Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(277,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.277");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 277.2 | ||
Character | \(\chi\) | \(=\) | 690.277 |
Dual form | 690.3.k.b.553.2 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | −4.35673 | + | 2.45335i | −0.871346 | + | 0.490669i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | −3.40648 | − | 3.40648i | −0.486640 | − | 0.486640i | 0.420604 | − | 0.907244i | \(-0.361818\pi\) |
−0.907244 | + | 0.420604i | \(0.861818\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 6.81008 | + | 1.90338i | 0.681008 | + | 0.190338i | ||||
\(11\) | −17.0916 | −1.55378 | −0.776890 | − | 0.629636i | \(-0.783204\pi\) | ||||
−0.776890 | + | 0.629636i | \(0.783204\pi\) | |||||||
\(12\) | −2.44949 | − | 2.44949i | −0.204124 | − | 0.204124i | ||||
\(13\) | 9.51988 | − | 9.51988i | 0.732298 | − | 0.732298i | −0.238776 | − | 0.971075i | \(-0.576746\pi\) |
0.971075 | + | 0.238776i | \(0.0767462\pi\) | |||||||
\(14\) | 6.81296i | 0.486640i | ||||||||
\(15\) | 2.33116 | − | 8.34061i | 0.155411 | − | 0.556040i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −1.23132 | − | 1.23132i | −0.0724308 | − | 0.0724308i | 0.669963 | − | 0.742394i | \(-0.266310\pi\) |
−0.742394 | + | 0.669963i | \(0.766310\pi\) | |||||||
\(18\) | −3.00000 | + | 3.00000i | −0.166667 | + | 0.166667i | ||||
\(19\) | − | 10.6522i | − | 0.560644i | −0.959906 | − | 0.280322i | \(-0.909559\pi\) | ||
0.959906 | − | 0.280322i | \(-0.0904413\pi\) | |||||||
\(20\) | −4.90669 | − | 8.71346i | −0.245335 | − | 0.435673i | ||||
\(21\) | 8.34414 | 0.397340 | ||||||||
\(22\) | 17.0916 | + | 17.0916i | 0.776890 | + | 0.776890i | ||||
\(23\) | −3.39116 | + | 3.39116i | −0.147442 | + | 0.147442i | ||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 12.9622 | − | 21.3771i | 0.518487 | − | 0.855085i | ||||
\(26\) | −19.0398 | −0.732298 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 6.81296 | − | 6.81296i | 0.243320 | − | 0.243320i | ||||
\(29\) | 16.4830i | 0.568380i | 0.958768 | + | 0.284190i | \(0.0917247\pi\) | ||||
−0.958768 | + | 0.284190i | \(0.908275\pi\) | |||||||
\(30\) | −10.6718 | + | 6.00945i | −0.355725 | + | 0.200315i | ||||
\(31\) | −21.1370 | −0.681839 | −0.340920 | − | 0.940092i | \(-0.610738\pi\) | ||||
−0.340920 | + | 0.940092i | \(0.610738\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | 20.9328 | − | 20.9328i | 0.634328 | − | 0.634328i | ||||
\(34\) | 2.46265i | 0.0724308i | ||||||||
\(35\) | 23.1984 | + | 6.48384i | 0.662811 | + | 0.185252i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 0.589707 | + | 0.589707i | 0.0159380 | + | 0.0159380i | 0.715031 | − | 0.699093i | \(-0.246413\pi\) |
−0.699093 | + | 0.715031i | \(0.746413\pi\) | |||||||
\(38\) | −10.6522 | + | 10.6522i | −0.280322 | + | 0.280322i | ||||
\(39\) | 23.3188i | 0.597919i | ||||||||
\(40\) | −3.80677 | + | 13.6202i | −0.0951692 | + | 0.340504i | ||||
\(41\) | 44.7585 | 1.09167 | 0.545835 | − | 0.837893i | \(-0.316213\pi\) | ||||
0.545835 | + | 0.837893i | \(0.316213\pi\) | |||||||
\(42\) | −8.34414 | − | 8.34414i | −0.198670 | − | 0.198670i | ||||
\(43\) | −49.7416 | + | 49.7416i | −1.15678 | + | 1.15678i | −0.171619 | + | 0.985163i | \(0.554900\pi\) |
−0.985163 | + | 0.171619i | \(0.945100\pi\) | |||||||
\(44\) | − | 34.1832i | − | 0.776890i | ||||||
\(45\) | 7.36004 | + | 13.0702i | 0.163556 | + | 0.290449i | ||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | 59.0386 | + | 59.0386i | 1.25614 | + | 1.25614i | 0.952920 | + | 0.303220i | \(0.0980619\pi\) |
0.303220 | + | 0.952920i | \(0.401938\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.102062 | − | 0.102062i | ||||
\(49\) | − | 25.7918i | − | 0.526363i | ||||||
\(50\) | −34.3393 | + | 8.41495i | −0.686786 | + | 0.168299i | ||||
\(51\) | 3.01611 | 0.0591395 | ||||||||
\(52\) | 19.0398 | + | 19.0398i | 0.366149 | + | 0.366149i | ||||
\(53\) | −38.1796 | + | 38.1796i | −0.720369 | + | 0.720369i | −0.968680 | − | 0.248311i | \(-0.920124\pi\) |
0.248311 | + | 0.968680i | \(0.420124\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 74.4634 | − | 41.9316i | 1.35388 | − | 0.762392i | ||||
\(56\) | −13.6259 | −0.243320 | ||||||||
\(57\) | 13.0463 | + | 13.0463i | 0.228882 | + | 0.228882i | ||||
\(58\) | 16.4830 | − | 16.4830i | 0.284190 | − | 0.284190i | ||||
\(59\) | 16.5016i | 0.279688i | 0.990174 | + | 0.139844i | \(0.0446601\pi\) | ||||
−0.990174 | + | 0.139844i | \(0.955340\pi\) | |||||||
\(60\) | 16.6812 | + | 4.66232i | 0.278020 | + | 0.0777053i | ||||
\(61\) | 85.3928 | 1.39988 | 0.699941 | − | 0.714201i | \(-0.253210\pi\) | ||||
0.699941 | + | 0.714201i | \(0.253210\pi\) | |||||||
\(62\) | 21.1370 | + | 21.1370i | 0.340920 | + | 0.340920i | ||||
\(63\) | −10.2194 | + | 10.2194i | −0.162213 | + | 0.162213i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | −18.1200 | + | 64.8311i | −0.278769 | + | 0.997402i | ||||
\(66\) | −41.8657 | −0.634328 | ||||||||
\(67\) | 87.1773 | + | 87.1773i | 1.30115 | + | 1.30115i | 0.927614 | + | 0.373540i | \(0.121856\pi\) |
0.373540 | + | 0.927614i | \(0.378144\pi\) | |||||||
\(68\) | 2.46265 | − | 2.46265i | 0.0362154 | − | 0.0362154i | ||||
\(69\) | − | 8.30662i | − | 0.120386i | ||||||
\(70\) | −16.7145 | − | 29.6822i | −0.238779 | − | 0.424032i | ||||
\(71\) | −18.0891 | −0.254776 | −0.127388 | − | 0.991853i | \(-0.540659\pi\) | ||||
−0.127388 | + | 0.991853i | \(0.540659\pi\) | |||||||
\(72\) | −6.00000 | − | 6.00000i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | −17.4717 | + | 17.4717i | −0.239338 | + | 0.239338i | −0.816576 | − | 0.577238i | \(-0.804130\pi\) |
0.577238 | + | 0.816576i | \(0.304130\pi\) | |||||||
\(74\) | − | 1.17941i | − | 0.0159380i | ||||||
\(75\) | 10.3062 | + | 42.0569i | 0.137416 | + | 0.560759i | ||||
\(76\) | 21.3045 | 0.280322 | ||||||||
\(77\) | 58.2221 | + | 58.2221i | 0.756132 | + | 0.756132i | ||||
\(78\) | 23.3188 | − | 23.3188i | 0.298960 | − | 0.298960i | ||||
\(79\) | − | 67.2838i | − | 0.851693i | −0.904795 | − | 0.425847i | \(-0.859976\pi\) | ||
0.904795 | − | 0.425847i | \(-0.140024\pi\) | |||||||
\(80\) | 17.4269 | − | 9.81339i | 0.217836 | − | 0.122667i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | −44.7585 | − | 44.7585i | −0.545835 | − | 0.545835i | ||||
\(83\) | 8.41202 | − | 8.41202i | 0.101350 | − | 0.101350i | −0.654614 | − | 0.755963i | \(-0.727169\pi\) |
0.755963 | + | 0.654614i | \(0.227169\pi\) | |||||||
\(84\) | 16.6883i | 0.198670i | ||||||||
\(85\) | 8.38541 | + | 2.34368i | 0.0986518 | + | 0.0275727i | ||||
\(86\) | 99.4833 | 1.15678 | ||||||||
\(87\) | −20.1875 | − | 20.1875i | −0.232040 | − | 0.232040i | ||||
\(88\) | −34.1832 | + | 34.1832i | −0.388445 | + | 0.388445i | ||||
\(89\) | − | 44.8108i | − | 0.503492i | −0.967793 | − | 0.251746i | \(-0.918995\pi\) | ||
0.967793 | − | 0.251746i | \(-0.0810047\pi\) | |||||||
\(90\) | 5.71015 | − | 20.4302i | 0.0634461 | − | 0.227003i | ||||
\(91\) | −64.8586 | −0.712731 | ||||||||
\(92\) | −6.78233 | − | 6.78233i | −0.0737210 | − | 0.0737210i | ||||
\(93\) | 25.8875 | − | 25.8875i | 0.278360 | − | 0.278360i | ||||
\(94\) | − | 118.077i | − | 1.25614i | ||||||
\(95\) | 26.1336 | + | 46.4089i | 0.275091 | + | 0.488515i | ||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | 84.0085 | + | 84.0085i | 0.866067 | + | 0.866067i | 0.992034 | − | 0.125967i | \(-0.0402034\pi\) |
−0.125967 | + | 0.992034i | \(0.540203\pi\) | |||||||
\(98\) | −25.7918 | + | 25.7918i | −0.263182 | + | 0.263182i | ||||
\(99\) | 51.2748i | 0.517927i | ||||||||
\(100\) | 42.7543 | + | 25.9244i | 0.427543 | + | 0.259244i | ||||
\(101\) | 110.266 | 1.09174 | 0.545871 | − | 0.837869i | \(-0.316199\pi\) | ||||
0.545871 | + | 0.837869i | \(0.316199\pi\) | |||||||
\(102\) | −3.01611 | − | 3.01611i | −0.0295697 | − | 0.0295697i | ||||
\(103\) | 103.363 | − | 103.363i | 1.00352 | − | 1.00352i | 0.00352878 | − | 0.999994i | \(-0.498877\pi\) |
0.999994 | − | 0.00352878i | \(-0.00112325\pi\) | |||||||
\(104\) | − | 38.0795i | − | 0.366149i | ||||||
\(105\) | −36.3531 | + | 20.4711i | −0.346220 | + | 0.194962i | ||||
\(106\) | 76.3591 | 0.720369 | ||||||||
\(107\) | −39.1624 | − | 39.1624i | −0.366004 | − | 0.366004i | 0.500014 | − | 0.866018i | \(-0.333328\pi\) |
−0.866018 | + | 0.500014i | \(0.833328\pi\) | |||||||
\(108\) | −7.34847 | + | 7.34847i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | − | 167.451i | − | 1.53625i | −0.640299 | − | 0.768126i | \(-0.721190\pi\) | ||
0.640299 | − | 0.768126i | \(-0.278810\pi\) | |||||||
\(110\) | −116.395 | − | 32.5318i | −1.05814 | − | 0.295744i | ||||
\(111\) | −1.44448 | −0.0130133 | ||||||||
\(112\) | 13.6259 | + | 13.6259i | 0.121660 | + | 0.121660i | ||||
\(113\) | −58.3978 | + | 58.3978i | −0.516794 | + | 0.516794i | −0.916600 | − | 0.399806i | \(-0.869078\pi\) |
0.399806 | + | 0.916600i | \(0.369078\pi\) | |||||||
\(114\) | − | 26.0925i | − | 0.228882i | ||||||
\(115\) | 6.45469 | − | 23.0941i | 0.0561277 | − | 0.200818i | ||||
\(116\) | −32.9661 | −0.284190 | ||||||||
\(117\) | −28.5596 | − | 28.5596i | −0.244099 | − | 0.244099i | ||||
\(118\) | 16.5016 | − | 16.5016i | 0.139844 | − | 0.139844i | ||||
\(119\) | 8.38896i | 0.0704954i | ||||||||
\(120\) | −12.0189 | − | 21.3435i | −0.100157 | − | 0.177863i | ||||
\(121\) | 171.122 | 1.41423 | ||||||||
\(122\) | −85.3928 | − | 85.3928i | −0.699941 | − | 0.699941i | ||||
\(123\) | −54.8177 | + | 54.8177i | −0.445672 | + | 0.445672i | ||||
\(124\) | − | 42.2740i | − | 0.340920i | ||||||
\(125\) | −4.02721 | + | 124.935i | −0.0322177 | + | 0.999481i | ||||
\(126\) | 20.4389 | 0.162213 | ||||||||
\(127\) | 38.7338 | + | 38.7338i | 0.304990 | + | 0.304990i | 0.842963 | − | 0.537972i | \(-0.180809\pi\) |
−0.537972 | + | 0.842963i | \(0.680809\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | − | 121.842i | − | 0.944509i | ||||||
\(130\) | 82.9511 | − | 46.7111i | 0.638085 | − | 0.359316i | ||||
\(131\) | 53.9132 | 0.411551 | 0.205776 | − | 0.978599i | \(-0.434028\pi\) | ||||
0.205776 | + | 0.978599i | \(0.434028\pi\) | |||||||
\(132\) | 41.8657 | + | 41.8657i | 0.317164 | + | 0.317164i | ||||
\(133\) | −36.2866 | + | 36.2866i | −0.272832 | + | 0.272832i | ||||
\(134\) | − | 174.355i | − | 1.30115i | ||||||
\(135\) | −25.0218 | − | 6.99348i | −0.185347 | − | 0.0518035i | ||||
\(136\) | −4.92529 | −0.0362154 | ||||||||
\(137\) | −77.4818 | − | 77.4818i | −0.565561 | − | 0.565561i | 0.365321 | − | 0.930882i | \(-0.380959\pi\) |
−0.930882 | + | 0.365321i | \(0.880959\pi\) | |||||||
\(138\) | −8.30662 | + | 8.30662i | −0.0601929 | + | 0.0601929i | ||||
\(139\) | − | 39.5073i | − | 0.284225i | −0.989850 | − | 0.142113i | \(-0.954610\pi\) | ||
0.989850 | − | 0.142113i | \(-0.0453895\pi\) | |||||||
\(140\) | −12.9677 | + | 46.3968i | −0.0926262 | + | 0.331405i | ||||
\(141\) | −144.614 | −1.02563 | ||||||||
\(142\) | 18.0891 | + | 18.0891i | 0.127388 | + | 0.127388i | ||||
\(143\) | −162.710 | + | 162.710i | −1.13783 | + | 1.13783i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | −40.4386 | − | 71.8121i | −0.278887 | − | 0.495256i | ||||
\(146\) | 34.9433 | 0.239338 | ||||||||
\(147\) | 31.5884 | + | 31.5884i | 0.214887 | + | 0.214887i | ||||
\(148\) | −1.17941 | + | 1.17941i | −0.00796901 | + | 0.00796901i | ||||
\(149\) | 124.537i | 0.835817i | 0.908489 | + | 0.417909i | \(0.137237\pi\) | ||||
−0.908489 | + | 0.417909i | \(0.862763\pi\) | |||||||
\(150\) | 31.7507 | − | 52.3631i | 0.211672 | − | 0.349087i | ||||
\(151\) | 100.260 | 0.663973 | 0.331986 | − | 0.943284i | \(-0.392281\pi\) | ||||
0.331986 | + | 0.943284i | \(0.392281\pi\) | |||||||
\(152\) | −21.3045 | − | 21.3045i | −0.140161 | − | 0.140161i | ||||
\(153\) | −3.69397 | + | 3.69397i | −0.0241436 | + | 0.0241436i | ||||
\(154\) | − | 116.444i | − | 0.756132i | ||||||
\(155\) | 92.0883 | − | 51.8564i | 0.594118 | − | 0.334558i | ||||
\(156\) | −46.6377 | −0.298960 | ||||||||
\(157\) | 169.452 | + | 169.452i | 1.07931 | + | 1.07931i | 0.996571 | + | 0.0827379i | \(0.0263664\pi\) |
0.0827379 | + | 0.996571i | \(0.473634\pi\) | |||||||
\(158\) | −67.2838 | + | 67.2838i | −0.425847 | + | 0.425847i | ||||
\(159\) | − | 93.5205i | − | 0.588179i | ||||||
\(160\) | −27.2403 | − | 7.61353i | −0.170252 | − | 0.0475846i | ||||
\(161\) | 23.1039 | 0.143502 | ||||||||
\(162\) | 9.00000 | + | 9.00000i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | 125.349 | − | 125.349i | 0.769014 | − | 0.769014i | −0.208919 | − | 0.977933i | \(-0.566994\pi\) |
0.977933 | + | 0.208919i | \(0.0669944\pi\) | |||||||
\(164\) | 89.5169i | 0.545835i | ||||||||
\(165\) | −39.8432 | + | 142.554i | −0.241474 | + | 0.863965i | ||||
\(166\) | −16.8240 | −0.101350 | ||||||||
\(167\) | 148.841 | + | 148.841i | 0.891262 | + | 0.891262i | 0.994642 | − | 0.103380i | \(-0.0329657\pi\) |
−0.103380 | + | 0.994642i | \(0.532966\pi\) | |||||||
\(168\) | 16.6883 | − | 16.6883i | 0.0993350 | − | 0.0993350i | ||||
\(169\) | − | 12.2562i | − | 0.0725222i | ||||||
\(170\) | −6.04173 | − | 10.7291i | −0.0355396 | − | 0.0631123i | ||||
\(171\) | −31.9567 | −0.186881 | ||||||||
\(172\) | −99.4833 | − | 99.4833i | −0.578391 | − | 0.578391i | ||||
\(173\) | 89.4157 | − | 89.4157i | 0.516854 | − | 0.516854i | −0.399764 | − | 0.916618i | \(-0.630908\pi\) |
0.916618 | + | 0.399764i | \(0.130908\pi\) | |||||||
\(174\) | 40.3750i | 0.232040i | ||||||||
\(175\) | −116.976 | + | 28.6654i | −0.668435 | + | 0.163802i | ||||
\(176\) | 68.3663 | 0.388445 | ||||||||
\(177\) | −20.2103 | − | 20.2103i | −0.114182 | − | 0.114182i | ||||
\(178\) | −44.8108 | + | 44.8108i | −0.251746 | + | 0.251746i | ||||
\(179\) | 82.4024i | 0.460349i | 0.973149 | + | 0.230174i | \(0.0739296\pi\) | ||||
−0.973149 | + | 0.230174i | \(0.926070\pi\) | |||||||
\(180\) | −26.1404 | + | 14.7201i | −0.145224 | + | 0.0817782i | ||||
\(181\) | −345.572 | −1.90924 | −0.954620 | − | 0.297828i | \(-0.903738\pi\) | ||||
−0.954620 | + | 0.297828i | \(0.903738\pi\) | |||||||
\(182\) | 64.8586 | + | 64.8586i | 0.356366 | + | 0.356366i | ||||
\(183\) | −104.584 | + | 104.584i | −0.571499 | + | 0.571499i | ||||
\(184\) | 13.5647i | 0.0737210i | ||||||||
\(185\) | −4.01595 | − | 1.12244i | −0.0217078 | − | 0.00606723i | ||||
\(186\) | −51.7749 | −0.278360 | ||||||||
\(187\) | 21.0453 | + | 21.0453i | 0.112542 | + | 0.112542i | ||||
\(188\) | −118.077 | + | 118.077i | −0.628070 | + | 0.628070i | ||||
\(189\) | − | 25.0324i | − | 0.132447i | ||||||
\(190\) | 20.2753 | − | 72.5425i | 0.106712 | − | 0.381803i | ||||
\(191\) | −263.122 | −1.37760 | −0.688801 | − | 0.724950i | \(-0.741863\pi\) | ||||
−0.688801 | + | 0.724950i | \(0.741863\pi\) | |||||||
\(192\) | 9.79796 | + | 9.79796i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | 140.875 | − | 140.875i | 0.729920 | − | 0.729920i | −0.240684 | − | 0.970604i | \(-0.577372\pi\) |
0.970604 | + | 0.240684i | \(0.0773717\pi\) | |||||||
\(194\) | − | 168.017i | − | 0.866067i | ||||||
\(195\) | −57.2092 | − | 101.594i | −0.293381 | − | 0.520994i | ||||
\(196\) | 51.5836 | 0.263182 | ||||||||
\(197\) | −85.4790 | − | 85.4790i | −0.433903 | − | 0.433903i | 0.456051 | − | 0.889954i | \(-0.349264\pi\) |
−0.889954 | + | 0.456051i | \(0.849264\pi\) | |||||||
\(198\) | 51.2748 | − | 51.2748i | 0.258963 | − | 0.258963i | ||||
\(199\) | 234.435i | 1.17806i | 0.808110 | + | 0.589032i | \(0.200491\pi\) | ||||
−0.808110 | + | 0.589032i | \(0.799509\pi\) | |||||||
\(200\) | −16.8299 | − | 68.6786i | −0.0841495 | − | 0.343393i | ||||
\(201\) | −213.540 | −1.06239 | ||||||||
\(202\) | −110.266 | − | 110.266i | −0.545871 | − | 0.545871i | ||||
\(203\) | 56.1491 | − | 56.1491i | 0.276597 | − | 0.276597i | ||||
\(204\) | 6.03223i | 0.0295697i | ||||||||
\(205\) | −195.001 | + | 109.808i | −0.951222 | + | 0.535649i | ||||
\(206\) | −206.726 | −1.00352 | ||||||||
\(207\) | 10.1735 | + | 10.1735i | 0.0491473 | + | 0.0491473i | ||||
\(208\) | −38.0795 | + | 38.0795i | −0.183075 | + | 0.183075i | ||||
\(209\) | 182.064i | 0.871118i | ||||||||
\(210\) | 56.8242 | + | 15.8821i | 0.270591 | + | 0.0756290i | ||||
\(211\) | −145.969 | −0.691795 | −0.345897 | − | 0.938272i | \(-0.612426\pi\) | ||||
−0.345897 | + | 0.938272i | \(0.612426\pi\) | |||||||
\(212\) | −76.3591 | − | 76.3591i | −0.360185 | − | 0.360185i | ||||
\(213\) | 22.1545 | − | 22.1545i | 0.104012 | − | 0.104012i | ||||
\(214\) | 78.3249i | 0.366004i | ||||||||
\(215\) | 94.6774 | − | 338.744i | 0.440360 | − | 1.57556i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | 72.0028 | + | 72.0028i | 0.331810 | + | 0.331810i | ||||
\(218\) | −167.451 | + | 167.451i | −0.768126 | + | 0.768126i | ||||
\(219\) | − | 42.7967i | − | 0.195419i | ||||||
\(220\) | 83.8632 | + | 148.927i | 0.381196 | + | 0.676940i | ||||
\(221\) | −23.4441 | −0.106082 | ||||||||
\(222\) | 1.44448 | + | 1.44448i | 0.00650667 | + | 0.00650667i | ||||
\(223\) | −227.734 | + | 227.734i | −1.02123 | + | 1.02123i | −0.0214593 | + | 0.999770i | \(0.506831\pi\) |
−0.999770 | + | 0.0214593i | \(0.993169\pi\) | |||||||
\(224\) | − | 27.2518i | − | 0.121660i | ||||||
\(225\) | −64.1314 | − | 38.8865i | −0.285028 | − | 0.172829i | ||||
\(226\) | 116.796 | 0.516794 | ||||||||
\(227\) | −63.6156 | − | 63.6156i | −0.280245 | − | 0.280245i | 0.552962 | − | 0.833207i | \(-0.313498\pi\) |
−0.833207 | + | 0.552962i | \(0.813498\pi\) | |||||||
\(228\) | −26.0925 | + | 26.0925i | −0.114441 | + | 0.114441i | ||||
\(229\) | − | 173.353i | − | 0.757000i | −0.925601 | − | 0.378500i | \(-0.876440\pi\) | ||
0.925601 | − | 0.378500i | \(-0.123560\pi\) | |||||||
\(230\) | −29.5488 | + | 16.6394i | −0.128473 | + | 0.0723452i | ||||
\(231\) | −142.615 | −0.617379 | ||||||||
\(232\) | 32.9661 | + | 32.9661i | 0.142095 | + | 0.142095i | ||||
\(233\) | 128.901 | − | 128.901i | 0.553225 | − | 0.553225i | −0.374145 | − | 0.927370i | \(-0.622064\pi\) |
0.927370 | + | 0.374145i | \(0.122064\pi\) | |||||||
\(234\) | 57.1193i | 0.244099i | ||||||||
\(235\) | −402.057 | − | 112.373i | −1.71088 | − | 0.478183i | ||||
\(236\) | −33.0032 | −0.139844 | ||||||||
\(237\) | 82.4054 | + | 82.4054i | 0.347702 | + | 0.347702i | ||||
\(238\) | 8.38896 | − | 8.38896i | 0.0352477 | − | 0.0352477i | ||||
\(239\) | − | 198.218i | − | 0.829366i | −0.909966 | − | 0.414683i | \(-0.863892\pi\) | ||
0.909966 | − | 0.414683i | \(-0.136108\pi\) | |||||||
\(240\) | −9.32463 | + | 33.3624i | −0.0388526 | + | 0.139010i | ||||
\(241\) | 134.329 | 0.557381 | 0.278690 | − | 0.960381i | \(-0.410100\pi\) | ||||
0.278690 | + | 0.960381i | \(0.410100\pi\) | |||||||
\(242\) | −171.122 | − | 171.122i | −0.707117 | − | 0.707117i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 170.786i | 0.699941i | ||||||||
\(245\) | 63.2762 | + | 112.368i | 0.258270 | + | 0.458644i | ||||
\(246\) | 109.635 | 0.445672 | ||||||||
\(247\) | −101.408 | − | 101.408i | −0.410559 | − | 0.410559i | ||||
\(248\) | −42.2740 | + | 42.2740i | −0.170460 | + | 0.170460i | ||||
\(249\) | 20.6052i | 0.0827517i | ||||||||
\(250\) | 128.962 | − | 120.908i | 0.515849 | − | 0.483632i | ||||
\(251\) | −85.1879 | −0.339394 | −0.169697 | − | 0.985496i | \(-0.554279\pi\) | ||||
−0.169697 | + | 0.985496i | \(0.554279\pi\) | |||||||
\(252\) | −20.4389 | − | 20.4389i | −0.0811067 | − | 0.0811067i | ||||
\(253\) | 57.9604 | − | 57.9604i | 0.229092 | − | 0.229092i | ||||
\(254\) | − | 77.4676i | − | 0.304990i | ||||||
\(255\) | −13.1404 | + | 7.39957i | −0.0515310 | + | 0.0290179i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −89.1736 | − | 89.1736i | −0.346979 | − | 0.346979i | 0.512004 | − | 0.858983i | \(-0.328903\pi\) |
−0.858983 | + | 0.512004i | \(0.828903\pi\) | |||||||
\(258\) | −121.842 | + | 121.842i | −0.472254 | + | 0.472254i | ||||
\(259\) | − | 4.01765i | − | 0.0155121i | ||||||
\(260\) | −129.662 | − | 36.2400i | −0.498701 | − | 0.139384i | ||||
\(261\) | 49.4491 | 0.189460 | ||||||||
\(262\) | −53.9132 | − | 53.9132i | −0.205776 | − | 0.205776i | ||||
\(263\) | 123.208 | − | 123.208i | 0.468473 | − | 0.468473i | −0.432947 | − | 0.901420i | \(-0.642526\pi\) |
0.901420 | + | 0.432947i | \(0.142526\pi\) | |||||||
\(264\) | − | 83.7313i | − | 0.317164i | ||||||
\(265\) | 72.6703 | − | 260.006i | 0.274228 | − | 0.981154i | ||||
\(266\) | 72.5733 | 0.272832 | ||||||||
\(267\) | 54.8818 | + | 54.8818i | 0.205550 | + | 0.205550i | ||||
\(268\) | −174.355 | + | 174.355i | −0.650577 | + | 0.650577i | ||||
\(269\) | − | 159.070i | − | 0.591340i | −0.955290 | − | 0.295670i | \(-0.904457\pi\) | ||
0.955290 | − | 0.295670i | \(-0.0955429\pi\) | |||||||
\(270\) | 18.0283 | + | 32.0153i | 0.0667716 | + | 0.118575i | ||||
\(271\) | 262.498 | 0.968627 | 0.484313 | − | 0.874895i | \(-0.339069\pi\) | ||||
0.484313 | + | 0.874895i | \(0.339069\pi\) | |||||||
\(272\) | 4.92529 | + | 4.92529i | 0.0181077 | + | 0.0181077i | ||||
\(273\) | 79.4352 | − | 79.4352i | 0.290971 | − | 0.290971i | ||||
\(274\) | 154.964i | 0.565561i | ||||||||
\(275\) | −221.544 | + | 365.369i | −0.805615 | + | 1.32861i | ||||
\(276\) | 16.6132 | 0.0601929 | ||||||||
\(277\) | 249.767 | + | 249.767i | 0.901686 | + | 0.901686i | 0.995582 | − | 0.0938960i | \(-0.0299321\pi\) |
−0.0938960 | + | 0.995582i | \(0.529932\pi\) | |||||||
\(278\) | −39.5073 | + | 39.5073i | −0.142113 | + | 0.142113i | ||||
\(279\) | 63.4111i | 0.227280i | ||||||||
\(280\) | 59.3644 | − | 33.4291i | 0.212016 | − | 0.119390i | ||||
\(281\) | 312.983 | 1.11382 | 0.556910 | − | 0.830573i | \(-0.311987\pi\) | ||||
0.556910 | + | 0.830573i | \(0.311987\pi\) | |||||||
\(282\) | 144.614 | + | 144.614i | 0.512817 | + | 0.512817i | ||||
\(283\) | −304.788 | + | 304.788i | −1.07699 | + | 1.07699i | −0.0802130 | + | 0.996778i | \(0.525560\pi\) |
−0.996778 | + | 0.0802130i | \(0.974440\pi\) | |||||||
\(284\) | − | 36.1782i | − | 0.127388i | ||||||
\(285\) | −88.8461 | − | 24.8321i | −0.311741 | − | 0.0871300i | ||||
\(286\) | 325.420 | 1.13783 | ||||||||
\(287\) | −152.469 | − | 152.469i | −0.531250 | − | 0.531250i | ||||
\(288\) | 12.0000 | − | 12.0000i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | − | 285.968i | − | 0.989508i | ||||||
\(290\) | −31.3735 | + | 112.251i | −0.108185 | + | 0.387071i | ||||
\(291\) | −205.778 | −0.707141 | ||||||||
\(292\) | −34.9433 | − | 34.9433i | −0.119669 | − | 0.119669i | ||||
\(293\) | −342.482 | + | 342.482i | −1.16888 | + | 1.16888i | −0.186408 | + | 0.982472i | \(0.559685\pi\) |
−0.982472 | + | 0.186408i | \(0.940315\pi\) | |||||||
\(294\) | − | 63.1767i | − | 0.214887i | ||||||
\(295\) | −40.4841 | − | 71.8930i | −0.137234 | − | 0.243705i | ||||
\(296\) | 2.35883 | 0.00796901 | ||||||||
\(297\) | −62.7985 | − | 62.7985i | −0.211443 | − | 0.211443i | ||||
\(298\) | 124.537 | − | 124.537i | 0.417909 | − | 0.417909i | ||||
\(299\) | 64.5670i | 0.215943i | ||||||||
\(300\) | −84.1138 | + | 20.6123i | −0.280379 | + | 0.0687078i | ||||
\(301\) | 338.888 | 1.12587 | ||||||||
\(302\) | −100.260 | − | 100.260i | −0.331986 | − | 0.331986i | ||||
\(303\) | −135.048 | + | 135.048i | −0.445702 | + | 0.445702i | ||||
\(304\) | 42.6090i | 0.140161i | ||||||||
\(305\) | −372.033 | + | 209.498i | −1.21978 | + | 0.686879i | ||||
\(306\) | 7.38794 | 0.0241436 | ||||||||
\(307\) | 242.539 | + | 242.539i | 0.790030 | + | 0.790030i | 0.981499 | − | 0.191469i | \(-0.0613250\pi\) |
−0.191469 | + | 0.981499i | \(0.561325\pi\) | |||||||
\(308\) | −116.444 | + | 116.444i | −0.378066 | + | 0.378066i | ||||
\(309\) | 253.186i | 0.819373i | ||||||||
\(310\) | −143.945 | − | 40.2319i | −0.464338 | − | 0.129780i | ||||
\(311\) | −486.480 | −1.56424 | −0.782122 | − | 0.623125i | \(-0.785863\pi\) | ||||
−0.782122 | + | 0.623125i | \(0.785863\pi\) | |||||||
\(312\) | 46.6377 | + | 46.6377i | 0.149480 | + | 0.149480i | ||||
\(313\) | 58.2031 | − | 58.2031i | 0.185953 | − | 0.185953i | −0.607991 | − | 0.793944i | \(-0.708024\pi\) |
0.793944 | + | 0.607991i | \(0.208024\pi\) | |||||||
\(314\) | − | 338.903i | − | 1.07931i | ||||||
\(315\) | 19.4515 | − | 69.5952i | 0.0617508 | − | 0.220937i | ||||
\(316\) | 134.568 | 0.425847 | ||||||||
\(317\) | 331.965 | + | 331.965i | 1.04721 | + | 1.04721i | 0.998829 | + | 0.0483793i | \(0.0154056\pi\) |
0.0483793 | + | 0.998829i | \(0.484594\pi\) | |||||||
\(318\) | −93.5205 | + | 93.5205i | −0.294089 | + | 0.294089i | ||||
\(319\) | − | 281.721i | − | 0.883138i | ||||||
\(320\) | 19.6268 | + | 34.8538i | 0.0613337 | + | 0.108918i | ||||
\(321\) | 95.9280 | 0.298841 | ||||||||
\(322\) | −23.1039 | − | 23.1039i | −0.0717511 | − | 0.0717511i | ||||
\(323\) | −13.1164 | + | 13.1164i | −0.0406079 | + | 0.0406079i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | −80.1093 | − | 326.906i | −0.246490 | − | 1.00587i | ||||
\(326\) | −250.699 | −0.769014 | ||||||||
\(327\) | 205.085 | + | 205.085i | 0.627172 | + | 0.627172i | ||||
\(328\) | 89.5169 | − | 89.5169i | 0.272917 | − | 0.272917i | ||||
\(329\) | − | 402.228i | − | 1.22258i | ||||||
\(330\) | 182.397 | − | 102.711i | 0.552719 | − | 0.311245i | ||||
\(331\) | 57.4084 | 0.173439 | 0.0867196 | − | 0.996233i | \(-0.472362\pi\) | ||||
0.0867196 | + | 0.996233i | \(0.472362\pi\) | |||||||
\(332\) | 16.8240 | + | 16.8240i | 0.0506748 | + | 0.0506748i | ||||
\(333\) | 1.76912 | − | 1.76912i | 0.00531267 | − | 0.00531267i | ||||
\(334\) | − | 297.682i | − | 0.891262i | ||||||
\(335\) | −593.684 | − | 165.932i | −1.77219 | − | 0.495319i | ||||
\(336\) | −33.3765 | −0.0993350 | ||||||||
\(337\) | 17.5680 | + | 17.5680i | 0.0521307 | + | 0.0521307i | 0.732692 | − | 0.680561i | \(-0.238264\pi\) |
−0.680561 | + | 0.732692i | \(0.738264\pi\) | |||||||
\(338\) | −12.2562 | + | 12.2562i | −0.0362611 | + | 0.0362611i | ||||
\(339\) | − | 143.045i | − | 0.421961i | ||||||
\(340\) | −4.68736 | + | 16.7708i | −0.0137864 | + | 0.0493259i | ||||
\(341\) | 361.265 | 1.05943 | ||||||||
\(342\) | 31.9567 | + | 31.9567i | 0.0934407 | + | 0.0934407i | ||||
\(343\) | −254.777 | + | 254.777i | −0.742789 | + | 0.742789i | ||||
\(344\) | 198.967i | 0.578391i | ||||||||
\(345\) | 20.3790 | + | 36.1897i | 0.0590696 | + | 0.104898i | ||||
\(346\) | −178.831 | −0.516854 | ||||||||
\(347\) | 71.5458 | + | 71.5458i | 0.206184 | + | 0.206184i | 0.802643 | − | 0.596459i | \(-0.203426\pi\) |
−0.596459 | + | 0.802643i | \(0.703426\pi\) | |||||||
\(348\) | 40.3750 | − | 40.3750i | 0.116020 | − | 0.116020i | ||||
\(349\) | 21.0922i | 0.0604360i | 0.999543 | + | 0.0302180i | \(0.00962015\pi\) | ||||
−0.999543 | + | 0.0302180i | \(0.990380\pi\) | |||||||
\(350\) | 145.642 | + | 88.3108i | 0.416119 | + | 0.252317i | ||||
\(351\) | 69.9565 | 0.199306 | ||||||||
\(352\) | −68.3663 | − | 68.3663i | −0.194223 | − | 0.194223i | ||||
\(353\) | 267.728 | − | 267.728i | 0.758436 | − | 0.758436i | −0.217601 | − | 0.976038i | \(-0.569823\pi\) |
0.976038 | + | 0.217601i | \(0.0698232\pi\) | |||||||
\(354\) | 40.4205i | 0.114182i | ||||||||
\(355\) | 78.8093 | − | 44.3788i | 0.221998 | − | 0.125011i | ||||
\(356\) | 89.6216 | 0.251746 | ||||||||
\(357\) | −10.2743 | − | 10.2743i | −0.0287796 | − | 0.0287796i | ||||
\(358\) | 82.4024 | − | 82.4024i | 0.230174 | − | 0.230174i | ||||
\(359\) | − | 184.468i | − | 0.513837i | −0.966433 | − | 0.256919i | \(-0.917293\pi\) | ||
0.966433 | − | 0.256919i | \(-0.0827073\pi\) | |||||||
\(360\) | 40.8605 | + | 11.4203i | 0.113501 | + | 0.0317231i | ||||
\(361\) | 247.530 | 0.685678 | ||||||||
\(362\) | 345.572 | + | 345.572i | 0.954620 | + | 0.954620i | ||||
\(363\) | −209.581 | + | 209.581i | −0.577358 | + | 0.577358i | ||||
\(364\) | − | 129.717i | − | 0.356366i | ||||||
\(365\) | 33.2553 | − | 118.983i | 0.0911103 | − | 0.325982i | ||||
\(366\) | 209.169 | 0.571499 | ||||||||
\(367\) | −370.206 | − | 370.206i | −1.00874 | − | 1.00874i | −0.999962 | − | 0.00877369i | \(-0.997207\pi\) |
−0.00877369 | − | 0.999962i | \(-0.502793\pi\) | |||||||
\(368\) | 13.5647 | − | 13.5647i | 0.0368605 | − | 0.0368605i | ||||
\(369\) | − | 134.275i | − | 0.363890i | ||||||
\(370\) | 2.89351 | + | 5.13838i | 0.00782029 | + | 0.0138875i | ||||
\(371\) | 260.116 | 0.701121 | ||||||||
\(372\) | 51.7749 | + | 51.7749i | 0.139180 | + | 0.139180i | ||||
\(373\) | 479.170 | − | 479.170i | 1.28464 | − | 1.28464i | 0.346638 | − | 0.937999i | \(-0.387323\pi\) |
0.937999 | − | 0.346638i | \(-0.112677\pi\) | |||||||
\(374\) | − | 42.0905i | − | 0.112542i | ||||||
\(375\) | −148.081 | − | 157.946i | −0.394884 | − | 0.421189i | ||||
\(376\) | 236.154 | 0.628070 | ||||||||
\(377\) | 156.916 | + | 156.916i | 0.416224 | + | 0.416224i | ||||
\(378\) | −25.0324 | + | 25.0324i | −0.0662233 | + | 0.0662233i | ||||
\(379\) | 415.235i | 1.09561i | 0.836607 | + | 0.547804i | \(0.184536\pi\) | ||||
−0.836607 | + | 0.547804i | \(0.815464\pi\) | |||||||
\(380\) | −92.8178 | + | 52.2673i | −0.244257 | + | 0.137545i | ||||
\(381\) | −94.8780 | −0.249024 | ||||||||
\(382\) | 263.122 | + | 263.122i | 0.688801 | + | 0.688801i | ||||
\(383\) | 445.768 | − | 445.768i | 1.16389 | − | 1.16389i | 0.180268 | − | 0.983617i | \(-0.442303\pi\) |
0.983617 | − | 0.180268i | \(-0.0576966\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | −396.497 | − | 110.819i | −1.02986 | − | 0.287842i | ||||
\(386\) | −281.749 | −0.729920 | ||||||||
\(387\) | 149.225 | + | 149.225i | 0.385594 | + | 0.385594i | ||||
\(388\) | −168.017 | + | 168.017i | −0.433034 | + | 0.433034i | ||||
\(389\) | 274.994i | 0.706925i | 0.935449 | + | 0.353462i | \(0.114996\pi\) | ||||
−0.935449 | + | 0.353462i | \(0.885004\pi\) | |||||||
\(390\) | −44.3847 | + | 158.803i | −0.113807 | + | 0.407188i | ||||
\(391\) | 8.35124 | 0.0213587 | ||||||||
\(392\) | −51.5836 | − | 51.5836i | −0.131591 | − | 0.131591i | ||||
\(393\) | −66.0299 | + | 66.0299i | −0.168015 | + | 0.168015i | ||||
\(394\) | 170.958i | 0.433903i | ||||||||
\(395\) | 165.070 | + | 293.137i | 0.417900 | + | 0.742119i | ||||
\(396\) | −102.550 | −0.258963 | ||||||||
\(397\) | 23.6184 | + | 23.6184i | 0.0594921 | + | 0.0594921i | 0.736227 | − | 0.676735i | \(-0.236606\pi\) |
−0.676735 | + | 0.736227i | \(0.736606\pi\) | |||||||
\(398\) | 234.435 | − | 234.435i | 0.589032 | − | 0.589032i | ||||
\(399\) | − | 88.8837i | − | 0.222766i | ||||||
\(400\) | −51.8487 | + | 85.5085i | −0.129622 | + | 0.213771i | ||||
\(401\) | 673.867 | 1.68047 | 0.840233 | − | 0.542225i | \(-0.182418\pi\) | ||||
0.840233 | + | 0.542225i | \(0.182418\pi\) | |||||||
\(402\) | 213.540 | + | 213.540i | 0.531194 | + | 0.531194i | ||||
\(403\) | −201.222 | + | 201.222i | −0.499310 | + | 0.499310i | ||||
\(404\) | 220.532i | 0.545871i | ||||||||
\(405\) | 39.2106 | − | 22.0801i | 0.0968162 | − | 0.0545188i | ||||
\(406\) | −112.298 | −0.276597 | ||||||||
\(407\) | −10.0790 | − | 10.0790i | −0.0247642 | − | 0.0247642i | ||||
\(408\) | 6.03223 | − | 6.03223i | 0.0147849 | − | 0.0147849i | ||||
\(409\) | 37.4601i | 0.0915894i | 0.998951 | + | 0.0457947i | \(0.0145820\pi\) | ||||
−0.998951 | + | 0.0457947i | \(0.985418\pi\) | |||||||
\(410\) | 304.809 | + | 85.1925i | 0.743435 | + | 0.207787i | ||||
\(411\) | 189.791 | 0.461778 | ||||||||
\(412\) | 206.726 | + | 206.726i | 0.501761 | + | 0.501761i | ||||
\(413\) | 56.2124 | − | 56.2124i | 0.136107 | − | 0.136107i | ||||
\(414\) | − | 20.3470i | − | 0.0491473i | ||||||
\(415\) | −16.0113 | + | 57.2865i | −0.0385815 | + | 0.138040i | ||||
\(416\) | 76.1590 | 0.183075 | ||||||||
\(417\) | 48.3864 | + | 48.3864i | 0.116035 | + | 0.116035i | ||||
\(418\) | 182.064 | − | 182.064i | 0.435559 | − | 0.435559i | ||||
\(419\) | − | 251.336i | − | 0.599846i | −0.953963 | − | 0.299923i | \(-0.903039\pi\) | ||
0.953963 | − | 0.299923i | \(-0.0969610\pi\) | |||||||
\(420\) | −40.9421 | − | 72.7063i | −0.0974812 | − | 0.173110i | ||||
\(421\) | 555.687 | 1.31992 | 0.659961 | − | 0.751300i | \(-0.270573\pi\) | ||||
0.659961 | + | 0.751300i | \(0.270573\pi\) | |||||||
\(422\) | 145.969 | + | 145.969i | 0.345897 | + | 0.345897i | ||||
\(423\) | 177.116 | − | 177.116i | 0.418714 | − | 0.418714i | ||||
\(424\) | 152.718i | 0.360185i | ||||||||
\(425\) | −42.2828 | + | 10.3615i | −0.0994890 | + | 0.0243801i | ||||
\(426\) | −44.3090 | −0.104012 | ||||||||
\(427\) | −290.889 | − | 290.889i | −0.681238 | − | 0.681238i | ||||
\(428\) | 78.3249 | − | 78.3249i | 0.183002 | − | 0.183002i | ||||
\(429\) | − | 398.556i | − | 0.929035i | ||||||
\(430\) | −433.422 | + | 244.067i | −1.00796 | + | 0.567598i | ||||
\(431\) | −61.4001 | −0.142460 | −0.0712298 | − | 0.997460i | \(-0.522692\pi\) | ||||
−0.0712298 | + | 0.997460i | \(0.522692\pi\) | |||||||
\(432\) | −14.6969 | − | 14.6969i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | 449.062 | − | 449.062i | 1.03709 | − | 1.03709i | 0.0378095 | − | 0.999285i | \(-0.487962\pi\) |
0.999285 | − | 0.0378095i | \(-0.0120380\pi\) | |||||||
\(434\) | − | 144.006i | − | 0.331810i | ||||||
\(435\) | 137.478 | + | 38.4246i | 0.316042 | + | 0.0883323i | ||||
\(436\) | 334.903 | 0.768126 | ||||||||
\(437\) | 36.1235 | + | 36.1235i | 0.0826625 | + | 0.0826625i | ||||
\(438\) | −42.7967 | + | 42.7967i | −0.0977093 | + | 0.0977093i | ||||
\(439\) | − | 522.143i | − | 1.18939i | −0.803951 | − | 0.594695i | \(-0.797273\pi\) | ||
0.803951 | − | 0.594695i | \(-0.202727\pi\) | |||||||
\(440\) | 65.0637 | − | 232.790i | 0.147872 | − | 0.529068i | ||||
\(441\) | −77.3754 | −0.175454 | ||||||||
\(442\) | 23.4441 | + | 23.4441i | 0.0530410 | + | 0.0530410i | ||||
\(443\) | −170.957 | + | 170.957i | −0.385907 | + | 0.385907i | −0.873225 | − | 0.487318i | \(-0.837975\pi\) |
0.487318 | + | 0.873225i | \(0.337975\pi\) | |||||||
\(444\) | − | 2.88896i | − | 0.00650667i | ||||||
\(445\) | 109.936 | + | 195.228i | 0.247048 | + | 0.438716i | ||||
\(446\) | 455.468 | 1.02123 | ||||||||
\(447\) | −152.526 | − | 152.526i | −0.341221 | − | 0.341221i | ||||
\(448\) | −27.2518 | + | 27.2518i | −0.0608300 | + | 0.0608300i | ||||
\(449\) | − | 129.721i | − | 0.288912i | −0.989511 | − | 0.144456i | \(-0.953857\pi\) | ||
0.989511 | − | 0.144456i | \(-0.0461432\pi\) | |||||||
\(450\) | 25.2448 | + | 103.018i | 0.0560997 | + | 0.228929i | ||||
\(451\) | −764.993 | −1.69622 | ||||||||
\(452\) | −116.796 | − | 116.796i | −0.258397 | − | 0.258397i | ||||
\(453\) | −122.793 | + | 122.793i | −0.271066 | + | 0.271066i | ||||
\(454\) | 127.231i | 0.280245i | ||||||||
\(455\) | 282.571 | − | 159.121i | 0.621036 | − | 0.349715i | ||||
\(456\) | 52.1851 | 0.114441 | ||||||||
\(457\) | 487.821 | + | 487.821i | 1.06744 | + | 1.06744i | 0.997555 | + | 0.0698870i | \(0.0222639\pi\) |
0.0698870 | + | 0.997555i | \(0.477736\pi\) | |||||||
\(458\) | −173.353 | + | 173.353i | −0.378500 | + | 0.378500i | ||||
\(459\) | − | 9.04834i | − | 0.0197132i | ||||||
\(460\) | 46.1882 | + | 12.9094i | 0.100409 | + | 0.0280639i | ||||
\(461\) | 10.8881 | 0.0236185 | 0.0118093 | − | 0.999930i | \(-0.496241\pi\) | ||||
0.0118093 | + | 0.999930i | \(0.496241\pi\) | |||||||
\(462\) | 142.615 | + | 142.615i | 0.308689 | + | 0.308689i | ||||
\(463\) | −400.834 | + | 400.834i | −0.865732 | + | 0.865732i | −0.991997 | − | 0.126265i | \(-0.959701\pi\) |
0.126265 | + | 0.991997i | \(0.459701\pi\) | |||||||
\(464\) | − | 65.9321i | − | 0.142095i | ||||||
\(465\) | −49.2738 | + | 176.296i | −0.105965 | + | 0.379130i | ||||
\(466\) | −257.803 | −0.553225 | ||||||||
\(467\) | 108.014 | + | 108.014i | 0.231293 | + | 0.231293i | 0.813232 | − | 0.581939i | \(-0.197706\pi\) |
−0.581939 | + | 0.813232i | \(0.697706\pi\) | |||||||
\(468\) | 57.1193 | − | 57.1193i | 0.122050 | − | 0.122050i | ||||
\(469\) | − | 593.935i | − | 1.26639i | ||||||
\(470\) | 289.684 | + | 514.431i | 0.616350 | + | 1.09453i | ||||
\(471\) | −415.070 | −0.881252 | ||||||||
\(472\) | 33.0032 | + | 33.0032i | 0.0699220 | + | 0.0699220i | ||||
\(473\) | 850.163 | − | 850.163i | 1.79739 | − | 1.79739i | ||||
\(474\) | − | 164.811i | − | 0.347702i | ||||||
\(475\) | −227.714 | − | 138.076i | −0.479399 | − | 0.290687i | ||||
\(476\) | −16.7779 | −0.0352477 | ||||||||
\(477\) | 114.539 | + | 114.539i | 0.240123 | + | 0.240123i | ||||
\(478\) | −198.218 | + | 198.218i | −0.414683 | + | 0.414683i | ||||
\(479\) | − | 517.840i | − | 1.08109i | −0.841316 | − | 0.540543i | \(-0.818219\pi\) | ||
0.841316 | − | 0.540543i | \(-0.181781\pi\) | |||||||
\(480\) | 42.6871 | − | 24.0378i | 0.0889314 | − | 0.0500787i | ||||
\(481\) | 11.2279 | 0.0233428 | ||||||||
\(482\) | −134.329 | − | 134.329i | −0.278690 | − | 0.278690i | ||||
\(483\) | −28.2963 | + | 28.2963i | −0.0585846 | + | 0.0585846i | ||||
\(484\) | 342.244i | 0.707117i | ||||||||
\(485\) | −572.105 | − | 159.900i | −1.17960 | − | 0.329692i | ||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | 389.872 | + | 389.872i | 0.800559 | + | 0.800559i | 0.983183 | − | 0.182623i | \(-0.0584589\pi\) |
−0.182623 | + | 0.983183i | \(0.558459\pi\) | |||||||
\(488\) | 170.786 | − | 170.786i | 0.349970 | − | 0.349970i | ||||
\(489\) | 307.042i | 0.627897i | ||||||||
\(490\) | 49.0917 | − | 175.644i | 0.100187 | − | 0.358457i | ||||
\(491\) | 559.841 | 1.14021 | 0.570103 | − | 0.821573i | \(-0.306903\pi\) | ||||
0.570103 | + | 0.821573i | \(0.306903\pi\) | |||||||
\(492\) | −109.635 | − | 109.635i | −0.222836 | − | 0.222836i | ||||
\(493\) | 20.2959 | − | 20.2959i | 0.0411682 | − | 0.0411682i | ||||
\(494\) | 202.816i | 0.410559i | ||||||||
\(495\) | −125.795 | − | 223.390i | −0.254131 | − | 0.451293i | ||||
\(496\) | 84.5481 | 0.170460 | ||||||||
\(497\) | 61.6201 | + | 61.6201i | 0.123984 | + | 0.123984i | ||||
\(498\) | 20.6052 | − | 20.6052i | 0.0413758 | − | 0.0413758i | ||||
\(499\) | 528.700i | 1.05952i | 0.848148 | + | 0.529760i | \(0.177718\pi\) | ||||
−0.848148 | + | 0.529760i | \(0.822282\pi\) | |||||||
\(500\) | −249.870 | − | 8.05443i | −0.499740 | − | 0.0161089i | ||||
\(501\) | −364.584 | −0.727713 | ||||||||
\(502\) | 85.1879 | + | 85.1879i | 0.169697 | + | 0.169697i | ||||
\(503\) | 424.981 | − | 424.981i | 0.844892 | − | 0.844892i | −0.144599 | − | 0.989490i | \(-0.546189\pi\) |
0.989490 | + | 0.144599i | \(0.0461891\pi\) | |||||||
\(504\) | 40.8778i | 0.0811067i | ||||||||
\(505\) | −480.399 | + | 270.521i | −0.951285 | + | 0.535684i | ||||
\(506\) | −115.921 | −0.229092 | ||||||||
\(507\) | 15.0108 | + | 15.0108i | 0.0296071 | + | 0.0296071i | ||||
\(508\) | −77.4676 | + | 77.4676i | −0.152495 | + | 0.152495i | ||||
\(509\) | − | 273.415i | − | 0.537161i | −0.963257 | − | 0.268580i | \(-0.913445\pi\) | ||
0.963257 | − | 0.268580i | \(-0.0865545\pi\) | |||||||
\(510\) | 20.5400 | + | 5.74082i | 0.0402744 | + | 0.0112565i | ||||
\(511\) | 119.034 | 0.232943 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 39.1388 | − | 39.1388i | 0.0762940 | − | 0.0762940i | ||||
\(514\) | 178.347i | 0.346979i | ||||||||
\(515\) | −196.739 | + | 703.909i | −0.382018 | + | 1.36681i | ||||
\(516\) | 243.683 | 0.472254 | ||||||||
\(517\) | −1009.06 | − | 1009.06i | −1.95177 | − | 1.95177i | ||||
\(518\) | −4.01765 | + | 4.01765i | −0.00775607 | + | 0.00775607i | ||||
\(519\) | 219.023i | 0.422009i | ||||||||
\(520\) | 93.4223 | + | 165.902i | 0.179658 | + | 0.319043i | ||||
\(521\) | −17.9068 | −0.0343701 | −0.0171850 | − | 0.999852i | \(-0.505470\pi\) | ||||
−0.0171850 | + | 0.999852i | \(0.505470\pi\) | |||||||
\(522\) | −49.4491 | − | 49.4491i | −0.0947300 | − | 0.0947300i | ||||
\(523\) | −709.418 | + | 709.418i | −1.35644 | + | 1.35644i | −0.478176 | + | 0.878264i | \(0.658702\pi\) |
−0.878264 | + | 0.478176i | \(0.841298\pi\) | |||||||
\(524\) | 107.826i | 0.205776i | ||||||||
\(525\) | 108.158 | − | 178.374i | 0.206016 | − | 0.339759i | ||||
\(526\) | −246.417 | −0.468473 | ||||||||
\(527\) | 26.0265 | + | 26.0265i | 0.0493862 | + | 0.0493862i | ||||
\(528\) | −83.7313 | + | 83.7313i | −0.158582 | + | 0.158582i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | −332.676 | + | 187.335i | −0.627691 | + | 0.353463i | ||||
\(531\) | 49.5048 | 0.0932294 | ||||||||
\(532\) | −72.5733 | − | 72.5733i | −0.136416 | − | 0.136416i | ||||
\(533\) | 426.095 | − | 426.095i | 0.799428 | − | 0.799428i | ||||
\(534\) | − | 109.764i | − | 0.205550i | ||||||
\(535\) | 266.699 | + | 74.5411i | 0.498503 | + | 0.139329i | ||||
\(536\) | 348.709 | 0.650577 | ||||||||
\(537\) | −100.922 | − | 100.922i | −0.187937 | − | 0.187937i | ||||
\(538\) | −159.070 | + | 159.070i | −0.295670 | + | 0.295670i | ||||
\(539\) | 440.823i | 0.817853i | ||||||||
\(540\) | 13.9870 | − | 50.0436i | 0.0259018 | − | 0.0926734i | ||||
\(541\) | −755.019 | −1.39560 | −0.697799 | − | 0.716293i | \(-0.745837\pi\) | ||||
−0.697799 | + | 0.716293i | \(0.745837\pi\) | |||||||
\(542\) | −262.498 | − | 262.498i | −0.484313 | − | 0.484313i | ||||
\(543\) | 423.238 | − | 423.238i | 0.779444 | − | 0.779444i | ||||
\(544\) | − | 9.85059i | − | 0.0181077i | ||||||
\(545\) | 410.816 | + | 729.540i | 0.753791 | + | 1.33861i | ||||
\(546\) | −158.870 | −0.290971 | ||||||||
\(547\) | −90.7385 | − | 90.7385i | −0.165884 | − | 0.165884i | 0.619283 | − | 0.785167i | \(-0.287423\pi\) |
−0.785167 | + | 0.619283i | \(0.787423\pi\) | |||||||
\(548\) | 154.964 | − | 154.964i | 0.282780 | − | 0.282780i | ||||
\(549\) | − | 256.178i | − | 0.466627i | ||||||
\(550\) | 586.913 | − | 143.825i | 1.06712 | − | 0.261500i | ||||
\(551\) | 175.581 | 0.318659 | ||||||||
\(552\) | −16.6132 | − | 16.6132i | −0.0300965 | − | 0.0300965i | ||||
\(553\) | −229.201 | + | 229.201i | −0.414468 | + | 0.414468i | ||||
\(554\) | − | 499.534i | − | 0.901686i | ||||||
\(555\) | 6.29321 | − | 3.54381i | 0.0113391 | − | 0.00638524i | ||||
\(556\) | 79.0147 | 0.142113 | ||||||||
\(557\) | 305.442 | + | 305.442i | 0.548370 | + | 0.548370i | 0.925969 | − | 0.377599i | \(-0.123250\pi\) |
−0.377599 | + | 0.925969i | \(0.623250\pi\) | |||||||
\(558\) | 63.4111 | − | 63.4111i | 0.113640 | − | 0.113640i | ||||
\(559\) | 947.069i | 1.69422i | ||||||||
\(560\) | −92.7935 | − | 25.9353i | −0.165703 | − | 0.0463131i | ||||
\(561\) | −51.5502 | −0.0918898 | ||||||||
\(562\) | −312.983 | − | 312.983i | −0.556910 | − | 0.556910i | ||||
\(563\) | 357.189 | − | 357.189i | 0.634438 | − | 0.634438i | −0.314740 | − | 0.949178i | \(-0.601917\pi\) |
0.949178 | + | 0.314740i | \(0.101917\pi\) | |||||||
\(564\) | − | 289.229i | − | 0.512817i | ||||||
\(565\) | 111.153 | − | 397.693i | 0.196732 | − | 0.703882i | ||||
\(566\) | 609.577 | 1.07699 | ||||||||
\(567\) | 30.6583 | + | 30.6583i | 0.0540711 | + | 0.0540711i | ||||
\(568\) | −36.1782 | + | 36.1782i | −0.0636940 | + | 0.0636940i | ||||
\(569\) | 661.718i | 1.16295i | 0.813565 | + | 0.581474i | \(0.197524\pi\) | ||||
−0.813565 | + | 0.581474i | \(0.802476\pi\) | |||||||
\(570\) | 64.0141 | + | 113.678i | 0.112305 | + | 0.199435i | ||||
\(571\) | 806.448 | 1.41234 | 0.706172 | − | 0.708041i | \(-0.250421\pi\) | ||||
0.706172 | + | 0.708041i | \(0.250421\pi\) | |||||||
\(572\) | −325.420 | − | 325.420i | −0.568916 | − | 0.568916i | ||||
\(573\) | 322.257 | − | 322.257i | 0.562404 | − | 0.562404i | ||||
\(574\) | 304.938i | 0.531250i | ||||||||
\(575\) | 28.5365 | + | 116.450i | 0.0496287 | + | 0.202522i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 308.495 | + | 308.495i | 0.534654 | + | 0.534654i | 0.921954 | − | 0.387300i | \(-0.126592\pi\) |
−0.387300 | + | 0.921954i | \(0.626592\pi\) | |||||||
\(578\) | −285.968 | + | 285.968i | −0.494754 | + | 0.494754i | ||||
\(579\) | 345.071i | 0.595977i | ||||||||
\(580\) | 143.624 | − | 80.8772i | 0.247628 | − | 0.139443i | ||||
\(581\) | −57.3108 | −0.0986416 | ||||||||
\(582\) | 205.778 | + | 205.778i | 0.353571 | + | 0.353571i | ||||
\(583\) | 652.549 | − | 652.549i | 1.11930 | − | 1.11930i | ||||
\(584\) | 69.8867i | 0.119669i | ||||||||
\(585\) | 194.493 | + | 54.3599i | 0.332467 | + | 0.0929230i | ||||
\(586\) | 684.964 | 1.16888 | ||||||||
\(587\) | 266.598 | + | 266.598i | 0.454170 | + | 0.454170i | 0.896736 | − | 0.442566i | \(-0.145932\pi\) |
−0.442566 | + | 0.896736i | \(0.645932\pi\) | |||||||
\(588\) | −63.1767 | + | 63.1767i | −0.107443 | + | 0.107443i | ||||
\(589\) | 225.157i | 0.382269i | ||||||||
\(590\) | −31.4089 | + | 112.377i | −0.0532354 | + | 0.190470i | ||||
\(591\) | 209.380 | 0.354281 | ||||||||
\(592\) | −2.35883 | − | 2.35883i | −0.00398450 | − | 0.00398450i | ||||
\(593\) | −167.862 | + | 167.862i | −0.283073 | + | 0.283073i | −0.834333 | − | 0.551260i | \(-0.814147\pi\) |
0.551260 | + | 0.834333i | \(0.314147\pi\) | |||||||
\(594\) | 125.597i | 0.211443i | ||||||||
\(595\) | −20.5810 | − | 36.5484i | −0.0345899 | − | 0.0614259i | ||||
\(596\) | −249.074 | −0.417909 | ||||||||
\(597\) | −287.123 | − | 287.123i | −0.480942 | − | 0.480942i | ||||
\(598\) | 64.5670 | − | 64.5670i | 0.107972 | − | 0.107972i | ||||
\(599\) | 356.744i | 0.595566i | 0.954634 | + | 0.297783i | \(0.0962472\pi\) | ||||
−0.954634 | + | 0.297783i | \(0.903753\pi\) | |||||||
\(600\) | 104.726 | + | 63.5015i | 0.174544 | + | 0.105836i | ||||
\(601\) | −18.7334 | −0.0311704 | −0.0155852 | − | 0.999879i | \(-0.504961\pi\) | ||||
−0.0155852 | + | 0.999879i | \(0.504961\pi\) | |||||||
\(602\) | −338.888 | − | 338.888i | −0.562936 | − | 0.562936i | ||||
\(603\) | 261.532 | − | 261.532i | 0.433718 | − | 0.433718i | ||||
\(604\) | 200.520i | 0.331986i | ||||||||
\(605\) | −745.533 | + | 419.822i | −1.23229 | + | 0.693921i | ||||
\(606\) | 270.095 | 0.445702 | ||||||||
\(607\) | 325.300 | + | 325.300i | 0.535914 | + | 0.535914i | 0.922326 | − | 0.386412i | \(-0.126286\pi\) |
−0.386412 | + | 0.922326i | \(0.626286\pi\) | |||||||
\(608\) | 42.6090 | − | 42.6090i | 0.0700805 | − | 0.0700805i | ||||
\(609\) | 137.537i | 0.225840i | ||||||||
\(610\) | 581.531 | + | 162.535i | 0.953330 | + | 0.266451i | ||||
\(611\) | 1124.08 | 1.83974 | ||||||||
\(612\) | −7.38794 | − | 7.38794i | −0.0120718 | − | 0.0120718i | ||||
\(613\) | −572.991 | + | 572.991i | −0.934733 | + | 0.934733i | −0.997997 | − | 0.0632636i | \(-0.979849\pi\) |
0.0632636 | + | 0.997997i | \(0.479849\pi\) | |||||||
\(614\) | − | 485.079i | − | 0.790030i | ||||||
\(615\) | 104.339 | − | 373.313i | 0.169657 | − | 0.607013i | ||||
\(616\) | 232.889 | 0.378066 | ||||||||
\(617\) | −136.873 | − | 136.873i | −0.221836 | − | 0.221836i | 0.587435 | − | 0.809271i | \(-0.300138\pi\) |
−0.809271 | + | 0.587435i | \(0.800138\pi\) | |||||||
\(618\) | 253.186 | − | 253.186i | 0.409686 | − | 0.409686i | ||||
\(619\) | 1159.59i | 1.87333i | 0.350221 | + | 0.936667i | \(0.386106\pi\) | ||||
−0.350221 | + | 0.936667i | \(0.613894\pi\) | |||||||
\(620\) | 103.713 | + | 184.177i | 0.167279 | + | 0.297059i | ||||
\(621\) | −24.9199 | −0.0401286 | ||||||||
\(622\) | 486.480 | + | 486.480i | 0.782122 | + | 0.782122i | ||||
\(623\) | −152.647 | + | 152.647i | −0.245019 | + | 0.245019i | ||||
\(624\) | − | 93.2754i | − | 0.149480i | ||||||
\(625\) | −288.964 | − | 554.189i | −0.462342 | − | 0.886702i | ||||
\(626\) | −116.406 | −0.185953 | ||||||||
\(627\) | −222.981 | − | 222.981i | −0.355632 | − | 0.355632i | ||||
\(628\) | −338.903 | + | 338.903i | −0.539655 | + | 0.539655i | ||||
\(629\) | − | 1.45224i | − | 0.00230881i | ||||||
\(630\) | −89.0467 | + | 50.1436i | −0.141344 | + | 0.0795931i | ||||
\(631\) | −625.005 | −0.990500 | −0.495250 | − | 0.868751i | \(-0.664924\pi\) | ||||
−0.495250 | + | 0.868751i | \(0.664924\pi\) | |||||||
\(632\) | −134.568 | − | 134.568i | −0.212923 | − | 0.212923i | ||||
\(633\) | 178.774 | − | 178.774i | 0.282424 | − | 0.282424i | ||||
\(634\) | − | 663.930i | − | 1.04721i | ||||||
\(635\) | −263.780 | − | 73.7252i | −0.415402 | − | 0.116103i | ||||
\(636\) | 187.041 | 0.294089 | ||||||||
\(637\) | −245.535 | − | 245.535i | −0.385455 | − | 0.385455i | ||||
\(638\) | −281.721 | + | 281.721i | −0.441569 | + | 0.441569i | ||||
\(639\) | 54.2673i | 0.0849253i | ||||||||
\(640\) | 15.2271 | − | 54.4806i | 0.0237923 | − | 0.0851259i | ||||
\(641\) | −73.3454 | −0.114423 | −0.0572117 | − | 0.998362i | \(-0.518221\pi\) | ||||
−0.0572117 | + | 0.998362i | \(0.518221\pi\) | |||||||
\(642\) | −95.9280 | − | 95.9280i | −0.149421 | − | 0.149421i | ||||
\(643\) | −268.941 | + | 268.941i | −0.418260 | + | 0.418260i | −0.884604 | − | 0.466343i | \(-0.845571\pi\) |
0.466343 | + | 0.884604i | \(0.345571\pi\) | |||||||
\(644\) | 46.2077i | 0.0717511i | ||||||||
\(645\) | 298.920 | + | 530.831i | 0.463441 | + | 0.822994i | ||||
\(646\) | 26.2327 | 0.0406079 | ||||||||
\(647\) | −529.742 | − | 529.742i | −0.818767 | − | 0.818767i | 0.167162 | − | 0.985929i | \(-0.446540\pi\) |
−0.985929 | + | 0.167162i | \(0.946540\pi\) | |||||||
\(648\) | −18.0000 | + | 18.0000i | −0.0277778 | + | 0.0277778i | ||||
\(649\) | − | 282.039i | − | 0.434574i | ||||||
\(650\) | −246.797 | + | 407.015i | −0.379687 | + | 0.626178i | ||||
\(651\) | −176.370 | −0.270922 | ||||||||
\(652\) | 250.699 | + | 250.699i | 0.384507 | + | 0.384507i | ||||
\(653\) | −541.919 | + | 541.919i | −0.829891 | + | 0.829891i | −0.987501 | − | 0.157610i | \(-0.949621\pi\) |
0.157610 | + | 0.987501i | \(0.449621\pi\) | |||||||
\(654\) | − | 410.170i | − | 0.627172i | ||||||
\(655\) | −234.885 | + | 132.268i | −0.358604 | + | 0.201936i | ||||
\(656\) | −179.034 | −0.272917 | ||||||||
\(657\) | 52.4150 | + | 52.4150i | 0.0797793 | + | 0.0797793i | ||||
\(658\) | −402.228 | + | 402.228i | −0.611288 | + | 0.611288i | ||||
\(659\) | 631.568i | 0.958374i | 0.877713 | + | 0.479187i | \(0.159068\pi\) | ||||
−0.877713 | + | 0.479187i | \(0.840932\pi\) | |||||||
\(660\) | −285.108 | − | 79.6864i | −0.431982 | − | 0.120737i | ||||
\(661\) | −556.971 | −0.842618 | −0.421309 | − | 0.906917i | \(-0.638429\pi\) | ||||
−0.421309 | + | 0.906917i | \(0.638429\pi\) | |||||||
\(662\) | −57.4084 | − | 57.4084i | −0.0867196 | − | 0.0867196i | ||||
\(663\) | 28.7130 | − | 28.7130i | 0.0433078 | − | 0.0433078i | ||||
\(664\) | − | 33.6481i | − | 0.0506748i | ||||||
\(665\) | 69.0674 | − | 247.115i | 0.103861 | − | 0.371601i | ||||
\(666\) | −3.53824 | −0.00531267 | ||||||||
\(667\) | −55.8967 | − | 55.8967i | −0.0838031 | − | 0.0838031i | ||||
\(668\) | −297.682 | + | 297.682i | −0.445631 | + | 0.445631i | ||||
\(669\) | − | 557.832i | − | 0.833830i | ||||||
\(670\) | 427.752 | + | 759.616i | 0.638436 | + | 1.13376i | ||||
\(671\) | −1459.50 | −2.17511 | ||||||||
\(672\) | 33.3765 | + | 33.3765i | 0.0496675 | + | 0.0496675i | ||||
\(673\) | −52.4456 | + | 52.4456i | −0.0779280 | + | 0.0779280i | −0.744996 | − | 0.667068i | \(-0.767549\pi\) |
0.667068 | + | 0.744996i | \(0.267549\pi\) | |||||||
\(674\) | − | 35.1361i | − | 0.0521307i | ||||||
\(675\) | 126.171 | − | 30.9185i | 0.186920 | − | 0.0458052i | ||||
\(676\) | 24.5125 | 0.0362611 | ||||||||
\(677\) | −82.3557 | − | 82.3557i | −0.121648 | − | 0.121648i | 0.643662 | − | 0.765310i | \(-0.277414\pi\) |
−0.765310 | + | 0.643662i | \(0.777414\pi\) | |||||||
\(678\) | −143.045 | + | 143.045i | −0.210980 | + | 0.210980i | ||||
\(679\) | − | 572.347i | − | 0.842926i | ||||||
\(680\) | 21.4582 | − | 12.0835i | 0.0315561 | − | 0.0177698i | ||||
\(681\) | 155.826 | 0.228819 | ||||||||
\(682\) | −361.265 | − | 361.265i | −0.529714 | − | 0.529714i | ||||
\(683\) | 532.493 | − | 532.493i | 0.779639 | − | 0.779639i | −0.200131 | − | 0.979769i | \(-0.564137\pi\) |
0.979769 | + | 0.200131i | \(0.0641367\pi\) | |||||||
\(684\) | − | 63.9134i | − | 0.0934407i | ||||||
\(685\) | 527.657 | + | 147.478i | 0.770302 | + | 0.215296i | ||||
\(686\) | 509.553 | 0.742789 | ||||||||
\(687\) | 212.313 | + | 212.313i | 0.309044 | + | 0.309044i | ||||
\(688\) | 198.967 | − | 198.967i | 0.289196 | − | 0.289196i | ||||
\(689\) | 726.930i | 1.05505i | ||||||||
\(690\) | 15.8107 | − | 56.5687i | 0.0229140 | − | 0.0819837i | ||||
\(691\) | −1042.26 | −1.50834 | −0.754171 | − | 0.656678i | \(-0.771961\pi\) | ||||
−0.754171 | + | 0.656678i | \(0.771961\pi\) | |||||||
\(692\) | 178.831 | + | 178.831i | 0.258427 | + | 0.258427i | ||||
\(693\) | 174.666 | − | 174.666i | 0.252044 | − | 0.252044i | ||||
\(694\) | − | 143.092i | − | 0.206184i | ||||||
\(695\) | 96.9252 | + | 172.123i | 0.139461 | + | 0.247659i | ||||
\(696\) | −80.7500 | −0.116020 | ||||||||
\(697\) | −55.1121 | − | 55.1121i | −0.0790705 | − | 0.0790705i | ||||
\(698\) | 21.0922 | − | 21.0922i | 0.0302180 | − | 0.0302180i | ||||
\(699\) | 315.743i | 0.451707i | ||||||||
\(700\) | −57.3307 | − | 233.952i | −0.0819010 | − | 0.334218i | ||||
\(701\) | 910.607 | 1.29901 | 0.649506 | − | 0.760357i | \(-0.274976\pi\) | ||||
0.649506 | + | 0.760357i | \(0.274976\pi\) | |||||||
\(702\) | −69.9565 | − | 69.9565i | −0.0996532 | − | 0.0996532i | ||||
\(703\) | 6.28169 | − | 6.28169i | 0.00893555 | − | 0.00893555i | ||||
\(704\) | 136.733i | 0.194223i | ||||||||
\(705\) | 630.046 | − | 354.789i | 0.893683 | − | 0.503247i | ||||
\(706\) | −535.456 | −0.758436 | ||||||||
\(707\) | −375.619 | − | 375.619i | −0.531285 | − | 0.531285i | ||||
\(708\) | 40.4205 | − | 40.4205i | 0.0570911 | − | 0.0570911i | ||||
\(709\) | − | 1061.58i | − | 1.49729i | −0.662970 | − | 0.748646i | \(-0.730704\pi\) | ||
0.662970 | − | 0.748646i | \(-0.269296\pi\) | |||||||
\(710\) | −123.188 | − | 34.4305i | −0.173504 | − | 0.0484936i | ||||
\(711\) | −201.851 | −0.283898 | ||||||||
\(712\) | −89.6216 | − | 89.6216i | −0.125873 | − | 0.125873i | ||||
\(713\) | 71.6791 | − | 71.6791i | 0.100532 | − | 0.100532i | ||||
\(714\) | 20.5487i | 0.0287796i | ||||||||
\(715\) | 309.699 | − | 1108.07i | 0.433146 | − | 1.54974i | ||||
\(716\) | −164.805 | −0.230174 | ||||||||
\(717\) | 242.767 | + | 242.767i | 0.338587 | + | 0.338587i | ||||
\(718\) | −184.468 | + | 184.468i | −0.256919 | + | 0.256919i | ||||
\(719\) | − | 126.651i | − | 0.176149i | −0.996114 | − | 0.0880745i | \(-0.971929\pi\) | ||
0.996114 | − | 0.0880745i | \(-0.0280714\pi\) | |||||||
\(720\) | −29.4402 | − | 52.2808i | −0.0408891 | − | 0.0726122i | ||||
\(721\) | −704.207 | −0.976708 | ||||||||
\(722\) | −247.530 | − | 247.530i | −0.342839 | − | 0.342839i | ||||
\(723\) | −164.518 | + | 164.518i | −0.227550 | + | 0.227550i | ||||
\(724\) | − | 691.145i | − | 0.954620i | ||||||
\(725\) | 352.360 | + | 213.656i | 0.486014 | + | 0.294698i | ||||
\(726\) | 419.162 | 0.577358 | ||||||||
\(727\) | −629.310 | − | 629.310i | −0.865626 | − | 0.865626i | 0.126358 | − | 0.991985i | \(-0.459671\pi\) |
−0.991985 | + | 0.126358i | \(0.959671\pi\) | |||||||
\(728\) | −129.717 | + | 129.717i | −0.178183 | + | 0.178183i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | −152.239 | + | 85.7281i | −0.208546 | + | 0.117436i | ||||
\(731\) | 122.496 | 0.167573 | ||||||||
\(732\) | −209.169 | − | 209.169i | −0.285750 | − | 0.285750i | ||||
\(733\) | −618.111 | + | 618.111i | −0.843262 | + | 0.843262i | −0.989282 | − | 0.146020i | \(-0.953354\pi\) |
0.146020 | + | 0.989282i | \(0.453354\pi\) | |||||||
\(734\) | 740.412i | 1.00874i | ||||||||
\(735\) | −215.119 | − | 60.1248i | −0.292679 | − | 0.0818024i | ||||
\(736\) | −27.1293 | −0.0368605 | ||||||||
\(737\) | −1490.00 | − | 1490.00i | −2.02171 | − | 2.02171i | ||||
\(738\) | −134.275 | + | 134.275i | −0.181945 | + | 0.181945i | ||||
\(739\) | − | 736.343i | − | 0.996405i | −0.867061 | − | 0.498202i | \(-0.833994\pi\) | ||
0.867061 | − | 0.498202i | \(-0.166006\pi\) | |||||||
\(740\) | 2.24487 | − | 8.03189i | 0.00303361 | − | 0.0108539i | ||||
\(741\) | 248.398 | 0.335220 | ||||||||
\(742\) | −260.116 | − | 260.116i | −0.350560 | − | 0.350560i | ||||
\(743\) | −276.121 | + | 276.121i | −0.371630 | + | 0.371630i | −0.868071 | − | 0.496441i | \(-0.834640\pi\) |
0.496441 | + | 0.868071i | \(0.334640\pi\) | |||||||
\(744\) | − | 103.550i | − | 0.139180i | ||||||
\(745\) | −305.532 | − | 542.573i | −0.410110 | − | 0.728286i | ||||
\(746\) | −958.339 | −1.28464 | ||||||||
\(747\) | −25.2361 | − | 25.2361i | −0.0337832 | − | 0.0337832i | ||||
\(748\) | −42.0905 | + | 42.0905i | −0.0562708 | + | 0.0562708i | ||||
\(749\) | 266.812i | 0.356224i | ||||||||
\(750\) | −9.86462 | + | 306.027i | −0.0131528 | + | 0.408036i | ||||
\(751\) | 189.510 | 0.252343 | 0.126172 | − | 0.992008i | \(-0.459731\pi\) | ||||
0.126172 | + | 0.992008i | \(0.459731\pi\) | |||||||
\(752\) | −236.154 | − | 236.154i | −0.314035 | − | 0.314035i | ||||
\(753\) | 104.333 | − | 104.333i | 0.138557 | − | 0.138557i | ||||
\(754\) | − | 313.833i | − | 0.416224i | ||||||
\(755\) | −436.805 | + | 245.972i | −0.578550 | + | 0.325791i | ||||
\(756\) | 50.0648 | 0.0662233 | ||||||||
\(757\) | 12.7982 | + | 12.7982i | 0.0169065 | + | 0.0169065i | 0.715509 | − | 0.698603i | \(-0.246195\pi\) |
−0.698603 | + | 0.715509i | \(0.746195\pi\) | |||||||
\(758\) | 415.235 | − | 415.235i | 0.547804 | − | 0.547804i | ||||
\(759\) | 141.973i | 0.187053i | ||||||||
\(760\) | 145.085 | + | 40.5506i | 0.190901 | + | 0.0533560i | ||||
\(761\) | −565.864 | −0.743579 | −0.371790 | − | 0.928317i | \(-0.621256\pi\) | ||||
−0.371790 | + | 0.928317i | \(0.621256\pi\) | |||||||
\(762\) | 94.8780 | + | 94.8780i | 0.124512 | + | 0.124512i | ||||
\(763\) | −570.420 | + | 570.420i | −0.747601 | + | 0.747601i | ||||
\(764\) | − | 526.244i | − | 0.688801i | ||||||
\(765\) | 7.03104 | − | 25.1562i | 0.00919090 | − | 0.0328839i | ||||
\(766\) | −891.537 | −1.16389 | ||||||||
\(767\) | 157.093 | + | 157.093i | 0.204815 | + | 0.204815i | ||||
\(768\) | −19.5959 | + | 19.5959i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | 973.731i | 1.26623i | 0.774058 | + | 0.633115i | \(0.218224\pi\) | ||||
−0.774058 | + | 0.633115i | \(0.781776\pi\) | |||||||
\(770\) | 285.678 | + | 507.316i | 0.371011 | + | 0.658852i | ||||
\(771\) | 218.430 | 0.283307 | ||||||||
\(772\) | 281.749 | + | 281.749i | 0.364960 | + | 0.364960i | ||||
\(773\) | 554.230 | − | 554.230i | 0.716986 | − | 0.716986i | −0.251001 | − | 0.967987i | \(-0.580760\pi\) |
0.967987 | + | 0.251001i | \(0.0807596\pi\) | |||||||
\(774\) | − | 298.450i | − | 0.385594i | ||||||
\(775\) | −273.982 | + | 451.849i | −0.353525 | + | 0.583031i | ||||
\(776\) | 336.034 | 0.433034 | ||||||||
\(777\) | 4.92059 | + | 4.92059i | 0.00633281 | + | 0.00633281i | ||||
\(778\) | 274.994 | − | 274.994i | 0.353462 | − | 0.353462i | ||||
\(779\) | − | 476.778i | − | 0.612038i | ||||||
\(780\) | 203.188 | − | 114.418i | 0.260497 | − | 0.146690i | ||||
\(781\) | 309.171 | 0.395866 | ||||||||
\(782\) | −8.35124 | − | 8.35124i | −0.0106793 | − | 0.0106793i | ||||
\(783\) | −60.5625 | + | 60.5625i | −0.0773468 | + | 0.0773468i | ||||
\(784\) | 103.167i | 0.131591i | ||||||||
\(785\) | −1153.98 | − | 322.531i | −1.47004 | − | 0.410868i | ||||
\(786\) | 132.060 | 0.168015 | ||||||||
\(787\) | 918.531 | + | 918.531i | 1.16713 | + | 1.16713i | 0.982880 | + | 0.184249i | \(0.0589854\pi\) |
0.184249 | + | 0.982880i | \(0.441015\pi\) | |||||||
\(788\) | 170.958 | − | 170.958i | 0.216952 | − | 0.216952i | ||||
\(789\) | 301.798i | 0.382506i | ||||||||
\(790\) | 128.067 | − | 458.208i | 0.162110 | − | 0.580010i | ||||
\(791\) | 397.862 | 0.502986 | ||||||||
\(792\) | 102.550 | + | 102.550i | 0.129482 | + | 0.129482i | ||||
\(793\) | 812.929 | − | 812.929i | 1.02513 | − | 1.02513i | ||||
\(794\) | − | 47.2368i | − | 0.0594921i | ||||||
\(795\) | 229.438 | + | 407.443i | 0.288601 | + | 0.512507i | ||||
\(796\) | −468.869 | −0.589032 | ||||||||
\(797\) | 268.841 | + | 268.841i | 0.337316 | + | 0.337316i | 0.855356 | − | 0.518040i | \(-0.173338\pi\) |
−0.518040 | + | 0.855356i | \(0.673338\pi\) | |||||||
\(798\) | −88.8837 | + | 88.8837i | −0.111383 | + | 0.111383i | ||||
\(799\) | − | 145.391i | − | 0.181967i | ||||||
\(800\) | 137.357 | − | 33.6598i | 0.171697 | − | 0.0420747i | ||||
\(801\) | −134.432 | −0.167831 | ||||||||
\(802\) | −673.867 | − | 673.867i | −0.840233 | − | 0.840233i | ||||
\(803\) | 298.618 | − | 298.618i | 0.371879 | − | 0.371879i | ||||
\(804\) | − | 427.080i | − | 0.531194i | ||||||
\(805\) | −100.657 | + | 56.6818i | −0.125040 | + | 0.0704122i | ||||
\(806\) | 402.444 | 0.499310 | ||||||||
\(807\) | 194.821 | + | 194.821i | 0.241414 | + | 0.241414i | ||||
\(808\) | 220.532 | − | 220.532i | 0.272936 | − | 0.272936i | ||||
\(809\) | 533.951i | 0.660013i | 0.943979 | + | 0.330007i | \(0.107051\pi\) | ||||
−0.943979 | + | 0.330007i | \(0.892949\pi\) | |||||||
\(810\) | −61.2907 | − | 17.1304i | −0.0756675 | − | 0.0211487i | ||||
\(811\) | −915.450 | −1.12879 | −0.564396 | − | 0.825504i | \(-0.690891\pi\) | ||||
−0.564396 | + | 0.825504i | \(0.690891\pi\) | |||||||
\(812\) | 112.298 | + | 112.298i | 0.138298 | + | 0.138298i | ||||
\(813\) | −321.493 | + | 321.493i | −0.395440 | + | 0.395440i | ||||
\(814\) | 20.1580i | 0.0247642i | ||||||||
\(815\) | −238.588 | + | 853.638i | −0.292746 | + | 1.04741i | ||||
\(816\) | −12.0645 | −0.0147849 | ||||||||
\(817\) | 529.860 | + | 529.860i | 0.648543 | + | 0.648543i | ||||
\(818\) | 37.4601 | − | 37.4601i | 0.0457947 | − | 0.0457947i | ||||
\(819\) | 194.576i | 0.237577i | ||||||||
\(820\) | −219.616 | − | 390.001i | −0.267824 | − | 0.475611i | ||||
\(821\) | 288.533 | 0.351441 | 0.175720 | − | 0.984440i | \(-0.443775\pi\) | ||||
0.175720 | + | 0.984440i | \(0.443775\pi\) | |||||||
\(822\) | −189.791 | − | 189.791i | −0.230889 | − | 0.230889i | ||||
\(823\) | −65.0196 | + | 65.0196i | −0.0790031 | + | 0.0790031i | −0.745504 | − | 0.666501i | \(-0.767791\pi\) |
0.666501 | + | 0.745504i | \(0.267791\pi\) | |||||||
\(824\) | − | 413.451i | − | 0.501761i | ||||||
\(825\) | −176.149 | − | 718.819i | −0.213514 | − | 0.871296i | ||||
\(826\) | −112.425 | −0.136107 | ||||||||
\(827\) | −5.39396 | − | 5.39396i | −0.00652232 | − | 0.00652232i | 0.703838 | − | 0.710360i | \(-0.251468\pi\) |
−0.710360 | + | 0.703838i | \(0.751468\pi\) | |||||||
\(828\) | −20.3470 | + | 20.3470i | −0.0245737 | + | 0.0245737i | ||||
\(829\) | 75.7343i | 0.0913563i | 0.998956 | + | 0.0456781i | \(0.0145449\pi\) | ||||
−0.998956 | + | 0.0456781i | \(0.985455\pi\) | |||||||
\(830\) | 73.2978 | − | 41.2752i | 0.0883106 | − | 0.0497292i | ||||
\(831\) | −611.802 | −0.736224 | ||||||||
\(832\) | −76.1590 | − | 76.1590i | −0.0915373 | − | 0.0915373i | ||||
\(833\) | −31.7580 | + | 31.7580i | −0.0381249 | + | 0.0381249i | ||||
\(834\) | − | 96.7728i | − | 0.116035i | ||||||
\(835\) | −1013.62 | − | 283.301i | −1.21391 | − | 0.339283i | ||||
\(836\) | −364.127 | −0.435559 | ||||||||
\(837\) | −77.6624 | − | 77.6624i | −0.0927866 | − | 0.0927866i | ||||
\(838\) | −251.336 | + | 251.336i | −0.299923 | + | 0.299923i | ||||
\(839\) | 121.963i | 0.145367i | 0.997355 | + | 0.0726837i | \(0.0231563\pi\) | ||||
−0.997355 | + | 0.0726837i | \(0.976844\pi\) | |||||||
\(840\) | −31.7642 | + | 113.648i | −0.0378145 | + | 0.135296i | ||||
\(841\) | 569.310 | 0.676944 | ||||||||
\(842\) | −555.687 | − | 555.687i | −0.659961 | − | 0.659961i | ||||
\(843\) | −383.325 | + | 383.325i | −0.454715 | + | 0.454715i | ||||
\(844\) | − | 291.937i | − | 0.345897i | ||||||
\(845\) | 30.0688 | + | 53.3971i | 0.0355844 | + | 0.0631919i | ||||
\(846\) | −354.232 | −0.418714 | ||||||||
\(847\) | −582.924 | − | 582.924i | −0.688222 | − | 0.688222i | ||||
\(848\) | 152.718 | − | 152.718i | 0.180092 | − | 0.180092i | ||||
\(849\) | − | 746.576i | − | 0.879359i | ||||||
\(850\) | 52.6443 | + | 31.9213i | 0.0619345 | + | 0.0375544i | ||||
\(851\) | −3.99958 | −0.00469986 | ||||||||
\(852\) | 44.3090 | + | 44.3090i | 0.0520059 | + | 0.0520059i | ||||
\(853\) | −744.108 | + | 744.108i | −0.872343 | + | 0.872343i | −0.992727 | − | 0.120385i | \(-0.961587\pi\) |
0.120385 | + | 0.992727i | \(0.461587\pi\) | |||||||
\(854\) | 581.777i | 0.681238i | ||||||||
\(855\) | 139.227 | − | 78.4009i | 0.162838 | − | 0.0916969i | ||||
\(856\) | −156.650 | −0.183002 | ||||||||
\(857\) | −426.217 | − | 426.217i | −0.497336 | − | 0.497336i | 0.413272 | − | 0.910608i | \(-0.364386\pi\) |
−0.910608 | + | 0.413272i | \(0.864386\pi\) | |||||||
\(858\) | −398.556 | + | 398.556i | −0.464518 | + | 0.464518i | ||||
\(859\) | 1528.65i | 1.77957i | 0.456380 | + | 0.889785i | \(0.349146\pi\) | ||||
−0.456380 | + | 0.889785i | \(0.650854\pi\) | |||||||
\(860\) | 677.489 | + | 189.355i | 0.787778 | + | 0.220180i | ||||
\(861\) | 373.471 | 0.433764 | ||||||||
\(862\) | 61.4001 | + | 61.4001i | 0.0712298 | + | 0.0712298i | ||||
\(863\) | 1016.16 | − | 1016.16i | 1.17747 | − | 1.17747i | 0.197089 | − | 0.980386i | \(-0.436851\pi\) |
0.980386 | − | 0.197089i | \(-0.0631489\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | −170.192 | + | 608.928i | −0.196754 | + | 0.703963i | ||||
\(866\) | −898.124 | −1.03709 | ||||||||
\(867\) | 350.237 | + | 350.237i | 0.403965 | + | 0.403965i | ||||
\(868\) | −144.006 | + | 144.006i | −0.165905 | + | 0.165905i | ||||
\(869\) | 1149.99i | 1.32334i | ||||||||
\(870\) | −99.0539 | − | 175.903i | −0.113855 | − | 0.202187i | ||||
\(871\) | 1659.84 | 1.90567 | ||||||||
\(872\) | −334.903 | − | 334.903i | −0.384063 | − | 0.384063i | ||||
\(873\) | 252.026 | − | 252.026i | 0.288689 | − | 0.288689i | ||||
\(874\) | − | 72.2470i | − | 0.0826625i | ||||||
\(875\) | 439.308 | − | 411.870i | 0.502066 | − | 0.470709i | ||||
\(876\) | 85.5933 | 0.0977093 | ||||||||
\(877\) | 266.773 | + | 266.773i | 0.304188 | + | 0.304188i | 0.842650 | − | 0.538462i | \(-0.180995\pi\) |
−0.538462 | + | 0.842650i | \(0.680995\pi\) | |||||||
\(878\) | −522.143 | + | 522.143i | −0.594695 | + | 0.594695i | ||||
\(879\) | − | 838.906i | − | 0.954387i | ||||||
\(880\) | −297.854 | + | 167.726i | −0.338470 | + | 0.190598i | ||||
\(881\) | −1409.54 | −1.59993 | −0.799963 | − | 0.600049i | \(-0.795148\pi\) | ||||
−0.799963 | + | 0.600049i | \(0.795148\pi\) | |||||||
\(882\) | 77.3754 | + | 77.3754i | 0.0877272 | + | 0.0877272i | ||||
\(883\) | 647.075 | − | 647.075i | 0.732815 | − | 0.732815i | −0.238362 | − | 0.971176i | \(-0.576610\pi\) |
0.971176 | + | 0.238362i | \(0.0766104\pi\) | |||||||
\(884\) | − | 46.8882i | − | 0.0530410i | ||||||
\(885\) | 137.633 | + | 38.4679i | 0.155518 | + | 0.0434665i | ||||
\(886\) | 341.913 | 0.385907 | ||||||||
\(887\) | −415.654 | − | 415.654i | −0.468606 | − | 0.468606i | 0.432857 | − | 0.901463i | \(-0.357506\pi\) |
−0.901463 | + | 0.432857i | \(0.857506\pi\) | |||||||
\(888\) | −2.88896 | + | 2.88896i | −0.00325333 | + | 0.00325333i | ||||
\(889\) | − | 263.892i | − | 0.296841i | ||||||
\(890\) | 85.2921 | − | 305.165i | 0.0958338 | − | 0.342882i | ||||
\(891\) | 153.824 | 0.172642 | ||||||||
\(892\) | −455.468 | − | 455.468i | −0.510615 | − | 0.510615i | ||||
\(893\) | 628.893 | − | 628.893i | 0.704248 | − | 0.704248i | ||||
\(894\) | 305.052i | 0.341221i | ||||||||
\(895\) | −202.162 | − | 359.005i | −0.225879 | − | 0.401123i | ||||
\(896\) | 54.5037 | 0.0608300 | ||||||||
\(897\) | −79.0781 | − | 79.0781i | −0.0881584 | − | 0.0881584i | ||||
\(898\) | −129.721 | + | 129.721i | −0.144456 | + | 0.144456i | ||||
\(899\) | − | 348.402i | − | 0.387544i | ||||||
\(900\) | 77.7731 | − | 128.263i | 0.0864146 | − | 0.142514i | ||||
\(901\) | 94.0228 | 0.104354 | ||||||||
\(902\) | 764.993 | + | 764.993i | 0.848108 | + | 0.848108i | ||||
\(903\) | −415.051 | + | 415.051i | −0.459636 | + | 0.459636i | ||||
\(904\) | 233.591i | 0.258397i | ||||||||
\(905\) | 1505.57 | − | 847.809i | 1.66361 | − | 0.936805i | ||||
\(906\) | 245.585 | 0.271066 | ||||||||
\(907\) | 104.950 | + | 104.950i | 0.115711 | + | 0.115711i | 0.762591 | − | 0.646881i | \(-0.223927\pi\) |
−0.646881 | + | 0.762591i | \(0.723927\pi\) | |||||||
\(908\) | 127.231 | − | 127.231i | 0.140122 | − | 0.140122i | ||||
\(909\) | − | 330.798i | − | 0.363914i | ||||||
\(910\) | −441.692 | − | 123.451i | −0.485375 | − | 0.135660i | ||||
\(911\) | −487.776 | −0.535430 | −0.267715 | − | 0.963498i | \(-0.586268\pi\) | ||||
−0.267715 | + | 0.963498i | \(0.586268\pi\) | |||||||
\(912\) | −52.1851 | − | 52.1851i | −0.0572205 | − | 0.0572205i | ||||
\(913\) | −143.775 | + | 143.775i | −0.157475 | + | 0.157475i | ||||
\(914\) | − | 975.642i | − | 1.06744i | ||||||
\(915\) | 199.064 | − | 712.227i | 0.217556 | − | 0.778390i | ||||
\(916\) | 346.706 | 0.378500 | ||||||||
\(917\) | −183.654 | − | 183.654i | −0.200277 | − | 0.200277i | ||||
\(918\) | −9.04834 | + | 9.04834i | −0.00985658 | + | 0.00985658i | ||||
\(919\) | − | 1682.30i | − | 1.83058i | −0.402795 | − | 0.915290i | \(-0.631961\pi\) | ||
0.402795 | − | 0.915290i | \(-0.368039\pi\) | |||||||
\(920\) | −33.2788 | − | 59.0976i | −0.0361726 | − | 0.0642365i | ||||
\(921\) | −594.097 | −0.645057 | ||||||||
\(922\) | −10.8881 | − | 10.8881i | −0.0118093 | − | 0.0118093i | ||||
\(923\) | −172.206 | + | 172.206i | −0.186572 | + | 0.186572i | ||||
\(924\) | − | 285.229i | − | 0.308689i | ||||||
\(925\) | 20.2501 | − | 4.96235i | 0.0218920 | − | 0.00536470i | ||||
\(926\) | 801.668 | 0.865732 | ||||||||
\(927\) | −310.088 | − | 310.088i | −0.334508 | − | 0.334508i | ||||
\(928\) | −65.9321 | + | 65.9321i | −0.0710475 | + | 0.0710475i | ||||
\(929\) | 1307.03i | 1.40692i | 0.710734 | + | 0.703461i | \(0.248363\pi\) | ||||
−0.710734 | + | 0.703461i | \(0.751637\pi\) | |||||||
\(930\) | 225.569 | − | 127.022i | 0.242548 | − | 0.136583i | ||||
\(931\) | −274.740 | −0.295102 | ||||||||
\(932\) | 257.803 | + | 257.803i | 0.276613 | + | 0.276613i | ||||
\(933\) | 595.814 | − | 595.814i | 0.638600 | − | 0.638600i | ||||
\(934\) | − | 216.028i | − | 0.231293i | ||||||
\(935\) | −143.320 | − | 40.0572i | −0.153283 | − | 0.0428419i | ||||
\(936\) | −114.239 | −0.122050 | ||||||||
\(937\) | 753.154 | + | 753.154i | 0.803792 | + | 0.803792i | 0.983686 | − | 0.179894i | \(-0.0575753\pi\) |
−0.179894 | + | 0.983686i | \(0.557575\pi\) | |||||||
\(938\) | −593.935 | + | 593.935i | −0.633193 | + | 0.633193i | ||||
\(939\) | 142.568i | 0.151830i | ||||||||
\(940\) | 224.746 | − | 804.115i | 0.239092 | − | 0.855441i | ||||
\(941\) | 1343.56 | 1.42780 | 0.713901 | − | 0.700247i | \(-0.246927\pi\) | ||||
0.713901 | + | 0.700247i | \(0.246927\pi\) | |||||||
\(942\) | 415.070 | + | 415.070i | 0.440626 | + | 0.440626i | ||||
\(943\) | −151.783 | + | 151.783i | −0.160958 | + | 0.160958i | ||||
\(944\) | − | 66.0064i | − | 0.0699220i | ||||||
\(945\) | 61.4132 | + | 109.059i | 0.0649875 | + | 0.115407i | ||||
\(946\) | −1700.33 | −1.79739 | ||||||||
\(947\) | 523.662 | + | 523.662i | 0.552970 | + | 0.552970i | 0.927297 | − | 0.374327i | \(-0.122126\pi\) |
−0.374327 | + | 0.927297i | \(0.622126\pi\) | |||||||
\(948\) | −164.811 | + | 164.811i | −0.173851 | + | 0.173851i | ||||
\(949\) | 332.656i | 0.350534i | ||||||||
\(950\) | 89.6380 | + | 365.791i | 0.0943558 | + | 0.385043i | ||||
\(951\) | −813.145 | −0.855042 | ||||||||
\(952\) | 16.7779 | + | 16.7779i | 0.0176239 | + | 0.0176239i | ||||
\(953\) | 367.314 | − | 367.314i | 0.385430 | − | 0.385430i | −0.487624 | − | 0.873054i | \(-0.662136\pi\) |
0.873054 | + | 0.487624i | \(0.162136\pi\) | |||||||
\(954\) | − | 229.077i | − | 0.240123i | ||||||
\(955\) | 1146.35 | − | 645.529i | 1.20037 | − | 0.675947i | ||||
\(956\) | 396.437 | 0.414683 | ||||||||
\(957\) | 345.036 | + | 345.036i | 0.360540 | + | 0.360540i | ||||
\(958\) | −517.840 | + | 517.840i | −0.540543 | + | 0.540543i | ||||
\(959\) | 527.880i | 0.550449i | ||||||||
\(960\) | −66.7248 | − | 18.6493i | −0.0695050 | − | 0.0194263i | ||||
\(961\) | −514.226 | −0.535095 | ||||||||
\(962\) | −11.2279 | − | 11.2279i | −0.0116714 | − | 0.0116714i | ||||
\(963\) | −117.487 | + | 117.487i | −0.122001 | + | 0.122001i | ||||
\(964\) | 268.657i | 0.278690i | ||||||||
\(965\) | −268.138 | + | 959.366i | −0.277863 | + | 0.994162i | ||||
\(966\) | 56.5927 | 0.0585846 | ||||||||
\(967\) | 712.118 | + | 712.118i | 0.736420 | + | 0.736420i | 0.971883 | − | 0.235463i | \(-0.0756608\pi\) |
−0.235463 | + | 0.971883i | \(0.575661\pi\) | |||||||
\(968\) | 342.244 | − | 342.244i | 0.353558 | − | 0.353558i | ||||
\(969\) | − | 32.1284i | − | 0.0331562i | ||||||
\(970\) | 412.204 | + | 732.005i | 0.424953 | + | 0.754644i | ||||
\(971\) | 614.628 | 0.632984 | 0.316492 | − | 0.948595i | \(-0.397495\pi\) | ||||
0.316492 | + | 0.948595i | \(0.397495\pi\) | |||||||
\(972\) | 22.0454 | + | 22.0454i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | −134.581 | + | 134.581i | −0.138315 | + | 0.138315i | ||||
\(974\) | − | 779.745i | − | 0.800559i | ||||||
\(975\) | 498.490 | + | 302.263i | 0.511272 | + | 0.310014i | ||||
\(976\) | −341.571 | −0.349970 | ||||||||
\(977\) | −620.888 | − | 620.888i | −0.635505 | − | 0.635505i | 0.313938 | − | 0.949443i | \(-0.398351\pi\) |
−0.949443 | + | 0.313938i | \(0.898351\pi\) | |||||||
\(978\) | 307.042 | − | 307.042i | 0.313949 | − | 0.313949i | ||||
\(979\) | 765.887i | 0.782316i | ||||||||
\(980\) | −224.736 | + | 126.552i | −0.229322 | + | 0.129135i | ||||
\(981\) | −502.354 | −0.512084 | ||||||||
\(982\) | −559.841 | − | 559.841i | −0.570103 | − | 0.570103i | ||||
\(983\) | 522.578 | − | 522.578i | 0.531615 | − | 0.531615i | −0.389438 | − | 0.921053i | \(-0.627331\pi\) |
0.921053 | + | 0.389438i | \(0.127331\pi\) | |||||||
\(984\) | 219.271i | 0.222836i | ||||||||
\(985\) | 582.118 | + | 162.699i | 0.590983 | + | 0.165177i | ||||
\(986\) | −40.5919 | −0.0411682 | ||||||||
\(987\) | 492.626 | + | 492.626i | 0.499115 | + | 0.499115i | ||||
\(988\) | 202.816 | − | 202.816i | 0.205279 | − | 0.205279i | ||||
\(989\) | − | 337.364i | − | 0.341116i | ||||||
\(990\) | −97.5955 | + | 349.185i | −0.0985813 | + | 0.352712i | ||||
\(991\) | 51.4856 | 0.0519532 | 0.0259766 | − | 0.999663i | \(-0.491730\pi\) | ||||
0.0259766 | + | 0.999663i | \(0.491730\pi\) | |||||||
\(992\) | −84.5481 | − | 84.5481i | −0.0852299 | − | 0.0852299i | ||||
\(993\) | −70.3106 | + | 70.3106i | −0.0708063 | + | 0.0708063i | ||||
\(994\) | − | 123.240i | − | 0.123984i | ||||||
\(995\) | −575.149 | − | 1021.37i | −0.578039 | − | 1.02650i | ||||
\(996\) | −41.2103 | −0.0413758 | ||||||||
\(997\) | −342.034 | − | 342.034i | −0.343063 | − | 0.343063i | 0.514455 | − | 0.857518i | \(-0.327994\pi\) |
−0.857518 | + | 0.514455i | \(0.827994\pi\) | |||||||
\(998\) | 528.700 | − | 528.700i | 0.529760 | − | 0.529760i | ||||
\(999\) | 4.33344i | 0.00433778i |
(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 | 690.3.k.b.277.2 | ✓ | 48 | |
5.3 | odd | 4 | inner | 690.3.k.b.553.2 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.b.277.2 | ✓ | 48 | 1.1 | even | 1 | trivial | |
690.3.k.b.553.2 | yes | 48 | 5.3 | odd | 4 | inner |