Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(101,400)]
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, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.19401608085\) |
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: | \( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + 112 x^{2} - 128 x + 64 \) |
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 | 101.6 | ||
Root | \(1.35979 - 0.388551i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.101 |
Dual form | 400.2.l.g.301.6 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.35979 | − | 0.388551i | 0.961516 | − | 0.274747i | ||||
\(3\) | 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 | ||||
\(7\) | 1.49668i | 0.565693i | 0.959165 | + | 0.282846i | \(0.0912786\pi\) | ||||
−0.959165 | + | 0.282846i | \(0.908721\pi\) | |||||||
\(8\) | 1.89842 | − | 2.09667i | 0.671192 | − | 0.741283i | ||||
\(9\) | 0.836925i | 0.278975i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.423260 | + | 0.423260i | 0.127618 | + | 0.127618i | 0.768031 | − | 0.640413i | \(-0.221237\pi\) |
−0.640413 | + | 0.768031i | \(0.721237\pi\) | |||||||
\(12\) | 0.666995 | − | 2.86486i | 0.192545 | − | 0.827014i | ||||
\(13\) | 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 | ||||
\(17\) | −6.50950 | −1.57879 | −0.789393 | − | 0.613888i | \(-0.789605\pi\) | ||||
−0.789393 | + | 0.613888i | \(0.789605\pi\) | |||||||
\(18\) | 0.325188 | + | 1.13804i | 0.0766476 | + | 0.268239i | ||||
\(19\) | −1.75725 | + | 1.75725i | −0.403141 | + | 0.403141i | −0.879338 | − | 0.476198i | \(-0.842015\pi\) |
0.476198 | + | 0.879338i | \(0.342015\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.55650 | + | 1.55650i | 0.339657 | + | 0.339657i | ||||
\(22\) | 0.740003 | + | 0.411086i | 0.157769 | + | 0.0876439i | ||||
\(23\) | − | 7.19295i | − | 1.49983i | −0.661532 | − | 0.749917i | \(-0.730094\pi\) | ||
0.661532 | − | 0.749917i | \(-0.269906\pi\) | |||||||
\(24\) | −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 | ||||
\(28\) | 1.58154 | + | 2.54145i | 0.298883 | + | 0.480289i | ||||
\(29\) | −6.57892 | + | 6.57892i | −1.22167 | + | 1.22167i | −0.254639 | + | 0.967036i | \(0.581957\pi\) |
−0.967036 | + | 0.254639i | \(0.918043\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.75252 | −1.21279 | −0.606394 | − | 0.795164i | \(-0.707385\pi\) | ||||
−0.606394 | + | 0.795164i | \(0.707385\pi\) | |||||||
\(32\) | 1.00808 | − | 5.56631i | 0.178205 | − | 0.983993i | ||||
\(33\) | 0.880355 | 0.153250 | ||||||||
\(34\) | −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 | \(0.822902\pi\) | |||||||
\(38\) | −1.70671 | + | 3.07227i | −0.276865 | + | 0.498388i | ||||
\(39\) | − | 3.86254i | − | 0.618501i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.70745i | 1.20370i | 0.798609 | + | 0.601851i | \(0.205570\pi\) | ||||
−0.798609 | + | 0.601851i | \(0.794430\pi\) | |||||||
\(42\) | 2.72130 | + | 1.51174i | 0.419906 | + | 0.233266i | ||||
\(43\) | 6.13581 | + | 6.13581i | 0.935702 | + | 0.935702i | 0.998054 | − | 0.0623522i | \(-0.0198602\pi\) |
−0.0623522 | + | 0.998054i | \(0.519860\pi\) | |||||||
\(44\) | 1.16598 | + | 0.271462i | 0.175778 | + | 0.0409244i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.79483 | − | 9.78090i | −0.412075 | − | 1.44211i | ||||
\(47\) | 6.65476 | 0.970697 | 0.485348 | − | 0.874321i | \(-0.338693\pi\) | ||||
0.485348 | + | 0.874321i | \(0.338693\pi\) | |||||||
\(48\) | −1.89469 | − | 5.56950i | −0.273475 | − | 0.803888i | ||||
\(49\) | 4.75994 | 0.679992 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.76969 | + | 6.76969i | −0.947946 | + | 0.947946i | ||||
\(52\) | 1.19103 | − | 5.11569i | 0.165167 | − | 0.709419i | ||||
\(53\) | −5.29390 | − | 5.29390i | −0.727173 | − | 0.727173i | 0.242882 | − | 0.970056i | \(-0.421907\pi\) |
−0.970056 | + | 0.242882i | \(0.921907\pi\) | |||||||
\(54\) | 6.97638 | + | 3.87552i | 0.949365 | + | 0.527391i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.13804 | + | 2.84133i | 0.419338 | + | 0.379688i | ||||
\(57\) | 3.65497i | 0.484113i | ||||||||
\(58\) | −6.38970 | + | 11.5022i | −0.839009 | + | 1.51031i | ||||
\(59\) | 5.91841 | + | 5.91841i | 0.770511 | + | 0.770511i | 0.978196 | − | 0.207685i | \(-0.0665929\pi\) |
−0.207685 | + | 0.978196i | \(0.566593\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.43686 | + | 1.43686i | −0.183971 | + | 0.183971i | −0.793084 | − | 0.609113i | \(-0.791526\pi\) |
0.609113 | + | 0.793084i | \(0.291526\pi\) | |||||||
\(62\) | −9.18201 | + | 2.62370i | −1.16612 | + | 0.333210i | ||||
\(63\) | −1.25261 | −0.157814 | ||||||||
\(64\) | −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 | −0.202712 | − | 0.979238i | \(-0.564976\pi\) |
0.979238 | + | 0.202712i | \(0.0649756\pi\) | |||||||
\(68\) | −11.0535 | + | 6.87857i | −1.34043 | + | 0.834149i | ||||
\(69\) | −7.48045 | − | 7.48045i | −0.900540 | − | 0.900540i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.08932i | − | 0.485313i | −0.970112 | − | 0.242657i | \(-0.921981\pi\) | ||
0.970112 | − | 0.242657i | \(-0.0780188\pi\) | |||||||
\(72\) | 1.75475 | + | 1.58883i | 0.206799 | + | 0.187246i | ||||
\(73\) | 2.43800i | 0.285346i | 0.989770 | + | 0.142673i | \(0.0455698\pi\) | ||||
−0.989770 | + | 0.142673i | \(0.954430\pi\) | |||||||
\(74\) | −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 | ||||
\(78\) | −1.50079 | − | 5.25224i | −0.169931 | − | 0.594699i | ||||
\(79\) | 11.6722 | 1.31323 | 0.656615 | − | 0.754226i | \(-0.271988\pi\) | ||||
0.656615 | + | 0.754226i | \(0.271988\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.78878 | 0.643198 | ||||||||
\(82\) | 2.99474 | + | 10.4805i | 0.330714 | + | 1.15738i | ||||
\(83\) | −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 | ||||
\(87\) | 13.6838i | 1.46705i | ||||||||
\(88\) | 1.69096 | − | 0.0839103i | 0.180257 | − | 0.00894487i | ||||
\(89\) | − | 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 | ||||
\(92\) | −7.60076 | − | 12.2140i | −0.792434 | − | 1.27340i | ||||
\(93\) | −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 | ||||
\(97\) | −18.1512 | −1.84298 | −0.921488 | − | 0.388407i | \(-0.873025\pi\) | ||||
−0.921488 | + | 0.388407i | \(0.873025\pi\) | |||||||
\(98\) | 6.47252 | − | 1.84948i | 0.653823 | − | 0.186826i | ||||
\(99\) | −0.354237 | + | 0.354237i | −0.0356021 | + | 0.0356021i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.04036 | − | 1.04036i | −0.103520 | − | 0.103520i | 0.653450 | − | 0.756970i | \(-0.273321\pi\) |
−0.756970 | + | 0.653450i | \(0.773321\pi\) | |||||||
\(102\) | −6.57498 | + | 11.8357i | −0.651020 | + | 1.17191i | ||||
\(103\) | − | 0.955267i | − | 0.0941253i | −0.998892 | − | 0.0470626i | \(-0.985014\pi\) | ||
0.998892 | − | 0.0470626i | \(-0.0149860\pi\) | |||||||
\(104\) | −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 | \(0.913867\pi\) | |||||||
\(108\) | 10.9922 | + | 2.55921i | 1.05773 | + | 0.246260i | ||||
\(109\) | −5.67807 | + | 5.67807i | −0.543861 | + | 0.543861i | −0.924658 | − | 0.380798i | \(-0.875649\pi\) |
0.380798 | + | 0.924658i | \(0.375649\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.06212 | −0.385560 | ||||||||
\(112\) | 5.37108 | + | 2.64432i | 0.507519 | + | 0.249865i | ||||
\(113\) | −1.94751 | −0.183206 | −0.0916029 | − | 0.995796i | \(-0.529199\pi\) | ||||
−0.0916029 | + | 0.995796i | \(0.529199\pi\) | |||||||
\(114\) | 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 | ||||
\(118\) | 10.3474 | + | 5.74818i | 0.952555 | + | 0.529163i | ||||
\(119\) | − | 9.74266i | − | 0.893108i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.6417i | − | 0.967427i | ||||||
\(122\) | −1.39553 | + | 2.51212i | −0.126346 | + | 0.227437i | ||||
\(123\) | 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 | ||||
\(127\) | 1.31796 | 0.116950 | 0.0584750 | − | 0.998289i | \(-0.481376\pi\) | ||||
0.0584750 | + | 0.998289i | \(0.481376\pi\) | |||||||
\(128\) | −4.17011 | − | 10.5171i | −0.368589 | − | 0.929592i | ||||
\(129\) | 12.7621 | 1.12364 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.03026 | − | 1.03026i | 0.0900139 | − | 0.0900139i | −0.660666 | − | 0.750680i | \(-0.729726\pi\) |
0.750680 | + | 0.660666i | \(0.229726\pi\) | |||||||
\(132\) | 1.49489 | − | 0.930268i | 0.130114 | − | 0.0809694i | ||||
\(133\) | −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 | ||||
\(137\) | − | 3.75559i | − | 0.320862i | −0.987047 | − | 0.160431i | \(-0.948712\pi\) | ||
0.987047 | − | 0.160431i | \(-0.0512884\pi\) | |||||||
\(138\) | −13.0784 | − | 7.26530i | −1.11331 | − | 0.618463i | ||||
\(139\) | 12.9485 | + | 12.9485i | 1.09828 | + | 1.09828i | 0.994612 | + | 0.103669i | \(0.0330584\pi\) |
0.103669 | + | 0.994612i | \(0.466942\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.92075 | − | 6.92075i | 0.582832 | − | 0.582832i | ||||
\(142\) | −1.58891 | − | 5.56062i | −0.133338 | − | 0.466637i | ||||
\(143\) | 1.57202 | 0.131459 | ||||||||
\(144\) | 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 | ||||
\(148\) | −5.38003 | − | 1.25258i | −0.442236 | − | 0.102961i | ||||
\(149\) | −15.8472 | − | 15.8472i | −1.29825 | − | 1.29825i | −0.929545 | − | 0.368709i | \(-0.879800\pi\) |
−0.368709 | − | 0.929545i | \(-0.620200\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 11.5316i | − | 0.938424i | −0.883085 | − | 0.469212i | \(-0.844538\pi\) | ||
0.883085 | − | 0.469212i | \(-0.155462\pi\) | |||||||
\(152\) | 0.348371 | + | 7.02036i | 0.0282566 | + | 0.569427i | ||||
\(153\) | − | 5.44797i | − | 0.440442i | ||||||
\(154\) | −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 | −0.456994 | − | 0.889470i | \(-0.651074\pi\) |
0.889470 | + | 0.456994i | \(0.151074\pi\) | |||||||
\(158\) | 15.8718 | − | 4.53526i | 1.26269 | − | 0.360806i | ||||
\(159\) | −11.0110 | −0.873229 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.7656 | 0.848445 | ||||||||
\(162\) | 7.87153 | − | 2.24924i | 0.618446 | − | 0.176717i | ||||
\(163\) | −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 | ||||
\(167\) | − | 8.29734i | − | 0.642068i | −0.947068 | − | 0.321034i | \(-0.895970\pi\) | ||
0.947068 | − | 0.321034i | \(-0.104030\pi\) | |||||||
\(168\) | 6.21837 | − | 0.308573i | 0.479757 | − | 0.0238069i | ||||
\(169\) | 6.10279i | 0.469445i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.47069 | − | 1.47069i | −0.112466 | − | 0.112466i | ||||
\(172\) | 16.9026 | + | 3.93526i | 1.28881 | + | 0.300061i | ||||
\(173\) | −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 | ||||
\(177\) | 12.3099 | 0.925271 | ||||||||
\(178\) | −4.10090 | − | 14.3517i | −0.307376 | − | 1.07570i | ||||
\(179\) | −10.8703 | + | 10.8703i | −0.812481 | + | 0.812481i | −0.985005 | − | 0.172524i | \(-0.944808\pi\) |
0.172524 | + | 0.985005i | \(0.444808\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.09403 | − | 4.09403i | −0.304307 | − | 0.304307i | 0.538389 | − | 0.842696i | \(-0.319033\pi\) |
−0.842696 | + | 0.538389i | \(0.819033\pi\) | |||||||
\(182\) | 4.85934 | + | 2.69946i | 0.360198 | + | 0.200097i | ||||
\(183\) | 2.98858i | 0.220922i | ||||||||
\(184\) | −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 | ||||
\(188\) | 11.3002 | − | 7.03206i | 0.824148 | − | 0.512866i | ||||
\(189\) | −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 | \(0.254698\pi\) | |||||||
\(192\) | −9.10256 | − | 7.45521i | −0.656921 | − | 0.538034i | ||||
\(193\) | 24.8152 | 1.78624 | 0.893119 | − | 0.449820i | \(-0.148512\pi\) | ||||
0.893119 | + | 0.449820i | \(0.148512\pi\) | |||||||
\(194\) | −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 | \(0.704734\pi\) | |||||||
\(198\) | −0.344048 | + | 0.619327i | −0.0244505 | + | 0.0440136i | ||||
\(199\) | − | 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 | ||||||
\(202\) | −1.81891 | − | 1.01044i | −0.127978 | − | 0.0710944i | ||||
\(203\) | −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 | ||||
\(207\) | 6.01996 | 0.418416 | ||||||||
\(208\) | −3.38329 | − | 9.94529i | −0.234589 | − | 0.689582i | ||||
\(209\) | −1.48755 | −0.102896 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.5715 | − | 15.5715i | 1.07199 | − | 1.07199i | 0.0747872 | − | 0.997200i | \(-0.476172\pi\) |
0.997200 | − | 0.0747872i | \(-0.0238278\pi\) | |||||||
\(212\) | −14.5834 | − | 3.39530i | −1.00159 | − | 0.233190i | ||||
\(213\) | −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 | ||||
\(217\) | − | 10.1064i | − | 0.686065i | ||||||
\(218\) | −5.51476 | + | 9.92721i | −0.373507 | + | 0.672355i | ||||
\(219\) | 2.53545 | + | 2.53545i | 0.171330 | + | 0.171330i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0884 | + | 12.0884i | −0.813155 | + | 0.813155i | ||||
\(222\) | −5.52363 | + | 1.57834i | −0.370722 | + | 0.105931i | ||||
\(223\) | 7.88779 | 0.528205 | 0.264103 | − | 0.964495i | \(-0.414924\pi\) | ||||
0.264103 | + | 0.964495i | \(0.414924\pi\) | |||||||
\(224\) | 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 | −0.479874 | − | 0.877337i | \(-0.659318\pi\) |
0.877337 | + | 0.479874i | \(0.159318\pi\) | |||||||
\(228\) | 3.86220 | + | 6.20635i | 0.255780 | + | 0.411026i | ||||
\(229\) | 19.4584 | + | 19.4584i | 1.28585 | + | 1.28585i | 0.937286 | + | 0.348563i | \(0.113330\pi\) |
0.348563 | + | 0.937286i | \(0.386670\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.31761i | 0.0866925i | ||||||||
\(232\) | 1.30426 | + | 26.2833i | 0.0856286 | + | 1.72559i | ||||
\(233\) | − | 2.68717i | − | 0.176042i | −0.996119 | − | 0.0880212i | \(-0.971946\pi\) | ||
0.996119 | − | 0.0880212i | \(-0.0280543\pi\) | |||||||
\(234\) | 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 | ||||
\(238\) | −3.78552 | − | 13.2480i | −0.245379 | − | 0.858738i | ||||
\(239\) | −12.6359 | −0.817346 | −0.408673 | − | 0.912681i | \(-0.634008\pi\) | ||||
−0.408673 | + | 0.912681i | \(0.634008\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.53314 | 0.485252 | 0.242626 | − | 0.970120i | \(-0.421991\pi\) | ||||
0.242626 | + | 0.970120i | \(0.421991\pi\) | |||||||
\(242\) | −4.13485 | − | 14.4705i | −0.265798 | − | 0.930197i | ||||
\(243\) | −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 | ||||
\(247\) | 6.52658i | 0.415276i | ||||||||
\(248\) | −12.8191 | + | 14.1578i | −0.814014 | + | 0.899020i | ||||
\(249\) | 5.85376i | 0.370967i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.95683 | − | 9.95683i | −0.628470 | − | 0.628470i | 0.319213 | − | 0.947683i | \(-0.396581\pi\) |
−0.947683 | + | 0.319213i | \(0.896581\pi\) | |||||||
\(252\) | −2.12700 | + | 1.32363i | −0.133989 | + | 0.0833807i | ||||
\(253\) | 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 | ||||
\(257\) | −4.51630 | −0.281719 | −0.140860 | − | 0.990030i | \(-0.544987\pi\) | ||||
−0.140860 | + | 0.990030i | \(0.544987\pi\) | |||||||
\(258\) | 17.3538 | − | 4.95874i | 1.08040 | − | 0.308717i | ||||
\(259\) | 2.92302 | − | 2.92302i | 0.181628 | − | 0.181628i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.50606 | − | 5.50606i | −0.340817 | − | 0.340817i | ||||
\(262\) | 1.00062 | − | 1.80124i | 0.0618188 | − | 0.111281i | ||||
\(263\) | − | 20.2127i | − | 1.24637i | −0.782075 | − | 0.623185i | \(-0.785838\pi\) | ||
0.782075 | − | 0.623185i | \(-0.214162\pi\) | |||||||
\(264\) | 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 | ||||
\(268\) | 4.07657 | − | 17.5096i | 0.249016 | − | 1.06957i | ||||
\(269\) | 16.9430 | − | 16.9430i | 1.03304 | − | 1.03304i | 0.0335999 | − | 0.999435i | \(-0.489303\pi\) |
0.999435 | − | 0.0335999i | \(-0.0106972\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.64054 | −0.221147 | −0.110573 | − | 0.993868i | \(-0.535269\pi\) | ||||
−0.110573 | + | 0.993868i | \(0.535269\pi\) | |||||||
\(272\) | −11.5009 | + | 23.3604i | −0.697345 | + | 1.41643i | ||||
\(273\) | 5.78099 | 0.349881 | ||||||||
\(274\) | −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 | \(0.511911\pi\) | |||||||
\(278\) | 22.6385 | + | 12.5761i | 1.35777 | + | 0.754266i | ||||
\(279\) | − | 5.65135i | − | 0.338338i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.51857i | 0.329210i | 0.986360 | + | 0.164605i | \(0.0526350\pi\) | ||||
−0.986360 | + | 0.164605i | \(0.947365\pi\) | |||||||
\(282\) | 6.72170 | − | 12.0998i | 0.400271 | − | 0.720535i | ||||
\(283\) | −2.36694 | − | 2.36694i | −0.140700 | − | 0.140700i | 0.633249 | − | 0.773949i | \(-0.281721\pi\) |
−0.773949 | + | 0.633249i | \(0.781721\pi\) | |||||||
\(284\) | −4.32117 | − | 6.94389i | −0.256414 | − | 0.412044i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.13762 | − | 0.610812i | 0.126400 | − | 0.0361180i | ||||
\(287\) | −11.5356 | −0.680925 | ||||||||
\(288\) | 4.65858 | + | 0.843689i | 0.274509 | + | 0.0497148i | ||||
\(289\) | 25.3736 | 1.49257 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.8767 | + | 18.8767i | −1.10657 | + | 1.10657i | ||||
\(292\) | 2.57623 | + | 4.13986i | 0.150762 | + | 0.242267i | ||||
\(293\) | 19.1812 | + | 19.1812i | 1.12058 | + | 1.12058i | 0.991655 | + | 0.128922i | \(0.0411517\pi\) |
0.128922 | + | 0.991655i | \(0.458848\pi\) | |||||||
\(294\) | 4.80782 | − | 8.65463i | 0.280398 | − | 0.504749i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.80240 | + | 0.387177i | −0.453505 | + | 0.0225042i | ||||
\(297\) | 3.37786i | 0.196003i | ||||||||
\(298\) | −27.7063 | − | 15.3914i | −1.60498 | − | 0.891601i | ||||
\(299\) | −13.3576 | − | 13.3576i | −0.772491 | − | 0.772491i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.18335 | + | 9.18335i | −0.529320 | + | 0.529320i | ||||
\(302\) | −4.48060 | − | 15.6805i | −0.257829 | − | 0.902311i | ||||
\(303\) | −2.16390 | −0.124313 | ||||||||
\(304\) | 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 | \(0.547447\pi\) |
−0.988911 | + | 0.148507i | \(0.952553\pi\) | |||||||
\(308\) | −0.406292 | + | 1.74510i | −0.0231506 | + | 0.0994360i | ||||
\(309\) | −0.993449 | − | 0.993449i | −0.0565153 | − | 0.0565153i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 5.73314i | − | 0.325096i | −0.986701 | − | 0.162548i | \(-0.948029\pi\) | ||
0.986701 | − | 0.162548i | \(-0.0519713\pi\) | |||||||
\(312\) | −8.09845 | − | 7.33271i | −0.458484 | − | 0.415133i | ||||
\(313\) | − | 0.212621i | − | 0.0120180i | −0.999982 | − | 0.00600902i | \(-0.998087\pi\) | ||
0.999982 | − | 0.00600902i | \(-0.00191274\pi\) | |||||||
\(314\) | 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 | −0.611007 | − | 0.791625i | \(-0.709235\pi\) |
0.791625 | + | 0.611007i | \(0.209235\pi\) | |||||||
\(318\) | −14.9726 | + | 4.27834i | −0.839624 | + | 0.239917i | ||||
\(319\) | −5.56919 | −0.311815 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.9811 | −0.836164 | ||||||||
\(322\) | 14.6389 | − | 4.18297i | 0.815793 | − | 0.233108i | ||||
\(323\) | 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 | ||||
\(327\) | 11.8101i | 0.653097i | ||||||||
\(328\) | 16.1599 | + | 14.6320i | 0.892284 | + | 0.807915i | ||||
\(329\) | 9.96006i | 0.549116i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.0295 | + | 22.0295i | 1.21085 | + | 1.21085i | 0.970747 | + | 0.240106i | \(0.0771824\pi\) |
0.240106 | + | 0.970747i | \(0.422818\pi\) | |||||||
\(332\) | −1.80504 | + | 7.75295i | −0.0990643 | + | 0.425498i | ||||
\(333\) | 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 | ||||
\(337\) | 11.2122 | 0.610767 | 0.305384 | − | 0.952229i | \(-0.401215\pi\) | ||||
0.305384 | + | 0.952229i | \(0.401215\pi\) | |||||||
\(338\) | 2.37125 | + | 8.29851i | 0.128979 | + | 0.451379i | ||||
\(339\) | −2.02535 | + | 2.02535i | −0.110002 | + | 0.110002i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.85807 | − | 2.85807i | −0.154773 | − | 0.154773i | ||||
\(342\) | −2.57126 | − | 1.42839i | −0.139038 | − | 0.0772383i | ||||
\(343\) | 17.6009i | 0.950359i | ||||||||
\(344\) | 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 | \(0.764946\pi\) | |||||||
\(348\) | 14.4596 | + | 23.2358i | 0.775115 | + | 1.24557i | ||||
\(349\) | −5.61778 | + | 5.61778i | −0.300713 | + | 0.300713i | −0.841293 | − | 0.540580i | \(-0.818205\pi\) |
0.540580 | + | 0.841293i | \(0.318205\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.8203 | 0.791047 | ||||||||
\(352\) | 2.78268 | − | 1.92931i | 0.148317 | − | 0.102833i | ||||
\(353\) | −0.748709 | −0.0398497 | −0.0199249 | − | 0.999801i | \(-0.506343\pi\) | ||||
−0.0199249 | + | 0.999801i | \(0.506343\pi\) | |||||||
\(354\) | 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 | ||||
\(358\) | −10.5576 | + | 19.0049i | −0.557987 | + | 1.00444i | ||||
\(359\) | − | 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 | ||||||||
\(362\) | −7.15776 | − | 3.97628i | −0.376204 | − | 0.208989i | ||||
\(363\) | −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 | ||||
\(367\) | −20.6101 | −1.07584 | −0.537920 | − | 0.842996i | \(-0.680790\pi\) | ||||
−0.537920 | + | 0.842996i | \(0.680790\pi\) | |||||||
\(368\) | −25.8130 | − | 12.7084i | −1.34560 | − | 0.662472i | ||||
\(369\) | −6.45056 | −0.335802 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.92329 | − | 7.92329i | 0.411357 | − | 0.411357i | ||||
\(372\) | −4.50390 | + | 19.3450i | −0.233516 | + | 1.00299i | ||||
\(373\) | −5.24143 | − | 5.24143i | −0.271391 | − | 0.271391i | 0.558269 | − | 0.829660i | \(-0.311466\pi\) |
−0.829660 | + | 0.558269i | \(0.811466\pi\) | |||||||
\(374\) | −4.81705 | − | 2.67597i | −0.249084 | − | 0.138371i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.6335 | − | 13.9528i | 0.651524 | − | 0.719561i | ||||
\(377\) | 24.4347i | 1.25845i | ||||||||
\(378\) | −5.80042 | + | 10.4414i | −0.298341 | + | 0.537049i | ||||
\(379\) | 5.41344 | + | 5.41344i | 0.278070 | + | 0.278070i | 0.832338 | − | 0.554268i | \(-0.187002\pi\) |
−0.554268 | + | 0.832338i | \(0.687002\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.37064 | − | 1.37064i | 0.0702199 | − | 0.0702199i | ||||
\(382\) | 26.1817 | − | 7.48125i | 1.33957 | − | 0.382774i | ||||
\(383\) | −29.5087 | −1.50782 | −0.753912 | − | 0.656975i | \(-0.771836\pi\) | ||||
−0.753912 | + | 0.656975i | \(0.771836\pi\) | |||||||
\(384\) | −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 | ||||
\(388\) | −30.8218 | + | 19.1803i | −1.56474 | + | 0.973732i | ||||
\(389\) | 1.37884 | + | 1.37884i | 0.0699099 | + | 0.0699099i | 0.741197 | − | 0.671287i | \(-0.234258\pi\) |
−0.671287 | + | 0.741197i | \(0.734258\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 46.8225i | 2.36792i | ||||||||
\(392\) | 9.03636 | − | 9.98001i | 0.456405 | − | 0.504067i | ||||
\(393\) | − | 2.14287i | − | 0.108094i | ||||||
\(394\) | 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 | \(0.534711\pi\) |
−0.994060 | + | 0.108832i | \(0.965289\pi\) | |||||||
\(398\) | −8.24482 | − | 28.8539i | −0.413275 | − | 1.44632i | ||||
\(399\) | −5.47033 | −0.273859 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.4584 | −1.57096 | −0.785479 | − | 0.618889i | \(-0.787583\pi\) | ||||
−0.785479 | + | 0.618889i | \(0.787583\pi\) | |||||||
\(402\) | −5.13680 | − | 17.9770i | −0.256200 | − | 0.896609i | ||||
\(403\) | −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 | ||||
\(407\) | − | 1.65325i | − | 0.0819487i | ||||||
\(408\) | 1.34207 | + | 27.0455i | 0.0664426 | + | 1.33895i | ||||
\(409\) | − | 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 | ||||
\(412\) | −1.00943 | − | 1.62210i | −0.0497309 | − | 0.0799150i | ||||
\(413\) | −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 | ||||
\(417\) | 26.9322 | 1.31888 | ||||||||
\(418\) | −2.02275 | + | 0.577988i | −0.0989360 | + | 0.0282703i | ||||
\(419\) | −11.4979 | + | 11.4979i | −0.561709 | + | 0.561709i | −0.929793 | − | 0.368084i | \(-0.880014\pi\) |
0.368084 | + | 0.929793i | \(0.380014\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.5714 | + | 12.5714i | 0.612690 | + | 0.612690i | 0.943646 | − | 0.330956i | \(-0.107371\pi\) |
−0.330956 | + | 0.943646i | \(0.607371\pi\) | |||||||
\(422\) | 15.1236 | − | 27.2243i | 0.736208 | − | 1.32526i | ||||
\(423\) | 5.56953i | 0.270800i | ||||||||
\(424\) | −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 | ||||
\(428\) | −19.8415 | − | 4.61950i | −0.959077 | − | 0.223292i | ||||
\(429\) | 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 | \(0.619777\pi\) | |||||||
\(432\) | 21.3698 | − | 7.26978i | 1.02815 | − | 0.349768i | ||||
\(433\) | −12.1705 | −0.584877 | −0.292439 | − | 0.956284i | \(-0.594467\pi\) | ||||
−0.292439 | + | 0.956284i | \(0.594467\pi\) | |||||||
\(434\) | −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 | ||||
\(438\) | 4.43283 | + | 2.46252i | 0.211809 | + | 0.117664i | ||||
\(439\) | 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 | ||||||||
\(442\) | −11.7407 | + | 21.1347i | −0.558450 | + | 1.00527i | ||||
\(443\) | 3.62318 | + | 3.62318i | 0.172142 | + | 0.172142i | 0.787920 | − | 0.615778i | \(-0.211158\pi\) |
−0.615778 | + | 0.787920i | \(0.711158\pi\) | |||||||
\(444\) | −6.89771 | + | 4.29243i | −0.327351 | + | 0.203710i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.7257 | − | 3.06481i | 0.507878 | − | 0.145123i | ||||
\(447\) | −32.9612 | −1.55901 | ||||||||
\(448\) | 11.9146 | − | 1.18540i | 0.562913 | − | 0.0560047i | ||||
\(449\) | −5.38425 | −0.254098 | −0.127049 | − | 0.991896i | \(-0.540551\pi\) | ||||
−0.127049 | + | 0.991896i | \(0.540551\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.26225 | + | 3.26225i | −0.153614 | + | 0.153614i | ||||
\(452\) | −3.30697 | + | 2.05792i | −0.155547 | + | 0.0967964i | ||||
\(453\) | −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 | ||||
\(457\) | − | 14.3039i | − | 0.669108i | −0.942377 | − | 0.334554i | \(-0.891414\pi\) | ||
0.942377 | − | 0.334554i | \(-0.108586\pi\) | |||||||
\(458\) | 34.0199 | + | 18.8988i | 1.58965 | + | 0.883081i | ||||
\(459\) | −25.9748 | − | 25.9748i | −1.21240 | − | 1.21240i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.50363 | + | 4.50363i | −0.209755 | + | 0.209755i | −0.804163 | − | 0.594408i | \(-0.797386\pi\) |
0.594408 | + | 0.804163i | \(0.297386\pi\) | |||||||
\(462\) | 0.511960 | + | 1.79167i | 0.0238185 | + | 0.0833563i | ||||
\(463\) | 19.3500 | 0.899271 | 0.449636 | − | 0.893212i | \(-0.351554\pi\) | ||||
0.449636 | + | 0.893212i | \(0.351554\pi\) | |||||||
\(464\) | 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 | −0.982282 | − | 0.187410i | \(-0.939991\pi\) |
0.187410 | + | 0.982282i | \(0.439991\pi\) | |||||||
\(468\) | 4.28145 | + | 0.996805i | 0.197910 | + | 0.0460773i | ||||
\(469\) | 9.51312 | + | 9.51312i | 0.439275 | + | 0.439275i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 11.2710i | − | 0.519341i | ||||||
\(472\) | 23.6445 | − | 1.17331i | 1.08833 | − | 0.0540060i | ||||
\(473\) | 5.19408i | 0.238824i | ||||||||
\(474\) | 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 | ||||
\(478\) | −17.1821 | + | 4.90968i | −0.785892 | + | 0.224564i | ||||
\(479\) | 5.54474 | 0.253346 | 0.126673 | − | 0.991945i | \(-0.459570\pi\) | ||||
0.126673 | + | 0.991945i | \(0.459570\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.25361 | −0.330736 | ||||||||
\(482\) | 10.2435 | − | 2.92701i | 0.466578 | − | 0.133322i | ||||
\(483\) | 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 | ||||
\(487\) | − | 31.7138i | − | 1.43709i | −0.695480 | − | 0.718546i | \(-0.744808\pi\) | ||
0.695480 | − | 0.718546i | \(-0.255192\pi\) | |||||||
\(488\) | 0.284854 | + | 5.74037i | 0.0128947 | + | 0.259855i | ||||
\(489\) | 13.4632i | 0.608827i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.39419 | + | 7.39419i | 0.333695 | + | 0.333695i | 0.853988 | − | 0.520293i | \(-0.174177\pi\) |
−0.520293 | + | 0.853988i | \(0.674177\pi\) | |||||||
\(492\) | 22.0808 | + | 5.14083i | 0.995477 | + | 0.231767i | ||||
\(493\) | 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 | ||||
\(497\) | 6.12041 | 0.274538 | ||||||||
\(498\) | 2.27449 | + | 7.95988i | 0.101922 | + | 0.356691i | ||||
\(499\) | 14.0103 | − | 14.0103i | 0.627189 | − | 0.627189i | −0.320171 | − | 0.947360i | \(-0.603740\pi\) |
0.947360 | + | 0.320171i | \(0.103740\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.62899 | − | 8.62899i | −0.385515 | − | 0.385515i | ||||
\(502\) | −17.4079 | − | 9.67046i | −0.776954 | − | 0.431614i | ||||
\(503\) | − | 8.43795i | − | 0.376230i | −0.982147 | − | 0.188115i | \(-0.939762\pi\) | ||
0.982147 | − | 0.188115i | \(-0.0602377\pi\) | |||||||
\(504\) | −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 | ||||
\(508\) | 2.23797 | − | 1.39268i | 0.0992937 | − | 0.0617902i | ||||
\(509\) | 2.09367 | − | 2.09367i | 0.0928004 | − | 0.0928004i | −0.659183 | − | 0.751983i | \(-0.729098\pi\) |
0.751983 | + | 0.659183i | \(0.229098\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.64891 | −0.161418 | ||||||||
\(512\) | −18.1945 | − | 13.4521i | −0.804091 | − | 0.594506i | ||||
\(513\) | −14.0239 | −0.619169 | ||||||||
\(514\) | −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 | ||||
\(518\) | 2.83895 | − | 5.11043i | 0.124736 | − | 0.224540i | ||||
\(519\) | 24.8387i | 1.09030i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.2558i | 1.23791i | 0.785428 | + | 0.618954i | \(0.212443\pi\) | ||||
−0.785428 | + | 0.618954i | \(0.787557\pi\) | |||||||
\(522\) | −9.62647 | − | 5.34770i | −0.421339 | − | 0.234062i | ||||
\(523\) | 10.1929 | + | 10.1929i | 0.445703 | + | 0.445703i | 0.893923 | − | 0.448220i | \(-0.147942\pi\) |
−0.448220 | + | 0.893923i | \(0.647942\pi\) | |||||||
\(524\) | 0.660765 | − | 2.83810i | 0.0288657 | − | 0.123983i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.85368 | − | 27.4851i | −0.342437 | − | 1.19841i | ||||
\(527\) | 43.9555 | 1.91473 | ||||||||
\(528\) | 1.55540 | − | 3.15929i | 0.0676901 | − | 0.137491i | ||||
\(529\) | −28.7385 | −1.24950 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.95326 | + | 4.95326i | −0.214953 | + | 0.214953i | ||||
\(532\) | −7.24512 | − | 1.68681i | −0.314116 | − | 0.0731323i | ||||
\(533\) | 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 | ||||
\(537\) | 22.6095i | 0.975671i | ||||||||
\(538\) | 16.4557 | − | 29.6222i | 0.709457 | − | 1.27710i | ||||
\(539\) | 2.01469 | + | 2.01469i | 0.0867790 | + | 0.0867790i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.86053 | − | 3.86053i | 0.165977 | − | 0.165977i | −0.619231 | − | 0.785209i | \(-0.712556\pi\) |
0.785209 | + | 0.619231i | \(0.212556\pi\) | |||||||
\(542\) | −4.95036 | + | 1.41453i | −0.212636 | + | 0.0607595i | ||||
\(543\) | −8.51534 | −0.365428 | ||||||||
\(544\) | −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 | −0.111935 | − | 0.993716i | \(-0.535705\pi\) |
0.993716 | + | 0.111935i | \(0.0357048\pi\) | |||||||
\(548\) | −3.96852 | − | 6.37720i | −0.169527 | − | 0.272421i | ||||
\(549\) | −1.20254 | − | 1.20254i | −0.0513233 | − | 0.0513233i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 23.1216i | − | 0.985014i | ||||||
\(552\) | −29.8850 | + | 1.48298i | −1.27199 | + | 0.0631199i | ||||
\(553\) | 17.4696i | 0.742884i | ||||||||
\(554\) | 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 | −0.733809 | − | 0.679356i | \(-0.762259\pi\) |
0.679356 | + | 0.733809i | \(0.262259\pi\) | |||||||
\(558\) | −2.19584 | − | 7.68465i | −0.0929573 | − | 0.325317i | ||||
\(559\) | 22.7889 | 0.963868 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.73068 | −0.241949 | ||||||||
\(562\) | 2.14425 | + | 7.50409i | 0.0904496 | + | 0.316541i | ||||
\(563\) | 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 | ||||
\(567\) | 8.66397i | 0.363852i | ||||||||
\(568\) | −8.57394 | − | 7.76324i | −0.359754 | − | 0.325738i | ||||
\(569\) | − | 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 | 0.814598 | − | 0.580026i | \(-0.196958\pi\) |
−0.580026 | + | 0.814598i | \(0.696958\pi\) | |||||||
\(572\) | 2.66938 | − | 1.66115i | 0.111613 | − | 0.0694562i | ||||
\(573\) | 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 | ||||
\(577\) | −2.43681 | −0.101446 | −0.0507230 | − | 0.998713i | \(-0.516153\pi\) | ||||
−0.0507230 | + | 0.998713i | \(0.516153\pi\) | |||||||
\(578\) | 34.5028 | − | 9.85896i | 1.43513 | − | 0.410079i | ||||
\(579\) | 25.8071 | − | 25.8071i | 1.07251 | − | 1.07251i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.21225 | − | 4.21225i | −0.174753 | − | 0.174753i | ||||
\(582\) | −18.3338 | + | 33.0029i | −0.759960 | + | 1.36802i | ||||
\(583\) | − | 4.48139i | − | 0.185600i | ||||||
\(584\) | 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 | \(0.746135\pi\) | |||||||
\(588\) | 3.17486 | − | 13.6366i | 0.130929 | − | 0.562363i | ||||
\(589\) | 11.8659 | − | 11.8659i | 0.488924 | − | 0.488924i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.85136 | 0.240693 | ||||||||
\(592\) | −10.4592 | + | 3.55811i | −0.429870 | + | 0.146237i | ||||
\(593\) | −15.3439 | −0.630098 | −0.315049 | − | 0.949075i | \(-0.602021\pi\) | ||||
−0.315049 | + | 0.949075i | \(0.602021\pi\) | |||||||
\(594\) | 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 | ||||
\(598\) | −23.3537 | − | 12.9734i | −0.955002 | − | 0.530523i | ||||
\(599\) | 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 | \(-0.710134\pi\) | ||
0.613239 | − | 0.789897i | \(-0.289866\pi\) | |||||||
\(602\) | −8.91923 | + | 16.0556i | −0.363520 | + | 0.654379i | ||||
\(603\) | 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 | ||||
\(607\) | −34.9068 | −1.41682 | −0.708412 | − | 0.705800i | \(-0.750588\pi\) | ||||
−0.708412 | + | 0.705800i | \(0.750588\pi\) | |||||||
\(608\) | 8.00994 | + | 11.5528i | 0.324846 | + | 0.468530i | ||||
\(609\) | −20.4802 | −0.829901 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.3582 | − | 12.3582i | 0.499958 | − | 0.499958i | ||||
\(612\) | −5.75684 | − | 9.25095i | −0.232707 | − | 0.373947i | ||||
\(613\) | −0.151779 | − | 0.151779i | −0.00613031 | − | 0.00613031i | 0.704035 | − | 0.710165i | \(-0.251380\pi\) |
−0.710165 | + | 0.704035i | \(0.751380\pi\) | |||||||
\(614\) | −19.3560 | + | 34.8430i | −0.781144 | + | 1.40615i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.125587 | + | 2.53083i | 0.00506004 | + | 0.101970i | ||||
\(617\) | 0.288199i | 0.0116025i | 0.999983 | + | 0.00580123i | \(0.00184660\pi\) | ||||
−0.999983 | + | 0.00580123i | \(0.998153\pi\) | |||||||
\(618\) | −1.73689 | − | 0.964876i | −0.0698679 | − | 0.0388130i | ||||
\(619\) | −11.5307 | − | 11.5307i | −0.463460 | − | 0.463460i | 0.436328 | − | 0.899788i | \(-0.356279\pi\) |
−0.899788 | + | 0.436328i | \(0.856279\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.7019 | − | 28.7019i | 1.15177 | − | 1.15177i | ||||
\(622\) | −2.22762 | − | 7.79586i | −0.0893193 | − | 0.312585i | ||||
\(623\) | 15.7965 | 0.632873 | ||||||||
\(624\) | −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 | ||||
\(628\) | 3.47547 | − | 14.9278i | 0.138686 | − | 0.595682i | ||||
\(629\) | 12.7131 | + | 12.7131i | 0.506903 | + | 0.506903i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.2062i | 0.565541i | 0.959188 | + | 0.282771i | \(0.0912536\pi\) | ||||
−0.959188 | + | 0.282771i | \(0.908746\pi\) | |||||||
\(632\) | 22.1588 | − | 24.4728i | 0.881430 | − | 0.973475i | ||||
\(633\) | − | 32.3878i | − | 1.28730i | ||||||
\(634\) | 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 | ||||
\(638\) | −7.57292 | + | 2.16391i | −0.299815 | + | 0.0856702i | ||||
\(639\) | 3.42245 | 0.135390 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.7372 | 0.779572 | 0.389786 | − | 0.920905i | \(-0.372549\pi\) | ||||
0.389786 | + | 0.920905i | \(0.372549\pi\) | |||||||
\(642\) | −20.3712 | + | 5.82093i | −0.803985 | + | 0.229734i | ||||
\(643\) | −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 | ||||
\(647\) | − | 46.3186i | − | 1.82097i | −0.413541 | − | 0.910485i | \(-0.635708\pi\) | ||
0.413541 | − | 0.910485i | \(-0.364292\pi\) | |||||||
\(648\) | 10.9895 | − | 12.1371i | 0.431710 | − | 0.476792i | ||||
\(649\) | 5.01005i | 0.196662i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.5103 | − | 10.5103i | −0.411932 | − | 0.411932i | ||||
\(652\) | −4.15144 | + | 17.8312i | −0.162583 | + | 0.698322i | ||||
\(653\) | −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 | ||||
\(657\) | −2.04042 | −0.0796045 | ||||||||
\(658\) | 3.86999 | + | 13.5436i | 0.150868 | + | 0.527984i | ||||
\(659\) | −15.2461 | + | 15.2461i | −0.593905 | + | 0.593905i | −0.938684 | − | 0.344779i | \(-0.887954\pi\) |
0.344779 | + | 0.938684i | \(0.387954\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.1271 | + | 19.1271i | 0.743958 | + | 0.743958i | 0.973337 | − | 0.229379i | \(-0.0736696\pi\) |
−0.229379 | + | 0.973337i | \(0.573670\pi\) | |||||||
\(662\) | 38.5151 | + | 21.3959i | 1.49693 | + | 0.831577i | ||||
\(663\) | 25.1432i | 0.976481i | ||||||||
\(664\) | 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 | ||||
\(668\) | −8.76777 | − | 14.0894i | −0.339235 | − | 0.545133i | ||||
\(669\) | 8.20306 | − | 8.20306i | 0.317149 | − | 0.317149i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.21633 | −0.0469559 | ||||||||
\(672\) | 10.2331 | − | 7.09490i | 0.394749 | − | 0.273692i | ||||
\(673\) | −18.5586 | −0.715382 | −0.357691 | − | 0.933840i | \(-0.616436\pi\) | ||||
−0.357691 | + | 0.933840i | \(0.616436\pi\) | |||||||
\(674\) | 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 | \(0.773537\pi\) | |||||||
\(678\) | −1.96709 | + | 3.54100i | −0.0755458 | + | 0.135991i | ||||
\(679\) | − | 27.1666i | − | 1.04256i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 12.4555i | − | 0.477295i | ||||||
\(682\) | −4.99688 | − | 2.77587i | −0.191340 | − | 0.106293i | ||||
\(683\) | −12.6646 | − | 12.6646i | −0.484598 | − | 0.484598i | 0.421999 | − | 0.906596i | \(-0.361329\pi\) |
−0.906596 | + | 0.421999i | \(0.861329\pi\) | |||||||
\(684\) | −4.05138 | − | 0.943239i | −0.154908 | − | 0.0360657i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.83885 | + | 23.9335i | 0.261108 | + | 0.913786i | ||||
\(687\) | 40.4723 | 1.54412 | ||||||||
\(688\) | 32.8600 | − | 11.1786i | 1.25278 | − | 0.426182i | ||||
\(689\) | −19.6620 | −0.749063 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.8892 | − | 26.8892i | 1.02291 | − | 1.02291i | 0.0231826 | − | 0.999731i | \(-0.492620\pi\) |
0.999731 | − | 0.0231826i | \(-0.00737991\pi\) | |||||||
\(692\) | −7.65914 | + | 32.8973i | −0.291157 | + | 1.25057i | ||||
\(693\) | −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 | ||||
\(697\) | − | 50.1717i | − | 1.90039i | ||||||
\(698\) | −5.45621 | + | 9.82180i | −0.206521 | + | 0.371761i | ||||
\(699\) | −2.79458 | − | 2.79458i | −0.105701 | − | 0.105701i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.3725 | − | 25.3725i | 0.958305 | − | 0.958305i | −0.0408602 | − | 0.999165i | \(-0.513010\pi\) |
0.999165 | + | 0.0408602i | \(0.0130098\pi\) | |||||||
\(702\) | 20.1524 | − | 5.75843i | 0.760605 | − | 0.217338i | ||||
\(703\) | 6.86382 | 0.258874 | ||||||||
\(704\) | 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 | ||||
\(708\) | 20.9029 | − | 13.0079i | 0.785581 | − | 0.488865i | ||||
\(709\) | 16.1117 | + | 16.1117i | 0.605089 | + | 0.605089i | 0.941659 | − | 0.336570i | \(-0.109267\pi\) |
−0.336570 | + | 0.941659i | \(0.609267\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.76879i | 0.366358i | ||||||||
\(712\) | −22.1289 | − | 20.0365i | −0.829316 | − | 0.750901i | ||||
\(713\) | 48.5705i | 1.81898i | ||||||||
\(714\) | −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 | ||||
\(718\) | −1.04864 | − | 3.66985i | −0.0391347 | − | 0.136958i | ||||
\(719\) | 29.1676 | 1.08777 | 0.543884 | − | 0.839160i | \(-0.316953\pi\) | ||||
0.543884 | + | 0.839160i | \(0.316953\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.42973 | 0.0532460 | ||||||||
\(722\) | 4.98284 | + | 17.4381i | 0.185442 | + | 0.648980i | ||||
\(723\) | 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 | ||||
\(727\) | 4.13463i | 0.153345i | 0.997056 | + | 0.0766724i | \(0.0244296\pi\) | ||||
−0.997056 | + | 0.0766724i | \(0.975570\pi\) | |||||||
\(728\) | 11.1039 | − | 0.551010i | 0.411540 | − | 0.0204218i | ||||
\(729\) | 29.7434i | 1.10161i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −39.9411 | − | 39.9411i | −1.47727 | − | 1.47727i | ||||
\(732\) | 3.15802 | + | 5.07478i | 0.116724 | + | 0.187569i | ||||
\(733\) | −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 | ||||
\(737\) | 5.38060 | 0.198197 | ||||||||
\(738\) | −8.77140 | + | 2.50637i | −0.322880 | + | 0.0922608i | ||||
\(739\) | 23.9820 | − | 23.9820i | 0.882194 | − | 0.882194i | −0.111564 | − | 0.993757i | \(-0.535586\pi\) |
0.993757 | + | 0.111564i | \(0.0355859\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.78744 | + | 6.78744i | 0.249343 | + | 0.249343i | ||||
\(742\) | 7.69540 | − | 13.8526i | 0.282507 | − | 0.508545i | ||||
\(743\) | 10.3473i | 0.379604i | 0.981822 | + | 0.189802i | \(0.0607846\pi\) | ||||
−0.981822 | + | 0.189802i | \(0.939215\pi\) | |||||||
\(744\) | 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 | ||||
\(748\) | −7.58993 | − | 1.76708i | −0.277515 | − | 0.0646109i | ||||
\(749\) | 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 | \(0.736059\pi\) | |||||||
\(752\) | 11.7575 | − | 23.8817i | 0.428754 | − | 0.870874i | ||||
\(753\) | −20.7096 | −0.754700 | ||||||||
\(754\) | 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 | \(-0.535836\pi\) | |||||||
\(758\) | 9.46454 | + | 5.25774i | 0.343768 | + | 0.190970i | ||||
\(759\) | − | 6.33235i | − | 0.229850i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.1054i | 1.56257i | 0.624174 | + | 0.781285i | \(0.285436\pi\) | ||||
−0.624174 | + | 0.781285i | \(0.714564\pi\) | |||||||
\(762\) | 1.33122 | − | 2.39634i | 0.0482249 | − | 0.0868103i | ||||
\(763\) | −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 | ||||
\(767\) | 21.9815 | 0.793705 | ||||||||
\(768\) | −23.3345 | − | 3.04073i | −0.842013 | − | 0.109723i | ||||
\(769\) | −31.2507 | −1.12693 | −0.563465 | − | 0.826140i | \(-0.690532\pi\) | ||||
−0.563465 | + | 0.826140i | \(0.690532\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.69682 | + | 4.69682i | −0.169152 | + | 0.169152i | ||||
\(772\) | 42.1376 | − | 26.2221i | 1.51657 | − | 0.943756i | ||||
\(773\) | 24.4047 | + | 24.4047i | 0.877778 | + | 0.877778i | 0.993304 | − | 0.115527i | \(-0.0368556\pi\) |
−0.115527 | + | 0.993304i | \(0.536856\pi\) | |||||||
\(774\) | −4.98751 | + | 8.97810i | −0.179272 | + | 0.322711i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −34.4586 | + | 38.0570i | −1.23699 | + | 1.36617i | ||||
\(777\) | − | 6.07970i | − | 0.218108i | ||||||
\(778\) | 2.41068 | + | 1.33918i | 0.0864271 | + | 0.0480120i | ||||
\(779\) | −13.5439 | − | 13.5439i | −0.485261 | − | 0.485261i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.73085 | − | 1.73085i | 0.0619345 | − | 0.0619345i | ||||
\(782\) | 18.1929 | + | 63.6688i | 0.650579 | + | 2.27679i | ||||
\(783\) | −52.5036 | −1.87632 | ||||||||
\(784\) | 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 | −0.943869 | − | 0.330320i | \(-0.892843\pi\) |
0.330320 | + | 0.943869i | \(0.392843\pi\) | |||||||
\(788\) | 7.74977 | + | 1.80430i | 0.276074 | + | 0.0642754i | ||||
\(789\) | −21.0206 | − | 21.0206i | −0.748354 | − | 0.748354i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 2.91480i | − | 0.103638i | ||||||
\(792\) | 0.0702266 | + | 1.41521i | 0.00249539 | + | 0.0502871i | ||||
\(793\) | 5.33662i | 0.189509i | ||||||||
\(794\) | −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 | −0.968573 | − | 0.248731i | \(-0.919986\pi\) |
0.248731 | + | 0.968573i | \(0.419986\pi\) | |||||||
\(798\) | −7.43850 | + | 2.12551i | −0.263320 | + | 0.0752421i | ||||
\(799\) | −43.3192 | −1.53252 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.83319 | 0.312105 | ||||||||
\(802\) | −42.7768 | + | 12.2232i | −1.51050 | + | 0.431616i | ||||
\(803\) | −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 | ||||
\(807\) | − | 35.2405i | − | 1.24052i | ||||||
\(808\) | −4.15634 | + | 0.206250i | −0.146220 | + | 0.00725584i | ||||
\(809\) | − | 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 | 0.567246 | − | 0.823549i | \(-0.308009\pi\) |
−0.823549 | + | 0.567246i | \(0.808009\pi\) | |||||||
\(812\) | −27.1248 | − | 6.31518i | −0.951894 | − | 0.221619i | ||||
\(813\) | −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 | ||||
\(817\) | −21.5643 | −0.754439 | ||||||||
\(818\) | −4.97411 | − | 17.4076i | −0.173916 | − | 0.608643i | ||||
\(819\) | −2.32615 | + | 2.32615i | −0.0812823 | + | 0.0812823i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.0517 | − | 10.0517i | −0.350806 | − | 0.350806i | 0.509603 | − | 0.860409i | \(-0.329792\pi\) |
−0.860409 | + | 0.509603i | \(0.829792\pi\) | |||||||
\(822\) | −6.82850 | − | 3.79337i | −0.238171 | − | 0.132309i | ||||
\(823\) | 34.2064i | 1.19236i | 0.802851 | + | 0.596179i | \(0.203315\pi\) | ||||
−0.802851 | + | 0.596179i | \(0.796685\pi\) | |||||||
\(824\) | −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 | \(0.469888\pi\) | |||||||
\(828\) | 10.2222 | − | 6.36126i | 0.355247 | − | 0.221069i | ||||
\(829\) | −3.87895 | + | 3.87895i | −0.134722 | + | 0.134722i | −0.771252 | − | 0.636530i | \(-0.780369\pi\) |
0.636530 | + | 0.771252i | \(0.280369\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.2978 | 1.15509 | ||||||||
\(832\) | −16.2542 | − | 13.3125i | −0.563512 | − | 0.461530i | ||||
\(833\) | −30.9849 | −1.07356 | ||||||||
\(834\) | 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 | ||||
\(838\) | −11.1672 | + | 20.1022i | −0.385765 | + | 0.694421i | ||||
\(839\) | 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 | ||||||
\(842\) | 21.9790 | + | 12.2098i | 0.757447 | + | 0.420777i | ||||
\(843\) | 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 | ||||
\(847\) | 15.9272 | 0.547267 | ||||||||
\(848\) | −28.3512 | + | 9.64480i | −0.973584 | + | 0.331204i | ||||
\(849\) | −4.92309 | −0.168960 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.0478 | + | 14.0478i | −0.481553 | + | 0.481553i | ||||
\(852\) | −11.7153 | − | 2.72756i | −0.401361 | − | 0.0934446i | ||||
\(853\) | 1.87566 | + | 1.87566i | 0.0642212 | + | 0.0642212i | 0.738488 | − | 0.674267i | \(-0.235540\pi\) |
−0.674267 | + | 0.738488i | \(0.735540\pi\) | |||||||
\(854\) | −3.75984 | − | 2.08867i | −0.128659 | − | 0.0714728i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −28.7752 | + | 1.42791i | −0.983517 | + | 0.0488050i | ||||
\(857\) | 23.1714i | 0.791521i | 0.918354 | + | 0.395760i | \(0.129519\pi\) | ||||
−0.918354 | + | 0.395760i | \(0.870481\pi\) | |||||||
\(858\) | 1.58784 | − | 2.85829i | 0.0542078 | − | 0.0975803i | ||||
\(859\) | −10.5073 | − | 10.5073i | −0.358506 | − | 0.358506i | 0.504756 | − | 0.863262i | \(-0.331582\pi\) |
−0.863262 | + | 0.504756i | \(0.831582\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.9967 | + | 11.9967i | −0.408846 | + | 0.408846i | ||||
\(862\) | −20.7475 | + | 5.92847i | −0.706663 | + | 0.201924i | ||||
\(863\) | 25.2777 | 0.860463 | 0.430231 | − | 0.902719i | \(-0.358432\pi\) | ||||
0.430231 | + | 0.902719i | \(0.358432\pi\) | |||||||
\(864\) | 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 | ||||
\(868\) | −10.6794 | − | 17.1612i | −0.362481 | − | 0.582489i | ||||
\(869\) | 4.94039 | + | 4.94039i | 0.167591 | + | 0.167591i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 23.6073i | − | 0.799901i | ||||||
\(872\) | 1.12566 | + | 22.6844i | 0.0381198 | + | 0.768190i | ||||
\(873\) | − | 15.1912i | − | 0.514144i | ||||||
\(874\) | 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 | −0.930752 | − | 0.365651i | \(-0.880846\pi\) |
0.365651 | + | 0.930752i | \(0.380846\pi\) | |||||||
\(878\) | 15.4463 | + | 54.0564i | 0.521286 | + | 1.82431i | ||||
\(879\) | 39.8957 | 1.34565 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.38791 | 0.316287 | 0.158143 | − | 0.987416i | \(-0.449449\pi\) | ||||
0.158143 | + | 0.987416i | \(0.449449\pi\) | |||||||
\(882\) | 1.54788 | + | 5.41701i | 0.0521197 | + | 0.182400i | ||||
\(883\) | −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 | ||||
\(887\) | 48.2072i | 1.61864i | 0.587368 | + | 0.809320i | \(0.300164\pi\) | ||||
−0.587368 | + | 0.809320i | \(0.699836\pi\) | |||||||
\(888\) | −7.71161 | + | 8.51691i | −0.258785 | + | 0.285809i | ||||
\(889\) | 1.97256i | 0.0661577i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.45016 | + | 2.45016i | 0.0820834 | + | 0.0820834i | ||||
\(892\) | 13.3939 | − | 8.33500i | 0.448461 | − | 0.279076i | ||||
\(893\) | −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 | ||||
\(897\) | −27.7830 | −0.927648 | ||||||||
\(898\) | −7.32144 | + | 2.09206i | −0.244320 | + | 0.0698128i | ||||
\(899\) | 44.4243 | − | 44.4243i | 1.48163 | − | 1.48163i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.4607 | + | 34.4607i | 1.14805 | + | 1.14805i | ||||
\(902\) | −3.16843 | + | 5.70353i | −0.105497 | + | 0.189907i | ||||
\(903\) | 19.1008i | 0.635636i | ||||||||
\(904\) | −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 | \(-0.518761\pi\) | |||||||
\(908\) | 3.84071 | − | 16.4965i | 0.127458 | − | 0.547456i | ||||
\(909\) | 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 | \(0.420791\pi\) | |||||||
\(912\) | 13.1165 | + | 6.45756i | 0.434329 | + | 0.213831i | ||||
\(913\) | −2.38244 | −0.0788472 | ||||||||
\(914\) | −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 | ||||
\(918\) | −45.4128 | − | 25.2277i | −1.49885 | − | 0.832638i | ||||
\(919\) | 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 | ||||||||
\(922\) | −4.37410 | + | 7.87389i | −0.144053 | + | 0.259313i | ||||
\(923\) | −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 | ||||
\(927\) | 0.799487 | 0.0262586 | ||||||||
\(928\) | 29.9882 | + | 43.2524i | 0.984411 | + | 1.41983i | ||||
\(929\) | −9.13997 | −0.299873 | −0.149936 | − | 0.988696i | \(-0.547907\pi\) | ||||
−0.149936 | + | 0.988696i | \(0.547907\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.36441 | + | 8.36441i | −0.274133 | + | 0.274133i | ||||
\(932\) | −2.83952 | − | 4.56297i | −0.0930116 | − | 0.149465i | ||||
\(933\) | −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 | ||||
\(937\) | − | 19.0036i | − | 0.620819i | −0.950603 | − | 0.310410i | \(-0.899534\pi\) | ||
0.950603 | − | 0.310410i | \(-0.100466\pi\) | |||||||
\(938\) | 16.6322 | + | 9.23951i | 0.543060 | + | 0.301681i | ||||
\(939\) | −0.221119 | − | 0.221119i | −0.00721596 | − | 0.00721596i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.48322 | − | 1.48322i | 0.0483517 | − | 0.0483517i | −0.682518 | − | 0.730869i | \(-0.739115\pi\) |
0.730869 | + | 0.682518i | \(0.239115\pi\) | |||||||
\(942\) | −4.37937 | − | 15.3262i | −0.142687 | − | 0.499355i | ||||
\(943\) | 55.4393 | 1.80535 | ||||||||
\(944\) | 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 | −0.768748 | − | 0.639552i | \(-0.779120\pi\) |
0.639552 | + | 0.768748i | \(0.279120\pi\) | |||||||
\(948\) | 7.78533 | − | 33.4393i | 0.252856 | − | 1.08606i | ||||
\(949\) | 4.52747 | + | 4.52747i | 0.146968 | + | 0.146968i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 6.68870i | − | 0.216896i | ||||||
\(952\) | −20.4271 | − | 18.4956i | −0.662046 | − | 0.599447i | ||||
\(953\) | 16.5970i | 0.537628i | 0.963192 | + | 0.268814i | \(0.0866317\pi\) | ||||
−0.963192 | + | 0.268814i | \(0.913368\pi\) | |||||||
\(954\) | 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 | ||||
\(958\) | 7.53968 | − | 2.15442i | 0.243596 | − | 0.0696060i | ||||
\(959\) | 5.62092 | 0.181509 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.5965 | 0.470855 | ||||||||
\(962\) | −9.86338 | + | 2.81840i | −0.318008 | + | 0.0908688i | ||||
\(963\) | 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 | ||||
\(967\) | 8.72635i | 0.280621i | 0.990108 | + | 0.140310i | \(0.0448100\pi\) | ||||
−0.990108 | + | 0.140310i | \(0.955190\pi\) | |||||||
\(968\) | −22.3121 | − | 20.2024i | −0.717138 | − | 0.649330i | ||||
\(969\) | − | 23.7921i | − | 0.764311i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.5421 | − | 14.5421i | −0.466677 | − | 0.466677i | 0.434159 | − | 0.900836i | \(-0.357045\pi\) |
−0.900836 | + | 0.434159i | \(0.857045\pi\) | |||||||
\(972\) | −3.81654 | + | 16.3927i | −0.122416 | + | 0.525796i | ||||
\(973\) | −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 | ||||
\(977\) | 25.2020 | 0.806284 | 0.403142 | − | 0.915137i | \(-0.367918\pi\) | ||||
0.403142 | + | 0.915137i | \(0.367918\pi\) | |||||||
\(978\) | 5.23114 | + | 18.3071i | 0.167273 | + | 0.585397i | ||||
\(979\) | 4.46723 | − | 4.46723i | 0.142773 | − | 0.142773i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.75212 | − | 4.75212i | −0.151724 | − | 0.151724i | ||||
\(982\) | 12.9276 | + | 7.18152i | 0.412535 | + | 0.229171i | ||||
\(983\) | − | 4.00157i | − | 0.127630i | −0.997962 | − | 0.0638151i | \(-0.979673\pi\) | ||
0.997962 | − | 0.0638151i | \(-0.0203268\pi\) | |||||||
\(984\) | 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 | ||||
\(988\) | 6.89661 | + | 11.0825i | 0.219410 | + | 0.352581i | ||||
\(989\) | 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 | \(0.955249\pi\) | |||||||
\(992\) | −6.80709 | + | 37.5866i | −0.216125 | + | 1.19338i | ||||
\(993\) | 45.8201 | 1.45406 | ||||||||
\(994\) | 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 | \(0.588590\pi\) | |||||||
\(998\) | 13.6074 | − | 24.4949i | 0.430734 | − | 0.775371i | ||||
\(999\) | − | 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.l.g.101.6 | yes | 12 | |
4.3 | odd | 2 | 1600.2.l.f.1201.2 | 12 | |||
5.2 | odd | 4 | 400.2.q.f.149.4 | 12 | |||
5.3 | odd | 4 | 400.2.q.e.149.3 | 12 | |||
5.4 | even | 2 | 400.2.l.f.101.1 | ✓ | 12 | ||
16.3 | odd | 4 | 1600.2.l.f.401.2 | 12 | |||
16.13 | even | 4 | inner | 400.2.l.g.301.6 | yes | 12 | |
20.3 | even | 4 | 1600.2.q.e.49.2 | 12 | |||
20.7 | even | 4 | 1600.2.q.f.49.5 | 12 | |||
20.19 | odd | 2 | 1600.2.l.g.1201.5 | 12 | |||
80.3 | even | 4 | 1600.2.q.f.849.5 | 12 | |||
80.13 | odd | 4 | 400.2.q.f.349.4 | 12 | |||
80.19 | odd | 4 | 1600.2.l.g.401.5 | 12 | |||
80.29 | even | 4 | 400.2.l.f.301.1 | yes | 12 | ||
80.67 | even | 4 | 1600.2.q.e.849.2 | 12 | |||
80.77 | odd | 4 | 400.2.q.e.349.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.1 | ✓ | 12 | 5.4 | even | 2 | ||
400.2.l.f.301.1 | yes | 12 | 80.29 | even | 4 | ||
400.2.l.g.101.6 | yes | 12 | 1.1 | even | 1 | trivial | |
400.2.l.g.301.6 | yes | 12 | 16.13 | even | 4 | inner | |
400.2.q.e.149.3 | 12 | 5.3 | odd | 4 | |||
400.2.q.e.349.3 | 12 | 80.77 | odd | 4 | |||
400.2.q.f.149.4 | 12 | 5.2 | odd | 4 | |||
400.2.q.f.349.4 | 12 | 80.13 | odd | 4 | |||
1600.2.l.f.401.2 | 12 | 16.3 | odd | 4 | |||
1600.2.l.f.1201.2 | 12 | 4.3 | odd | 2 | |||
1600.2.l.g.401.5 | 12 | 80.19 | odd | 4 | |||
1600.2.l.g.1201.5 | 12 | 20.19 | odd | 2 | |||
1600.2.q.e.49.2 | 12 | 20.3 | even | 4 | |||
1600.2.q.e.849.2 | 12 | 80.67 | even | 4 | |||
1600.2.q.f.49.5 | 12 | 20.7 | even | 4 | |||
1600.2.q.f.849.5 | 12 | 80.3 | even | 4 |