86382i | − | 0.258874i | ||||||
\(704\) | −3.03422 | − | 3.70467i | −0.114356 | − | 0.139625i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.01809 | − | 0.290912i | −0.0383162 | − | 0.0109486i | ||||
\(707\) | −1.55709 | + | 1.55709i | −0.0585606 | + | 0.0585606i | ||||
\(708\) | 13.0079 | − | 20.9029i | 0.488865 | − | 0.785581i | ||||
\(709\) | −16.1117 | + | 16.1117i | −0.605089 | + | 0.605089i | −0.941659 | − | 0.336570i | \(-0.890733\pi\) |
0.336570 | + | 0.941659i | \(0.390733\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 9.76879i | − | 0.366358i | ||||||
\(712\) | −20.0365 | − | 22.1289i | −0.750901 | − | 0.829316i | ||||
\(713\) | −48.5705 | −1.81898 | ||||||||
\(714\) | 17.7143 | − | 9.84066i | 0.662941 | − | 0.368277i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.97175 | − | 29.9449i | −0.260546 | − | 1.11909i | ||||
\(717\) | 13.1409 | − | 13.1409i | 0.490757 | − | 0.490757i | ||||
\(718\) | 3.66985 | + | 1.04864i | 0.136958 | + | 0.0391347i | ||||
\(719\) | −29.1676 | −1.08777 | −0.543884 | − | 0.839160i | \(-0.683047\pi\) | ||||
−0.543884 | + | 0.839160i | \(0.683047\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.42973 | 0.0532460 | ||||||||
\(722\) | 17.4381 | + | 4.98284i | 0.648980 | + | 0.185442i | ||||
\(723\) | 7.83424 | − | 7.83424i | 0.291358 | − | 0.291358i | ||||
\(724\) | 11.2780 | − | 2.62575i | 0.419145 | − | 0.0975852i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −19.3490 | + | 10.7487i | −0.718108 | + | 0.398923i | ||||
\(727\) | 4.13463 | 0.153345 | 0.0766724 | − | 0.997056i | \(-0.475570\pi\) | ||||
0.0766724 | + | 0.997056i | \(0.475570\pi\) | |||||||
\(728\) | 0.551010 | − | 11.1039i | 0.0204218 | − | 0.411540i | ||||
\(729\) | 29.7434i | 1.10161i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −39.9411 | + | 39.9411i | −1.47727 | + | 1.47727i | ||||
\(732\) | 5.07478 | + | 3.15802i | 0.187569 | + | 0.116724i | ||||
\(733\) | −19.3838 | + | 19.3838i | −0.715957 | + | 0.715957i | −0.967775 | − | 0.251817i | \(-0.918972\pi\) |
0.251817 | + | 0.967775i | \(0.418972\pi\) | |||||||
\(734\) | 28.0255 | + | 8.00809i | 1.03444 | + | 0.295584i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −40.0382 | + | 7.25108i | −1.47583 | + | 0.267278i | ||||
\(737\) | 5.38060i | 0.198197i | ||||||||
\(738\) | −2.50637 | + | 8.77140i | −0.0922608 | + | 0.322880i | ||||
\(739\) | −23.9820 | − | 23.9820i | −0.882194 | − | 0.882194i | 0.111564 | − | 0.993757i | \(-0.464414\pi\) |
−0.993757 | + | 0.111564i | \(0.964414\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.78744 | − | 6.78744i | 0.249343 | − | 0.249343i | ||||
\(742\) | −13.8526 | + | 7.69540i | −0.508545 | + | 0.282507i | ||||
\(743\) | −10.3473 | −0.379604 | −0.189802 | − | 0.981822i | \(-0.560785\pi\) | ||||
−0.189802 | + | 0.981822i | \(0.560785\pi\) | |||||||
\(744\) | −1.39218 | + | 28.0551i | −0.0510397 | + | 1.02855i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.16380 | + | 5.09068i | −0.335511 | + | 0.186383i | ||||
\(747\) | −2.35543 | − | 2.35543i | −0.0861808 | − | 0.0861808i | ||||
\(748\) | 1.76708 | + | 7.58993i | 0.0646109 | + | 0.277515i | ||||
\(749\) | −10.7801 | − | 10.7801i | −0.393896 | − | 0.393896i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.0217 | −1.35094 | −0.675470 | − | 0.737387i | \(-0.736059\pi\) | ||||
−0.675470 | + | 0.737387i | \(0.736059\pi\) | |||||||
\(752\) | −23.8817 | + | 11.7575i | −0.870874 | + | 0.428754i | ||||
\(753\) | 20.7096i | 0.754700i | ||||||||
\(754\) | −9.49412 | + | 33.2260i | −0.345756 | + | 1.21002i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.83032 | − | 16.4519i | −0.139308 | − | 0.598350i | ||||
\(757\) | −30.4305 | − | 30.4305i | −1.10601 | − | 1.10601i | −0.993669 | − | 0.112345i | \(-0.964164\pi\) |
−0.112345 | − | 0.993669i | \(-0.535836\pi\) | |||||||
\(758\) | −5.25774 | − | 9.46454i | −0.190970 | − | 0.343768i | ||||
\(759\) | − | 6.33235i | − | 0.229850i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 43.1054i | − | 1.56257i | −0.624174 | − | 0.781285i | \(-0.714564\pi\) | ||
0.624174 | − | 0.781285i | \(-0.285436\pi\) | |||||||
\(762\) | −2.39634 | + | 1.33122i | −0.0868103 | + | 0.0482249i | ||||
\(763\) | 8.49827 | + | 8.49827i | 0.307658 | + | 0.307658i | ||||
\(764\) | −32.6948 | − | 20.3459i | −1.18285 | − | 0.736088i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −40.1256 | − | 11.4656i | −1.44980 | − | 0.414271i | ||||
\(767\) | 21.9815i | 0.793705i | ||||||||
\(768\) | 3.04073 | + | 23.3345i | 0.109723 | + | 0.842013i | ||||
\(769\) | 31.2507 | 1.12693 | 0.563465 | − | 0.826140i | \(-0.309468\pi\) | ||||
0.563465 | + | 0.826140i | \(0.309468\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.69682 | − | 4.69682i | −0.169152 | − | 0.169152i | ||||
\(772\) | −26.2221 | + | 42.1376i | −0.943756 | + | 1.51657i | ||||
\(773\) | −24.4047 | − | 24.4047i | −0.877778 | − | 0.877778i | 0.115527 | − | 0.993304i | \(-0.463144\pi\) |
−0.993304 | + | 0.115527i | \(0.963144\pi\) | |||||||
\(774\) | 4.98751 | + | 8.97810i | 0.179272 | + | 0.322711i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −34.4586 | − | 38.0570i | −1.23699 | − | 1.36617i | ||||
\(777\) | −6.07970 | −0.218108 | ||||||||
\(778\) | −1.33918 | − | 2.41068i | −0.0480120 | − | 0.0864271i | ||||
\(779\) | 13.5439 | − | 13.5439i | 0.485261 | − | 0.485261i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.73085 | + | 1.73085i | 0.0619345 | + | 0.0619345i | ||||
\(782\) | 63.6688 | + | 18.1929i | 2.27679 | + | 0.650579i | ||||
\(783\) | 52.5036i | 1.87632i | ||||||||
\(784\) | −8.40981 | − | 17.0818i | −0.300350 | − | 0.610065i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.832616 | + | 2.91386i | −0.0296984 | + | 0.103934i | ||||
\(787\) | 17.2122 | − | 17.2122i | 0.613549 | − | 0.613549i | −0.330320 | − | 0.943869i | \(-0.607157\pi\) |
0.943869 | + | 0.330320i | \(0.107157\pi\) | |||||||
\(788\) | −1.80430 | − | 7.74977i | −0.0642754 | − | 0.276074i | ||||
\(789\) | 21.0206 | − | 21.0206i | 0.748354 | − | 0.748354i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.91480i | 0.103638i | ||||||||
\(792\) | 1.41521 | + | 0.0702266i | 0.0502871 | + | 0.00249539i | ||||
\(793\) | −5.33662 | −0.189509 | ||||||||
\(794\) | 21.3429 | + | 38.4197i | 0.757432 | + | 1.36347i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.4224 | + | 36.0317i | −0.794742 | + | 1.27711i | ||||
\(797\) | 20.3220 | − | 20.3220i | 0.719841 | − | 0.719841i | −0.248731 | − | 0.968573i | \(-0.580014\pi\) |
0.968573 | + | 0.248731i | \(0.0800136\pi\) | |||||||
\(798\) | −2.12551 | + | 7.43850i | −0.0752421 | + | 0.263320i | ||||
\(799\) | 43.3192 | 1.53252 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.83319 | 0.312105 | ||||||||
\(802\) | 12.2232 | − | 42.7768i | 0.431616 | − | 1.51050i | ||||
\(803\) | −1.03191 | + | 1.03191i | −0.0364153 | + | 0.0364153i | ||||
\(804\) | 13.9699 | − | 22.4490i | 0.492682 | − | 0.791714i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.1791 | − | 21.9237i | −0.428989 | − | 0.772229i | ||||
\(807\) | −35.2405 | −1.24052 | ||||||||
\(808\) | −0.206250 | + | 4.15634i | −0.00725584 | + | 0.146220i | ||||
\(809\) | − | 2.80407i | − | 0.0985859i | −0.998784 | − | 0.0492930i | \(-0.984303\pi\) | ||
0.998784 | − | 0.0492930i | \(-0.0156968\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.29902 | + | 7.29902i | −0.256303 | + | 0.256303i | −0.823549 | − | 0.567246i | \(-0.808009\pi\) |
0.567246 | + | 0.823549i | \(0.308009\pi\) | |||||||
\(812\) | −6.31518 | − | 27.1248i | −0.221619 | − | 0.951894i | ||||
\(813\) | −3.78605 | + | 3.78605i | −0.132782 | + | 0.132782i | ||||
\(814\) | 0.642373 | − | 2.24808i | 0.0225152 | − | 0.0787950i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.3335 | − | 36.2547i | 0.431759 | − | 1.26917i | ||||
\(817\) | − | 21.5643i | − | 0.754439i | ||||||
\(818\) | 17.4076 | + | 4.97411i | 0.608643 | + | 0.173916i | ||||
\(819\) | 2.32615 | + | 2.32615i | 0.0812823 | + | 0.0812823i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.0517 | + | 10.0517i | −0.350806 | + | 0.350806i | −0.860409 | − | 0.509603i | \(-0.829792\pi\) |
0.509603 | + | 0.860409i | \(0.329792\pi\) | |||||||
\(822\) | −3.79337 | − | 6.82850i | −0.132309 | − | 0.238171i | ||||
\(823\) | −34.2064 | −1.19236 | −0.596179 | − | 0.802851i | \(-0.703315\pi\) | ||||
−0.596179 | + | 0.802851i | \(0.703315\pi\) | |||||||
\(824\) | 2.00288 | − | 1.81350i | 0.0697735 | − | 0.0631761i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.60320 | − | 15.4868i | −0.299344 | − | 0.538853i | ||||
\(827\) | 31.3455 | + | 31.3455i | 1.08999 | + | 1.08999i | 0.995529 | + | 0.0944595i | \(0.0301123\pi\) |
0.0944595 | + | 0.995529i | \(0.469888\pi\) | |||||||
\(828\) | 6.36126 | − | 10.2222i | 0.221069 | − | 0.355247i | ||||
\(829\) | 3.87895 | + | 3.87895i | 0.134722 | + | 0.134722i | 0.771252 | − | 0.636530i | \(-0.219631\pi\) |
−0.636530 | + | 0.771252i | \(0.719631\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.2978 | 1.15509 | ||||||||
\(832\) | −13.3125 | − | 16.2542i | −0.461530 | − | 0.563512i | ||||
\(833\) | 30.9849i | 1.07356i | ||||||||
\(834\) | −36.6221 | − | 10.4645i | −1.26812 | − | 0.362357i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.52594 | − | 1.57189i | −0.0873614 | − | 0.0543648i | ||||
\(837\) | −26.9445 | − | 26.9445i | −0.931338 | − | 0.931338i | ||||
\(838\) | −20.1022 | + | 11.1672i | −0.694421 | + | 0.385765i | ||||
\(839\) | 32.9463i | 1.13743i | 0.822533 | + | 0.568717i | \(0.192560\pi\) | ||||
−0.822533 | + | 0.568717i | \(0.807440\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.5644i | 1.98498i | ||||||||
\(842\) | 12.2098 | + | 21.9790i | 0.420777 | + | 0.757447i | ||||
\(843\) | −5.73915 | − | 5.73915i | −0.197667 | − | 0.197667i | ||||
\(844\) | −9.98694 | − | 42.8956i | −0.343765 | − | 1.47653i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.16405 | − | 7.57340i | 0.0744016 | − | 0.260379i | ||||
\(847\) | 15.9272i | 0.547267i | ||||||||
\(848\) | −9.64480 | + | 28.3512i | −0.331204 | + | 0.973584i | ||||
\(849\) | 4.92309 | 0.168960 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.0478 | − | 14.0478i | −0.481553 | − | 0.481553i | ||||
\(852\) | −2.72756 | − | 11.7153i | −0.0934446 | − | 0.401361i | ||||
\(853\) | −1.87566 | − | 1.87566i | −0.0642212 | − | 0.0642212i | 0.674267 | − | 0.738488i | \(-0.264460\pi\) |
−0.738488 | + | 0.674267i | \(0.764460\pi\) | |||||||
\(854\) | 3.75984 | − | 2.08867i | 0.128659 | − | 0.0714728i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −28.7752 | − | 1.42791i | −0.983517 | − | 0.0488050i | ||||
\(857\) | 23.1714 | 0.791521 | 0.395760 | − | 0.918354i | \(-0.370481\pi\) | ||||
0.395760 | + | 0.918354i | \(0.370481\pi\) | |||||||
\(858\) | 2.85829 | − | 1.58784i | 0.0975803 | − | 0.0542078i | ||||
\(859\) | 10.5073 | − | 10.5073i | 0.358506 | − | 0.358506i | −0.504756 | − | 0.863262i | \(-0.668418\pi\) |
0.863262 | + | 0.504756i | \(0.168418\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.9967 | − | 11.9967i | −0.408846 | − | 0.408846i | ||||
\(862\) | 5.92847 | − | 20.7475i | 0.201924 | − | 0.706663i | ||||
\(863\) | − | 25.2777i | − | 0.860463i | −0.902719 | − | 0.430231i | \(-0.858432\pi\) | ||
0.902719 | − | 0.430231i | \(-0.141568\pi\) | |||||||
\(864\) | −26.2337 | − | 18.1886i | −0.892488 | − | 0.618790i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.5493 | − | 4.72887i | −0.562369 | − | 0.160693i | ||||
\(867\) | −26.3878 | + | 26.3878i | −0.896177 | + | 0.896177i | ||||
\(868\) | 17.1612 | + | 10.6794i | 0.582489 | + | 0.362481i | ||||
\(869\) | −4.94039 | + | 4.94039i | −0.167591 | + | 0.167591i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.6073i | 0.799901i | ||||||||
\(872\) | 22.6844 | + | 1.12566i | 0.768190 | + | 0.0381198i | ||||
\(873\) | 15.1912 | 0.514144 | ||||||||
\(874\) | −22.0987 | + | 12.2763i | −0.747500 | + | 0.415251i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.98453 | − | 1.62613i | 0.235985 | − | 0.0549420i | ||||
\(877\) | 16.7350 | − | 16.7350i | 0.565101 | − | 0.565101i | −0.365651 | − | 0.930752i | \(-0.619154\pi\) |
0.930752 | + | 0.365651i | \(0.119154\pi\) | |||||||
\(878\) | −54.0564 | − | 15.4463i | −1.82431 | − | 0.521286i | ||||
\(879\) | −39.8957 | −1.34565 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.38791 | 0.316287 | 0.158143 | − | 0.987416i | \(-0.449449\pi\) | ||||
0.158143 | + | 0.987416i | \(0.449449\pi\) | |||||||
\(882\) | 5.41701 | + | 1.54788i | 0.182400 | + | 0.0521197i | ||||
\(883\) | −21.5593 | + | 21.5593i | −0.725527 | + | 0.725527i | −0.969725 | − | 0.244198i | \(-0.921475\pi\) |
0.244198 | + | 0.969725i | \(0.421475\pi\) | |||||||
\(884\) | 7.75303 | + | 33.3006i | 0.260763 | + | 1.12002i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.33455 | − | 3.51897i | 0.212813 | − | 0.118222i | ||||
\(887\) | 48.2072 | 1.61864 | 0.809320 | − | 0.587368i | \(-0.199836\pi\) | ||||
0.809320 | + | 0.587368i | \(0.199836\pi\) | |||||||
\(888\) | −8.51691 | + | 7.71161i | −0.285809 | + | 0.258785i | ||||
\(889\) | 1.97256i | 0.0661577i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.45016 | − | 2.45016i | 0.0820834 | − | 0.0820834i | ||||
\(892\) | −8.33500 | + | 13.3939i | −0.279076 | + | 0.448461i | ||||
\(893\) | −11.6941 | + | 11.6941i | −0.391327 | + | 0.391327i | ||||
\(894\) | 44.8204 | + | 12.8071i | 1.49902 | + | 0.428335i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 15.7408 | + | 6.24133i | 0.525863 | + | 0.208508i | ||||
\(897\) | − | 27.7830i | − | 0.927648i | ||||||
\(898\) | −2.09206 | + | 7.32144i | −0.0698128 | + | 0.244320i | ||||
\(899\) | −44.4243 | − | 44.4243i | −1.48163 | − | 1.48163i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.4607 | − | 34.4607i | 1.14805 | − | 1.14805i | ||||
\(902\) | 5.70353 | − | 3.16843i | 0.189907 | − | 0.105497i | ||||
\(903\) | −19.1008 | −0.635636 | ||||||||
\(904\) | 3.69718 | + | 4.08327i | 0.122966 | + | 0.135807i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −20.9669 | + | 11.6475i | −0.696579 | + | 0.386964i | ||||
\(907\) | −31.8381 | − | 31.8381i | −1.05717 | − | 1.05717i | −0.998264 | − | 0.0589044i | \(-0.981239\pi\) |
−0.0589044 | − | 0.998264i | \(-0.518761\pi\) | |||||||
\(908\) | 16.4965 | − | 3.84071i | 0.547456 | − | 0.127458i | ||||
\(909\) | −0.870707 | − | 0.870707i | −0.0288795 | − | 0.0288795i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.8669 | 0.492561 | 0.246281 | − | 0.969199i | \(-0.420791\pi\) | ||||
0.246281 | + | 0.969199i | \(0.420791\pi\) | |||||||
\(912\) | 6.45756 | + | 13.1165i | 0.213831 | + | 0.434329i | ||||
\(913\) | 2.38244i | 0.0788472i | ||||||||
\(914\) | 5.55780 | − | 19.4503i | 0.183836 | − | 0.643358i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 53.6031 | − | 12.4798i | 1.77110 | − | 0.412346i | ||||
\(917\) | 1.54197 | + | 1.54197i | 0.0509202 | + | 0.0509202i | ||||
\(918\) | 25.2277 | + | 45.4128i | 0.832638 | + | 1.49885i | ||||
\(919\) | 5.27591i | 0.174036i | 0.996207 | + | 0.0870181i | \(0.0277338\pi\) | ||||
−0.996207 | + | 0.0870181i | \(0.972266\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 41.4515i | − | 1.36587i | ||||||
\(922\) | 7.87389 | − | 4.37410i | 0.259313 | − | 0.144053i | ||||
\(923\) | 7.59404 | + | 7.59404i | 0.249961 | + | 0.249961i | ||||
\(924\) | −1.39231 | + | 2.23738i | −0.0458038 | + | 0.0736043i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 26.3119 | + | 7.51847i | 0.864664 | + | 0.247072i | ||||
\(927\) | 0.799487i | 0.0262586i | ||||||||
\(928\) | −43.2524 | − | 29.9882i | −1.41983 | − | 0.984411i | ||||
\(929\) | 9.13997 | 0.299873 | 0.149936 | − | 0.988696i | \(-0.452093\pi\) | ||||
0.149936 | + | 0.988696i | \(0.452093\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.36441 | − | 8.36441i | −0.274133 | − | 0.274133i | ||||
\(932\) | −4.56297 | − | 2.83952i | −0.149465 | − | 0.0930116i | ||||
\(933\) | 5.96229 | + | 5.96229i | 0.195197 | + | 0.195197i | ||||
\(934\) | 16.6833 | + | 30.0318i | 0.545893 | + | 0.982671i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.20918 | + | 0.308117i | 0.202953 | + | 0.0100711i | ||||
\(937\) | −19.0036 | −0.620819 | −0.310410 | − | 0.950603i | \(-0.600466\pi\) | ||||
−0.310410 | + | 0.950603i | \(0.600466\pi\) | |||||||
\(938\) | −9.23951 | − | 16.6322i | −0.301681 | − | 0.543060i | ||||
\(939\) | 0.221119 | − | 0.221119i | 0.00721596 | − | 0.00721596i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.48322 | + | 1.48322i | 0.0483517 | + | 0.0483517i | 0.730869 | − | 0.682518i | \(-0.239115\pi\) |
−0.682518 | + | 0.730869i | \(0.739115\pi\) | |||||||
\(942\) | −15.3262 | − | 4.37937i | −0.499355 | − | 0.142687i | ||||
\(943\) | − | 55.4393i | − | 1.80535i | ||||||
\(944\) | −31.6957 | − | 10.7826i | −1.03161 | − | 0.350943i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.01817 | − | 7.06286i | 0.0656163 | − | 0.229633i | ||||
\(947\) | 3.97577 | − | 3.97577i | 0.129195 | − | 0.129195i | −0.639552 | − | 0.768748i | \(-0.720880\pi\) |
0.768748 | + | 0.639552i | \(0.220880\pi\) | |||||||
\(948\) | 33.4393 | − | 7.78533i | 1.08606 | − | 0.252856i | ||||
\(949\) | −4.52747 | + | 4.52747i | −0.146968 | + | 0.146968i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.68870i | 0.216896i | ||||||||
\(952\) | −18.4956 | − | 20.4271i | −0.599447 | − | 0.662046i | ||||
\(953\) | −16.5970 | −0.537628 | −0.268814 | − | 0.963192i | \(-0.586632\pi\) | ||||
−0.268814 | + | 0.963192i | \(0.586632\pi\) | |||||||
\(954\) | −4.30317 | − | 7.74620i | −0.139320 | − | 0.250792i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −21.4564 | − | 13.3523i | −0.693950 | − | 0.431843i | ||||
\(957\) | 5.79179 | − | 5.79179i | 0.187222 | − | 0.187222i | ||||
\(958\) | 2.15442 | − | 7.53968i | 0.0696060 | − | 0.243596i | ||||
\(959\) | −5.62092 | −0.181509 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.5965 | 0.470855 | ||||||||
\(962\) | 2.81840 | − | 9.86338i | 0.0908688 | − | 0.318008i | ||||
\(963\) | 6.02809 | − | 6.02809i | 0.194252 | − | 0.194252i | ||||
\(964\) | −12.7917 | − | 7.96024i | −0.411993 | − | 0.256382i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 10.8738 | + | 19.5742i | 0.349860 | + | 0.629789i | ||||
\(967\) | 8.72635 | 0.280621 | 0.140310 | − | 0.990108i | \(-0.455190\pi\) | ||||
0.140310 | + | 0.990108i | \(0.455190\pi\) | |||||||
\(968\) | 20.2024 | + | 22.3121i | 0.649330 | + | 0.717138i | ||||
\(969\) | − | 23.7921i | − | 0.764311i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.5421 | + | 14.5421i | −0.466677 | + | 0.466677i | −0.900836 | − | 0.434159i | \(-0.857045\pi\) |
0.434159 | + | 0.900836i | \(0.357045\pi\) | |||||||
\(972\) | 16.3927 | − | 3.81654i | 0.525796 | − | 0.122416i | ||||
\(973\) | −19.3799 | + | 19.3799i | −0.621289 | + | 0.621289i | ||||
\(974\) | 12.3225 | − | 43.1242i | 0.394837 | − | 1.38179i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.61777 | − | 7.69502i | 0.0837928 | − | 0.246312i | ||||
\(977\) | 25.2020i | 0.806284i | 0.915137 | + | 0.403142i | \(0.132082\pi\) | ||||
−0.915137 | + | 0.403142i | \(0.867918\pi\) | |||||||
\(978\) | −18.3071 | − | 5.23114i | −0.585397 | − | 0.167273i | ||||
\(979\) | −4.46723 | − | 4.46723i | −0.142773 | − | 0.142773i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.75212 | + | 4.75212i | −0.151724 | + | 0.151724i | ||||
\(982\) | 7.18152 | + | 12.9276i | 0.229171 | + | 0.412535i | ||||
\(983\) | 4.00157 | 0.127630 | 0.0638151 | − | 0.997962i | \(-0.479673\pi\) | ||||
0.0638151 | + | 0.997962i | \(0.479673\pi\) | |||||||
\(984\) | −32.0227 | − | 1.58906i | −1.02085 | − | 0.0506573i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 41.5938 | + | 74.8736i | 1.32462 | + | 2.38446i | ||||
\(987\) | 10.3582 | + | 10.3582i | 0.329704 | + | 0.329704i | ||||
\(988\) | −11.0825 | − | 6.89661i | −0.352581 | − | 0.219410i | ||||
\(989\) | −44.1346 | − | 44.1346i | −1.40340 | − | 1.40340i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −62.3391 | −1.98027 | −0.990134 | − | 0.140127i | \(-0.955249\pi\) | ||||
−0.990134 | + | 0.140127i | \(0.955249\pi\) | |||||||
\(992\) | 37.5866 | − | 6.80709i | 1.19338 | − | 0.216125i | ||||
\(993\) | − | 45.8201i | − | 1.45406i | ||||||
\(994\) | −8.32247 | − | 2.37809i | −0.263973 | − | 0.0754285i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.18565 | − | 9.94001i | 0.196000 | − | 0.314961i | ||||
\(997\) | 21.6855 | + | 21.6855i | 0.686787 | + | 0.686787i | 0.961521 | − | 0.274733i | \(-0.0885895\pi\) |
−0.274733 | + | 0.961521i | \(0.588590\pi\) | |||||||
\(998\) | 24.4949 | − | 13.6074i | 0.775371 | − | 0.430734i | ||||
\(999\) | − | 15.5861i | − | 0.493121i |
(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 | 400.2.q.e.349.3 | 12 | ||
4.3 | odd | 2 | 1600.2.q.e.849.2 | 12 | |||
5.2 | odd | 4 | 400.2.l.f.301.1 | yes | 12 | ||
5.3 | odd | 4 | 400.2.l.g.301.6 | yes | 12 | ||
5.4 | even | 2 | 400.2.q.f.349.4 | 12 | |||
16.5 | even | 4 | 400.2.q.f.149.4 | 12 | |||
16.11 | odd | 4 | 1600.2.q.f.49.5 | 12 | |||
20.3 | even | 4 | 1600.2.l.f.401.2 | 12 | |||
20.7 | even | 4 | 1600.2.l.g.401.5 | 12 | |||
20.19 | odd | 2 | 1600.2.q.f.849.5 | 12 | |||
80.27 | even | 4 | 1600.2.l.g.1201.5 | 12 | |||
80.37 | odd | 4 | 400.2.l.f.101.1 | ✓ | 12 | ||
80.43 | even | 4 | 1600.2.l.f.1201.2 | 12 | |||
80.53 | odd | 4 | 400.2.l.g.101.6 | yes | 12 | ||
80.59 | odd | 4 | 1600.2.q.e.49.2 | 12 | |||
80.69 | even | 4 | inner | 400.2.q.e.149.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.1 | ✓ | 12 | 80.37 | odd | 4 | ||
400.2.l.f.301.1 | yes | 12 | 5.2 | odd | 4 | ||
400.2.l.g.101.6 | yes | 12 | 80.53 | odd | 4 | ||
400.2.l.g.301.6 | yes | 12 | 5.3 | odd | 4 | ||
400.2.q.e.149.3 | 12 | 80.69 | even | 4 | inner | ||
400.2.q.e.349.3 | 12 | 1.1 | even | 1 | trivial | ||
400.2.q.f.149.4 | 12 | 16.5 | even | 4 | |||
400.2.q.f.349.4 | 12 | 5.4 | even | 2 | |||
1600.2.l.f.401.2 | 12 | 20.3 | even | 4 | |||
1600.2.l.f.1201.2 | 12 | 80.43 | even | 4 | |||
1600.2.l.g.401.5 | 12 | 20.7 | even | 4 | |||
1600.2.l.g.1201.5 | 12 | 80.27 | even | 4 | |||
1600.2.q.e.49.2 | 12 | 80.59 | odd | 4 | |||
1600.2.q.e.849.2 | 12 | 4.3 | odd | 2 | |||
1600.2.q.f.49.5 | 12 | 16.11 | odd | 4 | |||
1600.2.q.f.849.5 | 12 | 20.19 | odd | 2 |